%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA144-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n019.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 06:33:52 PM UTC 2026
% Result : Unsatisfiable 5.50s 5.76s
% Output : Proof 12.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRA144-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.11/0.30 % Computer : n019.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Mon May 4 23:29:00 EDT 2026
% 0.11/0.30 % CPUTime :
% 5.50/5.76 % SZS status Unsatisfiable
% 5.50/5.76 % SZS output start Proof
% 5.50/5.76 tff(r_type, type, (
% 5.50/5.76 r: ( $i * $i ) > $o)).
% 5.50/5.76 tff(elem_1_type, type, (
% 5.50/5.76 elem_1: $i)).
% 5.50/5.76 tff(s_type, type, (
% 5.50/5.76 s: $i > $i)).
% 5.50/5.76 tff(z_type, type, (
% 5.50/5.76 z: $i)).
% 5.50/5.76 tff(b_type, type, (
% 5.50/5.76 b: ( $i * $i ) > $o)).
% 5.50/5.76 tff(inj_0_type, type, (
% 5.50/5.76 inj_0: $i > $i)).
% 5.50/5.76 tff(1,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 5.50/5.76 tff(2,assumption,(~(elem!1 = z)), introduced(assumption)).
% 5.50/5.76 tff(3,plain,
% 5.50/5.76 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 5.50/5.76 inference(commutativity,[status(thm)],[])).
% 5.50/5.76 tff(4,plain,
% 5.50/5.76 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 5.50/5.76 inference(symmetry,[status(thm)],[3])).
% 5.50/5.76 tff(5,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 5.50/5.76 tff(6,plain,
% 5.50/5.76 (elem!1 = s(s(s(elem!1)))),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[5, 4])).
% 5.50/5.76 tff(7,plain,
% 5.50/5.76 ($false),
% 5.50/5.76 inference(unit_resolution,[status(thm)],[1, 6])).
% 5.50/5.76 tff(8,plain,((~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.76 tff(9,plain,
% 5.50/5.76 (~(s(s(s(elem!1))) = elem!1)),
% 5.50/5.76 inference(unit_resolution,[status(thm)],[8, 1])).
% 5.50/5.76 tff(10,assumption,(~b(z, s(s(s(elem!1))))), introduced(assumption)).
% 5.50/5.76 tff(11,assumption,(elem!1 = z), introduced(assumption)).
% 5.50/5.76 tff(12,plain,
% 5.50/5.76 ((s(z) = elem!1) <=> (s(z) = z)),
% 5.50/5.76 inference(monotonicity,[status(thm)],[11])).
% 5.50/5.76 tff(13,plain,
% 5.50/5.76 ((s(z) = z) <=> (s(z) = elem!1)),
% 5.50/5.76 inference(symmetry,[status(thm)],[12])).
% 5.50/5.76 tff(14,plain,
% 5.50/5.76 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 5.50/5.76 inference(monotonicity,[status(thm)],[13])).
% 5.50/5.76 tff(15,plain,
% 5.50/5.76 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 5.50/5.76 inference(bind,[status(th)],[])).
% 5.50/5.76 tff(16,plain,
% 5.50/5.76 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 5.50/5.76 inference(quant_intro,[status(thm)],[15])).
% 5.50/5.76 tff(17,plain,
% 5.50/5.76 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 5.50/5.76 inference(rewrite,[status(thm)],[])).
% 5.50/5.76 tff(18,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 5.50/5.76 tff(19,plain,
% 5.50/5.76 (![X: $i] : (~(s(X) = z))),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[18, 17])).
% 5.50/5.76 tff(20,plain,(
% 5.50/5.76 ![X: $i] : (~(s(X) = z))),
% 5.50/5.76 inference(skolemize,[status(sab)],[19])).
% 5.50/5.76 tff(21,plain,
% 5.50/5.76 (![X: $i] : (~(s(X) = z))),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[20, 16])).
% 5.50/5.76 tff(22,plain,
% 5.50/5.76 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 5.50/5.76 inference(quant_inst,[status(thm)],[])).
% 5.50/5.76 tff(23,plain,
% 5.50/5.76 (~(s(z) = z)),
% 5.50/5.76 inference(unit_resolution,[status(thm)],[22, 21])).
% 5.50/5.76 tff(24,plain,
% 5.50/5.76 (~(s(z) = elem!1)),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[23, 14])).
% 5.50/5.76 tff(25,assumption,(z = s(z)), introduced(assumption)).
% 5.50/5.76 tff(26,plain,
% 5.50/5.76 (s(z) = z),
% 5.50/5.76 inference(symmetry,[status(thm)],[25])).
% 5.50/5.76 tff(27,plain,
% 5.50/5.76 ($false),
% 5.50/5.76 inference(unit_resolution,[status(thm)],[23, 26])).
% 5.50/5.76 tff(28,plain,(~(z = s(z))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.76 tff(29,plain,
% 5.50/5.76 (b(elem!1, s(z)) <=> b(z, s(z))),
% 5.50/5.76 inference(monotonicity,[status(thm)],[11])).
% 5.50/5.76 tff(30,plain,
% 5.50/5.76 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 5.50/5.76 inference(monotonicity,[status(thm)],[29])).
% 5.50/5.76 tff(31,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 5.50/5.76 tff(32,plain,
% 5.50/5.76 (~b(z, s(z))),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[31, 30])).
% 5.50/5.76 tff(33,plain,
% 5.50/5.76 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 5.50/5.76 inference(bind,[status(th)],[])).
% 5.50/5.76 tff(34,plain,
% 5.50/5.76 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 5.50/5.76 inference(quant_intro,[status(thm)],[33])).
% 5.50/5.76 tff(35,plain,
% 5.50/5.76 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 5.50/5.76 inference(rewrite,[status(thm)],[])).
% 5.50/5.76 tff(36,plain,
% 5.50/5.76 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 5.50/5.76 inference(bind,[status(th)],[])).
% 5.50/5.76 tff(37,plain,
% 5.50/5.76 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 5.50/5.76 inference(quant_intro,[status(thm)],[36])).
% 5.50/5.76 tff(38,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 5.50/5.76 tff(39,plain,
% 5.50/5.76 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[38, 37])).
% 5.50/5.76 tff(40,plain,
% 5.50/5.76 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[39, 35])).
% 5.50/5.76 tff(41,plain,(
% 5.50/5.76 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 5.50/5.76 inference(skolemize,[status(sab)],[40])).
% 5.50/5.76 tff(42,plain,
% 5.50/5.76 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[41, 34])).
% 5.50/5.76 tff(43,plain,
% 5.50/5.76 (((~![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)))),
% 5.50/5.76 inference(rewrite,[status(thm)],[])).
% 5.50/5.76 tff(44,plain,
% 5.50/5.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 5.50/5.76 inference(quant_inst,[status(thm)],[])).
% 5.50/5.76 tff(45,plain,
% 5.50/5.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[44, 43])).
% 5.50/5.76 tff(46,plain,
% 5.50/5.76 (r(z, s(z))),
% 5.50/5.76 inference(unit_resolution,[status(thm)],[45, 42, 32, 28])).
% 5.50/5.76 tff(47,assumption,(z = s(s(s(elem!1)))), introduced(assumption)).
% 5.50/5.76 tff(48,plain,
% 5.50/5.76 (s(s(s(elem!1))) = z),
% 5.50/5.76 inference(symmetry,[status(thm)],[47])).
% 5.50/5.76 tff(49,plain,
% 5.50/5.76 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 5.50/5.76 inference(quant_inst,[status(thm)],[])).
% 5.50/5.76 tff(50,plain,
% 5.50/5.76 (~(s(s(s(elem!1))) = z)),
% 5.50/5.76 inference(unit_resolution,[status(thm)],[49, 21])).
% 5.50/5.76 tff(51,plain,
% 5.50/5.76 ($false),
% 5.50/5.76 inference(unit_resolution,[status(thm)],[50, 48])).
% 5.50/5.76 tff(52,plain,(~(z = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.76 tff(53,assumption,(~r(z, s(s(s(elem!1))))), introduced(assumption)).
% 5.50/5.76 tff(54,plain,
% 5.50/5.76 (((~![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)))))),
% 5.50/5.76 inference(rewrite,[status(thm)],[])).
% 5.50/5.76 tff(55,plain,
% 5.50/5.76 ((~![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)))))),
% 5.50/5.76 inference(quant_inst,[status(thm)],[])).
% 5.50/5.76 tff(56,plain,
% 5.50/5.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[55, 54])).
% 5.50/5.76 tff(57,plain,
% 5.50/5.76 ($false),
% 5.50/5.76 inference(unit_resolution,[status(thm)],[56, 42, 53, 10, 52])).
% 5.50/5.76 tff(58,plain,(r(z, s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.76 tff(59,plain,
% 5.50/5.76 (r(z, s(s(s(elem!1))))),
% 5.50/5.76 inference(unit_resolution,[status(thm)],[58, 10])).
% 5.50/5.76 tff(60,plain,
% 5.50/5.76 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 5.50/5.76 inference(monotonicity,[status(thm)],[11])).
% 5.50/5.76 tff(61,plain,
% 5.50/5.76 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 5.50/5.76 inference(symmetry,[status(thm)],[60])).
% 5.50/5.76 tff(62,plain,
% 5.50/5.76 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 5.50/5.76 inference(monotonicity,[status(thm)],[11])).
% 5.50/5.76 tff(63,plain,
% 5.50/5.76 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 5.50/5.76 inference(symmetry,[status(thm)],[62])).
% 5.50/5.76 tff(64,plain,
% 5.50/5.76 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 5.50/5.76 inference(transitivity,[status(thm)],[63, 4])).
% 5.50/5.76 tff(65,plain,
% 5.50/5.76 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 5.50/5.76 inference(monotonicity,[status(thm)],[64])).
% 5.50/5.76 tff(66,plain,
% 5.50/5.76 (~(elem!1 = s(s(s(elem!1))))),
% 5.50/5.76 inference(modus_ponens,[status(thm)],[50, 65])).
% 5.50/5.76 tff(67,plain,
% 5.50/5.76 (r(z, elem!1) <=> r(z, z)),
% 5.50/5.76 inference(monotonicity,[status(thm)],[11])).
% 5.50/5.76 tff(68,plain,
% 5.50/5.76 (r(z, z) <=> r(z, elem!1)),
% 5.50/5.76 inference(symmetry,[status(thm)],[67])).
% 5.50/5.76 tff(69,plain,
% 5.50/5.76 ((~r(z, z)) <=> (~r(z, elem!1))),
% 5.50/5.76 inference(monotonicity,[status(thm)],[68])).
% 5.50/5.76 tff(70,plain,
% 5.50/5.76 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 5.50/5.76 inference(bind,[status(th)],[])).
% 5.50/5.76 tff(71,plain,
% 5.50/5.76 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 5.50/5.77 inference(quant_intro,[status(thm)],[70])).
% 5.50/5.77 tff(72,plain,
% 5.50/5.77 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 5.50/5.77 inference(rewrite,[status(thm)],[])).
% 5.50/5.77 tff(73,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ri')).
% 5.50/5.77 tff(74,plain,
% 5.50/5.77 (![X: $i] : (~r(X, X))),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[73, 72])).
% 5.50/5.77 tff(75,plain,(
% 5.50/5.77 ![X: $i] : (~r(X, X))),
% 5.50/5.77 inference(skolemize,[status(sab)],[74])).
% 5.50/5.77 tff(76,plain,
% 5.50/5.77 (![X: $i] : (~r(X, X))),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[75, 71])).
% 5.50/5.77 tff(77,plain,
% 5.50/5.77 ((~![X: $i] : (~r(X, X))) | (~r(z, z))),
% 5.50/5.77 inference(quant_inst,[status(thm)],[])).
% 5.50/5.77 tff(78,plain,
% 5.50/5.77 (~r(z, z)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[77, 76])).
% 5.50/5.77 tff(79,plain,
% 5.50/5.77 (~r(z, elem!1)),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[78, 69])).
% 5.50/5.77 tff(80,assumption,(~r(z, elem!1)), introduced(assumption)).
% 5.50/5.77 tff(81,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 5.50/5.77 tff(82,plain,
% 5.50/5.77 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 5.50/5.77 inference(quant_inst,[status(thm)],[])).
% 5.50/5.77 tff(83,plain,
% 5.50/5.77 (~(s(s(s(s(z)))) = z)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[82, 21])).
% 5.50/5.77 tff(84,plain,
% 5.50/5.77 (((~![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))),
% 5.50/5.77 inference(rewrite,[status(thm)],[])).
% 5.50/5.77 tff(85,plain,
% 5.50/5.77 ((~![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))),
% 5.50/5.77 inference(quant_inst,[status(thm)],[])).
% 5.50/5.77 tff(86,plain,
% 5.50/5.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[85, 84])).
% 5.50/5.77 tff(87,plain,
% 5.50/5.77 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[86, 42, 83])).
% 5.50/5.77 tff(88,plain,
% 5.50/5.77 (b(s(s(s(s(z)))), z)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[87, 81])).
% 5.50/5.77 tff(89,assumption,(~b(z, elem!1)), introduced(assumption)).
% 5.50/5.77 tff(90,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 5.50/5.77 tff(91,assumption,(~b(s(z), z)), introduced(assumption)).
% 5.50/5.77 tff(92,plain,
% 5.50/5.77 ((elem!1 = z) <=> (z = elem!1)),
% 5.50/5.77 inference(commutativity,[status(thm)],[])).
% 5.50/5.77 tff(93,plain,
% 5.50/5.77 ((z = elem!1) <=> (elem!1 = z)),
% 5.50/5.77 inference(symmetry,[status(thm)],[92])).
% 5.50/5.77 tff(94,assumption,(z = elem!1), introduced(assumption)).
% 5.50/5.77 tff(95,plain,
% 5.50/5.77 (elem!1 = z),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[94, 93])).
% 5.50/5.77 tff(96,plain,
% 5.50/5.77 ($false),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[2, 95])).
% 5.50/5.77 tff(97,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 5.50/5.77 tff(98,plain,
% 5.50/5.77 (~(z = elem!1)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[97, 2])).
% 5.50/5.77 tff(99,plain,
% 5.50/5.77 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 5.50/5.77 inference(rewrite,[status(thm)],[])).
% 5.50/5.77 tff(100,plain,
% 5.50/5.77 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 5.50/5.77 inference(rewrite,[status(thm)],[])).
% 5.50/5.77 tff(101,plain,
% 5.50/5.77 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 5.50/5.77 inference(rewrite,[status(thm)],[])).
% 5.50/5.77 tff(102,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 5.50/5.77 tff(103,plain,
% 5.50/5.77 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[102, 101])).
% 5.50/5.77 tff(104,plain,(
% 5.50/5.77 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 5.50/5.77 inference(skolemize,[status(sab)],[103])).
% 5.50/5.77 tff(105,plain,
% 5.50/5.77 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[104, 100])).
% 5.50/5.77 tff(106,plain,
% 5.50/5.77 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[105, 99])).
% 5.50/5.77 tff(107,plain,
% 5.50/5.77 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 5.50/5.77 inference(quant_inst,[status(thm)],[])).
% 5.50/5.77 tff(108,plain,
% 5.50/5.77 (inj_0(s(elem!1)) = elem!1),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[107, 106])).
% 5.50/5.77 tff(109,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 5.50/5.77 tff(110,plain,
% 5.50/5.77 (inj_0(s(z)) = inj_0(s(elem!1))),
% 5.50/5.77 inference(monotonicity,[status(thm)],[109])).
% 5.50/5.77 tff(111,plain,
% 5.50/5.77 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 5.50/5.77 inference(quant_inst,[status(thm)],[])).
% 5.50/5.77 tff(112,plain,
% 5.50/5.77 (inj_0(s(z)) = z),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[111, 106])).
% 5.50/5.77 tff(113,plain,
% 5.50/5.77 (z = inj_0(s(z))),
% 5.50/5.77 inference(symmetry,[status(thm)],[112])).
% 5.50/5.77 tff(114,plain,
% 5.50/5.77 (z = elem!1),
% 5.50/5.77 inference(transitivity,[status(thm)],[113, 110, 108])).
% 5.50/5.77 tff(115,assumption,(~(z = elem!1)), introduced(assumption)).
% 5.50/5.77 tff(116,plain,
% 5.50/5.77 ($false),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[115, 114])).
% 5.50/5.77 tff(117,plain,((~(s(z) = s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.50/5.77 tff(118,plain,
% 5.50/5.77 (~(s(z) = s(elem!1))),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[117, 98])).
% 5.50/5.77 tff(119,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 5.50/5.77 tff(120,plain,
% 5.50/5.77 (s(z) = s(elem!1)),
% 5.50/5.77 inference(symmetry,[status(thm)],[119])).
% 5.50/5.77 tff(121,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 5.50/5.77 tff(122,plain,
% 5.50/5.77 ($false),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[121, 120])).
% 5.50/5.77 tff(123,plain,((~(s(elem!1) = s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.77 tff(124,plain,
% 5.50/5.77 (~(s(elem!1) = s(z))),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[123, 118])).
% 5.50/5.77 tff(125,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 5.50/5.77 tff(126,plain,
% 5.50/5.77 (s(s(s(elem!1))) = elem!1),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[125, 3])).
% 5.50/5.77 tff(127,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 5.50/5.77 tff(128,plain,
% 5.50/5.77 ($false),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[127, 126])).
% 5.50/5.77 tff(129,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.50/5.77 tff(130,plain,
% 5.50/5.77 (s(s(s(elem!1))) = elem!1),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[129, 125])).
% 5.50/5.77 tff(131,plain,
% 5.50/5.77 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 5.50/5.77 inference(monotonicity,[status(thm)],[5])).
% 5.50/5.77 tff(132,plain,
% 5.50/5.77 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 5.50/5.77 inference(symmetry,[status(thm)],[131])).
% 5.50/5.77 tff(133,assumption,(b(z, elem!1)), introduced(assumption)).
% 5.50/5.77 tff(134,plain,
% 5.50/5.77 (b(z, s(s(s(elem!1))))),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[133, 132])).
% 5.50/5.77 tff(135,plain,
% 5.50/5.77 ($false),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[10, 134])).
% 5.50/5.77 tff(136,plain,((~(s(s(s(elem!1))) = elem!1)) | b(z, s(s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.77 tff(137,plain,
% 5.50/5.77 (~b(z, elem!1)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[136, 130, 10])).
% 5.50/5.77 tff(138,plain,
% 5.50/5.77 (((~![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))),
% 5.50/5.77 inference(rewrite,[status(thm)],[])).
% 5.50/5.77 tff(139,plain,
% 5.50/5.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 5.50/5.77 inference(quant_inst,[status(thm)],[])).
% 5.50/5.77 tff(140,plain,
% 5.50/5.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[139, 138])).
% 5.50/5.77 tff(141,plain,
% 5.50/5.77 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[140, 42])).
% 5.50/5.77 tff(142,plain,
% 5.50/5.77 (z = elem!1),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[141, 137, 80])).
% 5.50/5.77 tff(143,plain,
% 5.50/5.77 (elem!1 = z),
% 5.50/5.77 inference(symmetry,[status(thm)],[142])).
% 5.50/5.77 tff(144,plain,
% 5.50/5.77 (s(s(s(elem!1))) = elem!1),
% 5.50/5.77 inference(symmetry,[status(thm)],[125])).
% 5.50/5.77 tff(145,plain,
% 5.50/5.77 (s(s(s(elem!1))) = z),
% 5.50/5.77 inference(transitivity,[status(thm)],[144, 143])).
% 5.50/5.77 tff(146,plain,
% 5.50/5.77 ($false),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[50, 145])).
% 5.50/5.77 tff(147,plain,((~(elem!1 = s(s(s(elem!1))))) | r(z, elem!1) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.77 tff(148,plain,
% 5.50/5.77 (~(elem!1 = s(s(s(elem!1))))),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[147, 10, 80])).
% 5.50/5.77 tff(149,plain,
% 5.50/5.77 (b(z, elem!1)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[141, 98, 80])).
% 5.50/5.77 tff(150,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 5.50/5.77 tff(151,plain,
% 5.50/5.77 (~(s(s(s(elem!1))) = elem!1)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[136, 10, 149])).
% 5.50/5.77 tff(152,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 5.50/5.77 tff(153,plain,
% 5.50/5.77 (s(s(elem!1)) = s(elem!1)),
% 5.50/5.77 inference(monotonicity,[status(thm)],[152])).
% 5.50/5.77 tff(154,plain,
% 5.50/5.77 (s(s(elem!1)) = elem!1),
% 5.50/5.77 inference(transitivity,[status(thm)],[153, 152])).
% 5.50/5.77 tff(155,plain,
% 5.50/5.77 (s(s(s(elem!1))) = s(elem!1)),
% 5.50/5.77 inference(monotonicity,[status(thm)],[154])).
% 5.50/5.77 tff(156,plain,
% 5.50/5.77 (s(s(s(elem!1))) = elem!1),
% 5.50/5.77 inference(transitivity,[status(thm)],[155, 152])).
% 5.50/5.77 tff(157,plain,
% 5.50/5.77 ($false),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[127, 156])).
% 5.50/5.77 tff(158,plain,((~(s(elem!1) = elem!1)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.50/5.77 tff(159,plain,
% 5.50/5.77 (~(s(elem!1) = elem!1)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[158, 151])).
% 5.50/5.77 tff(160,plain,
% 5.50/5.77 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 5.50/5.77 inference(commutativity,[status(thm)],[])).
% 5.50/5.77 tff(161,plain,
% 5.50/5.77 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 5.50/5.77 inference(symmetry,[status(thm)],[160])).
% 5.50/5.77 tff(162,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 5.50/5.77 tff(163,plain,
% 5.50/5.77 (s(elem!1) = elem!1),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[162, 161])).
% 5.50/5.77 tff(164,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 5.50/5.77 tff(165,plain,
% 5.50/5.77 ($false),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[164, 163])).
% 5.50/5.77 tff(166,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.50/5.77 tff(167,plain,
% 5.50/5.77 (~(elem!1 = s(elem!1))),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[166, 159])).
% 5.50/5.77 tff(168,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 5.50/5.77 tff(169,assumption,(elem!1 = s(z)), introduced(assumption)).
% 5.50/5.77 tff(170,plain,
% 5.50/5.77 (s(z) = elem!1),
% 5.50/5.77 inference(symmetry,[status(thm)],[169])).
% 5.50/5.77 tff(171,plain,
% 5.50/5.77 ($false),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[150, 170])).
% 5.50/5.77 tff(172,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.50/5.77 tff(173,plain,
% 5.50/5.77 (~(elem!1 = s(z))),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[172, 150])).
% 5.50/5.77 tff(174,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 5.50/5.77 tff(175,assumption,(~r(s(z), z)), introduced(assumption)).
% 5.50/5.77 tff(176,plain,
% 5.50/5.77 (((~![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))),
% 5.50/5.77 inference(rewrite,[status(thm)],[])).
% 5.50/5.77 tff(177,plain,
% 5.50/5.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 5.50/5.77 inference(quant_inst,[status(thm)],[])).
% 5.50/5.77 tff(178,plain,
% 5.50/5.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[177, 176])).
% 5.50/5.77 tff(179,plain,
% 5.50/5.77 ($false),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[178, 42, 23, 175, 91])).
% 5.50/5.77 tff(180,plain,(r(s(z), z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 5.50/5.77 tff(181,plain,
% 5.50/5.77 (r(s(z), z)),
% 5.50/5.77 inference(unit_resolution,[status(thm)],[180, 91])).
% 5.50/5.77 tff(182,assumption,(r(s(z), z)), introduced(assumption)).
% 5.50/5.77 tff(183,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 5.50/5.77 tff(184,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 5.50/5.77 tff(185,plain,
% 5.50/5.77 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 5.50/5.77 inference(bind,[status(th)],[])).
% 5.50/5.77 tff(186,plain,
% 5.50/5.77 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 5.50/5.77 inference(quant_intro,[status(thm)],[185])).
% 5.50/5.77 tff(187,plain,
% 5.50/5.77 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 5.50/5.77 inference(rewrite,[status(thm)],[])).
% 5.50/5.77 tff(188,plain,
% 5.50/5.77 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> (((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))))),
% 5.50/5.77 inference(bind,[status(th)],[])).
% 5.50/5.77 tff(189,plain,
% 5.50/5.77 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 5.50/5.77 inference(quant_intro,[status(thm)],[188])).
% 5.50/5.77 tff(190,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 5.50/5.77 tff(191,plain,
% 5.50/5.77 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[190, 189])).
% 5.50/5.77 tff(192,plain,
% 5.50/5.77 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[191, 187])).
% 5.50/5.77 tff(193,plain,(
% 5.50/5.77 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 5.50/5.77 inference(skolemize,[status(sab)],[192])).
% 5.50/5.77 tff(194,plain,
% 5.50/5.77 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 5.50/5.77 inference(modus_ponens,[status(thm)],[193, 186])).
% 5.50/5.77 tff(195,plain,
% 5.50/5.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 5.50/5.77 inference(rewrite,[status(thm)],[])).
% 5.50/5.77 tff(196,plain,
% 5.50/5.77 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 5.50/5.77 inference(rewrite,[status(thm)],[])).
% 5.50/5.77 tff(197,plain,
% 5.50/5.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))))),
% 5.50/5.77 inference(monotonicity,[status(thm)],[196])).
% 5.50/5.77 tff(198,plain,
% 5.50/5.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 5.50/5.77 inference(transitivity,[status(thm)],[197, 195])).
% 5.50/5.77 tff(199,plain,
% 5.50/5.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 5.50/5.77 inference(quant_inst,[status(thm)],[])).
% 5.50/5.77 tff(200,plain,
% 5.50/5.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 5.50/5.78 inference(modus_ponens,[status(thm)],[199, 198])).
% 5.50/5.78 tff(201,plain,
% 5.50/5.78 ($false),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[200, 194, 174, 184, 183, 182])).
% 5.50/5.78 tff(202,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.78 tff(203,plain,
% 5.50/5.78 (~r(s(s(s(elem!1))), s(z))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[202, 181, 59, 174])).
% 5.50/5.78 tff(204,plain,
% 5.50/5.78 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 5.50/5.78 inference(commutativity,[status(thm)],[])).
% 5.50/5.78 tff(205,plain,
% 5.50/5.78 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 5.50/5.78 inference(symmetry,[status(thm)],[204])).
% 5.50/5.78 tff(206,plain,
% 5.50/5.78 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(z)))),
% 5.50/5.78 inference(monotonicity,[status(thm)],[205])).
% 5.50/5.78 tff(207,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 5.50/5.78 tff(208,plain,
% 5.50/5.78 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 5.50/5.78 inference(monotonicity,[status(thm)],[207])).
% 5.50/5.78 tff(209,plain,
% 5.50/5.78 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 5.50/5.78 inference(symmetry,[status(thm)],[208])).
% 5.50/5.78 tff(210,plain,
% 5.50/5.78 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 5.50/5.78 inference(quant_inst,[status(thm)],[])).
% 5.50/5.78 tff(211,plain,
% 5.50/5.78 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[210, 106])).
% 5.50/5.78 tff(212,plain,
% 5.50/5.78 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 5.50/5.78 inference(symmetry,[status(thm)],[211])).
% 5.50/5.78 tff(213,plain,
% 5.50/5.78 (s(s(elem!1)) = z),
% 5.50/5.78 inference(transitivity,[status(thm)],[212, 209, 112])).
% 5.50/5.78 tff(214,plain,
% 5.50/5.78 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 5.50/5.78 inference(quant_inst,[status(thm)],[])).
% 5.50/5.78 tff(215,plain,
% 5.50/5.78 (~(s(s(elem!1)) = z)),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[214, 21])).
% 5.50/5.78 tff(216,plain,
% 5.50/5.78 ($false),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[215, 213])).
% 5.50/5.78 tff(217,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.78 tff(218,plain,
% 5.50/5.78 (~(s(s(s(elem!1))) = s(z))),
% 5.50/5.78 inference(modus_ponens,[status(thm)],[217, 206])).
% 5.50/5.78 tff(219,plain,
% 5.50/5.78 (((~![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)))),
% 5.50/5.78 inference(rewrite,[status(thm)],[])).
% 5.50/5.78 tff(220,plain,
% 5.50/5.78 ((~![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)))),
% 5.50/5.78 inference(quant_inst,[status(thm)],[])).
% 5.50/5.78 tff(221,plain,
% 5.50/5.78 ((~![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))),
% 5.50/5.78 inference(modus_ponens,[status(thm)],[220, 219])).
% 5.50/5.78 tff(222,plain,
% 5.50/5.78 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[221, 42])).
% 5.50/5.78 tff(223,plain,
% 5.50/5.78 (b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[222, 218])).
% 5.50/5.78 tff(224,plain,
% 5.50/5.78 (b(s(s(s(elem!1))), s(z))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[223, 203])).
% 5.50/5.78 tff(225,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 5.50/5.78 tff(226,plain,
% 5.50/5.78 (((~![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))),
% 5.50/5.78 inference(rewrite,[status(thm)],[])).
% 5.50/5.78 tff(227,plain,
% 5.50/5.78 ((~![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))),
% 5.50/5.78 inference(quant_inst,[status(thm)],[])).
% 5.50/5.78 tff(228,plain,
% 5.50/5.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 5.50/5.78 inference(modus_ponens,[status(thm)],[227, 226])).
% 5.50/5.78 tff(229,plain,
% 5.50/5.78 ($false),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[228, 42, 225, 127, 168])).
% 5.50/5.78 tff(230,plain,(b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.50/5.78 tff(231,plain,
% 5.50/5.78 (r(s(s(s(elem!1))), elem!1)),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[230, 168, 151])).
% 5.50/5.78 tff(232,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 5.50/5.78 tff(233,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 5.50/5.78 tff(234,plain,
% 5.50/5.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.50/5.78 inference(rewrite,[status(thm)],[])).
% 5.50/5.78 tff(235,plain,
% 5.50/5.78 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.50/5.78 inference(rewrite,[status(thm)],[])).
% 5.50/5.78 tff(236,plain,
% 5.50/5.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 5.50/5.78 inference(monotonicity,[status(thm)],[235])).
% 5.50/5.78 tff(237,plain,
% 5.50/5.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.50/5.78 inference(transitivity,[status(thm)],[236, 234])).
% 5.50/5.78 tff(238,plain,
% 5.50/5.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 5.50/5.78 inference(quant_inst,[status(thm)],[])).
% 5.50/5.78 tff(239,plain,
% 5.50/5.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 5.50/5.78 inference(modus_ponens,[status(thm)],[238, 237])).
% 5.50/5.78 tff(240,plain,
% 5.50/5.78 ($false),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[239, 194, 233, 184, 232, 182])).
% 5.50/5.78 tff(241,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.78 tff(242,plain,
% 5.50/5.78 (~r(s(z), s(s(s(elem!1))))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[241, 181, 59, 231])).
% 5.50/5.78 tff(243,plain,
% 5.50/5.78 (((~![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)))))),
% 5.50/5.78 inference(rewrite,[status(thm)],[])).
% 5.50/5.78 tff(244,plain,
% 5.50/5.78 ((~![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)))))),
% 5.50/5.78 inference(quant_inst,[status(thm)],[])).
% 5.50/5.78 tff(245,plain,
% 5.50/5.78 ((~![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))))),
% 5.50/5.78 inference(modus_ponens,[status(thm)],[244, 243])).
% 5.50/5.78 tff(246,plain,
% 5.50/5.78 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[245, 42])).
% 5.50/5.78 tff(247,plain,
% 5.50/5.78 (b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[246, 217])).
% 5.50/5.78 tff(248,plain,
% 5.50/5.78 (b(s(z), s(s(s(elem!1))))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[247, 242])).
% 5.50/5.78 tff(249,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 5.50/5.78 tff(250,plain,
% 5.50/5.78 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 5.50/5.78 inference(commutativity,[status(thm)],[])).
% 5.50/5.78 tff(251,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 5.50/5.78 tff(252,plain,
% 5.50/5.78 (s(elem!1) = s(s(elem!1))),
% 5.50/5.78 inference(symmetry,[status(thm)],[251])).
% 5.50/5.78 tff(253,plain,
% 5.50/5.78 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(elem!1)))),
% 5.50/5.78 inference(monotonicity,[status(thm)],[252])).
% 5.50/5.78 tff(254,plain,
% 5.50/5.78 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = elem!1)),
% 5.50/5.78 inference(transitivity,[status(thm)],[253, 250])).
% 5.50/5.78 tff(255,plain,
% 5.50/5.78 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(elem!1))),
% 5.50/5.78 inference(symmetry,[status(thm)],[254])).
% 5.50/5.78 tff(256,plain,
% 5.50/5.78 ((~(s(s(elem!1)) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 5.50/5.78 inference(monotonicity,[status(thm)],[255])).
% 5.50/5.78 tff(257,plain,
% 5.50/5.78 (~(elem!1 = s(elem!1))),
% 5.50/5.78 inference(modus_ponens,[status(thm)],[249, 256])).
% 5.50/5.78 tff(258,plain,
% 5.50/5.78 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 5.50/5.78 inference(quant_inst,[status(thm)],[])).
% 5.50/5.78 tff(259,plain,
% 5.50/5.78 (inj_0(s(s(elem!1))) = s(elem!1)),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[258, 106])).
% 5.50/5.78 tff(260,plain,
% 5.50/5.78 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 5.50/5.78 inference(monotonicity,[status(thm)],[252])).
% 5.50/5.78 tff(261,plain,
% 5.50/5.78 (elem!1 = inj_0(s(elem!1))),
% 5.50/5.78 inference(symmetry,[status(thm)],[108])).
% 5.50/5.78 tff(262,plain,
% 5.50/5.78 (elem!1 = s(elem!1)),
% 5.50/5.78 inference(transitivity,[status(thm)],[261, 260, 259])).
% 5.50/5.78 tff(263,plain,
% 5.50/5.78 ($false),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[262, 257])).
% 5.50/5.78 tff(264,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.50/5.78 tff(265,plain,
% 5.50/5.78 (~(s(s(elem!1)) = s(elem!1))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[264, 249])).
% 5.50/5.78 tff(266,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 5.50/5.78 tff(267,plain,
% 5.50/5.78 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 5.50/5.78 inference(commutativity,[status(thm)],[])).
% 5.50/5.78 tff(268,plain,
% 5.50/5.78 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 5.50/5.78 inference(symmetry,[status(thm)],[267])).
% 5.50/5.78 tff(269,plain,
% 5.50/5.78 (s(s(elem!1)) = s(s(s(elem!1)))),
% 5.50/5.78 inference(modus_ponens,[status(thm)],[266, 268])).
% 5.50/5.78 tff(270,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 5.50/5.78 tff(271,plain,
% 5.50/5.78 ($false),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[270, 269])).
% 5.50/5.78 tff(272,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.78 tff(273,plain,
% 5.50/5.78 (s(s(elem!1)) = s(s(s(elem!1)))),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[272, 266])).
% 5.50/5.78 tff(274,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 5.50/5.78 tff(275,plain,
% 5.50/5.78 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 5.50/5.78 inference(monotonicity,[status(thm)],[274])).
% 5.50/5.78 tff(276,plain,
% 5.50/5.78 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 5.50/5.78 inference(symmetry,[status(thm)],[275])).
% 5.50/5.78 tff(277,plain,
% 5.50/5.78 (s(s(s(elem!1))) = s(s(elem!1))),
% 5.50/5.78 inference(symmetry,[status(thm)],[274])).
% 5.50/5.78 tff(278,plain,
% 5.50/5.78 (s(s(s(elem!1))) = s(elem!1)),
% 5.50/5.78 inference(transitivity,[status(thm)],[277, 212, 276, 259])).
% 5.50/5.78 tff(279,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 5.50/5.78 tff(280,plain,
% 5.50/5.78 ($false),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[279, 278])).
% 5.50/5.78 tff(281,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.78 tff(282,plain,
% 5.50/5.78 (s(s(s(elem!1))) = s(elem!1)),
% 5.50/5.78 inference(unit_resolution,[status(thm)],[281, 273])).
% 5.50/5.78 tff(283,plain,
% 5.50/5.78 (s(s(elem!1)) = s(s(s(elem!1)))),
% 5.50/5.78 inference(symmetry,[status(thm)],[266])).
% 5.50/5.78 tff(284,plain,
% 5.50/5.78 (s(s(elem!1)) = s(elem!1)),
% 5.50/5.78 inference(transitivity,[status(thm)],[283, 282])).
% 5.50/5.78 tff(285,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 5.50/5.79 tff(286,plain,
% 5.50/5.79 ($false),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[285, 284])).
% 5.50/5.79 tff(287,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.79 tff(288,plain,
% 5.50/5.79 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[287, 265])).
% 5.50/5.79 tff(289,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 5.50/5.79 tff(290,plain,
% 5.50/5.79 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 5.50/5.79 inference(symmetry,[status(thm)],[289])).
% 5.50/5.79 tff(291,plain,
% 5.50/5.79 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 5.50/5.79 inference(monotonicity,[status(thm)],[290])).
% 5.50/5.79 tff(292,plain,
% 5.50/5.79 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(elem!1))))),
% 5.50/5.79 inference(symmetry,[status(thm)],[291])).
% 5.50/5.79 tff(293,plain,
% 5.50/5.79 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 5.50/5.79 inference(quant_inst,[status(thm)],[])).
% 5.50/5.79 tff(294,plain,
% 5.50/5.79 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[293, 106])).
% 5.50/5.79 tff(295,plain,
% 5.50/5.79 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 5.50/5.79 inference(symmetry,[status(thm)],[294])).
% 5.50/5.79 tff(296,plain,
% 5.50/5.79 (s(s(s(elem!1))) = s(s(elem!1))),
% 5.50/5.79 inference(transitivity,[status(thm)],[295, 292, 211])).
% 5.50/5.79 tff(297,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 5.50/5.79 tff(298,plain,
% 5.50/5.79 ($false),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[297, 296])).
% 5.50/5.79 tff(299,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.79 tff(300,plain,
% 5.50/5.79 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[299, 288])).
% 5.50/5.79 tff(301,plain,
% 5.50/5.79 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 5.50/5.79 inference(commutativity,[status(thm)],[])).
% 5.50/5.79 tff(302,plain,
% 5.50/5.79 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 5.50/5.79 inference(symmetry,[status(thm)],[301])).
% 5.50/5.79 tff(303,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 5.50/5.79 tff(304,plain,
% 5.50/5.79 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 5.50/5.79 inference(modus_ponens,[status(thm)],[303, 302])).
% 5.50/5.79 tff(305,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 5.50/5.79 tff(306,plain,
% 5.50/5.79 ($false),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[305, 304])).
% 5.50/5.79 tff(307,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.79 tff(308,plain,
% 5.50/5.79 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[307, 300])).
% 5.50/5.79 tff(309,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 5.50/5.79 tff(310,plain,
% 5.50/5.79 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[299, 297])).
% 5.50/5.79 tff(311,plain,
% 5.50/5.79 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[307, 310])).
% 5.50/5.79 tff(312,plain,
% 5.50/5.79 (s(s(s(elem!1))) = s(s(elem!1))),
% 5.50/5.79 inference(modus_ponens,[status(thm)],[274, 267])).
% 5.50/5.79 tff(313,plain,
% 5.50/5.79 ($false),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[297, 312])).
% 5.50/5.79 tff(314,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.79 tff(315,plain,
% 5.50/5.79 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[314, 297])).
% 5.50/5.79 tff(316,plain,
% 5.50/5.79 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 5.50/5.79 inference(commutativity,[status(thm)],[])).
% 5.50/5.79 tff(317,plain,
% 5.50/5.79 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 5.50/5.79 inference(symmetry,[status(thm)],[316])).
% 5.50/5.79 tff(318,plain,
% 5.50/5.79 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 5.50/5.79 inference(monotonicity,[status(thm)],[317])).
% 5.50/5.79 tff(319,plain,
% 5.50/5.79 (~(z = s(s(elem!1)))),
% 5.50/5.79 inference(modus_ponens,[status(thm)],[215, 318])).
% 5.50/5.79 tff(320,plain,
% 5.50/5.79 (((~![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))))),
% 5.50/5.79 inference(rewrite,[status(thm)],[])).
% 5.50/5.79 tff(321,plain,
% 5.50/5.79 ((~![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))))),
% 5.50/5.79 inference(quant_inst,[status(thm)],[])).
% 5.50/5.79 tff(322,plain,
% 5.50/5.79 ((~![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)))),
% 5.50/5.79 inference(modus_ponens,[status(thm)],[321, 320])).
% 5.50/5.79 tff(323,plain,
% 5.50/5.79 ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[322, 42])).
% 5.50/5.79 tff(324,plain,
% 5.50/5.79 (b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[323, 319])).
% 5.50/5.79 tff(325,plain,
% 5.50/5.79 (r(z, s(s(elem!1)))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[324, 309])).
% 5.50/5.79 tff(326,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 5.50/5.79 tff(327,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 5.50/5.79 tff(328,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 5.50/5.79 tff(329,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 5.50/5.79 tff(330,plain,
% 5.50/5.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.50/5.79 inference(rewrite,[status(thm)],[])).
% 5.50/5.79 tff(331,plain,
% 5.50/5.79 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.50/5.79 inference(rewrite,[status(thm)],[])).
% 5.50/5.79 tff(332,plain,
% 5.50/5.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 5.50/5.79 inference(monotonicity,[status(thm)],[331])).
% 5.50/5.79 tff(333,plain,
% 5.50/5.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.50/5.79 inference(transitivity,[status(thm)],[332, 330])).
% 5.50/5.79 tff(334,plain,
% 5.50/5.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 5.50/5.79 inference(quant_inst,[status(thm)],[])).
% 5.50/5.79 tff(335,plain,
% 5.50/5.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 5.50/5.79 inference(modus_ponens,[status(thm)],[334, 333])).
% 5.50/5.79 tff(336,plain,
% 5.50/5.79 ($false),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[335, 194, 184, 327, 232, 182])).
% 5.50/5.79 tff(337,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.79 tff(338,plain,
% 5.50/5.79 (~r(s(z), s(s(s(elem!1))))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[337, 327, 184, 182])).
% 5.50/5.79 tff(339,plain,
% 5.50/5.79 (b(s(z), s(s(s(elem!1))))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[247, 338])).
% 5.50/5.79 tff(340,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 5.50/5.79 tff(341,plain,
% 5.50/5.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 5.50/5.79 inference(rewrite,[status(thm)],[])).
% 5.50/5.79 tff(342,plain,
% 5.50/5.79 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 5.50/5.79 inference(rewrite,[status(thm)],[])).
% 5.50/5.79 tff(343,plain,
% 5.50/5.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 5.50/5.79 inference(monotonicity,[status(thm)],[342])).
% 5.50/5.79 tff(344,plain,
% 5.50/5.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 5.50/5.79 inference(transitivity,[status(thm)],[343, 341])).
% 5.50/5.79 tff(345,plain,
% 5.50/5.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 5.50/5.79 inference(quant_inst,[status(thm)],[])).
% 5.50/5.79 tff(346,plain,
% 5.50/5.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 5.50/5.79 inference(modus_ponens,[status(thm)],[345, 344])).
% 5.50/5.79 tff(347,plain,
% 5.50/5.79 ($false),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[346, 194, 340, 184, 327, 326])).
% 5.50/5.79 tff(348,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.79 tff(349,plain,
% 5.50/5.79 (~r(s(s(elem!1)), s(z))),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[348, 327, 184, 326])).
% 5.50/5.79 tff(350,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 5.50/5.79 tff(351,plain,
% 5.50/5.79 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 5.50/5.79 inference(monotonicity,[status(thm)],[350])).
% 5.50/5.79 tff(352,plain,
% 5.50/5.79 (s(elem!1) = inj_0(s(s(elem!1)))),
% 5.50/5.79 inference(symmetry,[status(thm)],[259])).
% 5.50/5.79 tff(353,plain,
% 5.50/5.79 (s(elem!1) = z),
% 5.50/5.79 inference(transitivity,[status(thm)],[352, 351, 112])).
% 5.50/5.79 tff(354,plain,
% 5.50/5.79 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 5.50/5.79 inference(quant_inst,[status(thm)],[])).
% 5.50/5.79 tff(355,plain,
% 5.50/5.79 (~(s(elem!1) = z)),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[354, 21])).
% 5.50/5.79 tff(356,plain,
% 5.50/5.79 ($false),
% 5.50/5.79 inference(unit_resolution,[status(thm)],[355, 353])).
% 5.50/5.79 tff(357,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 5.50/5.79 tff(358,plain,
% 5.50/5.79 (((~![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)))),
% 5.50/5.79 inference(rewrite,[status(thm)],[])).
% 5.50/5.79 tff(359,plain,
% 5.50/5.79 ((~![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)))),
% 5.50/5.79 inference(quant_inst,[status(thm)],[])).
% 5.50/5.79 tff(360,plain,
% 5.50/5.79 ((~![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))),
% 5.50/5.79 inference(modus_ponens,[status(thm)],[359, 358])).
% 5.60/5.80 tff(361,plain,
% 5.60/5.80 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[360, 42])).
% 5.60/5.80 tff(362,plain,
% 5.60/5.80 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[361, 357])).
% 5.60/5.80 tff(363,plain,
% 5.60/5.80 (b(s(s(elem!1)), s(z))),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[362, 349])).
% 5.60/5.80 tff(364,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 5.60/5.80 tff(365,plain,
% 5.60/5.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 5.60/5.80 inference(rewrite,[status(thm)],[])).
% 5.60/5.80 tff(366,plain,
% 5.60/5.80 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 5.60/5.80 inference(rewrite,[status(thm)],[])).
% 5.60/5.80 tff(367,plain,
% 5.60/5.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 5.60/5.80 inference(monotonicity,[status(thm)],[366])).
% 5.60/5.80 tff(368,plain,
% 5.60/5.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 5.60/5.80 inference(transitivity,[status(thm)],[367, 365])).
% 5.60/5.80 tff(369,plain,
% 5.60/5.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 5.60/5.80 inference(quant_inst,[status(thm)],[])).
% 5.60/5.80 tff(370,plain,
% 5.60/5.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 5.60/5.80 inference(modus_ponens,[status(thm)],[369, 368])).
% 5.60/5.80 tff(371,plain,
% 5.60/5.80 ($false),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[370, 194, 184, 364, 327, 326])).
% 5.60/5.80 tff(372,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.80 tff(373,plain,
% 5.60/5.80 (~r(s(s(elem!1)), elem!1)),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[372, 327, 184, 326])).
% 5.60/5.80 tff(374,plain,
% 5.60/5.80 (((~![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))),
% 5.60/5.80 inference(rewrite,[status(thm)],[])).
% 5.60/5.80 tff(375,plain,
% 5.60/5.80 ((~![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))),
% 5.60/5.80 inference(quant_inst,[status(thm)],[])).
% 5.60/5.80 tff(376,plain,
% 5.60/5.80 ((~![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)),
% 5.60/5.80 inference(modus_ponens,[status(thm)],[375, 374])).
% 5.60/5.80 tff(377,plain,
% 5.60/5.80 (b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[376, 42, 50])).
% 5.60/5.80 tff(378,plain,
% 5.60/5.80 (b(s(s(s(elem!1))), z)),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[377, 329])).
% 5.60/5.80 tff(379,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 5.60/5.80 tff(380,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 5.60/5.80 tff(381,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 5.60/5.80 tff(382,plain,
% 5.60/5.80 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 5.60/5.80 inference(bind,[status(th)],[])).
% 5.60/5.80 tff(383,plain,
% 5.60/5.80 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 5.60/5.80 inference(quant_intro,[status(thm)],[382])).
% 5.60/5.80 tff(384,plain,
% 5.60/5.80 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 5.60/5.80 inference(rewrite,[status(thm)],[])).
% 5.60/5.80 tff(385,plain,
% 5.60/5.80 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 5.60/5.80 inference(bind,[status(th)],[])).
% 5.60/5.80 tff(386,plain,
% 5.60/5.80 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 5.60/5.80 inference(quant_intro,[status(thm)],[385])).
% 5.60/5.80 tff(387,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 5.60/5.80 tff(388,plain,
% 5.60/5.80 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 5.60/5.80 inference(modus_ponens,[status(thm)],[387, 386])).
% 5.60/5.80 tff(389,plain,
% 5.60/5.80 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 5.60/5.80 inference(modus_ponens,[status(thm)],[388, 384])).
% 5.60/5.80 tff(390,plain,(
% 5.60/5.80 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 5.60/5.80 inference(skolemize,[status(sab)],[389])).
% 5.60/5.80 tff(391,plain,
% 5.60/5.80 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 5.60/5.80 inference(modus_ponens,[status(thm)],[390, 383])).
% 5.60/5.80 tff(392,plain,
% 5.60/5.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.80 inference(rewrite,[status(thm)],[])).
% 5.60/5.80 tff(393,plain,
% 5.60/5.80 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.80 inference(rewrite,[status(thm)],[])).
% 5.60/5.80 tff(394,plain,
% 5.60/5.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 5.60/5.80 inference(monotonicity,[status(thm)],[393])).
% 5.60/5.80 tff(395,plain,
% 5.60/5.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.80 inference(transitivity,[status(thm)],[394, 392])).
% 5.60/5.80 tff(396,plain,
% 5.60/5.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 5.60/5.80 inference(quant_inst,[status(thm)],[])).
% 5.60/5.80 tff(397,plain,
% 5.60/5.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 5.60/5.80 inference(modus_ponens,[status(thm)],[396, 395])).
% 5.60/5.80 tff(398,plain,
% 5.60/5.80 ($false),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[397, 391, 133, 381, 380, 379, 328])).
% 5.60/5.80 tff(399,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.80 tff(400,plain,
% 5.60/5.80 (~b(z, elem!1)),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[399, 378, 339, 328, 363])).
% 5.60/5.80 tff(401,plain,
% 5.60/5.80 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 5.60/5.80 inference(monotonicity,[status(thm)],[11])).
% 5.60/5.80 tff(402,plain,
% 5.60/5.80 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 5.60/5.80 inference(symmetry,[status(thm)],[401])).
% 5.60/5.80 tff(403,plain,
% 5.60/5.80 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 5.60/5.80 inference(monotonicity,[status(thm)],[402])).
% 5.60/5.80 tff(404,plain,
% 5.60/5.80 (~r(s(s(s(elem!1))), elem!1)),
% 5.60/5.80 inference(modus_ponens,[status(thm)],[329, 403])).
% 5.60/5.80 tff(405,plain,
% 5.60/5.80 ($false),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[233, 404])).
% 5.60/5.80 tff(406,plain,((~(elem!1 = z)) | (~r(s(s(s(elem!1))), elem!1)) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 5.60/5.80 tff(407,plain,
% 5.60/5.80 (~(elem!1 = z)),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[406, 233, 329])).
% 5.60/5.80 tff(408,plain,
% 5.60/5.80 (~(z = elem!1)),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[97, 407])).
% 5.60/5.80 tff(409,plain,
% 5.60/5.80 (r(z, elem!1)),
% 5.60/5.80 inference(unit_resolution,[status(thm)],[141, 408, 89])).
% 5.60/5.80 tff(410,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 5.60/5.80 tff(411,assumption,(r(z, elem!1)), introduced(assumption)).
% 5.60/5.80 tff(412,plain,
% 5.60/5.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 5.60/5.81 inference(rewrite,[status(thm)],[])).
% 5.60/5.81 tff(413,plain,
% 5.60/5.81 (((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 5.60/5.81 inference(rewrite,[status(thm)],[])).
% 5.60/5.81 tff(414,plain,
% 5.60/5.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 5.60/5.81 inference(monotonicity,[status(thm)],[413])).
% 5.60/5.81 tff(415,plain,
% 5.60/5.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 5.60/5.81 inference(transitivity,[status(thm)],[414, 412])).
% 5.60/5.81 tff(416,plain,
% 5.60/5.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 5.60/5.81 inference(quant_inst,[status(thm)],[])).
% 5.60/5.81 tff(417,plain,
% 5.60/5.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[416, 415])).
% 5.60/5.81 tff(418,plain,
% 5.60/5.81 ($false),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[417, 194, 411, 233, 184, 410])).
% 5.60/5.81 tff(419,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.81 tff(420,plain,
% 5.60/5.81 (~r(elem!1, s(s(s(elem!1))))),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[419, 409, 233, 184])).
% 5.60/5.81 tff(421,plain,
% 5.60/5.81 (((~![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)))))),
% 5.60/5.81 inference(rewrite,[status(thm)],[])).
% 5.60/5.81 tff(422,plain,
% 5.60/5.81 ((~![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)))))),
% 5.60/5.81 inference(quant_inst,[status(thm)],[])).
% 5.60/5.81 tff(423,plain,
% 5.60/5.81 ((~![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))))),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[422, 421])).
% 5.60/5.81 tff(424,plain,
% 5.60/5.81 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[423, 42])).
% 5.60/5.81 tff(425,plain,
% 5.60/5.81 (b(elem!1, s(s(s(elem!1))))),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[424, 420, 1])).
% 5.60/5.81 tff(426,plain,
% 5.60/5.81 (~(s(elem!1) = elem!1)),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[158, 9])).
% 5.60/5.81 tff(427,plain,
% 5.60/5.81 (~(elem!1 = s(elem!1))),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[166, 426])).
% 5.60/5.81 tff(428,plain,
% 5.60/5.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 5.60/5.81 inference(rewrite,[status(thm)],[])).
% 5.60/5.81 tff(429,plain,
% 5.60/5.81 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 5.60/5.81 inference(rewrite,[status(thm)],[])).
% 5.60/5.81 tff(430,plain,
% 5.60/5.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))))),
% 5.60/5.81 inference(monotonicity,[status(thm)],[429])).
% 5.60/5.81 tff(431,plain,
% 5.60/5.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 5.60/5.81 inference(transitivity,[status(thm)],[430, 428])).
% 5.60/5.81 tff(432,plain,
% 5.60/5.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 5.60/5.81 inference(quant_inst,[status(thm)],[])).
% 5.60/5.81 tff(433,plain,
% 5.60/5.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[432, 431])).
% 5.60/5.81 tff(434,plain,
% 5.60/5.81 ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[433, 194])).
% 5.60/5.81 tff(435,plain,
% 5.60/5.81 (~r(elem!1, s(elem!1))),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[434, 409, 184, 233])).
% 5.60/5.81 tff(436,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 5.60/5.81 tff(437,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 5.60/5.81 tff(438,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 5.60/5.81 tff(439,plain,
% 5.60/5.81 (((~![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)))),
% 5.60/5.81 inference(rewrite,[status(thm)],[])).
% 5.60/5.81 tff(440,plain,
% 5.60/5.81 ((~![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)))),
% 5.60/5.81 inference(quant_inst,[status(thm)],[])).
% 5.60/5.81 tff(441,plain,
% 5.60/5.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[440, 439])).
% 5.60/5.81 tff(442,plain,
% 5.60/5.81 ($false),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[441, 42, 438, 437, 436])).
% 5.60/5.81 tff(443,plain,(b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.81 tff(444,plain,
% 5.60/5.81 (b(elem!1, s(elem!1))),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[443, 435, 427])).
% 5.60/5.81 tff(445,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 5.60/5.81 tff(446,plain,
% 5.60/5.81 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 5.60/5.81 inference(monotonicity,[status(thm)],[445])).
% 5.60/5.81 tff(447,plain,
% 5.60/5.81 (b(elem!1, s(z))),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[381, 446])).
% 5.60/5.81 tff(448,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 5.60/5.81 tff(449,plain,
% 5.60/5.81 (s(s(s(elem!1))) = s(elem!1)),
% 5.60/5.81 inference(monotonicity,[status(thm)],[445])).
% 5.60/5.81 tff(450,plain,
% 5.60/5.81 ($false),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[279, 449])).
% 5.60/5.81 tff(451,plain,((~(s(s(elem!1)) = elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.81 tff(452,plain,
% 5.60/5.81 (s(s(s(elem!1))) = s(elem!1)),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[451, 445])).
% 5.60/5.81 tff(453,plain,
% 5.60/5.81 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 5.60/5.81 inference(monotonicity,[status(thm)],[452])).
% 5.60/5.81 tff(454,plain,
% 5.60/5.81 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 5.60/5.81 inference(monotonicity,[status(thm)],[453])).
% 5.60/5.81 tff(455,plain,
% 5.60/5.81 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 5.60/5.81 inference(bind,[status(th)],[])).
% 5.60/5.81 tff(456,plain,
% 5.60/5.81 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 5.60/5.81 inference(quant_intro,[status(thm)],[455])).
% 5.60/5.81 tff(457,plain,
% 5.60/5.81 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 5.60/5.81 inference(rewrite,[status(thm)],[])).
% 5.60/5.81 tff(458,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 5.60/5.81 tff(459,plain,
% 5.60/5.81 (![X: $i] : (~b(X, X))),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[458, 457])).
% 5.60/5.81 tff(460,plain,(
% 5.60/5.81 ![X: $i] : (~b(X, X))),
% 5.60/5.81 inference(skolemize,[status(sab)],[459])).
% 5.60/5.81 tff(461,plain,
% 5.60/5.81 (![X: $i] : (~b(X, X))),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[460, 456])).
% 5.60/5.81 tff(462,plain,
% 5.60/5.81 ((~![X: $i] : (~b(X, X))) | (~b(s(s(s(elem!1))), s(s(s(elem!1)))))),
% 5.60/5.81 inference(quant_inst,[status(thm)],[])).
% 5.60/5.81 tff(463,plain,
% 5.60/5.81 (~b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[462, 461])).
% 5.60/5.81 tff(464,plain,
% 5.60/5.81 (~b(s(s(s(elem!1))), s(elem!1))),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[463, 454])).
% 5.60/5.81 tff(465,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 5.60/5.81 tff(466,plain,
% 5.60/5.81 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 5.60/5.81 inference(monotonicity,[status(thm)],[465])).
% 5.60/5.81 tff(467,plain,
% 5.60/5.81 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 5.60/5.81 inference(symmetry,[status(thm)],[466])).
% 5.60/5.81 tff(468,plain,
% 5.60/5.81 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 5.60/5.81 inference(monotonicity,[status(thm)],[467])).
% 5.60/5.81 tff(469,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 5.60/5.81 tff(470,plain,
% 5.60/5.81 (~r(s(s(s(elem!1))), elem!1)),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[469, 468])).
% 5.60/5.81 tff(471,plain,
% 5.60/5.81 ($false),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[233, 470])).
% 5.60/5.81 tff(472,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.60/5.81 tff(473,plain,
% 5.60/5.81 (r(s(elem!1), elem!1)),
% 5.60/5.81 inference(unit_resolution,[status(thm)],[472, 452, 233])).
% 5.60/5.81 tff(474,plain,
% 5.60/5.81 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 5.60/5.81 inference(commutativity,[status(thm)],[])).
% 5.60/5.81 tff(475,plain,
% 5.60/5.81 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 5.60/5.81 inference(monotonicity,[status(thm)],[445])).
% 5.60/5.81 tff(476,plain,
% 5.60/5.81 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 5.60/5.81 inference(transitivity,[status(thm)],[475, 474])).
% 5.60/5.81 tff(477,plain,
% 5.60/5.81 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 5.60/5.81 inference(monotonicity,[status(thm)],[476])).
% 5.60/5.81 tff(478,plain,
% 5.60/5.81 (~(s(z) = elem!1)),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[357, 477])).
% 5.60/5.81 tff(479,plain,
% 5.60/5.81 (s(elem!1) = s(s(s(elem!1)))),
% 5.60/5.81 inference(symmetry,[status(thm)],[452])).
% 5.60/5.81 tff(480,plain,
% 5.60/5.81 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 5.60/5.81 inference(monotonicity,[status(thm)],[479, 452])).
% 5.60/5.81 tff(481,plain,
% 5.60/5.81 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(elem!1), s(s(s(elem!1))))),
% 5.60/5.81 inference(symmetry,[status(thm)],[480])).
% 5.60/5.81 tff(482,plain,
% 5.60/5.81 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 5.60/5.81 inference(monotonicity,[status(thm)],[481])).
% 5.60/5.81 tff(483,plain,
% 5.60/5.81 (~b(s(elem!1), s(s(s(elem!1))))),
% 5.60/5.81 inference(modus_ponens,[status(thm)],[464, 482])).
% 5.60/5.81 tff(484,assumption,(~b(elem!1, z)), introduced(assumption)).
% 5.60/5.81 tff(485,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 5.60/5.81 tff(486,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 5.60/5.81 tff(487,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 5.60/5.81 tff(488,plain,
% 5.60/5.81 (s(elem!1) = s(z)),
% 5.60/5.81 inference(monotonicity,[status(thm)],[11])).
% 5.60/5.82 tff(489,plain,
% 5.60/5.82 (s(s(elem!1)) = s(s(z))),
% 5.60/5.82 inference(monotonicity,[status(thm)],[488])).
% 5.60/5.82 tff(490,plain,
% 5.60/5.82 (s(s(s(elem!1))) = s(s(s(z)))),
% 5.60/5.82 inference(monotonicity,[status(thm)],[489])).
% 5.60/5.82 tff(491,plain,
% 5.60/5.82 (s(s(s(z))) = s(s(s(elem!1)))),
% 5.60/5.82 inference(symmetry,[status(thm)],[490])).
% 5.60/5.82 tff(492,plain,
% 5.60/5.82 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 5.60/5.82 inference(monotonicity,[status(thm)],[491])).
% 5.60/5.82 tff(493,plain,
% 5.60/5.82 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 5.60/5.82 inference(symmetry,[status(thm)],[492])).
% 5.60/5.82 tff(494,plain,
% 5.60/5.82 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 5.60/5.82 inference(monotonicity,[status(thm)],[488])).
% 5.60/5.82 tff(495,plain,
% 5.60/5.82 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 5.60/5.82 inference(monotonicity,[status(thm)],[494])).
% 5.60/5.82 tff(496,plain,
% 5.60/5.82 (~b(s(s(s(elem!1))), s(z))),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[486, 495])).
% 5.60/5.82 tff(497,plain,
% 5.60/5.82 (r(s(s(s(elem!1))), s(z))),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[223, 496])).
% 5.60/5.82 tff(498,plain,
% 5.60/5.82 (r(s(s(s(z))), s(z))),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[497, 493])).
% 5.60/5.82 tff(499,plain,
% 5.60/5.82 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 5.60/5.82 inference(monotonicity,[status(thm)],[491])).
% 5.60/5.82 tff(500,plain,
% 5.60/5.82 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 5.60/5.82 inference(symmetry,[status(thm)],[499])).
% 5.60/5.82 tff(501,plain,
% 5.60/5.82 (r(z, s(s(s(z))))),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[184, 500])).
% 5.60/5.82 tff(502,plain,
% 5.60/5.82 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 5.60/5.82 inference(monotonicity,[status(thm)],[491])).
% 5.60/5.82 tff(503,plain,
% 5.60/5.82 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 5.60/5.82 inference(symmetry,[status(thm)],[502])).
% 5.60/5.82 tff(504,plain,
% 5.60/5.82 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 5.60/5.82 inference(monotonicity,[status(thm)],[488])).
% 5.60/5.82 tff(505,plain,
% 5.60/5.82 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 5.60/5.82 inference(monotonicity,[status(thm)],[504])).
% 5.60/5.82 tff(506,plain,
% 5.60/5.82 (~b(s(z), s(s(s(elem!1))))),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[487, 505])).
% 5.60/5.82 tff(507,plain,
% 5.60/5.82 (r(s(z), s(s(s(elem!1))))),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[247, 506])).
% 5.60/5.82 tff(508,plain,
% 5.60/5.82 (r(s(z), s(s(s(z))))),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[507, 503])).
% 5.60/5.82 tff(509,plain,
% 5.60/5.82 (r(s(elem!1), z) <=> r(s(z), z)),
% 5.60/5.82 inference(monotonicity,[status(thm)],[488])).
% 5.60/5.82 tff(510,plain,
% 5.60/5.82 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 5.60/5.82 inference(monotonicity,[status(thm)],[11])).
% 5.60/5.82 tff(511,plain,
% 5.60/5.82 (r(s(elem!1), z)),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[485, 510])).
% 5.60/5.82 tff(512,plain,
% 5.60/5.82 (r(s(z), z)),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[511, 509])).
% 5.60/5.82 tff(513,plain,
% 5.60/5.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 5.60/5.82 inference(rewrite,[status(thm)],[])).
% 5.60/5.82 tff(514,plain,
% 5.60/5.82 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 5.60/5.82 inference(rewrite,[status(thm)],[])).
% 5.60/5.82 tff(515,plain,
% 5.60/5.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 5.60/5.82 inference(monotonicity,[status(thm)],[514])).
% 5.60/5.82 tff(516,plain,
% 5.60/5.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 5.60/5.82 inference(transitivity,[status(thm)],[515, 513])).
% 5.60/5.82 tff(517,plain,
% 5.60/5.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 5.60/5.82 inference(quant_inst,[status(thm)],[])).
% 5.60/5.82 tff(518,plain,
% 5.60/5.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[517, 516])).
% 5.60/5.82 tff(519,plain,
% 5.60/5.82 (~r(s(s(s(z))), s(z))),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[518, 194, 512, 508, 501])).
% 5.60/5.82 tff(520,plain,
% 5.60/5.82 ($false),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[519, 498])).
% 5.60/5.82 tff(521,plain,((~(elem!1 = z)) | (~r(z, s(s(s(elem!1))))) | b(s(elem!1), s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.82 tff(522,plain,
% 5.60/5.82 (~(elem!1 = z)),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[521, 184, 487, 486, 485])).
% 5.60/5.82 tff(523,plain,
% 5.60/5.82 (((~![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))),
% 5.60/5.82 inference(rewrite,[status(thm)],[])).
% 5.60/5.82 tff(524,plain,
% 5.60/5.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 5.60/5.82 inference(quant_inst,[status(thm)],[])).
% 5.60/5.82 tff(525,plain,
% 5.60/5.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[524, 523])).
% 5.60/5.82 tff(526,plain,
% 5.60/5.82 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[525, 42])).
% 5.60/5.82 tff(527,plain,
% 5.60/5.82 (r(elem!1, z)),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[526, 522, 484])).
% 5.60/5.82 tff(528,plain,
% 5.60/5.82 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 5.60/5.82 inference(monotonicity,[status(thm)],[5])).
% 5.60/5.82 tff(529,plain,
% 5.60/5.82 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 5.60/5.82 inference(symmetry,[status(thm)],[528])).
% 5.60/5.82 tff(530,assumption,(r(elem!1, z)), introduced(assumption)).
% 5.60/5.82 tff(531,plain,
% 5.60/5.82 (r(s(s(s(elem!1))), z)),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[530, 529])).
% 5.60/5.82 tff(532,plain,
% 5.60/5.82 ($false),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[329, 531])).
% 5.60/5.82 tff(533,plain,((~(s(s(s(elem!1))) = elem!1)) | r(s(s(s(elem!1))), z) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.82 tff(534,plain,
% 5.60/5.82 (~(s(s(s(elem!1))) = elem!1)),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[533, 527, 329])).
% 5.60/5.82 tff(535,plain,
% 5.60/5.82 (~(elem!1 = s(s(s(elem!1))))),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[129, 534])).
% 5.60/5.82 tff(536,plain,
% 5.60/5.82 (~(z = elem!1)),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[97, 522])).
% 5.60/5.82 tff(537,plain,
% 5.60/5.82 (r(z, elem!1)),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[141, 536, 89])).
% 5.60/5.82 tff(538,plain,
% 5.60/5.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 5.60/5.82 inference(rewrite,[status(thm)],[])).
% 5.60/5.82 tff(539,plain,
% 5.60/5.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 5.60/5.82 inference(quant_inst,[status(thm)],[])).
% 5.60/5.82 tff(540,plain,
% 5.60/5.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 5.60/5.82 inference(modus_ponens,[status(thm)],[539, 538])).
% 5.60/5.82 tff(541,plain,
% 5.60/5.82 ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 5.60/5.82 inference(unit_resolution,[status(thm)],[540, 194])).
% 5.60/5.83 tff(542,plain,
% 5.60/5.83 (~r(s(elem!1), z)),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[541, 537, 485, 527])).
% 5.60/5.83 tff(543,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 5.60/5.83 tff(544,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 5.60/5.83 tff(545,plain,
% 5.60/5.83 (((~![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))),
% 5.60/5.83 inference(rewrite,[status(thm)],[])).
% 5.60/5.83 tff(546,plain,
% 5.60/5.83 ((~![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))),
% 5.60/5.83 inference(quant_inst,[status(thm)],[])).
% 5.60/5.83 tff(547,plain,
% 5.60/5.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 5.60/5.83 inference(modus_ponens,[status(thm)],[546, 545])).
% 5.60/5.83 tff(548,plain,
% 5.60/5.83 ($false),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[547, 42, 355, 544, 543])).
% 5.60/5.83 tff(549,plain,(b(s(elem!1), z) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 5.60/5.83 tff(550,plain,
% 5.60/5.83 (b(s(elem!1), z)),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[549, 542])).
% 5.60/5.83 tff(551,plain,
% 5.60/5.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 5.60/5.83 inference(rewrite,[status(thm)],[])).
% 5.60/5.83 tff(552,plain,
% 5.60/5.83 (((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 5.60/5.83 inference(rewrite,[status(thm)],[])).
% 5.60/5.83 tff(553,plain,
% 5.60/5.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 5.60/5.83 inference(monotonicity,[status(thm)],[552])).
% 5.60/5.83 tff(554,plain,
% 5.60/5.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 5.60/5.83 inference(transitivity,[status(thm)],[553, 551])).
% 5.60/5.83 tff(555,plain,
% 5.60/5.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 5.60/5.83 inference(quant_inst,[status(thm)],[])).
% 5.60/5.83 tff(556,plain,
% 5.60/5.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))),
% 5.60/5.83 inference(modus_ponens,[status(thm)],[555, 554])).
% 5.60/5.83 tff(557,plain,
% 5.60/5.83 (~r(z, s(elem!1))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[556, 194, 537, 527, 485])).
% 5.60/5.83 tff(558,plain,
% 5.60/5.83 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 5.60/5.83 inference(commutativity,[status(thm)],[])).
% 5.60/5.83 tff(559,plain,
% 5.60/5.83 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 5.60/5.83 inference(symmetry,[status(thm)],[558])).
% 5.60/5.83 tff(560,plain,
% 5.60/5.83 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 5.60/5.83 inference(monotonicity,[status(thm)],[559])).
% 5.60/5.83 tff(561,plain,
% 5.60/5.83 (~(z = s(elem!1))),
% 5.60/5.83 inference(modus_ponens,[status(thm)],[355, 560])).
% 5.60/5.83 tff(562,plain,
% 5.60/5.83 (((~![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)))),
% 5.60/5.83 inference(rewrite,[status(thm)],[])).
% 5.60/5.83 tff(563,plain,
% 5.60/5.83 ((~![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)))),
% 5.60/5.83 inference(quant_inst,[status(thm)],[])).
% 5.60/5.83 tff(564,plain,
% 5.60/5.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 5.60/5.83 inference(modus_ponens,[status(thm)],[563, 562])).
% 5.60/5.83 tff(565,plain,
% 5.60/5.83 ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[564, 42])).
% 5.60/5.83 tff(566,plain,
% 5.60/5.83 (b(z, s(elem!1)) | r(z, s(elem!1))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[565, 561])).
% 5.60/5.83 tff(567,plain,
% 5.60/5.83 (b(z, s(elem!1))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[566, 557])).
% 5.60/5.83 tff(568,plain,
% 5.60/5.83 (~(s(z) = s(elem!1))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[117, 536])).
% 5.60/5.83 tff(569,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 5.60/5.83 tff(570,plain,
% 5.60/5.83 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 5.60/5.83 inference(monotonicity,[status(thm)],[569])).
% 5.60/5.83 tff(571,plain,
% 5.60/5.83 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 5.60/5.83 inference(symmetry,[status(thm)],[570])).
% 5.60/5.83 tff(572,plain,
% 5.60/5.83 (r(z, s(elem!1))),
% 5.60/5.83 inference(modus_ponens,[status(thm)],[184, 571])).
% 5.60/5.83 tff(573,assumption,(~r(z, s(elem!1))), introduced(assumption)).
% 5.60/5.83 tff(574,plain,
% 5.60/5.83 ($false),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[573, 572])).
% 5.60/5.83 tff(575,plain,((~(s(elem!1) = s(s(s(elem!1))))) | r(z, s(elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.83 tff(576,plain,
% 5.60/5.83 (~(s(elem!1) = s(s(s(elem!1))))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[575, 557, 184])).
% 5.60/5.83 tff(577,plain,
% 5.60/5.83 (((~![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)))))),
% 5.60/5.83 inference(rewrite,[status(thm)],[])).
% 5.60/5.83 tff(578,plain,
% 5.60/5.83 ((~![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)))))),
% 5.60/5.83 inference(quant_inst,[status(thm)],[])).
% 5.60/5.83 tff(579,plain,
% 5.60/5.83 ((~![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))))),
% 5.60/5.83 inference(modus_ponens,[status(thm)],[578, 577])).
% 5.60/5.83 tff(580,plain,
% 5.60/5.83 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[579, 42, 487])).
% 5.60/5.83 tff(581,plain,
% 5.60/5.83 (r(s(elem!1), s(s(s(elem!1))))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[580, 576])).
% 5.60/5.83 tff(582,plain,
% 5.60/5.83 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.60/5.83 inference(commutativity,[status(thm)],[])).
% 5.60/5.83 tff(583,plain,
% 5.60/5.83 ((~(s(elem!1) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 5.60/5.83 inference(monotonicity,[status(thm)],[582])).
% 5.60/5.83 tff(584,plain,
% 5.60/5.83 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.60/5.83 inference(modus_ponens,[status(thm)],[576, 583])).
% 5.60/5.83 tff(585,plain,
% 5.60/5.83 (((~![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)))),
% 5.60/5.83 inference(rewrite,[status(thm)],[])).
% 5.60/5.83 tff(586,plain,
% 5.60/5.83 ((~![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)))),
% 5.60/5.83 inference(quant_inst,[status(thm)],[])).
% 5.60/5.83 tff(587,plain,
% 5.60/5.83 ((~![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))),
% 5.60/5.83 inference(modus_ponens,[status(thm)],[586, 585])).
% 5.60/5.83 tff(588,plain,
% 5.60/5.83 ((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))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[587, 42])).
% 5.60/5.83 tff(589,plain,
% 5.60/5.83 (r(s(s(s(elem!1))), s(elem!1))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[588, 584, 486])).
% 5.60/5.83 tff(590,assumption,(b(s(z), z)), introduced(assumption)).
% 5.60/5.83 tff(591,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 5.60/5.83 tff(592,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 5.60/5.83 tff(593,plain,
% 5.60/5.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))))),
% 5.60/5.83 inference(rewrite,[status(thm)],[])).
% 5.60/5.83 tff(594,plain,
% 5.60/5.83 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))))),
% 5.60/5.83 inference(rewrite,[status(thm)],[])).
% 5.60/5.83 tff(595,plain,
% 5.60/5.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1)))))),
% 5.60/5.83 inference(monotonicity,[status(thm)],[594])).
% 5.60/5.83 tff(596,plain,
% 5.60/5.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))))),
% 5.60/5.83 inference(transitivity,[status(thm)],[595, 593])).
% 5.60/5.83 tff(597,plain,
% 5.60/5.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 5.60/5.83 inference(quant_inst,[status(thm)],[])).
% 5.60/5.83 tff(598,plain,
% 5.60/5.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1)))),
% 5.60/5.83 inference(modus_ponens,[status(thm)],[597, 596])).
% 5.60/5.83 tff(599,plain,
% 5.60/5.83 (~b(s(z), s(elem!1))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[598, 391, 592, 591, 590])).
% 5.60/5.83 tff(600,plain,
% 5.60/5.83 (((~![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)))),
% 5.60/5.83 inference(rewrite,[status(thm)],[])).
% 5.60/5.83 tff(601,plain,
% 5.60/5.83 ((~![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)))),
% 5.60/5.83 inference(quant_inst,[status(thm)],[])).
% 5.60/5.83 tff(602,plain,
% 5.60/5.83 ((~![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))),
% 5.60/5.83 inference(modus_ponens,[status(thm)],[601, 600])).
% 5.60/5.83 tff(603,plain,
% 5.60/5.83 (r(s(z), s(elem!1))),
% 5.60/5.83 inference(unit_resolution,[status(thm)],[602, 42, 121, 599])).
% 5.60/5.83 tff(604,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 5.60/5.83 tff(605,plain,
% 5.60/5.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.83 inference(rewrite,[status(thm)],[])).
% 5.60/5.83 tff(606,plain,
% 5.60/5.83 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.84 inference(rewrite,[status(thm)],[])).
% 5.60/5.84 tff(607,plain,
% 5.60/5.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 5.60/5.84 inference(monotonicity,[status(thm)],[606])).
% 5.60/5.84 tff(608,plain,
% 5.60/5.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.84 inference(transitivity,[status(thm)],[607, 605])).
% 5.60/5.84 tff(609,plain,
% 5.60/5.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.84 inference(quant_inst,[status(thm)],[])).
% 5.60/5.84 tff(610,plain,
% 5.60/5.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 5.60/5.84 inference(modus_ponens,[status(thm)],[609, 608])).
% 5.60/5.84 tff(611,plain,
% 5.60/5.84 (~b(s(z), s(s(s(elem!1))))),
% 5.60/5.84 inference(unit_resolution,[status(thm)],[610, 391, 380, 592, 591, 590])).
% 5.60/5.84 tff(612,plain,
% 5.60/5.84 (r(s(z), s(s(s(elem!1))))),
% 5.60/5.84 inference(unit_resolution,[status(thm)],[247, 611])).
% 5.60/5.84 tff(613,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 5.60/5.84 tff(614,plain,
% 5.60/5.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 5.60/5.84 inference(rewrite,[status(thm)],[])).
% 5.60/5.84 tff(615,plain,
% 5.60/5.84 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 5.60/5.84 inference(rewrite,[status(thm)],[])).
% 5.60/5.84 tff(616,plain,
% 5.60/5.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 5.60/5.84 inference(monotonicity,[status(thm)],[615])).
% 5.60/5.84 tff(617,plain,
% 5.60/5.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 5.60/5.84 inference(transitivity,[status(thm)],[616, 614])).
% 5.60/5.84 tff(618,plain,
% 5.60/5.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))),
% 5.60/5.84 inference(quant_inst,[status(thm)],[])).
% 5.60/5.84 tff(619,plain,
% 5.60/5.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 5.60/5.84 inference(modus_ponens,[status(thm)],[618, 617])).
% 5.60/5.84 tff(620,plain,
% 5.60/5.84 ($false),
% 5.60/5.84 inference(unit_resolution,[status(thm)],[619, 194, 613, 612, 604, 603])).
% 5.60/5.84 tff(621,plain,((~b(s(z), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.84 tff(622,plain,
% 5.60/5.84 (~b(s(z), z)),
% 5.60/5.84 inference(unit_resolution,[status(thm)],[621, 589, 581, 568, 567, 550, 378])).
% 5.60/5.84 tff(623,plain,
% 5.60/5.84 (r(s(z), z)),
% 5.60/5.84 inference(unit_resolution,[status(thm)],[180, 622])).
% 5.60/5.84 tff(624,plain,
% 5.60/5.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 5.60/5.84 inference(rewrite,[status(thm)],[])).
% 5.60/5.84 tff(625,plain,
% 5.60/5.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 5.60/5.84 inference(quant_inst,[status(thm)],[])).
% 5.60/5.84 tff(626,plain,
% 5.60/5.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 5.60/5.84 inference(modus_ponens,[status(thm)],[625, 624])).
% 5.60/5.84 tff(627,plain,
% 5.60/5.84 ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 5.60/5.84 inference(unit_resolution,[status(thm)],[626, 194])).
% 5.60/5.84 tff(628,plain,
% 5.60/5.84 (~r(s(z), elem!1)),
% 5.60/5.84 inference(unit_resolution,[status(thm)],[627, 623, 527, 537])).
% 5.60/5.84 tff(629,plain,
% 5.60/5.84 (((~![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))),
% 5.60/5.84 inference(rewrite,[status(thm)],[])).
% 5.60/5.84 tff(630,plain,
% 5.60/5.84 ((~![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))),
% 5.60/5.84 inference(quant_inst,[status(thm)],[])).
% 5.60/5.84 tff(631,plain,
% 5.60/5.84 ((~![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)),
% 5.60/5.84 inference(modus_ponens,[status(thm)],[630, 629])).
% 5.60/5.84 tff(632,plain,
% 5.60/5.84 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 5.60/5.84 inference(unit_resolution,[status(thm)],[631, 42])).
% 5.60/5.84 tff(633,plain,
% 5.60/5.84 (b(s(z), elem!1)),
% 5.60/5.84 inference(unit_resolution,[status(thm)],[632, 628, 150])).
% 5.60/5.84 tff(634,plain,
% 5.60/5.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.60/5.84 inference(rewrite,[status(thm)],[])).
% 5.60/5.84 tff(635,plain,
% 5.60/5.84 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.60/5.84 inference(rewrite,[status(thm)],[])).
% 5.60/5.84 tff(636,plain,
% 5.60/5.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 5.60/5.85 inference(monotonicity,[status(thm)],[635])).
% 5.60/5.85 tff(637,plain,
% 5.60/5.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.60/5.85 inference(transitivity,[status(thm)],[636, 634])).
% 5.60/5.85 tff(638,plain,
% 5.60/5.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 5.60/5.85 inference(quant_inst,[status(thm)],[])).
% 5.60/5.85 tff(639,plain,
% 5.60/5.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 5.60/5.85 inference(modus_ponens,[status(thm)],[638, 637])).
% 5.60/5.85 tff(640,plain,
% 5.60/5.85 ($false),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[639, 194, 613, 184, 232, 182])).
% 5.60/5.85 tff(641,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.85 tff(642,plain,
% 5.60/5.85 (~r(s(z), s(s(s(elem!1))))),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[641, 589, 184, 623])).
% 5.60/5.85 tff(643,plain,
% 5.60/5.85 (b(s(z), s(s(s(elem!1))))),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[247, 642])).
% 5.60/5.85 tff(644,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 5.60/5.85 tff(645,plain,
% 5.60/5.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.85 inference(rewrite,[status(thm)],[])).
% 5.60/5.85 tff(646,plain,
% 5.60/5.85 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.85 inference(rewrite,[status(thm)],[])).
% 5.60/5.85 tff(647,plain,
% 5.60/5.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 5.60/5.85 inference(monotonicity,[status(thm)],[646])).
% 5.60/5.85 tff(648,plain,
% 5.60/5.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.85 inference(transitivity,[status(thm)],[647, 645])).
% 5.60/5.85 tff(649,plain,
% 5.60/5.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 5.60/5.85 inference(quant_inst,[status(thm)],[])).
% 5.60/5.85 tff(650,plain,
% 5.60/5.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 5.60/5.85 inference(modus_ponens,[status(thm)],[649, 648])).
% 5.60/5.85 tff(651,plain,
% 5.60/5.85 ($false),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[650, 391, 380, 448, 592, 644, 379])).
% 5.60/5.85 tff(652,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.85 tff(653,plain,
% 5.60/5.85 (~b(elem!1, s(s(s(elem!1))))),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[652, 643, 378, 567, 633])).
% 5.60/5.85 tff(654,plain,
% 5.60/5.85 (r(elem!1, s(s(s(elem!1))))),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[424, 653, 535])).
% 5.60/5.85 tff(655,plain,
% 5.60/5.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 5.60/5.85 inference(rewrite,[status(thm)],[])).
% 5.60/5.85 tff(656,plain,
% 5.60/5.85 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 5.60/5.85 inference(rewrite,[status(thm)],[])).
% 5.60/5.85 tff(657,plain,
% 5.60/5.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 5.60/5.85 inference(monotonicity,[status(thm)],[656])).
% 5.60/5.85 tff(658,plain,
% 5.60/5.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 5.60/5.85 inference(transitivity,[status(thm)],[657, 655])).
% 5.60/5.85 tff(659,plain,
% 5.60/5.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 5.60/5.85 inference(quant_inst,[status(thm)],[])).
% 5.60/5.85 tff(660,plain,
% 5.60/5.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 5.60/5.85 inference(modus_ponens,[status(thm)],[659, 658])).
% 5.60/5.85 tff(661,plain,
% 5.60/5.85 ($false),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[660, 194, 527, 589, 184, 654])).
% 5.60/5.85 tff(662,plain,((~r(z, s(s(s(elem!1))))) | (s(z) = elem!1) | b(s(s(s(elem!1))), s(elem!1)) | b(s(elem!1), s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | b(z, elem!1) | r(s(s(s(elem!1))), z) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.60/5.85 tff(663,plain,
% 5.60/5.85 (b(elem!1, z)),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[662, 483, 89, 184, 478, 473, 329, 464])).
% 5.60/5.85 tff(664,assumption,(b(z, s(z))), introduced(assumption)).
% 5.60/5.85 tff(665,assumption,(b(elem!1, z)), introduced(assumption)).
% 5.60/5.85 tff(666,plain,
% 5.60/5.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.85 inference(rewrite,[status(thm)],[])).
% 5.60/5.85 tff(667,plain,
% 5.60/5.85 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.85 inference(rewrite,[status(thm)],[])).
% 5.60/5.85 tff(668,plain,
% 5.60/5.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 5.60/5.85 inference(monotonicity,[status(thm)],[667])).
% 5.60/5.85 tff(669,plain,
% 5.60/5.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.85 inference(transitivity,[status(thm)],[668, 666])).
% 5.60/5.85 tff(670,plain,
% 5.60/5.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 5.60/5.85 inference(quant_inst,[status(thm)],[])).
% 5.60/5.85 tff(671,plain,
% 5.60/5.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 5.60/5.85 inference(modus_ponens,[status(thm)],[670, 669])).
% 5.60/5.85 tff(672,plain,
% 5.60/5.85 ($false),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[671, 391, 665, 380, 448, 379, 664])).
% 5.60/5.85 tff(673,plain,((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.85 tff(674,plain,
% 5.60/5.85 (~b(z, s(z))),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[673, 663, 379, 378, 448])).
% 5.60/5.85 tff(675,assumption,(~b(z, s(z))), introduced(assumption)).
% 5.60/5.85 tff(676,assumption,(~r(z, s(z))), introduced(assumption)).
% 5.60/5.85 tff(677,plain,
% 5.60/5.85 ($false),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[45, 42, 676, 675, 28])).
% 5.60/5.85 tff(678,plain,(r(z, s(z)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.85 tff(679,plain,
% 5.60/5.85 (r(z, s(z))),
% 5.60/5.85 inference(unit_resolution,[status(thm)],[678, 674])).
% 5.60/5.85 tff(680,plain,
% 5.60/5.85 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 5.60/5.85 inference(monotonicity,[status(thm)],[452])).
% 5.60/5.85 tff(681,plain,
% 5.60/5.85 (b(s(z), s(elem!1))),
% 5.60/5.85 inference(modus_ponens,[status(thm)],[379, 680])).
% 5.60/5.85 tff(682,plain,
% 5.60/5.85 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 5.60/5.85 inference(monotonicity,[status(thm)],[452])).
% 5.60/5.85 tff(683,plain,
% 5.60/5.85 (b(s(elem!1), z)),
% 5.60/5.85 inference(modus_ponens,[status(thm)],[378, 682])).
% 5.60/5.85 tff(684,plain,
% 5.60/5.85 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 5.60/5.85 inference(quant_inst,[status(thm)],[])).
% 5.60/5.86 tff(685,plain,
% 5.60/5.86 (inj_0(s(s(s(z)))) = s(s(z))),
% 5.60/5.86 inference(unit_resolution,[status(thm)],[684, 106])).
% 5.60/5.86 tff(686,plain,
% 5.60/5.86 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 5.60/5.86 inference(monotonicity,[status(thm)],[465])).
% 5.60/5.86 tff(687,plain,
% 5.60/5.86 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 5.60/5.86 inference(symmetry,[status(thm)],[686])).
% 5.60/5.86 tff(688,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 5.60/5.86 tff(689,plain,
% 5.60/5.86 (s(s(s(s(z)))) = s(s(elem!1))),
% 5.60/5.86 inference(transitivity,[status(thm)],[688, 261, 687, 211])).
% 5.60/5.86 tff(690,plain,
% 5.60/5.86 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 5.60/5.86 inference(monotonicity,[status(thm)],[689])).
% 5.60/5.86 tff(691,plain,
% 5.60/5.86 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 5.60/5.86 inference(quant_inst,[status(thm)],[])).
% 5.60/5.86 tff(692,plain,
% 5.60/5.86 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 5.60/5.86 inference(unit_resolution,[status(thm)],[691, 106])).
% 5.60/5.86 tff(693,plain,
% 5.60/5.86 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 5.60/5.86 inference(symmetry,[status(thm)],[692])).
% 5.60/5.86 tff(694,plain,
% 5.60/5.86 (s(s(s(z))) = s(elem!1)),
% 5.60/5.86 inference(transitivity,[status(thm)],[693, 690, 259])).
% 5.60/5.86 tff(695,plain,
% 5.60/5.86 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 5.60/5.86 inference(monotonicity,[status(thm)],[694])).
% 5.60/5.86 tff(696,plain,
% 5.60/5.86 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 5.60/5.86 inference(symmetry,[status(thm)],[695])).
% 5.60/5.86 tff(697,plain,
% 5.60/5.86 (elem!1 = s(s(z))),
% 5.60/5.86 inference(transitivity,[status(thm)],[261, 696, 685])).
% 5.60/5.86 tff(698,plain,
% 5.60/5.86 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 5.60/5.86 inference(commutativity,[status(thm)],[])).
% 5.60/5.86 tff(699,plain,
% 5.60/5.86 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 5.60/5.86 inference(monotonicity,[status(thm)],[688])).
% 5.60/5.86 tff(700,plain,
% 5.60/5.86 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 5.60/5.86 inference(transitivity,[status(thm)],[699, 698])).
% 5.60/5.86 tff(701,plain,
% 5.60/5.86 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(z))))),
% 5.60/5.86 inference(monotonicity,[status(thm)],[700])).
% 5.60/5.86 tff(702,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 5.60/5.86 tff(703,plain,
% 5.60/5.86 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 5.60/5.86 inference(monotonicity,[status(thm)],[702])).
% 5.60/5.86 tff(704,plain,
% 5.60/5.86 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 5.60/5.86 inference(quant_inst,[status(thm)],[])).
% 5.60/5.86 tff(705,plain,
% 5.60/5.86 (inj_0(s(s(z))) = s(z)),
% 5.60/5.86 inference(unit_resolution,[status(thm)],[704, 106])).
% 5.60/5.86 tff(706,plain,
% 5.60/5.86 (s(z) = inj_0(s(s(z)))),
% 5.60/5.86 inference(symmetry,[status(thm)],[705])).
% 5.60/5.86 tff(707,plain,
% 5.60/5.86 (s(z) = s(s(s(z)))),
% 5.60/5.86 inference(transitivity,[status(thm)],[706, 703, 692])).
% 5.60/5.86 tff(708,plain,
% 5.60/5.86 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 5.60/5.86 inference(monotonicity,[status(thm)],[707])).
% 5.60/5.86 tff(709,plain,
% 5.60/5.86 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 5.60/5.86 inference(symmetry,[status(thm)],[708])).
% 5.60/5.86 tff(710,plain,
% 5.60/5.86 (s(s(z)) = inj_0(s(s(s(z))))),
% 5.60/5.86 inference(symmetry,[status(thm)],[685])).
% 5.60/5.86 tff(711,plain,
% 5.60/5.86 (s(s(s(s(z)))) = s(s(z))),
% 5.60/5.86 inference(symmetry,[status(thm)],[702])).
% 5.60/5.86 tff(712,plain,
% 5.60/5.86 (s(s(s(s(z)))) = z),
% 5.60/5.86 inference(transitivity,[status(thm)],[711, 710, 709, 112])).
% 5.60/5.86 tff(713,plain,
% 5.60/5.86 ($false),
% 5.60/5.86 inference(unit_resolution,[status(thm)],[83, 712])).
% 5.60/5.86 tff(714,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.86 tff(715,plain,
% 5.60/5.86 (~(elem!1 = s(s(z)))),
% 5.60/5.86 inference(modus_ponens,[status(thm)],[714, 701])).
% 5.60/5.86 tff(716,plain,
% 5.60/5.86 ($false),
% 5.60/5.86 inference(unit_resolution,[status(thm)],[715, 697])).
% 5.60/5.86 tff(717,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.86 tff(718,plain,
% 5.60/5.86 (~(s(s(s(s(z)))) = elem!1)),
% 5.60/5.86 inference(unit_resolution,[status(thm)],[717, 452])).
% 5.60/5.86 tff(719,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 5.60/5.86 tff(720,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 5.60/5.86 tff(721,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 5.60/5.86 tff(722,assumption,(r(z, s(z))), introduced(assumption)).
% 5.60/5.86 tff(723,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 5.60/5.86 tff(724,plain,
% 5.60/5.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 5.60/5.86 inference(rewrite,[status(thm)],[])).
% 5.60/5.86 tff(725,plain,
% 5.60/5.86 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 5.60/5.86 inference(rewrite,[status(thm)],[])).
% 5.60/5.86 tff(726,plain,
% 5.60/5.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 5.60/5.86 inference(monotonicity,[status(thm)],[725])).
% 5.60/5.86 tff(727,plain,
% 5.60/5.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 5.60/5.86 inference(transitivity,[status(thm)],[726, 724])).
% 5.60/5.86 tff(728,plain,
% 5.60/5.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 5.60/5.86 inference(quant_inst,[status(thm)],[])).
% 5.60/5.86 tff(729,plain,
% 5.60/5.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 5.60/5.86 inference(modus_ponens,[status(thm)],[728, 727])).
% 5.60/5.86 tff(730,plain,
% 5.60/5.86 ($false),
% 5.60/5.86 inference(unit_resolution,[status(thm)],[729, 194, 722, 182, 723, 719])).
% 5.60/5.86 tff(731,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.86 tff(732,plain,
% 5.60/5.86 (~r(s(s(s(s(z)))), s(z))),
% 5.60/5.86 inference(unit_resolution,[status(thm)],[731, 719, 182, 722])).
% 5.60/5.86 tff(733,plain,
% 5.60/5.86 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 5.60/5.86 inference(commutativity,[status(thm)],[])).
% 5.60/5.86 tff(734,plain,
% 5.60/5.86 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 5.60/5.86 inference(symmetry,[status(thm)],[733])).
% 5.60/5.86 tff(735,plain,
% 5.60/5.86 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 5.60/5.86 inference(monotonicity,[status(thm)],[734])).
% 5.60/5.86 tff(736,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 5.60/5.86 tff(737,plain,
% 5.60/5.86 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 5.60/5.86 inference(monotonicity,[status(thm)],[736])).
% 5.60/5.86 tff(738,plain,
% 5.60/5.86 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 5.60/5.86 inference(symmetry,[status(thm)],[737])).
% 5.60/5.86 tff(739,plain,
% 5.60/5.86 (s(s(s(z))) = z),
% 5.60/5.86 inference(transitivity,[status(thm)],[693, 738, 112])).
% 5.60/5.86 tff(740,plain,
% 5.60/5.86 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 5.60/5.86 inference(quant_inst,[status(thm)],[])).
% 5.60/5.86 tff(741,plain,
% 5.60/5.86 (~(s(s(s(z))) = z)),
% 5.60/5.86 inference(unit_resolution,[status(thm)],[740, 21])).
% 5.60/5.86 tff(742,plain,
% 5.60/5.86 ($false),
% 5.60/5.86 inference(unit_resolution,[status(thm)],[741, 739])).
% 5.60/5.86 tff(743,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.86 tff(744,plain,
% 5.60/5.86 (~(s(s(s(s(z)))) = s(z))),
% 5.60/5.86 inference(modus_ponens,[status(thm)],[743, 735])).
% 5.60/5.86 tff(745,plain,
% 5.60/5.86 (((~![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)))),
% 5.60/5.86 inference(rewrite,[status(thm)],[])).
% 5.60/5.86 tff(746,plain,
% 5.60/5.86 ((~![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)))),
% 5.60/5.86 inference(quant_inst,[status(thm)],[])).
% 5.60/5.86 tff(747,plain,
% 5.60/5.86 ((~![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))),
% 5.60/5.87 inference(modus_ponens,[status(thm)],[746, 745])).
% 5.60/5.87 tff(748,plain,
% 5.60/5.87 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[747, 42])).
% 5.60/5.87 tff(749,plain,
% 5.60/5.87 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[748, 744])).
% 5.60/5.87 tff(750,plain,
% 5.60/5.87 (b(s(s(s(s(z)))), s(z))),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[749, 732])).
% 5.60/5.87 tff(751,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 5.60/5.87 tff(752,plain,
% 5.60/5.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 5.60/5.87 inference(rewrite,[status(thm)],[])).
% 5.60/5.87 tff(753,plain,
% 5.60/5.87 (((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 5.60/5.87 inference(rewrite,[status(thm)],[])).
% 5.60/5.87 tff(754,plain,
% 5.60/5.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 5.60/5.87 inference(monotonicity,[status(thm)],[753])).
% 5.60/5.87 tff(755,plain,
% 5.60/5.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 5.60/5.87 inference(transitivity,[status(thm)],[754, 752])).
% 5.60/5.87 tff(756,plain,
% 5.60/5.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.60/5.87 inference(quant_inst,[status(thm)],[])).
% 5.60/5.87 tff(757,plain,
% 5.60/5.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 5.60/5.87 inference(modus_ponens,[status(thm)],[756, 755])).
% 5.60/5.87 tff(758,plain,
% 5.60/5.87 (~b(s(s(s(s(z)))), elem!1)),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[757, 391, 591, 751, 750, 721])).
% 5.60/5.87 tff(759,plain,
% 5.60/5.87 (((~![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))),
% 5.60/5.87 inference(rewrite,[status(thm)],[])).
% 5.60/5.87 tff(760,plain,
% 5.60/5.87 ((~![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))),
% 5.60/5.87 inference(quant_inst,[status(thm)],[])).
% 5.60/5.87 tff(761,plain,
% 5.60/5.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 5.60/5.87 inference(modus_ponens,[status(thm)],[760, 759])).
% 5.60/5.87 tff(762,plain,
% 5.60/5.87 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[761, 42])).
% 5.60/5.87 tff(763,plain,
% 5.60/5.87 (r(s(s(s(s(z)))), elem!1)),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[762, 758, 720])).
% 5.60/5.87 tff(764,plain,
% 5.60/5.87 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 5.60/5.87 inference(commutativity,[status(thm)],[])).
% 5.60/5.87 tff(765,plain,
% 5.60/5.87 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 5.60/5.87 inference(symmetry,[status(thm)],[764])).
% 5.60/5.87 tff(766,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 5.60/5.87 tff(767,plain,
% 5.60/5.87 (s(s(s(s(z)))) = elem!1),
% 5.60/5.87 inference(modus_ponens,[status(thm)],[766, 765])).
% 5.60/5.87 tff(768,plain,
% 5.60/5.87 ($false),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[720, 767])).
% 5.60/5.87 tff(769,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.60/5.87 tff(770,plain,
% 5.60/5.87 (~(elem!1 = s(s(s(s(z)))))),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[769, 720])).
% 5.60/5.87 tff(771,plain,
% 5.60/5.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 5.60/5.87 inference(rewrite,[status(thm)],[])).
% 5.60/5.87 tff(772,plain,
% 5.60/5.87 (((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 5.60/5.87 inference(rewrite,[status(thm)],[])).
% 5.60/5.87 tff(773,plain,
% 5.60/5.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 5.60/5.87 inference(monotonicity,[status(thm)],[772])).
% 5.60/5.87 tff(774,plain,
% 5.60/5.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 5.60/5.87 inference(transitivity,[status(thm)],[773, 771])).
% 5.60/5.87 tff(775,plain,
% 5.60/5.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 5.60/5.87 inference(quant_inst,[status(thm)],[])).
% 5.60/5.87 tff(776,plain,
% 5.60/5.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 5.60/5.87 inference(modus_ponens,[status(thm)],[775, 774])).
% 5.60/5.87 tff(777,plain,
% 5.60/5.87 (~b(elem!1, s(s(s(s(z)))))),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[776, 391, 591, 751, 750, 721])).
% 5.60/5.87 tff(778,plain,
% 5.60/5.87 (((~![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))))))),
% 5.60/5.87 inference(rewrite,[status(thm)],[])).
% 5.60/5.87 tff(779,plain,
% 5.60/5.87 ((~![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))))))),
% 5.60/5.87 inference(quant_inst,[status(thm)],[])).
% 5.60/5.87 tff(780,plain,
% 5.60/5.87 ((~![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)))))),
% 5.60/5.87 inference(modus_ponens,[status(thm)],[779, 778])).
% 5.60/5.87 tff(781,plain,
% 5.60/5.87 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[780, 42])).
% 5.60/5.87 tff(782,plain,
% 5.60/5.87 (r(elem!1, s(s(s(s(z)))))),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[781, 777, 770])).
% 5.60/5.87 tff(783,plain,
% 5.60/5.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.60/5.87 inference(rewrite,[status(thm)],[])).
% 5.60/5.87 tff(784,plain,
% 5.60/5.87 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.60/5.87 inference(rewrite,[status(thm)],[])).
% 5.60/5.87 tff(785,plain,
% 5.60/5.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 5.60/5.87 inference(monotonicity,[status(thm)],[784])).
% 5.60/5.87 tff(786,plain,
% 5.60/5.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.60/5.87 inference(transitivity,[status(thm)],[785, 783])).
% 5.60/5.87 tff(787,plain,
% 5.60/5.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 5.60/5.87 inference(quant_inst,[status(thm)],[])).
% 5.60/5.87 tff(788,plain,
% 5.60/5.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 5.60/5.87 inference(modus_ponens,[status(thm)],[787, 786])).
% 5.60/5.87 tff(789,plain,
% 5.60/5.87 ($false),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[788, 194, 411, 782, 763, 719])).
% 5.60/5.87 tff(790,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.87 tff(791,plain,
% 5.60/5.87 (~r(z, s(s(s(s(z)))))),
% 5.60/5.87 inference(unit_resolution,[status(thm)],[790, 718, 409, 683, 681, 447, 182, 679])).
% 5.60/5.87 tff(792,plain,
% 5.60/5.87 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 5.60/5.87 inference(commutativity,[status(thm)],[])).
% 5.60/5.87 tff(793,plain,
% 5.60/5.87 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 5.60/5.87 inference(symmetry,[status(thm)],[792])).
% 5.60/5.87 tff(794,plain,
% 5.60/5.87 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 5.60/5.87 inference(monotonicity,[status(thm)],[793])).
% 5.60/5.87 tff(795,plain,
% 5.60/5.87 (~(z = s(s(s(s(z)))))),
% 5.60/5.87 inference(modus_ponens,[status(thm)],[83, 794])).
% 5.60/5.87 tff(796,plain,
% 5.60/5.87 (((~![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))))))),
% 5.60/5.88 inference(rewrite,[status(thm)],[])).
% 5.60/5.88 tff(797,plain,
% 5.60/5.88 ((~![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))))))),
% 5.60/5.88 inference(quant_inst,[status(thm)],[])).
% 5.60/5.88 tff(798,plain,
% 5.60/5.88 ((~![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)))))),
% 5.60/5.88 inference(modus_ponens,[status(thm)],[797, 796])).
% 5.60/5.88 tff(799,plain,
% 5.60/5.88 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 5.60/5.88 inference(unit_resolution,[status(thm)],[798, 42])).
% 5.60/5.88 tff(800,plain,
% 5.60/5.88 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 5.60/5.88 inference(unit_resolution,[status(thm)],[799, 795])).
% 5.60/5.88 tff(801,plain,
% 5.60/5.88 (b(z, s(s(s(s(z)))))),
% 5.60/5.88 inference(unit_resolution,[status(thm)],[800, 791])).
% 5.60/5.88 tff(802,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 5.60/5.88 tff(803,plain,
% 5.60/5.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 5.60/5.88 inference(rewrite,[status(thm)],[])).
% 5.60/5.88 tff(804,plain,
% 5.60/5.88 (((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 5.60/5.88 inference(rewrite,[status(thm)],[])).
% 5.60/5.88 tff(805,plain,
% 5.60/5.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z))))))))),
% 5.60/5.88 inference(monotonicity,[status(thm)],[804])).
% 5.60/5.88 tff(806,plain,
% 5.60/5.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 5.60/5.88 inference(transitivity,[status(thm)],[805, 803])).
% 5.60/5.88 tff(807,plain,
% 5.60/5.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 5.60/5.88 inference(quant_inst,[status(thm)],[])).
% 5.60/5.88 tff(808,plain,
% 5.60/5.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z))))))),
% 5.60/5.88 inference(modus_ponens,[status(thm)],[807, 806])).
% 5.60/5.88 tff(809,plain,
% 5.60/5.88 ($false),
% 5.60/5.88 inference(unit_resolution,[status(thm)],[808, 391, 683, 802, 681, 801, 447])).
% 5.60/5.88 tff(810,plain,((~(s(s(elem!1)) = elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | b(z, elem!1) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), z) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.88 tff(811,plain,
% 5.60/5.88 (~(s(s(elem!1)) = elem!1)),
% 5.60/5.88 inference(unit_resolution,[status(thm)],[810, 444, 182, 379, 425, 89, 184, 329, 381, 233])).
% 5.60/5.88 tff(812,assumption,(s(z) = elem!1), introduced(assumption)).
% 5.60/5.88 tff(813,plain,
% 5.60/5.88 (r(z, s(z)) <=> r(z, elem!1)),
% 5.60/5.88 inference(monotonicity,[status(thm)],[812])).
% 5.60/5.88 tff(814,plain,
% 5.60/5.88 (r(z, elem!1) <=> r(z, s(z))),
% 5.60/5.88 inference(symmetry,[status(thm)],[813])).
% 5.60/5.88 tff(815,plain,
% 5.60/5.88 (r(z, s(z))),
% 5.60/5.88 inference(modus_ponens,[status(thm)],[411, 814])).
% 5.60/5.88 tff(816,plain,
% 5.60/5.88 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 5.60/5.88 inference(monotonicity,[status(thm)],[812])).
% 5.60/5.88 tff(817,plain,
% 5.60/5.88 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 5.60/5.88 inference(symmetry,[status(thm)],[816])).
% 5.60/5.88 tff(818,plain,
% 5.60/5.88 (s(s(z)) = s(elem!1)),
% 5.60/5.88 inference(monotonicity,[status(thm)],[812])).
% 5.60/5.88 tff(819,plain,
% 5.60/5.88 (s(s(s(z))) = s(s(elem!1))),
% 5.60/5.88 inference(monotonicity,[status(thm)],[818])).
% 5.60/5.88 tff(820,plain,
% 5.60/5.88 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 5.60/5.88 inference(monotonicity,[status(thm)],[819])).
% 5.60/5.88 tff(821,plain,
% 5.60/5.88 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 5.60/5.88 inference(monotonicity,[status(thm)],[820])).
% 5.60/5.88 tff(822,plain,
% 5.60/5.88 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 5.60/5.88 inference(symmetry,[status(thm)],[821])).
% 5.60/5.88 tff(823,plain,
% 5.60/5.88 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 5.60/5.88 inference(transitivity,[status(thm)],[822, 817])).
% 5.60/5.88 tff(824,plain,
% 5.60/5.88 (r(s(s(s(s(z)))), s(z))),
% 5.60/5.88 inference(modus_ponens,[status(thm)],[233, 823])).
% 5.60/5.88 tff(825,plain,
% 5.60/5.88 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(elem!1))))),
% 5.60/5.88 inference(monotonicity,[status(thm)],[820])).
% 5.60/5.88 tff(826,plain,
% 5.60/5.88 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 5.60/5.88 inference(symmetry,[status(thm)],[825])).
% 5.60/5.88 tff(827,plain,
% 5.60/5.88 (r(z, s(s(s(s(z)))))),
% 5.60/5.88 inference(modus_ponens,[status(thm)],[184, 826])).
% 5.60/5.88 tff(828,plain,
% 5.60/5.88 ($false),
% 5.60/5.88 inference(unit_resolution,[status(thm)],[731, 827, 824, 182, 815])).
% 5.60/5.88 tff(829,plain,((~(s(z) = elem!1)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.88 tff(830,plain,
% 5.60/5.88 (~(s(z) = elem!1)),
% 5.60/5.88 inference(unit_resolution,[status(thm)],[829, 233, 184, 182, 409])).
% 5.60/5.88 tff(831,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 5.60/5.88 tff(832,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 5.60/5.88 tff(833,plain,
% 5.60/5.88 (((~![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)))),
% 5.60/5.88 inference(rewrite,[status(thm)],[])).
% 5.60/5.88 tff(834,plain,
% 5.60/5.88 ((~![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)))),
% 5.60/5.88 inference(quant_inst,[status(thm)],[])).
% 5.60/5.88 tff(835,plain,
% 5.60/5.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 5.60/5.88 inference(modus_ponens,[status(thm)],[834, 833])).
% 5.60/5.88 tff(836,plain,
% 5.60/5.88 ($false),
% 5.60/5.88 inference(unit_resolution,[status(thm)],[835, 42, 832, 31, 831])).
% 5.60/5.88 tff(837,plain,(r(elem!1, s(z)) | b(elem!1, s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.88 tff(838,plain,
% 5.60/5.88 (r(elem!1, s(z))),
% 5.60/5.88 inference(unit_resolution,[status(thm)],[837, 173, 31])).
% 5.60/5.88 tff(839,plain,
% 5.60/5.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 5.60/5.88 inference(rewrite,[status(thm)],[])).
% 5.60/5.88 tff(840,plain,
% 5.60/5.88 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 5.60/5.88 inference(rewrite,[status(thm)],[])).
% 5.60/5.88 tff(841,plain,
% 5.60/5.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z)))))),
% 5.60/5.89 inference(monotonicity,[status(thm)],[840])).
% 5.60/5.89 tff(842,plain,
% 5.60/5.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 5.60/5.89 inference(transitivity,[status(thm)],[841, 839])).
% 5.60/5.89 tff(843,plain,
% 5.60/5.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 5.60/5.89 inference(quant_inst,[status(thm)],[])).
% 5.60/5.89 tff(844,plain,
% 5.60/5.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 5.60/5.89 inference(modus_ponens,[status(thm)],[843, 842])).
% 5.60/5.89 tff(845,plain,
% 5.60/5.89 ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[844, 194])).
% 5.60/5.89 tff(846,plain,
% 5.60/5.89 (~r(z, s(z))),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[845, 838, 182, 411])).
% 5.60/5.89 tff(847,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 5.60/5.89 tff(848,plain,
% 5.60/5.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 5.60/5.89 inference(rewrite,[status(thm)],[])).
% 5.60/5.89 tff(849,plain,
% 5.60/5.89 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 5.60/5.89 inference(rewrite,[status(thm)],[])).
% 5.60/5.89 tff(850,plain,
% 5.60/5.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z)))))),
% 5.60/5.89 inference(monotonicity,[status(thm)],[849])).
% 5.60/5.89 tff(851,plain,
% 5.60/5.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 5.60/5.89 inference(transitivity,[status(thm)],[850, 848])).
% 5.60/5.89 tff(852,plain,
% 5.60/5.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 5.60/5.89 inference(quant_inst,[status(thm)],[])).
% 5.60/5.89 tff(853,plain,
% 5.60/5.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 5.60/5.89 inference(modus_ponens,[status(thm)],[852, 851])).
% 5.60/5.89 tff(854,plain,
% 5.60/5.89 ($false),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[853, 194, 530, 326, 847, 182])).
% 5.60/5.89 tff(855,plain,((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.89 tff(856,plain,
% 5.60/5.89 (~r(elem!1, s(z))),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[855, 530, 326, 182])).
% 5.60/5.89 tff(857,plain,
% 5.60/5.89 (b(elem!1, s(z))),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[835, 42, 856, 173])).
% 5.60/5.89 tff(858,plain,
% 5.60/5.89 (~r(s(z), elem!1)),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[627, 530, 182, 411])).
% 5.60/5.89 tff(859,plain,
% 5.60/5.89 (b(s(z), elem!1)),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[632, 858, 150])).
% 5.60/5.89 tff(860,plain,
% 5.60/5.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 5.60/5.89 inference(rewrite,[status(thm)],[])).
% 5.60/5.89 tff(861,plain,
% 5.60/5.89 (((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 5.60/5.89 inference(rewrite,[status(thm)],[])).
% 5.60/5.89 tff(862,plain,
% 5.60/5.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 5.60/5.89 inference(monotonicity,[status(thm)],[861])).
% 5.60/5.89 tff(863,plain,
% 5.60/5.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 5.60/5.89 inference(transitivity,[status(thm)],[862, 860])).
% 5.60/5.89 tff(864,plain,
% 5.60/5.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 5.60/5.89 inference(quant_inst,[status(thm)],[])).
% 5.60/5.89 tff(865,plain,
% 5.60/5.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 5.60/5.89 inference(modus_ponens,[status(thm)],[864, 863])).
% 5.60/5.89 tff(866,plain,
% 5.60/5.89 ($false),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[865, 194, 411, 530, 364, 326])).
% 5.60/5.89 tff(867,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.89 tff(868,plain,
% 5.60/5.89 (~r(s(s(elem!1)), elem!1)),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[867, 530, 326, 411])).
% 5.60/5.89 tff(869,plain,
% 5.60/5.89 (((~![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))),
% 5.60/5.89 inference(rewrite,[status(thm)],[])).
% 5.60/5.89 tff(870,plain,
% 5.60/5.89 ((~![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))),
% 5.60/5.89 inference(quant_inst,[status(thm)],[])).
% 5.60/5.89 tff(871,plain,
% 5.60/5.89 ((~![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)),
% 5.60/5.89 inference(modus_ponens,[status(thm)],[870, 869])).
% 5.60/5.89 tff(872,plain,
% 5.60/5.89 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[871, 42])).
% 5.60/5.89 tff(873,plain,
% 5.60/5.89 (b(s(s(elem!1)), elem!1)),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[872, 868, 249])).
% 5.60/5.89 tff(874,plain,
% 5.60/5.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 5.60/5.89 inference(rewrite,[status(thm)],[])).
% 5.60/5.89 tff(875,plain,
% 5.60/5.89 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 5.60/5.89 inference(rewrite,[status(thm)],[])).
% 5.60/5.89 tff(876,plain,
% 5.60/5.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))))),
% 5.60/5.89 inference(monotonicity,[status(thm)],[875])).
% 5.60/5.89 tff(877,plain,
% 5.60/5.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 5.60/5.89 inference(transitivity,[status(thm)],[876, 874])).
% 5.60/5.89 tff(878,plain,
% 5.60/5.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 5.60/5.89 inference(quant_inst,[status(thm)],[])).
% 5.60/5.89 tff(879,plain,
% 5.60/5.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))),
% 5.60/5.89 inference(modus_ponens,[status(thm)],[878, 877])).
% 5.60/5.89 tff(880,plain,
% 5.60/5.89 ($false),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[879, 391, 381, 873, 859, 857])).
% 5.60/5.89 tff(881,plain,((~r(elem!1, z)) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = elem!1) | (s(z) = elem!1) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.89 tff(882,plain,
% 5.60/5.89 (~r(elem!1, z)),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[881, 150, 411, 249, 326, 381, 182])).
% 5.60/5.89 tff(883,plain,
% 5.60/5.89 (b(elem!1, z)),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[526, 882, 2])).
% 5.60/5.89 tff(884,plain,
% 5.60/5.89 (~b(z, s(z))),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[673, 883, 379, 380, 448])).
% 5.60/5.89 tff(885,plain,
% 5.60/5.89 ($false),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[678, 884, 846])).
% 5.60/5.89 tff(886,plain,((s(z) = elem!1) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, elem!1)) | (elem!1 = z) | b(elem!1, s(z)) | (s(s(elem!1)) = elem!1) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.60/5.89 tff(887,plain,
% 5.60/5.89 (b(elem!1, s(z))),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[886, 830, 378, 425, 182, 409, 407, 379, 811, 326, 381])).
% 5.60/5.89 tff(888,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 5.60/5.89 tff(889,plain,
% 5.60/5.89 (b(s(s(elem!1)), elem!1)),
% 5.60/5.89 inference(unit_resolution,[status(thm)],[872, 811, 888])).
% 5.60/5.89 tff(890,plain,
% 5.60/5.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 5.60/5.89 inference(rewrite,[status(thm)],[])).
% 5.60/5.89 tff(891,plain,
% 5.60/5.89 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 5.70/5.90 inference(rewrite,[status(thm)],[])).
% 5.70/5.90 tff(892,plain,
% 5.70/5.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 5.70/5.90 inference(monotonicity,[status(thm)],[891])).
% 5.70/5.90 tff(893,plain,
% 5.70/5.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 5.70/5.90 inference(transitivity,[status(thm)],[892, 890])).
% 5.70/5.90 tff(894,plain,
% 5.70/5.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 5.70/5.90 inference(quant_inst,[status(thm)],[])).
% 5.70/5.90 tff(895,plain,
% 5.70/5.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 5.70/5.90 inference(modus_ponens,[status(thm)],[894, 893])).
% 5.70/5.90 tff(896,plain,
% 5.70/5.90 ($false),
% 5.70/5.90 inference(unit_resolution,[status(thm)],[895, 391, 381, 378, 889, 379, 887])).
% 5.70/5.90 tff(897,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | r(s(s(elem!1)), elem!1) | b(z, elem!1) | r(s(s(s(elem!1))), z) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.90 tff(898,plain,
% 5.70/5.90 (~r(s(s(s(elem!1))), elem!1)),
% 5.70/5.90 inference(unit_resolution,[status(thm)],[897, 1, 339, 182, 326, 184, 373, 400, 329, 363])).
% 5.70/5.90 tff(899,plain,
% 5.70/5.90 (b(s(s(s(elem!1))), elem!1)),
% 5.70/5.90 inference(unit_resolution,[status(thm)],[230, 898, 9])).
% 5.70/5.90 tff(900,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 5.70/5.90 tff(901,plain,
% 5.70/5.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.70/5.90 inference(rewrite,[status(thm)],[])).
% 5.70/5.90 tff(902,plain,
% 5.70/5.90 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.70/5.90 inference(rewrite,[status(thm)],[])).
% 5.70/5.90 tff(903,plain,
% 5.70/5.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 5.70/5.90 inference(monotonicity,[status(thm)],[902])).
% 5.70/5.90 tff(904,plain,
% 5.70/5.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.70/5.90 inference(transitivity,[status(thm)],[903, 901])).
% 5.70/5.90 tff(905,plain,
% 5.70/5.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 5.70/5.90 inference(quant_inst,[status(thm)],[])).
% 5.70/5.90 tff(906,plain,
% 5.70/5.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 5.70/5.90 inference(modus_ponens,[status(thm)],[905, 904])).
% 5.70/5.90 tff(907,plain,
% 5.70/5.90 (~b(elem!1, s(z))),
% 5.70/5.90 inference(unit_resolution,[status(thm)],[906, 391, 900, 448, 379])).
% 5.70/5.90 tff(908,plain,
% 5.70/5.90 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 5.70/5.90 inference(symmetry,[status(thm)],[446])).
% 5.70/5.90 tff(909,plain,
% 5.70/5.90 ((~b(elem!1, s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 5.70/5.90 inference(monotonicity,[status(thm)],[908])).
% 5.70/5.90 tff(910,plain,
% 5.70/5.90 (~b(s(s(elem!1)), s(z))),
% 5.70/5.90 inference(modus_ponens,[status(thm)],[31, 909])).
% 5.70/5.90 tff(911,plain,
% 5.70/5.90 ($false),
% 5.70/5.90 inference(unit_resolution,[status(thm)],[381, 910])).
% 5.70/5.90 tff(912,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(s(elem!1)), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.90 tff(913,plain,
% 5.70/5.90 (~(s(s(elem!1)) = elem!1)),
% 5.70/5.90 inference(unit_resolution,[status(thm)],[912, 907, 381])).
% 5.70/5.90 tff(914,plain,
% 5.70/5.90 (b(s(s(elem!1)), elem!1)),
% 5.70/5.90 inference(unit_resolution,[status(thm)],[872, 913, 888])).
% 5.70/5.90 tff(915,plain,
% 5.70/5.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 5.70/5.90 inference(rewrite,[status(thm)],[])).
% 5.70/5.90 tff(916,plain,
% 5.70/5.90 (((~b(s(s(s(elem!1))), elem!1)) | (~b(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)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 5.70/5.90 inference(rewrite,[status(thm)],[])).
% 5.70/5.90 tff(917,plain,
% 5.70/5.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))))),
% 5.70/5.90 inference(monotonicity,[status(thm)],[916])).
% 5.70/5.90 tff(918,plain,
% 5.70/5.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 5.70/5.91 inference(transitivity,[status(thm)],[917, 915])).
% 5.70/5.91 tff(919,plain,
% 5.70/5.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(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))))))),
% 5.70/5.91 inference(quant_inst,[status(thm)],[])).
% 5.70/5.91 tff(920,plain,
% 5.70/5.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[919, 918])).
% 5.70/5.91 tff(921,plain,
% 5.70/5.91 ($false),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[920, 391, 900, 914, 448, 328])).
% 5.70/5.91 tff(922,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | r(s(s(elem!1)), elem!1) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.91 tff(923,plain,
% 5.70/5.91 (~b(elem!1, s(s(s(elem!1))))),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[922, 899, 328, 373, 363, 339])).
% 5.70/5.91 tff(924,plain,
% 5.70/5.91 (r(elem!1, s(s(s(elem!1))))),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[424, 923, 1])).
% 5.70/5.91 tff(925,assumption,(s(s(s(s(elem!1)))) = s(elem!1)), introduced(assumption)).
% 5.70/5.91 tff(926,plain,
% 5.70/5.91 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[925])).
% 5.70/5.91 tff(927,plain,
% 5.70/5.91 (s(s(s(elem!1))) = elem!1),
% 5.70/5.91 inference(transitivity,[status(thm)],[295, 926, 108])).
% 5.70/5.91 tff(928,plain,
% 5.70/5.91 ($false),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[127, 927])).
% 5.70/5.91 tff(929,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.70/5.91 tff(930,plain,
% 5.70/5.91 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[929, 9])).
% 5.70/5.91 tff(931,plain,
% 5.70/5.91 (s(z) = s(elem!1)),
% 5.70/5.91 inference(monotonicity,[status(thm)],[94])).
% 5.70/5.91 tff(932,plain,
% 5.70/5.91 (s(s(z)) = s(s(elem!1))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[931])).
% 5.70/5.91 tff(933,plain,
% 5.70/5.91 (s(s(s(z))) = s(s(s(elem!1)))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[932])).
% 5.70/5.91 tff(934,plain,
% 5.70/5.91 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[933])).
% 5.70/5.91 tff(935,plain,
% 5.70/5.91 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 5.70/5.91 inference(symmetry,[status(thm)],[934])).
% 5.70/5.91 tff(936,plain,
% 5.70/5.91 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[935])).
% 5.70/5.91 tff(937,plain,
% 5.70/5.91 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[935])).
% 5.70/5.91 tff(938,plain,
% 5.70/5.91 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 5.70/5.91 inference(symmetry,[status(thm)],[937])).
% 5.70/5.91 tff(939,plain,
% 5.70/5.91 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[938])).
% 5.70/5.91 tff(940,plain,
% 5.70/5.91 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 5.70/5.91 inference(commutativity,[status(thm)],[])).
% 5.70/5.91 tff(941,plain,
% 5.70/5.91 (s(s(elem!1)) = s(s(z))),
% 5.70/5.91 inference(symmetry,[status(thm)],[932])).
% 5.70/5.91 tff(942,plain,
% 5.70/5.91 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[941])).
% 5.70/5.91 tff(943,plain,
% 5.70/5.91 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 5.70/5.91 inference(transitivity,[status(thm)],[942, 940])).
% 5.70/5.91 tff(944,plain,
% 5.70/5.91 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 5.70/5.91 inference(symmetry,[status(thm)],[943])).
% 5.70/5.91 tff(945,plain,
% 5.70/5.91 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[944])).
% 5.70/5.91 tff(946,plain,
% 5.70/5.91 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[714, 945])).
% 5.70/5.91 tff(947,plain,
% 5.70/5.91 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[946, 939])).
% 5.70/5.91 tff(948,plain,
% 5.70/5.91 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[94])).
% 5.70/5.91 tff(949,plain,
% 5.70/5.91 (r(elem!1, s(s(elem!1)))),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[326, 948])).
% 5.70/5.91 tff(950,plain,
% 5.70/5.91 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 5.70/5.91 inference(commutativity,[status(thm)],[])).
% 5.70/5.91 tff(951,plain,
% 5.70/5.91 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 5.70/5.91 inference(monotonicity,[status(thm)],[94])).
% 5.70/5.91 tff(952,plain,
% 5.70/5.91 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 5.70/5.91 inference(transitivity,[status(thm)],[951, 950])).
% 5.70/5.91 tff(953,plain,
% 5.70/5.91 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[952])).
% 5.70/5.91 tff(954,plain,
% 5.70/5.91 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 5.70/5.91 inference(quant_inst,[status(thm)],[])).
% 5.70/5.91 tff(955,plain,
% 5.70/5.91 (~(s(s(s(s(elem!1)))) = z)),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[954, 21])).
% 5.70/5.91 tff(956,plain,
% 5.70/5.91 (~(elem!1 = s(s(s(s(elem!1)))))),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[955, 953])).
% 5.70/5.91 tff(957,assumption,(~(s(s(s(s(elem!1)))) = s(elem!1))), introduced(assumption)).
% 5.70/5.91 tff(958,plain,
% 5.70/5.91 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 5.70/5.91 inference(monotonicity,[status(thm)],[931])).
% 5.70/5.91 tff(959,plain,
% 5.70/5.91 (r(s(z), z) <=> r(s(z), elem!1)),
% 5.70/5.91 inference(monotonicity,[status(thm)],[94])).
% 5.70/5.91 tff(960,plain,
% 5.70/5.91 (r(s(z), elem!1)),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[182, 959])).
% 5.70/5.91 tff(961,plain,
% 5.70/5.91 (r(s(elem!1), elem!1)),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[960, 958])).
% 5.70/5.91 tff(962,plain,
% 5.70/5.91 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[94])).
% 5.70/5.91 tff(963,plain,
% 5.70/5.91 (r(elem!1, s(s(s(elem!1))))),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[184, 962])).
% 5.70/5.91 tff(964,plain,
% 5.70/5.91 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 5.70/5.91 inference(symmetry,[status(thm)],[950])).
% 5.70/5.91 tff(965,plain,
% 5.70/5.91 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 5.70/5.91 inference(transitivity,[status(thm)],[952, 964])).
% 5.70/5.91 tff(966,plain,
% 5.70/5.91 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[965])).
% 5.70/5.91 tff(967,plain,
% 5.70/5.91 (~(s(s(s(s(elem!1)))) = elem!1)),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[955, 966])).
% 5.70/5.91 tff(968,plain,
% 5.70/5.91 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 5.70/5.91 inference(monotonicity,[status(thm)],[94])).
% 5.70/5.91 tff(969,plain,
% 5.70/5.91 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[968])).
% 5.70/5.91 tff(970,plain,
% 5.70/5.91 (~(s(s(elem!1)) = elem!1)),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[215, 969])).
% 5.70/5.91 tff(971,plain,
% 5.70/5.91 (b(s(s(elem!1)), elem!1)),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[872, 970, 373])).
% 5.70/5.91 tff(972,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 5.70/5.91 tff(973,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 5.70/5.91 tff(974,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 5.70/5.91 tff(975,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 5.70/5.91 tff(976,plain,
% 5.70/5.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 5.70/5.91 inference(rewrite,[status(thm)],[])).
% 5.70/5.91 tff(977,plain,
% 5.70/5.91 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(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)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 5.70/5.91 inference(rewrite,[status(thm)],[])).
% 5.70/5.91 tff(978,plain,
% 5.70/5.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 5.70/5.91 inference(monotonicity,[status(thm)],[977])).
% 5.70/5.91 tff(979,plain,
% 5.70/5.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 5.70/5.91 inference(transitivity,[status(thm)],[978, 976])).
% 5.70/5.91 tff(980,plain,
% 5.70/5.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(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))))))),
% 5.70/5.91 inference(quant_inst,[status(thm)],[])).
% 5.70/5.91 tff(981,plain,
% 5.70/5.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[980, 979])).
% 5.70/5.91 tff(982,plain,
% 5.70/5.91 ($false),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[981, 391, 900, 973, 974, 328, 975])).
% 5.70/5.91 tff(983,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.91 tff(984,plain,
% 5.70/5.91 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[983, 974, 973, 900, 328])).
% 5.70/5.91 tff(985,plain,
% 5.70/5.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 5.70/5.91 inference(rewrite,[status(thm)],[])).
% 5.70/5.91 tff(986,plain,
% 5.70/5.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 5.70/5.91 inference(quant_inst,[status(thm)],[])).
% 5.70/5.91 tff(987,plain,
% 5.70/5.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 5.70/5.91 inference(modus_ponens,[status(thm)],[986, 985])).
% 5.70/5.91 tff(988,plain,
% 5.70/5.91 ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[987, 42])).
% 5.70/5.91 tff(989,plain,
% 5.70/5.91 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 5.70/5.91 inference(unit_resolution,[status(thm)],[988, 984, 957])).
% 5.70/5.91 tff(990,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 5.70/5.91 tff(991,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 5.70/5.91 tff(992,plain,
% 5.70/5.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.92 inference(rewrite,[status(thm)],[])).
% 5.70/5.92 tff(993,plain,
% 5.70/5.92 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.92 inference(rewrite,[status(thm)],[])).
% 5.70/5.92 tff(994,plain,
% 5.70/5.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 5.70/5.92 inference(monotonicity,[status(thm)],[993])).
% 5.70/5.92 tff(995,plain,
% 5.70/5.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.92 inference(transitivity,[status(thm)],[994, 992])).
% 5.70/5.92 tff(996,plain,
% 5.70/5.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.92 inference(quant_inst,[status(thm)],[])).
% 5.70/5.92 tff(997,plain,
% 5.70/5.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 5.70/5.92 inference(modus_ponens,[status(thm)],[996, 995])).
% 5.70/5.92 tff(998,plain,
% 5.70/5.92 ($false),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[997, 194, 485, 410, 991, 990])).
% 5.70/5.92 tff(999,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.92 tff(1000,plain,
% 5.70/5.92 (~r(s(s(s(s(elem!1)))), elem!1)),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[999, 989, 410, 485])).
% 5.70/5.92 tff(1001,plain,
% 5.70/5.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 5.70/5.92 inference(rewrite,[status(thm)],[])).
% 5.70/5.92 tff(1002,plain,
% 5.70/5.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 5.70/5.92 inference(quant_inst,[status(thm)],[])).
% 5.70/5.92 tff(1003,plain,
% 5.70/5.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 5.70/5.92 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 5.70/5.92 tff(1004,plain,
% 5.70/5.92 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[1003, 42])).
% 5.70/5.92 tff(1005,plain,
% 5.70/5.92 (b(s(s(s(s(elem!1)))), elem!1)),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[1004, 1000, 972])).
% 5.70/5.92 tff(1006,plain,
% 5.70/5.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 5.70/5.92 inference(rewrite,[status(thm)],[])).
% 5.70/5.92 tff(1007,plain,
% 5.70/5.92 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 5.70/5.92 inference(rewrite,[status(thm)],[])).
% 5.70/5.92 tff(1008,plain,
% 5.70/5.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 5.70/5.92 inference(monotonicity,[status(thm)],[1007])).
% 5.70/5.92 tff(1009,plain,
% 5.70/5.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 5.70/5.92 inference(transitivity,[status(thm)],[1008, 1006])).
% 5.70/5.92 tff(1010,plain,
% 5.70/5.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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))))))),
% 5.70/5.92 inference(quant_inst,[status(thm)],[])).
% 5.70/5.92 tff(1011,plain,
% 5.70/5.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 5.70/5.92 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 5.70/5.92 tff(1012,plain,
% 5.70/5.92 ($false),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[1011, 391, 900, 973, 974, 328, 1005])).
% 5.70/5.92 tff(1013,plain,((~b(elem!1, s(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))))) | (s(s(s(s(elem!1)))) = elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.92 tff(1014,plain,
% 5.70/5.92 (~b(elem!1, s(s(s(s(elem!1)))))),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[1013, 971, 900, 328, 967, 963, 961, 957])).
% 5.70/5.92 tff(1015,plain,
% 5.70/5.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 5.70/5.92 inference(rewrite,[status(thm)],[])).
% 5.70/5.92 tff(1016,plain,
% 5.70/5.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 5.70/5.92 inference(quant_inst,[status(thm)],[])).
% 5.70/5.92 tff(1017,plain,
% 5.70/5.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 5.70/5.92 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 5.70/5.92 tff(1018,plain,
% 5.70/5.92 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[1017, 42])).
% 5.70/5.92 tff(1019,plain,
% 5.70/5.92 (r(elem!1, s(s(s(s(elem!1)))))),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[1018, 1014, 956])).
% 5.70/5.92 tff(1020,plain,
% 5.70/5.92 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 5.70/5.92 inference(commutativity,[status(thm)],[])).
% 5.70/5.92 tff(1021,plain,
% 5.70/5.92 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 5.70/5.92 inference(symmetry,[status(thm)],[1020])).
% 5.70/5.92 tff(1022,plain,
% 5.70/5.92 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 5.70/5.92 inference(transitivity,[status(thm)],[938, 1021])).
% 5.70/5.92 tff(1023,plain,
% 5.70/5.92 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 5.70/5.92 inference(monotonicity,[status(thm)],[1022])).
% 5.70/5.92 tff(1024,plain,
% 5.70/5.92 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 5.70/5.92 inference(modus_ponens,[status(thm)],[946, 1023])).
% 5.70/5.92 tff(1025,plain,
% 5.70/5.92 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 5.70/5.92 inference(monotonicity,[status(thm)],[931])).
% 5.70/5.92 tff(1026,plain,
% 5.70/5.92 (b(s(elem!1), s(s(s(elem!1))))),
% 5.70/5.92 inference(modus_ponens,[status(thm)],[339, 1025])).
% 5.70/5.92 tff(1027,plain,
% 5.70/5.92 (elem!1 = z),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[97, 94])).
% 5.70/5.92 tff(1028,plain,
% 5.70/5.92 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 5.70/5.92 inference(monotonicity,[status(thm)],[488])).
% 5.70/5.92 tff(1029,plain,
% 5.70/5.92 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 5.70/5.92 inference(symmetry,[status(thm)],[1028])).
% 5.70/5.92 tff(1030,plain,
% 5.70/5.92 (b(s(s(elem!1)), s(elem!1))),
% 5.70/5.92 inference(modus_ponens,[status(thm)],[381, 1029])).
% 5.70/5.92 tff(1031,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 5.70/5.92 tff(1032,plain,
% 5.70/5.92 ($false),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[1031, 1030])).
% 5.70/5.92 tff(1033,plain,((~b(s(s(elem!1)), s(z))) | b(s(s(elem!1)), s(elem!1)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.92 tff(1034,plain,
% 5.70/5.92 (b(s(s(elem!1)), s(elem!1))),
% 5.70/5.92 inference(unit_resolution,[status(thm)],[1033, 1027, 363])).
% 5.70/5.92 tff(1035,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 5.70/5.92 tff(1036,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 5.70/5.92 tff(1037,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 5.70/5.92 tff(1038,plain,
% 5.70/5.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.92 inference(rewrite,[status(thm)],[])).
% 5.70/5.92 tff(1039,plain,
% 5.70/5.92 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.92 inference(rewrite,[status(thm)],[])).
% 5.70/5.92 tff(1040,plain,
% 5.70/5.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 5.70/5.93 inference(monotonicity,[status(thm)],[1039])).
% 5.70/5.93 tff(1041,plain,
% 5.70/5.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.93 inference(transitivity,[status(thm)],[1040, 1038])).
% 5.70/5.93 tff(1042,plain,
% 5.70/5.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.93 inference(quant_inst,[status(thm)],[])).
% 5.70/5.93 tff(1043,plain,
% 5.70/5.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 5.70/5.93 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 5.70/5.93 tff(1044,plain,
% 5.70/5.93 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.70/5.93 inference(unit_resolution,[status(thm)],[1043, 391, 900, 1037, 975, 1036])).
% 5.70/5.93 tff(1045,plain,
% 5.70/5.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), 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(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 5.70/5.93 inference(rewrite,[status(thm)],[])).
% 5.70/5.93 tff(1046,plain,
% 5.70/5.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 5.70/5.93 inference(quant_inst,[status(thm)],[])).
% 5.70/5.93 tff(1047,plain,
% 5.70/5.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.70/5.93 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 5.70/5.93 tff(1048,plain,
% 5.70/5.93 ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.70/5.93 inference(unit_resolution,[status(thm)],[1047, 42])).
% 5.70/5.93 tff(1049,plain,
% 5.70/5.93 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.70/5.93 inference(unit_resolution,[status(thm)],[1048, 1044, 1035])).
% 5.70/5.93 tff(1050,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 5.70/5.93 tff(1051,plain,
% 5.70/5.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.93 inference(rewrite,[status(thm)],[])).
% 5.70/5.93 tff(1052,plain,
% 5.70/5.93 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.93 inference(rewrite,[status(thm)],[])).
% 5.70/5.93 tff(1053,plain,
% 5.70/5.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 5.70/5.93 inference(monotonicity,[status(thm)],[1052])).
% 5.70/5.93 tff(1054,plain,
% 5.70/5.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.93 inference(transitivity,[status(thm)],[1053, 1051])).
% 5.70/5.93 tff(1055,plain,
% 5.70/5.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 5.70/5.93 inference(quant_inst,[status(thm)],[])).
% 5.70/5.93 tff(1056,plain,
% 5.70/5.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 5.70/5.93 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 5.70/5.93 tff(1057,plain,
% 5.70/5.93 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.70/5.93 inference(unit_resolution,[status(thm)],[1056, 391, 900, 1037, 975, 1036])).
% 5.70/5.93 tff(1058,plain,
% 5.70/5.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(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(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 5.70/5.93 inference(rewrite,[status(thm)],[])).
% 5.70/5.93 tff(1059,plain,
% 5.70/5.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 5.70/5.93 inference(quant_inst,[status(thm)],[])).
% 5.70/5.93 tff(1060,plain,
% 5.70/5.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.70/5.93 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 5.70/5.93 tff(1061,plain,
% 5.70/5.93 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.70/5.93 inference(unit_resolution,[status(thm)],[1060, 42])).
% 5.70/5.93 tff(1062,plain,
% 5.70/5.93 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.70/5.93 inference(unit_resolution,[status(thm)],[1061, 1057, 1050])).
% 5.70/5.93 tff(1063,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 5.70/5.93 tff(1064,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 5.70/5.93 tff(1065,plain,
% 5.70/5.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 5.70/5.94 inference(rewrite,[status(thm)],[])).
% 5.70/5.94 tff(1066,plain,
% 5.70/5.94 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 5.70/5.94 inference(rewrite,[status(thm)],[])).
% 5.70/5.94 tff(1067,plain,
% 5.70/5.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 5.70/5.94 inference(monotonicity,[status(thm)],[1066])).
% 5.70/5.94 tff(1068,plain,
% 5.70/5.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 5.70/5.94 inference(transitivity,[status(thm)],[1067, 1065])).
% 5.70/5.94 tff(1069,plain,
% 5.70/5.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 5.70/5.94 inference(quant_inst,[status(thm)],[])).
% 5.70/5.94 tff(1070,plain,
% 5.70/5.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 5.70/5.94 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 5.70/5.94 tff(1071,plain,
% 5.70/5.94 ($false),
% 5.70/5.94 inference(unit_resolution,[status(thm)],[1070, 194, 1064, 1063, 1062, 1049])).
% 5.70/5.94 tff(1072,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.94 tff(1073,plain,
% 5.70/5.94 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 5.70/5.94 inference(unit_resolution,[status(thm)],[1072, 949, 1019, 1024, 947, 900, 1034, 1026])).
% 5.70/5.94 tff(1074,plain,
% 5.70/5.94 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 5.70/5.94 inference(unit_resolution,[status(thm)],[988, 1073, 957])).
% 5.70/5.94 tff(1075,plain,
% 5.70/5.94 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 5.70/5.94 inference(monotonicity,[status(thm)],[931])).
% 5.70/5.94 tff(1076,plain,
% 5.70/5.94 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.70/5.94 inference(transitivity,[status(thm)],[1075, 582])).
% 5.70/5.94 tff(1077,plain,
% 5.70/5.94 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 5.70/5.94 inference(monotonicity,[status(thm)],[1076])).
% 5.70/5.94 tff(1078,plain,
% 5.70/5.94 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.70/5.94 inference(modus_ponens,[status(thm)],[217, 1077])).
% 5.70/5.94 tff(1079,plain,
% 5.70/5.94 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 5.70/5.94 inference(monotonicity,[status(thm)],[931])).
% 5.70/5.94 tff(1080,plain,
% 5.70/5.94 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 5.70/5.94 inference(monotonicity,[status(thm)],[1079])).
% 5.70/5.94 tff(1081,plain,
% 5.70/5.94 (~(s(s(elem!1)) = s(elem!1))),
% 5.70/5.94 inference(modus_ponens,[status(thm)],[357, 1080])).
% 5.70/5.94 tff(1082,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 5.70/5.94 tff(1083,plain,
% 5.70/5.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 5.70/5.94 inference(rewrite,[status(thm)],[])).
% 5.70/5.94 tff(1084,plain,
% 5.70/5.94 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 5.70/5.94 inference(rewrite,[status(thm)],[])).
% 5.70/5.94 tff(1085,plain,
% 5.70/5.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 5.70/5.94 inference(monotonicity,[status(thm)],[1084])).
% 5.70/5.94 tff(1086,plain,
% 5.70/5.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 5.70/5.94 inference(transitivity,[status(thm)],[1085, 1083])).
% 5.70/5.94 tff(1087,plain,
% 5.70/5.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 5.70/5.94 inference(quant_inst,[status(thm)],[])).
% 5.70/5.94 tff(1088,plain,
% 5.70/5.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 5.70/5.94 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 5.70/5.94 tff(1089,plain,
% 5.70/5.94 ($false),
% 5.70/5.94 inference(unit_resolution,[status(thm)],[1088, 194, 410, 327, 1063, 1082])).
% 5.70/5.94 tff(1090,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.94 tff(1091,plain,
% 5.70/5.94 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 5.70/5.94 inference(unit_resolution,[status(thm)],[1090, 963, 327, 1019])).
% 5.70/5.94 tff(1092,plain,
% 5.70/5.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(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(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 5.70/5.94 inference(rewrite,[status(thm)],[])).
% 5.70/5.94 tff(1093,plain,
% 5.70/5.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 5.70/5.94 inference(quant_inst,[status(thm)],[])).
% 5.70/5.94 tff(1094,plain,
% 5.70/5.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 5.70/5.94 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 5.70/5.94 tff(1095,plain,
% 5.70/5.94 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 5.70/5.94 inference(unit_resolution,[status(thm)],[1094, 42])).
% 5.70/5.94 tff(1096,plain,
% 5.70/5.94 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 5.70/5.94 inference(unit_resolution,[status(thm)],[1095, 1091, 305])).
% 5.70/5.94 tff(1097,plain,
% 5.70/5.94 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 5.70/5.94 inference(commutativity,[status(thm)],[])).
% 5.70/5.94 tff(1098,plain,
% 5.70/5.94 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 5.70/5.94 inference(symmetry,[status(thm)],[1097])).
% 5.70/5.94 tff(1099,plain,
% 5.70/5.94 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 5.70/5.94 inference(monotonicity,[status(thm)],[1098])).
% 5.70/5.94 tff(1100,plain,
% 5.70/5.94 (~(s(elem!1) = s(s(elem!1)))),
% 5.70/5.94 inference(modus_ponens,[status(thm)],[285, 1099])).
% 5.70/5.94 tff(1101,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 5.70/5.94 tff(1102,plain,
% 5.70/5.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 5.70/5.94 inference(rewrite,[status(thm)],[])).
% 5.70/5.94 tff(1103,plain,
% 5.70/5.94 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 5.70/5.94 inference(rewrite,[status(thm)],[])).
% 5.70/5.94 tff(1104,plain,
% 5.70/5.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))))),
% 5.70/5.94 inference(monotonicity,[status(thm)],[1103])).
% 5.70/5.94 tff(1105,plain,
% 5.70/5.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 5.70/5.94 inference(transitivity,[status(thm)],[1104, 1102])).
% 5.70/5.94 tff(1106,plain,
% 5.70/5.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 5.70/5.94 inference(quant_inst,[status(thm)],[])).
% 5.70/5.94 tff(1107,plain,
% 5.70/5.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))),
% 5.70/5.94 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 5.70/5.94 tff(1108,plain,
% 5.70/5.94 (~b(s(elem!1), s(s(elem!1)))),
% 5.70/5.94 inference(unit_resolution,[status(thm)],[1107, 391, 1101, 328, 1036])).
% 5.70/5.95 tff(1109,plain,
% 5.70/5.95 (((~![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))))),
% 5.70/5.95 inference(rewrite,[status(thm)],[])).
% 5.70/5.95 tff(1110,plain,
% 5.70/5.95 ((~![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))))),
% 5.70/5.95 inference(quant_inst,[status(thm)],[])).
% 5.70/5.95 tff(1111,plain,
% 5.70/5.95 ((~![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)))),
% 5.70/5.95 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 5.70/5.95 tff(1112,plain,
% 5.70/5.95 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 5.70/5.95 inference(unit_resolution,[status(thm)],[1111, 42, 1108])).
% 5.70/5.95 tff(1113,plain,
% 5.70/5.95 (r(s(elem!1), s(s(elem!1)))),
% 5.70/5.95 inference(unit_resolution,[status(thm)],[1112, 1100])).
% 5.70/5.95 tff(1114,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 5.70/5.95 tff(1115,plain,
% 5.70/5.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.95 inference(rewrite,[status(thm)],[])).
% 5.70/5.95 tff(1116,plain,
% 5.70/5.95 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(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(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.95 inference(rewrite,[status(thm)],[])).
% 5.70/5.95 tff(1117,plain,
% 5.70/5.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 5.70/5.95 inference(monotonicity,[status(thm)],[1116])).
% 5.70/5.95 tff(1118,plain,
% 5.70/5.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.95 inference(transitivity,[status(thm)],[1117, 1115])).
% 5.70/5.95 tff(1119,plain,
% 5.70/5.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(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(elem!1)))))))),
% 5.70/5.95 inference(quant_inst,[status(thm)],[])).
% 5.70/5.95 tff(1120,plain,
% 5.70/5.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 5.70/5.95 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 5.70/5.95 tff(1121,plain,
% 5.70/5.95 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.70/5.95 inference(unit_resolution,[status(thm)],[1120, 391, 1101, 328, 1114, 1036])).
% 5.70/5.95 tff(1122,plain,
% 5.70/5.95 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.70/5.95 inference(unit_resolution,[status(thm)],[1048, 1121, 1035])).
% 5.70/5.95 tff(1123,plain,
% 5.70/5.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 5.70/5.95 inference(rewrite,[status(thm)],[])).
% 5.70/5.95 tff(1124,plain,
% 5.70/5.95 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 5.70/5.95 inference(rewrite,[status(thm)],[])).
% 5.70/5.95 tff(1125,plain,
% 5.70/5.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 5.70/5.95 inference(monotonicity,[status(thm)],[1124])).
% 5.70/5.95 tff(1126,plain,
% 5.70/5.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 5.70/5.95 inference(transitivity,[status(thm)],[1125, 1123])).
% 5.70/5.95 tff(1127,plain,
% 5.70/5.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 5.70/5.95 inference(quant_inst,[status(thm)],[])).
% 5.70/5.95 tff(1128,plain,
% 5.70/5.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 5.70/5.95 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 5.70/5.95 tff(1129,plain,
% 5.70/5.95 (~b(s(s(elem!1)), s(elem!1))),
% 5.70/5.95 inference(unit_resolution,[status(thm)],[1128, 391, 1101, 328, 1036])).
% 5.70/5.95 tff(1130,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 5.70/5.95 tff(1131,plain,
% 5.70/5.95 (((~![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)))),
% 5.70/5.95 inference(rewrite,[status(thm)],[])).
% 5.70/5.95 tff(1132,plain,
% 5.70/5.95 ((~![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)))),
% 5.70/5.95 inference(quant_inst,[status(thm)],[])).
% 5.70/5.95 tff(1133,plain,
% 5.70/5.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 5.70/5.95 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 5.70/5.95 tff(1134,plain,
% 5.70/5.95 ($false),
% 5.70/5.95 inference(unit_resolution,[status(thm)],[1133, 42, 1031, 285, 1130])).
% 5.70/5.95 tff(1135,plain,(r(s(s(elem!1)), s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.95 tff(1136,plain,
% 5.70/5.95 (r(s(s(elem!1)), s(elem!1))),
% 5.70/5.95 inference(unit_resolution,[status(thm)],[1135, 1129, 285])).
% 5.70/5.95 tff(1137,plain,
% 5.70/5.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.95 inference(rewrite,[status(thm)],[])).
% 5.70/5.95 tff(1138,plain,
% 5.70/5.95 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.95 inference(rewrite,[status(thm)],[])).
% 5.70/5.95 tff(1139,plain,
% 5.70/5.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 5.70/5.95 inference(monotonicity,[status(thm)],[1138])).
% 5.70/5.95 tff(1140,plain,
% 5.70/5.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.95 inference(transitivity,[status(thm)],[1139, 1137])).
% 5.70/5.95 tff(1141,plain,
% 5.70/5.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.95 inference(quant_inst,[status(thm)],[])).
% 5.70/5.95 tff(1142,plain,
% 5.70/5.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 5.70/5.95 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 5.70/5.95 tff(1143,plain,
% 5.70/5.95 ($false),
% 5.70/5.95 inference(unit_resolution,[status(thm)],[1142, 194, 1136, 1122, 990, 1113])).
% 5.70/5.95 tff(1144,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.95 tff(1145,plain,
% 5.70/5.95 (~b(s(s(s(elem!1))), s(elem!1))),
% 5.70/5.95 inference(unit_resolution,[status(thm)],[1144, 1096, 1081, 1024, 1026, 1074, 328])).
% 5.70/5.96 tff(1146,plain,
% 5.70/5.96 (r(s(s(s(elem!1))), s(elem!1))),
% 5.70/5.96 inference(unit_resolution,[status(thm)],[588, 1145, 1078])).
% 5.70/5.96 tff(1147,plain,
% 5.70/5.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 5.70/5.96 inference(rewrite,[status(thm)],[])).
% 5.70/5.96 tff(1148,plain,
% 5.70/5.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 5.70/5.96 inference(quant_inst,[status(thm)],[])).
% 5.70/5.96 tff(1149,plain,
% 5.70/5.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 5.70/5.96 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 5.70/5.96 tff(1150,plain,
% 5.70/5.96 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 5.70/5.96 inference(unit_resolution,[status(thm)],[1149, 194, 613, 485, 990])).
% 5.70/5.96 tff(1151,plain,
% 5.70/5.96 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 5.70/5.96 inference(unit_resolution,[status(thm)],[1095, 1150, 305])).
% 5.70/5.96 tff(1152,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 5.70/5.96 tff(1153,plain,
% 5.70/5.96 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 5.70/5.96 inference(unit_resolution,[status(thm)],[307, 305])).
% 5.70/5.96 tff(1154,plain,
% 5.70/5.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.96 inference(rewrite,[status(thm)],[])).
% 5.70/5.96 tff(1155,plain,
% 5.70/5.96 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.96 inference(rewrite,[status(thm)],[])).
% 5.70/5.96 tff(1156,plain,
% 5.70/5.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 5.70/5.96 inference(monotonicity,[status(thm)],[1155])).
% 5.70/5.96 tff(1157,plain,
% 5.70/5.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 5.70/5.96 inference(transitivity,[status(thm)],[1156, 1154])).
% 5.70/5.96 tff(1158,plain,
% 5.70/5.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 5.70/5.96 inference(quant_inst,[status(thm)],[])).
% 5.70/5.96 tff(1159,plain,
% 5.70/5.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 5.70/5.96 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 5.70/5.96 tff(1160,plain,
% 5.70/5.96 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.70/5.96 inference(unit_resolution,[status(thm)],[1159, 194, 613, 485, 990])).
% 5.70/5.96 tff(1161,plain,
% 5.70/5.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), 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(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 5.70/5.96 inference(rewrite,[status(thm)],[])).
% 5.70/5.96 tff(1162,plain,
% 5.70/5.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 5.70/5.96 inference(quant_inst,[status(thm)],[])).
% 5.70/5.96 tff(1163,plain,
% 5.70/5.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.70/5.96 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 5.70/5.96 tff(1164,plain,
% 5.70/5.96 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.70/5.96 inference(unit_resolution,[status(thm)],[1163, 42])).
% 5.70/5.96 tff(1165,plain,
% 5.70/5.96 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.70/5.96 inference(unit_resolution,[status(thm)],[1164, 1160, 1153])).
% 5.70/5.96 tff(1166,plain,
% 5.70/5.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.96 inference(rewrite,[status(thm)],[])).
% 5.70/5.96 tff(1167,plain,
% 5.70/5.96 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(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)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.96 inference(rewrite,[status(thm)],[])).
% 5.70/5.96 tff(1168,plain,
% 5.70/5.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 5.70/5.96 inference(monotonicity,[status(thm)],[1167])).
% 5.70/5.96 tff(1169,plain,
% 5.70/5.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.70/5.97 inference(transitivity,[status(thm)],[1168, 1166])).
% 5.70/5.97 tff(1170,plain,
% 5.70/5.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/5.97 inference(quant_inst,[status(thm)],[])).
% 5.70/5.97 tff(1171,plain,
% 5.70/5.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 5.70/5.97 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 5.70/5.97 tff(1172,plain,
% 5.70/5.97 ($false),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1171, 391, 900, 328, 1165, 1152, 1151])).
% 5.70/5.97 tff(1173,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.97 tff(1174,plain,
% 5.70/5.97 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1173, 1146, 328, 900, 305, 961, 1074])).
% 5.70/5.97 tff(1175,plain,
% 5.70/5.97 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1048, 1174, 1024])).
% 5.70/5.97 tff(1176,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 5.70/5.97 tff(1177,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 5.70/5.97 tff(1178,plain,
% 5.70/5.97 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 5.70/5.97 inference(rewrite,[status(thm)],[])).
% 5.70/5.97 tff(1179,plain,
% 5.70/5.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 5.70/5.97 inference(monotonicity,[status(thm)],[1178])).
% 5.70/5.97 tff(1180,plain,
% 5.70/5.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 5.70/5.97 inference(transitivity,[status(thm)],[1179, 1065])).
% 5.70/5.97 tff(1181,plain,
% 5.70/5.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))),
% 5.70/5.97 inference(quant_inst,[status(thm)],[])).
% 5.70/5.97 tff(1182,plain,
% 5.70/5.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 5.70/5.97 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 5.70/5.97 tff(1183,plain,
% 5.70/5.97 ($false),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1182, 194, 1064, 1063, 1177, 1176])).
% 5.70/5.97 tff(1184,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.97 tff(1185,plain,
% 5.70/5.97 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1184, 1175, 1019, 949])).
% 5.70/5.97 tff(1186,plain,
% 5.70/5.97 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1061, 1185, 947])).
% 5.70/5.97 tff(1187,plain,
% 5.70/5.97 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 5.70/5.97 inference(modus_ponens,[status(thm)],[1186, 936])).
% 5.70/5.97 tff(1188,plain,
% 5.70/5.97 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 5.70/5.97 inference(monotonicity,[status(thm)],[94])).
% 5.70/5.97 tff(1189,plain,
% 5.70/5.97 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 5.70/5.97 inference(symmetry,[status(thm)],[1188])).
% 5.70/5.97 tff(1190,plain,
% 5.70/5.97 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 5.70/5.97 inference(monotonicity,[status(thm)],[934])).
% 5.70/5.97 tff(1191,plain,
% 5.70/5.97 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 5.70/5.97 inference(symmetry,[status(thm)],[1190])).
% 5.70/5.97 tff(1192,plain,
% 5.70/5.97 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 5.70/5.97 inference(transitivity,[status(thm)],[1191, 1189])).
% 5.70/5.97 tff(1193,plain,
% 5.70/5.97 (r(z, s(s(s(s(z)))))),
% 5.70/5.97 inference(modus_ponens,[status(thm)],[1019, 1192])).
% 5.70/5.97 tff(1194,plain,
% 5.70/5.97 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 5.70/5.97 inference(monotonicity,[status(thm)],[934, 931])).
% 5.70/5.97 tff(1195,plain,
% 5.70/5.97 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 5.70/5.97 inference(symmetry,[status(thm)],[1194])).
% 5.70/5.97 tff(1196,plain,
% 5.70/5.97 (r(s(s(s(s(z)))), s(z))),
% 5.70/5.97 inference(modus_ponens,[status(thm)],[1074, 1195])).
% 5.70/5.97 tff(1197,plain,
% 5.70/5.97 (~r(z, s(z))),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[731, 1196, 182, 1193])).
% 5.70/5.97 tff(1198,plain,
% 5.70/5.97 (b(z, s(z))),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[678, 1197])).
% 5.70/5.97 tff(1199,plain,
% 5.70/5.97 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 5.70/5.97 inference(monotonicity,[status(thm)],[94])).
% 5.70/5.97 tff(1200,plain,
% 5.70/5.97 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 5.70/5.97 inference(symmetry,[status(thm)],[1199])).
% 5.70/5.97 tff(1201,plain,
% 5.70/5.97 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 5.70/5.97 inference(monotonicity,[status(thm)],[932])).
% 5.70/5.97 tff(1202,plain,
% 5.70/5.97 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 5.70/5.97 inference(symmetry,[status(thm)],[1201])).
% 5.70/5.97 tff(1203,plain,
% 5.70/5.97 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), z)),
% 5.70/5.97 inference(transitivity,[status(thm)],[1202, 1200])).
% 5.70/5.97 tff(1204,plain,
% 5.70/5.97 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(z)), z))),
% 5.70/5.97 inference(monotonicity,[status(thm)],[1203])).
% 5.70/5.97 tff(1205,plain,
% 5.70/5.97 (~r(s(s(z)), z)),
% 5.70/5.97 inference(modus_ponens,[status(thm)],[373, 1204])).
% 5.70/5.97 tff(1206,plain,
% 5.70/5.97 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 5.70/5.97 inference(quant_inst,[status(thm)],[])).
% 5.70/5.97 tff(1207,plain,
% 5.70/5.97 (~(s(s(z)) = z)),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1206, 21])).
% 5.70/5.97 tff(1208,plain,
% 5.70/5.97 (((~![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))),
% 5.70/5.97 inference(rewrite,[status(thm)],[])).
% 5.70/5.97 tff(1209,plain,
% 5.70/5.97 ((~![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))),
% 5.70/5.97 inference(quant_inst,[status(thm)],[])).
% 5.70/5.97 tff(1210,plain,
% 5.70/5.97 ((~![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)),
% 5.70/5.97 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 5.70/5.97 tff(1211,plain,
% 5.70/5.97 (b(s(s(z)), z) | r(s(s(z)), z)),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1210, 42, 1207])).
% 5.70/5.97 tff(1212,plain,
% 5.70/5.97 (b(s(s(z)), z)),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1211, 1205])).
% 5.70/5.97 tff(1213,plain,
% 5.70/5.97 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 5.70/5.97 inference(monotonicity,[status(thm)],[932, 931])).
% 5.70/5.97 tff(1214,plain,
% 5.70/5.97 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 5.70/5.97 inference(symmetry,[status(thm)],[1213])).
% 5.70/5.97 tff(1215,plain,
% 5.70/5.97 (b(s(s(z)), s(z))),
% 5.70/5.97 inference(modus_ponens,[status(thm)],[1034, 1214])).
% 5.70/5.97 tff(1216,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 5.70/5.97 tff(1217,plain,
% 5.70/5.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 5.70/5.97 inference(rewrite,[status(thm)],[])).
% 5.70/5.97 tff(1218,plain,
% 5.70/5.97 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 5.70/5.97 inference(rewrite,[status(thm)],[])).
% 5.70/5.97 tff(1219,plain,
% 5.70/5.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 5.70/5.97 inference(monotonicity,[status(thm)],[1218])).
% 5.70/5.97 tff(1220,plain,
% 5.70/5.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 5.70/5.97 inference(transitivity,[status(thm)],[1219, 1217])).
% 5.70/5.97 tff(1221,plain,
% 5.70/5.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 5.70/5.97 inference(quant_inst,[status(thm)],[])).
% 5.70/5.97 tff(1222,plain,
% 5.70/5.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 5.70/5.97 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 5.70/5.97 tff(1223,plain,
% 5.70/5.97 ($false),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1222, 194, 182, 1216, 723, 719])).
% 5.70/5.97 tff(1224,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.97 tff(1225,plain,
% 5.70/5.97 (~r(s(z), s(s(s(s(z)))))),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1224, 1196, 182, 1193])).
% 5.70/5.97 tff(1226,plain,
% 5.70/5.97 (((~![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))))))),
% 5.70/5.97 inference(rewrite,[status(thm)],[])).
% 5.70/5.97 tff(1227,plain,
% 5.70/5.97 ((~![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))))))),
% 5.70/5.97 inference(quant_inst,[status(thm)],[])).
% 5.70/5.97 tff(1228,plain,
% 5.70/5.97 ((~![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)))))),
% 5.70/5.97 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 5.70/5.97 tff(1229,plain,
% 5.70/5.97 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1228, 42])).
% 5.70/5.97 tff(1230,plain,
% 5.70/5.97 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1229, 743])).
% 5.70/5.97 tff(1231,plain,
% 5.70/5.97 (b(s(z), s(s(s(s(z)))))),
% 5.70/5.97 inference(unit_resolution,[status(thm)],[1230, 1225])).
% 5.70/5.97 tff(1232,assumption,(b(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 5.70/5.97 tff(1233,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 5.70/5.98 tff(1234,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 5.70/5.98 tff(1235,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 5.70/5.98 tff(1236,plain,
% 5.70/5.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.70/5.98 inference(rewrite,[status(thm)],[])).
% 5.70/5.98 tff(1237,plain,
% 5.70/5.98 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.70/5.98 inference(rewrite,[status(thm)],[])).
% 5.70/5.98 tff(1238,plain,
% 5.70/5.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 5.70/5.98 inference(monotonicity,[status(thm)],[1237])).
% 5.70/5.98 tff(1239,plain,
% 5.70/5.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.70/5.98 inference(transitivity,[status(thm)],[1238, 1236])).
% 5.70/5.98 tff(1240,plain,
% 5.70/5.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 5.70/5.98 inference(quant_inst,[status(thm)],[])).
% 5.70/5.98 tff(1241,plain,
% 5.70/5.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 5.70/5.98 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 5.70/5.98 tff(1242,plain,
% 5.70/5.98 ($false),
% 5.70/5.98 inference(unit_resolution,[status(thm)],[1241, 391, 1235, 1234, 1233, 664, 1232])).
% 5.70/5.98 tff(1243,plain,((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.98 tff(1244,plain,
% 5.70/5.98 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 5.70/5.98 inference(unit_resolution,[status(thm)],[1243, 1231, 1215, 1212, 1198])).
% 5.70/5.98 tff(1245,plain,
% 5.70/5.98 ($false),
% 5.70/5.98 inference(unit_resolution,[status(thm)],[1244, 1187])).
% 5.70/5.98 tff(1246,plain,((~(z = elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.98 tff(1247,plain,
% 5.70/5.98 (~(z = elem!1)),
% 5.70/5.98 inference(unit_resolution,[status(thm)],[1246, 899, 328, 305, 327, 182, 930, 326, 184])).
% 5.70/5.98 tff(1248,plain,
% 5.70/5.98 (r(z, elem!1)),
% 5.70/5.98 inference(unit_resolution,[status(thm)],[141, 1247, 400])).
% 5.70/5.98 tff(1249,plain,
% 5.70/5.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 5.70/5.98 inference(rewrite,[status(thm)],[])).
% 5.70/5.98 tff(1250,plain,
% 5.70/5.98 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 5.70/5.98 inference(rewrite,[status(thm)],[])).
% 5.70/5.98 tff(1251,plain,
% 5.70/5.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 5.70/5.98 inference(monotonicity,[status(thm)],[1250])).
% 5.70/5.98 tff(1252,plain,
% 5.70/5.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 5.70/5.98 inference(transitivity,[status(thm)],[1251, 1249])).
% 5.70/5.98 tff(1253,plain,
% 5.70/5.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 5.70/5.98 inference(quant_inst,[status(thm)],[])).
% 5.70/5.98 tff(1254,plain,
% 5.70/5.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 5.70/5.98 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 5.70/5.98 tff(1255,plain,
% 5.70/5.98 ($false),
% 5.70/5.98 inference(unit_resolution,[status(thm)],[1254, 194, 1248, 184, 924, 327])).
% 5.70/5.98 tff(1256,plain,((elem!1 = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 5.70/5.98 tff(1257,plain,
% 5.70/5.98 (elem!1 = s(s(s(elem!1)))),
% 5.70/5.98 inference(unit_resolution,[status(thm)],[1256, 329, 327, 328, 310, 182, 326, 59])).
% 5.70/5.98 tff(1258,plain,
% 5.70/5.98 (s(elem!1) = s(s(s(s(elem!1))))),
% 5.70/5.98 inference(monotonicity,[status(thm)],[1257])).
% 5.70/5.98 tff(1259,plain,
% 5.70/5.98 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 5.70/5.98 inference(monotonicity,[status(thm)],[1258])).
% 5.70/5.98 tff(1260,plain,
% 5.70/5.98 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 5.70/5.98 inference(symmetry,[status(thm)],[1259])).
% 5.70/5.98 tff(1261,plain,
% 5.70/5.98 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 5.70/5.98 inference(monotonicity,[status(thm)],[1260])).
% 5.70/5.98 tff(1262,plain,
% 5.70/5.98 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 5.70/5.98 inference(symmetry,[status(thm)],[1261])).
% 5.70/5.98 tff(1263,plain,
% 5.70/5.98 (~r(s(s(elem!1)), s(z))),
% 5.70/5.98 inference(unit_resolution,[status(thm)],[348, 327, 59, 326])).
% 5.70/5.98 tff(1264,plain,
% 5.70/5.98 (b(s(s(elem!1)), s(z))),
% 5.70/5.98 inference(unit_resolution,[status(thm)],[362, 1263])).
% 5.70/5.98 tff(1265,plain,
% 5.70/5.98 (b(s(s(s(s(s(elem!1))))), s(z))),
% 5.70/5.98 inference(modus_ponens,[status(thm)],[1264, 1262])).
% 5.70/5.98 tff(1266,plain,
% 5.70/5.98 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 5.70/5.98 inference(monotonicity,[status(thm)],[1260])).
% 5.70/5.98 tff(1267,plain,
% 5.70/5.98 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 5.70/5.98 inference(symmetry,[status(thm)],[1266])).
% 5.70/5.98 tff(1268,plain,
% 5.70/5.98 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 5.70/5.98 inference(modus_ponens,[status(thm)],[328, 1267])).
% 5.70/5.98 tff(1269,plain,
% 5.70/5.98 (r(z, elem!1)),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[147, 1257, 10])).
% 5.70/5.99 tff(1270,plain,
% 5.70/5.99 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 5.70/5.99 inference(symmetry,[status(thm)],[474])).
% 5.70/5.99 tff(1271,plain,
% 5.70/5.99 ((s(z) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 5.70/5.99 inference(monotonicity,[status(thm)],[1257])).
% 5.70/5.99 tff(1272,plain,
% 5.70/5.99 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 5.70/5.99 inference(symmetry,[status(thm)],[1271])).
% 5.70/5.99 tff(1273,plain,
% 5.70/5.99 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 5.70/5.99 inference(transitivity,[status(thm)],[1272, 1270])).
% 5.70/5.99 tff(1274,plain,
% 5.70/5.99 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 5.70/5.99 inference(monotonicity,[status(thm)],[1273])).
% 5.70/5.99 tff(1275,plain,
% 5.70/5.99 (~(elem!1 = s(z))),
% 5.70/5.99 inference(modus_ponens,[status(thm)],[217, 1274])).
% 5.70/5.99 tff(1276,plain,
% 5.70/5.99 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 5.70/5.99 inference(monotonicity,[status(thm)],[1257])).
% 5.70/5.99 tff(1277,plain,
% 5.70/5.99 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 5.70/5.99 inference(symmetry,[status(thm)],[1276])).
% 5.70/5.99 tff(1278,plain,
% 5.70/5.99 (b(elem!1, z)),
% 5.70/5.99 inference(modus_ponens,[status(thm)],[378, 1277])).
% 5.70/5.99 tff(1279,plain,
% 5.70/5.99 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 5.70/5.99 inference(monotonicity,[status(thm)],[1257])).
% 5.70/5.99 tff(1280,plain,
% 5.70/5.99 ((s(s(elem!1)) = elem!1) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 5.70/5.99 inference(transitivity,[status(thm)],[1279, 267])).
% 5.70/5.99 tff(1281,plain,
% 5.70/5.99 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 5.70/5.99 inference(symmetry,[status(thm)],[1280])).
% 5.70/5.99 tff(1282,plain,
% 5.70/5.99 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 5.70/5.99 inference(monotonicity,[status(thm)],[1281])).
% 5.70/5.99 tff(1283,plain,
% 5.70/5.99 (~(s(s(elem!1)) = elem!1)),
% 5.70/5.99 inference(modus_ponens,[status(thm)],[297, 1282])).
% 5.70/5.99 tff(1284,plain,
% 5.70/5.99 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 5.70/5.99 inference(monotonicity,[status(thm)],[1257])).
% 5.70/5.99 tff(1285,plain,
% 5.70/5.99 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 5.70/5.99 inference(symmetry,[status(thm)],[1284])).
% 5.70/5.99 tff(1286,plain,
% 5.70/5.99 (~r(s(z), s(s(s(elem!1))))),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[337, 327, 59, 182])).
% 5.70/5.99 tff(1287,plain,
% 5.70/5.99 (b(s(z), s(s(s(elem!1))))),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[247, 1286])).
% 5.70/5.99 tff(1288,plain,
% 5.70/5.99 (b(s(z), elem!1)),
% 5.70/5.99 inference(modus_ponens,[status(thm)],[1287, 1285])).
% 5.70/5.99 tff(1289,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 5.70/5.99 tff(1290,plain,
% 5.70/5.99 (s(s(elem!1)) = elem!1),
% 5.70/5.99 inference(modus_ponens,[status(thm)],[1289, 250])).
% 5.70/5.99 tff(1291,plain,
% 5.70/5.99 ($false),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[249, 1290])).
% 5.70/5.99 tff(1292,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.70/5.99 tff(1293,plain,
% 5.70/5.99 (~(elem!1 = s(s(elem!1)))),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[1292, 249])).
% 5.70/5.99 tff(1294,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 5.70/5.99 tff(1295,plain,
% 5.70/5.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 5.70/5.99 inference(rewrite,[status(thm)],[])).
% 5.70/5.99 tff(1296,plain,
% 5.70/5.99 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 5.70/5.99 inference(rewrite,[status(thm)],[])).
% 5.70/5.99 tff(1297,plain,
% 5.70/5.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 5.70/5.99 inference(monotonicity,[status(thm)],[1296])).
% 5.70/5.99 tff(1298,plain,
% 5.70/5.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 5.70/5.99 inference(transitivity,[status(thm)],[1297, 1295])).
% 5.70/5.99 tff(1299,plain,
% 5.70/5.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 5.70/5.99 inference(quant_inst,[status(thm)],[])).
% 5.70/5.99 tff(1300,plain,
% 5.70/5.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))),
% 5.70/5.99 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 5.70/5.99 tff(1301,plain,
% 5.70/5.99 ($false),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[1300, 391, 381, 644, 1294, 721])).
% 5.70/5.99 tff(1302,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.99 tff(1303,plain,
% 5.70/5.99 (~b(elem!1, s(s(elem!1)))),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[1302, 644, 381, 721])).
% 5.70/5.99 tff(1304,plain,
% 5.70/5.99 (((~![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))))),
% 5.70/5.99 inference(rewrite,[status(thm)],[])).
% 5.70/5.99 tff(1305,plain,
% 5.70/5.99 ((~![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))))),
% 5.70/5.99 inference(quant_inst,[status(thm)],[])).
% 5.70/5.99 tff(1306,plain,
% 5.70/5.99 ((~![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)))),
% 5.70/5.99 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 5.70/5.99 tff(1307,plain,
% 5.70/5.99 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[1306, 42])).
% 5.70/5.99 tff(1308,plain,
% 5.70/5.99 (r(elem!1, s(s(elem!1)))),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[1307, 1303, 1293])).
% 5.70/5.99 tff(1309,plain,
% 5.70/5.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 5.70/5.99 inference(rewrite,[status(thm)],[])).
% 5.70/5.99 tff(1310,plain,
% 5.70/5.99 (((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 5.70/5.99 inference(rewrite,[status(thm)],[])).
% 5.70/5.99 tff(1311,plain,
% 5.70/5.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))))),
% 5.70/5.99 inference(monotonicity,[status(thm)],[1310])).
% 5.70/5.99 tff(1312,plain,
% 5.70/5.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 5.70/5.99 inference(transitivity,[status(thm)],[1311, 1309])).
% 5.70/5.99 tff(1313,plain,
% 5.70/5.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 5.70/5.99 inference(quant_inst,[status(thm)],[])).
% 5.70/5.99 tff(1314,plain,
% 5.70/5.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))),
% 5.70/5.99 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 5.70/5.99 tff(1315,plain,
% 5.70/5.99 (~b(s(s(elem!1)), elem!1)),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[1314, 391, 665, 381, 644, 721])).
% 5.70/5.99 tff(1316,plain,
% 5.70/5.99 (r(s(s(elem!1)), elem!1)),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[872, 1315, 249])).
% 5.70/5.99 tff(1317,plain,
% 5.70/5.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 5.70/5.99 inference(rewrite,[status(thm)],[])).
% 5.70/5.99 tff(1318,plain,
% 5.70/5.99 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, 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)) | (~r(elem!1, s(s(elem!1)))))),
% 5.70/5.99 inference(rewrite,[status(thm)],[])).
% 5.70/5.99 tff(1319,plain,
% 5.70/5.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))))),
% 5.70/5.99 inference(monotonicity,[status(thm)],[1318])).
% 5.70/5.99 tff(1320,plain,
% 5.70/5.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 5.70/5.99 inference(transitivity,[status(thm)],[1319, 1317])).
% 5.70/5.99 tff(1321,plain,
% 5.70/5.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 5.70/5.99 inference(quant_inst,[status(thm)],[])).
% 5.70/5.99 tff(1322,plain,
% 5.70/5.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 5.70/5.99 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 5.70/5.99 tff(1323,plain,
% 5.70/5.99 ($false),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[1322, 194, 411, 1316, 326, 1308])).
% 5.70/5.99 tff(1324,plain,((~b(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.99 tff(1325,plain,
% 5.70/5.99 (~b(elem!1, s(z))),
% 5.70/5.99 inference(unit_resolution,[status(thm)],[1324, 1288, 326, 1283, 1269, 1264, 1278])).
% 5.70/6.00 tff(1326,plain,
% 5.70/6.00 (r(elem!1, s(z))),
% 5.70/6.00 inference(unit_resolution,[status(thm)],[837, 1325, 1275])).
% 5.70/6.00 tff(1327,plain,
% 5.70/6.00 (~r(z, s(z))),
% 5.70/6.00 inference(unit_resolution,[status(thm)],[845, 1326, 182, 1269])).
% 5.70/6.00 tff(1328,plain,
% 5.70/6.00 (b(z, s(z))),
% 5.70/6.00 inference(unit_resolution,[status(thm)],[678, 1327])).
% 5.70/6.00 tff(1329,plain,
% 5.70/6.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), 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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), 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(elem!1))))))),
% 5.70/6.00 inference(rewrite,[status(thm)],[])).
% 5.70/6.00 tff(1330,plain,
% 5.70/6.00 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(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(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), 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(elem!1))))))),
% 5.70/6.00 inference(rewrite,[status(thm)],[])).
% 5.70/6.00 tff(1331,plain,
% 5.70/6.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), 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(elem!1)))))))),
% 5.70/6.00 inference(monotonicity,[status(thm)],[1330])).
% 5.70/6.00 tff(1332,plain,
% 5.70/6.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), 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(elem!1))))))),
% 5.70/6.00 inference(transitivity,[status(thm)],[1331, 1329])).
% 5.70/6.00 tff(1333,plain,
% 5.70/6.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(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(z))))),
% 5.70/6.00 inference(quant_inst,[status(thm)],[])).
% 5.70/6.00 tff(1334,plain,
% 5.70/6.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 5.70/6.00 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 5.70/6.00 tff(1335,plain,
% 5.70/6.00 ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 5.70/6.00 inference(unit_resolution,[status(thm)],[1334, 391, 378, 1287, 1328])).
% 5.70/6.00 tff(1336,plain,
% 5.70/6.00 ($false),
% 5.70/6.00 inference(unit_resolution,[status(thm)],[1335, 1268, 1265])).
% 5.70/6.00 tff(1337,plain,(r(s(s(s(elem!1))), z) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.00 tff(1338,plain,
% 5.70/6.00 (r(s(s(s(elem!1))), z)),
% 5.70/6.00 inference(unit_resolution,[status(thm)],[1337, 328, 182, 326, 297, 10, 327])).
% 5.70/6.00 tff(1339,plain,
% 5.70/6.00 (~r(s(s(s(elem!1))), s(z))),
% 5.70/6.00 inference(unit_resolution,[status(thm)],[200, 194, 1338, 59, 182])).
% 5.70/6.00 tff(1340,plain,
% 5.70/6.00 (b(s(s(s(elem!1))), s(z))),
% 5.70/6.00 inference(unit_resolution,[status(thm)],[223, 1339])).
% 5.70/6.00 tff(1341,plain,
% 5.70/6.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.70/6.00 inference(rewrite,[status(thm)],[])).
% 5.70/6.00 tff(1342,plain,
% 5.70/6.00 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.70/6.00 inference(rewrite,[status(thm)],[])).
% 5.70/6.00 tff(1343,plain,
% 5.70/6.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 5.70/6.00 inference(monotonicity,[status(thm)],[1342])).
% 5.70/6.00 tff(1344,plain,
% 5.70/6.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.70/6.00 inference(transitivity,[status(thm)],[1343, 1341])).
% 5.70/6.00 tff(1345,plain,
% 5.70/6.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.00 inference(quant_inst,[status(thm)],[])).
% 5.70/6.00 tff(1346,plain,
% 5.70/6.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 5.70/6.00 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 5.70/6.00 tff(1347,plain,
% 5.70/6.00 ($false),
% 5.70/6.00 inference(unit_resolution,[status(thm)],[1346, 391, 1264, 1287, 1340, 328])).
% 5.70/6.00 tff(1348,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.00 tff(1349,plain,
% 5.70/6.00 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 5.70/6.00 inference(unit_resolution,[status(thm)],[1348, 327, 326, 297, 10, 182])).
% 5.70/6.00 tff(1350,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 5.70/6.00 tff(1351,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 5.70/6.00 tff(1352,plain,
% 5.70/6.00 (((~![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)))))),
% 5.70/6.00 inference(rewrite,[status(thm)],[])).
% 5.70/6.00 tff(1353,plain,
% 5.70/6.00 ((~![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)))))),
% 5.70/6.01 inference(quant_inst,[status(thm)],[])).
% 5.70/6.01 tff(1354,plain,
% 5.70/6.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 5.70/6.01 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 5.70/6.01 tff(1355,plain,
% 5.70/6.01 ($false),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1354, 42, 1351, 270, 1350])).
% 5.70/6.01 tff(1356,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.01 tff(1357,plain,
% 5.70/6.01 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1356, 1349, 315])).
% 5.70/6.01 tff(1358,plain,
% 5.70/6.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.01 inference(rewrite,[status(thm)],[])).
% 5.70/6.01 tff(1359,plain,
% 5.70/6.01 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.01 inference(rewrite,[status(thm)],[])).
% 5.70/6.01 tff(1360,plain,
% 5.70/6.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 5.70/6.01 inference(monotonicity,[status(thm)],[1359])).
% 5.70/6.01 tff(1361,plain,
% 5.70/6.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.01 inference(transitivity,[status(thm)],[1360, 1358])).
% 5.70/6.01 tff(1362,plain,
% 5.70/6.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 5.70/6.01 inference(quant_inst,[status(thm)],[])).
% 5.70/6.01 tff(1363,plain,
% 5.70/6.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 5.70/6.01 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 5.70/6.01 tff(1364,plain,
% 5.70/6.01 ($false),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1363, 194, 59, 327, 326, 1357])).
% 5.70/6.01 tff(1365,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.01 tff(1366,plain,
% 5.70/6.01 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1365, 325, 297, 10, 181])).
% 5.70/6.01 tff(1367,plain,
% 5.70/6.01 (((~![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))))),
% 5.70/6.01 inference(rewrite,[status(thm)],[])).
% 5.70/6.01 tff(1368,plain,
% 5.70/6.01 ((~![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))))),
% 5.70/6.01 inference(quant_inst,[status(thm)],[])).
% 5.70/6.01 tff(1369,plain,
% 5.70/6.01 ((~![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)))),
% 5.70/6.01 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 5.70/6.01 tff(1370,plain,
% 5.70/6.01 ((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)))),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1369, 42])).
% 5.70/6.01 tff(1371,plain,
% 5.70/6.01 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1370, 1366, 297])).
% 5.70/6.01 tff(1372,plain,
% 5.70/6.01 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1356, 1351, 270])).
% 5.70/6.01 tff(1373,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 5.70/6.01 tff(1374,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 5.70/6.01 tff(1375,plain,
% 5.70/6.01 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 5.70/6.01 inference(commutativity,[status(thm)],[])).
% 5.70/6.01 tff(1376,plain,
% 5.70/6.01 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 5.70/6.01 inference(symmetry,[status(thm)],[1375])).
% 5.70/6.01 tff(1377,plain,
% 5.70/6.01 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 5.70/6.01 inference(monotonicity,[status(thm)],[1376])).
% 5.70/6.01 tff(1378,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 5.70/6.01 tff(1379,plain,
% 5.70/6.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.01 inference(rewrite,[status(thm)],[])).
% 5.70/6.01 tff(1380,plain,
% 5.70/6.01 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.01 inference(rewrite,[status(thm)],[])).
% 5.70/6.01 tff(1381,plain,
% 5.70/6.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 5.70/6.01 inference(monotonicity,[status(thm)],[1380])).
% 5.70/6.01 tff(1382,plain,
% 5.70/6.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.01 inference(transitivity,[status(thm)],[1381, 1379])).
% 5.70/6.01 tff(1383,plain,
% 5.70/6.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 5.70/6.01 inference(quant_inst,[status(thm)],[])).
% 5.70/6.01 tff(1384,plain,
% 5.70/6.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 5.70/6.01 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 5.70/6.01 tff(1385,plain,
% 5.70/6.01 ($false),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1384, 194, 233, 184, 326, 1378])).
% 5.70/6.01 tff(1386,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.01 tff(1387,plain,
% 5.70/6.01 (~r(s(s(s(elem!1))), elem!1)),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1386, 1378, 326, 59])).
% 5.70/6.01 tff(1388,plain,
% 5.70/6.01 (s(s(s(elem!1))) = elem!1),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[230, 168, 1387])).
% 5.70/6.01 tff(1389,plain,
% 5.70/6.01 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 5.70/6.01 inference(monotonicity,[status(thm)],[1388])).
% 5.70/6.01 tff(1390,plain,
% 5.70/6.01 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 5.70/6.01 inference(transitivity,[status(thm)],[1389, 698])).
% 5.70/6.01 tff(1391,plain,
% 5.70/6.01 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 5.70/6.01 inference(monotonicity,[status(thm)],[1390])).
% 5.70/6.01 tff(1392,assumption,(s(s(z)) = s(s(s(elem!1)))), introduced(assumption)).
% 5.70/6.01 tff(1393,plain,
% 5.70/6.01 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 5.70/6.01 inference(monotonicity,[status(thm)],[1392])).
% 5.70/6.01 tff(1394,plain,
% 5.70/6.01 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 5.70/6.01 inference(symmetry,[status(thm)],[1393])).
% 5.70/6.01 tff(1395,plain,
% 5.70/6.01 (s(s(elem!1)) = s(z)),
% 5.70/6.01 inference(transitivity,[status(thm)],[212, 1394, 705])).
% 5.70/6.01 tff(1396,plain,
% 5.70/6.01 ($false),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[357, 1395])).
% 5.70/6.01 tff(1397,plain,(~(s(s(z)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.01 tff(1398,plain,
% 5.70/6.01 (~(elem!1 = s(s(z)))),
% 5.70/6.01 inference(modus_ponens,[status(thm)],[1397, 1391])).
% 5.70/6.01 tff(1399,assumption,(s(s(s(s(z)))) = s(s(elem!1))), introduced(assumption)).
% 5.70/6.01 tff(1400,plain,
% 5.70/6.01 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 5.70/6.01 inference(monotonicity,[status(thm)],[1399])).
% 5.70/6.01 tff(1401,plain,
% 5.70/6.01 (s(s(s(z))) = s(elem!1)),
% 5.70/6.01 inference(transitivity,[status(thm)],[693, 1400, 259])).
% 5.70/6.01 tff(1402,plain,
% 5.70/6.01 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 5.70/6.01 inference(monotonicity,[status(thm)],[1401])).
% 5.70/6.01 tff(1403,plain,
% 5.70/6.01 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 5.70/6.01 inference(symmetry,[status(thm)],[1402])).
% 5.70/6.01 tff(1404,plain,
% 5.70/6.01 (elem!1 = s(s(z))),
% 5.70/6.01 inference(transitivity,[status(thm)],[261, 1403, 685])).
% 5.70/6.01 tff(1405,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 5.70/6.01 tff(1406,plain,
% 5.70/6.01 ($false),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1405, 1404])).
% 5.70/6.01 tff(1407,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.01 tff(1408,plain,
% 5.70/6.01 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 5.70/6.01 inference(unit_resolution,[status(thm)],[1407, 1398])).
% 5.70/6.01 tff(1409,plain,
% 5.70/6.01 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 5.70/6.01 inference(modus_ponens,[status(thm)],[1408, 1377])).
% 5.70/6.01 tff(1410,plain,
% 5.70/6.01 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 5.70/6.01 inference(monotonicity,[status(thm)],[1388])).
% 5.70/6.01 tff(1411,plain,
% 5.70/6.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.01 inference(rewrite,[status(thm)],[])).
% 5.70/6.01 tff(1412,plain,
% 5.70/6.01 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.01 inference(rewrite,[status(thm)],[])).
% 5.70/6.01 tff(1413,plain,
% 5.70/6.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 5.70/6.01 inference(monotonicity,[status(thm)],[1412])).
% 5.70/6.01 tff(1414,plain,
% 5.70/6.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.02 inference(transitivity,[status(thm)],[1413, 1411])).
% 5.70/6.02 tff(1415,plain,
% 5.70/6.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 5.70/6.02 inference(quant_inst,[status(thm)],[])).
% 5.70/6.02 tff(1416,plain,
% 5.70/6.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 5.70/6.02 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 5.70/6.02 tff(1417,plain,
% 5.70/6.02 ($false),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1416, 194, 184, 326, 183, 1378])).
% 5.70/6.02 tff(1418,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.02 tff(1419,plain,
% 5.70/6.02 (~r(s(s(s(elem!1))), s(z))),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1418, 1378, 326, 59])).
% 5.70/6.02 tff(1420,plain,
% 5.70/6.02 (b(s(s(s(elem!1))), s(z))),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[223, 1419])).
% 5.70/6.02 tff(1421,plain,
% 5.70/6.02 (b(elem!1, s(z))),
% 5.70/6.02 inference(modus_ponens,[status(thm)],[1420, 1410])).
% 5.70/6.02 tff(1422,plain,
% 5.70/6.02 (elem!1 = s(s(s(elem!1)))),
% 5.70/6.02 inference(symmetry,[status(thm)],[5])).
% 5.70/6.02 tff(1423,plain,
% 5.70/6.02 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 5.70/6.02 inference(transitivity,[status(thm)],[688, 1422])).
% 5.70/6.02 tff(1424,plain,
% 5.70/6.02 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 5.70/6.02 inference(monotonicity,[status(thm)],[1423])).
% 5.70/6.02 tff(1425,plain,
% 5.70/6.02 (s(s(s(z))) = s(s(elem!1))),
% 5.70/6.02 inference(transitivity,[status(thm)],[693, 1424, 211])).
% 5.70/6.02 tff(1426,plain,
% 5.70/6.02 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 5.70/6.02 inference(monotonicity,[status(thm)],[1425])).
% 5.70/6.02 tff(1427,plain,
% 5.70/6.02 (s(s(z)) = s(elem!1)),
% 5.70/6.02 inference(transitivity,[status(thm)],[710, 1426, 259])).
% 5.70/6.02 tff(1428,plain,
% 5.70/6.02 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 5.70/6.02 inference(monotonicity,[status(thm)],[1427])).
% 5.70/6.02 tff(1429,plain,
% 5.70/6.02 (s(z) = elem!1),
% 5.70/6.02 inference(transitivity,[status(thm)],[706, 1428, 108])).
% 5.70/6.02 tff(1430,plain,
% 5.70/6.02 (elem!1 = s(s(s(s(z))))),
% 5.70/6.02 inference(symmetry,[status(thm)],[688])).
% 5.70/6.02 tff(1431,plain,
% 5.70/6.02 ((s(z) = elem!1) <=> (s(z) = s(s(s(s(z)))))),
% 5.70/6.02 inference(monotonicity,[status(thm)],[1430])).
% 5.70/6.02 tff(1432,plain,
% 5.70/6.02 ((s(z) = s(s(s(s(z))))) <=> (s(z) = elem!1)),
% 5.70/6.02 inference(symmetry,[status(thm)],[1431])).
% 5.70/6.02 tff(1433,plain,
% 5.70/6.02 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(z) = elem!1))),
% 5.70/6.02 inference(monotonicity,[status(thm)],[1432])).
% 5.70/6.02 tff(1434,plain,
% 5.70/6.02 (~(s(z) = elem!1)),
% 5.70/6.02 inference(modus_ponens,[status(thm)],[743, 1433])).
% 5.70/6.02 tff(1435,plain,
% 5.70/6.02 ($false),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1434, 1429])).
% 5.70/6.02 tff(1436,plain,((~(s(s(s(elem!1))) = elem!1)) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.02 tff(1437,plain,
% 5.70/6.02 (~(s(s(s(s(z)))) = elem!1)),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1436, 1388])).
% 5.70/6.02 tff(1438,plain,
% 5.70/6.02 (~(elem!1 = s(s(s(s(z)))))),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[769, 1437])).
% 5.70/6.02 tff(1439,plain,
% 5.70/6.02 (~(elem!1 = s(s(s(elem!1))))),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[147, 80, 10])).
% 5.70/6.02 tff(1440,plain,
% 5.70/6.02 (~(s(s(s(elem!1))) = elem!1)),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[8, 1439])).
% 5.70/6.02 tff(1441,plain,
% 5.70/6.02 (b(s(s(s(elem!1))), elem!1)),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[230, 1440, 1387])).
% 5.70/6.02 tff(1442,plain,
% 5.70/6.02 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[929, 1440])).
% 5.70/6.02 tff(1443,plain,
% 5.70/6.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.02 inference(rewrite,[status(thm)],[])).
% 5.70/6.02 tff(1444,plain,
% 5.70/6.02 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.02 inference(rewrite,[status(thm)],[])).
% 5.70/6.02 tff(1445,plain,
% 5.70/6.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 5.70/6.02 inference(monotonicity,[status(thm)],[1444])).
% 5.70/6.02 tff(1446,plain,
% 5.70/6.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.70/6.02 inference(transitivity,[status(thm)],[1445, 1443])).
% 5.70/6.02 tff(1447,plain,
% 5.70/6.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 5.70/6.02 inference(quant_inst,[status(thm)],[])).
% 5.70/6.02 tff(1448,plain,
% 5.70/6.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 5.70/6.02 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 5.70/6.02 tff(1449,plain,
% 5.70/6.02 ($false),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1448, 194, 174, 184, 326, 1378])).
% 5.70/6.02 tff(1450,plain,((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.02 tff(1451,plain,
% 5.70/6.02 (~r(s(s(s(elem!1))), z)),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1450, 1378, 326, 59])).
% 5.70/6.02 tff(1452,plain,
% 5.70/6.02 (b(s(s(s(elem!1))), z)),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[377, 1451])).
% 5.70/6.02 tff(1453,plain,
% 5.70/6.02 (~r(s(s(s(elem!1))), z)),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1450, 1378, 326, 184])).
% 5.70/6.02 tff(1454,plain,
% 5.70/6.02 (b(s(s(s(elem!1))), z)),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[377, 1453])).
% 5.70/6.02 tff(1455,plain,
% 5.70/6.02 (~(s(s(elem!1)) = elem!1)),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[912, 381, 31])).
% 5.70/6.02 tff(1456,plain,
% 5.70/6.02 (~(elem!1 = s(s(elem!1)))),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1292, 1455])).
% 5.70/6.02 tff(1457,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 5.70/6.02 tff(1458,plain,
% 5.70/6.02 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 5.70/6.02 inference(monotonicity,[status(thm)],[812])).
% 5.70/6.02 tff(1459,plain,
% 5.70/6.02 (b(s(s(elem!1)), elem!1)),
% 5.70/6.02 inference(modus_ponens,[status(thm)],[381, 1458])).
% 5.70/6.02 tff(1460,plain,
% 5.70/6.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 5.70/6.02 inference(rewrite,[status(thm)],[])).
% 5.70/6.02 tff(1461,plain,
% 5.70/6.02 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 5.70/6.02 inference(rewrite,[status(thm)],[])).
% 5.70/6.02 tff(1462,plain,
% 5.70/6.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 5.70/6.02 inference(monotonicity,[status(thm)],[1461])).
% 5.70/6.02 tff(1463,plain,
% 5.70/6.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 5.70/6.02 inference(transitivity,[status(thm)],[1462, 1460])).
% 5.70/6.02 tff(1464,plain,
% 5.70/6.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 5.70/6.02 inference(quant_inst,[status(thm)],[])).
% 5.70/6.02 tff(1465,plain,
% 5.70/6.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 5.70/6.02 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 5.70/6.02 tff(1466,plain,
% 5.70/6.02 ($false),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1465, 391, 900, 973, 1374, 1294])).
% 5.70/6.02 tff(1467,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.70/6.02 tff(1468,plain,
% 5.70/6.02 (~b(elem!1, s(s(elem!1)))),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1467, 1459, 1374, 900])).
% 5.70/6.02 tff(1469,plain,
% 5.70/6.02 (r(elem!1, s(s(elem!1)))),
% 5.70/6.02 inference(unit_resolution,[status(thm)],[1307, 1468, 1457])).
% 5.70/6.02 tff(1470,plain,
% 5.70/6.02 (r(s(z), z) <=> r(elem!1, z)),
% 5.70/6.02 inference(monotonicity,[status(thm)],[812])).
% 5.70/6.02 tff(1471,plain,
% 5.70/6.02 (r(elem!1, z)),
% 5.70/6.02 inference(modus_ponens,[status(thm)],[182, 1470])).
% 5.70/6.02 tff(1472,plain,
% 5.70/6.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 5.70/6.02 inference(rewrite,[status(thm)],[])).
% 5.70/6.02 tff(1473,plain,
% 5.70/6.02 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 5.70/6.02 inference(rewrite,[status(thm)],[])).
% 5.70/6.02 tff(1474,plain,
% 5.70/6.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))))),
% 5.82/6.03 inference(monotonicity,[status(thm)],[1473])).
% 5.82/6.03 tff(1475,plain,
% 5.82/6.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 5.82/6.03 inference(transitivity,[status(thm)],[1474, 1472])).
% 5.82/6.03 tff(1476,plain,
% 5.82/6.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 5.82/6.03 inference(quant_inst,[status(thm)],[])).
% 5.82/6.03 tff(1477,plain,
% 5.82/6.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))),
% 5.82/6.03 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 5.82/6.03 tff(1478,plain,
% 5.82/6.03 ($false),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[1477, 194, 1471, 326, 1469, 1378])).
% 5.82/6.03 tff(1479,plain,((~(s(z) = elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.03 tff(1480,plain,
% 5.82/6.03 (~(s(z) = elem!1)),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[1479, 1456, 1378, 326, 1374, 900, 182, 381])).
% 5.82/6.03 tff(1481,plain,
% 5.82/6.03 (~(elem!1 = s(z))),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[172, 1480])).
% 5.82/6.03 tff(1482,plain,
% 5.82/6.03 (r(elem!1, z)),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[526, 2, 484])).
% 5.82/6.03 tff(1483,plain,
% 5.82/6.03 (~r(elem!1, s(z))),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[855, 1482, 326, 182])).
% 5.82/6.03 tff(1484,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 5.82/6.03 tff(1485,plain,
% 5.82/6.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 5.82/6.03 inference(rewrite,[status(thm)],[])).
% 5.82/6.03 tff(1486,plain,
% 5.82/6.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 5.82/6.03 inference(quant_inst,[status(thm)],[])).
% 5.82/6.03 tff(1487,plain,
% 5.82/6.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 5.82/6.03 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 5.82/6.03 tff(1488,plain,
% 5.82/6.03 ($false),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[1487, 194, 530, 184, 1484, 182])).
% 5.82/6.03 tff(1489,plain,((~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.03 tff(1490,plain,
% 5.82/6.03 (~r(s(z), elem!1)),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[1489, 1482, 184, 182])).
% 5.82/6.03 tff(1491,plain,
% 5.82/6.03 (b(elem!1, s(z))),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[837, 831, 832])).
% 5.82/6.03 tff(1492,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 5.82/6.03 tff(1493,plain,
% 5.82/6.03 (elem!1 = s(z)),
% 5.82/6.03 inference(modus_ponens,[status(thm)],[812, 1270])).
% 5.82/6.03 tff(1494,plain,
% 5.82/6.03 ($false),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[831, 1493])).
% 5.82/6.03 tff(1495,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.03 tff(1496,plain,
% 5.82/6.03 (~(s(z) = elem!1)),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[1495, 831])).
% 5.82/6.03 tff(1497,plain,
% 5.82/6.03 (b(s(z), elem!1)),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[632, 1496, 1492])).
% 5.82/6.03 tff(1498,plain,
% 5.82/6.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 5.82/6.03 inference(rewrite,[status(thm)],[])).
% 5.82/6.03 tff(1499,plain,
% 5.82/6.03 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 5.82/6.03 inference(rewrite,[status(thm)],[])).
% 5.82/6.03 tff(1500,plain,
% 5.82/6.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 5.82/6.03 inference(monotonicity,[status(thm)],[1499])).
% 5.82/6.03 tff(1501,plain,
% 5.82/6.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 5.82/6.03 inference(transitivity,[status(thm)],[1500, 1498])).
% 5.82/6.03 tff(1502,plain,
% 5.82/6.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 5.82/6.03 inference(quant_inst,[status(thm)],[])).
% 5.82/6.03 tff(1503,plain,
% 5.82/6.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 5.82/6.03 inference(modus_ponens,[status(thm)],[1502, 1501])).
% 5.82/6.03 tff(1504,plain,
% 5.82/6.03 ($false),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[1503, 391, 133, 900, 380, 1497, 1491])).
% 5.82/6.03 tff(1505,plain,((elem!1 = s(z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.03 tff(1506,plain,
% 5.82/6.03 ($false),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[1505, 1490, 149, 900, 380, 831, 1483])).
% 5.82/6.03 tff(1507,plain,((elem!1 = z) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (elem!1 = s(z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | r(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 5.82/6.03 tff(1508,plain,
% 5.82/6.03 (b(elem!1, z)),
% 5.82/6.03 inference(unit_resolution,[status(thm)],[1507, 2, 380, 831, 326, 182, 184, 80, 900])).
% 5.82/6.03 tff(1509,plain,
% 5.82/6.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 5.82/6.03 inference(rewrite,[status(thm)],[])).
% 5.82/6.03 tff(1510,plain,
% 5.82/6.03 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 5.82/6.04 inference(rewrite,[status(thm)],[])).
% 5.82/6.04 tff(1511,plain,
% 5.82/6.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1510])).
% 5.82/6.04 tff(1512,plain,
% 5.82/6.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 5.82/6.04 inference(transitivity,[status(thm)],[1511, 1509])).
% 5.82/6.04 tff(1513,plain,
% 5.82/6.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 5.82/6.04 inference(quant_inst,[status(thm)],[])).
% 5.82/6.04 tff(1514,plain,
% 5.82/6.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))),
% 5.82/6.04 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 5.82/6.04 tff(1515,plain,
% 5.82/6.04 ($false),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1514, 391, 149, 1508, 900, 380])).
% 5.82/6.04 tff(1516,plain,((elem!1 = z) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | r(z, elem!1) | (elem!1 = s(z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.04 tff(1517,plain,
% 5.82/6.04 (elem!1 = z),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1516, 1481, 1454, 80, 900, 326, 182, 184])).
% 5.82/6.04 tff(1518,plain,
% 5.82/6.04 (s(elem!1) = s(z)),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1517])).
% 5.82/6.04 tff(1519,plain,
% 5.82/6.04 (s(s(elem!1)) = s(s(z))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1518])).
% 5.82/6.04 tff(1520,plain,
% 5.82/6.04 (s(s(z)) = s(s(elem!1))),
% 5.82/6.04 inference(symmetry,[status(thm)],[1519])).
% 5.82/6.04 tff(1521,plain,
% 5.82/6.04 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1520])).
% 5.82/6.04 tff(1522,plain,
% 5.82/6.04 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 5.82/6.04 inference(symmetry,[status(thm)],[1521])).
% 5.82/6.04 tff(1523,plain,
% 5.82/6.04 (b(s(s(z)), s(z))),
% 5.82/6.04 inference(modus_ponens,[status(thm)],[381, 1522])).
% 5.82/6.04 tff(1524,plain,
% 5.82/6.04 (~r(s(s(s(elem!1))), s(z))),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1418, 1378, 326, 184])).
% 5.82/6.04 tff(1525,plain,
% 5.82/6.04 (b(s(s(s(elem!1))), s(z))),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[223, 1524])).
% 5.82/6.04 tff(1526,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 5.82/6.04 tff(1527,plain,
% 5.82/6.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.82/6.04 inference(rewrite,[status(thm)],[])).
% 5.82/6.04 tff(1528,plain,
% 5.82/6.04 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(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))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.82/6.04 inference(rewrite,[status(thm)],[])).
% 5.82/6.04 tff(1529,plain,
% 5.82/6.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1528])).
% 5.82/6.04 tff(1530,plain,
% 5.82/6.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 5.82/6.04 inference(transitivity,[status(thm)],[1529, 1527])).
% 5.82/6.04 tff(1531,plain,
% 5.82/6.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(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)))))),
% 5.82/6.04 inference(quant_inst,[status(thm)],[])).
% 5.82/6.04 tff(1532,plain,
% 5.82/6.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 5.82/6.04 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 5.82/6.04 tff(1533,plain,
% 5.82/6.04 ($false),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1532, 391, 381, 380, 1374, 379, 1526])).
% 5.82/6.04 tff(1534,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.04 tff(1535,plain,
% 5.82/6.04 (~b(s(z), s(s(s(elem!1))))),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1534, 381, 1454, 1374, 1525])).
% 5.82/6.04 tff(1536,plain,
% 5.82/6.04 (r(s(z), s(s(s(elem!1))))),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[247, 1535])).
% 5.82/6.04 tff(1537,plain,
% 5.82/6.04 (~r(s(s(s(elem!1))), s(elem!1))),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[641, 1536, 184, 182])).
% 5.82/6.04 tff(1538,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 5.82/6.04 tff(1539,plain,
% 5.82/6.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 5.82/6.04 inference(rewrite,[status(thm)],[])).
% 5.82/6.04 tff(1540,plain,
% 5.82/6.04 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 5.82/6.04 inference(rewrite,[status(thm)],[])).
% 5.82/6.04 tff(1541,plain,
% 5.82/6.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1540])).
% 5.82/6.04 tff(1542,plain,
% 5.82/6.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 5.82/6.04 inference(transitivity,[status(thm)],[1541, 1539])).
% 5.82/6.04 tff(1543,plain,
% 5.82/6.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 5.82/6.04 inference(quant_inst,[status(thm)],[])).
% 5.82/6.04 tff(1544,plain,
% 5.82/6.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 5.82/6.04 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 5.82/6.04 tff(1545,plain,
% 5.82/6.04 ($false),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1544, 194, 184, 232, 1538, 182])).
% 5.82/6.04 tff(1546,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.04 tff(1547,plain,
% 5.82/6.04 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1546, 1536, 184, 182])).
% 5.82/6.04 tff(1548,plain,
% 5.82/6.04 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1164, 1547, 1373])).
% 5.82/6.04 tff(1549,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 5.82/6.04 tff(1550,plain,
% 5.82/6.04 (s(elem!1) = s(s(z))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[169])).
% 5.82/6.04 tff(1551,plain,
% 5.82/6.04 (s(s(elem!1)) = s(s(s(z)))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1550])).
% 5.82/6.04 tff(1552,plain,
% 5.82/6.04 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1551])).
% 5.82/6.04 tff(1553,plain,
% 5.82/6.04 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1552])).
% 5.82/6.04 tff(1554,plain,
% 5.82/6.04 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 5.82/6.04 inference(symmetry,[status(thm)],[1553])).
% 5.82/6.04 tff(1555,plain,
% 5.82/6.04 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1554])).
% 5.82/6.04 tff(1556,plain,
% 5.82/6.04 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[169])).
% 5.82/6.04 tff(1557,plain,
% 5.82/6.04 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(z)))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1556])).
% 5.82/6.04 tff(1558,plain,
% 5.82/6.04 (~b(s(s(s(s(z)))), s(z))),
% 5.82/6.04 inference(modus_ponens,[status(thm)],[1549, 1557])).
% 5.82/6.04 tff(1559,plain,
% 5.82/6.04 (~b(s(s(s(elem!1))), s(z))),
% 5.82/6.04 inference(modus_ponens,[status(thm)],[1558, 1555])).
% 5.82/6.04 tff(1560,plain,
% 5.82/6.04 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 5.82/6.04 inference(monotonicity,[status(thm)],[169])).
% 5.82/6.04 tff(1561,plain,
% 5.82/6.04 (b(s(s(s(elem!1))), s(z))),
% 5.82/6.04 inference(modus_ponens,[status(thm)],[900, 1560])).
% 5.82/6.04 tff(1562,plain,
% 5.82/6.04 ($false),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1561, 1559])).
% 5.82/6.04 tff(1563,plain,((~(elem!1 = s(z))) | b(s(s(s(s(z)))), elem!1) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.04 tff(1564,plain,
% 5.82/6.04 (~(elem!1 = s(z))),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1563, 1549, 900])).
% 5.82/6.04 tff(1565,plain,
% 5.82/6.04 (elem!1 = z),
% 5.82/6.04 inference(unit_resolution,[status(thm)],[1516, 1564, 380, 80, 900, 326, 182, 184])).
% 5.82/6.04 tff(1566,plain,
% 5.82/6.04 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1565])).
% 5.82/6.04 tff(1567,plain,
% 5.82/6.04 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 5.82/6.04 inference(symmetry,[status(thm)],[1566])).
% 5.82/6.04 tff(1568,plain,
% 5.82/6.04 (s(elem!1) = s(z)),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1565])).
% 5.82/6.04 tff(1569,plain,
% 5.82/6.04 (r(s(elem!1), z) <=> r(s(z), z)),
% 5.82/6.04 inference(monotonicity,[status(thm)],[1568])).
% 5.82/6.04 tff(1570,plain,
% 5.82/6.04 (r(s(z), z) <=> r(s(elem!1), z)),
% 5.82/6.04 inference(symmetry,[status(thm)],[1569])).
% 5.82/6.04 tff(1571,plain,
% 5.82/6.05 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 5.82/6.05 inference(transitivity,[status(thm)],[1570, 1567])).
% 5.82/6.05 tff(1572,plain,
% 5.82/6.05 (r(s(elem!1), elem!1)),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[182, 1571])).
% 5.82/6.05 tff(1573,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 5.82/6.05 tff(1574,plain,
% 5.82/6.05 (r(s(elem!1), z)),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[182, 1570])).
% 5.82/6.05 tff(1575,assumption,(~r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 5.82/6.05 tff(1576,plain,
% 5.82/6.05 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(z))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1568])).
% 5.82/6.05 tff(1577,plain,
% 5.82/6.05 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 5.82/6.05 inference(transitivity,[status(thm)],[1576, 204])).
% 5.82/6.05 tff(1578,plain,
% 5.82/6.05 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.82/6.05 inference(symmetry,[status(thm)],[1577])).
% 5.82/6.05 tff(1579,plain,
% 5.82/6.05 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1578])).
% 5.82/6.05 tff(1580,plain,
% 5.82/6.05 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[217, 1579])).
% 5.82/6.05 tff(1581,plain,
% 5.82/6.05 (b(s(s(s(elem!1))), s(elem!1))),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[588, 1580, 1575])).
% 5.82/6.05 tff(1582,plain,
% 5.82/6.05 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[11])).
% 5.82/6.05 tff(1583,plain,
% 5.82/6.05 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 5.82/6.05 inference(symmetry,[status(thm)],[1582])).
% 5.82/6.05 tff(1584,plain,
% 5.82/6.05 (r(elem!1, s(s(s(elem!1))))),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[184, 1583])).
% 5.82/6.05 tff(1585,plain,
% 5.82/6.05 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 5.82/6.05 inference(commutativity,[status(thm)],[])).
% 5.82/6.05 tff(1586,plain,
% 5.82/6.05 ((elem!1 = s(s(s(s(elem!1))))) <=> (z = s(s(s(s(elem!1)))))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[11])).
% 5.82/6.05 tff(1587,plain,
% 5.82/6.05 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 5.82/6.05 inference(transitivity,[status(thm)],[1586, 1585])).
% 5.82/6.05 tff(1588,plain,
% 5.82/6.05 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 5.82/6.05 inference(symmetry,[status(thm)],[1587])).
% 5.82/6.05 tff(1589,plain,
% 5.82/6.05 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 5.82/6.05 inference(transitivity,[status(thm)],[1588, 964])).
% 5.82/6.05 tff(1590,plain,
% 5.82/6.05 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1589])).
% 5.82/6.05 tff(1591,plain,
% 5.82/6.05 (~(s(s(s(s(elem!1)))) = elem!1)),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[955, 1590])).
% 5.82/6.05 tff(1592,plain,
% 5.82/6.05 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 5.82/6.05 inference(monotonicity,[status(thm)],[11])).
% 5.82/6.05 tff(1593,plain,
% 5.82/6.05 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 5.82/6.05 inference(symmetry,[status(thm)],[1592])).
% 5.82/6.05 tff(1594,plain,
% 5.82/6.05 (s(z) = s(elem!1)),
% 5.82/6.05 inference(symmetry,[status(thm)],[488])).
% 5.82/6.05 tff(1595,plain,
% 5.82/6.05 ($false),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[121, 1594])).
% 5.82/6.05 tff(1596,plain,((~(elem!1 = z)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.05 tff(1597,plain,
% 5.82/6.05 (s(z) = s(elem!1)),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[1596, 11])).
% 5.82/6.05 tff(1598,plain,
% 5.82/6.05 (s(s(z)) = s(s(elem!1))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1597])).
% 5.82/6.05 tff(1599,plain,
% 5.82/6.05 (s(s(s(z))) = s(s(s(elem!1)))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1598])).
% 5.82/6.05 tff(1600,plain,
% 5.82/6.05 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1599])).
% 5.82/6.05 tff(1601,plain,
% 5.82/6.05 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1600])).
% 5.82/6.05 tff(1602,plain,
% 5.82/6.05 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 5.82/6.05 inference(transitivity,[status(thm)],[1601, 1593])).
% 5.82/6.05 tff(1603,plain,
% 5.82/6.05 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1602])).
% 5.82/6.05 tff(1604,plain,
% 5.82/6.05 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 5.82/6.05 inference(monotonicity,[status(thm)],[11])).
% 5.82/6.05 tff(1605,plain,
% 5.82/6.05 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), z))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1604])).
% 5.82/6.05 tff(1606,plain,
% 5.82/6.05 (~b(s(s(s(s(z)))), z)),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[1549, 1605])).
% 5.82/6.05 tff(1607,plain,
% 5.82/6.05 (~b(s(s(s(s(elem!1)))), elem!1)),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[1606, 1603])).
% 5.82/6.05 tff(1608,plain,
% 5.82/6.05 (r(s(s(s(s(elem!1)))), elem!1)),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[1004, 1607, 1591])).
% 5.82/6.05 tff(1609,plain,
% 5.82/6.05 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[999, 1608, 1584, 485])).
% 5.82/6.05 tff(1610,plain,
% 5.82/6.05 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[988, 1609, 957])).
% 5.82/6.05 tff(1611,plain,
% 5.82/6.05 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 5.82/6.05 inference(symmetry,[status(thm)],[1600])).
% 5.82/6.05 tff(1612,plain,
% 5.82/6.05 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1611])).
% 5.82/6.05 tff(1613,plain,
% 5.82/6.05 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 5.82/6.05 inference(symmetry,[status(thm)],[1612])).
% 5.82/6.05 tff(1614,plain,
% 5.82/6.05 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1613])).
% 5.82/6.05 tff(1615,plain,
% 5.82/6.05 (s(elem!1) = s(z)),
% 5.82/6.05 inference(symmetry,[status(thm)],[1597])).
% 5.82/6.05 tff(1616,plain,
% 5.82/6.05 ((s(elem!1) = s(s(s(s(z))))) <=> (s(z) = s(s(s(s(z)))))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1615])).
% 5.82/6.05 tff(1617,plain,
% 5.82/6.05 ((s(z) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 5.82/6.05 inference(symmetry,[status(thm)],[1616])).
% 5.82/6.05 tff(1618,plain,
% 5.82/6.05 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1617])).
% 5.82/6.05 tff(1619,plain,
% 5.82/6.05 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[743, 1618])).
% 5.82/6.05 tff(1620,plain,
% 5.82/6.05 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[1619, 1614])).
% 5.82/6.05 tff(1621,plain,
% 5.82/6.05 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1601])).
% 5.82/6.05 tff(1622,plain,
% 5.82/6.05 (~b(s(s(s(s(elem!1)))), z)),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[1606, 1621])).
% 5.82/6.05 tff(1623,plain,
% 5.82/6.05 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 5.82/6.05 inference(rewrite,[status(thm)],[])).
% 5.82/6.05 tff(1624,plain,
% 5.82/6.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 5.82/6.05 inference(quant_inst,[status(thm)],[])).
% 5.82/6.05 tff(1625,plain,
% 5.82/6.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 5.82/6.05 tff(1626,plain,
% 5.82/6.05 (b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[1625, 42, 955])).
% 5.82/6.05 tff(1627,plain,
% 5.82/6.05 (r(s(s(s(s(elem!1)))), z)),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[1626, 1622])).
% 5.82/6.05 tff(1628,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 5.82/6.05 tff(1629,plain,
% 5.82/6.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 5.82/6.05 inference(rewrite,[status(thm)],[])).
% 5.82/6.05 tff(1630,plain,
% 5.82/6.05 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 5.82/6.05 inference(rewrite,[status(thm)],[])).
% 5.82/6.05 tff(1631,plain,
% 5.82/6.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 5.82/6.05 inference(monotonicity,[status(thm)],[1630])).
% 5.82/6.05 tff(1632,plain,
% 5.82/6.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 5.82/6.05 inference(transitivity,[status(thm)],[1631, 1629])).
% 5.82/6.05 tff(1633,plain,
% 5.82/6.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 5.82/6.05 inference(quant_inst,[status(thm)],[])).
% 5.82/6.05 tff(1634,plain,
% 5.82/6.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 5.82/6.05 tff(1635,plain,
% 5.82/6.05 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[1634, 194, 1628, 184, 1627])).
% 5.82/6.05 tff(1636,plain,
% 5.82/6.05 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), 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(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 5.82/6.05 inference(rewrite,[status(thm)],[])).
% 5.82/6.05 tff(1637,plain,
% 5.82/6.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 5.82/6.05 inference(quant_inst,[status(thm)],[])).
% 5.82/6.05 tff(1638,plain,
% 5.82/6.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 5.82/6.05 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 5.82/6.05 tff(1639,plain,
% 5.82/6.05 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[1638, 42])).
% 5.82/6.05 tff(1640,plain,
% 5.82/6.05 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 5.82/6.05 inference(unit_resolution,[status(thm)],[1639, 1635, 1620])).
% 5.82/6.05 tff(1641,plain,
% 5.82/6.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 5.82/6.05 inference(rewrite,[status(thm)],[])).
% 5.82/6.05 tff(1642,plain,
% 5.82/6.05 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 5.82/6.05 inference(rewrite,[status(thm)],[])).
% 5.82/6.05 tff(1643,plain,
% 5.82/6.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 5.82/6.06 inference(monotonicity,[status(thm)],[1642])).
% 5.82/6.06 tff(1644,plain,
% 5.82/6.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 5.82/6.06 inference(transitivity,[status(thm)],[1643, 1641])).
% 5.82/6.06 tff(1645,plain,
% 5.82/6.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 5.82/6.06 inference(quant_inst,[status(thm)],[])).
% 5.82/6.06 tff(1646,plain,
% 5.82/6.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 5.82/6.06 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 5.82/6.06 tff(1647,plain,
% 5.82/6.06 ($false),
% 5.82/6.06 inference(unit_resolution,[status(thm)],[1646, 391, 1101, 1573, 1640, 1610])).
% 5.82/6.06 tff(1648,plain,((~(elem!1 = z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.82/6.06 tff(1649,plain,
% 5.82/6.06 ($false),
% 5.82/6.06 inference(unit_resolution,[status(thm)],[1648, 1581, 1574, 1573, 1565, 184, 957, 1572, 1549])).
% 5.82/6.06 tff(1650,plain,(b(s(s(s(s(z)))), elem!1) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | r(z, elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.06 tff(1651,plain,
% 5.82/6.06 (b(s(s(s(s(z)))), elem!1)),
% 5.82/6.06 inference(unit_resolution,[status(thm)],[1650, 1548, 184, 80, 1537, 182, 1454, 957, 900, 326])).
% 5.82/6.06 tff(1652,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 5.82/6.06 tff(1653,plain,
% 5.82/6.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 5.82/6.06 inference(rewrite,[status(thm)],[])).
% 5.82/6.06 tff(1654,plain,
% 5.82/6.06 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~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))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 5.82/6.06 inference(rewrite,[status(thm)],[])).
% 5.82/6.06 tff(1655,plain,
% 5.82/6.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 5.82/6.06 inference(monotonicity,[status(thm)],[1654])).
% 5.82/6.06 tff(1656,plain,
% 5.82/6.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 5.82/6.06 inference(transitivity,[status(thm)],[1655, 1653])).
% 5.82/6.06 tff(1657,plain,
% 5.82/6.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~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)))))),
% 5.82/6.06 inference(quant_inst,[status(thm)],[])).
% 5.82/6.06 tff(1658,plain,
% 5.82/6.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 5.82/6.06 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 5.82/6.06 tff(1659,plain,
% 5.82/6.06 ($false),
% 5.82/6.06 inference(unit_resolution,[status(thm)],[1658, 391, 381, 1374, 1526, 1652, 1234])).
% 5.82/6.06 tff(1660,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.06 tff(1661,plain,
% 5.82/6.06 (~b(s(z), s(s(s(s(z)))))),
% 5.82/6.06 inference(unit_resolution,[status(thm)],[1660, 381, 1374, 1525, 1651])).
% 5.82/6.06 tff(1662,plain,
% 5.82/6.06 (r(s(z), s(s(s(s(z)))))),
% 5.82/6.06 inference(unit_resolution,[status(thm)],[1230, 1661])).
% 5.82/6.06 tff(1663,plain,
% 5.82/6.06 (s(s(s(elem!1))) = s(s(s(z)))),
% 5.82/6.06 inference(monotonicity,[status(thm)],[1519])).
% 5.82/6.06 tff(1664,plain,
% 5.82/6.06 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 5.82/6.06 inference(monotonicity,[status(thm)],[1663])).
% 5.82/6.06 tff(1665,plain,
% 5.82/6.06 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.82/6.06 inference(monotonicity,[status(thm)],[1664])).
% 5.82/6.06 tff(1666,plain,
% 5.82/6.06 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.82/6.06 inference(modus_ponens,[status(thm)],[1548, 1665])).
% 5.82/6.06 tff(1667,plain,
% 5.82/6.06 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 5.82/6.06 inference(monotonicity,[status(thm)],[491])).
% 5.82/6.06 tff(1668,plain,
% 5.82/6.06 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 5.82/6.06 inference(symmetry,[status(thm)],[1667])).
% 5.82/6.06 tff(1669,assumption,(b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 5.82/6.06 tff(1670,plain,
% 5.82/6.06 (b(s(s(s(z))), s(s(s(s(z)))))),
% 5.82/6.06 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 5.82/6.06 tff(1671,assumption,(~b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 5.82/6.06 tff(1672,plain,
% 5.82/6.06 ($false),
% 5.82/6.06 inference(unit_resolution,[status(thm)],[1671, 1670])).
% 5.82/6.06 tff(1673,plain,(b(s(s(s(z))), s(s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.06 tff(1674,plain,
% 5.82/6.06 (b(s(s(s(z))), s(s(s(s(z)))))),
% 5.82/6.06 inference(unit_resolution,[status(thm)],[1673, 1666, 1517])).
% 5.82/6.06 tff(1675,plain,
% 5.82/6.06 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 5.82/6.06 inference(monotonicity,[status(thm)],[491])).
% 5.82/6.06 tff(1676,plain,
% 5.82/6.06 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 5.82/6.06 inference(symmetry,[status(thm)],[1675])).
% 5.82/6.06 tff(1677,plain,
% 5.82/6.06 (b(s(s(s(z))), z)),
% 5.82/6.06 inference(modus_ponens,[status(thm)],[380, 1676])).
% 5.82/6.06 tff(1678,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 5.82/6.06 tff(1679,plain,
% 5.82/6.06 ($false),
% 5.82/6.06 inference(unit_resolution,[status(thm)],[1678, 1677])).
% 5.82/6.06 tff(1680,plain,(b(s(s(s(z))), z) | (~b(s(s(s(elem!1))), z)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.06 tff(1681,plain,
% 5.82/6.06 (b(s(s(s(z))), z)),
% 5.82/6.06 inference(unit_resolution,[status(thm)],[1680, 1517, 1454])).
% 5.82/6.06 tff(1682,plain,
% 5.82/6.06 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 5.82/6.06 inference(monotonicity,[status(thm)],[1517])).
% 5.82/6.06 tff(1683,plain,
% 5.82/6.06 (b(s(s(s(s(z)))), z)),
% 5.82/6.06 inference(modus_ponens,[status(thm)],[1651, 1682])).
% 5.82/6.06 tff(1684,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 5.82/6.06 tff(1685,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 5.82/6.06 tff(1686,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 5.82/6.06 tff(1687,plain,
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% 5.82/6.06 inference(rewrite,[status(thm)],[])).
% 5.82/6.06 tff(1688,plain,
% 5.82/6.06 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 5.82/6.06 inference(rewrite,[status(thm)],[])).
% 5.82/6.06 tff(1689,plain,
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% 5.82/6.06 inference(monotonicity,[status(thm)],[1688])).
% 5.82/6.07 tff(1690,plain,
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% 5.82/6.07 inference(transitivity,[status(thm)],[1689, 1687])).
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% 5.82/6.07 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 5.82/6.07 tff(1693,plain,
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% 5.82/6.07 inference(unit_resolution,[status(thm)],[1692, 391, 90, 1686, 1685, 1684])).
% 5.82/6.07 tff(1694,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.07 tff(1695,plain,
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% 5.82/6.07 inference(unit_resolution,[status(thm)],[1694, 1683, 1681, 1674])).
% 5.82/6.07 tff(1696,plain,
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% 5.82/6.07 inference(unit_resolution,[status(thm)],[800, 1695])).
% 5.82/6.07 tff(1697,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
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% 5.82/6.07 tff(1699,plain,
% 5.82/6.07 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
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% 5.82/6.07 tff(1700,plain,
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% 5.82/6.07 inference(monotonicity,[status(thm)],[1699])).
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% 5.82/6.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 5.82/6.07 inference(transitivity,[status(thm)],[1700, 1698])).
% 5.82/6.07 tff(1702,plain,
% 5.82/6.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 5.82/6.07 inference(quant_inst,[status(thm)],[])).
% 5.82/6.07 tff(1703,plain,
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% 5.82/6.07 tff(1704,plain,
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% 5.82/6.07 inference(unit_resolution,[status(thm)],[1703, 194, 182, 1216, 1697, 719])).
% 5.82/6.07 tff(1705,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.07 tff(1706,plain,
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% 5.82/6.07 tff(1707,plain,
% 5.82/6.07 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 5.82/6.07 inference(symmetry,[status(thm)],[940])).
% 5.82/6.07 tff(1708,plain,
% 5.82/6.07 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 5.82/6.07 inference(monotonicity,[status(thm)],[1707])).
% 5.82/6.07 tff(1709,plain,
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% 5.82/6.07 inference(modus_ponens,[status(thm)],[714, 1708])).
% 5.82/6.07 tff(1710,plain,
% 5.82/6.07 (((~![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))))),
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% 5.82/6.07 tff(1711,plain,
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% 5.82/6.07 tff(1712,plain,
% 5.82/6.07 ((~![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)))),
% 5.82/6.07 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 5.82/6.07 tff(1713,plain,
% 5.82/6.07 ((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)))),
% 5.82/6.07 inference(unit_resolution,[status(thm)],[1712, 42])).
% 5.82/6.07 tff(1714,plain,
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% 5.82/6.07 tff(1715,plain,
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% 5.82/6.07 tff(1717,plain,
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% 5.82/6.07 tff(1718,plain,
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% 5.82/6.07 tff(1719,plain,
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% 5.82/6.07 tff(1724,plain,
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% 5.82/6.07 inference(monotonicity,[status(thm)],[1727])).
% 5.82/6.07 tff(1729,plain,
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% 5.82/6.07 inference(monotonicity,[status(thm)],[1664, 1519])).
% 5.82/6.07 tff(1731,plain,
% 5.82/6.07 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
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% 5.82/6.07 tff(1732,plain,
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% 5.82/6.07 tff(1733,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
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% 5.82/6.07 tff(1735,plain,
% 5.82/6.07 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(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(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
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% 5.82/6.07 tff(1736,plain,
% 5.82/6.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 5.82/6.07 inference(monotonicity,[status(thm)],[1735])).
% 5.82/6.07 tff(1737,plain,
% 5.82/6.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 5.82/6.08 inference(transitivity,[status(thm)],[1736, 1734])).
% 5.82/6.08 tff(1738,plain,
% 5.82/6.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(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(elem!1)))))))),
% 5.82/6.08 inference(quant_inst,[status(thm)],[])).
% 5.82/6.08 tff(1739,plain,
% 5.82/6.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 5.82/6.08 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 5.82/6.08 tff(1740,plain,
% 5.82/6.08 ($false),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1739, 391, 1374, 1733, 1573, 1152])).
% 5.82/6.08 tff(1741,plain,((~b(s(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(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.08 tff(1742,plain,
% 5.82/6.08 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1741, 1732, 1374, 1548])).
% 5.82/6.08 tff(1743,plain,
% 5.82/6.08 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1048, 1742, 1729])).
% 5.82/6.08 tff(1744,plain,
% 5.82/6.08 (r(s(s(z)), s(s(s(s(z)))))),
% 5.82/6.08 inference(modus_ponens,[status(thm)],[1743, 1723])).
% 5.82/6.08 tff(1745,plain,
% 5.82/6.08 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(z)))),
% 5.82/6.08 inference(monotonicity,[status(thm)],[1270])).
% 5.82/6.08 tff(1746,plain,
% 5.82/6.08 (~(elem!1 = s(z))),
% 5.82/6.08 inference(modus_ponens,[status(thm)],[150, 1745])).
% 5.82/6.08 tff(1747,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 5.82/6.08 tff(1748,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 5.82/6.08 tff(1749,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 5.82/6.08 tff(1750,plain,
% 5.82/6.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 5.82/6.08 inference(rewrite,[status(thm)],[])).
% 5.82/6.08 tff(1751,plain,
% 5.82/6.08 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 5.82/6.08 inference(rewrite,[status(thm)],[])).
% 5.82/6.08 tff(1752,plain,
% 5.82/6.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))))),
% 5.82/6.08 inference(monotonicity,[status(thm)],[1751])).
% 5.82/6.08 tff(1753,plain,
% 5.82/6.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 5.82/6.08 inference(transitivity,[status(thm)],[1752, 1750])).
% 5.82/6.08 tff(1754,plain,
% 5.82/6.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))),
% 5.82/6.08 inference(quant_inst,[status(thm)],[])).
% 5.82/6.08 tff(1755,plain,
% 5.82/6.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))),
% 5.82/6.08 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 5.82/6.08 tff(1756,plain,
% 5.82/6.08 (~r(elem!1, s(z))),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1755, 194, 1749, 1748, 1747])).
% 5.82/6.08 tff(1757,plain,
% 5.82/6.08 ((elem!1 = s(z)) | b(elem!1, s(z))),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[835, 42, 1756])).
% 5.82/6.08 tff(1758,plain,
% 5.82/6.08 (b(elem!1, s(z))),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1757, 1746])).
% 5.82/6.08 tff(1759,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 5.82/6.08 tff(1760,plain,
% 5.82/6.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 5.82/6.08 inference(rewrite,[status(thm)],[])).
% 5.82/6.08 tff(1761,plain,
% 5.82/6.08 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 5.82/6.08 inference(rewrite,[status(thm)],[])).
% 5.82/6.08 tff(1762,plain,
% 5.82/6.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))))),
% 5.82/6.08 inference(monotonicity,[status(thm)],[1761])).
% 5.82/6.08 tff(1763,plain,
% 5.82/6.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 5.82/6.08 inference(transitivity,[status(thm)],[1762, 1760])).
% 5.82/6.08 tff(1764,plain,
% 5.82/6.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)))),
% 5.82/6.08 inference(quant_inst,[status(thm)],[])).
% 5.82/6.08 tff(1765,plain,
% 5.82/6.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))),
% 5.82/6.08 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 5.82/6.08 tff(1766,plain,
% 5.82/6.08 (~r(s(z), elem!1)),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1765, 194, 1749, 1748, 1747])).
% 5.82/6.08 tff(1767,plain,
% 5.82/6.08 (b(s(z), elem!1)),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[632, 1766, 150])).
% 5.82/6.08 tff(1768,plain,
% 5.82/6.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 5.82/6.08 inference(rewrite,[status(thm)],[])).
% 5.82/6.08 tff(1769,plain,
% 5.82/6.08 (((~b(elem!1, s(z))) | (~b(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))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 5.82/6.08 inference(rewrite,[status(thm)],[])).
% 5.82/6.08 tff(1770,plain,
% 5.82/6.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 5.82/6.08 inference(monotonicity,[status(thm)],[1769])).
% 5.82/6.08 tff(1771,plain,
% 5.82/6.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 5.82/6.08 inference(transitivity,[status(thm)],[1770, 1768])).
% 5.82/6.08 tff(1772,plain,
% 5.82/6.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(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)))),
% 5.82/6.08 inference(quant_inst,[status(thm)],[])).
% 5.82/6.08 tff(1773,plain,
% 5.82/6.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 5.82/6.08 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 5.82/6.08 tff(1774,plain,
% 5.82/6.08 ($false),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1773, 391, 1767, 1652, 1759, 1758])).
% 5.82/6.08 tff(1775,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (s(z) = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.08 tff(1776,plain,
% 5.82/6.08 (~r(s(z), s(s(z)))),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1775, 1744, 1722, 1480, 1717, 1651])).
% 5.82/6.08 tff(1777,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 5.82/6.08 tff(1778,plain,
% 5.82/6.08 (inj_0(s(z)) = inj_0(s(s(z)))),
% 5.82/6.08 inference(monotonicity,[status(thm)],[1777])).
% 5.82/6.08 tff(1779,plain,
% 5.82/6.08 (inj_0(s(s(z))) = inj_0(s(z))),
% 5.82/6.08 inference(symmetry,[status(thm)],[1778])).
% 5.82/6.08 tff(1780,plain,
% 5.82/6.08 (s(s(z)) = s(z)),
% 5.82/6.08 inference(symmetry,[status(thm)],[1777])).
% 5.82/6.08 tff(1781,plain,
% 5.82/6.08 (s(s(z)) = z),
% 5.82/6.08 inference(transitivity,[status(thm)],[1780, 706, 1779, 112])).
% 5.82/6.08 tff(1782,plain,
% 5.82/6.08 ($false),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1207, 1781])).
% 5.82/6.08 tff(1783,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.08 tff(1784,plain,
% 5.82/6.08 (((~![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))))),
% 5.82/6.08 inference(rewrite,[status(thm)],[])).
% 5.82/6.08 tff(1785,plain,
% 5.82/6.08 ((~![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))))),
% 5.82/6.08 inference(quant_inst,[status(thm)],[])).
% 5.82/6.08 tff(1786,plain,
% 5.82/6.08 ((~![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)))),
% 5.82/6.08 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 5.82/6.08 tff(1787,plain,
% 5.82/6.08 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1786, 42])).
% 5.82/6.08 tff(1788,plain,
% 5.82/6.08 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 5.82/6.08 inference(unit_resolution,[status(thm)],[1787, 1783])).
% 5.82/6.08 tff(1789,plain,
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% 5.82/6.08 inference(unit_resolution,[status(thm)],[1788, 1776])).
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% 5.82/6.09 inference(rewrite,[status(thm)],[])).
% 5.82/6.09 tff(1791,plain,
% 5.82/6.09 (((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(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(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 5.82/6.09 inference(rewrite,[status(thm)],[])).
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% 5.82/6.09 inference(monotonicity,[status(thm)],[1791])).
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% 5.82/6.09 inference(transitivity,[status(thm)],[1792, 1790])).
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% 5.82/6.10 inference(monotonicity,[status(thm)],[1833])).
% 5.82/6.10 tff(1857,plain,
% 5.82/6.10 (b(elem!1, s(s(s(s(elem!1)))))),
% 5.82/6.10 inference(modus_ponens,[status(thm)],[1573, 1856])).
% 5.82/6.10 tff(1858,plain,
% 5.82/6.10 (b(elem!1, s(elem!1))),
% 5.82/6.10 inference(modus_ponens,[status(thm)],[1857, 1855])).
% 5.82/6.10 tff(1859,plain,
% 5.82/6.10 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 5.82/6.10 inference(monotonicity,[status(thm)],[1833])).
% 5.82/6.10 tff(1860,plain,
% 5.82/6.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.82/6.10 inference(rewrite,[status(thm)],[])).
% 5.82/6.10 tff(1861,plain,
% 5.82/6.10 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.82/6.10 inference(rewrite,[status(thm)],[])).
% 5.82/6.10 tff(1862,plain,
% 5.82/6.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 5.82/6.10 inference(monotonicity,[status(thm)],[1861])).
% 5.82/6.10 tff(1863,plain,
% 5.82/6.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 5.82/6.10 inference(transitivity,[status(thm)],[1862, 1860])).
% 5.82/6.10 tff(1864,plain,
% 5.82/6.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 5.82/6.10 inference(quant_inst,[status(thm)],[])).
% 5.82/6.10 tff(1865,plain,
% 5.82/6.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 5.82/6.10 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 5.82/6.10 tff(1866,plain,
% 5.82/6.10 ($false),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[1865, 194, 174, 184, 232, 182])).
% 5.82/6.10 tff(1867,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.10 tff(1868,plain,
% 5.82/6.10 (~r(s(s(s(elem!1))), z)),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[1867, 232, 59, 182])).
% 5.82/6.10 tff(1869,plain,
% 5.82/6.10 (b(s(s(s(elem!1))), z)),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[377, 1868])).
% 5.82/6.10 tff(1870,plain,
% 5.82/6.10 (b(elem!1, z)),
% 5.82/6.10 inference(modus_ponens,[status(thm)],[1869, 1859])).
% 5.82/6.10 tff(1871,plain,
% 5.82/6.10 (elem!1 = s(s(s(elem!1)))),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[8, 1833])).
% 5.82/6.10 tff(1872,plain,
% 5.82/6.10 (r(z, elem!1)),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[147, 1871, 10])).
% 5.82/6.10 tff(1873,plain,
% 5.82/6.10 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 5.82/6.10 inference(monotonicity,[status(thm)],[1833])).
% 5.82/6.10 tff(1874,plain,
% 5.82/6.10 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 5.82/6.10 inference(transitivity,[status(thm)],[1873, 92])).
% 5.82/6.10 tff(1875,plain,
% 5.82/6.10 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 5.82/6.10 inference(monotonicity,[status(thm)],[1874])).
% 5.82/6.10 tff(1876,plain,
% 5.82/6.10 (~(z = elem!1)),
% 5.82/6.10 inference(modus_ponens,[status(thm)],[50, 1875])).
% 5.82/6.10 tff(1877,plain,
% 5.82/6.10 (~(s(z) = s(elem!1))),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[117, 1876])).
% 5.82/6.10 tff(1878,plain,
% 5.82/6.10 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 5.82/6.10 inference(monotonicity,[status(thm)],[1833])).
% 5.82/6.10 tff(1879,plain,
% 5.82/6.10 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 5.82/6.10 inference(transitivity,[status(thm)],[1878, 1270])).
% 5.82/6.10 tff(1880,plain,
% 5.82/6.10 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 5.82/6.10 inference(monotonicity,[status(thm)],[1879])).
% 5.82/6.10 tff(1881,plain,
% 5.82/6.10 (~(elem!1 = s(z))),
% 5.82/6.10 inference(modus_ponens,[status(thm)],[217, 1880])).
% 5.82/6.10 tff(1882,plain,
% 5.82/6.10 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 5.82/6.10 inference(monotonicity,[status(thm)],[125])).
% 5.82/6.10 tff(1883,plain,
% 5.82/6.10 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 5.82/6.10 inference(symmetry,[status(thm)],[1882])).
% 5.82/6.10 tff(1884,plain,
% 5.82/6.10 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), elem!1))),
% 5.82/6.10 inference(monotonicity,[status(thm)],[1883])).
% 5.82/6.10 tff(1885,plain,
% 5.82/6.10 (~b(s(s(elem!1)), elem!1)),
% 5.82/6.10 inference(modus_ponens,[status(thm)],[1351, 1884])).
% 5.82/6.10 tff(1886,plain,
% 5.82/6.10 ($false),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[973, 1885])).
% 5.82/6.10 tff(1887,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.10 tff(1888,plain,
% 5.82/6.10 (~b(s(s(elem!1)), elem!1)),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[1887, 1871, 1351])).
% 5.82/6.10 tff(1889,plain,
% 5.82/6.10 (r(s(s(elem!1)), elem!1)),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[872, 1888, 1846])).
% 5.82/6.10 tff(1890,plain,
% 5.82/6.10 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 5.82/6.10 inference(monotonicity,[status(thm)],[1833])).
% 5.82/6.10 tff(1891,plain,
% 5.82/6.10 (r(s(z), elem!1)),
% 5.82/6.10 inference(modus_ponens,[status(thm)],[232, 1890])).
% 5.82/6.10 tff(1892,plain,
% 5.82/6.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 5.82/6.10 inference(rewrite,[status(thm)],[])).
% 5.82/6.10 tff(1893,plain,
% 5.82/6.10 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 5.82/6.10 inference(rewrite,[status(thm)],[])).
% 5.82/6.10 tff(1894,plain,
% 5.82/6.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 5.82/6.10 inference(monotonicity,[status(thm)],[1893])).
% 5.82/6.10 tff(1895,plain,
% 5.82/6.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 5.82/6.10 inference(transitivity,[status(thm)],[1894, 1892])).
% 5.82/6.10 tff(1896,plain,
% 5.82/6.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 5.82/6.10 inference(quant_inst,[status(thm)],[])).
% 5.82/6.10 tff(1897,plain,
% 5.82/6.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))),
% 5.82/6.10 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 5.82/6.10 tff(1898,plain,
% 5.82/6.10 ($false),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[1897, 194, 340, 364, 1484, 847])).
% 5.82/6.10 tff(1899,plain,((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.10 tff(1900,plain,
% 5.82/6.10 (~r(elem!1, s(z))),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[1899, 1891, 340, 1889])).
% 5.82/6.10 tff(1901,plain,
% 5.82/6.10 (b(elem!1, s(z))),
% 5.82/6.10 inference(unit_resolution,[status(thm)],[837, 1900, 1881])).
% 5.82/6.10 tff(1902,plain,
% 5.82/6.10 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 5.82/6.10 inference(commutativity,[status(thm)],[])).
% 5.82/6.10 tff(1903,plain,
% 5.82/6.10 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 5.82/6.10 inference(symmetry,[status(thm)],[1902])).
% 5.82/6.10 tff(1904,plain,
% 5.82/6.10 ((~(s(z) = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 5.82/6.10 inference(monotonicity,[status(thm)],[1903])).
% 5.82/6.10 tff(1905,plain,
% 5.82/6.10 (~(s(elem!1) = s(z))),
% 5.82/6.10 inference(modus_ponens,[status(thm)],[121, 1904])).
% 5.82/6.10 tff(1906,plain,
% 5.82/6.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 5.82/6.10 inference(rewrite,[status(thm)],[])).
% 5.82/6.10 tff(1907,plain,
% 5.82/6.10 (((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 5.82/6.11 inference(rewrite,[status(thm)],[])).
% 5.82/6.11 tff(1908,plain,
% 5.82/6.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 5.82/6.11 inference(monotonicity,[status(thm)],[1907])).
% 5.82/6.11 tff(1909,plain,
% 5.82/6.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 5.82/6.11 inference(transitivity,[status(thm)],[1908, 1906])).
% 5.82/6.11 tff(1910,plain,
% 5.82/6.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 5.82/6.11 inference(quant_inst,[status(thm)],[])).
% 5.82/6.11 tff(1911,plain,
% 5.82/6.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 5.82/6.11 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 5.82/6.11 tff(1912,plain,
% 5.82/6.11 (~r(s(elem!1), s(z))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1911, 194, 411, 1628, 182])).
% 5.82/6.11 tff(1913,plain,
% 5.82/6.11 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 5.82/6.11 inference(rewrite,[status(thm)],[])).
% 5.82/6.11 tff(1914,plain,
% 5.82/6.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 5.82/6.11 inference(quant_inst,[status(thm)],[])).
% 5.82/6.11 tff(1915,plain,
% 5.82/6.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 5.82/6.11 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 5.82/6.11 tff(1916,plain,
% 5.82/6.11 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1915, 42, 1912])).
% 5.82/6.11 tff(1917,plain,
% 5.82/6.11 (b(s(elem!1), s(z))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1916, 1905])).
% 5.82/6.11 tff(1918,plain,
% 5.82/6.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 5.82/6.11 inference(rewrite,[status(thm)],[])).
% 5.82/6.11 tff(1919,plain,
% 5.82/6.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 5.82/6.11 inference(quant_inst,[status(thm)],[])).
% 5.82/6.11 tff(1920,plain,
% 5.82/6.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 5.82/6.11 inference(modus_ponens,[status(thm)],[1919, 1918])).
% 5.82/6.11 tff(1921,plain,
% 5.82/6.11 (~r(s(z), s(elem!1))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1920, 194, 411, 1628, 182])).
% 5.82/6.11 tff(1922,plain,
% 5.82/6.11 (b(s(z), s(elem!1))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[602, 42, 121, 1921])).
% 5.82/6.11 tff(1923,plain,
% 5.82/6.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 5.82/6.11 inference(rewrite,[status(thm)],[])).
% 5.82/6.11 tff(1924,plain,
% 5.82/6.11 (((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 5.82/6.11 inference(rewrite,[status(thm)],[])).
% 5.82/6.11 tff(1925,plain,
% 5.82/6.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))))),
% 5.82/6.11 inference(monotonicity,[status(thm)],[1924])).
% 5.82/6.11 tff(1926,plain,
% 5.82/6.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 5.82/6.11 inference(transitivity,[status(thm)],[1925, 1923])).
% 5.82/6.11 tff(1927,plain,
% 5.82/6.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))),
% 5.82/6.11 inference(quant_inst,[status(thm)],[])).
% 5.82/6.11 tff(1928,plain,
% 5.82/6.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))),
% 5.82/6.11 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 5.82/6.11 tff(1929,plain,
% 5.82/6.11 ($false),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1928, 391, 802, 1922, 721, 1917])).
% 5.82/6.11 tff(1930,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.11 tff(1931,plain,
% 5.82/6.11 (~r(s(elem!1), z)),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1930, 1901, 1858, 1877, 1872, 182])).
% 5.82/6.11 tff(1932,plain,
% 5.82/6.11 (b(s(elem!1), z)),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[549, 1931])).
% 5.82/6.11 tff(1933,plain,
% 5.82/6.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 5.82/6.11 inference(rewrite,[status(thm)],[])).
% 5.82/6.11 tff(1934,plain,
% 5.82/6.11 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 5.82/6.11 inference(rewrite,[status(thm)],[])).
% 5.82/6.11 tff(1935,plain,
% 5.82/6.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))))),
% 5.82/6.11 inference(monotonicity,[status(thm)],[1934])).
% 5.82/6.11 tff(1936,plain,
% 5.82/6.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 5.82/6.11 inference(transitivity,[status(thm)],[1935, 1933])).
% 5.82/6.11 tff(1937,plain,
% 5.82/6.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 5.82/6.11 inference(quant_inst,[status(thm)],[])).
% 5.82/6.11 tff(1938,plain,
% 5.82/6.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))),
% 5.82/6.11 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 5.82/6.11 tff(1939,plain,
% 5.82/6.11 ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1938, 391])).
% 5.82/6.11 tff(1940,plain,
% 5.82/6.11 (~b(z, s(elem!1))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1939, 1932, 1870, 1858])).
% 5.82/6.11 tff(1941,plain,
% 5.82/6.11 (r(z, s(elem!1))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[566, 1940])).
% 5.82/6.11 tff(1942,plain,
% 5.82/6.11 ($false),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[249, 154])).
% 5.82/6.11 tff(1943,plain,((~(s(elem!1) = elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.82/6.11 tff(1944,plain,
% 5.82/6.11 (~(s(elem!1) = elem!1)),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1943, 1846])).
% 5.82/6.11 tff(1945,assumption,(s(elem!1) = s(s(s(s(z))))), introduced(assumption)).
% 5.82/6.11 tff(1946,plain,
% 5.82/6.11 (s(s(s(s(z)))) = s(elem!1)),
% 5.82/6.11 inference(symmetry,[status(thm)],[1945])).
% 5.82/6.11 tff(1947,plain,
% 5.82/6.11 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 5.82/6.11 inference(monotonicity,[status(thm)],[1946])).
% 5.82/6.11 tff(1948,plain,
% 5.82/6.11 (s(s(s(z))) = s(s(s(elem!1)))),
% 5.82/6.11 inference(transitivity,[status(thm)],[693, 1947, 108, 1422])).
% 5.82/6.11 tff(1949,plain,
% 5.82/6.11 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 5.82/6.11 inference(monotonicity,[status(thm)],[1948])).
% 5.82/6.11 tff(1950,plain,
% 5.82/6.11 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 5.82/6.11 inference(symmetry,[status(thm)],[1949])).
% 5.82/6.11 tff(1951,plain,
% 5.82/6.11 (s(s(elem!1)) = s(s(z))),
% 5.82/6.11 inference(transitivity,[status(thm)],[212, 1950, 685])).
% 5.82/6.11 tff(1952,plain,
% 5.82/6.11 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 5.82/6.11 inference(monotonicity,[status(thm)],[5])).
% 5.82/6.11 tff(1953,plain,
% 5.82/6.11 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 5.82/6.11 inference(transitivity,[status(thm)],[1952, 92])).
% 5.82/6.11 tff(1954,plain,
% 5.82/6.11 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 5.82/6.11 inference(monotonicity,[status(thm)],[1953])).
% 5.82/6.11 tff(1955,plain,
% 5.82/6.11 (~(z = elem!1)),
% 5.82/6.11 inference(modus_ponens,[status(thm)],[50, 1954])).
% 5.82/6.11 tff(1956,plain,
% 5.82/6.11 (~(s(z) = s(elem!1))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[117, 1955])).
% 5.82/6.11 tff(1957,assumption,(s(s(elem!1)) = s(s(z))), introduced(assumption)).
% 5.82/6.11 tff(1958,plain,
% 5.82/6.11 (s(s(z)) = s(s(elem!1))),
% 5.82/6.11 inference(symmetry,[status(thm)],[1957])).
% 5.82/6.11 tff(1959,plain,
% 5.82/6.11 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 5.82/6.11 inference(monotonicity,[status(thm)],[1958])).
% 5.82/6.11 tff(1960,plain,
% 5.82/6.11 (s(z) = s(elem!1)),
% 5.82/6.11 inference(transitivity,[status(thm)],[706, 1959, 259])).
% 5.82/6.11 tff(1961,plain,
% 5.82/6.11 ($false),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[121, 1960])).
% 5.82/6.11 tff(1962,plain,((~(s(s(elem!1)) = s(s(z)))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.11 tff(1963,plain,
% 5.82/6.11 (~(s(s(elem!1)) = s(s(z)))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1962, 1956])).
% 5.82/6.11 tff(1964,plain,
% 5.82/6.11 ($false),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1963, 1951])).
% 5.82/6.11 tff(1965,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.11 tff(1966,plain,
% 5.82/6.11 (~(s(elem!1) = s(s(s(s(z)))))),
% 5.82/6.11 inference(unit_resolution,[status(thm)],[1965, 1833])).
% 5.82/6.11 tff(1967,plain,
% 5.82/6.11 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 5.82/6.11 inference(monotonicity,[status(thm)],[1833])).
% 5.82/6.11 tff(1968,plain,
% 5.82/6.11 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 5.82/6.11 inference(transitivity,[status(thm)],[1967, 698])).
% 5.82/6.12 tff(1969,plain,
% 5.82/6.12 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 5.82/6.12 inference(monotonicity,[status(thm)],[1968])).
% 5.82/6.12 tff(1970,plain,
% 5.82/6.12 (~(elem!1 = s(s(z)))),
% 5.82/6.12 inference(modus_ponens,[status(thm)],[1397, 1969])).
% 5.82/6.12 tff(1971,plain,
% 5.82/6.12 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 5.82/6.12 inference(unit_resolution,[status(thm)],[1407, 1970])).
% 5.82/6.12 tff(1972,plain,
% 5.82/6.12 (~(elem!1 = s(s(elem!1)))),
% 5.82/6.12 inference(unit_resolution,[status(thm)],[1292, 1846])).
% 5.82/6.12 tff(1973,plain,
% 5.82/6.12 (((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 5.82/6.12 inference(rewrite,[status(thm)],[])).
% 5.82/6.12 tff(1974,plain,
% 5.82/6.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))))),
% 5.82/6.12 inference(monotonicity,[status(thm)],[1973])).
% 5.82/6.12 tff(1975,plain,
% 5.82/6.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 5.82/6.12 inference(transitivity,[status(thm)],[1974, 1317])).
% 5.82/6.12 tff(1976,plain,
% 5.82/6.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 5.82/6.12 inference(quant_inst,[status(thm)],[])).
% 5.82/6.12 tff(1977,plain,
% 5.82/6.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 5.82/6.12 inference(modus_ponens,[status(thm)],[1976, 1975])).
% 5.82/6.12 tff(1978,plain,
% 5.82/6.12 ($false),
% 5.82/6.12 inference(unit_resolution,[status(thm)],[1977, 194, 411, 364, 326, 1064])).
% 5.82/6.12 tff(1979,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.82/6.12 tff(1980,plain,
% 5.82/6.12 (~r(elem!1, s(s(elem!1)))),
% 5.82/6.12 inference(unit_resolution,[status(thm)],[1979, 1889, 1872, 326])).
% 5.82/6.12 tff(1981,plain,
% 5.82/6.12 (b(elem!1, s(s(elem!1)))),
% 5.82/6.12 inference(unit_resolution,[status(thm)],[1307, 1980, 1972])).
% 5.82/6.12 tff(1982,plain,
% 5.82/6.12 (~(s(s(s(s(z)))) = elem!1)),
% 5.82/6.12 inference(unit_resolution,[status(thm)],[1436, 1833])).
% 5.82/6.12 tff(1983,assumption,(~(s(s(s(s(z)))) = s(s(elem!1)))), introduced(assumption)).
% 5.82/6.12 tff(1984,plain,
% 5.82/6.12 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 5.82/6.12 inference(modus_ponens,[status(thm)],[1983, 1377])).
% 5.82/6.12 tff(1985,plain,
% 5.82/6.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 5.82/6.12 inference(rewrite,[status(thm)],[])).
% 5.82/6.12 tff(1986,plain,
% 5.82/6.12 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 5.82/6.12 inference(rewrite,[status(thm)],[])).
% 5.82/6.12 tff(1987,plain,
% 5.82/6.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 5.82/6.12 inference(monotonicity,[status(thm)],[1986])).
% 5.82/6.12 tff(1988,plain,
% 5.82/6.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 5.82/6.12 inference(transitivity,[status(thm)],[1987, 1985])).
% 5.82/6.12 tff(1989,plain,
% 5.82/6.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 5.82/6.12 inference(quant_inst,[status(thm)],[])).
% 5.82/6.12 tff(1990,plain,
% 5.82/6.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 5.82/6.12 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 5.82/6.12 tff(1991,plain,
% 5.82/6.12 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 5.82/6.12 inference(unit_resolution,[status(thm)],[1990, 194, 340, 1484, 723])).
% 5.82/6.12 tff(1992,plain,
% 5.82/6.12 (((~![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))))))),
% 5.82/6.12 inference(rewrite,[status(thm)],[])).
% 5.82/6.12 tff(1993,plain,
% 5.82/6.12 ((~![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))))))),
% 5.82/6.12 inference(quant_inst,[status(thm)],[])).
% 5.82/6.12 tff(1994,plain,
% 5.82/6.12 ((~![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)))))),
% 5.82/6.12 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 5.82/6.12 tff(1995,plain,
% 5.82/6.12 ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z)))))),
% 5.82/6.12 inference(unit_resolution,[status(thm)],[1994, 42, 1991])).
% 5.82/6.12 tff(1996,plain,
% 5.82/6.12 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 5.82/6.12 inference(unit_resolution,[status(thm)],[1995, 1984])).
% 5.82/6.12 tff(1997,plain,
% 5.82/6.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 5.82/6.12 inference(rewrite,[status(thm)],[])).
% 5.82/6.12 tff(1998,plain,
% 5.82/6.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 5.82/6.12 inference(quant_inst,[status(thm)],[])).
% 5.82/6.12 tff(1999,plain,
% 5.82/6.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 5.82/6.12 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 5.82/6.12 tff(2000,plain,
% 5.82/6.12 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 5.82/6.12 inference(unit_resolution,[status(thm)],[1999, 194, 340, 1484, 723])).
% 5.82/6.12 tff(2001,plain,
% 5.82/6.12 (((~![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))))),
% 5.92/6.13 inference(rewrite,[status(thm)],[])).
% 5.92/6.13 tff(2002,plain,
% 5.92/6.13 ((~![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))))),
% 5.92/6.13 inference(quant_inst,[status(thm)],[])).
% 5.92/6.13 tff(2003,plain,
% 5.92/6.13 ((~![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)))),
% 5.92/6.13 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 5.92/6.13 tff(2004,plain,
% 5.92/6.13 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 5.92/6.13 inference(unit_resolution,[status(thm)],[2003, 42, 2000, 1983])).
% 5.92/6.13 tff(2005,plain,
% 5.92/6.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 5.92/6.13 inference(rewrite,[status(thm)],[])).
% 5.92/6.13 tff(2006,plain,
% 5.92/6.13 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 5.92/6.13 inference(rewrite,[status(thm)],[])).
% 5.92/6.13 tff(2007,plain,
% 5.92/6.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 5.92/6.13 inference(monotonicity,[status(thm)],[2006])).
% 5.92/6.13 tff(2008,plain,
% 5.92/6.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 5.92/6.13 inference(transitivity,[status(thm)],[2007, 2005])).
% 5.92/6.13 tff(2009,plain,
% 5.92/6.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.92/6.13 inference(quant_inst,[status(thm)],[])).
% 5.92/6.13 tff(2010,plain,
% 5.92/6.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 5.92/6.13 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 5.92/6.13 tff(2011,plain,
% 5.92/6.13 (~b(s(s(s(s(z)))), elem!1)),
% 5.92/6.13 inference(unit_resolution,[status(thm)],[2010, 391, 1294, 2004, 1996])).
% 5.92/6.13 tff(2012,plain,
% 5.92/6.13 (r(s(s(s(s(z)))), elem!1)),
% 5.92/6.13 inference(unit_resolution,[status(thm)],[762, 2011, 720])).
% 5.92/6.13 tff(2013,plain,
% 5.92/6.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 5.92/6.13 inference(rewrite,[status(thm)],[])).
% 5.92/6.13 tff(2014,plain,
% 5.92/6.13 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 5.92/6.13 inference(rewrite,[status(thm)],[])).
% 5.92/6.13 tff(2015,plain,
% 5.92/6.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 5.92/6.13 inference(monotonicity,[status(thm)],[2014])).
% 5.92/6.13 tff(2016,plain,
% 5.92/6.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 5.92/6.13 inference(transitivity,[status(thm)],[2015, 2013])).
% 5.92/6.13 tff(2017,plain,
% 5.92/6.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 5.92/6.13 inference(quant_inst,[status(thm)],[])).
% 5.92/6.13 tff(2018,plain,
% 5.92/6.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 5.92/6.13 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 5.92/6.13 tff(2019,plain,
% 5.92/6.13 (~b(elem!1, s(s(s(s(z)))))),
% 5.92/6.13 inference(unit_resolution,[status(thm)],[2018, 391, 1294, 2004, 1996])).
% 5.92/6.13 tff(2020,plain,
% 5.92/6.13 (r(elem!1, s(s(s(s(z)))))),
% 5.92/6.13 inference(unit_resolution,[status(thm)],[781, 2019, 770])).
% 5.92/6.13 tff(2021,plain,
% 5.92/6.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.92/6.13 inference(rewrite,[status(thm)],[])).
% 5.92/6.13 tff(2022,plain,
% 5.92/6.13 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.92/6.13 inference(rewrite,[status(thm)],[])).
% 5.92/6.13 tff(2023,plain,
% 5.92/6.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 5.92/6.13 inference(monotonicity,[status(thm)],[2022])).
% 5.92/6.13 tff(2024,plain,
% 5.92/6.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.92/6.13 inference(transitivity,[status(thm)],[2023, 2021])).
% 5.92/6.13 tff(2025,plain,
% 5.92/6.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 5.92/6.13 inference(quant_inst,[status(thm)],[])).
% 5.92/6.13 tff(2026,plain,
% 5.92/6.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 5.92/6.13 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 5.92/6.13 tff(2027,plain,
% 5.92/6.13 ($false),
% 5.92/6.13 inference(unit_resolution,[status(thm)],[2026, 194, 1484, 2020, 2012, 723])).
% 5.92/6.13 tff(2028,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.13 tff(2029,plain,
% 5.92/6.13 (~r(s(s(s(s(z)))), s(z))),
% 5.92/6.13 inference(unit_resolution,[status(thm)],[2028, 1891, 1982, 1981, 1971, 340])).
% 5.92/6.13 tff(2030,plain,
% 5.92/6.13 (b(s(s(s(s(z)))), s(z))),
% 5.92/6.13 inference(unit_resolution,[status(thm)],[749, 2029])).
% 5.92/6.13 tff(2031,plain,
% 5.92/6.13 (~(elem!1 = s(s(s(s(z)))))),
% 5.92/6.13 inference(unit_resolution,[status(thm)],[769, 1982])).
% 5.92/6.13 tff(2032,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 5.92/6.13 tff(2033,plain,
% 5.92/6.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.92/6.13 inference(rewrite,[status(thm)],[])).
% 5.92/6.13 tff(2034,plain,
% 5.92/6.13 (((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.92/6.13 inference(rewrite,[status(thm)],[])).
% 5.92/6.13 tff(2035,plain,
% 5.92/6.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z))))))))),
% 5.92/6.13 inference(monotonicity,[status(thm)],[2034])).
% 5.92/6.13 tff(2036,plain,
% 5.92/6.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.92/6.13 inference(transitivity,[status(thm)],[2035, 2033])).
% 5.92/6.13 tff(2037,plain,
% 5.92/6.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 5.92/6.13 inference(quant_inst,[status(thm)],[])).
% 5.92/6.13 tff(2038,plain,
% 5.92/6.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 5.92/6.13 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 5.92/6.13 tff(2039,plain,
% 5.92/6.13 ($false),
% 5.92/6.13 inference(unit_resolution,[status(thm)],[2038, 194, 411, 1484, 182, 2032])).
% 5.92/6.13 tff(2040,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.14 tff(2041,plain,
% 5.92/6.14 (~r(elem!1, s(s(s(s(z)))))),
% 5.92/6.14 inference(unit_resolution,[status(thm)],[2040, 1872, 1891, 182])).
% 5.92/6.14 tff(2042,plain,
% 5.92/6.14 (b(elem!1, s(s(s(s(z)))))),
% 5.92/6.14 inference(unit_resolution,[status(thm)],[781, 2041, 2031])).
% 5.92/6.14 tff(2043,plain,
% 5.92/6.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.92/6.14 inference(rewrite,[status(thm)],[])).
% 5.92/6.14 tff(2044,plain,
% 5.92/6.14 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.92/6.14 inference(rewrite,[status(thm)],[])).
% 5.92/6.14 tff(2045,plain,
% 5.92/6.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 5.92/6.14 inference(monotonicity,[status(thm)],[2044])).
% 5.92/6.14 tff(2046,plain,
% 5.92/6.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 5.92/6.14 inference(transitivity,[status(thm)],[2045, 2043])).
% 5.92/6.14 tff(2047,plain,
% 5.92/6.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 5.92/6.14 inference(quant_inst,[status(thm)],[])).
% 5.92/6.14 tff(2048,plain,
% 5.92/6.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 5.92/6.14 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 5.92/6.14 tff(2049,plain,
% 5.92/6.14 ($false),
% 5.92/6.14 inference(unit_resolution,[status(thm)],[2048, 391, 665, 591, 802, 90, 1686])).
% 5.92/6.14 tff(2050,plain,((~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.14 tff(2051,plain,
% 5.92/6.14 (~b(s(s(s(s(z)))), z)),
% 5.92/6.14 inference(unit_resolution,[status(thm)],[2050, 1686, 591, 802, 665])).
% 5.92/6.14 tff(2052,plain,
% 5.92/6.14 (r(s(s(s(s(z)))), z)),
% 5.92/6.14 inference(unit_resolution,[status(thm)],[87, 2051])).
% 5.92/6.14 tff(2053,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 5.92/6.14 tff(2054,plain,
% 5.92/6.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 5.92/6.14 inference(rewrite,[status(thm)],[])).
% 5.92/6.14 tff(2055,plain,
% 5.92/6.14 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 5.92/6.14 inference(rewrite,[status(thm)],[])).
% 5.92/6.14 tff(2056,plain,
% 5.92/6.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 5.92/6.14 inference(monotonicity,[status(thm)],[2055])).
% 5.92/6.14 tff(2057,plain,
% 5.92/6.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 5.92/6.14 inference(transitivity,[status(thm)],[2056, 2054])).
% 5.92/6.14 tff(2058,plain,
% 5.92/6.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 5.92/6.14 inference(quant_inst,[status(thm)],[])).
% 5.92/6.14 tff(2059,plain,
% 5.92/6.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 5.92/6.14 inference(modus_ponens,[status(thm)],[2058, 2057])).
% 5.92/6.14 tff(2060,plain,
% 5.92/6.14 ($false),
% 5.92/6.14 inference(unit_resolution,[status(thm)],[2059, 194, 411, 182, 2053, 1216])).
% 5.92/6.14 tff(2061,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.14 tff(2062,plain,
% 5.92/6.14 (~r(s(z), s(s(s(s(z)))))),
% 5.92/6.14 inference(unit_resolution,[status(thm)],[2061, 2052, 182, 411])).
% 5.92/6.14 tff(2063,plain,
% 5.92/6.14 (b(s(z), s(s(s(s(z)))))),
% 5.92/6.14 inference(unit_resolution,[status(thm)],[1230, 2062])).
% 5.92/6.14 tff(2064,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 5.92/6.14 tff(2065,plain,
% 5.92/6.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.92/6.14 inference(rewrite,[status(thm)],[])).
% 5.92/6.14 tff(2066,plain,
% 5.92/6.14 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.92/6.14 inference(rewrite,[status(thm)],[])).
% 5.92/6.14 tff(2067,plain,
% 5.92/6.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 5.92/6.14 inference(monotonicity,[status(thm)],[2066])).
% 5.92/6.14 tff(2068,plain,
% 5.92/6.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.92/6.15 inference(transitivity,[status(thm)],[2067, 2065])).
% 5.92/6.15 tff(2069,plain,
% 5.92/6.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))),
% 5.92/6.15 inference(quant_inst,[status(thm)],[])).
% 5.92/6.15 tff(2070,plain,
% 5.92/6.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 5.92/6.15 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 5.92/6.15 tff(2071,plain,
% 5.92/6.15 ($false),
% 5.92/6.15 inference(unit_resolution,[status(thm)],[2070, 391, 665, 2064, 2063, 1759, 1686])).
% 5.92/6.15 tff(2072,plain,((~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.15 tff(2073,plain,
% 5.92/6.15 (~b(z, s(s(s(s(z)))))),
% 5.92/6.15 inference(unit_resolution,[status(thm)],[2072, 1870, 2042, 2030, 182, 1872, 1932, 1858])).
% 5.92/6.15 tff(2074,plain,
% 5.92/6.15 (r(z, s(s(s(s(z)))))),
% 5.92/6.15 inference(unit_resolution,[status(thm)],[800, 2073])).
% 5.92/6.15 tff(2075,plain,
% 5.92/6.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.92/6.15 inference(rewrite,[status(thm)],[])).
% 5.92/6.15 tff(2076,plain,
% 5.92/6.15 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.92/6.15 inference(rewrite,[status(thm)],[])).
% 5.92/6.15 tff(2077,plain,
% 5.92/6.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 5.92/6.15 inference(monotonicity,[status(thm)],[2076])).
% 5.92/6.15 tff(2078,plain,
% 5.92/6.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.92/6.15 inference(transitivity,[status(thm)],[2077, 2075])).
% 5.92/6.15 tff(2079,plain,
% 5.92/6.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 5.92/6.15 inference(quant_inst,[status(thm)],[])).
% 5.92/6.15 tff(2080,plain,
% 5.92/6.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 5.92/6.15 inference(modus_ponens,[status(thm)],[2079, 2078])).
% 5.92/6.15 tff(2081,plain,
% 5.92/6.15 (~b(s(s(s(s(z)))), elem!1)),
% 5.92/6.15 inference(unit_resolution,[status(thm)],[2080, 391, 1234, 1759, 721])).
% 5.92/6.15 tff(2082,plain,
% 5.92/6.15 (r(s(s(s(s(z)))), elem!1)),
% 5.92/6.15 inference(unit_resolution,[status(thm)],[762, 2081, 720])).
% 5.92/6.15 tff(2083,plain,
% 5.92/6.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.92/6.15 inference(rewrite,[status(thm)],[])).
% 5.92/6.15 tff(2084,plain,
% 5.92/6.15 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.92/6.15 inference(rewrite,[status(thm)],[])).
% 5.92/6.15 tff(2085,plain,
% 5.92/6.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 5.92/6.15 inference(monotonicity,[status(thm)],[2084])).
% 5.92/6.15 tff(2086,plain,
% 5.92/6.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 5.92/6.15 inference(transitivity,[status(thm)],[2085, 2083])).
% 5.92/6.15 tff(2087,plain,
% 5.92/6.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 5.92/6.15 inference(quant_inst,[status(thm)],[])).
% 5.92/6.15 tff(2088,plain,
% 5.92/6.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 5.92/6.15 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 5.92/6.15 tff(2089,plain,
% 5.92/6.15 (~b(elem!1, s(s(s(s(z)))))),
% 5.92/6.15 inference(unit_resolution,[status(thm)],[2088, 391, 1234, 1759, 721])).
% 5.92/6.15 tff(2090,plain,
% 5.92/6.15 (r(elem!1, s(s(s(s(z)))))),
% 5.92/6.15 inference(unit_resolution,[status(thm)],[781, 2089, 770])).
% 5.92/6.15 tff(2091,plain,
% 5.92/6.15 (((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.92/6.15 inference(rewrite,[status(thm)],[])).
% 5.92/6.15 tff(2092,plain,
% 5.92/6.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 5.92/6.15 inference(monotonicity,[status(thm)],[2091])).
% 5.92/6.15 tff(2093,plain,
% 5.92/6.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 5.92/6.15 inference(transitivity,[status(thm)],[2092, 783])).
% 5.92/6.15 tff(2094,plain,
% 5.92/6.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))),
% 5.92/6.15 inference(quant_inst,[status(thm)],[])).
% 5.92/6.15 tff(2095,plain,
% 5.92/6.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 5.92/6.15 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 5.92/6.15 tff(2096,plain,
% 5.92/6.15 ($false),
% 5.92/6.15 inference(unit_resolution,[status(thm)],[2095, 194, 411, 2090, 2082, 719])).
% 5.92/6.15 tff(2097,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.15 tff(2098,plain,
% 5.92/6.15 (~b(s(z), s(s(s(s(z)))))),
% 5.92/6.15 inference(unit_resolution,[status(thm)],[2097, 2074, 2030, 1982, 1872, 1901])).
% 5.92/6.15 tff(2099,plain,
% 5.92/6.15 (r(s(z), s(s(s(s(z)))))),
% 5.92/6.15 inference(unit_resolution,[status(thm)],[1230, 2098])).
% 5.92/6.15 tff(2100,assumption,(r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 5.92/6.15 tff(2101,plain,
% 5.92/6.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 5.92/6.15 inference(rewrite,[status(thm)],[])).
% 5.92/6.15 tff(2102,plain,
% 5.92/6.15 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 5.92/6.15 inference(rewrite,[status(thm)],[])).
% 5.92/6.15 tff(2103,plain,
% 5.92/6.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 5.92/6.15 inference(monotonicity,[status(thm)],[2102])).
% 5.92/6.15 tff(2104,plain,
% 5.92/6.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 5.92/6.15 inference(transitivity,[status(thm)],[2103, 2101])).
% 5.92/6.15 tff(2105,plain,
% 5.92/6.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 5.92/6.16 inference(quant_inst,[status(thm)],[])).
% 5.92/6.16 tff(2106,plain,
% 5.92/6.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 5.92/6.16 tff(2107,plain,
% 5.92/6.16 ($false),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[2106, 194, 182, 1216, 719, 2100])).
% 5.92/6.16 tff(2108,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.16 tff(2109,plain,
% 5.92/6.16 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[2108, 2099, 182, 2074])).
% 5.92/6.16 tff(2110,plain,
% 5.92/6.16 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), elem!1)),
% 5.92/6.16 inference(monotonicity,[status(thm)],[5])).
% 5.92/6.16 tff(2111,plain,
% 5.92/6.16 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.92/6.16 inference(symmetry,[status(thm)],[2110])).
% 5.92/6.16 tff(2112,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 5.92/6.16 tff(2113,plain,
% 5.92/6.16 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 5.92/6.16 tff(2114,assumption,(~r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 5.92/6.16 tff(2115,plain,
% 5.92/6.16 ($false),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[2114, 2113])).
% 5.92/6.16 tff(2116,plain,((~r(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.16 tff(2117,plain,
% 5.92/6.16 (~r(s(s(s(s(z)))), elem!1)),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[2116, 2109, 1833])).
% 5.92/6.16 tff(2118,plain,
% 5.92/6.16 (b(s(s(s(s(z)))), elem!1)),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[762, 2117, 1982])).
% 5.92/6.16 tff(2119,plain,
% 5.92/6.16 (~b(z, s(elem!1))),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[1939, 591, 665, 802])).
% 5.92/6.16 tff(2120,plain,
% 5.92/6.16 (r(z, s(elem!1))),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[566, 2119])).
% 5.92/6.16 tff(2121,assumption,(~(s(elem!1) = s(s(s(s(z)))))), introduced(assumption)).
% 5.92/6.16 tff(2122,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 5.92/6.16 tff(2123,plain,
% 5.92/6.16 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 5.92/6.16 inference(commutativity,[status(thm)],[])).
% 5.92/6.16 tff(2124,plain,
% 5.92/6.16 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 5.92/6.16 inference(symmetry,[status(thm)],[2123])).
% 5.92/6.16 tff(2125,plain,
% 5.92/6.16 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 5.92/6.16 inference(monotonicity,[status(thm)],[2124])).
% 5.92/6.16 tff(2126,plain,
% 5.92/6.16 (~(s(s(s(s(z)))) = s(elem!1))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[2121, 2125])).
% 5.92/6.16 tff(2127,plain,
% 5.92/6.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.92/6.16 inference(rewrite,[status(thm)],[])).
% 5.92/6.16 tff(2128,plain,
% 5.92/6.16 (((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.92/6.16 inference(rewrite,[status(thm)],[])).
% 5.92/6.16 tff(2129,plain,
% 5.92/6.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 5.92/6.16 inference(monotonicity,[status(thm)],[2128])).
% 5.92/6.16 tff(2130,plain,
% 5.92/6.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.92/6.16 inference(transitivity,[status(thm)],[2129, 2127])).
% 5.92/6.16 tff(2131,plain,
% 5.92/6.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 5.92/6.16 inference(quant_inst,[status(thm)],[])).
% 5.92/6.16 tff(2132,plain,
% 5.92/6.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[2131, 2130])).
% 5.92/6.16 tff(2133,plain,
% 5.92/6.16 (~b(s(s(s(s(z)))), s(elem!1))),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[2132, 391, 591, 802, 2122, 1652])).
% 5.92/6.16 tff(2134,plain,
% 5.92/6.16 (((~![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)))),
% 5.92/6.16 inference(rewrite,[status(thm)],[])).
% 5.92/6.16 tff(2135,plain,
% 5.92/6.16 ((~![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)))),
% 5.92/6.16 inference(quant_inst,[status(thm)],[])).
% 5.92/6.16 tff(2136,plain,
% 5.92/6.16 ((~![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))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 5.92/6.16 tff(2137,plain,
% 5.92/6.16 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[2136, 42, 2133])).
% 5.92/6.16 tff(2138,plain,
% 5.92/6.16 (r(s(s(s(s(z)))), s(elem!1))),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[2137, 2126])).
% 5.92/6.16 tff(2139,assumption,(~b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 5.92/6.16 tff(2140,plain,
% 5.92/6.16 (((~![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))))))),
% 5.92/6.16 inference(rewrite,[status(thm)],[])).
% 5.92/6.16 tff(2141,plain,
% 5.92/6.16 ((~![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))))))),
% 5.92/6.16 inference(quant_inst,[status(thm)],[])).
% 5.92/6.16 tff(2142,plain,
% 5.92/6.16 ((~![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)))))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[2141, 2140])).
% 5.92/6.16 tff(2143,plain,
% 5.92/6.16 (r(s(elem!1), s(s(s(s(z)))))),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[2142, 42, 2139, 2121])).
% 5.92/6.16 tff(2144,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 5.92/6.16 tff(2145,plain,
% 5.92/6.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 5.92/6.16 inference(rewrite,[status(thm)],[])).
% 5.92/6.16 tff(2146,plain,
% 5.92/6.16 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 5.92/6.16 inference(rewrite,[status(thm)],[])).
% 5.92/6.16 tff(2147,plain,
% 5.92/6.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 5.92/6.16 inference(monotonicity,[status(thm)],[2146])).
% 5.92/6.16 tff(2148,plain,
% 5.92/6.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 5.92/6.17 inference(transitivity,[status(thm)],[2147, 2145])).
% 5.92/6.17 tff(2149,plain,
% 5.92/6.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 5.92/6.17 inference(quant_inst,[status(thm)],[])).
% 5.92/6.17 tff(2150,plain,
% 5.92/6.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 5.92/6.17 tff(2151,plain,
% 5.92/6.17 ($false),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[2150, 194, 2144, 719, 2143, 2138])).
% 5.92/6.17 tff(2152,plain,(b(s(elem!1), s(s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.17 tff(2153,plain,
% 5.92/6.17 (b(s(elem!1), s(s(s(s(z)))))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[2152, 2122, 719, 2121, 591, 802, 2120, 1652])).
% 5.92/6.17 tff(2154,plain,
% 5.92/6.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(2155,plain,
% 5.92/6.17 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(2156,plain,
% 5.92/6.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 5.92/6.17 inference(monotonicity,[status(thm)],[2155])).
% 5.92/6.17 tff(2157,plain,
% 5.92/6.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 5.92/6.17 inference(transitivity,[status(thm)],[2156, 2154])).
% 5.92/6.17 tff(2158,plain,
% 5.92/6.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))),
% 5.92/6.17 inference(quant_inst,[status(thm)],[])).
% 5.92/6.17 tff(2159,plain,
% 5.92/6.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 5.92/6.17 tff(2160,plain,
% 5.92/6.17 ($false),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[2159, 391, 665, 2122, 2064, 1652, 2153])).
% 5.92/6.17 tff(2161,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.17 tff(2162,plain,
% 5.92/6.17 (~b(s(elem!1), elem!1)),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[2161, 1870, 2042, 2118, 2074, 1966, 1932, 1858])).
% 5.92/6.17 tff(2163,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 5.92/6.17 tff(2164,plain,
% 5.92/6.17 (((~![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))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(2165,plain,
% 5.92/6.17 ((~![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))),
% 5.92/6.17 inference(quant_inst,[status(thm)],[])).
% 5.92/6.17 tff(2166,plain,
% 5.92/6.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 5.92/6.17 tff(2167,plain,
% 5.92/6.17 ($false),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[2166, 42, 469, 164, 2163])).
% 5.92/6.17 tff(2168,plain,(b(s(elem!1), elem!1) | r(s(elem!1), elem!1) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.92/6.17 tff(2169,plain,
% 5.92/6.17 (r(s(elem!1), elem!1)),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[2168, 2162, 1944])).
% 5.92/6.17 tff(2170,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 5.92/6.17 tff(2171,plain,
% 5.92/6.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(2172,plain,
% 5.92/6.17 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(2173,plain,
% 5.92/6.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 5.92/6.17 inference(monotonicity,[status(thm)],[2172])).
% 5.92/6.17 tff(2174,plain,
% 5.92/6.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 5.92/6.17 inference(transitivity,[status(thm)],[2173, 2171])).
% 5.92/6.17 tff(2175,plain,
% 5.92/6.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 5.92/6.17 inference(quant_inst,[status(thm)],[])).
% 5.92/6.17 tff(2176,plain,
% 5.92/6.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[2175, 2174])).
% 5.92/6.17 tff(2177,plain,
% 5.92/6.17 ($false),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[2176, 194, 485, 2144, 326, 2170])).
% 5.92/6.17 tff(2178,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.17 tff(2179,plain,
% 5.92/6.17 (~r(s(s(elem!1)), s(elem!1))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[2178, 2169, 1941, 326])).
% 5.92/6.17 tff(2180,plain,
% 5.92/6.17 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[2179, 1854])).
% 5.92/6.17 tff(2181,plain,
% 5.92/6.17 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[1048, 2180, 1851])).
% 5.92/6.17 tff(2182,plain,
% 5.92/6.17 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[1741, 2181, 1374, 1573])).
% 5.92/6.17 tff(2183,plain,
% 5.92/6.17 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[1061, 2182, 1848])).
% 5.92/6.17 tff(2184,plain,
% 5.92/6.17 (r(s(elem!1), s(s(elem!1)))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[2183, 1835])).
% 5.92/6.17 tff(2185,plain,
% 5.92/6.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(2186,plain,
% 5.92/6.17 (((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(2187,plain,
% 5.92/6.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 5.92/6.17 inference(monotonicity,[status(thm)],[2186])).
% 5.92/6.17 tff(2188,plain,
% 5.92/6.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 5.92/6.17 inference(transitivity,[status(thm)],[2187, 2185])).
% 5.92/6.17 tff(2189,plain,
% 5.92/6.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 5.92/6.17 inference(quant_inst,[status(thm)],[])).
% 5.92/6.17 tff(2190,plain,
% 5.92/6.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[2189, 2188])).
% 5.92/6.17 tff(2191,plain,
% 5.92/6.17 ($false),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[2190, 194, 340, 1941, 326, 2184])).
% 5.92/6.17 tff(2192,plain,(b(s(s(s(elem!1))), elem!1) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.17 tff(2193,plain,
% 5.92/6.17 (b(s(s(s(elem!1))), elem!1)),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[2192, 1829, 326, 1374, 1831, 182, 232, 1351, 10])).
% 5.92/6.17 tff(2194,plain,
% 5.92/6.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.92/6.18 inference(rewrite,[status(thm)],[])).
% 5.92/6.18 tff(2195,plain,
% 5.92/6.18 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.92/6.18 inference(rewrite,[status(thm)],[])).
% 5.92/6.18 tff(2196,plain,
% 5.92/6.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 5.92/6.18 inference(monotonicity,[status(thm)],[2195])).
% 5.92/6.18 tff(2197,plain,
% 5.92/6.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.92/6.18 inference(transitivity,[status(thm)],[2196, 2194])).
% 5.92/6.18 tff(2198,plain,
% 5.92/6.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 5.92/6.18 inference(quant_inst,[status(thm)],[])).
% 5.92/6.18 tff(2199,plain,
% 5.92/6.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 5.92/6.18 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 5.92/6.18 tff(2200,plain,
% 5.92/6.18 ($false),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[2199, 194, 340, 232, 183, 1378])).
% 5.92/6.18 tff(2201,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.18 tff(2202,plain,
% 5.92/6.18 (~r(s(s(s(elem!1))), s(z))),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[2201, 232, 1831, 1378])).
% 5.92/6.18 tff(2203,plain,
% 5.92/6.18 (b(s(s(s(elem!1))), s(z))),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[223, 2202])).
% 5.92/6.18 tff(2204,plain,
% 5.92/6.18 (~(s(elem!1) = elem!1)),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[158, 1440])).
% 5.92/6.18 tff(2205,plain,
% 5.92/6.18 (~(elem!1 = s(elem!1))),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[166, 2204])).
% 5.92/6.18 tff(2206,plain,
% 5.92/6.18 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 5.92/6.18 inference(symmetry,[status(thm)],[250])).
% 5.92/6.18 tff(2207,plain,
% 5.92/6.18 (~r(s(s(s(elem!1))), z)),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[1867, 232, 184, 182])).
% 5.92/6.18 tff(2208,plain,
% 5.92/6.18 (b(s(s(s(elem!1))), z)),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[377, 2207])).
% 5.92/6.18 tff(2209,plain,
% 5.92/6.18 (elem!1 = s(z)),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[1516, 2, 2208, 80, 900, 326, 182, 184])).
% 5.92/6.18 tff(2210,plain,
% 5.92/6.18 (s(z) = elem!1),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[172, 2209])).
% 5.92/6.18 tff(2211,plain,
% 5.92/6.18 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 5.92/6.18 inference(monotonicity,[status(thm)],[2210])).
% 5.92/6.18 tff(2212,plain,
% 5.92/6.18 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 5.92/6.18 inference(transitivity,[status(thm)],[2211, 2206])).
% 5.92/6.18 tff(2213,plain,
% 5.92/6.18 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 5.92/6.18 inference(monotonicity,[status(thm)],[2212])).
% 5.92/6.18 tff(2214,plain,
% 5.92/6.18 (~(elem!1 = s(s(elem!1)))),
% 5.92/6.18 inference(modus_ponens,[status(thm)],[357, 2213])).
% 5.92/6.18 tff(2215,plain,
% 5.92/6.18 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 5.92/6.18 inference(monotonicity,[status(thm)],[812])).
% 5.92/6.18 tff(2216,plain,
% 5.92/6.18 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 5.92/6.18 inference(symmetry,[status(thm)],[2215])).
% 5.92/6.18 tff(2217,plain,
% 5.92/6.18 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(elem!1)), s(z)))),
% 5.92/6.18 inference(monotonicity,[status(thm)],[2216])).
% 5.92/6.18 tff(2218,plain,
% 5.92/6.18 (~r(s(s(elem!1)), s(z))),
% 5.92/6.18 inference(modus_ponens,[status(thm)],[888, 2217])).
% 5.92/6.18 tff(2219,plain,
% 5.92/6.18 ($false),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[340, 2218])).
% 5.92/6.18 tff(2220,plain,((~(s(z) = elem!1)) | (~r(s(s(elem!1)), s(z))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 5.92/6.18 tff(2221,plain,
% 5.92/6.18 (r(s(s(elem!1)), elem!1)),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[2220, 2210, 1831])).
% 5.92/6.18 tff(2222,plain,
% 5.92/6.18 (r(s(z), z) <=> r(elem!1, z)),
% 5.92/6.18 inference(monotonicity,[status(thm)],[2210])).
% 5.92/6.18 tff(2223,plain,
% 5.92/6.18 (r(elem!1, z)),
% 5.92/6.18 inference(modus_ponens,[status(thm)],[182, 2222])).
% 5.92/6.18 tff(2224,plain,
% 5.92/6.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 5.92/6.18 inference(rewrite,[status(thm)],[])).
% 5.92/6.18 tff(2225,plain,
% 5.92/6.18 (((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 5.92/6.18 inference(rewrite,[status(thm)],[])).
% 5.92/6.18 tff(2226,plain,
% 5.92/6.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))))),
% 5.92/6.18 inference(monotonicity,[status(thm)],[2225])).
% 5.92/6.18 tff(2227,plain,
% 5.92/6.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 5.92/6.18 inference(transitivity,[status(thm)],[2226, 2224])).
% 5.92/6.18 tff(2228,plain,
% 5.92/6.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 5.92/6.18 inference(quant_inst,[status(thm)],[])).
% 5.92/6.18 tff(2229,plain,
% 5.92/6.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 5.92/6.18 inference(modus_ponens,[status(thm)],[2228, 2227])).
% 5.92/6.18 tff(2230,plain,
% 5.92/6.18 ($false),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[2229, 194, 530, 364, 326, 1064])).
% 5.92/6.18 tff(2231,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.18 tff(2232,plain,
% 5.92/6.18 (~r(elem!1, s(s(elem!1)))),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[2231, 2223, 2221, 326])).
% 5.92/6.18 tff(2233,plain,
% 5.92/6.18 (b(elem!1, s(s(elem!1)))),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[1307, 2232, 2214])).
% 5.92/6.18 tff(2234,plain,
% 5.92/6.18 (~r(s(s(s(elem!1))), s(elem!1))),
% 5.92/6.18 inference(unit_resolution,[status(thm)],[641, 232, 184, 182])).
% 5.92/6.18 tff(2235,plain,
% 5.92/6.18 (s(s(z)) = s(elem!1)),
% 5.92/6.18 inference(monotonicity,[status(thm)],[2210])).
% 5.92/6.19 tff(2236,plain,
% 5.92/6.19 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 5.92/6.19 inference(monotonicity,[status(thm)],[2235])).
% 5.92/6.19 tff(2237,plain,
% 5.92/6.19 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 5.92/6.19 inference(transitivity,[status(thm)],[2236, 582])).
% 5.92/6.19 tff(2238,plain,
% 5.92/6.19 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 5.92/6.19 inference(monotonicity,[status(thm)],[2237])).
% 5.92/6.19 tff(2239,plain,
% 5.92/6.19 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.92/6.19 inference(modus_ponens,[status(thm)],[1397, 2238])).
% 5.92/6.19 tff(2240,plain,
% 5.92/6.19 (b(s(s(s(elem!1))), s(elem!1))),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[588, 2239, 2234])).
% 5.92/6.19 tff(2241,plain,
% 5.92/6.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 5.92/6.19 inference(rewrite,[status(thm)],[])).
% 5.92/6.19 tff(2242,plain,
% 5.92/6.19 (((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(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)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 5.92/6.19 inference(rewrite,[status(thm)],[])).
% 5.92/6.19 tff(2243,plain,
% 5.92/6.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 5.92/6.19 inference(monotonicity,[status(thm)],[2242])).
% 5.92/6.19 tff(2244,plain,
% 5.92/6.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 5.92/6.19 inference(transitivity,[status(thm)],[2243, 2241])).
% 5.92/6.19 tff(2245,plain,
% 5.92/6.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 5.92/6.19 inference(quant_inst,[status(thm)],[])).
% 5.92/6.19 tff(2246,plain,
% 5.92/6.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 5.92/6.19 inference(modus_ponens,[status(thm)],[2245, 2244])).
% 5.92/6.19 tff(2247,plain,
% 5.92/6.19 ($false),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[2246, 391, 133, 1101, 380, 1294, 591])).
% 5.92/6.19 tff(2248,plain,((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.19 tff(2249,plain,
% 5.92/6.19 (~b(s(elem!1), z)),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[2248, 149, 2240, 2208, 2233])).
% 5.92/6.19 tff(2250,plain,
% 5.92/6.19 (r(s(elem!1), z)),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[549, 2249])).
% 5.92/6.19 tff(2251,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 5.92/6.19 tff(2252,plain,
% 5.92/6.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 5.92/6.19 inference(rewrite,[status(thm)],[])).
% 5.92/6.19 tff(2253,plain,
% 5.92/6.19 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 5.92/6.19 inference(rewrite,[status(thm)],[])).
% 5.92/6.19 tff(2254,plain,
% 5.92/6.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))))),
% 5.92/6.19 inference(monotonicity,[status(thm)],[2253])).
% 5.92/6.19 tff(2255,plain,
% 5.92/6.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 5.92/6.19 inference(transitivity,[status(thm)],[2254, 2252])).
% 5.92/6.19 tff(2256,plain,
% 5.92/6.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 5.92/6.19 inference(quant_inst,[status(thm)],[])).
% 5.92/6.19 tff(2257,plain,
% 5.92/6.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))),
% 5.92/6.19 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 5.92/6.19 tff(2258,plain,
% 5.92/6.19 ($false),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[2257, 194, 530, 1628, 184, 2251])).
% 5.92/6.19 tff(2259,plain,((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.19 tff(2260,plain,
% 5.92/6.19 (~r(elem!1, z)),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[2259, 1628, 184, 2251])).
% 5.92/6.19 tff(2261,plain,
% 5.92/6.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 5.92/6.19 inference(rewrite,[status(thm)],[])).
% 5.92/6.19 tff(2262,plain,
% 5.92/6.19 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 5.92/6.19 inference(rewrite,[status(thm)],[])).
% 5.92/6.19 tff(2263,plain,
% 5.92/6.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))))),
% 5.92/6.19 inference(monotonicity,[status(thm)],[2262])).
% 5.92/6.19 tff(2264,plain,
% 5.92/6.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 5.92/6.19 inference(transitivity,[status(thm)],[2263, 2261])).
% 5.92/6.19 tff(2265,plain,
% 5.92/6.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 5.92/6.19 inference(quant_inst,[status(thm)],[])).
% 5.92/6.19 tff(2266,plain,
% 5.92/6.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 5.92/6.19 inference(modus_ponens,[status(thm)],[2265, 2264])).
% 5.92/6.19 tff(2267,plain,
% 5.92/6.19 (~r(s(z), s(elem!1))),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[2266, 194, 1628, 184, 182])).
% 5.92/6.19 tff(2268,plain,
% 5.92/6.19 (s(elem!1) = s(s(s(elem!1)))),
% 5.92/6.19 inference(symmetry,[status(thm)],[465])).
% 5.92/6.19 tff(2269,plain,
% 5.92/6.19 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 5.92/6.19 inference(monotonicity,[status(thm)],[2268])).
% 5.92/6.19 tff(2270,plain,
% 5.92/6.19 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 5.92/6.19 inference(symmetry,[status(thm)],[2269])).
% 5.92/6.19 tff(2271,plain,
% 5.92/6.19 (r(s(z), s(elem!1))),
% 5.92/6.19 inference(modus_ponens,[status(thm)],[232, 2270])).
% 5.92/6.19 tff(2272,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 5.92/6.19 tff(2273,plain,
% 5.92/6.19 ($false),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[2272, 2271])).
% 5.92/6.19 tff(2274,plain,(r(s(z), s(elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.19 tff(2275,plain,
% 5.92/6.19 (~(s(s(s(elem!1))) = s(elem!1))),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[2274, 2267, 232])).
% 5.92/6.19 tff(2276,plain,
% 5.92/6.19 (s(s(s(elem!1))) = s(s(elem!1))),
% 5.92/6.19 inference(monotonicity,[status(thm)],[251])).
% 5.92/6.19 tff(2277,plain,
% 5.92/6.19 (s(s(s(elem!1))) = s(elem!1)),
% 5.92/6.19 inference(transitivity,[status(thm)],[2276, 251])).
% 5.92/6.19 tff(2278,plain,
% 5.92/6.19 ($false),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[279, 2277])).
% 5.92/6.19 tff(2279,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.19 tff(2280,plain,
% 5.92/6.19 (~(s(s(elem!1)) = s(elem!1))),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[2279, 2275])).
% 5.92/6.19 tff(2281,plain,
% 5.92/6.19 (b(z, s(elem!1))),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[566, 573])).
% 5.92/6.19 tff(2282,assumption,(~r(elem!1, z)), introduced(assumption)).
% 5.92/6.19 tff(2283,plain,
% 5.92/6.19 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 5.92/6.19 inference(monotonicity,[status(thm)],[11])).
% 5.92/6.19 tff(2284,plain,
% 5.92/6.19 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 5.92/6.19 inference(symmetry,[status(thm)],[2283])).
% 5.92/6.19 tff(2285,plain,
% 5.92/6.19 ((~r(z, s(elem!1))) <=> (~r(elem!1, s(elem!1)))),
% 5.92/6.19 inference(monotonicity,[status(thm)],[2284])).
% 5.92/6.19 tff(2286,plain,
% 5.92/6.19 (~r(elem!1, s(elem!1))),
% 5.92/6.19 inference(modus_ponens,[status(thm)],[573, 2285])).
% 5.92/6.19 tff(2287,plain,
% 5.92/6.19 ($false),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[2251, 2286])).
% 5.92/6.19 tff(2288,plain,((~(elem!1 = z)) | (~r(elem!1, s(elem!1))) | r(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.19 tff(2289,plain,
% 5.92/6.19 (~(elem!1 = z)),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[2288, 573, 2251])).
% 5.92/6.19 tff(2290,plain,
% 5.92/6.19 (b(elem!1, z)),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[526, 2289, 2282])).
% 5.92/6.19 tff(2291,plain,
% 5.92/6.19 (~(z = elem!1)),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[97, 2289])).
% 5.92/6.19 tff(2292,plain,
% 5.92/6.19 (b(z, elem!1)),
% 5.92/6.19 inference(unit_resolution,[status(thm)],[141, 2291, 80])).
% 5.92/6.19 tff(2293,plain,
% 5.92/6.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 5.92/6.19 inference(rewrite,[status(thm)],[])).
% 5.92/6.19 tff(2294,plain,
% 5.92/6.19 (((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 5.92/6.19 inference(rewrite,[status(thm)],[])).
% 5.92/6.19 tff(2295,plain,
% 5.92/6.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 6.00/6.20 inference(monotonicity,[status(thm)],[2294])).
% 6.00/6.20 tff(2296,plain,
% 6.00/6.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 6.00/6.20 inference(transitivity,[status(thm)],[2295, 2293])).
% 6.00/6.20 tff(2297,plain,
% 6.00/6.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 6.00/6.20 inference(quant_inst,[status(thm)],[])).
% 6.00/6.20 tff(2298,plain,
% 6.00/6.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 6.00/6.20 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 6.00/6.20 tff(2299,plain,
% 6.00/6.20 ($false),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2298, 391, 2292, 2290, 900, 380, 2281])).
% 6.00/6.20 tff(2300,plain,(r(z, s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | r(z, elem!1) | r(elem!1, z) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.20 tff(2301,plain,
% 6.00/6.20 (r(z, s(elem!1))),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2300, 2260, 2208, 80, 900, 2251])).
% 6.00/6.20 tff(2302,plain,
% 6.00/6.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 6.00/6.20 inference(rewrite,[status(thm)],[])).
% 6.00/6.20 tff(2303,plain,
% 6.00/6.20 (((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 6.00/6.20 inference(rewrite,[status(thm)],[])).
% 6.00/6.20 tff(2304,plain,
% 6.00/6.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 6.00/6.20 inference(monotonicity,[status(thm)],[2303])).
% 6.00/6.20 tff(2305,plain,
% 6.00/6.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 6.00/6.20 inference(transitivity,[status(thm)],[2304, 2302])).
% 6.00/6.20 tff(2306,plain,
% 6.00/6.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 6.00/6.20 inference(quant_inst,[status(thm)],[])).
% 6.00/6.20 tff(2307,plain,
% 6.00/6.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 6.00/6.20 inference(modus_ponens,[status(thm)],[2306, 2305])).
% 6.00/6.20 tff(2308,plain,
% 6.00/6.20 ($false),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2307, 194, 1628, 2144, 326, 2170])).
% 6.00/6.20 tff(2309,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.20 tff(2310,plain,
% 6.00/6.20 (~r(s(s(elem!1)), s(elem!1))),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2309, 1628, 2301, 326])).
% 6.00/6.20 tff(2311,plain,
% 6.00/6.20 (b(s(s(elem!1)), s(elem!1))),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[1135, 2310, 2280])).
% 6.00/6.20 tff(2312,plain,
% 6.00/6.20 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 6.00/6.20 inference(monotonicity,[status(thm)],[109])).
% 6.00/6.20 tff(2313,plain,
% 6.00/6.20 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 6.00/6.20 inference(symmetry,[status(thm)],[2312])).
% 6.00/6.20 tff(2314,plain,
% 6.00/6.20 (b(s(s(elem!1)), s(z))),
% 6.00/6.20 inference(modus_ponens,[status(thm)],[1037, 2313])).
% 6.00/6.20 tff(2315,plain,
% 6.00/6.20 ($false),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[1830, 2314])).
% 6.00/6.20 tff(2316,plain,((~(s(z) = s(elem!1))) | b(s(s(elem!1)), s(z)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.20 tff(2317,plain,
% 6.00/6.20 (~(s(z) = s(elem!1))),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2316, 2311, 1830])).
% 6.00/6.20 tff(2318,plain,
% 6.00/6.20 (~(elem!1 = z)),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[1596, 2317])).
% 6.00/6.20 tff(2319,plain,
% 6.00/6.20 (b(elem!1, z)),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[526, 2318, 2260])).
% 6.00/6.20 tff(2320,plain,
% 6.00/6.20 (~(z = elem!1)),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[97, 2318])).
% 6.00/6.20 tff(2321,plain,
% 6.00/6.20 (b(z, elem!1)),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[141, 2320, 80])).
% 6.00/6.20 tff(2322,plain,
% 6.00/6.20 ($false),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[1514, 391, 2321, 2319, 900, 2208])).
% 6.00/6.20 tff(2323,plain,((~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), elem!1)) | r(z, elem!1) | b(s(s(elem!1)), s(z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.20 tff(2324,plain,
% 6.00/6.20 (~r(elem!1, s(elem!1))),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2323, 2250, 80, 1830, 326, 900, 184, 232, 182])).
% 6.00/6.20 tff(2325,plain,
% 6.00/6.20 (elem!1 = s(elem!1)),
% 6.00/6.20 inference(modus_ponens,[status(thm)],[152, 160])).
% 6.00/6.20 tff(2326,plain,
% 6.00/6.20 ($false),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[437, 2325])).
% 6.00/6.20 tff(2327,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.20 tff(2328,plain,
% 6.00/6.20 (~(s(elem!1) = elem!1)),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2327, 437])).
% 6.00/6.20 tff(2329,plain,
% 6.00/6.20 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1)),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2166, 42, 469])).
% 6.00/6.20 tff(2330,plain,
% 6.00/6.20 (b(s(elem!1), elem!1)),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2329, 2328])).
% 6.00/6.20 tff(2331,plain,
% 6.00/6.20 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1))),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[441, 42, 438])).
% 6.00/6.20 tff(2332,plain,
% 6.00/6.20 (b(elem!1, s(elem!1))),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2331, 437])).
% 6.00/6.20 tff(2333,plain,
% 6.00/6.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 6.00/6.20 inference(rewrite,[status(thm)],[])).
% 6.00/6.20 tff(2334,plain,
% 6.00/6.20 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~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(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 6.00/6.20 inference(rewrite,[status(thm)],[])).
% 6.00/6.20 tff(2335,plain,
% 6.00/6.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 6.00/6.20 inference(monotonicity,[status(thm)],[2334])).
% 6.00/6.20 tff(2336,plain,
% 6.00/6.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 6.00/6.20 inference(transitivity,[status(thm)],[2335, 2333])).
% 6.00/6.20 tff(2337,plain,
% 6.00/6.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 6.00/6.20 inference(quant_inst,[status(thm)],[])).
% 6.00/6.20 tff(2338,plain,
% 6.00/6.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 6.00/6.20 inference(modus_ponens,[status(thm)],[2337, 2336])).
% 6.00/6.20 tff(2339,plain,
% 6.00/6.20 ($false),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2338, 391, 1101, 900, 2332, 2330])).
% 6.00/6.20 tff(2340,plain,((elem!1 = s(elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | r(s(elem!1), elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.20 tff(2341,plain,
% 6.00/6.20 (r(s(elem!1), elem!1)),
% 6.00/6.20 inference(unit_resolution,[status(thm)],[2340, 2324, 900, 437, 2240])).
% 6.00/6.20 tff(2342,plain,
% 6.00/6.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 6.00/6.20 inference(rewrite,[status(thm)],[])).
% 6.00/6.20 tff(2343,plain,
% 6.00/6.20 (((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 6.00/6.20 inference(rewrite,[status(thm)],[])).
% 6.00/6.20 tff(2344,plain,
% 6.00/6.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))))),
% 6.00/6.20 inference(monotonicity,[status(thm)],[2343])).
% 6.00/6.20 tff(2345,plain,
% 6.00/6.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 6.00/6.20 inference(transitivity,[status(thm)],[2344, 2342])).
% 6.00/6.20 tff(2346,plain,
% 6.00/6.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 6.00/6.21 inference(quant_inst,[status(thm)],[])).
% 6.00/6.21 tff(2347,plain,
% 6.00/6.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[2346, 2345])).
% 6.00/6.21 tff(2348,plain,
% 6.00/6.21 ($false),
% 6.00/6.21 inference(unit_resolution,[status(thm)],[2347, 194, 2223, 2341, 2250, 184])).
% 6.00/6.21 tff(2349,plain,((elem!1 = z) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(elem!1)) | r(z, elem!1) | b(s(s(elem!1)), s(z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.21 tff(2350,plain,
% 6.00/6.21 (elem!1 = z),
% 6.00/6.21 inference(unit_resolution,[status(thm)],[2349, 2205, 900, 59, 80, 1830, 326, 232, 182])).
% 6.00/6.21 tff(2351,plain,
% 6.00/6.21 (s(elem!1) = s(z)),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2350])).
% 6.00/6.21 tff(2352,plain,
% 6.00/6.21 (s(s(elem!1)) = s(s(z))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2351])).
% 6.00/6.21 tff(2353,plain,
% 6.00/6.21 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2352])).
% 6.00/6.21 tff(2354,plain,
% 6.00/6.21 (r(z, s(s(z)))),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[326, 2353])).
% 6.00/6.21 tff(2355,plain,
% 6.00/6.21 (s(s(z)) = s(s(elem!1))),
% 6.00/6.21 inference(symmetry,[status(thm)],[2352])).
% 6.00/6.21 tff(2356,plain,
% 6.00/6.21 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2355])).
% 6.00/6.21 tff(2357,plain,
% 6.00/6.21 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 6.00/6.21 inference(symmetry,[status(thm)],[2356])).
% 6.00/6.21 tff(2358,plain,
% 6.00/6.21 (r(s(s(z)), s(z))),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[1831, 2357])).
% 6.00/6.21 tff(2359,plain,
% 6.00/6.21 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2352])).
% 6.00/6.21 tff(2360,plain,
% 6.00/6.21 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2350])).
% 6.00/6.21 tff(2361,plain,
% 6.00/6.21 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 6.00/6.21 inference(transitivity,[status(thm)],[2360, 2359])).
% 6.00/6.21 tff(2362,plain,
% 6.00/6.21 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2350])).
% 6.00/6.21 tff(2363,plain,
% 6.00/6.21 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 6.00/6.21 inference(symmetry,[status(thm)],[2362])).
% 6.00/6.21 tff(2364,plain,
% 6.00/6.21 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2363])).
% 6.00/6.21 tff(2365,plain,
% 6.00/6.21 (~(s(s(elem!1)) = elem!1)),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[215, 2364])).
% 6.00/6.21 tff(2366,plain,
% 6.00/6.21 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2350])).
% 6.00/6.21 tff(2367,plain,
% 6.00/6.21 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 6.00/6.21 inference(symmetry,[status(thm)],[2366])).
% 6.00/6.21 tff(2368,plain,
% 6.00/6.21 (r(elem!1, s(s(s(elem!1))))),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[59, 2367])).
% 6.00/6.21 tff(2369,plain,
% 6.00/6.21 (r(s(z), elem!1) <=> r(s(z), z)),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2350])).
% 6.00/6.21 tff(2370,plain,
% 6.00/6.21 (r(s(z), z) <=> r(s(z), elem!1)),
% 6.00/6.21 inference(symmetry,[status(thm)],[2369])).
% 6.00/6.21 tff(2371,plain,
% 6.00/6.21 (r(s(z), elem!1)),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[182, 2370])).
% 6.00/6.21 tff(2372,plain,
% 6.00/6.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 6.00/6.21 inference(rewrite,[status(thm)],[])).
% 6.00/6.21 tff(2373,plain,
% 6.00/6.21 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 6.00/6.21 inference(rewrite,[status(thm)],[])).
% 6.00/6.21 tff(2374,plain,
% 6.00/6.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2373])).
% 6.00/6.21 tff(2375,plain,
% 6.00/6.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 6.00/6.21 inference(transitivity,[status(thm)],[2374, 2372])).
% 6.00/6.21 tff(2376,plain,
% 6.00/6.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 6.00/6.21 inference(quant_inst,[status(thm)],[])).
% 6.00/6.21 tff(2377,plain,
% 6.00/6.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[2376, 2375])).
% 6.00/6.21 tff(2378,plain,
% 6.00/6.21 ($false),
% 6.00/6.21 inference(unit_resolution,[status(thm)],[2377, 194, 340, 364, 410, 1484])).
% 6.00/6.21 tff(2379,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.21 tff(2380,plain,
% 6.00/6.21 (~r(s(s(elem!1)), elem!1)),
% 6.00/6.21 inference(unit_resolution,[status(thm)],[2379, 2371, 1831, 2368])).
% 6.00/6.21 tff(2381,plain,
% 6.00/6.21 (b(s(s(elem!1)), elem!1)),
% 6.00/6.21 inference(unit_resolution,[status(thm)],[872, 2380, 2365])).
% 6.00/6.21 tff(2382,plain,
% 6.00/6.21 (b(s(s(z)), z)),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[2381, 2361])).
% 6.00/6.21 tff(2383,plain,
% 6.00/6.21 (b(elem!1, s(z)) <=> b(z, s(z))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2350])).
% 6.00/6.21 tff(2384,plain,
% 6.00/6.21 (b(z, s(z)) <=> b(elem!1, s(z))),
% 6.00/6.21 inference(symmetry,[status(thm)],[2383])).
% 6.00/6.21 tff(2385,plain,
% 6.00/6.21 (b(z, s(elem!1)) <=> b(z, s(z))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2351])).
% 6.00/6.21 tff(2386,plain,
% 6.00/6.21 (b(z, s(elem!1)) <=> b(elem!1, s(z))),
% 6.00/6.21 inference(transitivity,[status(thm)],[2385, 2384])).
% 6.00/6.21 tff(2387,plain,
% 6.00/6.21 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2350])).
% 6.00/6.21 tff(2388,plain,
% 6.00/6.21 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 6.00/6.21 inference(symmetry,[status(thm)],[2387])).
% 6.00/6.21 tff(2389,plain,
% 6.00/6.21 (r(s(elem!1), z) <=> r(s(z), z)),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2351])).
% 6.00/6.21 tff(2390,plain,
% 6.00/6.21 (r(s(z), z) <=> r(s(elem!1), z)),
% 6.00/6.21 inference(symmetry,[status(thm)],[2389])).
% 6.00/6.21 tff(2391,plain,
% 6.00/6.21 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 6.00/6.21 inference(transitivity,[status(thm)],[2390, 2388])).
% 6.00/6.21 tff(2392,plain,
% 6.00/6.21 (r(s(elem!1), elem!1)),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[182, 2391])).
% 6.00/6.21 tff(2393,plain,
% 6.00/6.21 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2351])).
% 6.00/6.21 tff(2394,plain,
% 6.00/6.21 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 6.00/6.21 inference(symmetry,[status(thm)],[2393])).
% 6.00/6.21 tff(2395,plain,
% 6.00/6.21 (r(s(s(elem!1)), s(elem!1))),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[1831, 2394])).
% 6.00/6.21 tff(2396,plain,
% 6.00/6.21 (~r(z, s(elem!1))),
% 6.00/6.21 inference(unit_resolution,[status(thm)],[2178, 2395, 2392, 326])).
% 6.00/6.21 tff(2397,plain,
% 6.00/6.21 (b(z, s(elem!1))),
% 6.00/6.21 inference(unit_resolution,[status(thm)],[566, 2396])).
% 6.00/6.21 tff(2398,plain,
% 6.00/6.21 (b(elem!1, s(z))),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[2397, 2386])).
% 6.00/6.21 tff(2399,plain,
% 6.00/6.21 (~r(s(s(s(elem!1))), s(elem!1))),
% 6.00/6.21 inference(unit_resolution,[status(thm)],[641, 232, 59, 182])).
% 6.00/6.21 tff(2400,plain,
% 6.00/6.21 (b(s(s(s(s(z)))), elem!1)),
% 6.00/6.21 inference(unit_resolution,[status(thm)],[1650, 1442, 59, 1573, 2399, 182, 1869, 80, 900, 326])).
% 6.00/6.21 tff(2401,plain,
% 6.00/6.21 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[490])).
% 6.00/6.21 tff(2402,plain,
% 6.00/6.21 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[489, 2401])).
% 6.00/6.21 tff(2403,plain,
% 6.00/6.21 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.00/6.21 inference(symmetry,[status(thm)],[2402])).
% 6.00/6.21 tff(2404,plain,
% 6.00/6.21 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2403])).
% 6.00/6.21 tff(2405,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 6.00/6.21 tff(2406,plain,
% 6.00/6.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 6.00/6.21 inference(rewrite,[status(thm)],[])).
% 6.00/6.21 tff(2407,plain,
% 6.00/6.21 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 6.00/6.21 inference(rewrite,[status(thm)],[])).
% 6.00/6.21 tff(2408,plain,
% 6.00/6.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2407])).
% 6.00/6.21 tff(2409,plain,
% 6.00/6.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 6.00/6.21 inference(transitivity,[status(thm)],[2408, 2406])).
% 6.00/6.21 tff(2410,plain,
% 6.00/6.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.00/6.21 inference(quant_inst,[status(thm)],[])).
% 6.00/6.21 tff(2411,plain,
% 6.00/6.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 6.00/6.21 tff(2412,plain,
% 6.00/6.21 (~r(s(s(z)), s(s(s(s(z)))))),
% 6.00/6.21 inference(unit_resolution,[status(thm)],[2411, 194, 182, 723, 2405])).
% 6.00/6.21 tff(2413,plain,
% 6.00/6.21 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[2412, 2404])).
% 6.00/6.21 tff(2414,plain,
% 6.00/6.21 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2401, 489])).
% 6.00/6.21 tff(2415,plain,
% 6.00/6.21 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 6.00/6.21 inference(transitivity,[status(thm)],[2414, 940])).
% 6.00/6.21 tff(2416,plain,
% 6.00/6.21 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 6.00/6.21 inference(symmetry,[status(thm)],[2415])).
% 6.00/6.21 tff(2417,plain,
% 6.00/6.21 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 6.00/6.21 inference(transitivity,[status(thm)],[2416, 1021])).
% 6.00/6.21 tff(2418,plain,
% 6.00/6.21 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2417])).
% 6.00/6.21 tff(2419,plain,
% 6.00/6.21 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 6.00/6.21 inference(modus_ponens,[status(thm)],[714, 2418])).
% 6.00/6.21 tff(2420,plain,
% 6.00/6.21 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 6.00/6.21 inference(monotonicity,[status(thm)],[2401, 489])).
% 6.00/6.21 tff(2421,plain,
% 6.00/6.21 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.00/6.22 inference(symmetry,[status(thm)],[2420])).
% 6.00/6.22 tff(2422,plain,
% 6.00/6.22 (r(s(z), elem!1) <=> r(s(z), z)),
% 6.00/6.22 inference(monotonicity,[status(thm)],[11])).
% 6.00/6.22 tff(2423,plain,
% 6.00/6.22 (r(s(z), z) <=> r(s(z), elem!1)),
% 6.00/6.22 inference(symmetry,[status(thm)],[2422])).
% 6.00/6.22 tff(2424,plain,
% 6.00/6.22 (r(s(z), elem!1)),
% 6.00/6.22 inference(modus_ponens,[status(thm)],[182, 2423])).
% 6.00/6.22 tff(2425,plain,
% 6.00/6.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 6.00/6.22 inference(rewrite,[status(thm)],[])).
% 6.00/6.22 tff(2426,plain,
% 6.00/6.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 6.00/6.22 inference(quant_inst,[status(thm)],[])).
% 6.00/6.22 tff(2427,plain,
% 6.00/6.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 6.00/6.22 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 6.00/6.22 tff(2428,plain,
% 6.00/6.22 ($false),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[2427, 194, 1484, 723, 1697, 2405])).
% 6.00/6.22 tff(2429,plain,((~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.22 tff(2430,plain,
% 6.00/6.22 (~r(s(s(s(s(z)))), s(s(z)))),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[2429, 723, 2405, 2424])).
% 6.00/6.22 tff(2431,plain,
% 6.00/6.22 (b(s(s(s(s(z)))), s(s(z)))),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[1714, 2430])).
% 6.00/6.22 tff(2432,plain,
% 6.00/6.22 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.00/6.22 inference(modus_ponens,[status(thm)],[2431, 2421])).
% 6.00/6.22 tff(2433,plain,
% 6.00/6.22 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[1741, 2432, 1374, 1573])).
% 6.00/6.22 tff(2434,plain,
% 6.00/6.22 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[1048, 2433, 2419])).
% 6.00/6.22 tff(2435,plain,
% 6.00/6.22 ($false),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[2434, 2413])).
% 6.00/6.22 tff(2436,plain,((~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.22 tff(2437,plain,
% 6.00/6.22 (~r(s(s(s(s(z)))), s(z))),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[2436, 2350, 1374, 1573, 182, 2358])).
% 6.00/6.22 tff(2438,plain,
% 6.00/6.22 (b(s(s(s(s(z)))), s(z))),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[749, 2437])).
% 6.00/6.22 tff(2439,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 6.00/6.22 tff(2440,plain,
% 6.00/6.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.00/6.22 inference(rewrite,[status(thm)],[])).
% 6.00/6.22 tff(2441,plain,
% 6.00/6.22 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.00/6.22 inference(rewrite,[status(thm)],[])).
% 6.00/6.22 tff(2442,plain,
% 6.00/6.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 6.00/6.22 inference(monotonicity,[status(thm)],[2441])).
% 6.00/6.22 tff(2443,plain,
% 6.00/6.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.00/6.22 inference(transitivity,[status(thm)],[2442, 2440])).
% 6.00/6.22 tff(2444,plain,
% 6.00/6.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.00/6.22 inference(quant_inst,[status(thm)],[])).
% 6.00/6.22 tff(2445,plain,
% 6.00/6.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 6.00/6.22 inference(modus_ponens,[status(thm)],[2444, 2443])).
% 6.00/6.22 tff(2446,plain,
% 6.00/6.22 ($false),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[2445, 391, 1235, 1652, 1759, 2439, 721])).
% 6.00/6.22 tff(2447,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.22 tff(2448,plain,
% 6.00/6.22 (~b(s(z), s(s(z)))),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[2447, 2438, 2400, 2398, 2382])).
% 6.00/6.22 tff(2449,plain,
% 6.00/6.22 (r(s(z), s(s(z)))),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[1788, 2448])).
% 6.00/6.22 tff(2450,plain,
% 6.00/6.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 6.00/6.22 inference(rewrite,[status(thm)],[])).
% 6.00/6.22 tff(2451,plain,
% 6.00/6.22 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 6.00/6.22 inference(rewrite,[status(thm)],[])).
% 6.00/6.22 tff(2452,plain,
% 6.00/6.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 6.00/6.22 inference(monotonicity,[status(thm)],[2451])).
% 6.00/6.22 tff(2453,plain,
% 6.00/6.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 6.00/6.22 inference(transitivity,[status(thm)],[2452, 2450])).
% 6.00/6.22 tff(2454,plain,
% 6.00/6.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 6.00/6.22 inference(quant_inst,[status(thm)],[])).
% 6.00/6.22 tff(2455,plain,
% 6.00/6.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 6.00/6.22 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 6.00/6.22 tff(2456,plain,
% 6.00/6.22 ($false),
% 6.00/6.22 inference(unit_resolution,[status(thm)],[2455, 194, 182, 2449, 2358, 2354])).
% 6.00/6.23 tff(2457,plain,(r(z, elem!1) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | b(s(s(elem!1)), s(z)) | (~r(s(z), s(s(s(elem!1))))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.23 tff(2458,plain,
% 6.00/6.23 (r(z, elem!1)),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2457, 1829, 1374, 182, 326, 2193, 1830, 232, 10])).
% 6.00/6.23 tff(2459,plain,
% 6.00/6.23 (s(s(elem!1)) = elem!1),
% 6.00/6.23 inference(transitivity,[status(thm)],[212, 686, 108])).
% 6.00/6.23 tff(2460,plain,
% 6.00/6.23 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 6.00/6.23 inference(monotonicity,[status(thm)],[2459])).
% 6.00/6.23 tff(2461,plain,
% 6.00/6.23 (r(elem!1, s(z))),
% 6.00/6.23 inference(modus_ponens,[status(thm)],[340, 2460])).
% 6.00/6.23 tff(2462,plain,
% 6.00/6.23 (~r(z, s(z))),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[845, 2461, 182, 411])).
% 6.00/6.23 tff(2463,plain,
% 6.00/6.23 (b(z, s(z))),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[678, 2462])).
% 6.00/6.23 tff(2464,plain,
% 6.00/6.23 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 6.00/6.23 inference(monotonicity,[status(thm)],[465])).
% 6.00/6.23 tff(2465,plain,
% 6.00/6.23 (b(s(elem!1), elem!1)),
% 6.00/6.23 inference(modus_ponens,[status(thm)],[900, 2464])).
% 6.00/6.23 tff(2466,plain,
% 6.00/6.23 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 6.00/6.23 inference(monotonicity,[status(thm)],[465])).
% 6.00/6.23 tff(2467,plain,
% 6.00/6.23 (b(s(elem!1), z)),
% 6.00/6.23 inference(modus_ponens,[status(thm)],[380, 2466])).
% 6.00/6.23 tff(2468,plain,
% 6.00/6.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))),
% 6.00/6.23 inference(rewrite,[status(thm)],[])).
% 6.00/6.23 tff(2469,plain,
% 6.00/6.23 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))),
% 6.00/6.23 inference(rewrite,[status(thm)],[])).
% 6.00/6.23 tff(2470,plain,
% 6.00/6.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))))),
% 6.00/6.23 inference(monotonicity,[status(thm)],[2469])).
% 6.00/6.23 tff(2471,plain,
% 6.00/6.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))),
% 6.00/6.23 inference(transitivity,[status(thm)],[2470, 2468])).
% 6.00/6.23 tff(2472,plain,
% 6.00/6.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 6.00/6.23 inference(quant_inst,[status(thm)],[])).
% 6.00/6.23 tff(2473,plain,
% 6.00/6.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))),
% 6.00/6.23 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 6.00/6.23 tff(2474,plain,
% 6.00/6.23 ($false),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2473, 194, 411, 1484, 847, 182])).
% 6.00/6.23 tff(2475,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.23 tff(2476,plain,
% 6.00/6.23 (~r(s(z), elem!1)),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2475, 2461, 411, 182])).
% 6.00/6.23 tff(2477,plain,
% 6.00/6.23 (b(s(z), elem!1)),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[632, 2476, 150])).
% 6.00/6.23 tff(2478,plain,
% 6.00/6.23 (~r(elem!1, z)),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[855, 2461, 326, 182])).
% 6.00/6.23 tff(2479,plain,
% 6.00/6.23 (b(elem!1, z)),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[526, 2478, 2])).
% 6.00/6.23 tff(2480,plain,
% 6.00/6.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 6.00/6.23 inference(rewrite,[status(thm)],[])).
% 6.00/6.23 tff(2481,plain,
% 6.00/6.23 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 6.00/6.23 inference(rewrite,[status(thm)],[])).
% 6.00/6.23 tff(2482,plain,
% 6.00/6.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), elem!1))))),
% 6.00/6.23 inference(monotonicity,[status(thm)],[2481])).
% 6.00/6.23 tff(2483,plain,
% 6.00/6.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 6.00/6.23 inference(transitivity,[status(thm)],[2482, 2480])).
% 6.00/6.23 tff(2484,plain,
% 6.00/6.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 6.00/6.23 inference(quant_inst,[status(thm)],[])).
% 6.00/6.23 tff(2485,plain,
% 6.00/6.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), elem!1))),
% 6.00/6.23 inference(modus_ponens,[status(thm)],[2484, 2483])).
% 6.00/6.23 tff(2486,plain,
% 6.00/6.23 ($false),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2485, 391, 2479, 2477, 2467, 2465, 2463])).
% 6.00/6.23 tff(2487,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(z) = elem!1) | (elem!1 = z) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.23 tff(2488,plain,
% 6.00/6.23 (s(z) = elem!1),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2487, 465, 2, 411, 182, 326, 340, 380, 900])).
% 6.00/6.23 tff(2489,plain,
% 6.00/6.23 (s(s(z)) = s(elem!1)),
% 6.00/6.23 inference(monotonicity,[status(thm)],[2488])).
% 6.00/6.23 tff(2490,assumption,(s(s(z)) = s(elem!1)), introduced(assumption)).
% 6.00/6.23 tff(2491,plain,
% 6.00/6.23 (s(s(z)) = s(s(s(elem!1)))),
% 6.00/6.23 inference(transitivity,[status(thm)],[2490, 2268])).
% 6.00/6.23 tff(2492,plain,
% 6.00/6.23 ($false),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[1397, 2491])).
% 6.00/6.23 tff(2493,plain,((~(s(s(z)) = s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.23 tff(2494,plain,
% 6.00/6.23 (~(s(s(z)) = s(elem!1))),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2493, 465])).
% 6.00/6.23 tff(2495,plain,
% 6.00/6.23 ($false),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2494, 2489])).
% 6.00/6.23 tff(2496,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (elem!1 = z) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.23 tff(2497,plain,
% 6.00/6.23 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2496, 2, 411, 182, 326, 340, 2208, 900])).
% 6.00/6.23 tff(2498,plain,
% 6.00/6.23 (b(s(s(s(elem!1))), s(elem!1))),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[588, 2497, 2234])).
% 6.00/6.23 tff(2499,plain,
% 6.00/6.23 (~(s(z) = elem!1)),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2220, 868, 340])).
% 6.00/6.23 tff(2500,plain,
% 6.00/6.23 (~r(s(z), elem!1)),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[1489, 530, 184, 182])).
% 6.00/6.23 tff(2501,plain,
% 6.00/6.23 (b(s(z), elem!1)),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[632, 2500, 2499])).
% 6.00/6.23 tff(2502,plain,
% 6.00/6.23 (~(elem!1 = s(z))),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[172, 2499])).
% 6.00/6.23 tff(2503,plain,
% 6.00/6.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.23 inference(rewrite,[status(thm)],[])).
% 6.00/6.23 tff(2504,plain,
% 6.00/6.23 (((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.23 inference(rewrite,[status(thm)],[])).
% 6.00/6.23 tff(2505,plain,
% 6.00/6.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 6.00/6.23 inference(monotonicity,[status(thm)],[2504])).
% 6.00/6.23 tff(2506,plain,
% 6.00/6.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.23 inference(transitivity,[status(thm)],[2505, 2503])).
% 6.00/6.23 tff(2507,plain,
% 6.00/6.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 6.00/6.23 inference(quant_inst,[status(thm)],[])).
% 6.00/6.23 tff(2508,plain,
% 6.00/6.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 6.00/6.23 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 6.00/6.23 tff(2509,plain,
% 6.00/6.23 ($false),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2508, 391, 665, 900, 644, 1526, 721])).
% 6.00/6.23 tff(2510,plain,((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.23 tff(2511,plain,
% 6.00/6.23 (~b(elem!1, s(z))),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[2510, 665, 900, 644, 1526])).
% 6.00/6.23 tff(2512,plain,
% 6.00/6.23 (r(elem!1, s(z))),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[837, 2511, 831])).
% 6.00/6.23 tff(2513,plain,
% 6.00/6.23 (~r(z, s(z))),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[845, 2512, 182, 411])).
% 6.00/6.23 tff(2514,plain,
% 6.00/6.23 (b(z, s(z))),
% 6.00/6.23 inference(unit_resolution,[status(thm)],[678, 2513])).
% 6.00/6.23 tff(2515,plain,
% 6.00/6.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.24 inference(rewrite,[status(thm)],[])).
% 6.00/6.24 tff(2516,plain,
% 6.00/6.24 (((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.24 inference(rewrite,[status(thm)],[])).
% 6.00/6.24 tff(2517,plain,
% 6.00/6.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 6.00/6.24 inference(monotonicity,[status(thm)],[2516])).
% 6.00/6.24 tff(2518,plain,
% 6.00/6.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.24 inference(transitivity,[status(thm)],[2517, 2515])).
% 6.00/6.24 tff(2519,plain,
% 6.00/6.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 6.00/6.24 inference(quant_inst,[status(thm)],[])).
% 6.00/6.24 tff(2520,plain,
% 6.00/6.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 6.00/6.24 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 6.00/6.24 tff(2521,plain,
% 6.00/6.24 ($false),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[2520, 391, 665, 380, 644, 1526, 2514])).
% 6.00/6.24 tff(2522,plain,((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (elem!1 = s(z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.24 tff(2523,plain,
% 6.00/6.24 (~b(elem!1, z)),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[2522, 644, 380, 1526, 182, 411, 831, 900])).
% 6.00/6.24 tff(2524,plain,
% 6.00/6.24 (r(elem!1, z)),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[526, 2523, 2])).
% 6.00/6.24 tff(2525,plain,
% 6.00/6.24 (~r(elem!1, s(z))),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[855, 2524, 326, 182])).
% 6.00/6.24 tff(2526,plain,
% 6.00/6.24 (b(elem!1, s(z))),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[837, 2525, 831])).
% 6.00/6.24 tff(2527,plain,
% 6.00/6.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.24 inference(rewrite,[status(thm)],[])).
% 6.00/6.24 tff(2528,plain,
% 6.00/6.24 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(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(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.24 inference(rewrite,[status(thm)],[])).
% 6.00/6.24 tff(2529,plain,
% 6.00/6.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 6.00/6.24 inference(monotonicity,[status(thm)],[2528])).
% 6.00/6.24 tff(2530,plain,
% 6.00/6.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.24 inference(transitivity,[status(thm)],[2529, 2527])).
% 6.00/6.24 tff(2531,plain,
% 6.00/6.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 6.00/6.24 inference(quant_inst,[status(thm)],[])).
% 6.00/6.24 tff(2532,plain,
% 6.00/6.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 6.00/6.24 inference(modus_ponens,[status(thm)],[2531, 2530])).
% 6.00/6.24 tff(2533,plain,
% 6.00/6.24 ($false),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[2532, 391, 900, 644, 1526, 2526])).
% 6.00/6.24 tff(2534,plain,((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (elem!1 = s(z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.24 tff(2535,plain,
% 6.00/6.24 ($false),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[2534, 2502, 2501, 1526, 900, 326, 182, 2, 380, 411])).
% 6.00/6.24 tff(2536,plain,((~r(elem!1, z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.24 tff(2537,plain,
% 6.00/6.24 (~r(elem!1, z)),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[2536, 2, 900, 326, 182, 1526, 2208, 411, 340, 184])).
% 6.00/6.24 tff(2538,plain,
% 6.00/6.24 (b(elem!1, z)),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[526, 2537, 2])).
% 6.00/6.24 tff(2539,plain,
% 6.00/6.24 (~(s(s(elem!1)) = elem!1)),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[451, 2497])).
% 6.00/6.24 tff(2540,plain,
% 6.00/6.24 (~(s(elem!1) = elem!1)),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[1943, 2539])).
% 6.00/6.24 tff(2541,plain,
% 6.00/6.24 (~(elem!1 = s(elem!1))),
% 6.00/6.24 inference(unit_resolution,[status(thm)],[166, 2540])).
% 6.00/6.24 tff(2542,plain,
% 6.00/6.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.00/6.24 inference(rewrite,[status(thm)],[])).
% 6.00/6.24 tff(2543,plain,
% 6.00/6.24 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.00/6.24 inference(rewrite,[status(thm)],[])).
% 6.00/6.24 tff(2544,plain,
% 6.00/6.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 6.00/6.24 inference(monotonicity,[status(thm)],[2543])).
% 6.00/6.25 tff(2545,plain,
% 6.00/6.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.00/6.25 inference(transitivity,[status(thm)],[2544, 2542])).
% 6.00/6.25 tff(2546,plain,
% 6.00/6.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 6.00/6.25 inference(quant_inst,[status(thm)],[])).
% 6.00/6.25 tff(2547,plain,
% 6.00/6.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 6.00/6.25 inference(modus_ponens,[status(thm)],[2546, 2545])).
% 6.00/6.25 tff(2548,plain,
% 6.00/6.25 ($false),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2547, 194, 411, 340, 326, 1064])).
% 6.00/6.25 tff(2549,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.25 tff(2550,plain,
% 6.00/6.25 (~r(elem!1, s(s(elem!1)))),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2549, 411, 340, 326])).
% 6.00/6.25 tff(2551,plain,
% 6.00/6.25 (~(elem!1 = s(s(elem!1)))),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[1292, 2539])).
% 6.00/6.25 tff(2552,plain,
% 6.00/6.25 (b(elem!1, s(s(elem!1)))),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[1307, 2551, 2550])).
% 6.00/6.25 tff(2553,plain,
% 6.00/6.25 (~b(s(s(elem!1)), elem!1)),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[1467, 2552, 1374, 900])).
% 6.00/6.25 tff(2554,plain,
% 6.00/6.25 (r(s(s(elem!1)), elem!1)),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[872, 2553, 2539])).
% 6.00/6.25 tff(2555,plain,
% 6.00/6.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 6.00/6.25 inference(rewrite,[status(thm)],[])).
% 6.00/6.25 tff(2556,plain,
% 6.00/6.25 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 6.00/6.25 inference(rewrite,[status(thm)],[])).
% 6.00/6.25 tff(2557,plain,
% 6.00/6.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 6.00/6.25 inference(monotonicity,[status(thm)],[2556])).
% 6.00/6.25 tff(2558,plain,
% 6.00/6.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 6.00/6.25 inference(transitivity,[status(thm)],[2557, 2555])).
% 6.00/6.25 tff(2559,plain,
% 6.00/6.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 6.00/6.25 inference(quant_inst,[status(thm)],[])).
% 6.00/6.25 tff(2560,plain,
% 6.00/6.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 6.00/6.25 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 6.00/6.25 tff(2561,plain,
% 6.00/6.25 ($false),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2560, 194, 411, 364, 410, 326])).
% 6.00/6.25 tff(2562,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.25 tff(2563,plain,
% 6.00/6.25 (~r(elem!1, s(s(s(elem!1))))),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2562, 2554, 411, 326])).
% 6.00/6.25 tff(2564,plain,
% 6.00/6.25 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 6.00/6.25 inference(monotonicity,[status(thm)],[812])).
% 6.00/6.25 tff(2565,plain,
% 6.00/6.25 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 6.00/6.25 inference(symmetry,[status(thm)],[2564])).
% 6.00/6.25 tff(2566,plain,
% 6.00/6.25 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 6.00/6.25 inference(monotonicity,[status(thm)],[2565])).
% 6.00/6.25 tff(2567,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 6.00/6.25 tff(2568,plain,
% 6.00/6.25 (~r(s(z), s(s(s(elem!1))))),
% 6.00/6.25 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 6.00/6.25 tff(2569,plain,
% 6.00/6.25 ($false),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[232, 2568])).
% 6.00/6.25 tff(2570,plain,((~(s(z) = elem!1)) | (~r(s(z), s(s(s(elem!1))))) | r(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.25 tff(2571,plain,
% 6.00/6.25 (~(s(z) = elem!1)),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2570, 2563, 232])).
% 6.00/6.25 tff(2572,plain,
% 6.00/6.25 (~(elem!1 = s(z))),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[172, 2571])).
% 6.00/6.25 tff(2573,plain,
% 6.00/6.25 (~b(s(z), elem!1)),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2534, 2572, 1526, 900, 326, 182, 2, 2208, 411])).
% 6.00/6.25 tff(2574,plain,
% 6.00/6.25 (r(s(z), elem!1)),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[632, 2573, 2571])).
% 6.00/6.25 tff(2575,plain,
% 6.00/6.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 6.00/6.25 inference(rewrite,[status(thm)],[])).
% 6.00/6.25 tff(2576,plain,
% 6.00/6.25 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 6.00/6.25 inference(rewrite,[status(thm)],[])).
% 6.00/6.25 tff(2577,plain,
% 6.00/6.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))))),
% 6.00/6.25 inference(monotonicity,[status(thm)],[2576])).
% 6.00/6.25 tff(2578,plain,
% 6.00/6.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 6.00/6.25 inference(transitivity,[status(thm)],[2577, 2575])).
% 6.00/6.25 tff(2579,plain,
% 6.00/6.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 6.00/6.25 inference(quant_inst,[status(thm)],[])).
% 6.00/6.25 tff(2580,plain,
% 6.00/6.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 6.00/6.25 inference(modus_ponens,[status(thm)],[2579, 2578])).
% 6.00/6.25 tff(2581,plain,
% 6.00/6.25 ($false),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2580, 194, 411, 2251, 1484, 182])).
% 6.00/6.25 tff(2582,plain,((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.25 tff(2583,plain,
% 6.00/6.25 (~r(elem!1, s(elem!1))),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2582, 2574, 182, 411])).
% 6.00/6.25 tff(2584,plain,
% 6.00/6.25 (b(elem!1, s(elem!1))),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[443, 2583, 2541])).
% 6.00/6.25 tff(2585,plain,
% 6.00/6.25 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2274, 1921, 232])).
% 6.00/6.25 tff(2586,plain,
% 6.00/6.25 (b(s(s(s(elem!1))), s(elem!1))),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[588, 2585, 1575])).
% 6.00/6.25 tff(2587,plain,
% 6.00/6.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.25 inference(rewrite,[status(thm)],[])).
% 6.00/6.25 tff(2588,plain,
% 6.00/6.25 (((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.25 inference(rewrite,[status(thm)],[])).
% 6.00/6.25 tff(2589,plain,
% 6.00/6.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 6.00/6.25 inference(monotonicity,[status(thm)],[2588])).
% 6.00/6.25 tff(2590,plain,
% 6.00/6.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 6.00/6.25 inference(transitivity,[status(thm)],[2589, 2587])).
% 6.00/6.25 tff(2591,plain,
% 6.00/6.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 6.00/6.25 inference(quant_inst,[status(thm)],[])).
% 6.00/6.25 tff(2592,plain,
% 6.00/6.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 6.00/6.25 inference(modus_ponens,[status(thm)],[2591, 2590])).
% 6.00/6.25 tff(2593,plain,
% 6.00/6.25 ($false),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2592, 391, 2586, 1526, 1922, 1917])).
% 6.00/6.25 tff(2594,plain,((~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(z) = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.25 tff(2595,plain,
% 6.00/6.25 (~r(s(elem!1), z)),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2594, 118, 1526, 2234, 232, 411, 182])).
% 6.00/6.25 tff(2596,plain,
% 6.00/6.25 (b(s(elem!1), z)),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[549, 2595])).
% 6.00/6.25 tff(2597,plain,
% 6.00/6.25 (~b(s(z), elem!1)),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[2534, 831, 1526, 900, 326, 182, 2, 380, 411])).
% 6.00/6.25 tff(2598,plain,
% 6.00/6.25 (r(s(z), elem!1)),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[632, 2597, 1496])).
% 6.00/6.25 tff(2599,plain,
% 6.00/6.25 ($false),
% 6.00/6.25 inference(unit_resolution,[status(thm)],[1899, 2598, 1810, 340, 364])).
% 6.00/6.25 tff(2600,plain,((elem!1 = s(z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | b(elem!1, s(z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.26 tff(2601,plain,
% 6.00/6.26 (b(elem!1, s(z))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2600, 2572, 2554, 340, 1526, 900, 326, 182, 2, 2208, 411])).
% 6.00/6.26 tff(2602,plain,
% 6.00/6.26 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 6.00/6.26 inference(symmetry,[status(thm)],[582])).
% 6.00/6.26 tff(2603,plain,
% 6.00/6.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, s(elem!1))))),
% 6.00/6.26 inference(rewrite,[status(thm)],[])).
% 6.00/6.26 tff(2604,plain,
% 6.00/6.26 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(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)) | (~b(z, s(elem!1))))),
% 6.00/6.26 inference(rewrite,[status(thm)],[])).
% 6.00/6.26 tff(2605,plain,
% 6.00/6.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, s(elem!1)))))),
% 6.00/6.26 inference(monotonicity,[status(thm)],[2604])).
% 6.00/6.26 tff(2606,plain,
% 6.00/6.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, s(elem!1))))),
% 6.00/6.26 inference(transitivity,[status(thm)],[2605, 2603])).
% 6.00/6.26 tff(2607,plain,
% 6.00/6.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 6.00/6.26 inference(quant_inst,[status(thm)],[])).
% 6.00/6.26 tff(2608,plain,
% 6.00/6.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))),
% 6.00/6.26 inference(modus_ponens,[status(thm)],[2607, 2606])).
% 6.00/6.26 tff(2609,plain,
% 6.00/6.26 (~b(s(s(s(elem!1))), s(elem!1))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2608, 391, 380, 2281, 591])).
% 6.00/6.26 tff(2610,plain,
% 6.00/6.26 (s(s(s(elem!1))) = s(elem!1)),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[588, 2609, 1575])).
% 6.00/6.26 tff(2611,plain,
% 6.00/6.26 (s(elem!1) = s(s(s(elem!1)))),
% 6.00/6.26 inference(modus_ponens,[status(thm)],[2610, 2602])).
% 6.00/6.26 tff(2612,plain,
% 6.00/6.26 (~(s(elem!1) = s(s(s(elem!1))))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[575, 573, 184])).
% 6.00/6.26 tff(2613,plain,
% 6.00/6.26 ($false),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2612, 2611])).
% 6.00/6.26 tff(2614,plain,(r(z, s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.26 tff(2615,plain,
% 6.00/6.26 (r(z, s(elem!1))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2614, 2596, 2208, 2234, 184])).
% 6.00/6.26 tff(2616,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 6.00/6.26 tff(2617,plain,
% 6.00/6.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 6.00/6.26 inference(rewrite,[status(thm)],[])).
% 6.00/6.26 tff(2618,plain,
% 6.00/6.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 6.00/6.26 inference(quant_inst,[status(thm)],[])).
% 6.00/6.26 tff(2619,plain,
% 6.00/6.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 6.00/6.26 inference(modus_ponens,[status(thm)],[2618, 2617])).
% 6.00/6.26 tff(2620,plain,
% 6.00/6.26 ($false),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2619, 194, 340, 2144, 182, 2616])).
% 6.00/6.26 tff(2621,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.26 tff(2622,plain,
% 6.00/6.26 (~r(s(s(elem!1)), z)),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2621, 2615, 340, 182])).
% 6.00/6.26 tff(2623,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 6.00/6.26 tff(2624,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 6.00/6.26 tff(2625,plain,
% 6.00/6.26 (((~![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))),
% 6.00/6.26 inference(rewrite,[status(thm)],[])).
% 6.00/6.26 tff(2626,plain,
% 6.00/6.26 ((~![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))),
% 6.00/6.26 inference(quant_inst,[status(thm)],[])).
% 6.00/6.26 tff(2627,plain,
% 6.00/6.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 6.00/6.26 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 6.00/6.26 tff(2628,plain,
% 6.00/6.26 ($false),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2627, 42, 215, 2624, 2623])).
% 6.00/6.26 tff(2629,plain,(r(s(s(elem!1)), z) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 6.00/6.26 tff(2630,plain,
% 6.00/6.26 (b(s(s(elem!1)), z)),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2629, 2622])).
% 6.00/6.26 tff(2631,plain,
% 6.00/6.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.00/6.26 inference(rewrite,[status(thm)],[])).
% 6.00/6.26 tff(2632,plain,
% 6.00/6.26 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(s(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)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.00/6.26 inference(rewrite,[status(thm)],[])).
% 6.00/6.26 tff(2633,plain,
% 6.00/6.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 6.00/6.26 inference(monotonicity,[status(thm)],[2632])).
% 6.00/6.26 tff(2634,plain,
% 6.00/6.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.00/6.26 inference(transitivity,[status(thm)],[2633, 2631])).
% 6.00/6.26 tff(2635,plain,
% 6.00/6.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 6.00/6.26 inference(quant_inst,[status(thm)],[])).
% 6.00/6.26 tff(2636,plain,
% 6.00/6.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 6.00/6.26 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 6.00/6.26 tff(2637,plain,
% 6.00/6.26 ($false),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2636, 391, 1101, 380, 591, 1759, 1686])).
% 6.00/6.26 tff(2638,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.26 tff(2639,plain,
% 6.00/6.26 (~b(s(s(s(s(z)))), s(z))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2638, 1686, 380, 591, 1101])).
% 6.00/6.26 tff(2640,plain,
% 6.00/6.26 (r(s(s(s(s(z)))), s(z))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[749, 2639])).
% 6.00/6.26 tff(2641,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 6.00/6.26 tff(2642,plain,
% 6.00/6.26 (~(s(s(s(s(z)))) = elem!1)),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[1436, 130])).
% 6.00/6.26 tff(2643,plain,
% 6.00/6.26 (s(s(s(s(z)))) = s(s(elem!1))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2028, 2642, 1294, 1484, 723, 340])).
% 6.00/6.26 tff(2644,plain,
% 6.00/6.26 (elem!1 = s(s(z))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[1407, 2643])).
% 6.00/6.26 tff(2645,plain,
% 6.00/6.26 (s(s(z)) = elem!1),
% 6.00/6.26 inference(symmetry,[status(thm)],[2644])).
% 6.00/6.26 tff(2646,plain,
% 6.00/6.26 (s(s(z)) = s(s(s(elem!1)))),
% 6.00/6.26 inference(transitivity,[status(thm)],[2645, 125])).
% 6.00/6.26 tff(2647,plain,
% 6.00/6.26 ($false),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[1397, 2646])).
% 6.00/6.26 tff(2648,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.26 tff(2649,plain,
% 6.00/6.26 (~(elem!1 = s(s(s(elem!1))))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[2648, 2640, 1484, 1294, 340])).
% 6.00/6.26 tff(2650,plain,
% 6.00/6.26 (b(elem!1, s(s(s(elem!1))))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[424, 2649, 2567])).
% 6.00/6.26 tff(2651,plain,
% 6.00/6.26 (elem!1 = s(s(z))),
% 6.00/6.26 inference(unit_resolution,[status(thm)],[1407, 1399])).
% 6.00/6.26 tff(2652,plain,
% 6.00/6.26 (s(s(z)) = elem!1),
% 6.00/6.26 inference(symmetry,[status(thm)],[2651])).
% 6.00/6.26 tff(2653,plain,
% 6.00/6.26 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 6.00/6.26 inference(monotonicity,[status(thm)],[2652])).
% 6.00/6.26 tff(2654,plain,
% 6.00/6.26 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 6.00/6.26 inference(symmetry,[status(thm)],[2653])).
% 6.00/6.26 tff(2655,plain,
% 6.00/6.26 (b(s(s(z)), s(s(s(elem!1))))),
% 6.00/6.26 inference(modus_ponens,[status(thm)],[448, 2654])).
% 6.00/6.26 tff(2656,plain,
% 6.00/6.26 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 6.00/6.26 inference(monotonicity,[status(thm)],[1399])).
% 6.00/6.26 tff(2657,plain,
% 6.00/6.26 (b(s(z), s(s(elem!1)))),
% 6.00/6.26 inference(modus_ponens,[status(thm)],[1234, 2656])).
% 6.00/6.26 tff(2658,plain,
% 6.00/6.26 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 6.00/6.26 inference(monotonicity,[status(thm)],[2651])).
% 6.00/6.26 tff(2659,plain,
% 6.00/6.26 (b(s(s(z)), s(z))),
% 6.00/6.26 inference(modus_ponens,[status(thm)],[721, 2658])).
% 6.00/6.26 tff(2660,plain,
% 6.00/6.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.00/6.27 inference(rewrite,[status(thm)],[])).
% 6.00/6.27 tff(2661,plain,
% 6.00/6.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.00/6.27 inference(quant_inst,[status(thm)],[])).
% 6.00/6.27 tff(2662,plain,
% 6.00/6.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 6.00/6.27 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 6.00/6.27 tff(2663,plain,
% 6.00/6.27 (~b(s(s(z)), s(s(s(elem!1))))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2662, 391, 1526, 2641, 2659, 2657])).
% 6.00/6.27 tff(2664,plain,
% 6.00/6.27 ($false),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2663, 2655])).
% 6.00/6.27 tff(2665,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.27 tff(2666,plain,
% 6.00/6.27 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2665, 2650, 1526, 2641, 721, 2063])).
% 6.00/6.27 tff(2667,plain,
% 6.00/6.27 (s(s(s(s(z)))) = elem!1),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2028, 2666, 1294, 1484, 2640, 340])).
% 6.00/6.27 tff(2668,plain,
% 6.00/6.27 (elem!1 = s(s(s(s(z))))),
% 6.00/6.27 inference(modus_ponens,[status(thm)],[2667, 764])).
% 6.00/6.27 tff(2669,plain,
% 6.00/6.27 (~r(elem!1, s(z))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2475, 1484, 411, 182])).
% 6.00/6.27 tff(2670,plain,
% 6.00/6.27 (r(elem!1, s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 6.00/6.27 inference(monotonicity,[status(thm)],[766])).
% 6.00/6.27 tff(2671,plain,
% 6.00/6.27 (r(s(s(s(s(z)))), s(z)) <=> r(elem!1, s(z))),
% 6.00/6.27 inference(symmetry,[status(thm)],[2670])).
% 6.00/6.27 tff(2672,plain,
% 6.00/6.27 (r(elem!1, s(z))),
% 6.00/6.27 inference(modus_ponens,[status(thm)],[723, 2671])).
% 6.00/6.27 tff(2673,plain,
% 6.00/6.27 ($false),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[832, 2672])).
% 6.00/6.27 tff(2674,plain,((~r(s(s(s(s(z)))), s(z))) | r(elem!1, s(z)) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.27 tff(2675,plain,
% 6.00/6.27 (~(elem!1 = s(s(s(s(z)))))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2674, 2640, 2669])).
% 6.00/6.27 tff(2676,plain,
% 6.00/6.27 ($false),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2675, 2668])).
% 6.00/6.27 tff(2677,plain,((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | r(elem!1, s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.27 tff(2678,plain,
% 6.00/6.27 (~b(z, s(s(s(s(z)))))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2677, 2552, 2574, 340, 1526, 2630, 2601, 2563, 182, 411, 2596, 2584, 2538, 2208, 2498])).
% 6.00/6.27 tff(2679,plain,
% 6.00/6.27 (r(z, s(s(s(s(z)))))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[800, 2678])).
% 6.00/6.27 tff(2680,plain,
% 6.00/6.27 (~(s(s(elem!1)) = s(s(z)))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[1962, 118])).
% 6.00/6.27 tff(2681,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 6.00/6.27 tff(2682,plain,
% 6.00/6.27 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 6.00/6.27 inference(symmetry,[status(thm)],[2681])).
% 6.00/6.27 tff(2683,plain,
% 6.00/6.27 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 6.00/6.27 inference(monotonicity,[status(thm)],[2682])).
% 6.00/6.27 tff(2684,plain,
% 6.00/6.27 (s(s(s(elem!1))) = s(elem!1)),
% 6.00/6.27 inference(transitivity,[status(thm)],[295, 2683, 259])).
% 6.00/6.27 tff(2685,plain,
% 6.00/6.27 ($false),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[279, 2684])).
% 6.00/6.27 tff(2686,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.27 tff(2687,plain,
% 6.00/6.27 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2686, 2497])).
% 6.00/6.27 tff(2688,plain,
% 6.00/6.27 (~r(elem!1, s(s(s(elem!1))))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2562, 364, 411, 326])).
% 6.00/6.27 tff(2689,assumption,(~(s(s(elem!1)) = s(s(z)))), introduced(assumption)).
% 6.00/6.27 tff(2690,plain,
% 6.00/6.27 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2108, 1216, 182, 719])).
% 6.00/6.27 tff(2691,plain,
% 6.00/6.27 (~(s(s(s(s(z)))) = elem!1)),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[1436, 5])).
% 6.00/6.27 tff(2692,plain,
% 6.00/6.27 (~r(s(s(s(s(z)))), elem!1)),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2116, 5, 2114])).
% 6.00/6.27 tff(2693,plain,
% 6.00/6.27 ($false),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[762, 2692, 2691, 1549])).
% 6.00/6.27 tff(2694,plain,((~(s(s(s(elem!1))) = elem!1)) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.27 tff(2695,plain,
% 6.00/6.27 (~(s(s(s(elem!1))) = elem!1)),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2694, 2690, 1549])).
% 6.00/6.27 tff(2696,plain,
% 6.00/6.27 (~(elem!1 = s(s(s(elem!1))))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[129, 2695])).
% 6.00/6.27 tff(2697,plain,
% 6.00/6.27 (b(elem!1, s(s(s(elem!1))))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[424, 2696, 2567])).
% 6.00/6.27 tff(2698,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 6.00/6.27 tff(2699,plain,
% 6.00/6.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 6.00/6.27 inference(rewrite,[status(thm)],[])).
% 6.00/6.27 tff(2700,plain,
% 6.00/6.27 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(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))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 6.00/6.27 inference(rewrite,[status(thm)],[])).
% 6.00/6.27 tff(2701,plain,
% 6.00/6.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 6.00/6.27 inference(monotonicity,[status(thm)],[2700])).
% 6.00/6.27 tff(2702,plain,
% 6.00/6.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 6.00/6.27 inference(transitivity,[status(thm)],[2701, 2699])).
% 6.00/6.27 tff(2703,plain,
% 6.00/6.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 6.00/6.27 inference(quant_inst,[status(thm)],[])).
% 6.00/6.27 tff(2704,plain,
% 6.00/6.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 6.00/6.27 inference(modus_ponens,[status(thm)],[2703, 2702])).
% 6.00/6.27 tff(2705,plain,
% 6.00/6.27 ($false),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2704, 391, 1101, 900, 448, 2698, 1573])).
% 6.00/6.27 tff(2706,plain,((~b(s(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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.27 tff(2707,plain,
% 6.00/6.27 (~b(s(s(s(s(elem!1)))), elem!1)),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2706, 2697, 900, 1101, 1573])).
% 6.00/6.27 tff(2708,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 6.00/6.27 tff(2709,plain,
% 6.00/6.27 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 6.00/6.27 inference(modus_ponens,[status(thm)],[2708, 1021])).
% 6.00/6.27 tff(2710,plain,
% 6.00/6.27 ($false),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[1035, 2709])).
% 6.00/6.27 tff(2711,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.27 tff(2712,plain,
% 6.00/6.27 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2711, 1035])).
% 6.00/6.27 tff(2713,plain,
% 6.00/6.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 6.00/6.27 inference(rewrite,[status(thm)],[])).
% 6.00/6.27 tff(2714,plain,
% 6.00/6.27 (((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 6.00/6.27 inference(rewrite,[status(thm)],[])).
% 6.00/6.27 tff(2715,plain,
% 6.00/6.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 6.00/6.27 inference(monotonicity,[status(thm)],[2714])).
% 6.00/6.27 tff(2716,plain,
% 6.00/6.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 6.00/6.27 inference(transitivity,[status(thm)],[2715, 2713])).
% 6.00/6.27 tff(2717,plain,
% 6.00/6.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 6.00/6.27 inference(quant_inst,[status(thm)],[])).
% 6.00/6.27 tff(2718,plain,
% 6.00/6.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 6.00/6.27 inference(modus_ponens,[status(thm)],[2717, 2716])).
% 6.00/6.27 tff(2719,plain,
% 6.00/6.27 ($false),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2718, 194, 182, 2112, 1216, 719])).
% 6.00/6.27 tff(2720,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.27 tff(2721,plain,
% 6.00/6.27 (~r(s(s(s(s(z)))), elem!1)),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[2720, 1216, 182, 719])).
% 6.00/6.27 tff(2722,plain,
% 6.00/6.27 (s(s(s(s(z)))) = elem!1),
% 6.00/6.27 inference(unit_resolution,[status(thm)],[762, 2721, 1549])).
% 6.00/6.27 tff(2723,plain,
% 6.00/6.28 (elem!1 = s(s(s(s(z))))),
% 6.00/6.28 inference(modus_ponens,[status(thm)],[2722, 764])).
% 6.00/6.28 tff(2724,plain,
% 6.00/6.28 (s(s(s(s(s(z))))) = s(elem!1)),
% 6.00/6.28 inference(monotonicity,[status(thm)],[2722])).
% 6.00/6.28 tff(2725,plain,
% 6.00/6.28 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 6.00/6.28 inference(monotonicity,[status(thm)],[2724])).
% 6.00/6.28 tff(2726,plain,
% 6.00/6.28 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 6.00/6.28 inference(monotonicity,[status(thm)],[2725])).
% 6.00/6.28 tff(2727,plain,
% 6.00/6.28 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 6.00/6.28 inference(symmetry,[status(thm)],[2726])).
% 6.00/6.28 tff(2728,plain,
% 6.00/6.28 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 6.00/6.28 inference(modus_ponens,[status(thm)],[364, 2727])).
% 6.00/6.28 tff(2729,plain,
% 6.00/6.28 (s(elem!1) = s(s(s(s(s(z)))))),
% 6.00/6.28 inference(monotonicity,[status(thm)],[766])).
% 6.00/6.28 tff(2730,plain,
% 6.00/6.28 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 6.00/6.28 inference(monotonicity,[status(thm)],[2729])).
% 6.00/6.28 tff(2731,plain,
% 6.00/6.28 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 6.00/6.28 inference(symmetry,[status(thm)],[2730])).
% 6.00/6.28 tff(2732,plain,
% 6.00/6.28 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.00/6.28 inference(monotonicity,[status(thm)],[2731])).
% 6.00/6.28 tff(2733,plain,
% 6.00/6.28 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 6.00/6.28 inference(symmetry,[status(thm)],[2732])).
% 6.00/6.28 tff(2734,plain,
% 6.00/6.28 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 6.00/6.28 inference(modus_ponens,[status(thm)],[1177, 2733])).
% 6.00/6.28 tff(2735,plain,
% 6.00/6.28 (r(z, s(s(s(s(s(s(z))))))) <=> r(z, s(s(elem!1)))),
% 6.00/6.28 inference(monotonicity,[status(thm)],[2731])).
% 6.00/6.28 tff(2736,plain,
% 6.00/6.28 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(s(z)))))))),
% 6.00/6.28 inference(symmetry,[status(thm)],[2735])).
% 6.00/6.28 tff(2737,plain,
% 6.00/6.28 (r(z, s(s(s(s(s(s(z)))))))),
% 6.00/6.28 inference(modus_ponens,[status(thm)],[326, 2736])).
% 6.00/6.28 tff(2738,plain,
% 6.00/6.28 (s(s(s(s(z)))) = elem!1),
% 6.00/6.28 inference(symmetry,[status(thm)],[766])).
% 6.00/6.28 tff(2739,plain,
% 6.00/6.28 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 6.00/6.28 inference(monotonicity,[status(thm)],[2738])).
% 6.00/6.28 tff(2740,plain,
% 6.00/6.28 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 6.00/6.28 inference(symmetry,[status(thm)],[2739])).
% 6.00/6.28 tff(2741,assumption,(r(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 6.00/6.28 tff(2742,plain,
% 6.00/6.28 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 6.00/6.28 inference(modus_ponens,[status(thm)],[2741, 2740])).
% 6.00/6.28 tff(2743,plain,
% 6.00/6.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 6.00/6.28 inference(rewrite,[status(thm)],[])).
% 6.00/6.28 tff(2744,plain,
% 6.00/6.28 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 6.00/6.28 inference(rewrite,[status(thm)],[])).
% 6.00/6.28 tff(2745,plain,
% 6.00/6.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 6.00/6.28 inference(monotonicity,[status(thm)],[2744])).
% 6.00/6.28 tff(2746,plain,
% 6.00/6.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 6.00/6.28 inference(transitivity,[status(thm)],[2745, 2743])).
% 6.00/6.28 tff(2747,plain,
% 6.00/6.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 6.00/6.28 inference(quant_inst,[status(thm)],[])).
% 6.00/6.28 tff(2748,plain,
% 6.00/6.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 6.00/6.28 inference(modus_ponens,[status(thm)],[2747, 2746])).
% 6.00/6.28 tff(2749,plain,
% 6.00/6.28 ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 6.00/6.28 inference(unit_resolution,[status(thm)],[2748, 194])).
% 6.00/6.28 tff(2750,plain,
% 6.00/6.28 (~r(s(s(s(s(elem!1)))), z)),
% 6.00/6.28 inference(unit_resolution,[status(thm)],[2749, 2742, 2737, 2734])).
% 6.00/6.28 tff(2751,plain,
% 6.00/6.28 (b(s(s(s(s(elem!1)))), z)),
% 6.00/6.28 inference(unit_resolution,[status(thm)],[1626, 2750])).
% 6.00/6.28 tff(2752,plain,
% 6.00/6.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 6.00/6.28 inference(rewrite,[status(thm)],[])).
% 6.00/6.28 tff(2753,plain,
% 6.00/6.28 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 6.00/6.28 inference(rewrite,[status(thm)],[])).
% 6.00/6.28 tff(2754,plain,
% 6.00/6.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 6.00/6.28 inference(monotonicity,[status(thm)],[2753])).
% 6.00/6.28 tff(2755,plain,
% 6.00/6.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 6.00/6.28 inference(transitivity,[status(thm)],[2754, 2752])).
% 6.00/6.28 tff(2756,plain,
% 6.00/6.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 6.00/6.28 inference(quant_inst,[status(thm)],[])).
% 6.00/6.28 tff(2757,plain,
% 6.00/6.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 6.00/6.29 inference(modus_ponens,[status(thm)],[2756, 2755])).
% 6.00/6.29 tff(2758,plain,
% 6.00/6.29 ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2757, 194])).
% 6.00/6.29 tff(2759,plain,
% 6.00/6.29 (~r(z, s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2758, 2742, 2737, 2734])).
% 6.00/6.29 tff(2760,plain,
% 6.00/6.29 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(symmetry,[status(thm)],[1585])).
% 6.00/6.29 tff(2761,plain,
% 6.00/6.29 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 6.00/6.29 inference(monotonicity,[status(thm)],[2760])).
% 6.00/6.29 tff(2762,plain,
% 6.00/6.29 (~(z = s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(modus_ponens,[status(thm)],[955, 2761])).
% 6.00/6.29 tff(2763,plain,
% 6.00/6.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 6.00/6.29 inference(rewrite,[status(thm)],[])).
% 6.00/6.29 tff(2764,plain,
% 6.00/6.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 6.00/6.29 inference(quant_inst,[status(thm)],[])).
% 6.00/6.29 tff(2765,plain,
% 6.00/6.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 6.00/6.29 tff(2766,plain,
% 6.00/6.29 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2765, 42])).
% 6.00/6.29 tff(2767,plain,
% 6.00/6.29 (b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2766, 2762])).
% 6.00/6.29 tff(2768,plain,
% 6.00/6.29 (b(z, s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2767, 2759])).
% 6.00/6.29 tff(2769,plain,
% 6.00/6.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 6.00/6.29 inference(rewrite,[status(thm)],[])).
% 6.00/6.29 tff(2770,plain,
% 6.00/6.29 (((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 6.00/6.29 inference(rewrite,[status(thm)],[])).
% 6.00/6.29 tff(2771,plain,
% 6.00/6.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 6.00/6.29 inference(monotonicity,[status(thm)],[2770])).
% 6.00/6.29 tff(2772,plain,
% 6.00/6.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 6.00/6.29 inference(transitivity,[status(thm)],[2771, 2769])).
% 6.00/6.29 tff(2773,plain,
% 6.00/6.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 6.00/6.29 inference(quant_inst,[status(thm)],[])).
% 6.00/6.29 tff(2774,plain,
% 6.00/6.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 6.00/6.29 inference(modus_ponens,[status(thm)],[2773, 2772])).
% 6.00/6.29 tff(2775,plain,
% 6.00/6.29 ($false),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2774, 391, 380, 2768, 1573, 2751])).
% 6.00/6.29 tff(2776,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.29 tff(2777,plain,
% 6.00/6.29 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2776, 2728, 1573, 380, 326, 2723])).
% 6.00/6.29 tff(2778,plain,
% 6.00/6.29 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[1061, 2777, 2712])).
% 6.00/6.29 tff(2779,plain,
% 6.00/6.29 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[1741, 2778, 1374, 1573])).
% 6.00/6.29 tff(2780,plain,
% 6.00/6.29 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[1048, 2779, 1035])).
% 6.00/6.29 tff(2781,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 6.00/6.29 tff(2782,plain,
% 6.00/6.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 6.00/6.29 inference(rewrite,[status(thm)],[])).
% 6.00/6.29 tff(2783,plain,
% 6.00/6.29 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 6.00/6.29 inference(rewrite,[status(thm)],[])).
% 6.00/6.29 tff(2784,plain,
% 6.00/6.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 6.00/6.29 inference(monotonicity,[status(thm)],[2783])).
% 6.00/6.29 tff(2785,plain,
% 6.00/6.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 6.00/6.29 inference(transitivity,[status(thm)],[2784, 2782])).
% 6.00/6.29 tff(2786,plain,
% 6.00/6.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 6.00/6.29 inference(quant_inst,[status(thm)],[])).
% 6.00/6.29 tff(2787,plain,
% 6.00/6.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 6.00/6.29 inference(modus_ponens,[status(thm)],[2786, 2785])).
% 6.00/6.29 tff(2788,plain,
% 6.00/6.29 ($false),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2787, 391, 380, 2641, 1733, 2781, 1573])).
% 6.00/6.29 tff(2789,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 6.00/6.29 tff(2790,plain,
% 6.00/6.29 (~b(z, s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2789, 2778, 2641, 380, 1573])).
% 6.00/6.29 tff(2791,plain,
% 6.00/6.29 (r(z, s(s(s(s(elem!1)))))),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2767, 2790])).
% 6.00/6.29 tff(2792,assumption,(r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 6.00/6.29 tff(2793,plain,
% 6.00/6.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 6.00/6.29 inference(rewrite,[status(thm)],[])).
% 6.00/6.29 tff(2794,plain,
% 6.00/6.29 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 6.00/6.29 inference(rewrite,[status(thm)],[])).
% 6.00/6.29 tff(2795,plain,
% 6.00/6.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 6.00/6.29 inference(monotonicity,[status(thm)],[2794])).
% 6.00/6.29 tff(2796,plain,
% 6.00/6.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 6.00/6.29 inference(transitivity,[status(thm)],[2795, 2793])).
% 6.00/6.29 tff(2797,plain,
% 6.00/6.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))),
% 6.00/6.29 inference(quant_inst,[status(thm)],[])).
% 6.00/6.29 tff(2798,plain,
% 6.00/6.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 6.00/6.29 inference(modus_ponens,[status(thm)],[2797, 2796])).
% 6.00/6.29 tff(2799,plain,
% 6.00/6.29 ($false),
% 6.00/6.29 inference(unit_resolution,[status(thm)],[2798, 194, 326, 991, 2792, 1176])).
% 6.10/6.30 tff(2800,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.30 tff(2801,plain,
% 6.10/6.30 (~r(s(s(s(s(elem!1)))), elem!1)),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2800, 2791, 326, 2780])).
% 6.10/6.30 tff(2802,plain,
% 6.10/6.30 (s(s(s(s(elem!1)))) = elem!1),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[1004, 2801, 2707])).
% 6.10/6.30 tff(2803,plain,
% 6.10/6.30 (elem!1 = s(s(s(s(elem!1))))),
% 6.10/6.30 inference(symmetry,[status(thm)],[2802])).
% 6.10/6.30 tff(2804,plain,
% 6.10/6.30 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 6.10/6.30 inference(transitivity,[status(thm)],[2722, 2803])).
% 6.10/6.30 tff(2805,plain,
% 6.10/6.30 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 6.10/6.30 inference(monotonicity,[status(thm)],[2804])).
% 6.10/6.30 tff(2806,plain,
% 6.10/6.30 (s(s(s(z))) = s(s(s(elem!1)))),
% 6.10/6.30 inference(transitivity,[status(thm)],[693, 2805, 294])).
% 6.10/6.30 tff(2807,plain,
% 6.10/6.30 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 6.10/6.30 inference(monotonicity,[status(thm)],[2806])).
% 6.10/6.30 tff(2808,plain,
% 6.10/6.30 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 6.10/6.30 inference(symmetry,[status(thm)],[2807])).
% 6.10/6.30 tff(2809,plain,
% 6.10/6.30 (s(s(elem!1)) = s(s(z))),
% 6.10/6.30 inference(transitivity,[status(thm)],[212, 2808, 685])).
% 6.10/6.30 tff(2810,plain,
% 6.10/6.30 ($false),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2689, 2809])).
% 6.10/6.30 tff(2811,plain,((~r(s(z), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(s(z)))), elem!1) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | r(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.30 tff(2812,plain,
% 6.10/6.30 (~r(s(z), s(s(s(s(z)))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2811, 719, 326, 2641, 380, 1573, 900, 1101, 1035, 1374, 364, 1549, 182, 2689, 2688])).
% 6.10/6.30 tff(2813,plain,
% 6.10/6.30 (b(s(z), s(s(s(s(z)))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[1230, 2812])).
% 6.10/6.30 tff(2814,plain,
% 6.10/6.30 (~r(s(s(s(s(z)))), s(z))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2648, 125, 1484, 1294, 340])).
% 6.10/6.30 tff(2815,plain,
% 6.10/6.30 (b(s(s(s(s(z)))), s(z))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[749, 2814])).
% 6.10/6.30 tff(2816,plain,
% 6.10/6.30 ($false),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2097, 2815, 2642, 411, 1234, 719, 721])).
% 6.10/6.30 tff(2817,plain,((~(elem!1 = s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.30 tff(2818,plain,
% 6.10/6.30 (~(elem!1 = s(s(s(elem!1))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2817, 2813, 411, 719, 721, 1484, 1294, 340])).
% 6.10/6.30 tff(2819,plain,
% 6.10/6.30 (b(elem!1, s(s(s(elem!1))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[424, 2818, 2688])).
% 6.10/6.30 tff(2820,plain,
% 6.10/6.30 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2665, 2819, 1526, 2641, 721, 2813])).
% 6.10/6.30 tff(2821,plain,
% 6.10/6.30 (~r(s(s(s(s(z)))), s(z))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2028, 720, 1294, 1484, 1983, 340])).
% 6.10/6.30 tff(2822,plain,
% 6.10/6.30 (~b(s(s(s(s(z)))), s(z))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2097, 720, 411, 1234, 719, 721])).
% 6.10/6.30 tff(2823,plain,
% 6.10/6.30 ($false),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[749, 2822, 2821])).
% 6.10/6.30 tff(2824,plain,((s(s(s(s(z)))) = elem!1) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.30 tff(2825,plain,
% 6.10/6.30 (s(s(s(s(z)))) = elem!1),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2824, 2813, 411, 719, 721, 1294, 1484, 2820, 340])).
% 6.10/6.30 tff(2826,plain,
% 6.10/6.30 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 6.10/6.30 inference(monotonicity,[status(thm)],[2825])).
% 6.10/6.30 tff(2827,plain,
% 6.10/6.30 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(z)))))),
% 6.10/6.30 inference(symmetry,[status(thm)],[2826])).
% 6.10/6.30 tff(2828,plain,
% 6.10/6.30 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(s(z))))))),
% 6.10/6.30 inference(monotonicity,[status(thm)],[2827])).
% 6.10/6.30 tff(2829,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 6.10/6.30 tff(2830,plain,
% 6.10/6.30 (~b(s(z), s(s(s(s(z)))))),
% 6.10/6.30 inference(modus_ponens,[status(thm)],[2829, 2828])).
% 6.10/6.30 tff(2831,plain,
% 6.10/6.30 ($false),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2813, 2830])).
% 6.10/6.30 tff(2832,plain,((~r(z, s(s(s(s(z)))))) | b(s(z), elem!1) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(s(z)))), elem!1) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.30 tff(2833,plain,
% 6.10/6.30 (b(s(s(s(s(z)))), elem!1)),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2832, 2679, 411, 2601, 2552, 2574, 340, 1526, 2630, 326, 2208, 1573, 900, 2498, 2687, 1374, 2554, 2573, 182, 2680])).
% 6.10/6.30 tff(2834,plain,
% 6.10/6.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.10/6.30 inference(rewrite,[status(thm)],[])).
% 6.10/6.30 tff(2835,plain,
% 6.10/6.30 (((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.10/6.30 inference(rewrite,[status(thm)],[])).
% 6.10/6.30 tff(2836,plain,
% 6.10/6.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 6.10/6.30 inference(monotonicity,[status(thm)],[2835])).
% 6.10/6.30 tff(2837,plain,
% 6.10/6.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.10/6.30 inference(transitivity,[status(thm)],[2836, 2834])).
% 6.10/6.30 tff(2838,plain,
% 6.10/6.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.10/6.30 inference(quant_inst,[status(thm)],[])).
% 6.10/6.30 tff(2839,plain,
% 6.10/6.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.10/6.30 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 6.10/6.30 tff(2840,plain,
% 6.10/6.30 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2839, 391, 900, 2552, 2630, 2833])).
% 6.10/6.30 tff(2841,assumption,(s(s(s(s(z)))) = s(s(s(elem!1)))), introduced(assumption)).
% 6.10/6.30 tff(2842,plain,
% 6.10/6.30 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 6.10/6.30 inference(monotonicity,[status(thm)],[2841])).
% 6.10/6.30 tff(2843,plain,
% 6.10/6.30 (s(s(s(z))) = s(s(elem!1))),
% 6.10/6.30 inference(transitivity,[status(thm)],[693, 2842, 211])).
% 6.10/6.30 tff(2844,plain,
% 6.10/6.30 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 6.10/6.30 inference(monotonicity,[status(thm)],[2843])).
% 6.10/6.30 tff(2845,plain,
% 6.10/6.30 (s(s(z)) = s(elem!1)),
% 6.10/6.30 inference(transitivity,[status(thm)],[710, 2844, 259])).
% 6.10/6.30 tff(2846,plain,
% 6.10/6.30 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 6.10/6.30 inference(monotonicity,[status(thm)],[2845])).
% 6.10/6.30 tff(2847,plain,
% 6.10/6.30 (s(z) = elem!1),
% 6.10/6.30 inference(transitivity,[status(thm)],[706, 2846, 108])).
% 6.10/6.30 tff(2848,plain,
% 6.10/6.30 ($false),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[150, 2847])).
% 6.10/6.30 tff(2849,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.10/6.30 tff(2850,plain,
% 6.10/6.30 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2849, 2571])).
% 6.10/6.30 tff(2851,plain,
% 6.10/6.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.10/6.30 inference(rewrite,[status(thm)],[])).
% 6.10/6.30 tff(2852,plain,
% 6.10/6.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.10/6.30 inference(quant_inst,[status(thm)],[])).
% 6.10/6.30 tff(2853,plain,
% 6.10/6.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.30 inference(modus_ponens,[status(thm)],[2852, 2851])).
% 6.10/6.30 tff(2854,plain,
% 6.10/6.30 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2853, 42, 2850, 2840])).
% 6.10/6.30 tff(2855,plain,
% 6.10/6.30 (~r(s(z), s(s(s(s(z)))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2108, 2854, 182, 2679])).
% 6.10/6.30 tff(2856,plain,
% 6.10/6.30 (b(s(z), s(s(s(s(z)))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[1230, 2855])).
% 6.10/6.30 tff(2857,plain,
% 6.10/6.30 (~(elem!1 = s(s(s(elem!1))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2817, 2856, 411, 2679, 2601, 2574, 2552, 340])).
% 6.10/6.30 tff(2858,plain,
% 6.10/6.30 (b(elem!1, s(s(s(elem!1))))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[424, 2857, 2563])).
% 6.10/6.30 tff(2859,plain,
% 6.10/6.30 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2665, 2858, 1526, 2630, 2601, 2856])).
% 6.10/6.30 tff(2860,plain,
% 6.10/6.30 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 6.10/6.30 inference(monotonicity,[status(thm)],[688])).
% 6.10/6.30 tff(2861,plain,
% 6.10/6.30 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.30 inference(symmetry,[status(thm)],[2860])).
% 6.10/6.30 tff(2862,plain,
% 6.10/6.30 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.30 inference(modus_ponens,[status(thm)],[448, 2861])).
% 6.10/6.30 tff(2863,assumption,(~b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 6.10/6.30 tff(2864,plain,
% 6.10/6.30 ($false),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2863, 2862])).
% 6.10/6.30 tff(2865,plain,((~(s(s(s(s(z)))) = elem!1)) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.30 tff(2866,plain,
% 6.10/6.30 (~(s(s(s(s(z)))) = elem!1)),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2865, 2858, 2840])).
% 6.10/6.30 tff(2867,plain,
% 6.10/6.30 ($false),
% 6.10/6.30 inference(unit_resolution,[status(thm)],[2824, 2866, 2859, 411, 2679, 2601, 2552, 2574, 2856, 340])).
% 6.10/6.30 tff(2868,plain,((elem!1 = z) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.31 tff(2869,plain,
% 6.10/6.31 (elem!1 = z),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2868, 2458, 1831, 2203, 182, 2193, 326, 1829, 1374, 232, 59])).
% 6.10/6.31 tff(2870,plain,
% 6.10/6.31 (r(z, elem!1) <=> r(z, z)),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2869])).
% 6.10/6.31 tff(2871,plain,
% 6.10/6.31 (r(z, z) <=> r(z, elem!1)),
% 6.10/6.31 inference(symmetry,[status(thm)],[2870])).
% 6.10/6.31 tff(2872,plain,
% 6.10/6.31 ((~r(z, z)) <=> (~r(z, elem!1))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2871])).
% 6.10/6.31 tff(2873,plain,
% 6.10/6.31 (~r(z, elem!1)),
% 6.10/6.31 inference(modus_ponens,[status(thm)],[78, 2872])).
% 6.10/6.31 tff(2874,plain,
% 6.10/6.31 ($false),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2458, 2873])).
% 6.10/6.31 tff(2875,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(elem!1)), s(z)) | b(z, s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.31 tff(2876,plain,
% 6.10/6.31 (~r(s(z), s(s(s(elem!1))))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2875, 1798, 326, 1374, 1378, 182, 10, 1351, 1373])).
% 6.10/6.31 tff(2877,plain,
% 6.10/6.31 (b(s(z), s(s(s(elem!1))))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[247, 2876])).
% 6.10/6.31 tff(2878,plain,
% 6.10/6.31 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[1552])).
% 6.10/6.31 tff(2879,plain,
% 6.10/6.31 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(elem!1))))),
% 6.10/6.31 inference(symmetry,[status(thm)],[2878])).
% 6.10/6.31 tff(2880,plain,
% 6.10/6.31 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2879])).
% 6.10/6.31 tff(2881,assumption,(~b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 6.10/6.31 tff(2882,plain,
% 6.10/6.31 (~b(s(z), s(s(s(elem!1))))),
% 6.10/6.31 inference(modus_ponens,[status(thm)],[2881, 2880])).
% 6.10/6.31 tff(2883,plain,
% 6.10/6.31 ($false),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[379, 2882])).
% 6.10/6.31 tff(2884,plain,((~(elem!1 = s(z))) | (~b(s(z), s(s(s(elem!1))))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.31 tff(2885,plain,
% 6.10/6.31 (b(s(z), s(s(s(s(z)))))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2884, 1820, 2877])).
% 6.10/6.31 tff(2886,plain,
% 6.10/6.31 (s(elem!1) = s(s(z))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[1820])).
% 6.10/6.31 tff(2887,plain,
% 6.10/6.31 (s(s(elem!1)) = s(s(s(z)))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2886])).
% 6.10/6.31 tff(2888,plain,
% 6.10/6.31 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2887])).
% 6.10/6.31 tff(2889,plain,
% 6.10/6.31 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2888])).
% 6.10/6.31 tff(2890,plain,
% 6.10/6.31 (b(s(s(s(s(z)))), z)),
% 6.10/6.31 inference(modus_ponens,[status(thm)],[1452, 2889])).
% 6.10/6.31 tff(2891,plain,
% 6.10/6.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.10/6.31 inference(rewrite,[status(thm)],[])).
% 6.10/6.31 tff(2892,plain,
% 6.10/6.31 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(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))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.10/6.31 inference(rewrite,[status(thm)],[])).
% 6.10/6.31 tff(2893,plain,
% 6.10/6.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2892])).
% 6.10/6.31 tff(2894,plain,
% 6.10/6.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.10/6.31 inference(transitivity,[status(thm)],[2893, 2891])).
% 6.10/6.31 tff(2895,plain,
% 6.10/6.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 6.10/6.31 inference(quant_inst,[status(thm)],[])).
% 6.10/6.31 tff(2896,plain,
% 6.10/6.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 6.10/6.31 inference(modus_ponens,[status(thm)],[2895, 2894])).
% 6.10/6.31 tff(2897,plain,
% 6.10/6.31 ($false),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2896, 391, 2890, 2885, 1827, 1824])).
% 6.10/6.31 tff(2898,plain,(b(elem!1, s(z)) | r(z, elem!1) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(z, s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.31 tff(2899,plain,
% 6.10/6.31 (b(elem!1, s(z))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2898, 80, 326, 182, 1374, 1378, 10, 1351, 1373])).
% 6.10/6.31 tff(2900,plain,
% 6.10/6.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.10/6.31 inference(rewrite,[status(thm)],[])).
% 6.10/6.31 tff(2901,plain,
% 6.10/6.31 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(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))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.10/6.31 inference(rewrite,[status(thm)],[])).
% 6.10/6.31 tff(2902,plain,
% 6.10/6.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2901])).
% 6.10/6.31 tff(2903,plain,
% 6.10/6.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.10/6.31 inference(transitivity,[status(thm)],[2902, 2900])).
% 6.10/6.31 tff(2904,plain,
% 6.10/6.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 6.10/6.31 inference(quant_inst,[status(thm)],[])).
% 6.10/6.31 tff(2905,plain,
% 6.10/6.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.10/6.31 inference(modus_ponens,[status(thm)],[2904, 2903])).
% 6.10/6.31 tff(2906,plain,
% 6.10/6.31 ($false),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2905, 391, 900, 379, 1526, 721])).
% 6.10/6.31 tff(2907,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.31 tff(2908,plain,
% 6.10/6.31 (~b(s(z), s(s(s(elem!1))))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2907, 1441, 1420, 2899])).
% 6.10/6.31 tff(2909,plain,
% 6.10/6.31 (r(s(z), s(s(s(elem!1))))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[247, 2908])).
% 6.10/6.31 tff(2910,plain,
% 6.10/6.31 (~r(s(s(s(elem!1))), s(elem!1))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[641, 2909, 59, 182])).
% 6.10/6.31 tff(2911,plain,
% 6.10/6.31 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[1546, 2909, 59, 182])).
% 6.10/6.31 tff(2912,plain,
% 6.10/6.31 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[1164, 2911, 1373])).
% 6.10/6.31 tff(2913,plain,
% 6.10/6.31 (r(s(z), s(s(s(s(z)))))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[1230, 2881])).
% 6.10/6.31 tff(2914,plain,
% 6.10/6.31 (elem!1 = s(s(elem!1))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[1479, 812, 1378, 326, 1374, 900, 182, 381])).
% 6.10/6.31 tff(2915,plain,
% 6.10/6.31 (s(s(elem!1)) = elem!1),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[1292, 2914])).
% 6.10/6.31 tff(2916,plain,
% 6.10/6.31 (s(s(s(elem!1))) = s(elem!1)),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[451, 2915])).
% 6.10/6.31 tff(2917,plain,
% 6.10/6.31 (~(s(s(z)) = s(elem!1))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2493, 2916])).
% 6.10/6.31 tff(2918,plain,
% 6.10/6.31 ($false),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2917, 818])).
% 6.10/6.31 tff(2919,plain,((~(s(z) = elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.31 tff(2920,plain,
% 6.10/6.31 (~(s(z) = elem!1)),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[2919, 381, 326, 1374, 900, 182, 1378])).
% 6.10/6.31 tff(2921,plain,
% 6.10/6.31 (~(elem!1 = s(z))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[172, 2920])).
% 6.10/6.31 tff(2922,plain,
% 6.10/6.31 (elem!1 = z),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[1516, 2921, 1454, 80, 900, 326, 182, 184])).
% 6.10/6.31 tff(2923,plain,
% 6.10/6.31 (s(elem!1) = s(z)),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2922])).
% 6.10/6.31 tff(2924,plain,
% 6.10/6.31 (s(s(elem!1)) = s(s(z))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2923])).
% 6.10/6.31 tff(2925,plain,
% 6.10/6.31 (s(s(z)) = s(s(elem!1))),
% 6.10/6.31 inference(symmetry,[status(thm)],[2924])).
% 6.10/6.31 tff(2926,plain,
% 6.10/6.31 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2925])).
% 6.10/6.31 tff(2927,plain,
% 6.10/6.31 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 6.10/6.31 inference(symmetry,[status(thm)],[2926])).
% 6.10/6.31 tff(2928,plain,
% 6.10/6.31 (b(s(s(z)), s(z))),
% 6.10/6.31 inference(modus_ponens,[status(thm)],[381, 2927])).
% 6.10/6.31 tff(2929,plain,
% 6.10/6.31 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2922])).
% 6.10/6.31 tff(2930,plain,
% 6.10/6.31 (b(s(s(s(s(z)))), z)),
% 6.10/6.31 inference(modus_ponens,[status(thm)],[1651, 2929])).
% 6.10/6.31 tff(2931,plain,
% 6.10/6.31 (b(s(s(s(z))), z)),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[1680, 2922, 1454])).
% 6.10/6.31 tff(2932,plain,
% 6.10/6.31 (s(s(s(elem!1))) = s(s(s(z)))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2924])).
% 6.10/6.31 tff(2933,plain,
% 6.10/6.31 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2932])).
% 6.10/6.31 tff(2934,plain,
% 6.10/6.31 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 6.10/6.31 inference(monotonicity,[status(thm)],[2932, 2933])).
% 6.10/6.31 tff(2935,plain,
% 6.10/6.31 (b(s(s(s(z))), s(s(s(s(z)))))),
% 6.10/6.31 inference(modus_ponens,[status(thm)],[1548, 2934])).
% 6.10/6.31 tff(2936,plain,
% 6.10/6.31 (~b(z, s(s(s(s(z)))))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[1694, 2935, 2931, 2930])).
% 6.10/6.31 tff(2937,plain,
% 6.10/6.31 (r(z, s(s(s(s(z)))))),
% 6.10/6.31 inference(unit_resolution,[status(thm)],[800, 2936])).
% 6.10/6.32 tff(2938,plain,
% 6.10/6.32 (~r(s(s(s(s(z)))), s(s(z)))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1705, 2937, 182, 1216])).
% 6.10/6.32 tff(2939,plain,
% 6.10/6.32 (b(s(s(s(s(z)))), s(s(z)))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1714, 2938])).
% 6.10/6.32 tff(2940,plain,
% 6.10/6.32 (~r(s(s(s(s(z)))), s(z))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1224, 2937, 182, 1216])).
% 6.10/6.32 tff(2941,plain,
% 6.10/6.32 (b(s(s(s(s(z)))), s(z))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[749, 2940])).
% 6.10/6.32 tff(2942,plain,
% 6.10/6.32 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2922])).
% 6.10/6.32 tff(2943,plain,
% 6.10/6.32 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 6.10/6.32 inference(symmetry,[status(thm)],[2942])).
% 6.10/6.32 tff(2944,plain,
% 6.10/6.32 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2924])).
% 6.10/6.32 tff(2945,plain,
% 6.10/6.32 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 6.10/6.32 inference(transitivity,[status(thm)],[2944, 2943])).
% 6.10/6.32 tff(2946,plain,
% 6.10/6.32 (r(elem!1, s(s(z)))),
% 6.10/6.32 inference(modus_ponens,[status(thm)],[326, 2945])).
% 6.10/6.32 tff(2947,plain,
% 6.10/6.32 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2924, 2933])).
% 6.10/6.32 tff(2948,plain,
% 6.10/6.32 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2933, 2924])).
% 6.10/6.32 tff(2949,plain,
% 6.10/6.32 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 6.10/6.32 inference(transitivity,[status(thm)],[2948, 940])).
% 6.10/6.32 tff(2950,plain,
% 6.10/6.32 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 6.10/6.32 inference(symmetry,[status(thm)],[2949])).
% 6.10/6.32 tff(2951,plain,
% 6.10/6.32 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 6.10/6.32 inference(transitivity,[status(thm)],[2950, 1021])).
% 6.10/6.32 tff(2952,plain,
% 6.10/6.32 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2951])).
% 6.10/6.32 tff(2953,plain,
% 6.10/6.32 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 6.10/6.32 inference(modus_ponens,[status(thm)],[714, 2952])).
% 6.10/6.32 tff(2954,plain,
% 6.10/6.32 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2933, 2924])).
% 6.10/6.32 tff(2955,plain,
% 6.10/6.32 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.10/6.32 inference(symmetry,[status(thm)],[2954])).
% 6.10/6.32 tff(2956,plain,
% 6.10/6.32 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.10/6.32 inference(modus_ponens,[status(thm)],[2939, 2955])).
% 6.10/6.32 tff(2957,plain,
% 6.10/6.32 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1741, 2956, 1374, 1548])).
% 6.10/6.32 tff(2958,plain,
% 6.10/6.32 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1048, 2957, 2953])).
% 6.10/6.32 tff(2959,plain,
% 6.10/6.32 (r(s(s(z)), s(s(s(s(z)))))),
% 6.10/6.32 inference(modus_ponens,[status(thm)],[2958, 2947])).
% 6.10/6.32 tff(2960,plain,
% 6.10/6.32 (~r(s(z), s(s(z)))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1775, 2959, 2946, 2920, 2941, 1651])).
% 6.10/6.32 tff(2961,plain,
% 6.10/6.32 (b(s(z), s(s(z)))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1788, 2960])).
% 6.10/6.32 tff(2962,plain,
% 6.10/6.32 ($false),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1795, 391, 2941, 2961, 2939, 2928])).
% 6.10/6.32 tff(2963,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))) | r(z, elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.32 tff(2964,plain,
% 6.10/6.32 (~b(s(s(elem!1)), s(z))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[2963, 2913, 182, 1374, 326, 80, 1441, 59, 1378, 1442, 1373])).
% 6.10/6.32 tff(2965,plain,
% 6.10/6.32 (~r(s(z), s(s(s(elem!1))))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[2875, 2964, 326, 1374, 1378, 182, 10, 1351, 1373])).
% 6.10/6.32 tff(2966,plain,
% 6.10/6.32 (b(s(z), s(s(s(elem!1))))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[247, 2965])).
% 6.10/6.32 tff(2967,plain,
% 6.10/6.32 (~(elem!1 = s(z))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[2884, 2966, 2881])).
% 6.10/6.32 tff(2968,plain,
% 6.10/6.32 (elem!1 = z),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1516, 2967, 1452, 80, 1441, 326, 182, 59])).
% 6.10/6.32 tff(2969,plain,
% 6.10/6.32 (b(s(s(s(z))), z)),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1680, 2968, 1452])).
% 6.10/6.32 tff(2970,plain,
% 6.10/6.32 (s(elem!1) = s(z)),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2968])).
% 6.10/6.32 tff(2971,plain,
% 6.10/6.32 (s(s(elem!1)) = s(s(z))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2970])).
% 6.10/6.32 tff(2972,plain,
% 6.10/6.32 (s(s(s(elem!1))) = s(s(s(z)))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2971])).
% 6.10/6.32 tff(2973,plain,
% 6.10/6.32 (s(s(s(z))) = s(s(s(elem!1)))),
% 6.10/6.32 inference(symmetry,[status(thm)],[2972])).
% 6.10/6.32 tff(2974,plain,
% 6.10/6.32 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2973])).
% 6.10/6.32 tff(2975,plain,
% 6.10/6.32 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 6.10/6.32 inference(symmetry,[status(thm)],[2974])).
% 6.10/6.32 tff(2976,plain,
% 6.10/6.32 (b(s(z), s(s(s(z))))),
% 6.10/6.32 inference(modus_ponens,[status(thm)],[2966, 2975])).
% 6.10/6.32 tff(2977,plain,
% 6.10/6.32 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2973])).
% 6.10/6.32 tff(2978,plain,
% 6.10/6.32 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 6.10/6.32 inference(symmetry,[status(thm)],[2977])).
% 6.10/6.32 tff(2979,plain,
% 6.10/6.32 (b(s(s(s(z))), s(z))),
% 6.10/6.32 inference(modus_ponens,[status(thm)],[1420, 2978])).
% 6.10/6.32 tff(2980,plain,
% 6.10/6.32 (s(s(z)) = s(s(elem!1))),
% 6.10/6.32 inference(symmetry,[status(thm)],[489])).
% 6.10/6.32 tff(2981,plain,
% 6.10/6.32 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[491, 2980])).
% 6.10/6.32 tff(2982,plain,
% 6.10/6.32 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 6.10/6.32 inference(symmetry,[status(thm)],[2981])).
% 6.10/6.32 tff(2983,plain,
% 6.10/6.32 (b(s(s(s(z))), s(s(z)))),
% 6.10/6.32 inference(modus_ponens,[status(thm)],[1374, 2982])).
% 6.10/6.32 tff(2984,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 6.10/6.32 tff(2985,plain,
% 6.10/6.32 ($false),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[2984, 2983])).
% 6.10/6.32 tff(2986,plain,(b(s(s(s(z))), s(s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.32 tff(2987,plain,
% 6.10/6.32 (b(s(s(s(z))), s(s(z)))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[2986, 2968, 1374])).
% 6.10/6.32 tff(2988,plain,
% 6.10/6.32 (b(elem!1, s(z)) <=> b(z, s(z))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2968])).
% 6.10/6.32 tff(2989,plain,
% 6.10/6.32 (b(z, s(z))),
% 6.10/6.32 inference(modus_ponens,[status(thm)],[2899, 2988])).
% 6.10/6.32 tff(2990,plain,
% 6.10/6.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 6.10/6.32 inference(rewrite,[status(thm)],[])).
% 6.10/6.32 tff(2991,plain,
% 6.10/6.32 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 6.10/6.32 inference(rewrite,[status(thm)],[])).
% 6.10/6.32 tff(2992,plain,
% 6.10/6.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 6.10/6.32 inference(monotonicity,[status(thm)],[2991])).
% 6.10/6.32 tff(2993,plain,
% 6.10/6.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 6.10/6.32 inference(transitivity,[status(thm)],[2992, 2990])).
% 6.10/6.32 tff(2994,plain,
% 6.10/6.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 6.10/6.32 inference(quant_inst,[status(thm)],[])).
% 6.10/6.32 tff(2995,plain,
% 6.10/6.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 6.10/6.32 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 6.10/6.32 tff(2996,plain,
% 6.10/6.32 ($false),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[2995, 391, 2989, 2987, 2979, 2976, 2969])).
% 6.10/6.32 tff(2997,plain,(b(s(z), s(s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | r(z, elem!1) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(z, s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.32 tff(2998,plain,
% 6.10/6.32 (b(s(z), s(s(s(s(z)))))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[2997, 80, 1374, 326, 182, 1378, 10, 1351, 1373])).
% 6.10/6.32 tff(2999,plain,
% 6.10/6.32 (b(s(s(elem!1)), s(z))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[2875, 2909, 326, 1374, 1378, 182, 10, 1351, 1373])).
% 6.10/6.32 tff(3000,plain,
% 6.10/6.32 (~b(s(s(s(s(z)))), elem!1)),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1660, 2999, 1374, 1420, 2998])).
% 6.10/6.32 tff(3001,plain,
% 6.10/6.32 ($false),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1650, 3000, 2912, 59, 80, 2910, 182, 1452, 1442, 1441, 326])).
% 6.10/6.32 tff(3002,plain,(r(z, elem!1) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(z, s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.32 tff(3003,plain,
% 6.10/6.32 (r(z, elem!1)),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[3002, 1378, 326, 1374, 1373, 182, 10, 1351])).
% 6.10/6.32 tff(3004,plain,
% 6.10/6.32 (elem!1 = s(s(s(elem!1)))),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[8, 1388])).
% 6.10/6.32 tff(3005,plain,
% 6.10/6.32 (~b(s(s(elem!1)), elem!1)),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[1887, 3004, 1351])).
% 6.10/6.32 tff(3006,plain,
% 6.10/6.32 (r(s(s(elem!1)), elem!1)),
% 6.10/6.32 inference(unit_resolution,[status(thm)],[872, 3005, 1846])).
% 6.10/6.32 tff(3007,plain,
% 6.10/6.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.10/6.32 inference(rewrite,[status(thm)],[])).
% 6.10/6.32 tff(3008,plain,
% 6.10/6.32 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, 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)) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.10/6.33 inference(rewrite,[status(thm)],[])).
% 6.10/6.33 tff(3009,plain,
% 6.10/6.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z))))))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3008])).
% 6.10/6.33 tff(3010,plain,
% 6.10/6.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.10/6.33 inference(transitivity,[status(thm)],[3009, 3007])).
% 6.10/6.33 tff(3011,plain,
% 6.10/6.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 6.10/6.33 inference(quant_inst,[status(thm)],[])).
% 6.10/6.33 tff(3012,plain,
% 6.10/6.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[3011, 3010])).
% 6.10/6.33 tff(3013,plain,
% 6.10/6.33 ($false),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[3012, 194, 411, 364, 326, 2032])).
% 6.10/6.33 tff(3014,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.33 tff(3015,plain,
% 6.10/6.33 (~r(elem!1, s(s(s(s(z)))))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[3014, 3006, 3003, 326])).
% 6.10/6.33 tff(3016,plain,
% 6.10/6.33 (b(elem!1, s(s(s(s(z)))))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[781, 3015, 1438])).
% 6.10/6.33 tff(3017,plain,
% 6.10/6.33 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 6.10/6.33 inference(monotonicity,[status(thm)],[1388])).
% 6.10/6.33 tff(3018,plain,
% 6.10/6.33 (~b(s(z), s(s(s(elem!1))))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[1534, 381, 1452, 1374, 1420])).
% 6.10/6.33 tff(3019,plain,
% 6.10/6.33 (r(s(z), s(s(s(elem!1))))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[247, 3018])).
% 6.10/6.33 tff(3020,plain,
% 6.10/6.33 (~r(s(s(s(elem!1))), elem!1)),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[241, 3019, 59, 182])).
% 6.10/6.33 tff(3021,plain,
% 6.10/6.33 (s(s(s(elem!1))) = elem!1),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[230, 3020, 168])).
% 6.10/6.33 tff(3022,plain,
% 6.10/6.33 (elem!1 = s(s(s(elem!1)))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[8, 3021])).
% 6.10/6.33 tff(3023,plain,
% 6.10/6.33 (s(elem!1) = s(s(s(s(elem!1))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3022])).
% 6.10/6.33 tff(3024,plain,
% 6.10/6.33 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3023])).
% 6.10/6.33 tff(3025,plain,
% 6.10/6.33 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 6.10/6.33 inference(symmetry,[status(thm)],[3024])).
% 6.10/6.33 tff(3026,plain,
% 6.10/6.33 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3025])).
% 6.10/6.33 tff(3027,plain,
% 6.10/6.33 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 6.10/6.33 inference(symmetry,[status(thm)],[3026])).
% 6.10/6.33 tff(3028,plain,
% 6.10/6.33 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[1374, 3027])).
% 6.10/6.33 tff(3029,plain,
% 6.10/6.33 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3025])).
% 6.10/6.33 tff(3030,plain,
% 6.10/6.33 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 6.10/6.33 inference(symmetry,[status(thm)],[3029])).
% 6.10/6.33 tff(3031,plain,
% 6.10/6.33 (b(s(s(s(s(s(elem!1))))), s(z))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[381, 3030])).
% 6.10/6.33 tff(3032,plain,
% 6.10/6.33 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3025])).
% 6.10/6.33 tff(3033,plain,
% 6.10/6.33 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 6.10/6.33 inference(symmetry,[status(thm)],[3032])).
% 6.10/6.33 tff(3034,plain,
% 6.10/6.33 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3023])).
% 6.10/6.33 tff(3035,plain,
% 6.10/6.33 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 6.10/6.33 inference(transitivity,[status(thm)],[3034, 1020])).
% 6.10/6.33 tff(3036,plain,
% 6.10/6.33 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3035])).
% 6.10/6.33 tff(3037,plain,
% 6.10/6.33 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[1847, 3036])).
% 6.10/6.33 tff(3038,plain,
% 6.10/6.33 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3025])).
% 6.10/6.33 tff(3039,plain,
% 6.10/6.33 ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3038])).
% 6.10/6.33 tff(3040,plain,
% 6.10/6.33 (r(z, s(elem!1)) <=> r(z, s(s(s(s(elem!1)))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3023])).
% 6.10/6.33 tff(3041,plain,
% 6.10/6.33 (~r(s(s(s(elem!1))), s(elem!1))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[641, 3019, 59, 182])).
% 6.10/6.33 tff(3042,plain,
% 6.10/6.33 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 6.10/6.33 inference(commutativity,[status(thm)],[])).
% 6.10/6.33 tff(3043,plain,
% 6.10/6.33 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3022])).
% 6.10/6.33 tff(3044,plain,
% 6.10/6.33 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 6.10/6.33 inference(transitivity,[status(thm)],[3043, 3042])).
% 6.10/6.33 tff(3045,plain,
% 6.10/6.33 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 6.10/6.33 inference(symmetry,[status(thm)],[3044])).
% 6.10/6.33 tff(3046,plain,
% 6.10/6.33 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3045])).
% 6.10/6.33 tff(3047,plain,
% 6.10/6.33 (~(z = elem!1)),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[50, 3046])).
% 6.10/6.33 tff(3048,plain,
% 6.10/6.33 (~(s(z) = s(elem!1))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[117, 3047])).
% 6.10/6.33 tff(3049,plain,
% 6.10/6.33 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3022])).
% 6.10/6.33 tff(3050,plain,
% 6.10/6.33 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 6.10/6.33 inference(symmetry,[status(thm)],[3049])).
% 6.10/6.33 tff(3051,plain,
% 6.10/6.33 (b(elem!1, s(z))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[1420, 3050])).
% 6.10/6.33 tff(3052,plain,
% 6.10/6.33 (r(z, elem!1)),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[147, 3022, 10])).
% 6.10/6.33 tff(3053,plain,
% 6.10/6.33 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3022])).
% 6.10/6.33 tff(3054,plain,
% 6.10/6.33 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 6.10/6.33 inference(symmetry,[status(thm)],[3053])).
% 6.10/6.33 tff(3055,plain,
% 6.10/6.33 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3023])).
% 6.10/6.33 tff(3056,plain,
% 6.10/6.33 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 6.10/6.33 inference(symmetry,[status(thm)],[3055])).
% 6.10/6.33 tff(3057,plain,
% 6.10/6.33 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(elem!1, s(elem!1))),
% 6.10/6.33 inference(transitivity,[status(thm)],[3056, 3054])).
% 6.10/6.33 tff(3058,plain,
% 6.10/6.33 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[1546, 3019, 59, 182])).
% 6.10/6.33 tff(3059,plain,
% 6.10/6.33 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[1164, 3058, 1373])).
% 6.10/6.33 tff(3060,plain,
% 6.10/6.33 (b(elem!1, s(elem!1))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[3059, 3057])).
% 6.10/6.33 tff(3061,plain,
% 6.10/6.33 (~r(s(elem!1), z)),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[1930, 3060, 3052, 3051, 3048, 182])).
% 6.10/6.33 tff(3062,plain,
% 6.10/6.33 (b(s(elem!1), z)),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[549, 3061])).
% 6.10/6.33 tff(3063,plain,
% 6.10/6.33 (r(z, s(elem!1))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[2614, 3062, 1452, 3041, 59])).
% 6.10/6.33 tff(3064,plain,
% 6.10/6.33 (r(z, s(s(s(s(elem!1)))))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[3063, 3040])).
% 6.10/6.33 tff(3065,plain,
% 6.10/6.33 (s(elem!1) = s(s(s(s(elem!1))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[125])).
% 6.10/6.33 tff(3066,plain,
% 6.10/6.33 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3065])).
% 6.10/6.33 tff(3067,plain,
% 6.10/6.33 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 6.10/6.33 inference(symmetry,[status(thm)],[3066])).
% 6.10/6.33 tff(3068,plain,
% 6.10/6.33 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3067])).
% 6.10/6.33 tff(3069,plain,
% 6.10/6.33 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 6.10/6.33 inference(symmetry,[status(thm)],[3068])).
% 6.10/6.33 tff(3070,plain,
% 6.10/6.33 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[1378, 3069])).
% 6.10/6.33 tff(3071,plain,
% 6.10/6.33 (r(z, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(elem!1)))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3067])).
% 6.10/6.33 tff(3072,plain,
% 6.10/6.33 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 6.10/6.33 inference(symmetry,[status(thm)],[3071])).
% 6.10/6.33 tff(3073,plain,
% 6.10/6.33 (r(z, s(s(s(s(s(elem!1))))))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[326, 3072])).
% 6.10/6.33 tff(3074,assumption,(r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 6.10/6.33 tff(3075,plain,
% 6.10/6.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 6.10/6.33 inference(rewrite,[status(thm)],[])).
% 6.10/6.33 tff(3076,plain,
% 6.10/6.33 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 6.10/6.33 inference(rewrite,[status(thm)],[])).
% 6.10/6.33 tff(3077,plain,
% 6.10/6.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))))),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3076])).
% 6.10/6.33 tff(3078,plain,
% 6.10/6.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 6.10/6.33 inference(transitivity,[status(thm)],[3077, 3075])).
% 6.10/6.33 tff(3079,plain,
% 6.10/6.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 6.10/6.33 inference(quant_inst,[status(thm)],[])).
% 6.10/6.33 tff(3080,plain,
% 6.10/6.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[3079, 3078])).
% 6.10/6.33 tff(3081,plain,
% 6.10/6.33 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[3080, 194, 2792, 3074])).
% 6.10/6.33 tff(3082,plain,
% 6.10/6.33 ($false),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[3081, 3073, 3070])).
% 6.10/6.33 tff(3083,plain,((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.33 tff(3084,plain,
% 6.10/6.33 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[3083, 3064, 326, 3022, 1378])).
% 6.10/6.33 tff(3085,plain,
% 6.10/6.33 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[3084, 3039])).
% 6.10/6.33 tff(3086,plain,
% 6.10/6.33 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.10/6.33 inference(unit_resolution,[status(thm)],[1061, 3085, 3037])).
% 6.10/6.33 tff(3087,plain,
% 6.10/6.33 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 6.10/6.33 inference(modus_ponens,[status(thm)],[3086, 3033])).
% 6.10/6.33 tff(3088,plain,
% 6.10/6.33 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 6.10/6.33 inference(monotonicity,[status(thm)],[3022])).
% 6.10/6.33 tff(3089,plain,
% 6.10/6.33 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 6.10/6.34 inference(symmetry,[status(thm)],[3088])).
% 6.10/6.34 tff(3090,plain,
% 6.10/6.34 (b(elem!1, z)),
% 6.10/6.34 inference(modus_ponens,[status(thm)],[1452, 3089])).
% 6.10/6.34 tff(3091,plain,
% 6.10/6.34 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 6.10/6.34 inference(monotonicity,[status(thm)],[3022])).
% 6.10/6.34 tff(3092,plain,
% 6.10/6.34 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), elem!1)),
% 6.10/6.34 inference(symmetry,[status(thm)],[3091])).
% 6.10/6.34 tff(3093,plain,
% 6.10/6.34 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 6.10/6.34 inference(monotonicity,[status(thm)],[3023])).
% 6.10/6.34 tff(3094,plain,
% 6.10/6.34 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 6.10/6.34 inference(symmetry,[status(thm)],[3093])).
% 6.10/6.34 tff(3095,plain,
% 6.10/6.34 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 6.10/6.34 inference(monotonicity,[status(thm)],[3022])).
% 6.10/6.34 tff(3096,plain,
% 6.10/6.34 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), elem!1)),
% 6.10/6.34 inference(transitivity,[status(thm)],[3095, 3094, 3092])).
% 6.10/6.34 tff(3097,plain,
% 6.10/6.34 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 6.10/6.34 inference(monotonicity,[status(thm)],[3022])).
% 6.10/6.34 tff(3098,plain,
% 6.10/6.34 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 6.10/6.34 inference(symmetry,[status(thm)],[3097])).
% 6.10/6.34 tff(3099,plain,
% 6.10/6.34 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 6.10/6.34 inference(transitivity,[status(thm)],[3098, 964])).
% 6.10/6.34 tff(3100,plain,
% 6.10/6.34 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 6.10/6.34 inference(monotonicity,[status(thm)],[3099])).
% 6.10/6.34 tff(3101,plain,
% 6.10/6.34 (~(s(s(s(s(elem!1)))) = elem!1)),
% 6.10/6.34 inference(modus_ponens,[status(thm)],[1373, 3100])).
% 6.10/6.34 tff(3102,plain,
% 6.10/6.34 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 6.10/6.34 inference(transitivity,[status(thm)],[3035, 1021])).
% 6.10/6.34 tff(3103,plain,
% 6.10/6.34 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 6.10/6.34 inference(monotonicity,[status(thm)],[3102])).
% 6.10/6.34 tff(3104,plain,
% 6.10/6.34 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 6.10/6.34 inference(modus_ponens,[status(thm)],[1847, 3103])).
% 6.10/6.34 tff(3105,plain,
% 6.10/6.34 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[1741, 3086, 1374, 3059])).
% 6.10/6.34 tff(3106,plain,
% 6.10/6.34 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[1048, 3105, 3104])).
% 6.10/6.34 tff(3107,plain,
% 6.10/6.34 (~r(s(s(s(s(elem!1)))), elem!1)),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[2800, 3106, 326, 3064])).
% 6.10/6.34 tff(3108,plain,
% 6.10/6.34 (b(s(s(s(s(elem!1)))), elem!1)),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[1004, 3107, 3101])).
% 6.10/6.34 tff(3109,plain,
% 6.10/6.34 (b(s(elem!1), elem!1)),
% 6.10/6.34 inference(modus_ponens,[status(thm)],[3108, 3096])).
% 6.10/6.34 tff(3110,plain,
% 6.10/6.34 (~(s(s(s(s(z)))) = elem!1)),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[1436, 3021])).
% 6.10/6.34 tff(3111,plain,
% 6.10/6.34 (~(elem!1 = s(s(s(s(z)))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[769, 3110])).
% 6.10/6.34 tff(3112,plain,
% 6.10/6.34 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 6.10/6.34 inference(monotonicity,[status(thm)],[3022])).
% 6.10/6.34 tff(3113,plain,
% 6.10/6.34 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 6.10/6.34 inference(symmetry,[status(thm)],[3112])).
% 6.10/6.34 tff(3114,plain,
% 6.10/6.34 (r(s(z), elem!1)),
% 6.10/6.34 inference(modus_ponens,[status(thm)],[3019, 3113])).
% 6.10/6.34 tff(3115,plain,
% 6.10/6.34 (~r(elem!1, s(s(s(s(z)))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[2040, 3114, 3052, 182])).
% 6.10/6.34 tff(3116,plain,
% 6.10/6.34 (b(elem!1, s(s(s(s(z)))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[781, 3115, 3111])).
% 6.10/6.34 tff(3117,plain,
% 6.10/6.34 (~r(s(s(s(s(z)))), z)),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[2061, 1216, 182, 411])).
% 6.10/6.34 tff(3118,plain,
% 6.10/6.34 (b(s(s(s(s(z)))), z)),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[87, 3117])).
% 6.10/6.34 tff(3119,plain,
% 6.10/6.34 (~b(z, s(s(s(s(z)))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[2050, 3118, 591, 802, 665])).
% 6.10/6.34 tff(3120,plain,
% 6.10/6.34 (r(z, s(s(s(s(z)))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[800, 3119])).
% 6.10/6.34 tff(3121,plain,
% 6.10/6.34 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[2108, 3120, 182, 1216])).
% 6.10/6.34 tff(3122,plain,
% 6.10/6.34 (~(s(elem!1) = s(s(s(s(z)))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[1965, 5])).
% 6.10/6.34 tff(3123,plain,
% 6.10/6.34 (~b(s(s(s(s(z)))), elem!1)),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[2161, 3120, 802, 2064, 2122, 3122, 591, 665])).
% 6.10/6.34 tff(3124,plain,
% 6.10/6.34 ($false),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[2694, 3123, 3121, 5])).
% 6.10/6.34 tff(3125,plain,((~r(s(z), s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.34 tff(3126,plain,
% 6.10/6.34 (~r(s(z), s(s(s(s(z)))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[3125, 3021, 3060, 3116, 3109, 3062, 3090, 182, 3052])).
% 6.10/6.34 tff(3127,plain,
% 6.10/6.34 (b(s(z), s(s(s(s(z)))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[1230, 3126])).
% 6.10/6.34 tff(3128,plain,
% 6.10/6.34 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 6.10/6.34 inference(modus_ponens,[status(thm)],[3108, 3095])).
% 6.10/6.34 tff(3129,plain,
% 6.10/6.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 6.10/6.34 inference(rewrite,[status(thm)],[])).
% 6.10/6.34 tff(3130,plain,
% 6.10/6.34 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 6.10/6.34 inference(rewrite,[status(thm)],[])).
% 6.10/6.34 tff(3131,plain,
% 6.10/6.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 6.10/6.34 inference(monotonicity,[status(thm)],[3130])).
% 6.10/6.34 tff(3132,plain,
% 6.10/6.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 6.10/6.34 inference(transitivity,[status(thm)],[3131, 3129])).
% 6.10/6.34 tff(3133,plain,
% 6.10/6.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 6.10/6.34 inference(quant_inst,[status(thm)],[])).
% 6.10/6.34 tff(3134,plain,
% 6.10/6.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 6.10/6.34 inference(modus_ponens,[status(thm)],[3133, 3132])).
% 6.10/6.34 tff(3135,plain,
% 6.10/6.34 ($false),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[3134, 391, 3128, 3127, 3087, 3031, 3028])).
% 6.10/6.34 tff(3136,plain,((~b(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(z, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.10/6.34 tff(3137,plain,
% 6.10/6.34 (~b(s(s(elem!1)), s(z))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[3136, 168, 1374, 326, 1378, 1373, 10, 182])).
% 6.10/6.34 tff(3138,plain,
% 6.10/6.34 (~r(s(z), s(s(s(elem!1))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[2875, 3137, 326, 1374, 1378, 182, 10, 1351, 1373])).
% 6.10/6.34 tff(3139,plain,
% 6.10/6.34 (b(s(z), s(s(s(elem!1))))),
% 6.10/6.34 inference(unit_resolution,[status(thm)],[247, 3138])).
% 6.10/6.34 tff(3140,plain,
% 6.10/6.34 (b(s(z), elem!1)),
% 6.10/6.34 inference(modus_ponens,[status(thm)],[3139, 3017])).
% 6.10/6.34 tff(3141,plain,
% 6.10/6.34 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 6.10/6.34 inference(monotonicity,[status(thm)],[1388])).
% 6.10/6.34 tff(3142,plain,
% 6.10/6.34 (b(elem!1, z)),
% 6.10/6.34 inference(modus_ponens,[status(thm)],[1452, 3141])).
% 6.10/6.34 tff(3143,plain,
% 6.10/6.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.10/6.34 inference(rewrite,[status(thm)],[])).
% 6.10/6.34 tff(3144,plain,
% 6.10/6.34 (((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.10/6.34 inference(rewrite,[status(thm)],[])).
% 6.10/6.34 tff(3145,plain,
% 6.10/6.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 6.10/6.34 inference(monotonicity,[status(thm)],[3144])).
% 6.10/6.34 tff(3146,plain,
% 6.10/6.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.10/6.34 inference(transitivity,[status(thm)],[3145, 3143])).
% 6.10/6.34 tff(3147,plain,
% 6.10/6.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.10/6.34 inference(quant_inst,[status(thm)],[])).
% 6.10/6.34 tff(3148,plain,
% 6.10/6.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 6.10/6.34 inference(modus_ponens,[status(thm)],[3147, 3146])).
% 6.10/6.35 tff(3149,plain,
% 6.10/6.35 ($false),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[3148, 391, 665, 644, 2064, 1759, 721])).
% 6.10/6.35 tff(3150,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.35 tff(3151,plain,
% 6.10/6.35 (~b(s(s(s(s(z)))), s(z))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[3150, 3142, 3140, 3016, 1421])).
% 6.10/6.35 tff(3152,plain,
% 6.10/6.35 (r(s(s(s(s(z)))), s(z))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[749, 3151])).
% 6.10/6.35 tff(3153,plain,
% 6.10/6.35 (r(s(s(elem!1)), s(z))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[362, 3137])).
% 6.10/6.35 tff(3154,plain,
% 6.10/6.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.10/6.35 inference(rewrite,[status(thm)],[])).
% 6.10/6.35 tff(3155,plain,
% 6.10/6.35 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.10/6.35 inference(rewrite,[status(thm)],[])).
% 6.10/6.35 tff(3156,plain,
% 6.10/6.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 6.10/6.35 inference(monotonicity,[status(thm)],[3155])).
% 6.10/6.35 tff(3157,plain,
% 6.10/6.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.10/6.35 inference(transitivity,[status(thm)],[3156, 3154])).
% 6.10/6.35 tff(3158,plain,
% 6.10/6.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.10/6.35 inference(quant_inst,[status(thm)],[])).
% 6.10/6.35 tff(3159,plain,
% 6.10/6.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 6.10/6.35 inference(modus_ponens,[status(thm)],[3158, 3157])).
% 6.10/6.35 tff(3160,plain,
% 6.10/6.35 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[3159, 194, 3153, 182, 3152])).
% 6.10/6.35 tff(3161,plain,
% 6.10/6.35 ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z)))))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[1994, 42, 3160])).
% 6.10/6.35 tff(3162,plain,
% 6.10/6.35 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[3161, 1409])).
% 6.10/6.35 tff(3163,plain,
% 6.10/6.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.10/6.35 inference(rewrite,[status(thm)],[])).
% 6.10/6.35 tff(3164,plain,
% 6.10/6.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.10/6.35 inference(quant_inst,[status(thm)],[])).
% 6.10/6.35 tff(3165,plain,
% 6.10/6.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 6.10/6.35 inference(modus_ponens,[status(thm)],[3164, 3163])).
% 6.10/6.35 tff(3166,plain,
% 6.10/6.35 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[3165, 194, 3153, 182, 3152])).
% 6.10/6.35 tff(3167,plain,
% 6.10/6.35 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[2003, 42, 3166, 1408])).
% 6.10/6.35 tff(3168,plain,
% 6.10/6.35 (~r(elem!1, s(s(elem!1)))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[2549, 3153, 3003, 326])).
% 6.10/6.35 tff(3169,plain,
% 6.10/6.35 (b(elem!1, s(s(elem!1)))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[1307, 3168, 1972])).
% 6.10/6.35 tff(3170,plain,
% 6.10/6.35 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.10/6.35 inference(rewrite,[status(thm)],[])).
% 6.10/6.35 tff(3171,plain,
% 6.10/6.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 6.10/6.35 inference(monotonicity,[status(thm)],[3170])).
% 6.10/6.35 tff(3172,plain,
% 6.10/6.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.10/6.35 inference(transitivity,[status(thm)],[3171, 2013])).
% 6.10/6.35 tff(3173,plain,
% 6.10/6.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))),
% 6.10/6.35 inference(quant_inst,[status(thm)],[])).
% 6.10/6.35 tff(3174,plain,
% 6.10/6.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 6.10/6.35 inference(modus_ponens,[status(thm)],[3173, 3172])).
% 6.10/6.35 tff(3175,plain,
% 6.10/6.35 ($false),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[3174, 391, 3169, 3016, 3167, 3162])).
% 6.10/6.35 tff(3176,plain,(b(s(s(s(elem!1))), elem!1) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(z, s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.35 tff(3177,plain,
% 6.10/6.35 (b(s(s(s(elem!1))), elem!1)),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[3176, 1351, 325, 181, 1374, 1372, 10, 1373])).
% 6.10/6.35 tff(3178,plain,
% 6.10/6.35 (r(z, elem!1)),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[3002, 1372, 325, 1374, 1373, 181, 10, 1351])).
% 6.10/6.35 tff(3179,plain,
% 6.10/6.35 (r(elem!1, z) <=> r(s(z), z)),
% 6.10/6.35 inference(symmetry,[status(thm)],[1470])).
% 6.10/6.35 tff(3180,plain,
% 6.10/6.35 ((~r(elem!1, z)) <=> (~r(s(z), z))),
% 6.10/6.35 inference(monotonicity,[status(thm)],[3179])).
% 6.10/6.35 tff(3181,plain,
% 6.10/6.35 (~b(s(s(elem!1)), s(z))),
% 6.10/6.35 inference(unit_resolution,[status(thm)],[2919, 812, 326, 1374, 900, 182, 1378])).
% 6.10/6.36 tff(3182,plain,
% 6.10/6.36 (r(s(s(elem!1)), s(z))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[362, 3181])).
% 6.10/6.36 tff(3183,plain,
% 6.10/6.36 (r(s(s(elem!1)), elem!1)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[2220, 3182, 812])).
% 6.10/6.36 tff(3184,plain,
% 6.10/6.36 (~r(elem!1, z)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[867, 3183, 326, 411])).
% 6.10/6.36 tff(3185,plain,
% 6.10/6.36 (~r(s(z), z)),
% 6.10/6.36 inference(modus_ponens,[status(thm)],[3184, 3180])).
% 6.10/6.36 tff(3186,plain,
% 6.10/6.36 ($false),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[182, 3185])).
% 6.10/6.36 tff(3187,plain,((~(s(z) = elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.36 tff(3188,plain,
% 6.10/6.36 (~(s(z) = elem!1)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[3187, 3178, 325, 181, 1374, 3177, 1372])).
% 6.10/6.36 tff(3189,plain,
% 6.10/6.36 (~r(s(s(s(elem!1))), s(z))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[1418, 1372, 325, 59])).
% 6.10/6.36 tff(3190,plain,
% 6.10/6.36 (b(s(s(s(elem!1))), s(z))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[223, 3189])).
% 6.10/6.36 tff(3191,plain,
% 6.10/6.36 (~r(s(s(s(elem!1))), z)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[1450, 1372, 325, 59])).
% 6.10/6.36 tff(3192,plain,
% 6.10/6.36 (b(s(s(s(elem!1))), z)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[377, 3191])).
% 6.10/6.36 tff(3193,plain,
% 6.10/6.36 (~(elem!1 = s(z))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[172, 3188])).
% 6.10/6.36 tff(3194,plain,
% 6.10/6.36 (~r(s(z), elem!1)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[2475, 1810, 411, 181])).
% 6.10/6.36 tff(3195,plain,
% 6.10/6.36 (z = elem!1),
% 6.10/6.36 inference(symmetry,[status(thm)],[11])).
% 6.10/6.36 tff(3196,plain,
% 6.10/6.36 (b(s(z), z) <=> b(s(z), elem!1)),
% 6.10/6.36 inference(monotonicity,[status(thm)],[3195])).
% 6.10/6.36 tff(3197,plain,
% 6.10/6.36 (b(s(z), elem!1) <=> b(s(z), z)),
% 6.10/6.36 inference(symmetry,[status(thm)],[3196])).
% 6.10/6.36 tff(3198,plain,
% 6.10/6.36 (b(s(z), z)),
% 6.10/6.36 inference(modus_ponens,[status(thm)],[644, 3197])).
% 6.10/6.36 tff(3199,plain,
% 6.10/6.36 ($false),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[91, 3198])).
% 6.10/6.36 tff(3200,plain,(b(s(z), z) | (~b(s(z), elem!1)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.36 tff(3201,plain,
% 6.10/6.36 (~b(s(z), elem!1)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[3200, 11, 91])).
% 6.10/6.36 tff(3202,plain,
% 6.10/6.36 (s(z) = elem!1),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[632, 3201, 1492])).
% 6.10/6.36 tff(3203,plain,
% 6.10/6.36 (s(z) = z),
% 6.10/6.36 inference(transitivity,[status(thm)],[3202, 11])).
% 6.10/6.36 tff(3204,plain,
% 6.10/6.36 ($false),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[23, 3203])).
% 6.10/6.36 tff(3205,plain,((~(elem!1 = z)) | r(s(z), elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 6.10/6.36 tff(3206,plain,
% 6.10/6.36 (~(elem!1 = z)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[3205, 3194, 91])).
% 6.10/6.36 tff(3207,plain,
% 6.10/6.36 (b(s(z), elem!1)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[632, 3194, 1496])).
% 6.10/6.36 tff(3208,plain,
% 6.10/6.36 ($false),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[2534, 3207, 3206, 1526, 900, 326, 181, 831, 380, 411])).
% 6.10/6.36 tff(3209,plain,((elem!1 = s(z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | b(s(z), z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.36 tff(3210,plain,
% 6.10/6.36 (b(elem!1, s(z))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[3209, 3193, 3177, 325, 3192, 3178, 91, 3190])).
% 6.10/6.36 tff(3211,plain,
% 6.10/6.36 (~b(s(z), s(s(s(elem!1))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[2907, 3210, 3190, 3177])).
% 6.10/6.36 tff(3212,plain,
% 6.10/6.36 (r(s(z), s(s(s(elem!1))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[247, 3211])).
% 6.10/6.36 tff(3213,plain,
% 6.10/6.36 (b(s(s(elem!1)), s(z))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[2875, 3212, 325, 1374, 1372, 181, 10, 1351, 1373])).
% 6.10/6.36 tff(3214,plain,
% 6.10/6.36 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[1546, 3212, 59, 181])).
% 6.10/6.36 tff(3215,plain,
% 6.10/6.36 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[1164, 3214, 1373])).
% 6.10/6.36 tff(3216,plain,
% 6.10/6.36 (~b(s(z), elem!1)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[2534, 2, 1526, 900, 326, 182, 173, 380, 411])).
% 6.10/6.36 tff(3217,plain,
% 6.10/6.36 (r(s(z), elem!1)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[632, 3216, 150])).
% 6.10/6.36 tff(3218,plain,
% 6.10/6.36 (~r(elem!1, s(z))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[2475, 3217, 411, 182])).
% 6.10/6.36 tff(3219,plain,
% 6.10/6.36 (~r(elem!1, s(s(s(s(z)))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[2040, 3217, 411, 182])).
% 6.10/6.36 tff(3220,plain,
% 6.10/6.36 (~r(elem!1, z)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[1489, 3217, 184, 182])).
% 6.10/6.36 tff(3221,plain,
% 6.10/6.36 (b(elem!1, z)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[526, 3220, 2])).
% 6.10/6.36 tff(3222,assumption,(~r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 6.10/6.36 tff(3223,plain,
% 6.10/6.36 (~(elem!1 = s(s(s(s(z)))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[2674, 723, 832])).
% 6.10/6.36 tff(3224,plain,
% 6.10/6.36 (b(elem!1, s(s(s(s(z)))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[781, 3223, 3222])).
% 6.10/6.36 tff(3225,plain,
% 6.10/6.36 (~r(z, s(s(s(s(z)))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[1224, 1216, 182, 723])).
% 6.10/6.36 tff(3226,plain,
% 6.10/6.36 (b(z, s(s(s(s(z)))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[800, 3225])).
% 6.10/6.36 tff(3227,plain,
% 6.10/6.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 6.10/6.36 inference(rewrite,[status(thm)],[])).
% 6.10/6.36 tff(3228,plain,
% 6.10/6.36 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 6.10/6.36 inference(rewrite,[status(thm)],[])).
% 6.10/6.36 tff(3229,plain,
% 6.10/6.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 6.10/6.36 inference(monotonicity,[status(thm)],[3228])).
% 6.10/6.36 tff(3230,plain,
% 6.10/6.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 6.10/6.36 inference(transitivity,[status(thm)],[3229, 3227])).
% 6.10/6.36 tff(3231,plain,
% 6.10/6.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))),
% 6.10/6.36 inference(quant_inst,[status(thm)],[])).
% 6.10/6.36 tff(3232,plain,
% 6.10/6.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 6.10/6.36 inference(modus_ponens,[status(thm)],[3231, 3230])).
% 6.10/6.36 tff(3233,plain,
% 6.10/6.36 ($false),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[3232, 391, 665, 90, 2064, 1686])).
% 6.10/6.36 tff(3234,plain,((~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.36 tff(3235,plain,
% 6.10/6.36 ($false),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[3234, 3226, 3118, 665, 2064])).
% 6.10/6.36 tff(3236,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.36 tff(3237,plain,
% 6.10/6.36 (~r(s(z), s(s(s(s(z)))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[3236, 3224, 665, 182, 723, 411])).
% 6.10/6.36 tff(3238,plain,
% 6.10/6.36 (b(s(z), s(s(s(s(z)))))),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[1230, 3237])).
% 6.10/6.36 tff(3239,plain,
% 6.10/6.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.10/6.36 inference(rewrite,[status(thm)],[])).
% 6.10/6.36 tff(3240,plain,
% 6.10/6.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.10/6.36 inference(quant_inst,[status(thm)],[])).
% 6.10/6.36 tff(3241,plain,
% 6.10/6.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 6.10/6.36 inference(modus_ponens,[status(thm)],[3240, 3239])).
% 6.10/6.36 tff(3242,plain,
% 6.10/6.36 ($false),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[3241, 194, 411, 182, 2053, 723])).
% 6.10/6.36 tff(3243,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.36 tff(3244,plain,
% 6.10/6.36 (~r(s(s(s(s(z)))), z)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[3243, 723, 182, 411])).
% 6.10/6.36 tff(3245,plain,
% 6.10/6.36 (b(s(s(s(s(z)))), z)),
% 6.10/6.36 inference(unit_resolution,[status(thm)],[87, 3244])).
% 6.10/6.36 tff(3246,plain,
% 6.10/6.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.10/6.36 inference(rewrite,[status(thm)],[])).
% 6.10/6.36 tff(3247,plain,
% 6.10/6.36 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~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))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.10/6.36 inference(rewrite,[status(thm)],[])).
% 6.10/6.36 tff(3248,plain,
% 6.10/6.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 6.10/6.36 inference(monotonicity,[status(thm)],[3247])).
% 6.10/6.36 tff(3249,plain,
% 6.10/6.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.10/6.36 inference(transitivity,[status(thm)],[3248, 3246])).
% 6.10/6.36 tff(3250,plain,
% 6.10/6.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~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)))))),
% 6.10/6.37 inference(quant_inst,[status(thm)],[])).
% 6.10/6.37 tff(3251,plain,
% 6.10/6.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 6.10/6.37 inference(modus_ponens,[status(thm)],[3250, 3249])).
% 6.10/6.37 tff(3252,plain,
% 6.10/6.37 ($false),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[3251, 391, 381, 1374, 1526, 3245, 3238])).
% 6.10/6.37 tff(3253,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~b(elem!1, z)) | r(elem!1, s(s(s(s(z))))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.37 tff(3254,plain,
% 6.10/6.37 (~r(s(s(s(s(z)))), s(z))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[3253, 3221, 1374, 1526, 182, 411, 381, 3219, 3218])).
% 6.10/6.37 tff(3255,plain,
% 6.10/6.37 (b(s(s(s(s(z)))), s(z))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[749, 3254])).
% 6.10/6.37 tff(3256,plain,
% 6.10/6.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.10/6.37 inference(rewrite,[status(thm)],[])).
% 6.10/6.37 tff(3257,plain,
% 6.10/6.37 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~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))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.10/6.37 inference(rewrite,[status(thm)],[])).
% 6.10/6.37 tff(3258,plain,
% 6.10/6.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 6.10/6.37 inference(monotonicity,[status(thm)],[3257])).
% 6.10/6.37 tff(3259,plain,
% 6.10/6.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.10/6.37 inference(transitivity,[status(thm)],[3258, 3256])).
% 6.10/6.37 tff(3260,plain,
% 6.10/6.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~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)))))),
% 6.10/6.37 inference(quant_inst,[status(thm)],[])).
% 6.10/6.37 tff(3261,plain,
% 6.10/6.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 6.10/6.37 inference(modus_ponens,[status(thm)],[3260, 3259])).
% 6.10/6.37 tff(3262,plain,
% 6.10/6.37 ($false),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[3261, 391, 381, 1374, 1526, 1234, 1759])).
% 6.10/6.37 tff(3263,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.37 tff(3264,plain,
% 6.10/6.37 (~b(s(z), s(s(s(s(z)))))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[3263, 3255, 1374, 1526, 381])).
% 6.10/6.37 tff(3265,plain,
% 6.10/6.37 (r(s(z), s(s(s(s(z)))))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[1230, 3264])).
% 6.10/6.37 tff(3266,plain,
% 6.10/6.37 (~r(s(s(s(s(z)))), z)),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[2061, 3265, 182, 411])).
% 6.10/6.37 tff(3267,plain,
% 6.10/6.37 (b(s(s(s(s(z)))), z)),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[87, 3266])).
% 6.10/6.37 tff(3268,plain,
% 6.10/6.37 (~r(s(elem!1), z)),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[2594, 118, 1526, 411, 232, 2234, 182])).
% 6.10/6.37 tff(3269,plain,
% 6.10/6.37 (b(s(elem!1), z)),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[549, 3268])).
% 6.10/6.37 tff(3270,plain,
% 6.10/6.37 (s(s(s(s(z)))) = elem!1),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[769, 766])).
% 6.10/6.37 tff(3271,plain,
% 6.10/6.37 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[717, 3270])).
% 6.10/6.37 tff(3272,plain,
% 6.10/6.37 (b(s(s(s(elem!1))), s(elem!1))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[588, 3271, 1575])).
% 6.10/6.37 tff(3273,plain,
% 6.10/6.37 (~(s(s(s(elem!1))) = elem!1)),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[1436, 3270])).
% 6.10/6.37 tff(3274,plain,
% 6.10/6.37 (~(elem!1 = s(s(s(elem!1))))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[129, 3273])).
% 6.10/6.37 tff(3275,plain,
% 6.10/6.37 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.37 inference(monotonicity,[status(thm)],[766])).
% 6.10/6.37 tff(3276,plain,
% 6.10/6.37 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 6.10/6.37 inference(symmetry,[status(thm)],[3275])).
% 6.10/6.37 tff(3277,plain,
% 6.10/6.37 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 6.10/6.37 inference(monotonicity,[status(thm)],[3276])).
% 6.10/6.37 tff(3278,plain,
% 6.10/6.37 (~b(z, s(s(s(s(z)))))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[2638, 3272, 380, 591, 1759])).
% 6.10/6.37 tff(3279,plain,
% 6.10/6.37 (r(z, s(s(s(s(z)))))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[800, 3278])).
% 6.10/6.37 tff(3280,plain,
% 6.10/6.37 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[2108, 3279, 182, 1216])).
% 6.10/6.37 tff(3281,plain,
% 6.10/6.37 (~r(elem!1, s(s(s(elem!1))))),
% 6.10/6.37 inference(modus_ponens,[status(thm)],[3280, 3277])).
% 6.10/6.37 tff(3282,plain,
% 6.10/6.37 (b(elem!1, s(s(s(elem!1))))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[424, 3281, 3274])).
% 6.10/6.37 tff(3283,plain,
% 6.10/6.37 (~b(s(s(s(s(elem!1)))), elem!1)),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[2706, 3282, 900, 3272, 1573])).
% 6.10/6.37 tff(3284,plain,
% 6.10/6.37 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[2686, 3271])).
% 6.10/6.37 tff(3285,plain,
% 6.10/6.37 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[2711, 3284])).
% 6.10/6.37 tff(3286,plain,
% 6.10/6.37 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.10/6.37 inference(monotonicity,[status(thm)],[2731, 766])).
% 6.10/6.37 tff(3287,plain,
% 6.10/6.37 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 6.10/6.37 inference(symmetry,[status(thm)],[3286])).
% 6.10/6.37 tff(3288,plain,
% 6.10/6.37 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.10/6.37 inference(monotonicity,[status(thm)],[766])).
% 6.10/6.37 tff(3289,plain,
% 6.10/6.37 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 6.10/6.37 inference(transitivity,[status(thm)],[3288, 3287])).
% 6.10/6.37 tff(3290,plain,
% 6.10/6.37 (~(s(s(elem!1)) = elem!1)),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[451, 3271])).
% 6.10/6.37 tff(3291,plain,
% 6.10/6.37 (~(elem!1 = s(s(elem!1)))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[1292, 3290])).
% 6.10/6.37 tff(3292,plain,
% 6.10/6.37 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.10/6.37 inference(monotonicity,[status(thm)],[766])).
% 6.10/6.37 tff(3293,plain,
% 6.10/6.37 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 6.10/6.37 inference(symmetry,[status(thm)],[3292])).
% 6.10/6.37 tff(3294,plain,
% 6.10/6.37 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.10/6.37 inference(monotonicity,[status(thm)],[2731])).
% 6.10/6.37 tff(3295,plain,
% 6.10/6.37 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(elem!1)))),
% 6.10/6.37 inference(transitivity,[status(thm)],[3294, 3293])).
% 6.10/6.37 tff(3296,plain,
% 6.10/6.37 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) <=> (~r(elem!1, s(s(elem!1))))),
% 6.10/6.37 inference(monotonicity,[status(thm)],[3295])).
% 6.10/6.37 tff(3297,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 6.10/6.37 tff(3298,plain,
% 6.10/6.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 6.10/6.37 inference(rewrite,[status(thm)],[])).
% 6.10/6.37 tff(3299,plain,
% 6.10/6.37 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 6.10/6.37 inference(rewrite,[status(thm)],[])).
% 6.10/6.37 tff(3300,plain,
% 6.10/6.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 6.10/6.37 inference(monotonicity,[status(thm)],[3299])).
% 6.10/6.37 tff(3301,plain,
% 6.10/6.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 6.10/6.37 inference(transitivity,[status(thm)],[3300, 3298])).
% 6.10/6.37 tff(3302,plain,
% 6.10/6.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 6.10/6.37 inference(quant_inst,[status(thm)],[])).
% 6.10/6.37 tff(3303,plain,
% 6.10/6.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 6.10/6.37 inference(modus_ponens,[status(thm)],[3302, 3301])).
% 6.10/6.37 tff(3304,plain,
% 6.10/6.37 ($false),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[3303, 194, 182, 1216, 719, 3297])).
% 6.10/6.37 tff(3305,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.37 tff(3306,plain,
% 6.10/6.37 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[3305, 3279, 1216, 182])).
% 6.10/6.37 tff(3307,plain,
% 6.10/6.37 (~r(elem!1, s(s(elem!1)))),
% 6.10/6.37 inference(modus_ponens,[status(thm)],[3306, 3296])).
% 6.10/6.37 tff(3308,plain,
% 6.10/6.37 (b(elem!1, s(s(elem!1)))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[1307, 3307, 3291])).
% 6.10/6.37 tff(3309,plain,
% 6.10/6.37 (~b(s(s(elem!1)), elem!1)),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[1467, 3308, 1374, 900])).
% 6.10/6.37 tff(3310,plain,
% 6.10/6.37 (r(s(s(elem!1)), elem!1)),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[872, 3309, 3290])).
% 6.10/6.37 tff(3311,plain,
% 6.10/6.37 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 6.10/6.37 inference(modus_ponens,[status(thm)],[3310, 3289])).
% 6.10/6.37 tff(3312,plain,
% 6.10/6.37 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[2776, 3311, 1573, 380, 326, 766])).
% 6.10/6.37 tff(3313,plain,
% 6.10/6.37 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[1061, 3312, 3285])).
% 6.10/6.37 tff(3314,plain,
% 6.10/6.37 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.10/6.37 inference(unit_resolution,[status(thm)],[1741, 3313, 1374, 1573])).
% 6.10/6.38 tff(3315,plain,
% 6.10/6.38 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[1048, 3314, 3284])).
% 6.10/6.38 tff(3316,plain,
% 6.10/6.38 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.10/6.38 inference(monotonicity,[status(thm)],[2731])).
% 6.10/6.38 tff(3317,plain,
% 6.10/6.38 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 6.10/6.38 inference(symmetry,[status(thm)],[3316])).
% 6.10/6.38 tff(3318,plain,
% 6.10/6.38 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 6.10/6.38 inference(modus_ponens,[status(thm)],[1733, 3317])).
% 6.10/6.38 tff(3319,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 6.10/6.38 tff(3320,plain,
% 6.10/6.38 ($false),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[3319, 3318])).
% 6.10/6.38 tff(3321,plain,(b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.38 tff(3322,plain,
% 6.10/6.38 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[3321, 3313, 766])).
% 6.10/6.38 tff(3323,plain,
% 6.10/6.38 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[2865, 3282, 3270])).
% 6.10/6.38 tff(3324,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 6.10/6.38 tff(3325,assumption,(b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 6.10/6.38 tff(3326,plain,
% 6.10/6.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 6.10/6.38 inference(rewrite,[status(thm)],[])).
% 6.10/6.38 tff(3327,plain,
% 6.10/6.38 (((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 6.10/6.38 inference(rewrite,[status(thm)],[])).
% 6.10/6.38 tff(3328,plain,
% 6.10/6.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 6.10/6.38 inference(monotonicity,[status(thm)],[3327])).
% 6.10/6.38 tff(3329,plain,
% 6.10/6.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 6.10/6.38 inference(transitivity,[status(thm)],[3328, 3326])).
% 6.10/6.38 tff(3330,plain,
% 6.10/6.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.10/6.38 inference(quant_inst,[status(thm)],[])).
% 6.10/6.38 tff(3331,plain,
% 6.10/6.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 6.10/6.38 inference(modus_ponens,[status(thm)],[3330, 3329])).
% 6.10/6.38 tff(3332,plain,
% 6.10/6.38 ($false),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[3331, 391, 380, 2781, 90, 3325, 3324])).
% 6.10/6.38 tff(3333,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.38 tff(3334,plain,
% 6.10/6.38 (~b(z, s(s(s(s(elem!1)))))),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[3333, 3323, 90, 380, 3322])).
% 6.10/6.38 tff(3335,plain,
% 6.10/6.38 (r(z, s(s(s(s(elem!1)))))),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[2767, 3334])).
% 6.10/6.38 tff(3336,plain,
% 6.10/6.38 (~r(s(s(s(s(elem!1)))), elem!1)),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[2800, 3335, 326, 3315])).
% 6.10/6.38 tff(3337,plain,
% 6.10/6.38 (s(s(s(s(elem!1)))) = elem!1),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[1004, 3336, 3283])).
% 6.10/6.38 tff(3338,plain,
% 6.10/6.38 (elem!1 = s(s(s(s(elem!1))))),
% 6.10/6.38 inference(symmetry,[status(thm)],[3337])).
% 6.10/6.38 tff(3339,plain,
% 6.10/6.38 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 6.10/6.38 inference(transitivity,[status(thm)],[2738, 3338])).
% 6.10/6.38 tff(3340,plain,
% 6.10/6.38 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 6.10/6.38 inference(monotonicity,[status(thm)],[3339])).
% 6.10/6.38 tff(3341,plain,
% 6.10/6.38 (s(s(s(z))) = s(s(s(elem!1)))),
% 6.10/6.38 inference(transitivity,[status(thm)],[693, 3340, 294])).
% 6.10/6.38 tff(3342,plain,
% 6.10/6.38 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 6.10/6.38 inference(monotonicity,[status(thm)],[3341])).
% 6.10/6.38 tff(3343,plain,
% 6.10/6.38 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 6.10/6.38 inference(symmetry,[status(thm)],[3342])).
% 6.10/6.38 tff(3344,plain,
% 6.10/6.38 (s(s(elem!1)) = s(s(z))),
% 6.10/6.38 inference(transitivity,[status(thm)],[212, 3343, 685])).
% 6.10/6.38 tff(3345,plain,
% 6.10/6.38 ($false),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[2689, 3344])).
% 6.10/6.38 tff(3346,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(z))) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.38 tff(3347,plain,
% 6.10/6.38 (~(elem!1 = s(s(s(s(z)))))),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[3346, 2680, 326, 3267, 380, 1374, 1573, 900, 3265, 182, 3269, 3255, 2234])).
% 6.10/6.38 tff(3348,plain,
% 6.10/6.38 (b(elem!1, s(s(s(s(z)))))),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[781, 3347, 3219])).
% 6.10/6.38 tff(3349,plain,
% 6.10/6.38 (~b(z, s(s(s(s(z)))))),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[3234, 3348, 3221, 3267])).
% 6.10/6.38 tff(3350,plain,
% 6.10/6.38 (r(z, s(s(s(s(z)))))),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[800, 3349])).
% 6.10/6.38 tff(3351,plain,
% 6.10/6.38 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[2108, 3350, 182, 3265])).
% 6.10/6.38 tff(3352,plain,
% 6.10/6.38 (~r(s(s(s(s(z)))), elem!1)),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[2720, 3350, 182, 3265])).
% 6.10/6.38 tff(3353,plain,
% 6.10/6.38 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 6.10/6.38 inference(monotonicity,[status(thm)],[765])).
% 6.10/6.38 tff(3354,plain,
% 6.10/6.38 (~(s(s(s(s(z)))) = elem!1)),
% 6.10/6.38 inference(modus_ponens,[status(thm)],[3347, 3353])).
% 6.10/6.38 tff(3355,plain,
% 6.10/6.38 (b(s(s(s(s(z)))), elem!1)),
% 6.10/6.38 inference(unit_resolution,[status(thm)],[762, 3354, 3352])).
% 6.10/6.38 tff(3356,plain,
% 6.10/6.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.10/6.39 inference(rewrite,[status(thm)],[])).
% 6.10/6.39 tff(3357,plain,
% 6.10/6.39 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.10/6.39 inference(rewrite,[status(thm)],[])).
% 6.10/6.39 tff(3358,plain,
% 6.10/6.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 6.10/6.39 inference(monotonicity,[status(thm)],[3357])).
% 6.10/6.39 tff(3359,plain,
% 6.10/6.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.10/6.39 inference(transitivity,[status(thm)],[3358, 3356])).
% 6.10/6.39 tff(3360,plain,
% 6.10/6.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.10/6.39 inference(quant_inst,[status(thm)],[])).
% 6.10/6.39 tff(3361,plain,
% 6.10/6.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.10/6.39 inference(modus_ponens,[status(thm)],[3360, 3359])).
% 6.10/6.39 tff(3362,plain,
% 6.10/6.39 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3361, 391, 900, 3267, 3348, 3355])).
% 6.10/6.39 tff(3363,plain,
% 6.10/6.39 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[2849, 150])).
% 6.10/6.39 tff(3364,plain,
% 6.10/6.39 ($false),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[2853, 42, 3363, 3362, 3351])).
% 6.10/6.39 tff(3365,plain,((elem!1 = z) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.10/6.39 tff(3366,plain,
% 6.10/6.39 (elem!1 = z),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3365, 3177, 181, 325, 3192, 1374, 3215, 3178, 3190, 3213, 59, 3212, 3188])).
% 6.10/6.39 tff(3367,plain,
% 6.10/6.39 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 6.10/6.39 inference(monotonicity,[status(thm)],[489])).
% 6.10/6.39 tff(3368,plain,
% 6.10/6.39 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 6.10/6.39 inference(symmetry,[status(thm)],[3367])).
% 6.10/6.39 tff(3369,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 6.10/6.39 tff(3370,plain,
% 6.10/6.39 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 6.10/6.39 inference(monotonicity,[status(thm)],[3195])).
% 6.10/6.39 tff(3371,plain,
% 6.10/6.39 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 6.10/6.39 inference(symmetry,[status(thm)],[3370])).
% 6.10/6.39 tff(3372,plain,
% 6.10/6.39 (b(z, s(s(z)))),
% 6.10/6.39 inference(modus_ponens,[status(thm)],[3369, 3371])).
% 6.10/6.39 tff(3373,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 6.10/6.39 tff(3374,plain,
% 6.10/6.39 ($false),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3373, 3372])).
% 6.10/6.39 tff(3375,plain,(b(z, s(s(z))) | (~b(elem!1, s(s(z)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.39 tff(3376,plain,
% 6.10/6.39 (b(z, s(s(z)))),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3375, 11, 3369])).
% 6.10/6.39 tff(3377,plain,
% 6.10/6.39 (b(z, s(s(elem!1)))),
% 6.10/6.39 inference(modus_ponens,[status(thm)],[3376, 3368])).
% 6.10/6.39 tff(3378,plain,
% 6.10/6.39 ($false),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[309, 3377])).
% 6.10/6.39 tff(3379,plain,((~(elem!1 = z)) | b(z, s(s(elem!1))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.39 tff(3380,plain,
% 6.10/6.39 (~b(elem!1, s(s(z)))),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3379, 3366, 309])).
% 6.10/6.39 tff(3381,plain,
% 6.10/6.39 (r(s(z), elem!1)),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3205, 3366, 91])).
% 6.10/6.39 tff(3382,plain,
% 6.10/6.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))))),
% 6.10/6.39 inference(rewrite,[status(thm)],[])).
% 6.10/6.39 tff(3383,plain,
% 6.10/6.39 (((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))))),
% 6.10/6.39 inference(rewrite,[status(thm)],[])).
% 6.10/6.39 tff(3384,plain,
% 6.10/6.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z))))))),
% 6.10/6.39 inference(monotonicity,[status(thm)],[3383])).
% 6.10/6.39 tff(3385,plain,
% 6.10/6.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))))),
% 6.10/6.39 inference(transitivity,[status(thm)],[3384, 3382])).
% 6.10/6.39 tff(3386,plain,
% 6.10/6.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 6.10/6.39 inference(quant_inst,[status(thm)],[])).
% 6.10/6.39 tff(3387,plain,
% 6.10/6.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z))))),
% 6.10/6.39 inference(modus_ponens,[status(thm)],[3386, 3385])).
% 6.10/6.39 tff(3388,plain,
% 6.10/6.39 ($false),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3387, 194, 411, 1484, 182, 1748])).
% 6.10/6.39 tff(3389,plain,((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.39 tff(3390,plain,
% 6.10/6.39 (~r(elem!1, s(s(z)))),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3389, 3381, 3178, 181])).
% 6.10/6.39 tff(3391,plain,
% 6.10/6.39 (((~![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))))),
% 6.10/6.39 inference(rewrite,[status(thm)],[])).
% 6.10/6.39 tff(3392,plain,
% 6.10/6.39 ((~![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))))),
% 6.10/6.39 inference(quant_inst,[status(thm)],[])).
% 6.10/6.39 tff(3393,plain,
% 6.10/6.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 6.10/6.39 inference(modus_ponens,[status(thm)],[3392, 3391])).
% 6.10/6.39 tff(3394,plain,
% 6.10/6.39 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3393, 42])).
% 6.10/6.39 tff(3395,plain,
% 6.10/6.39 (elem!1 = s(s(z))),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3394, 3390, 3380])).
% 6.10/6.39 tff(3396,plain,
% 6.10/6.39 (s(s(z)) = elem!1),
% 6.10/6.39 inference(symmetry,[status(thm)],[3395])).
% 6.10/6.39 tff(3397,plain,
% 6.10/6.39 (s(s(z)) = z),
% 6.10/6.39 inference(transitivity,[status(thm)],[3396, 3366])).
% 6.10/6.39 tff(3398,plain,
% 6.10/6.39 ($false),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[1207, 3397])).
% 6.10/6.39 tff(3399,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(z), z) | b(z, s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(z, s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.10/6.39 tff(3400,plain,
% 6.10/6.39 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.10/6.39 inference(unit_resolution,[status(thm)],[3399, 309, 91, 1371, 311, 10, 315])).
% 6.10/6.39 tff(3401,plain,
% 6.10/6.39 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 6.10/6.39 inference(commutativity,[status(thm)],[])).
% 6.10/6.39 tff(3402,plain,
% 6.10/6.39 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 6.10/6.39 inference(symmetry,[status(thm)],[3401])).
% 6.10/6.39 tff(3403,plain,
% 6.10/6.39 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(elem!1))))),
% 6.10/6.39 inference(monotonicity,[status(thm)],[3402])).
% 6.10/6.39 tff(3404,plain,
% 6.10/6.39 (~(s(z) = s(s(elem!1)))),
% 6.10/6.39 inference(modus_ponens,[status(thm)],[357, 3403])).
% 6.10/6.39 tff(3405,plain,
% 6.10/6.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.10/6.39 inference(rewrite,[status(thm)],[])).
% 6.10/6.39 tff(3406,plain,
% 6.10/6.39 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.10/6.39 inference(rewrite,[status(thm)],[])).
% 6.10/6.39 tff(3407,plain,
% 6.10/6.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.10/6.39 inference(monotonicity,[status(thm)],[3406])).
% 6.10/6.39 tff(3408,plain,
% 6.10/6.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.10/6.39 inference(transitivity,[status(thm)],[3407, 3405])).
% 6.10/6.39 tff(3409,plain,
% 6.10/6.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 6.10/6.39 inference(quant_inst,[status(thm)],[])).
% 6.10/6.39 tff(3410,plain,
% 6.10/6.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.20/6.40 inference(modus_ponens,[status(thm)],[3409, 3408])).
% 6.20/6.40 tff(3411,plain,
% 6.20/6.40 (~b(s(z), s(s(elem!1)))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[3410, 391, 1374, 379, 328])).
% 6.20/6.40 tff(3412,plain,
% 6.20/6.40 (((~![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))))),
% 6.20/6.40 inference(rewrite,[status(thm)],[])).
% 6.20/6.40 tff(3413,plain,
% 6.20/6.40 ((~![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))))),
% 6.20/6.40 inference(quant_inst,[status(thm)],[])).
% 6.20/6.40 tff(3414,plain,
% 6.20/6.40 ((~![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)))),
% 6.20/6.40 inference(modus_ponens,[status(thm)],[3413, 3412])).
% 6.20/6.40 tff(3415,plain,
% 6.20/6.40 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[3414, 42, 3411])).
% 6.20/6.40 tff(3416,plain,
% 6.20/6.40 (r(s(z), s(s(elem!1)))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[3415, 3404])).
% 6.20/6.40 tff(3417,plain,
% 6.20/6.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.20/6.40 inference(rewrite,[status(thm)],[])).
% 6.20/6.40 tff(3418,plain,
% 6.20/6.40 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.20/6.40 inference(rewrite,[status(thm)],[])).
% 6.20/6.40 tff(3419,plain,
% 6.20/6.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.20/6.40 inference(monotonicity,[status(thm)],[3418])).
% 6.20/6.40 tff(3420,plain,
% 6.20/6.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.20/6.40 inference(transitivity,[status(thm)],[3419, 3417])).
% 6.20/6.40 tff(3421,plain,
% 6.20/6.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 6.20/6.40 inference(quant_inst,[status(thm)],[])).
% 6.20/6.40 tff(3422,plain,
% 6.20/6.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.20/6.40 inference(modus_ponens,[status(thm)],[3421, 3420])).
% 6.20/6.40 tff(3423,plain,
% 6.20/6.40 (~b(s(s(elem!1)), s(z))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[3422, 391, 1374, 379, 328])).
% 6.20/6.40 tff(3424,plain,
% 6.20/6.40 (r(s(s(elem!1)), s(z))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[362, 3423])).
% 6.20/6.40 tff(3425,plain,
% 6.20/6.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))))),
% 6.20/6.40 inference(rewrite,[status(thm)],[])).
% 6.20/6.40 tff(3426,plain,
% 6.20/6.40 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))))),
% 6.20/6.40 inference(rewrite,[status(thm)],[])).
% 6.20/6.40 tff(3427,plain,
% 6.20/6.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))))),
% 6.20/6.40 inference(monotonicity,[status(thm)],[3426])).
% 6.20/6.40 tff(3428,plain,
% 6.20/6.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))))),
% 6.20/6.40 inference(transitivity,[status(thm)],[3427, 3425])).
% 6.20/6.40 tff(3429,plain,
% 6.20/6.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))),
% 6.20/6.40 inference(quant_inst,[status(thm)],[])).
% 6.20/6.40 tff(3430,plain,
% 6.20/6.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))),
% 6.20/6.40 inference(modus_ponens,[status(thm)],[3429, 3428])).
% 6.20/6.40 tff(3431,plain,
% 6.20/6.40 ($false),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[3430, 194, 3424, 326, 182, 3416])).
% 6.20/6.40 tff(3432,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.40 tff(3433,plain,
% 6.20/6.40 (~b(s(z), s(s(s(elem!1))))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[3432, 325, 181, 1371, 3400])).
% 6.20/6.40 tff(3434,plain,
% 6.20/6.40 (r(s(z), s(s(s(elem!1))))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[247, 3433])).
% 6.20/6.40 tff(3435,plain,
% 6.20/6.40 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[1546, 3434, 59, 181])).
% 6.20/6.40 tff(3436,plain,
% 6.20/6.40 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[1164, 3435, 311])).
% 6.20/6.40 tff(3437,plain,
% 6.20/6.40 (~b(s(z), s(s(s(elem!1))))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[3432, 325, 181, 1374, 328])).
% 6.20/6.40 tff(3438,plain,
% 6.20/6.40 (r(s(z), s(s(s(elem!1))))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[247, 3437])).
% 6.20/6.40 tff(3439,plain,
% 6.20/6.40 (~r(s(s(s(elem!1))), elem!1)),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[241, 3438, 59, 181])).
% 6.20/6.40 tff(3440,plain,
% 6.20/6.40 (b(s(s(s(elem!1))), elem!1)),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[230, 1440, 3439])).
% 6.20/6.40 tff(3441,plain,
% 6.20/6.40 (~r(s(s(s(elem!1))), z)),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[1867, 3438, 59, 181])).
% 6.20/6.40 tff(3442,plain,
% 6.20/6.40 (b(s(s(s(elem!1))), z)),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[377, 3441])).
% 6.20/6.40 tff(3443,plain,
% 6.20/6.40 (b(s(s(elem!1)), s(z))),
% 6.20/6.40 inference(unit_resolution,[status(thm)],[2457, 3440, 1374, 181, 325, 1573, 80, 3438, 10])).
% 6.20/6.40 tff(3444,plain,
% 6.20/6.40 (~r(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[641, 3438, 59, 181])).
% 6.20/6.41 tff(3445,plain,
% 6.20/6.41 (b(s(s(s(s(z)))), elem!1)),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[1650, 1442, 59, 1573, 3444, 181, 3442, 80, 3440, 325])).
% 6.20/6.41 tff(3446,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 6.20/6.41 tff(3447,plain,
% 6.20/6.41 (r(s(s(s(s(z)))), z)),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[87, 3446])).
% 6.20/6.41 tff(3448,plain,
% 6.20/6.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.20/6.41 inference(rewrite,[status(thm)],[])).
% 6.20/6.41 tff(3449,plain,
% 6.20/6.41 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.20/6.41 inference(rewrite,[status(thm)],[])).
% 6.20/6.41 tff(3450,plain,
% 6.20/6.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 6.20/6.41 inference(monotonicity,[status(thm)],[3449])).
% 6.20/6.41 tff(3451,plain,
% 6.20/6.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.20/6.41 inference(transitivity,[status(thm)],[3450, 3448])).
% 6.20/6.41 tff(3452,plain,
% 6.20/6.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.20/6.41 inference(quant_inst,[status(thm)],[])).
% 6.20/6.41 tff(3453,plain,
% 6.20/6.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 6.20/6.41 inference(modus_ponens,[status(thm)],[3452, 3451])).
% 6.20/6.41 tff(3454,plain,
% 6.20/6.41 (~r(s(s(s(s(z)))), s(z))),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[3453, 194, 326, 182, 2053])).
% 6.20/6.41 tff(3455,plain,
% 6.20/6.41 (b(s(s(s(s(z)))), s(z))),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[749, 3454])).
% 6.20/6.41 tff(3456,plain,
% 6.20/6.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.20/6.41 inference(rewrite,[status(thm)],[])).
% 6.20/6.41 tff(3457,plain,
% 6.20/6.41 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.20/6.41 inference(rewrite,[status(thm)],[])).
% 6.20/6.41 tff(3458,plain,
% 6.20/6.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 6.20/6.41 inference(monotonicity,[status(thm)],[3457])).
% 6.20/6.41 tff(3459,plain,
% 6.20/6.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.20/6.41 inference(transitivity,[status(thm)],[3458, 3456])).
% 6.20/6.41 tff(3460,plain,
% 6.20/6.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.20/6.41 inference(quant_inst,[status(thm)],[])).
% 6.20/6.41 tff(3461,plain,
% 6.20/6.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 6.20/6.41 inference(modus_ponens,[status(thm)],[3460, 3459])).
% 6.20/6.41 tff(3462,plain,
% 6.20/6.41 (~r(s(z), s(s(s(s(z)))))),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[3461, 194, 326, 182, 2053])).
% 6.20/6.41 tff(3463,plain,
% 6.20/6.41 (b(s(z), s(s(s(s(z)))))),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[1230, 3462])).
% 6.20/6.41 tff(3464,plain,
% 6.20/6.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.20/6.41 inference(rewrite,[status(thm)],[])).
% 6.20/6.41 tff(3465,plain,
% 6.20/6.41 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.20/6.41 inference(rewrite,[status(thm)],[])).
% 6.20/6.41 tff(3466,plain,
% 6.20/6.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 6.20/6.41 inference(monotonicity,[status(thm)],[3465])).
% 6.20/6.41 tff(3467,plain,
% 6.20/6.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.20/6.41 inference(transitivity,[status(thm)],[3466, 3464])).
% 6.20/6.41 tff(3468,plain,
% 6.20/6.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.20/6.41 inference(quant_inst,[status(thm)],[])).
% 6.20/6.41 tff(3469,plain,
% 6.20/6.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 6.20/6.41 inference(modus_ponens,[status(thm)],[3468, 3467])).
% 6.20/6.41 tff(3470,plain,
% 6.20/6.41 ($false),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[3469, 391, 381, 3463, 3455, 1232])).
% 6.20/6.41 tff(3471,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.41 tff(3472,plain,
% 6.20/6.41 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[3471, 3447, 381, 326, 182])).
% 6.20/6.41 tff(3473,plain,
% 6.20/6.41 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 6.20/6.41 inference(monotonicity,[status(thm)],[1552, 1551])).
% 6.20/6.41 tff(3474,plain,
% 6.20/6.41 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.20/6.41 inference(symmetry,[status(thm)],[3473])).
% 6.20/6.41 tff(3475,plain,
% 6.20/6.41 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 6.20/6.41 inference(monotonicity,[status(thm)],[3474])).
% 6.20/6.41 tff(3476,plain,
% 6.20/6.41 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 6.20/6.41 inference(monotonicity,[status(thm)],[1551])).
% 6.20/6.41 tff(3477,plain,
% 6.20/6.41 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 6.20/6.41 inference(monotonicity,[status(thm)],[3476])).
% 6.20/6.41 tff(3478,assumption,(~b(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 6.20/6.41 tff(3479,plain,
% 6.20/6.41 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 6.20/6.41 inference(modus_ponens,[status(thm)],[3478, 3477])).
% 6.20/6.41 tff(3480,plain,
% 6.20/6.41 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.20/6.41 inference(modus_ponens,[status(thm)],[3479, 3475])).
% 6.20/6.41 tff(3481,plain,
% 6.20/6.41 ($false),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[1374, 3480])).
% 6.20/6.41 tff(3482,plain,((~(elem!1 = s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.41 tff(3483,plain,
% 6.20/6.41 (~(elem!1 = s(z))),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[3482, 3472, 1374])).
% 6.20/6.41 tff(3484,plain,
% 6.20/6.41 (elem!1 = z),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[1516, 3483, 380, 80, 900, 326, 182, 184])).
% 6.20/6.41 tff(3485,plain,
% 6.20/6.41 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 6.20/6.41 inference(monotonicity,[status(thm)],[3484])).
% 6.20/6.41 tff(3486,plain,
% 6.20/6.41 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 6.20/6.41 inference(symmetry,[status(thm)],[3485])).
% 6.20/6.41 tff(3487,plain,
% 6.20/6.41 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(s(z)))), elem!1))),
% 6.20/6.41 inference(monotonicity,[status(thm)],[3486])).
% 6.20/6.41 tff(3488,plain,
% 6.20/6.41 (~b(s(s(s(s(z)))), elem!1)),
% 6.20/6.41 inference(modus_ponens,[status(thm)],[3446, 3487])).
% 6.20/6.41 tff(3489,plain,
% 6.20/6.41 ($false),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[1652, 3488])).
% 6.20/6.41 tff(3490,plain,(b(s(s(s(s(z)))), z) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), z)) | r(z, elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.41 tff(3491,plain,
% 6.20/6.41 (b(s(s(s(s(z)))), z)),
% 6.20/6.41 inference(unit_resolution,[status(thm)],[3490, 3445, 3442, 80, 3440, 325, 181, 59, 1374, 3443])).
% 6.20/6.41 tff(3492,plain,
% 6.20/6.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 6.20/6.41 inference(rewrite,[status(thm)],[])).
% 6.20/6.41 tff(3493,plain,
% 6.20/6.41 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 6.20/6.41 inference(rewrite,[status(thm)],[])).
% 6.20/6.41 tff(3494,plain,
% 6.20/6.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 6.20/6.41 inference(monotonicity,[status(thm)],[3493])).
% 6.20/6.41 tff(3495,plain,
% 6.20/6.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 6.20/6.42 inference(transitivity,[status(thm)],[3494, 3492])).
% 6.20/6.42 tff(3496,plain,
% 6.20/6.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 6.20/6.42 inference(quant_inst,[status(thm)],[])).
% 6.20/6.42 tff(3497,plain,
% 6.20/6.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 6.20/6.42 inference(modus_ponens,[status(thm)],[3496, 3495])).
% 6.20/6.42 tff(3498,plain,
% 6.20/6.42 ($false),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[3497, 194, 184, 232, 183, 182])).
% 6.20/6.42 tff(3499,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.42 tff(3500,plain,
% 6.20/6.42 (~r(s(s(s(elem!1))), s(z))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[3499, 3438, 59, 181])).
% 6.20/6.42 tff(3501,plain,
% 6.20/6.42 (b(s(s(s(elem!1))), s(z))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[223, 3500])).
% 6.20/6.42 tff(3502,plain,
% 6.20/6.42 (~b(s(z), s(s(s(s(z)))))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[1660, 3445, 1374, 3501, 3443])).
% 6.20/6.42 tff(3503,plain,
% 6.20/6.42 (r(s(z), s(s(s(s(z)))))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[1230, 3502])).
% 6.20/6.42 tff(3504,plain,
% 6.20/6.42 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[490, 2401])).
% 6.20/6.42 tff(3505,plain,
% 6.20/6.42 (b(s(s(s(z))), s(s(s(s(z)))))),
% 6.20/6.42 inference(modus_ponens,[status(thm)],[1573, 3504])).
% 6.20/6.42 tff(3506,plain,
% 6.20/6.42 (b(s(s(s(z))), s(s(z)))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[2986, 11, 1374])).
% 6.20/6.42 tff(3507,plain,
% 6.20/6.42 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[489, 490])).
% 6.20/6.42 tff(3508,plain,
% 6.20/6.42 (b(s(s(z)), s(s(s(z))))),
% 6.20/6.42 inference(modus_ponens,[status(thm)],[328, 3507])).
% 6.20/6.42 tff(3509,plain,
% 6.20/6.42 (b(s(s(s(z))), z)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[1680, 11, 380])).
% 6.20/6.42 tff(3510,plain,
% 6.20/6.42 (~b(z, s(s(s(s(z)))))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[1694, 3505, 3509, 90])).
% 6.20/6.42 tff(3511,plain,
% 6.20/6.42 (r(z, s(s(s(s(z)))))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[800, 3510])).
% 6.20/6.42 tff(3512,plain,
% 6.20/6.42 (~r(s(s(s(s(z)))), s(s(z)))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[1705, 3511, 182, 1216])).
% 6.20/6.42 tff(3513,plain,
% 6.20/6.42 (b(s(s(s(s(z)))), s(s(z)))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[1714, 3512])).
% 6.20/6.42 tff(3514,plain,
% 6.20/6.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 6.20/6.42 inference(rewrite,[status(thm)],[])).
% 6.20/6.42 tff(3515,plain,
% 6.20/6.42 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 6.20/6.42 inference(rewrite,[status(thm)],[])).
% 6.20/6.42 tff(3516,plain,
% 6.20/6.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3515])).
% 6.20/6.42 tff(3517,plain,
% 6.20/6.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 6.20/6.42 inference(transitivity,[status(thm)],[3516, 3514])).
% 6.20/6.42 tff(3518,plain,
% 6.20/6.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 6.20/6.42 inference(quant_inst,[status(thm)],[])).
% 6.20/6.42 tff(3519,plain,
% 6.20/6.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 6.20/6.42 inference(modus_ponens,[status(thm)],[3518, 3517])).
% 6.20/6.42 tff(3520,plain,
% 6.20/6.42 ($false),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[3519, 391, 3513, 3508, 3506, 3505])).
% 6.20/6.42 tff(3521,plain,((~(elem!1 = z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.42 tff(3522,plain,
% 6.20/6.42 (~(elem!1 = z)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[3521, 3503, 181, 3491, 1573, 328, 1374, 3442])).
% 6.20/6.42 tff(3523,plain,
% 6.20/6.42 (elem!1 = s(z)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[1516, 3522, 3442, 80, 3440, 325, 181, 59])).
% 6.20/6.42 tff(3524,plain,
% 6.20/6.42 (s(z) = elem!1),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[172, 3523])).
% 6.20/6.42 tff(3525,plain,
% 6.20/6.42 (s(s(z)) = s(elem!1)),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3524])).
% 6.20/6.42 tff(3526,plain,
% 6.20/6.42 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3525])).
% 6.20/6.42 tff(3527,plain,
% 6.20/6.42 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3526])).
% 6.20/6.42 tff(3528,plain,
% 6.20/6.42 (~(z = elem!1)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[97, 3522])).
% 6.20/6.42 tff(3529,plain,
% 6.20/6.42 (~(s(z) = s(elem!1))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[117, 3528])).
% 6.20/6.42 tff(3530,plain,
% 6.20/6.42 (~(s(s(elem!1)) = s(s(z)))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[1962, 3529])).
% 6.20/6.42 tff(3531,plain,
% 6.20/6.42 (~(s(s(elem!1)) = s(elem!1))),
% 6.20/6.42 inference(modus_ponens,[status(thm)],[3530, 3527])).
% 6.20/6.42 tff(3532,plain,
% 6.20/6.42 (s(s(s(z))) = s(s(elem!1))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3525])).
% 6.20/6.42 tff(3533,plain,
% 6.20/6.42 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3532])).
% 6.20/6.42 tff(3534,plain,
% 6.20/6.42 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 6.20/6.42 inference(symmetry,[status(thm)],[3533])).
% 6.20/6.42 tff(3535,plain,
% 6.20/6.42 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3534])).
% 6.20/6.42 tff(3536,plain,
% 6.20/6.42 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 6.20/6.42 inference(symmetry,[status(thm)],[3535])).
% 6.20/6.42 tff(3537,plain,
% 6.20/6.42 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3525])).
% 6.20/6.42 tff(3538,plain,
% 6.20/6.42 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 6.20/6.42 inference(transitivity,[status(thm)],[3537, 3536])).
% 6.20/6.42 tff(3539,plain,
% 6.20/6.42 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3533, 3525])).
% 6.20/6.42 tff(3540,plain,
% 6.20/6.42 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 6.20/6.42 inference(symmetry,[status(thm)],[3539])).
% 6.20/6.42 tff(3541,plain,
% 6.20/6.42 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3540])).
% 6.20/6.42 tff(3542,plain,
% 6.20/6.42 (~r(s(s(s(s(z)))), s(s(z)))),
% 6.20/6.42 inference(modus_ponens,[status(thm)],[3444, 3541])).
% 6.20/6.42 tff(3543,plain,
% 6.20/6.42 (b(s(s(s(s(z)))), s(s(z)))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[1714, 3542])).
% 6.20/6.42 tff(3544,plain,
% 6.20/6.42 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3525])).
% 6.20/6.42 tff(3545,plain,
% 6.20/6.42 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 6.20/6.42 inference(transitivity,[status(thm)],[3544, 582])).
% 6.20/6.42 tff(3546,plain,
% 6.20/6.42 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3545])).
% 6.20/6.42 tff(3547,plain,
% 6.20/6.42 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.20/6.42 inference(modus_ponens,[status(thm)],[1397, 3546])).
% 6.20/6.42 tff(3548,plain,
% 6.20/6.42 (b(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[588, 3547, 3444])).
% 6.20/6.42 tff(3549,plain,
% 6.20/6.42 (r(s(z), z) <=> r(elem!1, z)),
% 6.20/6.42 inference(monotonicity,[status(thm)],[3524])).
% 6.20/6.42 tff(3550,plain,
% 6.20/6.42 (r(elem!1, z)),
% 6.20/6.42 inference(modus_ponens,[status(thm)],[181, 3549])).
% 6.20/6.42 tff(3551,plain,
% 6.20/6.42 (~r(elem!1, s(elem!1))),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[2259, 1628, 184, 530])).
% 6.20/6.42 tff(3552,plain,
% 6.20/6.42 (r(s(elem!1), elem!1)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[2340, 3551, 437, 900, 1101])).
% 6.20/6.42 tff(3553,plain,
% 6.20/6.42 ($false),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[2347, 194, 530, 3552, 1628, 184])).
% 6.20/6.42 tff(3554,plain,((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.42 tff(3555,plain,
% 6.20/6.42 (~r(s(elem!1), z)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[3554, 3550, 59, 2205, 3440, 3548])).
% 6.20/6.42 tff(3556,plain,
% 6.20/6.42 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 6.20/6.42 inference(monotonicity,[status(thm)],[818])).
% 6.20/6.42 tff(3557,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 6.20/6.42 tff(3558,plain,
% 6.20/6.42 (r(s(elem!1), z)),
% 6.20/6.42 inference(modus_ponens,[status(thm)],[3557, 3556])).
% 6.20/6.42 tff(3559,plain,
% 6.20/6.42 ($false),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[544, 3558])).
% 6.20/6.42 tff(3560,plain,((~r(s(s(z)), z)) | r(s(elem!1), z) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.42 tff(3561,plain,
% 6.20/6.42 (~r(s(s(z)), z)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[3560, 3555, 3524])).
% 6.20/6.42 tff(3562,plain,
% 6.20/6.42 (b(s(s(z)), z)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[1211, 3561])).
% 6.20/6.42 tff(3563,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 6.20/6.42 tff(3564,plain,
% 6.20/6.42 (~(elem!1 = z)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[3379, 3369, 309])).
% 6.20/6.42 tff(3565,plain,
% 6.20/6.42 (~(z = elem!1)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[97, 3564])).
% 6.20/6.42 tff(3566,plain,
% 6.20/6.42 (b(z, elem!1)),
% 6.20/6.42 inference(unit_resolution,[status(thm)],[141, 3565, 80])).
% 6.20/6.42 tff(3567,plain,
% 6.20/6.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.42 inference(rewrite,[status(thm)],[])).
% 6.20/6.42 tff(3568,plain,
% 6.20/6.42 (((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.42 inference(rewrite,[status(thm)],[])).
% 6.20/6.42 tff(3569,plain,
% 6.20/6.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 6.20/6.43 inference(monotonicity,[status(thm)],[3568])).
% 6.20/6.43 tff(3570,plain,
% 6.20/6.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.43 inference(transitivity,[status(thm)],[3569, 3567])).
% 6.20/6.43 tff(3571,plain,
% 6.20/6.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.43 inference(quant_inst,[status(thm)],[])).
% 6.20/6.43 tff(3572,plain,
% 6.20/6.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 6.20/6.43 inference(modus_ponens,[status(thm)],[3571, 3570])).
% 6.20/6.43 tff(3573,plain,
% 6.20/6.43 ($false),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3572, 391, 3566, 90, 1235, 3369, 3563])).
% 6.20/6.43 tff(3574,plain,((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | r(z, elem!1) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.43 tff(3575,plain,
% 6.20/6.43 (~b(elem!1, s(s(z)))),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3574, 3562, 80, 3543, 3491, 309])).
% 6.20/6.43 tff(3576,plain,
% 6.20/6.43 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 6.20/6.43 inference(monotonicity,[status(thm)],[3524])).
% 6.20/6.43 tff(3577,plain,
% 6.20/6.43 (r(elem!1, s(s(z))) <=> r(s(z), s(s(z)))),
% 6.20/6.43 inference(symmetry,[status(thm)],[3576])).
% 6.20/6.43 tff(3578,plain,
% 6.20/6.43 ((s(z) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 6.20/6.43 inference(monotonicity,[status(thm)],[3524])).
% 6.20/6.43 tff(3579,plain,
% 6.20/6.43 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 6.20/6.43 inference(monotonicity,[status(thm)],[3578])).
% 6.20/6.43 tff(3580,plain,
% 6.20/6.43 (~(elem!1 = s(s(z)))),
% 6.20/6.43 inference(modus_ponens,[status(thm)],[1783, 3579])).
% 6.20/6.43 tff(3581,plain,
% 6.20/6.43 (r(elem!1, s(s(z)))),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3394, 3575, 3580])).
% 6.20/6.43 tff(3582,plain,
% 6.20/6.43 (r(s(z), s(s(z)))),
% 6.20/6.43 inference(modus_ponens,[status(thm)],[3581, 3577])).
% 6.20/6.43 tff(3583,assumption,(~b(elem!1, s(s(z)))), introduced(assumption)).
% 6.20/6.43 tff(3584,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 6.20/6.43 tff(3585,plain,
% 6.20/6.43 (b(elem!1, z) <=> b(s(s(z)), z)),
% 6.20/6.43 inference(monotonicity,[status(thm)],[3584])).
% 6.20/6.43 tff(3586,plain,
% 6.20/6.43 (b(s(s(z)), z) <=> b(elem!1, z)),
% 6.20/6.43 inference(symmetry,[status(thm)],[3585])).
% 6.20/6.43 tff(3587,plain,
% 6.20/6.43 (b(elem!1, z)),
% 6.20/6.43 inference(modus_ponens,[status(thm)],[1235, 3586])).
% 6.20/6.43 tff(3588,plain,
% 6.20/6.43 ($false),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[484, 3587])).
% 6.20/6.43 tff(3589,plain,((~(elem!1 = s(s(z)))) | b(elem!1, z) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.43 tff(3590,plain,
% 6.20/6.43 (~(elem!1 = s(s(z)))),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3589, 484, 1235])).
% 6.20/6.43 tff(3591,plain,
% 6.20/6.43 (r(elem!1, s(s(z)))),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3394, 3590, 3583])).
% 6.20/6.43 tff(3592,plain,
% 6.20/6.43 (b(elem!1, s(z))),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[835, 42, 1756, 831])).
% 6.20/6.43 tff(3593,plain,
% 6.20/6.43 (b(s(z), elem!1)),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[632, 1766, 1496])).
% 6.20/6.43 tff(3594,plain,
% 6.20/6.43 (~(elem!1 = z)),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3200, 3593, 91])).
% 6.20/6.43 tff(3595,plain,
% 6.20/6.43 (~(z = elem!1)),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[97, 3594])).
% 6.20/6.43 tff(3596,plain,
% 6.20/6.43 (b(z, elem!1)),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[141, 3595, 80])).
% 6.20/6.43 tff(3597,plain,
% 6.20/6.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.43 inference(rewrite,[status(thm)],[])).
% 6.20/6.43 tff(3598,plain,
% 6.20/6.43 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.43 inference(rewrite,[status(thm)],[])).
% 6.20/6.43 tff(3599,plain,
% 6.20/6.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 6.20/6.43 inference(monotonicity,[status(thm)],[3598])).
% 6.20/6.43 tff(3600,plain,
% 6.20/6.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.43 inference(transitivity,[status(thm)],[3599, 3597])).
% 6.20/6.43 tff(3601,plain,
% 6.20/6.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.43 inference(quant_inst,[status(thm)],[])).
% 6.20/6.43 tff(3602,plain,
% 6.20/6.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 6.20/6.43 inference(modus_ponens,[status(thm)],[3601, 3600])).
% 6.20/6.43 tff(3603,plain,
% 6.20/6.43 ($false),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3602, 391, 3596, 90, 1235, 3563, 3592])).
% 6.20/6.43 tff(3604,plain,((~r(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(z)) | r(z, elem!1) | b(s(z), z) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.43 tff(3605,plain,
% 6.20/6.43 (elem!1 = s(z)),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3604, 3591, 1235, 3563, 90, 80, 91, 1749, 1747])).
% 6.20/6.43 tff(3606,plain,
% 6.20/6.43 (s(z) = elem!1),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[172, 3605])).
% 6.20/6.43 tff(3607,plain,
% 6.20/6.43 (s(s(z)) = s(elem!1)),
% 6.20/6.43 inference(monotonicity,[status(thm)],[3606])).
% 6.20/6.43 tff(3608,plain,
% 6.20/6.43 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 6.20/6.43 inference(monotonicity,[status(thm)],[3607])).
% 6.20/6.43 tff(3609,plain,
% 6.20/6.43 (b(s(elem!1), z)),
% 6.20/6.43 inference(modus_ponens,[status(thm)],[1235, 3608])).
% 6.20/6.43 tff(3610,plain,
% 6.20/6.43 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 6.20/6.43 inference(monotonicity,[status(thm)],[818, 820])).
% 6.20/6.43 tff(3611,plain,
% 6.20/6.43 (r(s(elem!1), s(s(s(elem!1))))),
% 6.20/6.43 inference(modus_ponens,[status(thm)],[1749, 3610])).
% 6.20/6.43 tff(3612,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 6.20/6.43 tff(3613,plain,
% 6.20/6.43 ($false),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3612, 3611])).
% 6.20/6.43 tff(3614,plain,((~r(s(s(z)), s(s(s(s(z)))))) | r(s(elem!1), s(s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.43 tff(3615,plain,
% 6.20/6.43 (r(s(elem!1), s(s(s(elem!1))))),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3614, 3606, 1749])).
% 6.20/6.43 tff(3616,plain,
% 6.20/6.43 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 6.20/6.43 inference(monotonicity,[status(thm)],[3607])).
% 6.20/6.43 tff(3617,plain,
% 6.20/6.43 (r(elem!1, s(elem!1))),
% 6.20/6.43 inference(modus_ponens,[status(thm)],[3591, 3616])).
% 6.20/6.43 tff(3618,plain,
% 6.20/6.43 (r(elem!1, z)),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[526, 484, 2])).
% 6.20/6.43 tff(3619,plain,
% 6.20/6.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.20/6.43 inference(rewrite,[status(thm)],[])).
% 6.20/6.43 tff(3620,plain,
% 6.20/6.43 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.20/6.43 inference(rewrite,[status(thm)],[])).
% 6.20/6.43 tff(3621,plain,
% 6.20/6.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 6.20/6.43 inference(monotonicity,[status(thm)],[3620])).
% 6.20/6.43 tff(3622,plain,
% 6.20/6.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.20/6.43 inference(transitivity,[status(thm)],[3621, 3619])).
% 6.20/6.43 tff(3623,plain,
% 6.20/6.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 6.20/6.43 inference(quant_inst,[status(thm)],[])).
% 6.20/6.43 tff(3624,plain,
% 6.20/6.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 6.20/6.43 inference(modus_ponens,[status(thm)],[3623, 3622])).
% 6.20/6.43 tff(3625,plain,
% 6.20/6.43 ($false),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3624, 194, 530, 2144, 2251, 604])).
% 6.20/6.43 tff(3626,plain,((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.43 tff(3627,plain,
% 6.20/6.43 (~r(z, s(elem!1))),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[3626, 3618, 3617, 3615])).
% 6.20/6.43 tff(3628,plain,
% 6.20/6.43 (b(z, s(elem!1))),
% 6.20/6.43 inference(unit_resolution,[status(thm)],[566, 3627])).
% 6.20/6.43 tff(3629,plain,
% 6.20/6.43 (s(s(s(z))) = s(s(elem!1))),
% 6.20/6.44 inference(monotonicity,[status(thm)],[3607])).
% 6.20/6.44 tff(3630,plain,
% 6.20/6.44 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 6.20/6.44 inference(monotonicity,[status(thm)],[3629])).
% 6.20/6.44 tff(3631,plain,
% 6.20/6.44 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.44 inference(monotonicity,[status(thm)],[3630, 3607])).
% 6.20/6.44 tff(3632,plain,
% 6.20/6.44 (b(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.44 inference(modus_ponens,[status(thm)],[3563, 3631])).
% 6.20/6.44 tff(3633,plain,
% 6.20/6.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 6.20/6.44 inference(rewrite,[status(thm)],[])).
% 6.20/6.44 tff(3634,plain,
% 6.20/6.44 (((~b(z, elem!1)) | (~b(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))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 6.20/6.44 inference(rewrite,[status(thm)],[])).
% 6.20/6.44 tff(3635,plain,
% 6.20/6.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 6.20/6.44 inference(monotonicity,[status(thm)],[3634])).
% 6.20/6.44 tff(3636,plain,
% 6.20/6.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 6.20/6.44 inference(transitivity,[status(thm)],[3635, 3633])).
% 6.20/6.44 tff(3637,plain,
% 6.20/6.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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)))),
% 6.20/6.44 inference(quant_inst,[status(thm)],[])).
% 6.20/6.44 tff(3638,plain,
% 6.20/6.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 6.20/6.44 inference(modus_ponens,[status(thm)],[3637, 3636])).
% 6.20/6.44 tff(3639,plain,
% 6.20/6.44 ($false),
% 6.20/6.44 inference(unit_resolution,[status(thm)],[3638, 391, 149, 3632, 380, 3628, 3609])).
% 6.20/6.44 tff(3640,plain,(b(elem!1, z) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | r(z, elem!1) | b(s(z), z) | (~r(s(z), s(s(z)))) | b(elem!1, s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 6.20/6.44 tff(3641,plain,
% 6.20/6.44 (b(elem!1, z)),
% 6.20/6.44 inference(unit_resolution,[status(thm)],[3640, 2, 3563, 1235, 1749, 90, 80, 91, 1747, 3583, 380])).
% 6.20/6.44 tff(3642,plain,
% 6.20/6.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.44 inference(rewrite,[status(thm)],[])).
% 6.20/6.44 tff(3643,plain,
% 6.20/6.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.44 inference(quant_inst,[status(thm)],[])).
% 6.20/6.44 tff(3644,plain,
% 6.20/6.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 6.20/6.44 inference(modus_ponens,[status(thm)],[3643, 3642])).
% 6.20/6.44 tff(3645,plain,
% 6.20/6.44 ($false),
% 6.20/6.44 inference(unit_resolution,[status(thm)],[3644, 391, 149, 3641, 90, 1235, 3563])).
% 6.20/6.44 tff(3646,plain,((elem!1 = z) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | r(z, elem!1) | b(s(z), z) | (~r(s(z), s(s(z)))) | b(elem!1, s(s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.44 tff(3647,plain,
% 6.20/6.44 (~r(s(s(z)), s(s(s(s(z)))))),
% 6.20/6.44 inference(unit_resolution,[status(thm)],[3646, 3582, 80, 3491, 3522, 3543, 91, 3562, 3575, 3442])).
% 6.20/6.44 tff(3648,plain,
% 6.20/6.44 (((~![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))))))),
% 6.20/6.44 inference(rewrite,[status(thm)],[])).
% 6.20/6.44 tff(3649,plain,
% 6.20/6.44 ((~![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))))))),
% 6.20/6.44 inference(quant_inst,[status(thm)],[])).
% 6.20/6.44 tff(3650,plain,
% 6.20/6.44 ((~![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)))))),
% 6.20/6.44 inference(modus_ponens,[status(thm)],[3649, 3648])).
% 6.20/6.44 tff(3651,plain,
% 6.20/6.44 ((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)))))),
% 6.20/6.44 inference(unit_resolution,[status(thm)],[3650, 42])).
% 6.20/6.44 tff(3652,plain,
% 6.20/6.44 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 6.20/6.44 inference(unit_resolution,[status(thm)],[3651, 714])).
% 6.20/6.44 tff(3653,plain,
% 6.20/6.44 (b(s(s(z)), s(s(s(s(z)))))),
% 6.20/6.44 inference(unit_resolution,[status(thm)],[3652, 3647])).
% 6.20/6.44 tff(3654,plain,
% 6.20/6.44 (b(s(elem!1), s(s(s(elem!1))))),
% 6.20/6.44 inference(modus_ponens,[status(thm)],[3653, 3538])).
% 6.20/6.44 tff(3655,plain,
% 6.20/6.44 (b(s(elem!1), z)),
% 6.20/6.44 inference(unit_resolution,[status(thm)],[549, 3555])).
% 6.20/6.44 tff(3656,plain,
% 6.20/6.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))),
% 6.20/6.44 inference(rewrite,[status(thm)],[])).
% 6.20/6.44 tff(3657,plain,
% 6.20/6.44 (((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))),
% 6.20/6.44 inference(rewrite,[status(thm)],[])).
% 6.20/6.44 tff(3658,plain,
% 6.20/6.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))))),
% 6.20/6.44 inference(monotonicity,[status(thm)],[3657])).
% 6.20/6.44 tff(3659,plain,
% 6.20/6.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))),
% 6.20/6.44 inference(transitivity,[status(thm)],[3658, 3656])).
% 6.20/6.44 tff(3660,plain,
% 6.20/6.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 6.20/6.45 inference(quant_inst,[status(thm)],[])).
% 6.20/6.45 tff(3661,plain,
% 6.20/6.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[3660, 3659])).
% 6.20/6.45 tff(3662,plain,
% 6.20/6.45 (~b(s(s(elem!1)), s(elem!1))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3661, 391, 3548, 3655, 328, 3654])).
% 6.20/6.45 tff(3663,plain,
% 6.20/6.45 (r(s(s(elem!1)), s(elem!1))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[1135, 3662, 3531])).
% 6.20/6.45 tff(3664,plain,
% 6.20/6.45 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 6.20/6.45 inference(monotonicity,[status(thm)],[3524])).
% 6.20/6.45 tff(3665,plain,
% 6.20/6.45 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 6.20/6.45 inference(transitivity,[status(thm)],[3664, 2206])).
% 6.20/6.45 tff(3666,plain,
% 6.20/6.45 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 6.20/6.45 inference(monotonicity,[status(thm)],[3665])).
% 6.20/6.45 tff(3667,plain,
% 6.20/6.45 (~(elem!1 = s(s(elem!1)))),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[357, 3666])).
% 6.20/6.45 tff(3668,plain,
% 6.20/6.45 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 6.20/6.45 inference(monotonicity,[status(thm)],[3524])).
% 6.20/6.45 tff(3669,plain,
% 6.20/6.45 (b(s(s(elem!1)), elem!1)),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[3443, 3668])).
% 6.20/6.45 tff(3670,plain,
% 6.20/6.45 (~b(elem!1, s(s(elem!1)))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[1467, 3669, 1374, 3440])).
% 6.20/6.45 tff(3671,plain,
% 6.20/6.45 (r(elem!1, s(s(elem!1)))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[1307, 3670, 3667])).
% 6.20/6.45 tff(3672,plain,
% 6.20/6.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.20/6.45 inference(rewrite,[status(thm)],[])).
% 6.20/6.45 tff(3673,plain,
% 6.20/6.45 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.20/6.45 inference(rewrite,[status(thm)],[])).
% 6.20/6.45 tff(3674,plain,
% 6.20/6.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 6.20/6.45 inference(monotonicity,[status(thm)],[3673])).
% 6.20/6.45 tff(3675,plain,
% 6.20/6.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.20/6.45 inference(transitivity,[status(thm)],[3674, 3672])).
% 6.20/6.45 tff(3676,plain,
% 6.20/6.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 6.20/6.45 inference(quant_inst,[status(thm)],[])).
% 6.20/6.45 tff(3677,plain,
% 6.20/6.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[3676, 3675])).
% 6.20/6.45 tff(3678,plain,
% 6.20/6.45 ($false),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3677, 194, 3550, 325, 3671, 3663])).
% 6.20/6.45 tff(3679,plain,(r(z, elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | b(s(z), z) | b(z, s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.45 tff(3680,plain,
% 6.20/6.45 (r(z, elem!1)),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3679, 3400, 91, 309, 1371, 3436, 10])).
% 6.20/6.45 tff(3681,plain,
% 6.20/6.45 (~b(elem!1, s(s(z)))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3379, 11, 309])).
% 6.20/6.45 tff(3682,plain,
% 6.20/6.45 (r(s(z), elem!1)),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3205, 11, 91])).
% 6.20/6.45 tff(3683,plain,
% 6.20/6.45 (~r(elem!1, s(s(z)))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3389, 3682, 411, 181])).
% 6.20/6.45 tff(3684,plain,
% 6.20/6.45 (elem!1 = s(s(z))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3394, 3683, 3681])).
% 6.20/6.45 tff(3685,plain,
% 6.20/6.45 (s(s(z)) = elem!1),
% 6.20/6.45 inference(symmetry,[status(thm)],[3684])).
% 6.20/6.45 tff(3686,plain,
% 6.20/6.45 (s(s(z)) = z),
% 6.20/6.45 inference(transitivity,[status(thm)],[3685, 11])).
% 6.20/6.45 tff(3687,plain,
% 6.20/6.45 ($false),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[1207, 3686])).
% 6.20/6.45 tff(3688,plain,((~(elem!1 = z)) | (~r(z, elem!1)) | b(s(z), z) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.45 tff(3689,plain,
% 6.20/6.45 (~(elem!1 = z)),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3688, 3680, 91, 309])).
% 6.20/6.45 tff(3690,plain,
% 6.20/6.45 (~r(s(s(s(elem!1))), elem!1)),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[241, 3434, 59, 181])).
% 6.20/6.45 tff(3691,plain,
% 6.20/6.45 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 6.20/6.45 inference(monotonicity,[status(thm)],[5])).
% 6.20/6.45 tff(3692,plain,
% 6.20/6.45 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 6.20/6.45 inference(transitivity,[status(thm)],[3691, 698])).
% 6.20/6.45 tff(3693,plain,
% 6.20/6.45 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 6.20/6.45 inference(monotonicity,[status(thm)],[3692])).
% 6.20/6.45 tff(3694,plain,
% 6.20/6.45 (~(elem!1 = s(s(z)))),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[1397, 3693])).
% 6.20/6.45 tff(3695,plain,
% 6.20/6.45 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[1407, 3694])).
% 6.20/6.45 tff(3696,plain,
% 6.20/6.45 (~(elem!1 = s(s(s(s(z)))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[769, 2691])).
% 6.20/6.45 tff(3697,plain,
% 6.20/6.45 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 6.20/6.45 inference(monotonicity,[status(thm)],[5])).
% 6.20/6.45 tff(3698,plain,
% 6.20/6.45 (~b(s(z), s(s(s(elem!1))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3432, 326, 182, 1374, 328])).
% 6.20/6.45 tff(3699,plain,
% 6.20/6.45 (r(s(z), s(s(s(elem!1))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[247, 3698])).
% 6.20/6.45 tff(3700,plain,
% 6.20/6.45 (r(s(z), elem!1)),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[3699, 3697])).
% 6.20/6.45 tff(3701,plain,
% 6.20/6.45 (~r(elem!1, s(s(s(s(z)))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[2040, 3700, 411, 182])).
% 6.20/6.45 tff(3702,plain,
% 6.20/6.45 (b(elem!1, s(s(s(s(z)))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[781, 3701, 3696])).
% 6.20/6.45 tff(3703,plain,
% 6.20/6.45 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 6.20/6.45 inference(monotonicity,[status(thm)],[5])).
% 6.20/6.45 tff(3704,plain,
% 6.20/6.45 (~r(s(s(s(elem!1))), z)),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[1867, 3699, 184, 182])).
% 6.20/6.45 tff(3705,plain,
% 6.20/6.45 (b(s(s(s(elem!1))), z)),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[377, 3704])).
% 6.20/6.45 tff(3706,plain,
% 6.20/6.45 (b(elem!1, z)),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[3705, 3703])).
% 6.20/6.45 tff(3707,plain,
% 6.20/6.45 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 6.20/6.45 inference(monotonicity,[status(thm)],[5])).
% 6.20/6.45 tff(3708,plain,
% 6.20/6.45 (~r(s(s(s(elem!1))), s(z))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3499, 3699, 184, 182])).
% 6.20/6.45 tff(3709,plain,
% 6.20/6.45 (b(s(s(s(elem!1))), s(z))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[223, 3708])).
% 6.20/6.45 tff(3710,plain,
% 6.20/6.45 (b(elem!1, s(z))),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[3709, 3707])).
% 6.20/6.45 tff(3711,plain,
% 6.20/6.45 (~r(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[641, 3699, 184, 182])).
% 6.20/6.45 tff(3712,plain,
% 6.20/6.45 (~r(s(elem!1), z)),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[2594, 1956, 3709, 411, 3699, 3711, 182])).
% 6.20/6.45 tff(3713,plain,
% 6.20/6.45 (b(s(elem!1), z)),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[549, 3712])).
% 6.20/6.45 tff(3714,plain,
% 6.20/6.45 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 6.20/6.45 inference(monotonicity,[status(thm)],[5])).
% 6.20/6.45 tff(3715,plain,
% 6.20/6.45 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.45 inference(symmetry,[status(thm)],[3714])).
% 6.20/6.45 tff(3716,plain,
% 6.20/6.45 (s(s(s(s(elem!1)))) = s(elem!1)),
% 6.20/6.45 inference(monotonicity,[status(thm)],[5])).
% 6.20/6.45 tff(3717,plain,
% 6.20/6.45 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(elem!1))),
% 6.20/6.45 inference(monotonicity,[status(thm)],[3716])).
% 6.20/6.45 tff(3718,plain,
% 6.20/6.45 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.45 inference(transitivity,[status(thm)],[3717, 3715])).
% 6.20/6.45 tff(3719,plain,
% 6.20/6.45 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 6.20/6.45 inference(monotonicity,[status(thm)],[5])).
% 6.20/6.45 tff(3720,plain,
% 6.20/6.45 (b(elem!1, s(s(s(s(elem!1)))))),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[1573, 3719])).
% 6.20/6.45 tff(3721,plain,
% 6.20/6.45 (b(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[3720, 3718])).
% 6.20/6.45 tff(3722,plain,
% 6.20/6.45 (~r(s(z), s(s(s(s(z)))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[2061, 2053, 182, 411])).
% 6.20/6.45 tff(3723,plain,
% 6.20/6.45 (b(s(z), s(s(s(s(z)))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[1230, 3722])).
% 6.20/6.45 tff(3724,plain,
% 6.20/6.45 (~r(s(s(s(s(z)))), s(z))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3243, 2053, 182, 411])).
% 6.20/6.45 tff(3725,plain,
% 6.20/6.45 (b(s(s(s(s(z)))), s(z))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[749, 3724])).
% 6.20/6.45 tff(3726,plain,
% 6.20/6.45 (~r(z, s(s(s(s(z)))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[2097, 3725, 411, 720, 3723, 721])).
% 6.20/6.45 tff(3727,plain,
% 6.20/6.45 (~b(z, s(s(s(s(z)))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[2638, 3725, 380, 1101, 591])).
% 6.20/6.45 tff(3728,plain,
% 6.20/6.45 ($false),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[800, 3727, 3726])).
% 6.20/6.45 tff(3729,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.45 tff(3730,plain,
% 6.20/6.45 (~r(s(s(s(s(z)))), z)),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3729, 3721, 3705, 3713, 411, 2691, 3710, 182])).
% 6.20/6.45 tff(3731,plain,
% 6.20/6.45 (b(s(s(s(s(z)))), z)),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[87, 3730])).
% 6.20/6.45 tff(3732,plain,
% 6.20/6.45 (~b(z, s(s(s(s(z)))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[3234, 3731, 3706, 3702])).
% 6.20/6.45 tff(3733,plain,
% 6.20/6.45 (r(z, s(s(s(s(z)))))),
% 6.20/6.45 inference(unit_resolution,[status(thm)],[800, 3732])).
% 6.20/6.45 tff(3734,plain,
% 6.20/6.45 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 6.20/6.45 inference(monotonicity,[status(thm)],[5])).
% 6.20/6.45 tff(3735,plain,
% 6.20/6.45 (b(elem!1, s(s(elem!1)))),
% 6.20/6.45 inference(modus_ponens,[status(thm)],[1374, 3734])).
% 6.20/6.45 tff(3736,plain,
% 6.20/6.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.20/6.45 inference(rewrite,[status(thm)],[])).
% 6.20/6.45 tff(3737,plain,
% 6.20/6.45 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.20/6.45 inference(rewrite,[status(thm)],[])).
% 6.20/6.45 tff(3738,plain,
% 6.20/6.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 6.20/6.46 inference(monotonicity,[status(thm)],[3737])).
% 6.20/6.46 tff(3739,plain,
% 6.20/6.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.20/6.46 inference(transitivity,[status(thm)],[3738, 3736])).
% 6.20/6.46 tff(3740,plain,
% 6.20/6.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 6.20/6.46 inference(quant_inst,[status(thm)],[])).
% 6.20/6.46 tff(3741,plain,
% 6.20/6.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 6.20/6.46 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 6.20/6.46 tff(3742,plain,
% 6.20/6.46 ($false),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[3741, 391, 381, 1294, 90, 1234, 721])).
% 6.20/6.46 tff(3743,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.46 tff(3744,plain,
% 6.20/6.46 (~b(s(s(elem!1)), s(z))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[3743, 1234, 1294, 90, 721])).
% 6.20/6.46 tff(3745,plain,
% 6.20/6.46 (~r(s(s(elem!1)), s(z))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[2824, 1234, 411, 720, 1484, 1294, 721, 1983, 719])).
% 6.20/6.46 tff(3746,plain,
% 6.20/6.46 ($false),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[362, 3745, 3744])).
% 6.20/6.46 tff(3747,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.46 tff(3748,plain,
% 6.20/6.46 (~b(s(z), s(s(s(s(z)))))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[3747, 2691, 411, 3700, 3735, 3710, 3695, 3733, 3731])).
% 6.20/6.46 tff(3749,plain,
% 6.20/6.46 (r(s(z), s(s(s(s(z)))))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[1230, 3748])).
% 6.20/6.46 tff(3750,plain,
% 6.20/6.46 (~r(s(s(s(s(z)))), s(z))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[3236, 3749, 3706, 182, 3702, 411])).
% 6.20/6.46 tff(3751,plain,
% 6.20/6.46 (b(s(s(s(s(z)))), s(z))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[749, 3750])).
% 6.20/6.46 tff(3752,plain,
% 6.20/6.46 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[2108, 3749, 182, 3733])).
% 6.20/6.46 tff(3753,plain,
% 6.20/6.46 (b(s(s(s(s(z)))), elem!1)),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[2694, 3752, 5])).
% 6.20/6.46 tff(3754,plain,
% 6.20/6.46 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 6.20/6.46 inference(monotonicity,[status(thm)],[5])).
% 6.20/6.46 tff(3755,plain,
% 6.20/6.46 (b(s(s(elem!1)), elem!1)),
% 6.20/6.46 inference(modus_ponens,[status(thm)],[328, 3754])).
% 6.20/6.46 tff(3756,plain,
% 6.20/6.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.20/6.46 inference(rewrite,[status(thm)],[])).
% 6.20/6.46 tff(3757,plain,
% 6.20/6.46 (((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.20/6.46 inference(rewrite,[status(thm)],[])).
% 6.20/6.46 tff(3758,plain,
% 6.20/6.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 6.20/6.46 inference(monotonicity,[status(thm)],[3757])).
% 6.20/6.46 tff(3759,plain,
% 6.20/6.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.20/6.46 inference(transitivity,[status(thm)],[3758, 3756])).
% 6.20/6.46 tff(3760,plain,
% 6.20/6.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(s(z)))), s(s(elem!1)))))),
% 6.20/6.46 inference(quant_inst,[status(thm)],[])).
% 6.20/6.46 tff(3761,plain,
% 6.20/6.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z)))),
% 6.20/6.46 inference(modus_ponens,[status(thm)],[3760, 3759])).
% 6.20/6.46 tff(3762,plain,
% 6.20/6.46 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[3761, 391, 3755, 3702, 3753, 3751])).
% 6.20/6.46 tff(3763,plain,
% 6.20/6.46 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[2003, 42, 3762, 3695])).
% 6.20/6.46 tff(3764,plain,
% 6.20/6.46 (~r(s(s(s(s(z)))), s(s(z)))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[1705, 3749, 182, 3733])).
% 6.20/6.46 tff(3765,plain,
% 6.20/6.46 (b(s(s(s(s(z)))), s(s(z)))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[1714, 3764])).
% 6.20/6.46 tff(3766,plain,
% 6.20/6.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 6.20/6.46 inference(rewrite,[status(thm)],[])).
% 6.20/6.46 tff(3767,plain,
% 6.20/6.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 6.20/6.46 inference(quant_inst,[status(thm)],[])).
% 6.20/6.46 tff(3768,plain,
% 6.20/6.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 6.20/6.46 inference(modus_ponens,[status(thm)],[3767, 3766])).
% 6.20/6.46 tff(3769,plain,
% 6.20/6.46 (~r(s(s(z)), s(z))),
% 6.20/6.46 inference(unit_resolution,[status(thm)],[3768, 194, 411, 182, 3557])).
% 6.20/6.46 tff(3770,plain,
% 6.20/6.46 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 6.20/6.46 inference(commutativity,[status(thm)],[])).
% 6.20/6.46 tff(3771,plain,
% 6.20/6.46 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 6.20/6.46 inference(symmetry,[status(thm)],[3770])).
% 6.20/6.46 tff(3772,plain,
% 6.20/6.46 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 6.20/6.46 inference(monotonicity,[status(thm)],[3771])).
% 6.20/6.46 tff(3773,plain,
% 6.20/6.46 (~(s(s(z)) = s(z))),
% 6.20/6.46 inference(modus_ponens,[status(thm)],[1783, 3772])).
% 6.20/6.46 tff(3774,plain,
% 6.20/6.46 (((~![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)))),
% 6.20/6.47 inference(rewrite,[status(thm)],[])).
% 6.20/6.47 tff(3775,plain,
% 6.20/6.47 ((~![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)))),
% 6.20/6.47 inference(quant_inst,[status(thm)],[])).
% 6.20/6.47 tff(3776,plain,
% 6.20/6.47 ((~![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))),
% 6.20/6.47 inference(modus_ponens,[status(thm)],[3775, 3774])).
% 6.20/6.47 tff(3777,plain,
% 6.20/6.47 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[3776, 42])).
% 6.20/6.47 tff(3778,plain,
% 6.20/6.47 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[3777, 3773])).
% 6.20/6.47 tff(3779,plain,
% 6.20/6.47 (b(s(s(z)), s(z))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[3778, 3769])).
% 6.20/6.47 tff(3780,plain,
% 6.20/6.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 6.20/6.47 inference(rewrite,[status(thm)],[])).
% 6.20/6.47 tff(3781,plain,
% 6.20/6.47 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 6.20/6.47 inference(rewrite,[status(thm)],[])).
% 6.20/6.47 tff(3782,plain,
% 6.20/6.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))))),
% 6.20/6.47 inference(monotonicity,[status(thm)],[3781])).
% 6.20/6.47 tff(3783,plain,
% 6.20/6.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 6.20/6.47 inference(transitivity,[status(thm)],[3782, 3780])).
% 6.20/6.47 tff(3784,plain,
% 6.20/6.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 6.20/6.47 inference(quant_inst,[status(thm)],[])).
% 6.20/6.47 tff(3785,plain,
% 6.20/6.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))),
% 6.20/6.47 inference(modus_ponens,[status(thm)],[3784, 3783])).
% 6.20/6.47 tff(3786,plain,
% 6.20/6.47 ($false),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[3785, 194, 326, 182, 3557, 1747])).
% 6.20/6.47 tff(3787,plain,((~r(s(s(z)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.47 tff(3788,plain,
% 6.20/6.47 (~r(s(z), s(s(z)))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[3787, 3557, 182, 326])).
% 6.20/6.47 tff(3789,plain,
% 6.20/6.47 (b(s(z), s(s(z)))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[1788, 3788])).
% 6.20/6.47 tff(3790,plain,
% 6.20/6.47 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.20/6.47 inference(rewrite,[status(thm)],[])).
% 6.20/6.47 tff(3791,plain,
% 6.20/6.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 6.20/6.47 inference(monotonicity,[status(thm)],[3790])).
% 6.20/6.47 tff(3792,plain,
% 6.20/6.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.20/6.47 inference(transitivity,[status(thm)],[3791, 1790])).
% 6.20/6.47 tff(3793,plain,
% 6.20/6.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 6.20/6.47 inference(quant_inst,[status(thm)],[])).
% 6.20/6.47 tff(3794,plain,
% 6.20/6.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 6.20/6.47 inference(modus_ponens,[status(thm)],[3793, 3792])).
% 6.20/6.47 tff(3795,plain,
% 6.20/6.47 ($false),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[3794, 391, 1759, 3789, 3563, 3779])).
% 6.20/6.47 tff(3796,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.47 tff(3797,plain,
% 6.20/6.47 (~r(s(s(z)), z)),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[3796, 3765, 411, 3751, 182, 326])).
% 6.20/6.47 tff(3798,plain,
% 6.20/6.47 (b(s(s(z)), z)),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[1211, 3797])).
% 6.20/6.47 tff(3799,plain,
% 6.20/6.47 (~b(s(z), s(s(z)))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[2447, 3798, 3710, 3753, 3751])).
% 6.20/6.47 tff(3800,plain,
% 6.20/6.47 (r(s(z), s(s(z)))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[1788, 3799])).
% 6.20/6.47 tff(3801,plain,
% 6.20/6.47 (~r(elem!1, s(s(z)))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[3389, 3700, 411, 182])).
% 6.20/6.47 tff(3802,plain,
% 6.20/6.47 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = elem!1)),
% 6.20/6.47 inference(monotonicity,[status(thm)],[5])).
% 6.20/6.47 tff(3803,plain,
% 6.20/6.47 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(z)))))),
% 6.20/6.47 inference(transitivity,[status(thm)],[3802, 764])).
% 6.20/6.47 tff(3804,plain,
% 6.20/6.47 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 6.20/6.47 inference(symmetry,[status(thm)],[3803])).
% 6.20/6.47 tff(3805,plain,
% 6.20/6.47 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 6.20/6.47 inference(monotonicity,[status(thm)],[3804])).
% 6.20/6.47 tff(3806,plain,
% 6.20/6.47 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 6.20/6.47 inference(modus_ponens,[status(thm)],[3696, 3805])).
% 6.20/6.47 tff(3807,plain,
% 6.20/6.47 (elem!1 = s(s(s(elem!1)))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[8, 5])).
% 6.20/6.47 tff(3808,plain,
% 6.20/6.47 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 6.20/6.47 inference(monotonicity,[status(thm)],[144])).
% 6.20/6.47 tff(3809,plain,
% 6.20/6.47 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.20/6.47 inference(symmetry,[status(thm)],[3808])).
% 6.20/6.47 tff(3810,plain,
% 6.20/6.47 (~(elem!1 = s(s(s(s(z)))))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[769, 2642])).
% 6.20/6.47 tff(3811,plain,
% 6.20/6.47 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.20/6.47 inference(monotonicity,[status(thm)],[125])).
% 6.20/6.47 tff(3812,plain,
% 6.20/6.47 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 6.20/6.47 inference(symmetry,[status(thm)],[3811])).
% 6.20/6.47 tff(3813,plain,
% 6.20/6.47 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 6.20/6.47 inference(monotonicity,[status(thm)],[3812])).
% 6.20/6.47 tff(3814,plain,
% 6.20/6.47 (b(s(s(s(elem!1))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 6.20/6.47 inference(monotonicity,[status(thm)],[144])).
% 6.20/6.47 tff(3815,plain,
% 6.20/6.47 (b(elem!1, s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 6.20/6.47 inference(symmetry,[status(thm)],[3814])).
% 6.20/6.47 tff(3816,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 6.20/6.47 tff(3817,plain,
% 6.20/6.47 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 6.20/6.47 inference(monotonicity,[status(thm)],[144])).
% 6.20/6.47 tff(3818,plain,
% 6.20/6.47 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 6.20/6.47 inference(transitivity,[status(thm)],[3817, 698])).
% 6.20/6.47 tff(3819,plain,
% 6.20/6.47 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 6.20/6.47 inference(monotonicity,[status(thm)],[3818])).
% 6.20/6.47 tff(3820,plain,
% 6.20/6.47 (~(elem!1 = s(s(z)))),
% 6.20/6.47 inference(modus_ponens,[status(thm)],[1397, 3819])).
% 6.20/6.47 tff(3821,plain,
% 6.20/6.47 (b(elem!1, s(s(z)))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[3394, 3820, 3816])).
% 6.20/6.47 tff(3822,plain,
% 6.20/6.47 (b(s(s(s(elem!1))), s(s(z)))),
% 6.20/6.47 inference(modus_ponens,[status(thm)],[3821, 3815])).
% 6.20/6.47 tff(3823,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 6.20/6.47 tff(3824,plain,
% 6.20/6.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 6.20/6.47 inference(rewrite,[status(thm)],[])).
% 6.20/6.47 tff(3825,plain,
% 6.20/6.47 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 6.20/6.47 inference(rewrite,[status(thm)],[])).
% 6.20/6.47 tff(3826,plain,
% 6.20/6.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 6.20/6.47 inference(monotonicity,[status(thm)],[3825])).
% 6.20/6.47 tff(3827,plain,
% 6.20/6.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 6.20/6.47 inference(transitivity,[status(thm)],[3826, 3824])).
% 6.20/6.47 tff(3828,plain,
% 6.20/6.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.20/6.47 inference(quant_inst,[status(thm)],[])).
% 6.20/6.47 tff(3829,plain,
% 6.20/6.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 6.20/6.47 inference(modus_ponens,[status(thm)],[3828, 3827])).
% 6.20/6.47 tff(3830,plain,
% 6.20/6.47 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 6.20/6.47 inference(unit_resolution,[status(thm)],[3829, 391, 3823, 90, 3563])).
% 6.20/6.47 tff(3831,plain,
% 6.20/6.47 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.20/6.48 inference(unit_resolution,[status(thm)],[3830, 3822])).
% 6.20/6.48 tff(3832,plain,
% 6.20/6.48 (~b(elem!1, s(s(s(s(z)))))),
% 6.20/6.48 inference(modus_ponens,[status(thm)],[3831, 3813])).
% 6.20/6.48 tff(3833,plain,
% 6.20/6.48 (r(elem!1, s(s(s(s(z)))))),
% 6.20/6.48 inference(unit_resolution,[status(thm)],[781, 3832, 3810])).
% 6.20/6.48 tff(3834,plain,
% 6.20/6.48 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.20/6.48 inference(modus_ponens,[status(thm)],[3833, 3809])).
% 6.20/6.48 tff(3835,plain,
% 6.20/6.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 6.20/6.48 inference(rewrite,[status(thm)],[])).
% 6.20/6.48 tff(3836,plain,
% 6.20/6.48 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 6.20/6.48 inference(rewrite,[status(thm)],[])).
% 6.20/6.48 tff(3837,plain,
% 6.20/6.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 6.20/6.48 inference(monotonicity,[status(thm)],[3836])).
% 6.20/6.48 tff(3838,plain,
% 6.20/6.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 6.20/6.48 inference(transitivity,[status(thm)],[3837, 3835])).
% 6.20/6.48 tff(3839,plain,
% 6.20/6.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.20/6.48 inference(quant_inst,[status(thm)],[])).
% 6.20/6.48 tff(3840,plain,
% 6.20/6.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 6.20/6.48 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 6.20/6.48 tff(3841,plain,
% 6.20/6.48 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 6.20/6.48 inference(unit_resolution,[status(thm)],[3840, 391, 3823, 90, 3563])).
% 6.20/6.48 tff(3842,plain,
% 6.20/6.48 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.20/6.48 inference(unit_resolution,[status(thm)],[3841, 3822])).
% 6.20/6.48 tff(3843,assumption,(~(s(s(s(s(z)))) = s(s(s(elem!1))))), introduced(assumption)).
% 6.20/6.48 tff(3844,plain,
% 6.20/6.48 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.20/6.48 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 3842])).
% 6.20/6.48 tff(3845,plain,
% 6.20/6.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.20/6.48 inference(rewrite,[status(thm)],[])).
% 6.20/6.48 tff(3846,plain,
% 6.20/6.48 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.20/6.48 inference(rewrite,[status(thm)],[])).
% 6.20/6.48 tff(3847,plain,
% 6.20/6.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 6.20/6.48 inference(monotonicity,[status(thm)],[3846])).
% 6.20/6.48 tff(3848,plain,
% 6.20/6.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.20/6.48 inference(transitivity,[status(thm)],[3847, 3845])).
% 6.20/6.48 tff(3849,plain,
% 6.20/6.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 6.20/6.48 inference(quant_inst,[status(thm)],[])).
% 6.20/6.48 tff(3850,plain,
% 6.20/6.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 6.20/6.48 inference(modus_ponens,[status(thm)],[3849, 3848])).
% 6.20/6.48 tff(3851,plain,
% 6.20/6.48 ($false),
% 6.20/6.48 inference(unit_resolution,[status(thm)],[3850, 194, 184, 719, 3844, 3834])).
% 6.20/6.48 tff(3852,plain,((~(elem!1 = s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | r(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.48 tff(3853,plain,
% 6.20/6.48 (~b(s(s(z)), s(s(s(s(z)))))),
% 6.20/6.48 inference(unit_resolution,[status(thm)],[3852, 3765, 184, 3807, 3806, 3801, 3731, 3733])).
% 6.20/6.48 tff(3854,plain,
% 6.20/6.48 (r(s(s(z)), s(s(s(s(z)))))),
% 6.20/6.48 inference(unit_resolution,[status(thm)],[3652, 3853])).
% 6.20/6.48 tff(3855,plain,
% 6.20/6.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.20/6.48 inference(rewrite,[status(thm)],[])).
% 6.20/6.48 tff(3856,plain,
% 6.20/6.48 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.20/6.48 inference(rewrite,[status(thm)],[])).
% 6.20/6.48 tff(3857,plain,
% 6.20/6.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3856])).
% 6.20/6.49 tff(3858,plain,
% 6.20/6.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.20/6.49 inference(transitivity,[status(thm)],[3857, 3855])).
% 6.20/6.49 tff(3859,plain,
% 6.20/6.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 6.20/6.49 inference(quant_inst,[status(thm)],[])).
% 6.20/6.49 tff(3860,plain,
% 6.20/6.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 6.20/6.49 tff(3861,plain,
% 6.20/6.49 ($false),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3860, 194, 3854, 3749, 3800, 3763])).
% 6.20/6.49 tff(3862,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.49 tff(3863,plain,
% 6.20/6.49 (~(s(s(s(elem!1))) = elem!1)),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3862, 3680, 59, 181, 325, 3436, 3400, 1371])).
% 6.20/6.49 tff(3864,plain,
% 6.20/6.49 (b(s(s(s(elem!1))), elem!1)),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[230, 3863, 3690])).
% 6.20/6.49 tff(3865,plain,
% 6.20/6.49 (~r(s(s(s(elem!1))), s(z))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3499, 3434, 59, 181])).
% 6.20/6.49 tff(3866,plain,
% 6.20/6.49 (b(s(s(s(elem!1))), s(z))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[223, 3865])).
% 6.20/6.49 tff(3867,plain,
% 6.20/6.49 (~r(s(s(s(elem!1))), z)),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[1867, 3434, 59, 181])).
% 6.20/6.49 tff(3868,plain,
% 6.20/6.49 (b(s(s(s(elem!1))), z)),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[377, 3867])).
% 6.20/6.49 tff(3869,plain,
% 6.20/6.49 (~r(s(s(elem!1)), s(z))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[2868, 3689, 3680, 3866, 181, 3864, 325, 3434, 1371, 3436, 59])).
% 6.20/6.49 tff(3870,plain,
% 6.20/6.49 (b(s(s(elem!1)), s(z))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[362, 3869])).
% 6.20/6.49 tff(3871,plain,
% 6.20/6.49 (s(z) = elem!1),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3365, 3870, 181, 325, 3868, 1371, 3436, 3680, 3866, 3864, 59, 3434, 3689])).
% 6.20/6.49 tff(3872,plain,
% 6.20/6.49 (s(s(z)) = s(elem!1)),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3871])).
% 6.20/6.49 tff(3873,plain,
% 6.20/6.49 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3872])).
% 6.20/6.49 tff(3874,plain,
% 6.20/6.49 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3873])).
% 6.20/6.49 tff(3875,plain,
% 6.20/6.49 (~(z = elem!1)),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[97, 3689])).
% 6.20/6.49 tff(3876,plain,
% 6.20/6.49 (~(s(z) = s(elem!1))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[117, 3875])).
% 6.20/6.49 tff(3877,plain,
% 6.20/6.49 (~(s(s(elem!1)) = s(s(z)))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[1962, 3876])).
% 6.20/6.49 tff(3878,plain,
% 6.20/6.49 (~(s(s(elem!1)) = s(elem!1))),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[3877, 3874])).
% 6.20/6.49 tff(3879,plain,
% 6.20/6.49 (s(s(s(z))) = s(s(elem!1))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3872])).
% 6.20/6.49 tff(3880,plain,
% 6.20/6.49 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3879])).
% 6.20/6.49 tff(3881,plain,
% 6.20/6.49 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 6.20/6.49 inference(symmetry,[status(thm)],[3880])).
% 6.20/6.49 tff(3882,plain,
% 6.20/6.49 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3881])).
% 6.20/6.49 tff(3883,plain,
% 6.20/6.49 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 6.20/6.49 inference(symmetry,[status(thm)],[3882])).
% 6.20/6.49 tff(3884,plain,
% 6.20/6.49 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3872])).
% 6.20/6.49 tff(3885,plain,
% 6.20/6.49 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 6.20/6.49 inference(transitivity,[status(thm)],[3884, 3883])).
% 6.20/6.49 tff(3886,plain,
% 6.20/6.49 (~r(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[641, 3434, 59, 181])).
% 6.20/6.49 tff(3887,plain,
% 6.20/6.49 (~r(s(elem!1), z)),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[2594, 3876, 3866, 3680, 3434, 3886, 181])).
% 6.20/6.49 tff(3888,plain,
% 6.20/6.49 (b(s(elem!1), z)),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[549, 3887])).
% 6.20/6.49 tff(3889,plain,
% 6.20/6.49 (r(z, s(elem!1))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[2614, 3888, 3868, 3886, 59])).
% 6.20/6.49 tff(3890,plain,
% 6.20/6.49 (r(s(z), z) <=> r(elem!1, z)),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3871])).
% 6.20/6.49 tff(3891,plain,
% 6.20/6.49 (r(elem!1, z)),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[181, 3890])).
% 6.20/6.49 tff(3892,plain,
% 6.20/6.49 (~(s(elem!1) = elem!1)),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[158, 3863])).
% 6.20/6.49 tff(3893,plain,
% 6.20/6.49 (~(elem!1 = s(elem!1))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[166, 3892])).
% 6.20/6.49 tff(3894,plain,
% 6.20/6.49 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3871])).
% 6.20/6.49 tff(3895,plain,
% 6.20/6.49 (b(s(s(elem!1)), elem!1)),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[3870, 3894])).
% 6.20/6.49 tff(3896,plain,
% 6.20/6.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 6.20/6.49 inference(rewrite,[status(thm)],[])).
% 6.20/6.49 tff(3897,plain,
% 6.20/6.49 (((~b(s(elem!1), z)) | (~b(elem!1, 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)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 6.20/6.49 inference(rewrite,[status(thm)],[])).
% 6.20/6.49 tff(3898,plain,
% 6.20/6.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1))))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3897])).
% 6.20/6.49 tff(3899,plain,
% 6.20/6.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 6.20/6.49 inference(transitivity,[status(thm)],[3898, 3896])).
% 6.20/6.49 tff(3900,plain,
% 6.20/6.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, 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))))))),
% 6.20/6.49 inference(quant_inst,[status(thm)],[])).
% 6.20/6.49 tff(3901,plain,
% 6.20/6.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1))),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[3900, 3899])).
% 6.20/6.49 tff(3902,plain,
% 6.20/6.49 ($false),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3901, 391, 900, 973, 591, 802, 328])).
% 6.20/6.49 tff(3903,plain,((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.49 tff(3904,plain,
% 6.20/6.49 (~b(elem!1, s(elem!1))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3903, 3864, 3895, 3888, 3400])).
% 6.20/6.49 tff(3905,plain,
% 6.20/6.49 (r(elem!1, s(elem!1))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[443, 3904, 3893])).
% 6.20/6.49 tff(3906,plain,
% 6.20/6.49 (~r(s(elem!1), s(s(s(elem!1))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3626, 3905, 3891, 3889])).
% 6.20/6.49 tff(3907,plain,
% 6.20/6.49 (~r(s(s(z)), s(s(s(s(z)))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3614, 3906, 3871])).
% 6.20/6.49 tff(3908,plain,
% 6.20/6.49 (b(s(s(z)), s(s(s(s(z)))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3652, 3907])).
% 6.20/6.49 tff(3909,plain,
% 6.20/6.49 (b(s(elem!1), s(s(s(elem!1))))),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[3908, 3885])).
% 6.20/6.49 tff(3910,plain,
% 6.20/6.49 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3872])).
% 6.20/6.49 tff(3911,plain,
% 6.20/6.49 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 6.20/6.49 inference(transitivity,[status(thm)],[3910, 582])).
% 6.20/6.49 tff(3912,plain,
% 6.20/6.49 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3911])).
% 6.20/6.49 tff(3913,plain,
% 6.20/6.49 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[1397, 3912])).
% 6.20/6.49 tff(3914,plain,
% 6.20/6.49 (b(s(s(s(elem!1))), s(elem!1))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[588, 3913, 3886])).
% 6.20/6.49 tff(3915,plain,
% 6.20/6.49 (~b(s(s(elem!1)), s(elem!1))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3661, 391, 3914, 3888, 3400, 3909])).
% 6.20/6.49 tff(3916,plain,
% 6.20/6.49 (r(s(s(elem!1)), s(elem!1))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[1135, 3915, 3878])).
% 6.20/6.49 tff(3917,plain,
% 6.20/6.49 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3871])).
% 6.20/6.49 tff(3918,plain,
% 6.20/6.49 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 6.20/6.49 inference(transitivity,[status(thm)],[3917, 2206])).
% 6.20/6.49 tff(3919,plain,
% 6.20/6.49 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3918])).
% 6.20/6.49 tff(3920,plain,
% 6.20/6.49 (~(elem!1 = s(s(elem!1)))),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[357, 3919])).
% 6.20/6.49 tff(3921,plain,
% 6.20/6.49 (~b(elem!1, s(s(elem!1)))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[1467, 3895, 1371, 3864])).
% 6.20/6.49 tff(3922,plain,
% 6.20/6.49 (r(elem!1, s(s(elem!1)))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[1307, 3921, 3920])).
% 6.20/6.49 tff(3923,plain,
% 6.20/6.49 ($false),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3677, 194, 3891, 325, 3922, 3916])).
% 6.20/6.49 tff(3924,plain,(b(z, s(s(elem!1))) | b(s(z), z) | b(z, s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.20/6.49 tff(3925,plain,
% 6.20/6.49 (b(z, s(s(elem!1)))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3924, 288, 10, 91])).
% 6.20/6.49 tff(3926,plain,
% 6.20/6.49 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[314, 288])).
% 6.20/6.49 tff(3927,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 6.20/6.49 tff(3928,plain,
% 6.20/6.49 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 6.20/6.49 inference(commutativity,[status(thm)],[])).
% 6.20/6.49 tff(3929,plain,
% 6.20/6.49 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 6.20/6.49 inference(symmetry,[status(thm)],[3928])).
% 6.20/6.49 tff(3930,plain,
% 6.20/6.49 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3929])).
% 6.20/6.49 tff(3931,plain,
% 6.20/6.49 (~r(s(s(s(elem!1))), s(z))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[200, 194, 174, 184, 181])).
% 6.20/6.49 tff(3932,plain,
% 6.20/6.49 (b(s(s(s(elem!1))), s(z))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[223, 3931])).
% 6.20/6.49 tff(3933,plain,
% 6.20/6.49 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 6.20/6.49 inference(monotonicity,[status(thm)],[812])).
% 6.20/6.49 tff(3934,plain,
% 6.20/6.49 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 6.20/6.49 inference(symmetry,[status(thm)],[3933])).
% 6.20/6.49 tff(3935,plain,
% 6.20/6.49 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), s(z)))),
% 6.20/6.49 inference(monotonicity,[status(thm)],[3934])).
% 6.20/6.49 tff(3936,plain,
% 6.20/6.49 (~b(s(s(s(elem!1))), s(z))),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[168, 3935])).
% 6.20/6.49 tff(3937,plain,
% 6.20/6.49 ($false),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[1526, 3936])).
% 6.20/6.49 tff(3938,plain,((~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.20/6.49 tff(3939,plain,
% 6.20/6.49 (~(s(z) = elem!1)),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3938, 168, 3932])).
% 6.20/6.49 tff(3940,plain,
% 6.20/6.49 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[2849, 3939])).
% 6.20/6.49 tff(3941,plain,
% 6.20/6.49 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[3940, 3930])).
% 6.20/6.49 tff(3942,plain,
% 6.20/6.49 (~r(s(s(s(elem!1))), s(z))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[200, 194, 174, 184, 182])).
% 6.20/6.49 tff(3943,plain,
% 6.20/6.49 (b(s(s(s(elem!1))), s(z))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[223, 3942])).
% 6.20/6.49 tff(3944,plain,
% 6.20/6.49 (~(s(z) = elem!1)),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3938, 168, 3943])).
% 6.20/6.49 tff(3945,plain,
% 6.20/6.49 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3159, 194, 340, 182, 723])).
% 6.20/6.49 tff(3946,plain,
% 6.20/6.49 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3165, 194, 340, 182, 723])).
% 6.20/6.49 tff(3947,plain,
% 6.20/6.49 (~(elem!1 = s(z))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[172, 3944])).
% 6.20/6.49 tff(3948,plain,
% 6.20/6.49 (~r(s(z), s(s(s(elem!1))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[1867, 174, 184, 182])).
% 6.20/6.49 tff(3949,plain,
% 6.20/6.49 (b(s(z), s(s(s(elem!1))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[247, 3948])).
% 6.20/6.49 tff(3950,assumption,(~r(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 6.20/6.49 tff(3951,plain,
% 6.20/6.49 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[2849, 3944])).
% 6.20/6.49 tff(3952,plain,
% 6.20/6.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.20/6.49 inference(rewrite,[status(thm)],[])).
% 6.20/6.49 tff(3953,plain,
% 6.20/6.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.20/6.49 inference(quant_inst,[status(thm)],[])).
% 6.20/6.49 tff(3954,plain,
% 6.20/6.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.20/6.49 inference(modus_ponens,[status(thm)],[3953, 3952])).
% 6.20/6.49 tff(3955,plain,
% 6.20/6.49 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[3954, 194, 174, 184, 2053])).
% 6.20/6.49 tff(3956,plain,
% 6.20/6.49 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.20/6.49 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 3955])).
% 6.20/6.49 tff(3957,plain,
% 6.20/6.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.20/6.49 inference(rewrite,[status(thm)],[])).
% 6.29/6.50 tff(3958,plain,
% 6.29/6.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.29/6.50 inference(quant_inst,[status(thm)],[])).
% 6.29/6.50 tff(3959,plain,
% 6.29/6.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 6.29/6.50 inference(modus_ponens,[status(thm)],[3958, 3957])).
% 6.29/6.50 tff(3960,plain,
% 6.29/6.50 (~r(s(s(s(s(z)))), s(z))),
% 6.29/6.50 inference(unit_resolution,[status(thm)],[3959, 194, 184, 182, 2053])).
% 6.29/6.50 tff(3961,plain,
% 6.29/6.50 (b(s(s(s(s(z)))), s(z))),
% 6.29/6.50 inference(unit_resolution,[status(thm)],[749, 3960])).
% 6.29/6.50 tff(3962,plain,
% 6.29/6.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.29/6.50 inference(rewrite,[status(thm)],[])).
% 6.29/6.50 tff(3963,plain,
% 6.29/6.50 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.29/6.50 inference(rewrite,[status(thm)],[])).
% 6.29/6.50 tff(3964,plain,
% 6.29/6.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 6.29/6.50 inference(monotonicity,[status(thm)],[3963])).
% 6.29/6.50 tff(3965,plain,
% 6.29/6.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.29/6.50 inference(transitivity,[status(thm)],[3964, 3962])).
% 6.29/6.50 tff(3966,plain,
% 6.29/6.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.29/6.50 inference(quant_inst,[status(thm)],[])).
% 6.29/6.50 tff(3967,plain,
% 6.29/6.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.29/6.50 inference(modus_ponens,[status(thm)],[3966, 3965])).
% 6.29/6.50 tff(3968,plain,
% 6.29/6.50 ($false),
% 6.29/6.50 inference(unit_resolution,[status(thm)],[3967, 391, 3949, 3943, 3961, 3956])).
% 6.29/6.50 tff(3969,plain,((~r(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.50 tff(3970,plain,
% 6.29/6.50 (~r(s(s(s(s(z)))), z)),
% 6.29/6.50 inference(unit_resolution,[status(thm)],[3969, 3951, 184, 182, 174])).
% 6.29/6.50 tff(3971,plain,
% 6.29/6.50 (b(s(s(s(s(z)))), z)),
% 6.29/6.50 inference(unit_resolution,[status(thm)],[87, 3970])).
% 6.29/6.50 tff(3972,plain,
% 6.29/6.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 6.29/6.50 inference(rewrite,[status(thm)],[])).
% 6.29/6.50 tff(3973,plain,
% 6.29/6.50 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 6.29/6.50 inference(rewrite,[status(thm)],[])).
% 6.29/6.50 tff(3974,plain,
% 6.29/6.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 6.29/6.50 inference(monotonicity,[status(thm)],[3973])).
% 6.29/6.50 tff(3975,plain,
% 6.29/6.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 6.29/6.50 inference(transitivity,[status(thm)],[3974, 3972])).
% 6.29/6.50 tff(3976,plain,
% 6.29/6.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 6.29/6.50 inference(quant_inst,[status(thm)],[])).
% 6.29/6.50 tff(3977,plain,
% 6.29/6.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 6.29/6.50 inference(modus_ponens,[status(thm)],[3976, 3975])).
% 6.29/6.50 tff(3978,plain,
% 6.29/6.50 ($false),
% 6.29/6.50 inference(unit_resolution,[status(thm)],[3977, 391, 133, 973, 3927, 1294])).
% 6.29/6.50 tff(3979,plain,((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.50 tff(3980,plain,
% 6.29/6.50 (~b(elem!1, s(s(elem!1)))),
% 6.29/6.50 inference(unit_resolution,[status(thm)],[3979, 973, 3927, 133])).
% 6.29/6.50 tff(3981,plain,
% 6.29/6.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.29/6.50 inference(rewrite,[status(thm)],[])).
% 6.29/6.50 tff(3982,plain,
% 6.29/6.50 (((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.29/6.50 inference(rewrite,[status(thm)],[])).
% 6.29/6.50 tff(3983,plain,
% 6.29/6.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))))),
% 6.29/6.51 inference(monotonicity,[status(thm)],[3982])).
% 6.29/6.51 tff(3984,plain,
% 6.29/6.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.29/6.51 inference(transitivity,[status(thm)],[3983, 3981])).
% 6.29/6.51 tff(3985,plain,
% 6.29/6.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.29/6.51 inference(quant_inst,[status(thm)],[])).
% 6.29/6.51 tff(3986,plain,
% 6.29/6.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))),
% 6.29/6.51 inference(modus_ponens,[status(thm)],[3985, 3984])).
% 6.29/6.51 tff(3987,plain,
% 6.29/6.51 (~r(elem!1, s(s(elem!1)))),
% 6.29/6.51 inference(unit_resolution,[status(thm)],[3986, 194, 340, 847, 182])).
% 6.29/6.51 tff(3988,plain,
% 6.29/6.51 (elem!1 = s(s(elem!1))),
% 6.29/6.51 inference(unit_resolution,[status(thm)],[1307, 3987, 3980])).
% 6.29/6.51 tff(3989,plain,
% 6.29/6.51 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 6.29/6.51 inference(monotonicity,[status(thm)],[3988])).
% 6.29/6.51 tff(3990,plain,
% 6.29/6.51 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(elem!1)), elem!1)),
% 6.29/6.51 inference(symmetry,[status(thm)],[3989])).
% 6.29/6.51 tff(3991,plain,
% 6.29/6.51 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(elem!1)), elem!1))),
% 6.29/6.51 inference(monotonicity,[status(thm)],[3990])).
% 6.29/6.51 tff(3992,plain,
% 6.29/6.51 ((~![X: $i] : (~b(X, X))) | (~b(s(s(elem!1)), s(s(elem!1))))),
% 6.29/6.51 inference(quant_inst,[status(thm)],[])).
% 6.29/6.51 tff(3993,plain,
% 6.29/6.51 (~b(s(s(elem!1)), s(s(elem!1)))),
% 6.29/6.51 inference(unit_resolution,[status(thm)],[3992, 461])).
% 6.29/6.51 tff(3994,plain,
% 6.29/6.51 (~b(s(s(elem!1)), elem!1)),
% 6.29/6.51 inference(modus_ponens,[status(thm)],[3993, 3991])).
% 6.29/6.51 tff(3995,plain,
% 6.29/6.51 ($false),
% 6.29/6.51 inference(unit_resolution,[status(thm)],[973, 3994])).
% 6.29/6.51 tff(3996,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.51 tff(3997,plain,
% 6.29/6.51 (~b(s(s(elem!1)), elem!1)),
% 6.29/6.51 inference(unit_resolution,[status(thm)],[3996, 847, 340, 182, 3927, 133])).
% 6.29/6.51 tff(3998,plain,
% 6.29/6.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 6.29/6.51 inference(rewrite,[status(thm)],[])).
% 6.29/6.51 tff(3999,plain,
% 6.29/6.51 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 6.29/6.51 inference(rewrite,[status(thm)],[])).
% 6.29/6.51 tff(4000,plain,
% 6.29/6.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 6.29/6.51 inference(monotonicity,[status(thm)],[3999])).
% 6.29/6.51 tff(4001,plain,
% 6.29/6.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 6.29/6.51 inference(transitivity,[status(thm)],[4000, 3998])).
% 6.29/6.51 tff(4002,plain,
% 6.29/6.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 6.29/6.51 inference(quant_inst,[status(thm)],[])).
% 6.29/6.51 tff(4003,plain,
% 6.29/6.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))),
% 6.29/6.51 inference(modus_ponens,[status(thm)],[4002, 4001])).
% 6.29/6.51 tff(4004,plain,
% 6.29/6.51 (~r(s(s(elem!1)), elem!1)),
% 6.29/6.51 inference(unit_resolution,[status(thm)],[4003, 194, 340, 847, 182])).
% 6.29/6.51 tff(4005,plain,
% 6.29/6.51 (s(s(elem!1)) = elem!1),
% 6.29/6.51 inference(unit_resolution,[status(thm)],[872, 4004, 3997])).
% 6.29/6.51 tff(4006,plain,
% 6.29/6.51 (s(s(s(elem!1))) = s(elem!1)),
% 6.29/6.51 inference(unit_resolution,[status(thm)],[451, 4005])).
% 6.29/6.51 tff(4007,plain,
% 6.29/6.51 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 6.29/6.51 inference(monotonicity,[status(thm)],[4006])).
% 6.29/6.51 tff(4008,plain,
% 6.29/6.51 (s(s(s(s(elem!1)))) = elem!1),
% 6.29/6.51 inference(transitivity,[status(thm)],[4007, 4005])).
% 6.29/6.51 tff(4009,plain,
% 6.29/6.51 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), elem!1)),
% 6.29/6.51 inference(monotonicity,[status(thm)],[4008])).
% 6.29/6.51 tff(4010,plain,
% 6.29/6.51 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 6.29/6.51 inference(symmetry,[status(thm)],[4009])).
% 6.29/6.51 tff(4011,plain,
% 6.29/6.51 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 6.29/6.51 inference(monotonicity,[status(thm)],[4010])).
% 6.29/6.51 tff(4012,plain,
% 6.29/6.51 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 6.29/6.51 inference(monotonicity,[status(thm)],[4006])).
% 6.29/6.51 tff(4013,plain,
% 6.29/6.51 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 6.29/6.51 inference(monotonicity,[status(thm)],[4012])).
% 6.29/6.51 tff(4014,plain,
% 6.29/6.51 (~b(s(elem!1), elem!1)),
% 6.29/6.51 inference(modus_ponens,[status(thm)],[168, 4013])).
% 6.29/6.51 tff(4015,plain,
% 6.29/6.51 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 6.29/6.51 inference(modus_ponens,[status(thm)],[4014, 4011])).
% 6.29/6.51 tff(4016,plain,
% 6.29/6.51 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 6.29/6.51 inference(monotonicity,[status(thm)],[4006])).
% 6.29/6.51 tff(4017,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 6.29/6.51 tff(4018,plain,
% 6.29/6.51 (~(s(z) = elem!1)),
% 6.29/6.51 inference(unit_resolution,[status(thm)],[3938, 168, 1526])).
% 6.29/6.51 tff(4019,plain,
% 6.29/6.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.29/6.51 inference(rewrite,[status(thm)],[])).
% 6.29/6.51 tff(4020,plain,
% 6.29/6.51 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.29/6.51 inference(rewrite,[status(thm)],[])).
% 6.29/6.51 tff(4021,plain,
% 6.29/6.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.29/6.51 inference(monotonicity,[status(thm)],[4020])).
% 6.29/6.51 tff(4022,plain,
% 6.29/6.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.29/6.52 inference(transitivity,[status(thm)],[4021, 4019])).
% 6.29/6.52 tff(4023,plain,
% 6.29/6.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 6.29/6.52 inference(quant_inst,[status(thm)],[])).
% 6.29/6.52 tff(4024,plain,
% 6.29/6.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.29/6.52 inference(modus_ponens,[status(thm)],[4023, 4022])).
% 6.29/6.52 tff(4025,plain,
% 6.29/6.52 ($false),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[4024, 391, 448, 644, 379, 1526])).
% 6.29/6.52 tff(4026,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.52 tff(4027,plain,
% 6.29/6.52 (~b(elem!1, s(s(s(elem!1))))),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[4026, 644, 1526, 379])).
% 6.29/6.52 tff(4028,assumption,(~b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 6.29/6.52 tff(4029,plain,
% 6.29/6.52 (~(elem!1 = s(s(s(elem!1))))),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[129, 127])).
% 6.29/6.52 tff(4030,plain,
% 6.29/6.52 (r(elem!1, s(s(s(elem!1))))),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[424, 4029, 4028])).
% 6.29/6.52 tff(4031,plain,
% 6.29/6.52 (r(s(s(s(elem!1))), elem!1)),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[230, 127, 168])).
% 6.29/6.52 tff(4032,plain,
% 6.29/6.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 6.29/6.52 inference(rewrite,[status(thm)],[])).
% 6.29/6.52 tff(4033,plain,
% 6.29/6.52 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 6.29/6.52 inference(rewrite,[status(thm)],[])).
% 6.29/6.52 tff(4034,plain,
% 6.29/6.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 6.29/6.52 inference(monotonicity,[status(thm)],[4033])).
% 6.29/6.52 tff(4035,plain,
% 6.29/6.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 6.29/6.52 inference(transitivity,[status(thm)],[4034, 4032])).
% 6.29/6.52 tff(4036,plain,
% 6.29/6.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.29/6.52 inference(quant_inst,[status(thm)],[])).
% 6.29/6.52 tff(4037,plain,
% 6.29/6.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 6.29/6.52 inference(modus_ponens,[status(thm)],[4036, 4035])).
% 6.29/6.52 tff(4038,plain,
% 6.29/6.52 ($false),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[4037, 194, 4031, 364, 4030, 327])).
% 6.29/6.52 tff(4039,plain,((s(s(s(elem!1))) = elem!1) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.29/6.52 tff(4040,plain,
% 6.29/6.52 (~r(s(s(elem!1)), elem!1)),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[4039, 4027, 9, 168, 327])).
% 6.29/6.52 tff(4041,plain,
% 6.29/6.52 (s(s(elem!1)) = elem!1),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[872, 4040, 4017])).
% 6.29/6.52 tff(4042,plain,
% 6.29/6.52 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 6.29/6.52 inference(monotonicity,[status(thm)],[4041])).
% 6.29/6.52 tff(4043,plain,
% 6.29/6.52 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.29/6.52 inference(symmetry,[status(thm)],[4042])).
% 6.29/6.52 tff(4044,plain,
% 6.29/6.52 (r(elem!1, s(s(s(elem!1))))),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[424, 4027, 1])).
% 6.29/6.52 tff(4045,plain,
% 6.29/6.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 6.29/6.52 inference(rewrite,[status(thm)],[])).
% 6.29/6.52 tff(4046,plain,
% 6.29/6.52 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 6.29/6.52 inference(rewrite,[status(thm)],[])).
% 6.29/6.52 tff(4047,plain,
% 6.29/6.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 6.29/6.52 inference(monotonicity,[status(thm)],[4046])).
% 6.29/6.52 tff(4048,plain,
% 6.29/6.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 6.29/6.52 inference(transitivity,[status(thm)],[4047, 4045])).
% 6.29/6.52 tff(4049,plain,
% 6.29/6.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 6.29/6.52 inference(quant_inst,[status(thm)],[])).
% 6.29/6.52 tff(4050,plain,
% 6.29/6.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 6.29/6.52 inference(modus_ponens,[status(thm)],[4049, 4048])).
% 6.29/6.52 tff(4051,plain,
% 6.29/6.52 ($false),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[4050, 194, 530, 184, 410, 1538])).
% 6.29/6.52 tff(4052,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.52 tff(4053,plain,
% 6.29/6.52 (~r(elem!1, z)),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[4052, 4044, 184, 1538])).
% 6.29/6.52 tff(4054,plain,
% 6.29/6.52 (b(elem!1, z)),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[526, 4053, 2])).
% 6.29/6.52 tff(4055,plain,
% 6.29/6.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.29/6.52 inference(rewrite,[status(thm)],[])).
% 6.29/6.52 tff(4056,plain,
% 6.29/6.52 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.29/6.52 inference(rewrite,[status(thm)],[])).
% 6.29/6.52 tff(4057,plain,
% 6.29/6.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 6.29/6.52 inference(monotonicity,[status(thm)],[4056])).
% 6.29/6.52 tff(4058,plain,
% 6.29/6.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.29/6.52 inference(transitivity,[status(thm)],[4057, 4055])).
% 6.29/6.52 tff(4059,plain,
% 6.29/6.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.29/6.52 inference(quant_inst,[status(thm)],[])).
% 6.29/6.52 tff(4060,plain,
% 6.29/6.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 6.29/6.52 inference(modus_ponens,[status(thm)],[4059, 4058])).
% 6.29/6.52 tff(4061,plain,
% 6.29/6.52 ($false),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[4060, 391, 133, 665, 644, 1652, 1234])).
% 6.29/6.52 tff(4062,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.52 tff(4063,plain,
% 6.29/6.52 (~b(s(s(s(s(z)))), elem!1)),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[4062, 4054, 133, 1234, 644])).
% 6.29/6.52 tff(4064,plain,
% 6.29/6.52 (s(s(s(elem!1))) = s(elem!1)),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[451, 4041])).
% 6.29/6.52 tff(4065,plain,
% 6.29/6.52 (~(s(s(s(s(z)))) = elem!1)),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[717, 4064])).
% 6.29/6.52 tff(4066,plain,
% 6.29/6.52 (r(s(s(s(s(z)))), elem!1)),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[762, 4065, 4063])).
% 6.29/6.52 tff(4067,plain,
% 6.29/6.52 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.29/6.52 inference(modus_ponens,[status(thm)],[4066, 4043])).
% 6.29/6.52 tff(4068,plain,
% 6.29/6.52 ($false),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[3950, 4067])).
% 6.29/6.52 tff(4069,plain,((~b(s(z), elem!1)) | r(s(s(s(s(z)))), s(s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = z) | b(s(s(elem!1)), elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.52 tff(4070,plain,
% 6.29/6.52 (~b(s(z), elem!1)),
% 6.29/6.52 inference(unit_resolution,[status(thm)],[4069, 4017, 133, 1234, 2, 3950, 184, 1538, 168, 327, 1, 1526, 379])).
% 6.29/6.52 tff(4071,plain,
% 6.29/6.52 (r(s(z), elem!1)),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[632, 4070, 4018])).
% 6.29/6.53 tff(4072,plain,
% 6.29/6.53 (~r(s(s(elem!1)), elem!1)),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[1899, 4071, 340, 847])).
% 6.29/6.53 tff(4073,plain,
% 6.29/6.53 (s(s(elem!1)) = elem!1),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[872, 4072, 4017])).
% 6.29/6.53 tff(4074,plain,
% 6.29/6.53 (s(s(s(elem!1))) = s(elem!1)),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[451, 4073])).
% 6.29/6.53 tff(4075,plain,
% 6.29/6.53 (~(s(s(s(s(z)))) = elem!1)),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[717, 4074])).
% 6.29/6.53 tff(4076,plain,
% 6.29/6.53 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 6.29/6.53 inference(monotonicity,[status(thm)],[4073])).
% 6.29/6.53 tff(4077,plain,
% 6.29/6.53 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 6.29/6.53 inference(monotonicity,[status(thm)],[4076])).
% 6.29/6.53 tff(4078,plain,
% 6.29/6.53 (~r(s(s(s(s(z)))), elem!1)),
% 6.29/6.53 inference(modus_ponens,[status(thm)],[3950, 4077])).
% 6.29/6.53 tff(4079,plain,
% 6.29/6.53 (~r(elem!1, z)),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[1489, 4071, 184, 182])).
% 6.29/6.53 tff(4080,plain,
% 6.29/6.53 (b(elem!1, z)),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[526, 4079, 2])).
% 6.29/6.53 tff(4081,plain,
% 6.29/6.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.29/6.53 inference(rewrite,[status(thm)],[])).
% 6.29/6.53 tff(4082,plain,
% 6.29/6.53 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.29/6.53 inference(rewrite,[status(thm)],[])).
% 6.29/6.53 tff(4083,plain,
% 6.29/6.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 6.29/6.53 inference(monotonicity,[status(thm)],[4082])).
% 6.29/6.53 tff(4084,plain,
% 6.29/6.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.29/6.53 inference(transitivity,[status(thm)],[4083, 4081])).
% 6.29/6.53 tff(4085,plain,
% 6.29/6.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.29/6.53 inference(quant_inst,[status(thm)],[])).
% 6.29/6.53 tff(4086,plain,
% 6.29/6.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 6.29/6.53 inference(modus_ponens,[status(thm)],[4085, 4084])).
% 6.29/6.53 tff(4087,plain,
% 6.29/6.53 (~b(s(s(s(s(z)))), elem!1)),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[4086, 391, 133, 4080, 90])).
% 6.29/6.53 tff(4088,plain,
% 6.29/6.53 ($false),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[762, 4087, 4078, 4075])).
% 6.29/6.53 tff(4089,plain,(b(s(s(elem!1)), elem!1) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | r(s(s(s(s(z)))), s(s(elem!1))) | (elem!1 = z) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.53 tff(4090,plain,
% 6.29/6.53 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[4089, 3997, 90, 3950, 2, 340, 847, 184, 182, 1234, 133, 168, 327, 1, 1526, 379])).
% 6.29/6.53 tff(4091,plain,
% 6.29/6.53 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[1164, 4090, 1373])).
% 6.29/6.53 tff(4092,plain,
% 6.29/6.53 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 6.29/6.53 inference(modus_ponens,[status(thm)],[4091, 4016])).
% 6.29/6.53 tff(4093,plain,
% 6.29/6.53 ($false),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[4092, 4015])).
% 6.29/6.53 tff(4094,plain,((~r(elem!1, s(z))) | b(s(s(s(elem!1))), elem!1) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | r(s(s(s(s(z)))), s(s(elem!1))) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.53 tff(4095,plain,
% 6.29/6.53 (~r(elem!1, s(z))),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[4094, 1234, 340, 182, 1373, 3971, 3950, 2, 184, 168, 133, 327, 1, 3943, 3949, 3927])).
% 6.29/6.53 tff(4096,plain,
% 6.29/6.53 (b(elem!1, s(z))),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[837, 4095, 3947])).
% 6.29/6.53 tff(4097,plain,
% 6.29/6.53 (r(s(s(s(elem!1))), elem!1)),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[230, 168, 9])).
% 6.29/6.53 tff(4098,assumption,(~r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 6.29/6.53 tff(4099,plain,
% 6.29/6.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 6.29/6.53 inference(rewrite,[status(thm)],[])).
% 6.29/6.53 tff(4100,plain,
% 6.29/6.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 6.29/6.53 inference(quant_inst,[status(thm)],[])).
% 6.29/6.53 tff(4101,plain,
% 6.29/6.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 6.29/6.53 inference(modus_ponens,[status(thm)],[4100, 4099])).
% 6.29/6.53 tff(4102,plain,
% 6.29/6.53 ($false),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[4101, 194, 340, 722, 182, 2616])).
% 6.29/6.53 tff(4103,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.53 tff(4104,plain,
% 6.29/6.53 (~r(s(s(elem!1)), z)),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[4103, 722, 182, 340])).
% 6.29/6.53 tff(4105,plain,
% 6.29/6.53 (b(s(s(elem!1)), z)),
% 6.29/6.53 inference(unit_resolution,[status(thm)],[2629, 4104])).
% 6.29/6.53 tff(4106,plain,
% 6.29/6.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))))),
% 6.29/6.53 inference(rewrite,[status(thm)],[])).
% 6.29/6.53 tff(4107,plain,
% 6.29/6.53 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))))),
% 6.29/6.53 inference(rewrite,[status(thm)],[])).
% 6.29/6.53 tff(4108,plain,
% 6.29/6.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z)))))),
% 6.29/6.54 inference(monotonicity,[status(thm)],[4107])).
% 6.29/6.54 tff(4109,plain,
% 6.29/6.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))))),
% 6.29/6.54 inference(transitivity,[status(thm)],[4108, 4106])).
% 6.29/6.54 tff(4110,plain,
% 6.29/6.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 6.29/6.54 inference(quant_inst,[status(thm)],[])).
% 6.29/6.54 tff(4111,plain,
% 6.29/6.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z)))),
% 6.29/6.54 inference(modus_ponens,[status(thm)],[4110, 4109])).
% 6.29/6.54 tff(4112,plain,
% 6.29/6.54 ($false),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[4111, 194, 530, 174, 233, 722])).
% 6.29/6.54 tff(4113,plain,((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.54 tff(4114,plain,
% 6.29/6.54 (~r(elem!1, z)),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[4113, 722, 233, 174])).
% 6.29/6.54 tff(4115,plain,
% 6.29/6.54 (b(elem!1, z)),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[526, 4114, 2])).
% 6.29/6.54 tff(4116,plain,
% 6.29/6.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 6.29/6.54 inference(rewrite,[status(thm)],[])).
% 6.29/6.54 tff(4117,plain,
% 6.29/6.54 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 6.29/6.54 inference(rewrite,[status(thm)],[])).
% 6.29/6.54 tff(4118,plain,
% 6.29/6.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 6.29/6.54 inference(monotonicity,[status(thm)],[4117])).
% 6.29/6.54 tff(4119,plain,
% 6.29/6.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 6.29/6.54 inference(transitivity,[status(thm)],[4118, 4116])).
% 6.29/6.54 tff(4120,plain,
% 6.29/6.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 6.29/6.54 inference(quant_inst,[status(thm)],[])).
% 6.29/6.54 tff(4121,plain,
% 6.29/6.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 6.29/6.54 inference(modus_ponens,[status(thm)],[4120, 4119])).
% 6.29/6.54 tff(4122,plain,
% 6.29/6.54 (~b(s(s(elem!1)), elem!1)),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[4121, 391, 133, 4115, 4105])).
% 6.29/6.54 tff(4123,plain,
% 6.29/6.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.29/6.54 inference(rewrite,[status(thm)],[])).
% 6.29/6.54 tff(4124,plain,
% 6.29/6.54 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.29/6.54 inference(rewrite,[status(thm)],[])).
% 6.29/6.54 tff(4125,plain,
% 6.29/6.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 6.29/6.54 inference(monotonicity,[status(thm)],[4124])).
% 6.29/6.54 tff(4126,plain,
% 6.29/6.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.29/6.54 inference(transitivity,[status(thm)],[4125, 4123])).
% 6.29/6.54 tff(4127,plain,
% 6.29/6.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.29/6.54 inference(quant_inst,[status(thm)],[])).
% 6.29/6.54 tff(4128,plain,
% 6.29/6.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 6.29/6.54 inference(modus_ponens,[status(thm)],[4127, 4126])).
% 6.29/6.54 tff(4129,plain,
% 6.29/6.54 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[4128, 391, 133, 4115, 4105, 90])).
% 6.29/6.54 tff(4130,plain,
% 6.29/6.54 ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z)))))),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[1994, 42, 4098])).
% 6.29/6.54 tff(4131,plain,
% 6.29/6.54 (s(s(elem!1)) = s(s(s(s(z))))),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[4130, 4129])).
% 6.29/6.54 tff(4132,plain,
% 6.29/6.54 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 6.29/6.54 inference(monotonicity,[status(thm)],[4131])).
% 6.29/6.54 tff(4133,plain,
% 6.29/6.54 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 6.29/6.54 inference(transitivity,[status(thm)],[4132, 764])).
% 6.29/6.54 tff(4134,plain,
% 6.29/6.54 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 6.29/6.54 inference(symmetry,[status(thm)],[4133])).
% 6.29/6.54 tff(4135,plain,
% 6.29/6.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.29/6.54 inference(rewrite,[status(thm)],[])).
% 6.29/6.54 tff(4136,plain,
% 6.29/6.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.29/6.54 inference(quant_inst,[status(thm)],[])).
% 6.29/6.54 tff(4137,plain,
% 6.29/6.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 6.29/6.54 inference(modus_ponens,[status(thm)],[4136, 4135])).
% 6.29/6.54 tff(4138,plain,
% 6.29/6.54 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[4137, 391, 133, 4115, 4105, 90])).
% 6.29/6.54 tff(4139,plain,
% 6.29/6.54 ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1)))),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[2003, 42, 3950])).
% 6.29/6.54 tff(4140,plain,
% 6.29/6.54 (s(s(s(s(z)))) = s(s(elem!1))),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[4139, 4138])).
% 6.29/6.54 tff(4141,plain,
% 6.29/6.54 (elem!1 = s(s(z))),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[1407, 4140])).
% 6.29/6.54 tff(4142,plain,
% 6.29/6.54 (s(s(z)) = elem!1),
% 6.29/6.54 inference(symmetry,[status(thm)],[4141])).
% 6.29/6.54 tff(4143,plain,
% 6.29/6.54 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 6.29/6.54 inference(monotonicity,[status(thm)],[4142])).
% 6.29/6.54 tff(4144,plain,
% 6.29/6.54 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 6.29/6.54 inference(transitivity,[status(thm)],[4143, 4134])).
% 6.29/6.54 tff(4145,plain,
% 6.29/6.54 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = elem!1))),
% 6.29/6.54 inference(monotonicity,[status(thm)],[4144])).
% 6.29/6.54 tff(4146,plain,
% 6.29/6.54 (~(s(s(elem!1)) = elem!1)),
% 6.29/6.54 inference(modus_ponens,[status(thm)],[714, 4145])).
% 6.29/6.54 tff(4147,plain,
% 6.29/6.54 (r(s(s(elem!1)), elem!1)),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[872, 4146, 4122])).
% 6.29/6.54 tff(4148,plain,
% 6.29/6.54 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(elem!1)))),
% 6.29/6.54 inference(transitivity,[status(thm)],[4143, 4134, 2206])).
% 6.29/6.54 tff(4149,plain,
% 6.29/6.54 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(elem!1))))),
% 6.29/6.54 inference(monotonicity,[status(thm)],[4148])).
% 6.29/6.54 tff(4150,plain,
% 6.29/6.54 (~(elem!1 = s(s(elem!1)))),
% 6.29/6.54 inference(modus_ponens,[status(thm)],[714, 4149])).
% 6.29/6.54 tff(4151,plain,
% 6.29/6.54 (b(s(s(s(elem!1))), elem!1)),
% 6.29/6.54 inference(unit_resolution,[status(thm)],[4039, 127, 4028, 327, 364])).
% 6.29/6.54 tff(4152,plain,
% 6.29/6.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.29/6.54 inference(rewrite,[status(thm)],[])).
% 6.29/6.54 tff(4153,plain,
% 6.29/6.54 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.29/6.54 inference(rewrite,[status(thm)],[])).
% 6.29/6.54 tff(4154,plain,
% 6.29/6.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 6.29/6.54 inference(monotonicity,[status(thm)],[4153])).
% 6.29/6.54 tff(4155,plain,
% 6.29/6.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.29/6.55 inference(transitivity,[status(thm)],[4154, 4152])).
% 6.29/6.55 tff(4156,plain,
% 6.29/6.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 6.29/6.55 inference(quant_inst,[status(thm)],[])).
% 6.29/6.55 tff(4157,plain,
% 6.29/6.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 6.29/6.55 inference(modus_ponens,[status(thm)],[4156, 4155])).
% 6.29/6.55 tff(4158,plain,
% 6.29/6.55 ($false),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[4157, 194, 340, 410, 327, 1064])).
% 6.29/6.55 tff(4159,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.55 tff(4160,plain,
% 6.29/6.55 (~r(elem!1, s(s(elem!1)))),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[4159, 4030, 340, 327])).
% 6.29/6.55 tff(4161,plain,
% 6.29/6.55 (b(elem!1, s(s(elem!1)))),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[1307, 4160, 1457])).
% 6.29/6.55 tff(4162,plain,
% 6.29/6.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 6.29/6.55 inference(rewrite,[status(thm)],[])).
% 6.29/6.55 tff(4163,plain,
% 6.29/6.55 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 6.29/6.55 inference(rewrite,[status(thm)],[])).
% 6.29/6.55 tff(4164,plain,
% 6.29/6.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 6.29/6.55 inference(monotonicity,[status(thm)],[4163])).
% 6.29/6.55 tff(4165,plain,
% 6.29/6.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 6.29/6.55 inference(transitivity,[status(thm)],[4164, 4162])).
% 6.29/6.55 tff(4166,plain,
% 6.29/6.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 6.29/6.55 inference(quant_inst,[status(thm)],[])).
% 6.29/6.55 tff(4167,plain,
% 6.29/6.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 6.29/6.55 inference(modus_ponens,[status(thm)],[4166, 4165])).
% 6.29/6.55 tff(4168,plain,
% 6.29/6.55 ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[4167, 391])).
% 6.29/6.55 tff(4169,plain,
% 6.29/6.55 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[4168, 4161, 133, 4151, 3927])).
% 6.29/6.55 tff(4170,plain,
% 6.29/6.55 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[1354, 42, 4169, 270])).
% 6.29/6.55 tff(4171,plain,
% 6.29/6.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.29/6.55 inference(rewrite,[status(thm)],[])).
% 6.29/6.55 tff(4172,plain,
% 6.29/6.55 (((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.29/6.55 inference(rewrite,[status(thm)],[])).
% 6.29/6.55 tff(4173,plain,
% 6.29/6.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 6.29/6.55 inference(monotonicity,[status(thm)],[4172])).
% 6.29/6.55 tff(4174,plain,
% 6.29/6.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.29/6.55 inference(transitivity,[status(thm)],[4173, 4171])).
% 6.29/6.55 tff(4175,plain,
% 6.29/6.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 6.29/6.55 inference(quant_inst,[status(thm)],[])).
% 6.29/6.55 tff(4176,plain,
% 6.29/6.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 6.29/6.55 inference(modus_ponens,[status(thm)],[4175, 4174])).
% 6.29/6.55 tff(4177,plain,
% 6.29/6.55 ($false),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[4176, 194, 174, 364, 4030, 4170])).
% 6.29/6.55 tff(4178,plain,((s(s(s(elem!1))) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.55 tff(4179,plain,
% 6.29/6.55 (b(elem!1, s(s(s(elem!1))))),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[4178, 4147, 270, 127, 174, 3927, 133, 340, 327, 4150])).
% 6.29/6.55 tff(4180,plain,
% 6.29/6.55 (~b(s(z), elem!1)),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[4026, 4179, 1526, 379])).
% 6.29/6.55 tff(4181,plain,
% 6.29/6.55 (r(s(z), elem!1)),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[632, 4180, 150])).
% 6.29/6.55 tff(4182,plain,
% 6.29/6.55 (~b(elem!1, s(z))),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[2665, 4179, 1526, 4105, 4140, 1234])).
% 6.29/6.55 tff(4183,plain,
% 6.29/6.55 (r(elem!1, s(z))),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[837, 4182, 173])).
% 6.29/6.55 tff(4184,plain,
% 6.29/6.55 ($false),
% 6.29/6.55 inference(unit_resolution,[status(thm)],[1899, 4183, 4181, 340, 4147])).
% 6.29/6.56 tff(4185,plain,((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (s(z) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.56 tff(4186,plain,
% 6.29/6.56 (~r(z, s(z))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[4185, 1234, 3944, 3943, 340, 3949, 270, 9, 174, 3927, 133, 327, 3950, 4098, 3971, 2, 182, 4097])).
% 6.29/6.56 tff(4187,plain,
% 6.29/6.56 (b(z, s(z))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[678, 4186])).
% 6.29/6.56 tff(4188,plain,
% 6.29/6.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.29/6.56 inference(rewrite,[status(thm)],[])).
% 6.29/6.56 tff(4189,plain,
% 6.29/6.56 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.29/6.56 inference(rewrite,[status(thm)],[])).
% 6.29/6.56 tff(4190,plain,
% 6.29/6.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.29/6.56 inference(monotonicity,[status(thm)],[4189])).
% 6.29/6.56 tff(4191,plain,
% 6.29/6.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.29/6.56 inference(transitivity,[status(thm)],[4190, 4188])).
% 6.29/6.56 tff(4192,plain,
% 6.29/6.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 6.29/6.56 inference(quant_inst,[status(thm)],[])).
% 6.29/6.56 tff(4193,plain,
% 6.29/6.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.29/6.56 inference(modus_ponens,[status(thm)],[4192, 4191])).
% 6.29/6.56 tff(4194,plain,
% 6.29/6.56 ($false),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[4193, 391, 133, 3949, 3943, 4187, 4096])).
% 6.29/6.56 tff(4195,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(elem!1))) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | r(s(s(elem!1)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.56 tff(4196,plain,
% 6.29/6.56 (~b(s(z), s(s(s(s(z)))))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[4195, 149, 340, 182, 1373, 3946, 2, 184, 168, 327, 1, 3927, 270, 174, 3945])).
% 6.29/6.56 tff(4197,plain,
% 6.29/6.56 (r(s(z), s(s(s(s(z)))))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[1230, 4196])).
% 6.29/6.56 tff(4198,plain,
% 6.29/6.56 (~r(z, s(s(s(s(z)))))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[1224, 4197, 182, 723])).
% 6.29/6.56 tff(4199,plain,
% 6.29/6.56 (b(z, s(s(s(s(z)))))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[800, 4198])).
% 6.29/6.56 tff(4200,plain,
% 6.29/6.56 (~(elem!1 = s(s(s(s(z)))))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[2674, 832, 723])).
% 6.29/6.56 tff(4201,plain,
% 6.29/6.56 (~r(s(s(s(s(z)))), z)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[3969, 3363, 184, 182, 174])).
% 6.29/6.56 tff(4202,plain,
% 6.29/6.56 (b(s(s(s(s(z)))), z)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[87, 4201])).
% 6.29/6.56 tff(4203,plain,
% 6.29/6.56 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 6.29/6.56 inference(monotonicity,[status(thm)],[445])).
% 6.29/6.56 tff(4204,plain,
% 6.29/6.56 (r(elem!1, s(z))),
% 6.29/6.56 inference(modus_ponens,[status(thm)],[340, 4203])).
% 6.29/6.56 tff(4205,plain,
% 6.29/6.56 ($false),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[832, 4204])).
% 6.29/6.56 tff(4206,plain,((~r(s(s(elem!1)), s(z))) | r(elem!1, s(z)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.56 tff(4207,plain,
% 6.29/6.56 (~(s(s(elem!1)) = elem!1)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[4206, 832, 340])).
% 6.29/6.56 tff(4208,plain,
% 6.29/6.56 (~(elem!1 = s(s(elem!1)))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[1292, 4207])).
% 6.29/6.56 tff(4209,plain,
% 6.29/6.56 (r(s(s(elem!1)), elem!1)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[872, 4207, 4017])).
% 6.29/6.56 tff(4210,plain,
% 6.29/6.56 (b(elem!1, s(s(s(elem!1))))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[4178, 4209, 270, 127, 174, 3927, 133, 340, 327, 4208])).
% 6.29/6.56 tff(4211,plain,
% 6.29/6.56 (~b(s(z), elem!1)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[4026, 4210, 3943, 3949])).
% 6.29/6.56 tff(4212,plain,
% 6.29/6.56 (r(s(z), elem!1)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[632, 4211, 150])).
% 6.29/6.56 tff(4213,plain,
% 6.29/6.56 (~r(elem!1, z)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[1489, 4212, 184, 182])).
% 6.29/6.56 tff(4214,plain,
% 6.29/6.56 (b(elem!1, z)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[526, 4213, 2])).
% 6.29/6.56 tff(4215,plain,
% 6.29/6.56 (~b(elem!1, s(s(s(s(z)))))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[3234, 4214, 4202, 1686])).
% 6.29/6.56 tff(4216,plain,
% 6.29/6.56 (r(elem!1, s(s(s(s(z)))))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[781, 4215, 4200])).
% 6.29/6.56 tff(4217,plain,
% 6.29/6.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.29/6.56 inference(rewrite,[status(thm)],[])).
% 6.29/6.56 tff(4218,plain,
% 6.29/6.56 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.29/6.56 inference(rewrite,[status(thm)],[])).
% 6.29/6.56 tff(4219,plain,
% 6.29/6.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z))))))))),
% 6.29/6.56 inference(monotonicity,[status(thm)],[4218])).
% 6.29/6.56 tff(4220,plain,
% 6.29/6.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.29/6.56 inference(transitivity,[status(thm)],[4219, 4217])).
% 6.29/6.56 tff(4221,plain,
% 6.29/6.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 6.29/6.56 inference(quant_inst,[status(thm)],[])).
% 6.29/6.56 tff(4222,plain,
% 6.29/6.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 6.29/6.56 inference(modus_ponens,[status(thm)],[4221, 4220])).
% 6.29/6.56 tff(4223,plain,
% 6.29/6.56 ($false),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[4222, 194, 340, 4209, 4212, 4216])).
% 6.29/6.56 tff(4224,plain,(r(elem!1, s(z)) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(z)))))) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(elem!1)), elem!1) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.56 tff(4225,plain,
% 6.29/6.56 (r(elem!1, s(z))),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[4224, 4017, 1686, 2, 184, 182, 150, 270, 127, 174, 3927, 133, 327, 340, 723])).
% 6.29/6.56 tff(4226,plain,
% 6.29/6.56 (~r(s(s(elem!1)), elem!1)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[4003, 194, 340, 4225, 182])).
% 6.29/6.56 tff(4227,plain,
% 6.29/6.56 (s(s(elem!1)) = elem!1),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[872, 4226, 4017])).
% 6.29/6.56 tff(4228,plain,
% 6.29/6.56 (s(s(s(elem!1))) = s(elem!1)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[451, 4227])).
% 6.29/6.56 tff(4229,plain,
% 6.29/6.56 (s(elem!1) = s(s(s(elem!1)))),
% 6.29/6.56 inference(modus_ponens,[status(thm)],[4228, 2602])).
% 6.29/6.56 tff(4230,plain,
% 6.29/6.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.29/6.56 inference(rewrite,[status(thm)],[])).
% 6.29/6.56 tff(4231,plain,
% 6.29/6.56 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.29/6.56 inference(rewrite,[status(thm)],[])).
% 6.29/6.56 tff(4232,plain,
% 6.29/6.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 6.29/6.56 inference(monotonicity,[status(thm)],[4231])).
% 6.29/6.56 tff(4233,plain,
% 6.29/6.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.29/6.56 inference(transitivity,[status(thm)],[4232, 4230])).
% 6.29/6.56 tff(4234,plain,
% 6.29/6.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 6.29/6.56 inference(quant_inst,[status(thm)],[])).
% 6.29/6.56 tff(4235,plain,
% 6.29/6.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 6.29/6.56 inference(modus_ponens,[status(thm)],[4234, 4233])).
% 6.29/6.56 tff(4236,plain,
% 6.29/6.56 (~r(s(s(s(s(z)))), elem!1)),
% 6.29/6.56 inference(unit_resolution,[status(thm)],[4235, 194, 4225, 182, 723])).
% 6.29/6.56 tff(4237,plain,
% 6.29/6.56 (~(s(s(s(s(z)))) = elem!1)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[717, 4228])).
% 6.29/6.57 tff(4238,plain,
% 6.29/6.57 (b(s(s(s(s(z)))), elem!1)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[762, 4237, 4236])).
% 6.29/6.57 tff(4239,plain,
% 6.29/6.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 6.29/6.57 inference(rewrite,[status(thm)],[])).
% 6.29/6.57 tff(4240,plain,
% 6.29/6.57 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 6.29/6.57 inference(rewrite,[status(thm)],[])).
% 6.29/6.57 tff(4241,plain,
% 6.29/6.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 6.29/6.57 inference(monotonicity,[status(thm)],[4240])).
% 6.29/6.57 tff(4242,plain,
% 6.29/6.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 6.29/6.57 inference(transitivity,[status(thm)],[4241, 4239])).
% 6.29/6.57 tff(4243,plain,
% 6.29/6.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.29/6.57 inference(quant_inst,[status(thm)],[])).
% 6.29/6.57 tff(4244,plain,
% 6.29/6.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 6.29/6.57 inference(modus_ponens,[status(thm)],[4243, 4242])).
% 6.29/6.57 tff(4245,plain,
% 6.29/6.57 ($false),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4244, 391, 665, 90, 1652, 1686])).
% 6.29/6.57 tff(4246,plain,((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.57 tff(4247,plain,
% 6.29/6.57 (~b(elem!1, z)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4246, 4238, 1686, 4202])).
% 6.29/6.57 tff(4248,plain,
% 6.29/6.57 (r(elem!1, z)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[526, 4247, 2])).
% 6.29/6.57 tff(4249,plain,
% 6.29/6.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 6.29/6.57 inference(rewrite,[status(thm)],[])).
% 6.29/6.57 tff(4250,plain,
% 6.29/6.57 (((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 6.29/6.57 inference(rewrite,[status(thm)],[])).
% 6.29/6.57 tff(4251,plain,
% 6.29/6.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))))),
% 6.29/6.57 inference(monotonicity,[status(thm)],[4250])).
% 6.29/6.57 tff(4252,plain,
% 6.29/6.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 6.29/6.57 inference(transitivity,[status(thm)],[4251, 4249])).
% 6.29/6.57 tff(4253,plain,
% 6.29/6.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 6.29/6.57 inference(quant_inst,[status(thm)],[])).
% 6.29/6.57 tff(4254,plain,
% 6.29/6.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))),
% 6.29/6.57 inference(modus_ponens,[status(thm)],[4253, 4252])).
% 6.29/6.57 tff(4255,plain,
% 6.29/6.57 ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4254, 194])).
% 6.29/6.57 tff(4256,plain,
% 6.29/6.57 (~r(z, s(elem!1))),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4255, 4248, 233, 174])).
% 6.29/6.57 tff(4257,plain,
% 6.29/6.57 (~(s(elem!1) = s(s(s(elem!1))))),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[575, 4256, 184])).
% 6.29/6.57 tff(4258,plain,
% 6.29/6.57 ($false),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4257, 4229])).
% 6.29/6.57 tff(4259,plain,(b(s(s(elem!1)), elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (elem!1 = z) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.57 tff(4260,plain,
% 6.29/6.57 (b(s(s(elem!1)), elem!1)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4259, 2, 4097, 174, 184, 4199, 182, 723, 340, 3944, 270, 9, 3927, 149, 327])).
% 6.29/6.57 tff(4261,plain,
% 6.29/6.57 (~b(elem!1, s(s(elem!1)))),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[3979, 4260, 3927, 149])).
% 6.29/6.57 tff(4262,plain,
% 6.29/6.57 (~r(elem!1, s(z))),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[3996, 4260, 340, 182, 3927, 149])).
% 6.29/6.57 tff(4263,plain,
% 6.29/6.57 (~(s(s(elem!1)) = elem!1)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4206, 4262, 340])).
% 6.29/6.57 tff(4264,plain,
% 6.29/6.57 (~(elem!1 = s(s(elem!1)))),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[1292, 4263])).
% 6.29/6.57 tff(4265,plain,
% 6.29/6.57 (r(elem!1, s(s(elem!1)))),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[1307, 4264, 4261])).
% 6.29/6.57 tff(4266,plain,
% 6.29/6.57 (~r(elem!1, s(s(s(elem!1))))),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4159, 4265, 327, 340])).
% 6.29/6.57 tff(4267,plain,
% 6.29/6.57 (b(elem!1, s(s(s(elem!1))))),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[424, 4266, 1])).
% 6.29/6.57 tff(4268,plain,
% 6.29/6.57 (~b(s(z), elem!1)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4026, 4267, 3943, 3949])).
% 6.29/6.57 tff(4269,plain,
% 6.29/6.57 (r(s(z), elem!1)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[632, 4268, 3944])).
% 6.29/6.57 tff(4270,plain,
% 6.29/6.57 (~r(elem!1, z)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[1489, 4269, 184, 182])).
% 6.29/6.57 tff(4271,plain,
% 6.29/6.57 (b(elem!1, z)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[526, 4270, 2])).
% 6.29/6.57 tff(4272,plain,
% 6.29/6.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.29/6.57 inference(rewrite,[status(thm)],[])).
% 6.29/6.57 tff(4273,plain,
% 6.29/6.57 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.29/6.57 inference(rewrite,[status(thm)],[])).
% 6.29/6.57 tff(4274,plain,
% 6.29/6.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 6.29/6.57 inference(monotonicity,[status(thm)],[4273])).
% 6.29/6.57 tff(4275,plain,
% 6.29/6.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.29/6.57 inference(transitivity,[status(thm)],[4274, 4272])).
% 6.29/6.57 tff(4276,plain,
% 6.29/6.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 6.29/6.57 inference(quant_inst,[status(thm)],[])).
% 6.29/6.57 tff(4277,plain,
% 6.29/6.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 6.29/6.57 inference(modus_ponens,[status(thm)],[4276, 4275])).
% 6.29/6.57 tff(4278,plain,
% 6.29/6.57 ($false),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4277, 391, 149, 4271, 4260, 3927])).
% 6.29/6.57 tff(4279,plain,((elem!1 = z) | (~b(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.29/6.57 tff(4280,plain,
% 6.29/6.57 (elem!1 = z),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[4279, 723, 184, 181, 1, 327, 340, 174, 3927, 270, 1373, 168, 80])).
% 6.29/6.57 tff(4281,plain,
% 6.29/6.57 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 6.29/6.57 inference(monotonicity,[status(thm)],[4280])).
% 6.29/6.57 tff(4282,plain,
% 6.29/6.57 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 6.29/6.57 inference(transitivity,[status(thm)],[4281, 792])).
% 6.29/6.57 tff(4283,plain,
% 6.29/6.57 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 6.29/6.57 inference(symmetry,[status(thm)],[4282])).
% 6.29/6.57 tff(4284,plain,
% 6.29/6.57 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 6.29/6.57 inference(transitivity,[status(thm)],[4283, 765])).
% 6.29/6.57 tff(4285,plain,
% 6.29/6.57 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 6.29/6.57 inference(monotonicity,[status(thm)],[4284])).
% 6.29/6.57 tff(4286,plain,
% 6.29/6.57 (~(s(s(s(s(z)))) = elem!1)),
% 6.29/6.57 inference(modus_ponens,[status(thm)],[83, 4285])).
% 6.29/6.57 tff(4287,plain,
% 6.29/6.57 (r(s(z), elem!1)),
% 6.29/6.57 inference(unit_resolution,[status(thm)],[3205, 4280, 91])).
% 6.29/6.57 tff(4288,plain,
% 6.29/6.57 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 6.29/6.57 inference(monotonicity,[status(thm)],[4280])).
% 6.29/6.57 tff(4289,plain,
% 6.29/6.57 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 6.29/6.57 inference(symmetry,[status(thm)],[4288])).
% 6.29/6.57 tff(4290,plain,
% 6.29/6.57 (b(elem!1, s(s(elem!1)))),
% 6.29/6.57 inference(modus_ponens,[status(thm)],[3927, 4289])).
% 6.29/6.57 tff(4291,plain,
% 6.29/6.57 (s(elem!1) = s(z)),
% 6.29/6.57 inference(monotonicity,[status(thm)],[4280])).
% 6.29/6.57 tff(4292,plain,
% 6.29/6.57 (s(s(elem!1)) = s(s(z))),
% 6.29/6.57 inference(monotonicity,[status(thm)],[4291])).
% 6.29/6.57 tff(4293,plain,
% 6.29/6.57 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 6.29/6.57 inference(monotonicity,[status(thm)],[4292])).
% 6.29/6.58 tff(4294,plain,
% 6.29/6.58 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 6.29/6.58 inference(transitivity,[status(thm)],[4293, 940])).
% 6.29/6.58 tff(4295,plain,
% 6.29/6.58 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 6.29/6.58 inference(symmetry,[status(thm)],[4294])).
% 6.29/6.58 tff(4296,plain,
% 6.29/6.58 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 6.29/6.58 inference(monotonicity,[status(thm)],[4295])).
% 6.29/6.58 tff(4297,plain,
% 6.29/6.58 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 6.29/6.58 inference(modus_ponens,[status(thm)],[714, 4296])).
% 6.29/6.58 tff(4298,plain,
% 6.29/6.58 ($false),
% 6.29/6.58 inference(unit_resolution,[status(thm)],[2028, 4297, 4290, 340, 723, 4287, 4286])).
% 6.29/6.58 tff(4299,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | b(s(z), z) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.29/6.58 tff(4300,plain,
% 6.29/6.58 (~r(s(s(s(s(z)))), s(z))),
% 6.29/6.58 inference(unit_resolution,[status(thm)],[4299, 340, 3927, 91, 184, 1, 327, 174, 270, 1373, 168, 80])).
% 6.29/6.58 tff(4301,plain,
% 6.29/6.58 (b(s(s(s(s(z)))), s(z))),
% 6.29/6.58 inference(unit_resolution,[status(thm)],[749, 4300])).
% 6.29/6.58 tff(4302,plain,
% 6.29/6.58 (~r(s(z), s(s(s(elem!1))))),
% 6.29/6.58 inference(unit_resolution,[status(thm)],[1867, 174, 184, 181])).
% 6.29/6.58 tff(4303,plain,
% 6.29/6.58 (b(s(z), s(s(s(elem!1))))),
% 6.29/6.58 inference(unit_resolution,[status(thm)],[247, 4302])).
% 6.29/6.58 tff(4304,plain,
% 6.29/6.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.29/6.58 inference(rewrite,[status(thm)],[])).
% 6.29/6.58 tff(4305,plain,
% 6.29/6.58 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.29/6.58 inference(rewrite,[status(thm)],[])).
% 6.29/6.58 tff(4306,plain,
% 6.29/6.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 6.29/6.58 inference(monotonicity,[status(thm)],[4305])).
% 6.29/6.58 tff(4307,plain,
% 6.29/6.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.29/6.58 inference(transitivity,[status(thm)],[4306, 4304])).
% 6.29/6.58 tff(4308,plain,
% 6.29/6.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.29/6.58 inference(quant_inst,[status(thm)],[])).
% 6.29/6.58 tff(4309,plain,
% 6.29/6.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 6.29/6.58 inference(modus_ponens,[status(thm)],[4308, 4307])).
% 6.29/6.58 tff(4310,plain,
% 6.29/6.58 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.29/6.58 inference(unit_resolution,[status(thm)],[4309, 391, 4303, 3932, 4301])).
% 6.29/6.58 tff(4311,plain,
% 6.29/6.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 6.29/6.58 inference(rewrite,[status(thm)],[])).
% 6.29/6.58 tff(4312,plain,
% 6.29/6.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 6.29/6.58 inference(quant_inst,[status(thm)],[])).
% 6.29/6.58 tff(4313,plain,
% 6.29/6.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.29/6.58 inference(modus_ponens,[status(thm)],[4312, 4311])).
% 6.29/6.58 tff(4314,plain,
% 6.29/6.58 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.29/6.58 inference(unit_resolution,[status(thm)],[4313, 42, 4310])).
% 6.29/6.58 tff(4315,plain,
% 6.29/6.58 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.29/6.58 inference(unit_resolution,[status(thm)],[4314, 3941])).
% 6.29/6.58 tff(4316,plain,
% 6.29/6.58 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.29/6.58 inference(unit_resolution,[status(thm)],[3967, 391, 4303, 3932, 4301])).
% 6.29/6.58 tff(4317,assumption,(r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 6.29/6.58 tff(4318,plain,
% 6.29/6.58 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.29/6.58 inference(unit_resolution,[status(thm)],[2853, 42, 3363, 2863])).
% 6.29/6.58 tff(4319,plain,
% 6.29/6.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.29/6.58 inference(rewrite,[status(thm)],[])).
% 6.29/6.58 tff(4320,plain,
% 6.29/6.58 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.29/6.58 inference(rewrite,[status(thm)],[])).
% 6.29/6.58 tff(4321,plain,
% 6.29/6.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 6.29/6.58 inference(monotonicity,[status(thm)],[4320])).
% 6.29/6.58 tff(4322,plain,
% 6.29/6.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.29/6.58 inference(transitivity,[status(thm)],[4321, 4319])).
% 6.29/6.58 tff(4323,plain,
% 6.29/6.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 6.29/6.58 inference(quant_inst,[status(thm)],[])).
% 6.29/6.58 tff(4324,plain,
% 6.29/6.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.29/6.59 inference(modus_ponens,[status(thm)],[4323, 4322])).
% 6.29/6.59 tff(4325,plain,
% 6.29/6.59 (~r(z, s(s(s(s(z)))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4324, 194, 174, 184, 4318])).
% 6.29/6.59 tff(4326,plain,
% 6.29/6.59 (b(z, s(s(s(s(z)))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[800, 4325])).
% 6.29/6.59 tff(4327,plain,
% 6.29/6.59 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 6.29/6.59 inference(monotonicity,[status(thm)],[452])).
% 6.29/6.59 tff(4328,plain,
% 6.29/6.59 (r(s(elem!1), s(s(s(s(z)))))),
% 6.29/6.59 inference(modus_ponens,[status(thm)],[4317, 4327])).
% 6.29/6.59 tff(4329,plain,
% 6.29/6.59 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 6.29/6.59 inference(monotonicity,[status(thm)],[452])).
% 6.29/6.59 tff(4330,plain,
% 6.29/6.59 (r(z, s(elem!1))),
% 6.29/6.59 inference(modus_ponens,[status(thm)],[184, 4329])).
% 6.29/6.59 tff(4331,plain,
% 6.29/6.59 (~r(elem!1, z)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4255, 4330, 233, 174])).
% 6.29/6.59 tff(4332,plain,
% 6.29/6.59 (b(elem!1, z)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[526, 4331, 2])).
% 6.29/6.59 tff(4333,plain,
% 6.29/6.59 (~b(s(s(s(s(z)))), elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4246, 4332, 1686, 90])).
% 6.29/6.59 tff(4334,plain,
% 6.29/6.59 (r(s(s(s(s(z)))), elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[762, 4333, 718])).
% 6.29/6.59 tff(4335,plain,
% 6.29/6.59 (r(elem!1, s(z))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4206, 445, 340])).
% 6.29/6.59 tff(4336,plain,
% 6.29/6.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.29/6.59 inference(rewrite,[status(thm)],[])).
% 6.29/6.59 tff(4337,plain,
% 6.29/6.59 (((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.29/6.59 inference(rewrite,[status(thm)],[])).
% 6.29/6.59 tff(4338,plain,
% 6.29/6.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 6.29/6.59 inference(monotonicity,[status(thm)],[4337])).
% 6.29/6.59 tff(4339,plain,
% 6.29/6.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.29/6.59 inference(transitivity,[status(thm)],[4338, 4336])).
% 6.29/6.59 tff(4340,plain,
% 6.29/6.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.29/6.59 inference(quant_inst,[status(thm)],[])).
% 6.29/6.59 tff(4341,plain,
% 6.29/6.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 6.29/6.59 inference(modus_ponens,[status(thm)],[4340, 4339])).
% 6.29/6.59 tff(4342,plain,
% 6.29/6.59 ($false),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4341, 194, 473, 4335, 4334, 4328])).
% 6.29/6.59 tff(4343,plain,((~(s(s(elem!1)) = elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.59 tff(4344,plain,
% 6.29/6.59 (~(s(s(elem!1)) = elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4343, 2, 4202, 4326, 233, 174, 4317, 184, 340])).
% 6.29/6.59 tff(4345,plain,
% 6.29/6.59 (r(s(s(elem!1)), elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[872, 249, 4017])).
% 6.29/6.59 tff(4346,plain,
% 6.29/6.59 (b(elem!1, s(s(s(elem!1))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4178, 4345, 270, 127, 174, 3927, 133, 340, 327, 1293])).
% 6.29/6.59 tff(4347,plain,
% 6.29/6.59 (~(s(s(s(s(z)))) = elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[2865, 4346, 2863])).
% 6.29/6.59 tff(4348,plain,
% 6.29/6.59 (~(elem!1 = s(s(s(s(z)))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[769, 4347])).
% 6.29/6.59 tff(4349,plain,
% 6.29/6.59 (~b(s(z), elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4026, 4346, 3943, 3949])).
% 6.29/6.59 tff(4350,plain,
% 6.29/6.59 (r(s(z), elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[632, 4349, 150])).
% 6.29/6.59 tff(4351,plain,
% 6.29/6.59 (~r(elem!1, z)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[1489, 4350, 184, 182])).
% 6.29/6.59 tff(4352,plain,
% 6.29/6.59 (b(elem!1, z)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[526, 4351, 2])).
% 6.29/6.59 tff(4353,plain,
% 6.29/6.59 (~b(elem!1, s(s(s(s(z)))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[3234, 4352, 4202, 4326])).
% 6.29/6.59 tff(4354,plain,
% 6.29/6.59 (r(elem!1, s(s(s(s(z)))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[781, 4353, 4348])).
% 6.29/6.59 tff(4355,plain,
% 6.29/6.59 ($false),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4222, 194, 340, 4345, 4350, 4354])).
% 6.29/6.59 tff(4356,plain,((s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(z))) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(z) = elem!1) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.29/6.59 tff(4357,plain,
% 6.29/6.59 (b(s(s(elem!1)), elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4356, 4344, 2, 184, 182, 150, 2863, 270, 9, 174, 3927, 149, 327, 340])).
% 6.29/6.59 tff(4358,plain,
% 6.29/6.59 (~(elem!1 = s(s(elem!1)))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[1292, 4344])).
% 6.29/6.59 tff(4359,plain,
% 6.29/6.59 (~b(elem!1, s(s(elem!1)))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[3979, 4357, 3927, 149])).
% 6.29/6.59 tff(4360,plain,
% 6.29/6.59 (r(elem!1, s(s(elem!1)))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[1307, 4359, 4358])).
% 6.29/6.59 tff(4361,plain,
% 6.29/6.59 (~r(elem!1, s(s(s(elem!1))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4159, 4360, 327, 340])).
% 6.29/6.59 tff(4362,plain,
% 6.29/6.59 (b(elem!1, s(s(s(elem!1))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[424, 4361, 1])).
% 6.29/6.59 tff(4363,plain,
% 6.29/6.59 (~b(s(z), elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4026, 4362, 3943, 3949])).
% 6.29/6.59 tff(4364,plain,
% 6.29/6.59 (r(s(z), elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[632, 4363, 150])).
% 6.29/6.59 tff(4365,plain,
% 6.29/6.59 (~r(elem!1, z)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[1489, 4364, 184, 182])).
% 6.29/6.59 tff(4366,plain,
% 6.29/6.59 (b(elem!1, z)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[526, 4365, 2])).
% 6.29/6.59 tff(4367,plain,
% 6.29/6.59 ($false),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4277, 391, 149, 4366, 4357, 3927])).
% 6.29/6.59 tff(4368,plain,((elem!1 = z) | (~b(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(z) = elem!1) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.29/6.59 tff(4369,plain,
% 6.29/6.59 (elem!1 = z),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4368, 340, 184, 181, 3939, 1, 327, 3927, 4316, 270, 174, 4097, 4315, 80])).
% 6.29/6.59 tff(4370,plain,
% 6.29/6.59 (s(elem!1) = s(z)),
% 6.29/6.59 inference(monotonicity,[status(thm)],[4369])).
% 6.29/6.59 tff(4371,plain,
% 6.29/6.59 (s(s(elem!1)) = s(s(z))),
% 6.29/6.59 inference(monotonicity,[status(thm)],[4370])).
% 6.29/6.59 tff(4372,plain,
% 6.29/6.59 (s(s(s(elem!1))) = s(s(s(z)))),
% 6.29/6.59 inference(monotonicity,[status(thm)],[4371])).
% 6.29/6.59 tff(4373,plain,
% 6.29/6.59 (s(s(s(z))) = s(s(s(elem!1)))),
% 6.29/6.59 inference(symmetry,[status(thm)],[4372])).
% 6.29/6.59 tff(4374,plain,
% 6.29/6.59 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.29/6.59 inference(monotonicity,[status(thm)],[4373])).
% 6.29/6.59 tff(4375,plain,
% 6.29/6.59 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 6.29/6.59 inference(symmetry,[status(thm)],[4374])).
% 6.29/6.59 tff(4376,plain,
% 6.29/6.59 (r(s(s(s(z))), s(s(s(s(z)))))),
% 6.29/6.59 inference(modus_ponens,[status(thm)],[4315, 4375])).
% 6.29/6.59 tff(4377,plain,
% 6.29/6.59 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 6.29/6.59 inference(monotonicity,[status(thm)],[4372])).
% 6.29/6.59 tff(4378,plain,
% 6.29/6.59 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[2853, 42, 3940, 4316])).
% 6.29/6.59 tff(4379,plain,
% 6.29/6.59 (r(s(s(s(s(z)))), s(s(s(z))))),
% 6.29/6.59 inference(modus_ponens,[status(thm)],[4378, 4377])).
% 6.29/6.59 tff(4380,plain,
% 6.29/6.59 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.29/6.59 inference(monotonicity,[status(thm)],[491, 2980])).
% 6.29/6.59 tff(4381,plain,
% 6.29/6.59 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 6.29/6.59 inference(symmetry,[status(thm)],[4380])).
% 6.29/6.59 tff(4382,plain,
% 6.29/6.59 (r(s(s(s(z))), s(s(z)))),
% 6.29/6.59 inference(modus_ponens,[status(thm)],[327, 4381])).
% 6.29/6.59 tff(4383,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 6.29/6.59 tff(4384,plain,
% 6.29/6.59 ($false),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4383, 4382])).
% 6.29/6.59 tff(4385,plain,(r(s(s(s(z))), s(s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.59 tff(4386,plain,
% 6.29/6.59 (r(s(s(s(z))), s(s(z)))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4385, 4369, 327])).
% 6.29/6.59 tff(4387,plain,
% 6.29/6.59 (~r(s(s(s(s(z)))), z)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[3969, 3940, 184, 181, 174])).
% 6.29/6.59 tff(4388,plain,
% 6.29/6.59 (b(s(s(s(s(z)))), z)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[87, 4387])).
% 6.29/6.59 tff(4389,plain,
% 6.29/6.59 (~r(z, s(s(s(s(z)))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4324, 194, 174, 184, 4378])).
% 6.29/6.59 tff(4390,plain,
% 6.29/6.59 (b(z, s(s(s(s(z)))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[800, 4389])).
% 6.29/6.59 tff(4391,plain,
% 6.29/6.59 (r(s(z), elem!1)),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[3205, 4369, 91])).
% 6.29/6.59 tff(4392,plain,
% 6.29/6.59 (s(s(z)) = s(s(elem!1))),
% 6.29/6.59 inference(symmetry,[status(thm)],[4371])).
% 6.29/6.59 tff(4393,plain,
% 6.29/6.59 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 6.29/6.59 inference(monotonicity,[status(thm)],[4392])).
% 6.29/6.59 tff(4394,plain,
% 6.29/6.59 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 6.29/6.59 inference(symmetry,[status(thm)],[4393])).
% 6.29/6.59 tff(4395,plain,
% 6.29/6.59 (r(s(s(z)), s(z))),
% 6.29/6.59 inference(modus_ponens,[status(thm)],[340, 4394])).
% 6.29/6.59 tff(4396,plain,
% 6.29/6.59 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 6.29/6.59 inference(monotonicity,[status(thm)],[4373])).
% 6.29/6.59 tff(4397,plain,
% 6.29/6.59 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 6.29/6.59 inference(symmetry,[status(thm)],[4396])).
% 6.29/6.59 tff(4398,plain,
% 6.29/6.59 (b(s(s(s(z))), s(z))),
% 6.29/6.59 inference(modus_ponens,[status(thm)],[3932, 4397])).
% 6.29/6.59 tff(4399,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 6.29/6.59 tff(4400,plain,
% 6.29/6.59 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 6.29/6.59 inference(transitivity,[status(thm)],[4399, 491])).
% 6.29/6.59 tff(4401,plain,
% 6.29/6.59 ($false),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[3843, 4400])).
% 6.29/6.59 tff(4402,plain,((~(s(s(s(s(z)))) = s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 6.29/6.59 tff(4403,plain,
% 6.29/6.59 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4402, 4369, 3940])).
% 6.29/6.59 tff(4404,plain,
% 6.29/6.59 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), z)),
% 6.29/6.59 inference(monotonicity,[status(thm)],[491])).
% 6.29/6.59 tff(4405,plain,
% 6.29/6.59 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), z)),
% 6.29/6.59 inference(symmetry,[status(thm)],[4404])).
% 6.29/6.59 tff(4406,plain,
% 6.29/6.59 (r(s(s(s(z))), z)),
% 6.29/6.59 inference(modus_ponens,[status(thm)],[174, 4405])).
% 6.29/6.59 tff(4407,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 6.29/6.59 tff(4408,plain,
% 6.29/6.59 ($false),
% 6.29/6.59 inference(unit_resolution,[status(thm)],[4407, 4406])).
% 6.29/6.59 tff(4409,plain,((~r(s(s(s(elem!1))), z)) | r(s(s(s(z))), z) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.60 tff(4410,plain,
% 6.39/6.60 (r(s(s(s(z))), z)),
% 6.39/6.60 inference(unit_resolution,[status(thm)],[4409, 4369, 174])).
% 6.39/6.60 tff(4411,plain,
% 6.39/6.60 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 6.39/6.60 inference(monotonicity,[status(thm)],[4373])).
% 6.39/6.60 tff(4412,plain,
% 6.39/6.60 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 6.39/6.60 inference(symmetry,[status(thm)],[4411])).
% 6.39/6.60 tff(4413,plain,
% 6.39/6.60 (b(s(z), s(s(s(z))))),
% 6.39/6.60 inference(modus_ponens,[status(thm)],[4303, 4412])).
% 6.39/6.60 tff(4414,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 6.39/6.60 tff(4415,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 6.39/6.60 tff(4416,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 6.39/6.60 tff(4417,plain,
% 6.39/6.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.39/6.60 inference(rewrite,[status(thm)],[])).
% 6.39/6.60 tff(4418,plain,
% 6.39/6.60 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.39/6.60 inference(rewrite,[status(thm)],[])).
% 6.39/6.60 tff(4419,plain,
% 6.39/6.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 6.39/6.60 inference(monotonicity,[status(thm)],[4418])).
% 6.39/6.60 tff(4420,plain,
% 6.39/6.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.39/6.60 inference(transitivity,[status(thm)],[4419, 4417])).
% 6.39/6.60 tff(4421,plain,
% 6.39/6.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 6.39/6.60 inference(quant_inst,[status(thm)],[])).
% 6.39/6.60 tff(4422,plain,
% 6.39/6.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 6.39/6.60 inference(modus_ponens,[status(thm)],[4421, 4420])).
% 6.39/6.60 tff(4423,plain,
% 6.39/6.60 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 6.39/6.60 inference(unit_resolution,[status(thm)],[4422, 391, 1759, 4416, 4415])).
% 6.39/6.60 tff(4424,plain,
% 6.39/6.60 (((~![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)))))),
% 6.39/6.60 inference(rewrite,[status(thm)],[])).
% 6.39/6.60 tff(4425,plain,
% 6.39/6.60 ((~![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)))))),
% 6.39/6.60 inference(quant_inst,[status(thm)],[])).
% 6.39/6.60 tff(4426,plain,
% 6.39/6.60 ((~![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))))),
% 6.39/6.60 inference(modus_ponens,[status(thm)],[4425, 4424])).
% 6.39/6.60 tff(4427,plain,
% 6.39/6.60 (r(s(s(s(s(z)))), s(s(s(z))))),
% 6.39/6.60 inference(unit_resolution,[status(thm)],[4426, 42, 4423, 4414])).
% 6.39/6.60 tff(4428,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 6.39/6.60 tff(4429,plain,
% 6.39/6.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.39/6.60 inference(rewrite,[status(thm)],[])).
% 6.39/6.60 tff(4430,plain,
% 6.39/6.60 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.39/6.60 inference(rewrite,[status(thm)],[])).
% 6.39/6.60 tff(4431,plain,
% 6.39/6.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 6.39/6.60 inference(monotonicity,[status(thm)],[4430])).
% 6.39/6.60 tff(4432,plain,
% 6.39/6.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.39/6.60 inference(transitivity,[status(thm)],[4431, 4429])).
% 6.39/6.60 tff(4433,plain,
% 6.39/6.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 6.39/6.60 inference(quant_inst,[status(thm)],[])).
% 6.39/6.60 tff(4434,plain,
% 6.39/6.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 6.39/6.60 inference(modus_ponens,[status(thm)],[4433, 4432])).
% 6.39/6.60 tff(4435,plain,
% 6.39/6.60 (~b(z, s(s(s(s(z)))))),
% 6.39/6.60 inference(unit_resolution,[status(thm)],[4434, 391, 1759, 664, 4416, 4415])).
% 6.39/6.60 tff(4436,plain,
% 6.39/6.60 (r(z, s(s(s(s(z)))))),
% 6.39/6.60 inference(unit_resolution,[status(thm)],[800, 4435])).
% 6.39/6.60 tff(4437,plain,
% 6.39/6.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.39/6.60 inference(rewrite,[status(thm)],[])).
% 6.39/6.60 tff(4438,plain,
% 6.39/6.60 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.39/6.60 inference(rewrite,[status(thm)],[])).
% 6.39/6.60 tff(4439,plain,
% 6.39/6.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 6.39/6.61 inference(monotonicity,[status(thm)],[4438])).
% 6.39/6.61 tff(4440,plain,
% 6.39/6.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.39/6.61 inference(transitivity,[status(thm)],[4439, 4437])).
% 6.39/6.61 tff(4441,plain,
% 6.39/6.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 6.39/6.61 inference(quant_inst,[status(thm)],[])).
% 6.39/6.61 tff(4442,plain,
% 6.39/6.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 6.39/6.61 inference(modus_ponens,[status(thm)],[4441, 4440])).
% 6.39/6.61 tff(4443,plain,
% 6.39/6.61 (~b(s(s(s(s(z)))), z)),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[4442, 391, 1759, 664, 4416, 4415])).
% 6.39/6.61 tff(4444,plain,
% 6.39/6.61 (r(s(s(s(s(z)))), z)),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[87, 4443])).
% 6.39/6.61 tff(4445,plain,
% 6.39/6.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 6.39/6.61 inference(rewrite,[status(thm)],[])).
% 6.39/6.61 tff(4446,plain,
% 6.39/6.61 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 6.39/6.61 inference(rewrite,[status(thm)],[])).
% 6.39/6.61 tff(4447,plain,
% 6.39/6.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 6.39/6.61 inference(monotonicity,[status(thm)],[4446])).
% 6.39/6.61 tff(4448,plain,
% 6.39/6.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 6.39/6.61 inference(transitivity,[status(thm)],[4447, 4445])).
% 6.39/6.61 tff(4449,plain,
% 6.39/6.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 6.39/6.61 inference(quant_inst,[status(thm)],[])).
% 6.39/6.61 tff(4450,plain,
% 6.39/6.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 6.39/6.61 inference(modus_ponens,[status(thm)],[4449, 4448])).
% 6.39/6.61 tff(4451,plain,
% 6.39/6.61 ($false),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[4450, 194, 4444, 4436, 4428, 4427])).
% 6.39/6.61 tff(4452,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), z)) | (s(s(s(s(z)))) = s(s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.61 tff(4453,plain,
% 6.39/6.61 (~b(z, s(z))),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[4452, 4413, 4301, 4410, 4403, 4398])).
% 6.39/6.61 tff(4454,plain,
% 6.39/6.61 (r(z, s(z))),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[678, 4453])).
% 6.39/6.61 tff(4455,plain,
% 6.39/6.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 6.39/6.61 inference(rewrite,[status(thm)],[])).
% 6.39/6.61 tff(4456,plain,
% 6.39/6.61 (((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 6.39/6.61 inference(rewrite,[status(thm)],[])).
% 6.39/6.61 tff(4457,plain,
% 6.39/6.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 6.39/6.61 inference(monotonicity,[status(thm)],[4456])).
% 6.39/6.61 tff(4458,plain,
% 6.39/6.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 6.39/6.61 inference(transitivity,[status(thm)],[4457, 4455])).
% 6.39/6.61 tff(4459,plain,
% 6.39/6.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 6.39/6.61 inference(quant_inst,[status(thm)],[])).
% 6.39/6.61 tff(4460,plain,
% 6.39/6.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 6.39/6.61 inference(modus_ponens,[status(thm)],[4459, 4458])).
% 6.39/6.61 tff(4461,plain,
% 6.39/6.61 ($false),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[4460, 194, 1484, 722, 3557, 2405])).
% 6.39/6.61 tff(4462,plain,((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.61 tff(4463,plain,
% 6.39/6.61 (~r(s(s(z)), z)),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[4462, 4454, 4395, 4391])).
% 6.39/6.61 tff(4464,plain,
% 6.39/6.61 (b(s(s(z)), z)),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[1211, 4463])).
% 6.39/6.61 tff(4465,plain,
% 6.39/6.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 6.39/6.61 inference(rewrite,[status(thm)],[])).
% 6.39/6.61 tff(4466,plain,
% 6.39/6.61 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 6.39/6.61 inference(rewrite,[status(thm)],[])).
% 6.39/6.61 tff(4467,plain,
% 6.39/6.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))))),
% 6.39/6.61 inference(monotonicity,[status(thm)],[4466])).
% 6.39/6.61 tff(4468,plain,
% 6.39/6.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 6.39/6.61 inference(transitivity,[status(thm)],[4467, 4465])).
% 6.39/6.61 tff(4469,plain,
% 6.39/6.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 6.39/6.61 inference(quant_inst,[status(thm)],[])).
% 6.39/6.61 tff(4470,plain,
% 6.39/6.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))),
% 6.39/6.61 inference(modus_ponens,[status(thm)],[4469, 4468])).
% 6.39/6.61 tff(4471,plain,
% 6.39/6.61 ($false),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[4470, 391, 3823, 90, 1235, 1686])).
% 6.39/6.61 tff(4472,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.61 tff(4473,plain,
% 6.39/6.61 (~b(s(s(z)), s(s(s(s(z)))))),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[4472, 4464, 4390, 4388])).
% 6.39/6.61 tff(4474,plain,
% 6.39/6.61 (r(s(s(z)), s(s(s(s(z)))))),
% 6.39/6.61 inference(unit_resolution,[status(thm)],[3652, 4473])).
% 6.39/6.61 tff(4475,plain,
% 6.39/6.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.39/6.61 inference(rewrite,[status(thm)],[])).
% 6.39/6.61 tff(4476,plain,
% 6.39/6.61 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(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(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.39/6.61 inference(rewrite,[status(thm)],[])).
% 6.39/6.61 tff(4477,plain,
% 6.39/6.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 6.39/6.61 inference(monotonicity,[status(thm)],[4476])).
% 6.39/6.61 tff(4478,plain,
% 6.39/6.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.39/6.61 inference(transitivity,[status(thm)],[4477, 4475])).
% 6.39/6.62 tff(4479,plain,
% 6.39/6.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 6.39/6.62 inference(quant_inst,[status(thm)],[])).
% 6.39/6.62 tff(4480,plain,
% 6.39/6.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 6.39/6.62 inference(modus_ponens,[status(thm)],[4479, 4478])).
% 6.39/6.62 tff(4481,plain,
% 6.39/6.62 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 6.39/6.62 inference(unit_resolution,[status(thm)],[4480, 194, 4474, 4386, 4379])).
% 6.39/6.62 tff(4482,plain,
% 6.39/6.62 ($false),
% 6.39/6.62 inference(unit_resolution,[status(thm)],[4481, 4376])).
% 6.39/6.62 tff(4483,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | b(s(z), z) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(z, elem!1) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.39/6.62 tff(4484,plain,
% 6.39/6.62 (~r(s(s(elem!1)), s(z))),
% 6.39/6.62 inference(unit_resolution,[status(thm)],[4483, 327, 174, 91, 184, 1, 3927, 270, 80, 1373, 168])).
% 6.39/6.62 tff(4485,plain,
% 6.39/6.62 (b(s(s(elem!1)), s(z))),
% 6.39/6.62 inference(unit_resolution,[status(thm)],[362, 4484])).
% 6.39/6.62 tff(4486,plain,
% 6.39/6.62 (r(s(s(s(elem!1))), elem!1)),
% 6.39/6.62 inference(unit_resolution,[status(thm)],[230, 168, 127])).
% 6.39/6.62 tff(4487,plain,
% 6.39/6.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 6.39/6.62 inference(rewrite,[status(thm)],[])).
% 6.39/6.62 tff(4488,plain,
% 6.39/6.62 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 6.39/6.62 inference(rewrite,[status(thm)],[])).
% 6.39/6.62 tff(4489,plain,
% 6.39/6.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))))),
% 6.39/6.62 inference(monotonicity,[status(thm)],[4488])).
% 6.39/6.62 tff(4490,plain,
% 6.39/6.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 6.39/6.62 inference(transitivity,[status(thm)],[4489, 4487])).
% 6.39/6.62 tff(4491,plain,
% 6.39/6.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 6.39/6.62 inference(quant_inst,[status(thm)],[])).
% 6.39/6.62 tff(4492,plain,
% 6.39/6.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))),
% 6.39/6.62 inference(modus_ponens,[status(thm)],[4491, 4490])).
% 6.39/6.62 tff(4493,plain,
% 6.39/6.62 ($false),
% 6.39/6.62 inference(unit_resolution,[status(thm)],[4492, 194, 233, 327, 1064, 1378])).
% 6.39/6.62 tff(4494,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)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.62 tff(4495,plain,
% 6.39/6.62 (~r(elem!1, s(s(elem!1)))),
% 6.39/6.62 inference(unit_resolution,[status(thm)],[4494, 327, 4486, 1378])).
% 6.39/6.62 tff(4496,plain,
% 6.39/6.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.39/6.62 inference(rewrite,[status(thm)],[])).
% 6.39/6.62 tff(4497,plain,
% 6.39/6.62 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.39/6.62 inference(rewrite,[status(thm)],[])).
% 6.39/6.62 tff(4498,plain,
% 6.39/6.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 6.39/6.62 inference(monotonicity,[status(thm)],[4497])).
% 6.39/6.62 tff(4499,plain,
% 6.39/6.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.39/6.62 inference(transitivity,[status(thm)],[4498, 4496])).
% 6.39/6.62 tff(4500,plain,
% 6.39/6.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 6.39/6.62 inference(quant_inst,[status(thm)],[])).
% 6.39/6.62 tff(4501,plain,
% 6.39/6.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 6.39/6.62 inference(modus_ponens,[status(thm)],[4500, 4499])).
% 6.39/6.62 tff(4502,plain,
% 6.39/6.62 (~r(s(s(elem!1)), z)),
% 6.39/6.62 inference(unit_resolution,[status(thm)],[4501, 194, 174, 184, 1378])).
% 6.39/6.62 tff(4503,plain,
% 6.39/6.62 (b(s(s(elem!1)), z)),
% 6.39/6.62 inference(unit_resolution,[status(thm)],[2629, 4502])).
% 6.39/6.62 tff(4504,plain,
% 6.39/6.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.39/6.62 inference(rewrite,[status(thm)],[])).
% 6.39/6.62 tff(4505,plain,
% 6.39/6.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.39/6.62 inference(quant_inst,[status(thm)],[])).
% 6.39/6.62 tff(4506,plain,
% 6.39/6.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 6.39/6.63 inference(modus_ponens,[status(thm)],[4505, 4504])).
% 6.39/6.63 tff(4507,plain,
% 6.39/6.63 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[4506, 391, 381, 3927, 4503, 3971])).
% 6.39/6.63 tff(4508,plain,
% 6.39/6.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.39/6.63 inference(rewrite,[status(thm)],[])).
% 6.39/6.63 tff(4509,plain,
% 6.39/6.63 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.39/6.63 inference(rewrite,[status(thm)],[])).
% 6.39/6.63 tff(4510,plain,
% 6.39/6.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 6.39/6.63 inference(monotonicity,[status(thm)],[4509])).
% 6.39/6.63 tff(4511,plain,
% 6.39/6.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.39/6.63 inference(transitivity,[status(thm)],[4510, 4508])).
% 6.39/6.63 tff(4512,plain,
% 6.39/6.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.39/6.63 inference(quant_inst,[status(thm)],[])).
% 6.39/6.63 tff(4513,plain,
% 6.39/6.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 6.39/6.63 inference(modus_ponens,[status(thm)],[4512, 4511])).
% 6.39/6.63 tff(4514,plain,
% 6.39/6.63 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[4513, 391, 381, 3927, 4503, 3971])).
% 6.39/6.63 tff(4515,plain,
% 6.39/6.63 (~r(elem!1, z)),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[1489, 1484, 184, 182])).
% 6.39/6.63 tff(4516,plain,
% 6.39/6.63 (b(elem!1, z)),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[526, 4515, 2])).
% 6.39/6.63 tff(4517,plain,
% 6.39/6.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 6.39/6.63 inference(rewrite,[status(thm)],[])).
% 6.39/6.63 tff(4518,plain,
% 6.39/6.63 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 6.39/6.63 inference(rewrite,[status(thm)],[])).
% 6.39/6.63 tff(4519,plain,
% 6.39/6.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))))),
% 6.39/6.63 inference(monotonicity,[status(thm)],[4518])).
% 6.39/6.63 tff(4520,plain,
% 6.39/6.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 6.39/6.63 inference(transitivity,[status(thm)],[4519, 4517])).
% 6.39/6.63 tff(4521,plain,
% 6.39/6.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 6.39/6.63 inference(quant_inst,[status(thm)],[])).
% 6.39/6.63 tff(4522,plain,
% 6.39/6.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))),
% 6.39/6.63 inference(modus_ponens,[status(thm)],[4521, 4520])).
% 6.39/6.63 tff(4523,plain,
% 6.39/6.63 (~b(elem!1, s(s(elem!1)))),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[4522, 391, 133, 4516, 2641])).
% 6.39/6.63 tff(4524,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 6.39/6.63 tff(4525,plain,
% 6.39/6.63 (r(elem!1, s(s(elem!1)))),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[1307, 1293, 4524])).
% 6.39/6.63 tff(4526,plain,
% 6.39/6.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(elem!1, s(s(elem!1)))))),
% 6.39/6.63 inference(rewrite,[status(thm)],[])).
% 6.39/6.63 tff(4527,plain,
% 6.39/6.63 (((~r(elem!1, 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)))))) <=> ((~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))))) | (~r(elem!1, s(s(elem!1)))))),
% 6.39/6.63 inference(rewrite,[status(thm)],[])).
% 6.39/6.63 tff(4528,plain,
% 6.39/6.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(elem!1, s(s(elem!1))))))),
% 6.39/6.63 inference(monotonicity,[status(thm)],[4527])).
% 6.39/6.63 tff(4529,plain,
% 6.39/6.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(elem!1, s(s(elem!1)))))),
% 6.39/6.63 inference(transitivity,[status(thm)],[4528, 4526])).
% 6.39/6.63 tff(4530,plain,
% 6.39/6.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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))))))),
% 6.39/6.63 inference(quant_inst,[status(thm)],[])).
% 6.39/6.63 tff(4531,plain,
% 6.39/6.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))),
% 6.39/6.63 inference(modus_ponens,[status(thm)],[4530, 4529])).
% 6.39/6.63 tff(4532,plain,
% 6.39/6.63 ($false),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[4531, 194, 233, 4345, 4525, 1378])).
% 6.39/6.63 tff(4533,plain,((s(s(elem!1)) = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(elem!1, s(s(elem!1))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.39/6.63 tff(4534,plain,
% 6.39/6.63 (s(s(elem!1)) = elem!1),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[4533, 4523, 1378, 233, 4017])).
% 6.39/6.63 tff(4535,plain,
% 6.39/6.63 (s(s(s(elem!1))) = s(elem!1)),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[451, 4534])).
% 6.39/6.63 tff(4536,plain,
% 6.39/6.63 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 6.39/6.63 inference(monotonicity,[status(thm)],[4535])).
% 6.39/6.63 tff(4537,plain,
% 6.39/6.63 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 6.39/6.63 inference(transitivity,[status(thm)],[4536, 2123])).
% 6.39/6.63 tff(4538,plain,
% 6.39/6.63 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 6.39/6.63 inference(monotonicity,[status(thm)],[4537])).
% 6.39/6.63 tff(4539,plain,
% 6.39/6.63 (~(s(elem!1) = s(s(s(s(z)))))),
% 6.39/6.63 inference(modus_ponens,[status(thm)],[3843, 4538])).
% 6.39/6.63 tff(4540,plain,
% 6.39/6.63 (~b(s(s(s(s(z)))), elem!1)),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[4086, 391, 133, 4516, 90])).
% 6.39/6.63 tff(4541,plain,
% 6.39/6.63 (~(s(s(s(s(z)))) = elem!1)),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[717, 4535])).
% 6.39/6.63 tff(4542,plain,
% 6.39/6.63 (r(s(s(s(s(z)))), elem!1)),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[762, 4541, 4540])).
% 6.39/6.63 tff(4543,plain,
% 6.39/6.63 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 6.39/6.63 inference(monotonicity,[status(thm)],[4535])).
% 6.39/6.63 tff(4544,plain,
% 6.39/6.63 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 6.39/6.63 inference(monotonicity,[status(thm)],[4534])).
% 6.39/6.63 tff(4545,plain,
% 6.39/6.63 (r(elem!1, s(s(s(elem!1))))),
% 6.39/6.63 inference(modus_ponens,[status(thm)],[1378, 4544])).
% 6.39/6.63 tff(4546,plain,
% 6.39/6.63 (r(elem!1, s(elem!1))),
% 6.39/6.63 inference(modus_ponens,[status(thm)],[4545, 4543])).
% 6.39/6.63 tff(4547,plain,
% 6.39/6.63 (r(s(elem!1), elem!1)),
% 6.39/6.63 inference(unit_resolution,[status(thm)],[472, 4535, 233])).
% 6.39/6.63 tff(4548,plain,
% 6.39/6.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(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)))))))),
% 6.39/6.63 inference(rewrite,[status(thm)],[])).
% 6.39/6.63 tff(4549,plain,
% 6.39/6.63 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(elem!1, s(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)))))))),
% 6.39/6.63 inference(rewrite,[status(thm)],[])).
% 6.39/6.63 tff(4550,plain,
% 6.39/6.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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))))))))),
% 6.39/6.63 inference(monotonicity,[status(thm)],[4549])).
% 6.39/6.63 tff(4551,plain,
% 6.39/6.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(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)))))))),
% 6.39/6.64 inference(transitivity,[status(thm)],[4550, 4548])).
% 6.39/6.64 tff(4552,plain,
% 6.39/6.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.39/6.64 inference(quant_inst,[status(thm)],[])).
% 6.39/6.64 tff(4553,plain,
% 6.39/6.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(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))))))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[4552, 4551])).
% 6.39/6.64 tff(4554,plain,
% 6.39/6.64 (~r(s(elem!1), s(s(s(s(z)))))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4553, 194, 4547, 4546, 4542])).
% 6.39/6.64 tff(4555,plain,
% 6.39/6.64 (b(s(elem!1), s(s(s(s(z)))))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[2142, 42, 4554, 4539])).
% 6.39/6.64 tff(4556,plain,
% 6.39/6.64 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 6.39/6.64 inference(monotonicity,[status(thm)],[4535])).
% 6.39/6.64 tff(4557,plain,
% 6.39/6.64 (b(s(elem!1), s(z))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[1526, 4556])).
% 6.39/6.64 tff(4558,plain,
% 6.39/6.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.39/6.64 inference(rewrite,[status(thm)],[])).
% 6.39/6.64 tff(4559,plain,
% 6.39/6.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.39/6.64 inference(quant_inst,[status(thm)],[])).
% 6.39/6.64 tff(4560,plain,
% 6.39/6.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[4559, 4558])).
% 6.39/6.64 tff(4561,plain,
% 6.39/6.64 (~r(s(s(s(s(z)))), s(z))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4560, 194, 4546, 1484, 4542])).
% 6.39/6.64 tff(4562,plain,
% 6.39/6.64 (b(s(s(s(s(z)))), s(z))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[749, 4561])).
% 6.39/6.64 tff(4563,plain,
% 6.39/6.64 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 6.39/6.64 inference(monotonicity,[status(thm)],[4535])).
% 6.39/6.64 tff(4564,plain,
% 6.39/6.64 (b(s(z), s(elem!1))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[379, 4563])).
% 6.39/6.64 tff(4565,plain,
% 6.39/6.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.39/6.64 inference(rewrite,[status(thm)],[])).
% 6.39/6.64 tff(4566,plain,
% 6.39/6.64 (((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.39/6.64 inference(rewrite,[status(thm)],[])).
% 6.39/6.64 tff(4567,plain,
% 6.39/6.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 6.39/6.64 inference(monotonicity,[status(thm)],[4566])).
% 6.39/6.64 tff(4568,plain,
% 6.39/6.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.39/6.64 inference(transitivity,[status(thm)],[4567, 4565])).
% 6.39/6.64 tff(4569,plain,
% 6.39/6.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.39/6.64 inference(quant_inst,[status(thm)],[])).
% 6.39/6.64 tff(4570,plain,
% 6.39/6.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[4569, 4568])).
% 6.39/6.64 tff(4571,plain,
% 6.39/6.64 ($false),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4570, 391, 4564, 4562, 4557, 4555])).
% 6.39/6.64 tff(4572,plain,((~r(s(z), elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | b(s(s(elem!1)), elem!1) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.64 tff(4573,plain,
% 6.39/6.64 (~r(s(z), elem!1)),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4572, 4017, 3943, 3949, 1378, 4486, 3951, 133, 3971, 4503, 2, 184, 182])).
% 6.39/6.64 tff(4574,plain,
% 6.39/6.64 (b(s(z), elem!1)),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[632, 4573, 3944])).
% 6.39/6.64 tff(4575,plain,
% 6.39/6.64 (~b(elem!1, s(s(s(elem!1))))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4026, 4574, 3943, 3949])).
% 6.39/6.64 tff(4576,plain,
% 6.39/6.64 (~r(s(s(elem!1)), elem!1)),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4039, 4575, 127, 168, 327])).
% 6.39/6.64 tff(4577,plain,
% 6.39/6.64 (s(s(elem!1)) = elem!1),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[872, 4576, 4017])).
% 6.39/6.64 tff(4578,plain,
% 6.39/6.64 (s(s(s(elem!1))) = s(elem!1)),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[451, 4577])).
% 6.39/6.64 tff(4579,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 6.39/6.64 tff(4580,plain,
% 6.39/6.64 (s(s(z)) = s(s(elem!1))),
% 6.39/6.64 inference(transitivity,[status(thm)],[4579, 261, 687, 211])).
% 6.39/6.64 tff(4581,plain,
% 6.39/6.64 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 6.39/6.64 inference(monotonicity,[status(thm)],[4580])).
% 6.39/6.64 tff(4582,plain,
% 6.39/6.64 (s(z) = s(elem!1)),
% 6.39/6.64 inference(transitivity,[status(thm)],[706, 4581, 259])).
% 6.39/6.64 tff(4583,plain,
% 6.39/6.64 ($false),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[121, 4582])).
% 6.39/6.64 tff(4584,plain,((~(s(s(z)) = elem!1)) | (s(z) = s(elem!1)) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.64 tff(4585,plain,
% 6.39/6.64 (~(s(s(z)) = elem!1)),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4584, 4578, 118])).
% 6.39/6.64 tff(4586,plain,
% 6.39/6.64 (b(elem!1, s(z))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[912, 4577, 381])).
% 6.39/6.64 tff(4587,plain,
% 6.39/6.64 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 6.39/6.64 inference(monotonicity,[status(thm)],[4578])).
% 6.39/6.64 tff(4588,plain,
% 6.39/6.64 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 6.39/6.64 inference(transitivity,[status(thm)],[4587, 2123])).
% 6.39/6.64 tff(4589,plain,
% 6.39/6.64 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 6.39/6.64 inference(monotonicity,[status(thm)],[4588])).
% 6.39/6.64 tff(4590,plain,
% 6.39/6.64 (~(s(elem!1) = s(s(s(s(z)))))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[3951, 4589])).
% 6.39/6.64 tff(4591,plain,
% 6.39/6.64 (~(s(s(s(s(z)))) = s(elem!1))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[4590, 2125])).
% 6.39/6.64 tff(4592,plain,
% 6.39/6.64 (~(s(s(s(s(z)))) = elem!1)),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[717, 4578])).
% 6.39/6.64 tff(4593,plain,
% 6.39/6.64 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 6.39/6.64 inference(monotonicity,[status(thm)],[4577])).
% 6.39/6.64 tff(4594,plain,
% 6.39/6.64 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 6.39/6.64 inference(monotonicity,[status(thm)],[4593])).
% 6.39/6.64 tff(4595,plain,
% 6.39/6.64 (~b(s(s(s(s(z)))), elem!1)),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[3478, 4594])).
% 6.39/6.64 tff(4596,plain,
% 6.39/6.64 (r(s(s(s(s(z)))), elem!1)),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[762, 4595, 4592])).
% 6.39/6.64 tff(4597,plain,
% 6.39/6.64 (~(s(elem!1) = elem!1)),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[158, 127])).
% 6.39/6.64 tff(4598,plain,
% 6.39/6.64 (~(elem!1 = s(elem!1))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[166, 4597])).
% 6.39/6.64 tff(4599,plain,
% 6.39/6.64 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 6.39/6.64 inference(monotonicity,[status(thm)],[465])).
% 6.39/6.64 tff(4600,plain,
% 6.39/6.64 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(elem!1))))),
% 6.39/6.64 inference(symmetry,[status(thm)],[4599])).
% 6.39/6.64 tff(4601,plain,
% 6.39/6.64 (b(elem!1, s(s(s(elem!1))))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[802, 4600])).
% 6.39/6.64 tff(4602,plain,
% 6.39/6.64 ($false),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4028, 4601])).
% 6.39/6.64 tff(4603,plain,((~(s(s(s(elem!1))) = s(elem!1))) | b(elem!1, s(s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.64 tff(4604,plain,
% 6.39/6.64 (~b(elem!1, s(elem!1))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4603, 4578, 4575])).
% 6.39/6.64 tff(4605,plain,
% 6.39/6.64 (r(elem!1, s(elem!1))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[443, 4604, 4598])).
% 6.39/6.64 tff(4606,plain,
% 6.39/6.64 (r(s(elem!1), elem!1)),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[472, 4578, 4486])).
% 6.39/6.64 tff(4607,plain,
% 6.39/6.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 6.39/6.64 inference(rewrite,[status(thm)],[])).
% 6.39/6.64 tff(4608,plain,
% 6.39/6.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 6.39/6.64 inference(quant_inst,[status(thm)],[])).
% 6.39/6.64 tff(4609,plain,
% 6.39/6.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[4608, 4607])).
% 6.39/6.64 tff(4610,plain,
% 6.39/6.64 (~r(s(s(s(s(z)))), s(elem!1))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4609, 194, 4606, 4605, 4596])).
% 6.39/6.64 tff(4611,plain,
% 6.39/6.64 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[2136, 42, 4610])).
% 6.39/6.64 tff(4612,plain,
% 6.39/6.64 (b(s(s(s(s(z)))), s(elem!1))),
% 6.39/6.64 inference(unit_resolution,[status(thm)],[4611, 4591])).
% 6.39/6.64 tff(4613,plain,
% 6.39/6.64 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 6.39/6.64 inference(monotonicity,[status(thm)],[4578])).
% 6.39/6.64 tff(4614,plain,
% 6.39/6.64 (b(s(elem!1), s(z))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[3943, 4613])).
% 6.39/6.64 tff(4615,plain,
% 6.39/6.64 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 6.39/6.64 inference(monotonicity,[status(thm)],[4578])).
% 6.39/6.64 tff(4616,plain,
% 6.39/6.64 (b(s(z), s(elem!1))),
% 6.39/6.64 inference(modus_ponens,[status(thm)],[3949, 4615])).
% 6.39/6.64 tff(4617,plain,
% 6.39/6.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.39/6.65 inference(rewrite,[status(thm)],[])).
% 6.39/6.65 tff(4618,plain,
% 6.39/6.65 (((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.39/6.65 inference(rewrite,[status(thm)],[])).
% 6.39/6.65 tff(4619,plain,
% 6.39/6.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 6.39/6.65 inference(monotonicity,[status(thm)],[4618])).
% 6.39/6.65 tff(4620,plain,
% 6.39/6.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.39/6.65 inference(transitivity,[status(thm)],[4619, 4617])).
% 6.39/6.65 tff(4621,plain,
% 6.39/6.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.39/6.65 inference(quant_inst,[status(thm)],[])).
% 6.39/6.65 tff(4622,plain,
% 6.39/6.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 6.39/6.65 inference(modus_ponens,[status(thm)],[4621, 4620])).
% 6.39/6.65 tff(4623,plain,
% 6.39/6.65 (~b(s(z), s(s(s(s(z)))))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[4622, 391, 4574, 4616, 4614, 4612])).
% 6.39/6.65 tff(4624,plain,
% 6.39/6.65 (r(s(z), s(s(s(s(z)))))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[1230, 4623])).
% 6.39/6.65 tff(4625,plain,
% 6.39/6.65 (~r(s(s(elem!1)), elem!1)),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[4039, 4027, 127, 168, 327])).
% 6.39/6.65 tff(4626,plain,
% 6.39/6.65 (s(s(elem!1)) = elem!1),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[872, 4625, 4017])).
% 6.39/6.65 tff(4627,plain,
% 6.39/6.65 (s(s(s(elem!1))) = s(elem!1)),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[451, 4626])).
% 6.39/6.65 tff(4628,plain,
% 6.39/6.65 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 6.39/6.65 inference(monotonicity,[status(thm)],[4627])).
% 6.39/6.65 tff(4629,plain,
% 6.39/6.65 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 6.39/6.65 inference(transitivity,[status(thm)],[4628, 2123])).
% 6.39/6.65 tff(4630,plain,
% 6.39/6.65 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 6.39/6.65 inference(monotonicity,[status(thm)],[4629])).
% 6.39/6.65 tff(4631,plain,
% 6.39/6.65 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[2849, 4018])).
% 6.39/6.65 tff(4632,plain,
% 6.39/6.65 (~(s(elem!1) = s(s(s(s(z)))))),
% 6.39/6.65 inference(modus_ponens,[status(thm)],[4631, 4630])).
% 6.39/6.65 tff(4633,plain,
% 6.39/6.65 (~(s(s(s(s(z)))) = elem!1)),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[717, 4627])).
% 6.39/6.65 tff(4634,plain,
% 6.39/6.65 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 6.39/6.65 inference(monotonicity,[status(thm)],[4626])).
% 6.39/6.65 tff(4635,plain,
% 6.39/6.65 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 6.39/6.65 inference(monotonicity,[status(thm)],[4634])).
% 6.39/6.65 tff(4636,plain,
% 6.39/6.65 (~b(s(s(s(s(z)))), elem!1)),
% 6.39/6.65 inference(modus_ponens,[status(thm)],[3478, 4635])).
% 6.39/6.65 tff(4637,plain,
% 6.39/6.65 (r(s(s(s(s(z)))), elem!1)),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[762, 4636, 4633])).
% 6.39/6.65 tff(4638,plain,
% 6.39/6.65 (~b(elem!1, s(elem!1))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[4603, 4627, 4027])).
% 6.39/6.65 tff(4639,plain,
% 6.39/6.65 (r(elem!1, s(elem!1))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[443, 4638, 4598])).
% 6.39/6.65 tff(4640,plain,
% 6.39/6.65 (r(s(elem!1), elem!1)),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[472, 4627, 4486])).
% 6.39/6.65 tff(4641,plain,
% 6.39/6.65 (~r(s(elem!1), s(s(s(s(z)))))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[4553, 194, 4640, 4639, 4637])).
% 6.39/6.65 tff(4642,plain,
% 6.39/6.65 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 6.39/6.65 inference(monotonicity,[status(thm)],[4627])).
% 6.39/6.65 tff(4643,plain,
% 6.39/6.65 (b(s(elem!1), s(z))),
% 6.39/6.65 inference(modus_ponens,[status(thm)],[1526, 4642])).
% 6.39/6.65 tff(4644,plain,
% 6.39/6.65 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 6.39/6.65 inference(monotonicity,[status(thm)],[4626])).
% 6.39/6.65 tff(4645,plain,
% 6.39/6.65 (b(elem!1, z)),
% 6.39/6.65 inference(modus_ponens,[status(thm)],[2641, 4644])).
% 6.39/6.65 tff(4646,plain,
% 6.39/6.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 6.39/6.65 inference(rewrite,[status(thm)],[])).
% 6.39/6.65 tff(4647,plain,
% 6.39/6.65 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 6.39/6.65 inference(rewrite,[status(thm)],[])).
% 6.39/6.65 tff(4648,plain,
% 6.39/6.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1))))),
% 6.39/6.65 inference(monotonicity,[status(thm)],[4647])).
% 6.39/6.65 tff(4649,plain,
% 6.39/6.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 6.39/6.65 inference(transitivity,[status(thm)],[4648, 4646])).
% 6.39/6.65 tff(4650,plain,
% 6.39/6.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 6.39/6.65 inference(quant_inst,[status(thm)],[])).
% 6.39/6.65 tff(4651,plain,
% 6.39/6.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1))),
% 6.39/6.65 inference(modus_ponens,[status(thm)],[4650, 4649])).
% 6.39/6.65 tff(4652,plain,
% 6.39/6.65 (~b(z, s(z))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[4651, 391, 133, 4645, 644])).
% 6.39/6.65 tff(4653,plain,
% 6.39/6.65 (r(z, s(z))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[678, 4652])).
% 6.39/6.65 tff(4654,plain,
% 6.39/6.65 (~r(s(s(s(s(z)))), s(z))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[731, 4653, 182, 719])).
% 6.39/6.65 tff(4655,plain,
% 6.39/6.65 (b(s(s(s(s(z)))), s(z))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[749, 4654])).
% 6.39/6.65 tff(4656,plain,
% 6.39/6.65 (~r(s(z), s(s(s(s(z)))))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[2720, 4637, 182, 719])).
% 6.39/6.65 tff(4657,plain,
% 6.39/6.65 (b(s(z), s(s(s(s(z)))))),
% 6.39/6.65 inference(unit_resolution,[status(thm)],[1230, 4656])).
% 6.39/6.65 tff(4658,plain,
% 6.39/6.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.39/6.66 inference(rewrite,[status(thm)],[])).
% 6.39/6.66 tff(4659,plain,
% 6.39/6.66 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.39/6.66 inference(rewrite,[status(thm)],[])).
% 6.39/6.66 tff(4660,plain,
% 6.39/6.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 6.39/6.66 inference(monotonicity,[status(thm)],[4659])).
% 6.39/6.66 tff(4661,plain,
% 6.39/6.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.39/6.66 inference(transitivity,[status(thm)],[4660, 4658])).
% 6.39/6.66 tff(4662,plain,
% 6.39/6.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.39/6.66 inference(quant_inst,[status(thm)],[])).
% 6.39/6.66 tff(4663,plain,
% 6.39/6.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 6.39/6.66 inference(modus_ponens,[status(thm)],[4662, 4661])).
% 6.39/6.66 tff(4664,plain,
% 6.39/6.66 (~b(s(elem!1), s(s(s(s(z)))))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[4663, 391, 90, 4657, 4655, 4643])).
% 6.39/6.66 tff(4665,plain,
% 6.39/6.66 ($false),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[2142, 42, 4664, 4641, 4632])).
% 6.39/6.66 tff(4666,plain,((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(z)))), s(s(elem!1))) | (~b(s(s(elem!1)), z)) | b(s(s(elem!1)), elem!1) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.66 tff(4667,plain,
% 6.39/6.66 (~r(z, s(s(s(s(z)))))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[4666, 4574, 182, 3971, 133, 3943, 3478, 4503, 4017, 127, 168, 327, 3949])).
% 6.39/6.66 tff(4668,plain,
% 6.39/6.66 (b(z, s(s(s(s(z)))))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[800, 4667])).
% 6.39/6.66 tff(4669,plain,
% 6.39/6.66 (~r(s(elem!1), s(s(s(s(z)))))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[4553, 194, 4606, 4605, 4596])).
% 6.39/6.66 tff(4670,plain,
% 6.39/6.66 (b(s(elem!1), s(s(s(s(z)))))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[2142, 42, 4669, 4590])).
% 6.39/6.66 tff(4671,plain,
% 6.39/6.66 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 6.39/6.66 inference(monotonicity,[status(thm)],[4578])).
% 6.39/6.66 tff(4672,plain,
% 6.39/6.66 (r(z, s(elem!1))),
% 6.39/6.66 inference(modus_ponens,[status(thm)],[184, 4671])).
% 6.39/6.66 tff(4673,plain,
% 6.39/6.66 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 6.39/6.66 inference(monotonicity,[status(thm)],[4578])).
% 6.39/6.66 tff(4674,plain,
% 6.39/6.66 (r(s(elem!1), z)),
% 6.39/6.66 inference(modus_ponens,[status(thm)],[174, 4673])).
% 6.39/6.66 tff(4675,plain,
% 6.39/6.66 (~(s(s(z)) = s(elem!1))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[2493, 4578])).
% 6.39/6.66 tff(4676,plain,
% 6.39/6.66 (~b(s(s(z)), z)),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[4472, 3823, 1686, 90])).
% 6.39/6.66 tff(4677,plain,
% 6.39/6.66 (r(s(s(z)), z)),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[1211, 4676])).
% 6.39/6.66 tff(4678,plain,
% 6.39/6.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 6.39/6.66 inference(rewrite,[status(thm)],[])).
% 6.39/6.66 tff(4679,plain,
% 6.39/6.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 6.39/6.66 inference(quant_inst,[status(thm)],[])).
% 6.39/6.66 tff(4680,plain,
% 6.39/6.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1)))),
% 6.39/6.66 inference(modus_ponens,[status(thm)],[4679, 4678])).
% 6.39/6.66 tff(4681,plain,
% 6.39/6.66 (~r(s(s(z)), s(elem!1))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[4680, 194, 1628, 2144, 4677])).
% 6.39/6.66 tff(4682,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 6.39/6.66 tff(4683,plain,
% 6.39/6.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.39/6.66 inference(rewrite,[status(thm)],[])).
% 6.39/6.66 tff(4684,plain,
% 6.39/6.66 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.39/6.66 inference(rewrite,[status(thm)],[])).
% 6.39/6.66 tff(4685,plain,
% 6.39/6.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))))),
% 6.39/6.66 inference(monotonicity,[status(thm)],[4684])).
% 6.39/6.66 tff(4686,plain,
% 6.39/6.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.39/6.66 inference(transitivity,[status(thm)],[4685, 4683])).
% 6.39/6.66 tff(4687,plain,
% 6.39/6.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.39/6.66 inference(quant_inst,[status(thm)],[])).
% 6.39/6.66 tff(4688,plain,
% 6.39/6.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))),
% 6.39/6.66 inference(modus_ponens,[status(thm)],[4687, 4686])).
% 6.39/6.66 tff(4689,plain,
% 6.39/6.66 (~b(s(s(z)), s(elem!1))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[4688, 391, 133, 3823, 90, 4682])).
% 6.39/6.66 tff(4690,assumption,(~(s(s(z)) = s(elem!1))), introduced(assumption)).
% 6.39/6.66 tff(4691,plain,
% 6.39/6.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 6.39/6.66 inference(rewrite,[status(thm)],[])).
% 6.39/6.66 tff(4692,plain,
% 6.39/6.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 6.39/6.66 inference(quant_inst,[status(thm)],[])).
% 6.39/6.66 tff(4693,plain,
% 6.39/6.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 6.39/6.66 inference(modus_ponens,[status(thm)],[4692, 4691])).
% 6.39/6.66 tff(4694,plain,
% 6.39/6.66 ($false),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[4693, 42, 4690, 4689, 4681])).
% 6.39/6.66 tff(4695,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = s(elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.66 tff(4696,plain,
% 6.39/6.66 (~b(s(s(z)), s(s(s(s(z)))))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[4695, 4675, 4674, 4672, 133, 3971, 4670, 4668])).
% 6.39/6.66 tff(4697,plain,
% 6.39/6.66 (r(s(s(z)), s(s(s(s(z)))))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[3652, 4696])).
% 6.39/6.66 tff(4698,plain,
% 6.39/6.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 6.39/6.66 inference(rewrite,[status(thm)],[])).
% 6.39/6.66 tff(4699,plain,
% 6.39/6.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 6.39/6.66 inference(quant_inst,[status(thm)],[])).
% 6.39/6.66 tff(4700,plain,
% 6.39/6.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))),
% 6.39/6.66 inference(modus_ponens,[status(thm)],[4699, 4698])).
% 6.39/6.66 tff(4701,plain,
% 6.39/6.66 ($false),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[4700, 194, 1749, 2112, 1216, 2405])).
% 6.39/6.66 tff(4702,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.66 tff(4703,plain,
% 6.39/6.66 (~r(s(s(z)), s(z))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[4702, 4697, 4596, 4624])).
% 6.39/6.66 tff(4704,plain,
% 6.39/6.66 (b(s(s(z)), s(z))),
% 6.39/6.66 inference(unit_resolution,[status(thm)],[3778, 4703])).
% 6.39/6.66 tff(4705,plain,
% 6.39/6.66 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 6.39/6.66 inference(monotonicity,[status(thm)],[4577])).
% 6.39/6.66 tff(4706,plain,
% 6.39/6.66 (b(elem!1, z)),
% 6.39/6.66 inference(modus_ponens,[status(thm)],[4503, 4705])).
% 6.39/6.66 tff(4707,plain,
% 6.39/6.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 6.39/6.66 inference(rewrite,[status(thm)],[])).
% 6.39/6.67 tff(4708,plain,
% 6.39/6.67 (((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 6.39/6.67 inference(rewrite,[status(thm)],[])).
% 6.39/6.67 tff(4709,plain,
% 6.39/6.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 6.39/6.67 inference(monotonicity,[status(thm)],[4708])).
% 6.39/6.67 tff(4710,plain,
% 6.39/6.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 6.39/6.67 inference(transitivity,[status(thm)],[4709, 4707])).
% 6.39/6.67 tff(4711,plain,
% 6.39/6.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 6.39/6.67 inference(quant_inst,[status(thm)],[])).
% 6.39/6.67 tff(4712,plain,
% 6.39/6.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 6.39/6.67 inference(modus_ponens,[status(thm)],[4711, 4710])).
% 6.39/6.67 tff(4713,plain,
% 6.39/6.67 (~b(s(s(z)), elem!1)),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[4712, 391, 4706, 4574, 4704, 4586])).
% 6.39/6.67 tff(4714,plain,
% 6.39/6.67 (~(elem!1 = s(s(s(s(z)))))),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[769, 4592])).
% 6.39/6.67 tff(4715,plain,
% 6.39/6.67 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 6.39/6.67 inference(monotonicity,[status(thm)],[4577])).
% 6.39/6.67 tff(4716,plain,
% 6.39/6.67 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 6.39/6.67 inference(monotonicity,[status(thm)],[4715])).
% 6.39/6.67 tff(4717,assumption,(~b(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 6.39/6.67 tff(4718,plain,
% 6.39/6.67 (~b(elem!1, s(s(s(s(z)))))),
% 6.39/6.67 inference(modus_ponens,[status(thm)],[4717, 4716])).
% 6.39/6.67 tff(4719,plain,
% 6.39/6.67 (r(elem!1, s(s(s(s(z)))))),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[781, 4718, 4714])).
% 6.39/6.67 tff(4720,plain,
% 6.39/6.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 6.39/6.67 inference(rewrite,[status(thm)],[])).
% 6.39/6.67 tff(4721,plain,
% 6.39/6.67 (((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 6.39/6.67 inference(rewrite,[status(thm)],[])).
% 6.39/6.67 tff(4722,plain,
% 6.39/6.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))))),
% 6.39/6.67 inference(monotonicity,[status(thm)],[4721])).
% 6.39/6.67 tff(4723,plain,
% 6.39/6.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 6.39/6.67 inference(transitivity,[status(thm)],[4722, 4720])).
% 6.39/6.67 tff(4724,plain,
% 6.39/6.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 6.39/6.67 inference(quant_inst,[status(thm)],[])).
% 6.39/6.67 tff(4725,plain,
% 6.39/6.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))),
% 6.39/6.67 inference(modus_ponens,[status(thm)],[4724, 4723])).
% 6.39/6.67 tff(4726,plain,
% 6.39/6.67 (~r(s(s(z)), elem!1)),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[4725, 194, 4697, 4719, 4596])).
% 6.39/6.67 tff(4727,plain,
% 6.39/6.67 (((~![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))),
% 6.39/6.67 inference(rewrite,[status(thm)],[])).
% 6.39/6.67 tff(4728,plain,
% 6.39/6.67 ((~![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))),
% 6.39/6.67 inference(quant_inst,[status(thm)],[])).
% 6.39/6.67 tff(4729,plain,
% 6.39/6.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 6.39/6.67 inference(modus_ponens,[status(thm)],[4728, 4727])).
% 6.39/6.67 tff(4730,plain,
% 6.39/6.67 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[4729, 42])).
% 6.39/6.67 tff(4731,plain,
% 6.39/6.67 ($false),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[4730, 4726, 4713, 4585])).
% 6.39/6.67 tff(4732,plain,(b(s(s(elem!1)), elem!1) | (~b(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | b(s(s(elem!1)), s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 6.39/6.67 tff(4733,plain,
% 6.39/6.67 (b(s(s(elem!1)), elem!1)),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[4732, 149, 184, 174, 4514, 4507, 381, 127, 168, 327, 182, 1378, 2])).
% 6.39/6.67 tff(4734,plain,
% 6.39/6.67 (~b(elem!1, s(s(elem!1)))),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[3979, 4733, 3927, 149])).
% 6.39/6.67 tff(4735,plain,
% 6.39/6.67 (elem!1 = s(s(elem!1))),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[1307, 4734, 4495])).
% 6.39/6.67 tff(4736,plain,
% 6.39/6.67 (s(s(elem!1)) = elem!1),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[1292, 4735])).
% 6.39/6.67 tff(4737,plain,
% 6.39/6.67 (b(s(s(elem!1)), elem!1) <=> b(elem!1, elem!1)),
% 6.39/6.67 inference(monotonicity,[status(thm)],[4736])).
% 6.39/6.67 tff(4738,plain,
% 6.39/6.67 (b(elem!1, elem!1) <=> b(s(s(elem!1)), elem!1)),
% 6.39/6.67 inference(symmetry,[status(thm)],[4737])).
% 6.39/6.67 tff(4739,plain,
% 6.39/6.67 ((~b(elem!1, elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 6.39/6.67 inference(monotonicity,[status(thm)],[4738])).
% 6.39/6.67 tff(4740,plain,
% 6.39/6.67 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 6.39/6.67 inference(quant_inst,[status(thm)],[])).
% 6.39/6.67 tff(4741,plain,
% 6.39/6.67 (~b(elem!1, elem!1)),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[4740, 461])).
% 6.39/6.67 tff(4742,plain,
% 6.39/6.67 (~b(s(s(elem!1)), elem!1)),
% 6.39/6.67 inference(modus_ponens,[status(thm)],[4741, 4739])).
% 6.39/6.67 tff(4743,plain,
% 6.39/6.67 ($false),
% 6.39/6.67 inference(unit_resolution,[status(thm)],[4733, 4742])).
% 6.39/6.67 tff(4744,plain,((elem!1 = z) | (~b(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.39/6.68 tff(4745,plain,
% 6.39/6.68 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[4744, 4485, 2, 184, 174, 127, 168, 3927, 181, 327, 80])).
% 6.39/6.68 tff(4746,plain,
% 6.39/6.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[1356, 4745, 270])).
% 6.39/6.68 tff(4747,plain,
% 6.39/6.68 (~r(s(s(s(elem!1))), s(z))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[202, 181, 184, 174])).
% 6.39/6.68 tff(4748,plain,
% 6.39/6.68 (b(s(s(s(elem!1))), s(z))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[223, 4747])).
% 6.39/6.68 tff(4749,plain,
% 6.39/6.68 (~r(s(z), s(s(s(elem!1))))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[241, 181, 184, 4486])).
% 6.39/6.68 tff(4750,plain,
% 6.39/6.68 (b(s(z), s(s(s(elem!1))))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[247, 4749])).
% 6.39/6.68 tff(4751,plain,
% 6.39/6.68 ($false),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[1346, 391, 4485, 4750, 4748, 4746])).
% 6.39/6.68 tff(4752,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~b(z, s(s(elem!1)))) | r(z, elem!1) | b(s(z), z) | (elem!1 = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.68 tff(4753,plain,
% 6.39/6.68 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[4752, 3926, 2, 59, 174, 151, 168, 3925, 80, 91, 148, 308])).
% 6.39/6.68 tff(4754,plain,
% 6.39/6.68 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[1370, 4753, 288])).
% 6.39/6.68 tff(4755,plain,
% 6.39/6.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.39/6.68 inference(rewrite,[status(thm)],[])).
% 6.39/6.68 tff(4756,plain,
% 6.39/6.68 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(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))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.39/6.68 inference(rewrite,[status(thm)],[])).
% 6.39/6.68 tff(4757,plain,
% 6.39/6.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.39/6.68 inference(monotonicity,[status(thm)],[4756])).
% 6.39/6.68 tff(4758,plain,
% 6.39/6.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.39/6.68 inference(transitivity,[status(thm)],[4757, 4755])).
% 6.39/6.68 tff(4759,plain,
% 6.39/6.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(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)))))),
% 6.39/6.68 inference(quant_inst,[status(thm)],[])).
% 6.39/6.68 tff(4760,plain,
% 6.39/6.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.39/6.68 inference(modus_ponens,[status(thm)],[4759, 4758])).
% 6.39/6.68 tff(4761,plain,
% 6.39/6.68 ($false),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[4760, 391, 381, 1374, 379, 1526])).
% 6.39/6.68 tff(4762,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.68 tff(4763,plain,
% 6.39/6.68 (~b(s(s(elem!1)), s(z))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[4762, 4754, 248, 224])).
% 6.39/6.68 tff(4764,plain,
% 6.39/6.68 (r(s(s(elem!1)), s(z))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[362, 4763])).
% 6.39/6.68 tff(4765,plain,
% 6.39/6.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 6.39/6.68 inference(rewrite,[status(thm)],[])).
% 6.39/6.68 tff(4766,plain,
% 6.39/6.68 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 6.39/6.68 inference(rewrite,[status(thm)],[])).
% 6.39/6.68 tff(4767,plain,
% 6.39/6.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 6.39/6.68 inference(monotonicity,[status(thm)],[4766])).
% 6.39/6.68 tff(4768,plain,
% 6.39/6.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 6.39/6.68 inference(transitivity,[status(thm)],[4767, 4765])).
% 6.39/6.68 tff(4769,plain,
% 6.39/6.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 6.39/6.68 inference(quant_inst,[status(thm)],[])).
% 6.39/6.68 tff(4770,plain,
% 6.39/6.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 6.39/6.68 inference(modus_ponens,[status(thm)],[4769, 4768])).
% 6.39/6.68 tff(4771,plain,
% 6.39/6.68 ($false),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[4770, 194, 530, 233, 184, 410])).
% 6.39/6.68 tff(4772,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.68 tff(4773,plain,
% 6.39/6.68 (~r(elem!1, s(s(s(elem!1))))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[4772, 530, 233, 59])).
% 6.39/6.68 tff(4774,plain,
% 6.39/6.68 (b(elem!1, s(s(s(elem!1))))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[424, 4773, 1])).
% 6.39/6.68 tff(4775,plain,
% 6.39/6.68 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 6.39/6.68 inference(monotonicity,[status(thm)],[479])).
% 6.39/6.68 tff(4776,plain,
% 6.39/6.68 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 6.39/6.68 inference(symmetry,[status(thm)],[4775])).
% 6.39/6.68 tff(4777,plain,
% 6.39/6.68 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 6.39/6.68 inference(monotonicity,[status(thm)],[452])).
% 6.39/6.68 tff(4778,plain,
% 6.39/6.68 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 6.39/6.68 inference(symmetry,[status(thm)],[4777])).
% 6.39/6.68 tff(4779,plain,
% 6.39/6.68 ((~b(s(elem!1), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 6.39/6.68 inference(monotonicity,[status(thm)],[4778])).
% 6.39/6.68 tff(4780,plain,
% 6.39/6.68 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 6.39/6.68 inference(monotonicity,[status(thm)],[445])).
% 6.39/6.68 tff(4781,plain,
% 6.39/6.68 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 6.39/6.68 inference(symmetry,[status(thm)],[4780])).
% 6.39/6.68 tff(4782,plain,
% 6.39/6.68 (r(s(s(elem!1)), z)),
% 6.39/6.68 inference(modus_ponens,[status(thm)],[530, 4781])).
% 6.39/6.68 tff(4783,plain,
% 6.39/6.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)))),
% 6.39/6.68 inference(rewrite,[status(thm)],[])).
% 6.39/6.68 tff(4784,plain,
% 6.39/6.68 (((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)))),
% 6.39/6.68 inference(rewrite,[status(thm)],[])).
% 6.39/6.68 tff(4785,plain,
% 6.39/6.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z))))),
% 6.39/6.68 inference(monotonicity,[status(thm)],[4784])).
% 6.39/6.68 tff(4786,plain,
% 6.39/6.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)))),
% 6.39/6.68 inference(transitivity,[status(thm)],[4785, 4783])).
% 6.39/6.68 tff(4787,plain,
% 6.39/6.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 6.39/6.68 inference(quant_inst,[status(thm)],[])).
% 6.39/6.68 tff(4788,plain,
% 6.39/6.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z))),
% 6.39/6.68 inference(modus_ponens,[status(thm)],[4787, 4786])).
% 6.39/6.68 tff(4789,plain,
% 6.39/6.68 ($false),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[4788, 194, 530, 174, 233, 184])).
% 6.39/6.68 tff(4790,plain,((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.68 tff(4791,plain,
% 6.39/6.68 (~r(s(s(s(elem!1))), z)),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[4790, 530, 233, 184])).
% 6.39/6.68 tff(4792,plain,
% 6.39/6.68 (b(s(s(s(elem!1))), z)),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[377, 4791])).
% 6.39/6.68 tff(4793,plain,
% 6.39/6.68 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 6.39/6.68 inference(monotonicity,[status(thm)],[445])).
% 6.39/6.68 tff(4794,plain,
% 6.39/6.68 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.39/6.68 inference(symmetry,[status(thm)],[4793])).
% 6.39/6.68 tff(4795,plain,
% 6.39/6.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.39/6.68 inference(modus_ponens,[status(thm)],[448, 4794])).
% 6.39/6.68 tff(4796,plain,
% 6.39/6.68 (~r(s(z), s(s(s(elem!1))))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[241, 182, 184, 233])).
% 6.39/6.68 tff(4797,plain,
% 6.39/6.68 (b(s(z), s(s(s(elem!1))))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[247, 4796])).
% 6.39/6.68 tff(4798,plain,
% 6.39/6.68 (~r(s(s(elem!1)), s(z))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[2621, 182, 2616, 2144])).
% 6.39/6.68 tff(4799,plain,
% 6.39/6.68 (b(s(s(elem!1)), s(z))),
% 6.39/6.68 inference(unit_resolution,[status(thm)],[362, 4798])).
% 6.39/6.69 tff(4800,plain,
% 6.39/6.69 ($false),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[399, 4799, 4797, 133, 380, 328])).
% 6.39/6.69 tff(4801,plain,((~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.69 tff(4802,plain,
% 6.39/6.69 (~r(s(z), z)),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[4801, 4795, 4792, 133, 4782, 4330, 184, 233])).
% 6.39/6.69 tff(4803,plain,
% 6.39/6.69 (b(s(z), z)),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[180, 4802])).
% 6.39/6.69 tff(4804,plain,
% 6.39/6.69 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 6.39/6.69 inference(monotonicity,[status(thm)],[452])).
% 6.39/6.69 tff(4805,plain,
% 6.39/6.69 (b(elem!1, s(elem!1))),
% 6.39/6.69 inference(modus_ponens,[status(thm)],[448, 4804])).
% 6.39/6.69 tff(4806,plain,
% 6.39/6.69 (b(s(elem!1), z)),
% 6.39/6.69 inference(modus_ponens,[status(thm)],[4792, 682])).
% 6.39/6.69 tff(4807,plain,
% 6.39/6.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 6.39/6.69 inference(rewrite,[status(thm)],[])).
% 6.39/6.69 tff(4808,plain,
% 6.39/6.69 (((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 6.39/6.69 inference(rewrite,[status(thm)],[])).
% 6.39/6.69 tff(4809,plain,
% 6.39/6.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 6.39/6.69 inference(monotonicity,[status(thm)],[4808])).
% 6.39/6.69 tff(4810,plain,
% 6.39/6.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 6.39/6.69 inference(transitivity,[status(thm)],[4809, 4807])).
% 6.39/6.69 tff(4811,plain,
% 6.39/6.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 6.39/6.69 inference(quant_inst,[status(thm)],[])).
% 6.39/6.69 tff(4812,plain,
% 6.39/6.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 6.39/6.69 inference(modus_ponens,[status(thm)],[4811, 4810])).
% 6.39/6.69 tff(4813,plain,
% 6.39/6.69 (~b(s(elem!1), s(z))),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[4812, 391, 133, 4806, 4805, 4803])).
% 6.39/6.69 tff(4814,plain,
% 6.39/6.69 (~b(s(s(s(elem!1))), s(z))),
% 6.39/6.69 inference(modus_ponens,[status(thm)],[4813, 4779])).
% 6.39/6.69 tff(4815,plain,
% 6.39/6.69 (r(s(s(s(elem!1))), s(z))),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[223, 4814])).
% 6.39/6.69 tff(4816,plain,
% 6.39/6.69 (r(s(elem!1), s(z))),
% 6.39/6.69 inference(modus_ponens,[status(thm)],[4815, 4776])).
% 6.39/6.69 tff(4817,plain,
% 6.39/6.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 6.39/6.69 inference(rewrite,[status(thm)],[])).
% 6.39/6.69 tff(4818,plain,
% 6.39/6.69 (((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 6.39/6.69 inference(rewrite,[status(thm)],[])).
% 6.39/6.69 tff(4819,plain,
% 6.39/6.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z))))),
% 6.39/6.69 inference(monotonicity,[status(thm)],[4818])).
% 6.39/6.69 tff(4820,plain,
% 6.39/6.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 6.39/6.69 inference(transitivity,[status(thm)],[4819, 4817])).
% 6.39/6.69 tff(4821,plain,
% 6.39/6.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 6.39/6.69 inference(quant_inst,[status(thm)],[])).
% 6.39/6.69 tff(4822,plain,
% 6.39/6.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z))),
% 6.39/6.69 inference(modus_ponens,[status(thm)],[4821, 4820])).
% 6.39/6.69 tff(4823,plain,
% 6.39/6.69 (~b(s(z), s(elem!1))),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[4822, 391, 133, 4806, 4805, 4803])).
% 6.39/6.69 tff(4824,plain,
% 6.39/6.69 (r(s(z), s(elem!1))),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[602, 42, 121, 4823])).
% 6.39/6.69 tff(4825,plain,
% 6.39/6.69 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), elem!1)),
% 6.39/6.69 inference(monotonicity,[status(thm)],[445])).
% 6.39/6.69 tff(4826,plain,
% 6.39/6.69 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.39/6.69 inference(symmetry,[status(thm)],[4825])).
% 6.39/6.69 tff(4827,plain,
% 6.39/6.69 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.39/6.69 inference(modus_ponens,[status(thm)],[233, 4826])).
% 6.39/6.69 tff(4828,plain,
% 6.39/6.69 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 6.39/6.69 inference(symmetry,[status(thm)],[680])).
% 6.39/6.69 tff(4829,plain,
% 6.39/6.69 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 6.39/6.69 inference(monotonicity,[status(thm)],[4828])).
% 6.39/6.69 tff(4830,plain,
% 6.39/6.69 (~b(s(z), s(s(s(elem!1))))),
% 6.39/6.69 inference(modus_ponens,[status(thm)],[4823, 4829])).
% 6.39/6.69 tff(4831,plain,
% 6.39/6.69 (r(s(z), s(s(s(elem!1))))),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[247, 4830])).
% 6.39/6.69 tff(4832,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 6.39/6.69 tff(4833,plain,
% 6.39/6.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 6.39/6.69 inference(rewrite,[status(thm)],[])).
% 6.39/6.69 tff(4834,plain,
% 6.39/6.69 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 6.39/6.69 inference(rewrite,[status(thm)],[])).
% 6.39/6.69 tff(4835,plain,
% 6.39/6.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))))),
% 6.39/6.69 inference(monotonicity,[status(thm)],[4834])).
% 6.39/6.69 tff(4836,plain,
% 6.39/6.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 6.39/6.69 inference(transitivity,[status(thm)],[4835, 4833])).
% 6.39/6.69 tff(4837,plain,
% 6.39/6.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 6.39/6.69 inference(quant_inst,[status(thm)],[])).
% 6.39/6.69 tff(4838,plain,
% 6.39/6.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))),
% 6.39/6.69 inference(modus_ponens,[status(thm)],[4837, 4836])).
% 6.39/6.69 tff(4839,plain,
% 6.39/6.69 ($false),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[4838, 194, 327, 232, 4832, 2616])).
% 6.39/6.69 tff(4840,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.69 tff(4841,plain,
% 6.39/6.69 (~r(s(z), s(s(elem!1)))),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[4840, 4831, 4827, 4782])).
% 6.39/6.69 tff(4842,plain,
% 6.39/6.69 (r(s(z), s(s(elem!1))) <=> r(s(z), elem!1)),
% 6.39/6.69 inference(monotonicity,[status(thm)],[445])).
% 6.39/6.69 tff(4843,plain,
% 6.39/6.69 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 6.39/6.69 inference(symmetry,[status(thm)],[4842])).
% 6.39/6.69 tff(4844,plain,
% 6.39/6.69 (r(s(z), s(s(elem!1)))),
% 6.39/6.69 inference(modus_ponens,[status(thm)],[1484, 4843])).
% 6.39/6.69 tff(4845,assumption,(~r(s(z), s(s(elem!1)))), introduced(assumption)).
% 6.39/6.69 tff(4846,plain,
% 6.39/6.69 ($false),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[4845, 4844])).
% 6.39/6.69 tff(4847,plain,((~r(s(z), elem!1)) | r(s(z), s(s(elem!1))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.39/6.69 tff(4848,plain,
% 6.39/6.69 (~r(s(z), elem!1)),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[4847, 4841, 445])).
% 6.39/6.69 tff(4849,plain,
% 6.39/6.69 (b(s(z), elem!1)),
% 6.39/6.69 inference(unit_resolution,[status(thm)],[632, 4848, 150])).
% 6.39/6.69 tff(4850,plain,
% 6.39/6.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.39/6.69 inference(rewrite,[status(thm)],[])).
% 6.39/6.69 tff(4851,plain,
% 6.39/6.69 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.39/6.69 inference(rewrite,[status(thm)],[])).
% 6.39/6.69 tff(4852,plain,
% 6.39/6.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 6.49/6.70 inference(monotonicity,[status(thm)],[4851])).
% 6.49/6.70 tff(4853,plain,
% 6.49/6.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.49/6.70 inference(transitivity,[status(thm)],[4852, 4850])).
% 6.49/6.70 tff(4854,plain,
% 6.49/6.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 6.49/6.70 inference(quant_inst,[status(thm)],[])).
% 6.49/6.70 tff(4855,plain,
% 6.49/6.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 6.49/6.70 inference(modus_ponens,[status(thm)],[4854, 4853])).
% 6.49/6.70 tff(4856,plain,
% 6.49/6.70 ($false),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[4855, 391, 133, 644, 590, 721])).
% 6.49/6.70 tff(4857,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.70 tff(4858,plain,
% 6.49/6.70 (~b(elem!1, s(z))),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[4857, 4849, 4803, 133])).
% 6.49/6.70 tff(4859,plain,
% 6.49/6.70 (r(elem!1, s(z))),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[837, 4858, 173])).
% 6.49/6.70 tff(4860,plain,
% 6.49/6.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 6.49/6.70 inference(rewrite,[status(thm)],[])).
% 6.49/6.70 tff(4861,plain,
% 6.49/6.70 (((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 6.49/6.70 inference(rewrite,[status(thm)],[])).
% 6.49/6.70 tff(4862,plain,
% 6.49/6.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z)))))),
% 6.49/6.70 inference(monotonicity,[status(thm)],[4861])).
% 6.49/6.70 tff(4863,plain,
% 6.49/6.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 6.49/6.70 inference(transitivity,[status(thm)],[4862, 4860])).
% 6.49/6.70 tff(4864,plain,
% 6.49/6.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 6.49/6.70 inference(quant_inst,[status(thm)],[])).
% 6.49/6.70 tff(4865,plain,
% 6.49/6.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z)))),
% 6.49/6.70 inference(modus_ponens,[status(thm)],[4864, 4863])).
% 6.49/6.70 tff(4866,plain,
% 6.49/6.70 ($false),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[4865, 194, 473, 4859, 4824, 4816])).
% 6.49/6.70 tff(4867,plain,((~(s(s(elem!1)) = elem!1)) | (~b(z, elem!1)) | (s(z) = elem!1) | (s(z) = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.70 tff(4868,plain,
% 6.49/6.70 (~(s(s(elem!1)) = elem!1)),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[4867, 4774, 150, 121, 59, 233, 133, 530])).
% 6.49/6.70 tff(4869,plain,
% 6.49/6.70 (~(s(s(elem!1)) = s(elem!1))),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[264, 4868])).
% 6.49/6.70 tff(4870,plain,
% 6.49/6.70 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[287, 4869])).
% 6.49/6.70 tff(4871,plain,
% 6.49/6.70 (~r(s(s(s(elem!1))), z)),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[4790, 530, 233, 59])).
% 6.49/6.70 tff(4872,plain,
% 6.49/6.70 (b(s(s(s(elem!1))), z)),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[377, 4871])).
% 6.49/6.70 tff(4873,plain,
% 6.49/6.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.49/6.70 inference(rewrite,[status(thm)],[])).
% 6.49/6.70 tff(4874,plain,
% 6.49/6.70 (((~r(elem!1, z)) | (~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)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.49/6.70 inference(rewrite,[status(thm)],[])).
% 6.49/6.70 tff(4875,plain,
% 6.49/6.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 6.49/6.70 inference(monotonicity,[status(thm)],[4874])).
% 6.49/6.70 tff(4876,plain,
% 6.49/6.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.49/6.70 inference(transitivity,[status(thm)],[4875, 4873])).
% 6.49/6.70 tff(4877,plain,
% 6.49/6.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~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))))))),
% 6.49/6.70 inference(quant_inst,[status(thm)],[])).
% 6.49/6.70 tff(4878,plain,
% 6.49/6.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 6.49/6.70 inference(modus_ponens,[status(thm)],[4877, 4876])).
% 6.49/6.70 tff(4879,plain,
% 6.49/6.70 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[4878, 194, 530, 233, 4345])).
% 6.49/6.70 tff(4880,plain,
% 6.49/6.70 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.49/6.70 inference(unit_resolution,[status(thm)],[1356, 4879, 3926])).
% 6.49/6.70 tff(4881,plain,
% 6.49/6.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.49/6.70 inference(rewrite,[status(thm)],[])).
% 6.49/6.70 tff(4882,plain,
% 6.49/6.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.49/6.71 inference(quant_inst,[status(thm)],[])).
% 6.49/6.71 tff(4883,plain,
% 6.49/6.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 6.49/6.71 inference(modus_ponens,[status(thm)],[4882, 4881])).
% 6.49/6.71 tff(4884,plain,
% 6.49/6.71 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.49/6.71 inference(unit_resolution,[status(thm)],[4883, 194, 530, 233, 4345])).
% 6.49/6.71 tff(4885,plain,
% 6.49/6.71 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.49/6.71 inference(unit_resolution,[status(thm)],[1370, 4884, 288])).
% 6.49/6.71 tff(4886,plain,
% 6.49/6.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.49/6.71 inference(rewrite,[status(thm)],[])).
% 6.49/6.71 tff(4887,plain,
% 6.49/6.71 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.49/6.71 inference(rewrite,[status(thm)],[])).
% 6.49/6.71 tff(4888,plain,
% 6.49/6.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 6.49/6.71 inference(monotonicity,[status(thm)],[4887])).
% 6.49/6.71 tff(4889,plain,
% 6.49/6.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.49/6.71 inference(transitivity,[status(thm)],[4888, 4886])).
% 6.49/6.71 tff(4890,plain,
% 6.49/6.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 6.49/6.71 inference(quant_inst,[status(thm)],[])).
% 6.49/6.71 tff(4891,plain,
% 6.49/6.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 6.49/6.71 inference(modus_ponens,[status(thm)],[4890, 4889])).
% 6.49/6.71 tff(4892,plain,
% 6.49/6.71 ($false),
% 6.49/6.71 inference(unit_resolution,[status(thm)],[4891, 391, 380, 1374, 3927, 328])).
% 6.49/6.71 tff(4893,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.71 tff(4894,plain,
% 6.49/6.71 (~b(z, s(s(elem!1)))),
% 6.49/6.71 inference(unit_resolution,[status(thm)],[4893, 4885, 380, 4880])).
% 6.49/6.71 tff(4895,plain,
% 6.49/6.71 (r(z, s(s(elem!1)))),
% 6.49/6.71 inference(unit_resolution,[status(thm)],[324, 4894])).
% 6.49/6.71 tff(4896,plain,
% 6.49/6.71 (~r(elem!1, s(s(elem!1)))),
% 6.49/6.71 inference(unit_resolution,[status(thm)],[2231, 4895, 4345, 530])).
% 6.49/6.71 tff(4897,plain,
% 6.49/6.71 (b(elem!1, s(s(elem!1)))),
% 6.49/6.71 inference(unit_resolution,[status(thm)],[1307, 4896, 1293])).
% 6.49/6.71 tff(4898,plain,
% 6.49/6.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 6.49/6.71 inference(rewrite,[status(thm)],[])).
% 6.49/6.71 tff(4899,plain,
% 6.49/6.71 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 6.49/6.71 inference(rewrite,[status(thm)],[])).
% 6.49/6.71 tff(4900,plain,
% 6.49/6.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 6.49/6.71 inference(monotonicity,[status(thm)],[4899])).
% 6.49/6.71 tff(4901,plain,
% 6.49/6.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 6.49/6.71 inference(transitivity,[status(thm)],[4900, 4898])).
% 6.49/6.71 tff(4902,plain,
% 6.49/6.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 6.49/6.71 inference(quant_inst,[status(thm)],[])).
% 6.49/6.71 tff(4903,plain,
% 6.49/6.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 6.49/6.71 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 6.49/6.71 tff(4904,plain,
% 6.49/6.71 ($false),
% 6.49/6.71 inference(unit_resolution,[status(thm)],[4903, 391, 133, 380, 448, 4897, 4880])).
% 6.49/6.71 tff(4905,plain,((s(s(elem!1)) = elem!1) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.49/6.71 tff(4906,plain,
% 6.49/6.71 (b(s(s(elem!1)), elem!1)),
% 6.49/6.71 inference(unit_resolution,[status(thm)],[4905, 4868, 4872, 4774, 530, 233, 133])).
% 6.49/6.71 tff(4907,plain,
% 6.49/6.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.49/6.71 inference(rewrite,[status(thm)],[])).
% 6.49/6.71 tff(4908,plain,
% 6.49/6.72 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.49/6.72 inference(rewrite,[status(thm)],[])).
% 6.49/6.72 tff(4909,plain,
% 6.49/6.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 6.49/6.72 inference(monotonicity,[status(thm)],[4908])).
% 6.49/6.72 tff(4910,plain,
% 6.49/6.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.49/6.72 inference(transitivity,[status(thm)],[4909, 4907])).
% 6.49/6.72 tff(4911,plain,
% 6.49/6.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 6.49/6.72 inference(quant_inst,[status(thm)],[])).
% 6.49/6.72 tff(4912,plain,
% 6.49/6.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 6.49/6.72 inference(modus_ponens,[status(thm)],[4911, 4910])).
% 6.49/6.72 tff(4913,plain,
% 6.49/6.72 (~b(z, s(s(elem!1)))),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[4912, 391, 133, 4872, 4906, 4774])).
% 6.49/6.72 tff(4914,plain,
% 6.49/6.72 (b(s(z), z)),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[3924, 4913, 10, 4870])).
% 6.49/6.72 tff(4915,plain,
% 6.49/6.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.49/6.72 inference(rewrite,[status(thm)],[])).
% 6.49/6.72 tff(4916,plain,
% 6.49/6.72 (((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.49/6.72 inference(rewrite,[status(thm)],[])).
% 6.49/6.72 tff(4917,plain,
% 6.49/6.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.49/6.72 inference(monotonicity,[status(thm)],[4916])).
% 6.49/6.72 tff(4918,plain,
% 6.49/6.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.49/6.72 inference(transitivity,[status(thm)],[4917, 4915])).
% 6.49/6.72 tff(4919,plain,
% 6.49/6.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.49/6.72 inference(quant_inst,[status(thm)],[])).
% 6.49/6.72 tff(4920,plain,
% 6.49/6.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 6.49/6.72 inference(modus_ponens,[status(thm)],[4919, 4918])).
% 6.49/6.72 tff(4921,plain,
% 6.49/6.72 (~b(s(z), s(s(s(elem!1))))),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[4920, 391, 133, 4872, 4774, 4914])).
% 6.49/6.72 tff(4922,plain,
% 6.49/6.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.49/6.72 inference(rewrite,[status(thm)],[])).
% 6.49/6.72 tff(4923,plain,
% 6.49/6.72 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.49/6.72 inference(rewrite,[status(thm)],[])).
% 6.49/6.72 tff(4924,plain,
% 6.49/6.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 6.49/6.72 inference(monotonicity,[status(thm)],[4923])).
% 6.49/6.72 tff(4925,plain,
% 6.49/6.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.49/6.72 inference(transitivity,[status(thm)],[4924, 4922])).
% 6.49/6.72 tff(4926,plain,
% 6.49/6.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 6.49/6.72 inference(quant_inst,[status(thm)],[])).
% 6.49/6.72 tff(4927,plain,
% 6.49/6.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 6.49/6.72 inference(modus_ponens,[status(thm)],[4926, 4925])).
% 6.49/6.72 tff(4928,plain,
% 6.49/6.72 ($false),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[4927, 391, 133, 380, 448, 644, 590])).
% 6.49/6.72 tff(4929,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.72 tff(4930,plain,
% 6.49/6.72 (~b(s(z), elem!1)),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[4929, 4872, 133, 4774, 4914])).
% 6.49/6.72 tff(4931,plain,
% 6.49/6.72 (r(s(z), elem!1)),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[632, 4930, 150])).
% 6.49/6.72 tff(4932,plain,
% 6.49/6.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.49/6.72 inference(rewrite,[status(thm)],[])).
% 6.49/6.72 tff(4933,plain,
% 6.49/6.72 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.49/6.72 inference(rewrite,[status(thm)],[])).
% 6.49/6.72 tff(4934,plain,
% 6.49/6.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))))),
% 6.49/6.72 inference(monotonicity,[status(thm)],[4933])).
% 6.49/6.72 tff(4935,plain,
% 6.49/6.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.49/6.72 inference(transitivity,[status(thm)],[4934, 4932])).
% 6.49/6.72 tff(4936,plain,
% 6.49/6.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.49/6.72 inference(quant_inst,[status(thm)],[])).
% 6.49/6.72 tff(4937,plain,
% 6.49/6.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))),
% 6.49/6.72 inference(modus_ponens,[status(thm)],[4936, 4935])).
% 6.49/6.72 tff(4938,plain,
% 6.49/6.72 (~r(s(z), s(s(s(elem!1))))),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[4937, 194, 530, 233, 4931])).
% 6.49/6.72 tff(4939,plain,
% 6.49/6.72 ($false),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[247, 4938, 4921])).
% 6.49/6.72 tff(4940,plain,((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (s(z) = elem!1) | b(z, s(s(s(elem!1)))) | (s(z) = s(elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.72 tff(4941,plain,
% 6.49/6.72 (~r(elem!1, z)),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[4940, 231, 149, 150, 10, 118, 148])).
% 6.49/6.72 tff(4942,plain,
% 6.49/6.72 (b(elem!1, z)),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[526, 4941, 2])).
% 6.49/6.72 tff(4943,plain,
% 6.49/6.72 ($false),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[4277, 391, 133, 665, 973, 3927])).
% 6.49/6.72 tff(4944,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.72 tff(4945,plain,
% 6.49/6.72 (~b(s(s(elem!1)), elem!1)),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[4944, 3925, 4942, 149])).
% 6.49/6.72 tff(4946,plain,
% 6.49/6.72 (r(s(s(elem!1)), elem!1)),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[872, 4945, 249])).
% 6.49/6.72 tff(4947,plain,
% 6.49/6.72 (~b(s(z), elem!1)),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[4026, 448, 1526, 379])).
% 6.49/6.72 tff(4948,plain,
% 6.49/6.72 (r(s(z), elem!1)),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[632, 4947, 150])).
% 6.49/6.72 tff(4949,plain,
% 6.49/6.72 (~r(elem!1, s(z))),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[1899, 4948, 364, 340])).
% 6.49/6.72 tff(4950,plain,
% 6.49/6.72 (b(elem!1, s(z))),
% 6.49/6.72 inference(unit_resolution,[status(thm)],[837, 4949, 173])).
% 6.49/6.72 tff(4951,plain,
% 6.49/6.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.49/6.73 inference(rewrite,[status(thm)],[])).
% 6.49/6.73 tff(4952,plain,
% 6.49/6.73 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.49/6.73 inference(rewrite,[status(thm)],[])).
% 6.49/6.73 tff(4953,plain,
% 6.49/6.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[4952])).
% 6.49/6.73 tff(4954,plain,
% 6.49/6.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.49/6.73 inference(transitivity,[status(thm)],[4953, 4951])).
% 6.49/6.73 tff(4955,plain,
% 6.49/6.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 6.49/6.73 inference(quant_inst,[status(thm)],[])).
% 6.49/6.73 tff(4956,plain,
% 6.49/6.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.49/6.73 inference(modus_ponens,[status(thm)],[4955, 4954])).
% 6.49/6.73 tff(4957,plain,
% 6.49/6.73 ($false),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[4956, 391, 448, 379, 1526, 4950])).
% 6.49/6.73 tff(4958,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.49/6.73 tff(4959,plain,
% 6.49/6.73 (~b(elem!1, s(s(s(elem!1))))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[4958, 4946, 224, 248, 4764, 150])).
% 6.49/6.73 tff(4960,plain,
% 6.49/6.73 (~r(s(s(s(s(z)))), z)),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[3969, 181, 59, 3363, 174])).
% 6.49/6.73 tff(4961,plain,
% 6.49/6.73 (b(s(s(s(s(z)))), z)),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[87, 4960])).
% 6.49/6.73 tff(4962,plain,
% 6.49/6.73 (r(elem!1, s(s(s(elem!1))))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[424, 4959, 148])).
% 6.49/6.73 tff(4963,plain,
% 6.49/6.73 (~b(s(s(s(s(z)))), elem!1)),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[4086, 391, 133, 665, 90])).
% 6.49/6.73 tff(4964,plain,
% 6.49/6.73 (~r(s(z), s(s(s(elem!1))))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[241, 182, 184, 4486])).
% 6.49/6.73 tff(4965,plain,
% 6.49/6.73 (b(s(z), s(s(s(elem!1))))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[247, 4964])).
% 6.49/6.73 tff(4966,plain,
% 6.49/6.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.49/6.73 inference(rewrite,[status(thm)],[])).
% 6.49/6.73 tff(4967,plain,
% 6.49/6.73 (((~r(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)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.49/6.73 inference(rewrite,[status(thm)],[])).
% 6.49/6.73 tff(4968,plain,
% 6.49/6.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[4967])).
% 6.49/6.73 tff(4969,plain,
% 6.49/6.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.49/6.73 inference(transitivity,[status(thm)],[4968, 4966])).
% 6.49/6.73 tff(4970,plain,
% 6.49/6.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))),
% 6.49/6.73 inference(quant_inst,[status(thm)],[])).
% 6.49/6.73 tff(4971,plain,
% 6.49/6.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 6.49/6.73 inference(modus_ponens,[status(thm)],[4970, 4969])).
% 6.49/6.73 tff(4972,plain,
% 6.49/6.73 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[4971, 194, 4486, 364, 410])).
% 6.49/6.73 tff(4973,plain,
% 6.49/6.73 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[1356, 4972, 315])).
% 6.49/6.73 tff(4974,plain,
% 6.49/6.73 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[4039, 364, 127, 4028, 168])).
% 6.49/6.73 tff(4975,plain,
% 6.49/6.73 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[1370, 4974, 297])).
% 6.49/6.73 tff(4976,plain,
% 6.49/6.73 (~b(s(s(elem!1)), s(z))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[3422, 391, 4975, 4965, 4973])).
% 6.49/6.73 tff(4977,plain,
% 6.49/6.73 (r(s(s(elem!1)), s(z))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[362, 4976])).
% 6.49/6.73 tff(4978,plain,
% 6.49/6.73 (~r(s(s(elem!1)), z)),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[4103, 4977, 722, 182])).
% 6.49/6.73 tff(4979,plain,
% 6.49/6.73 (b(s(s(elem!1)), z)),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[2629, 4978])).
% 6.49/6.73 tff(4980,plain,
% 6.49/6.73 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[1399])).
% 6.49/6.73 tff(4981,plain,
% 6.49/6.73 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[4980])).
% 6.49/6.73 tff(4982,plain,
% 6.49/6.73 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[1399, 4981])).
% 6.49/6.73 tff(4983,plain,
% 6.49/6.73 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 6.49/6.73 inference(transitivity,[status(thm)],[4982, 1020])).
% 6.49/6.73 tff(4984,plain,
% 6.49/6.73 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[4983])).
% 6.49/6.73 tff(4985,plain,
% 6.49/6.73 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 6.49/6.73 inference(quant_inst,[status(thm)],[])).
% 6.49/6.73 tff(4986,plain,
% 6.49/6.73 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[4985, 106])).
% 6.49/6.73 tff(4987,plain,
% 6.49/6.73 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 6.49/6.73 inference(quant_inst,[status(thm)],[])).
% 6.49/6.73 tff(4988,plain,
% 6.49/6.73 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[4987, 106])).
% 6.49/6.73 tff(4989,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 6.49/6.73 tff(4990,plain,
% 6.49/6.73 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[4989])).
% 6.49/6.73 tff(4991,plain,
% 6.49/6.73 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 6.49/6.73 inference(transitivity,[status(thm)],[693, 4990, 4988])).
% 6.49/6.73 tff(4992,plain,
% 6.49/6.73 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[4991])).
% 6.49/6.73 tff(4993,plain,
% 6.49/6.73 (s(s(z)) = s(s(s(s(z))))),
% 6.49/6.73 inference(transitivity,[status(thm)],[710, 4992, 4986])).
% 6.49/6.73 tff(4994,plain,
% 6.49/6.73 ($false),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[714, 4993])).
% 6.49/6.73 tff(4995,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.73 tff(4996,plain,
% 6.49/6.73 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 6.49/6.73 inference(modus_ponens,[status(thm)],[4995, 4984])).
% 6.49/6.73 tff(4997,plain,
% 6.49/6.73 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 6.49/6.73 inference(monotonicity,[status(thm)],[4981, 2652])).
% 6.49/6.73 tff(4998,plain,
% 6.49/6.73 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 6.49/6.73 inference(transitivity,[status(thm)],[4997, 950])).
% 6.49/6.73 tff(4999,plain,
% 6.49/6.73 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 6.49/6.73 inference(transitivity,[status(thm)],[4998, 964])).
% 6.49/6.73 tff(5000,plain,
% 6.49/6.73 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[4999])).
% 6.49/6.73 tff(5001,assumption,(s(s(s(s(s(s(z)))))) = s(s(z))), introduced(assumption)).
% 6.49/6.73 tff(5002,plain,
% 6.49/6.73 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[5001])).
% 6.49/6.73 tff(5003,plain,
% 6.49/6.73 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 6.49/6.73 inference(symmetry,[status(thm)],[4988])).
% 6.49/6.73 tff(5004,plain,
% 6.49/6.73 (s(s(s(s(s(z))))) = s(z)),
% 6.49/6.73 inference(transitivity,[status(thm)],[5003, 5002, 705])).
% 6.49/6.73 tff(5005,plain,
% 6.49/6.73 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[5004])).
% 6.49/6.73 tff(5006,plain,
% 6.49/6.73 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 6.49/6.73 inference(symmetry,[status(thm)],[4986])).
% 6.49/6.73 tff(5007,plain,
% 6.49/6.73 (s(s(s(s(z)))) = z),
% 6.49/6.73 inference(transitivity,[status(thm)],[5006, 5005, 112])).
% 6.49/6.73 tff(5008,plain,
% 6.49/6.73 ($false),
% 6.49/6.73 inference(unit_resolution,[status(thm)],[83, 5007])).
% 6.49/6.73 tff(5009,plain,(~(s(s(s(s(s(s(z)))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.73 tff(5010,plain,
% 6.49/6.73 (~(s(s(s(s(elem!1)))) = elem!1)),
% 6.49/6.73 inference(modus_ponens,[status(thm)],[5009, 5000])).
% 6.49/6.73 tff(5011,plain,
% 6.49/6.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 6.49/6.73 inference(rewrite,[status(thm)],[])).
% 6.49/6.73 tff(5012,plain,
% 6.49/6.73 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 6.49/6.73 inference(rewrite,[status(thm)],[])).
% 6.49/6.73 tff(5013,plain,
% 6.49/6.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 6.49/6.73 inference(monotonicity,[status(thm)],[5012])).
% 6.49/6.74 tff(5014,plain,
% 6.49/6.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 6.49/6.74 inference(transitivity,[status(thm)],[5013, 5011])).
% 6.49/6.74 tff(5015,plain,
% 6.49/6.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 6.49/6.74 inference(quant_inst,[status(thm)],[])).
% 6.49/6.74 tff(5016,plain,
% 6.49/6.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 6.49/6.74 inference(modus_ponens,[status(thm)],[5015, 5014])).
% 6.49/6.74 tff(5017,plain,
% 6.49/6.74 (~r(s(s(s(s(elem!1)))), z)),
% 6.49/6.74 inference(unit_resolution,[status(thm)],[5016, 194, 174, 184, 1082])).
% 6.49/6.74 tff(5018,plain,
% 6.49/6.74 (b(s(s(s(s(elem!1)))), z)),
% 6.49/6.74 inference(unit_resolution,[status(thm)],[1626, 5017])).
% 6.49/6.74 tff(5019,plain,
% 6.49/6.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 6.49/6.74 inference(rewrite,[status(thm)],[])).
% 6.49/6.74 tff(5020,plain,
% 6.49/6.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 6.49/6.74 inference(quant_inst,[status(thm)],[])).
% 6.49/6.74 tff(5021,plain,
% 6.49/6.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 6.49/6.74 inference(modus_ponens,[status(thm)],[5020, 5019])).
% 6.49/6.74 tff(5022,plain,
% 6.49/6.74 (~r(s(s(s(s(elem!1)))), elem!1)),
% 6.49/6.74 inference(unit_resolution,[status(thm)],[5021, 194, 174, 410, 1082])).
% 6.49/6.74 tff(5023,plain,
% 6.49/6.74 (b(s(s(s(s(elem!1)))), elem!1)),
% 6.49/6.74 inference(unit_resolution,[status(thm)],[1004, 5022, 972])).
% 6.49/6.74 tff(5024,plain,
% 6.49/6.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 6.49/6.74 inference(rewrite,[status(thm)],[])).
% 6.49/6.74 tff(5025,plain,
% 6.49/6.74 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 6.49/6.74 inference(rewrite,[status(thm)],[])).
% 6.49/6.74 tff(5026,plain,
% 6.49/6.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 6.49/6.74 inference(monotonicity,[status(thm)],[5025])).
% 6.49/6.74 tff(5027,plain,
% 6.49/6.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 6.49/6.74 inference(transitivity,[status(thm)],[5026, 5024])).
% 6.49/6.74 tff(5028,plain,
% 6.49/6.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 6.49/6.74 inference(quant_inst,[status(thm)],[])).
% 6.49/6.74 tff(5029,plain,
% 6.49/6.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 6.49/6.74 inference(modus_ponens,[status(thm)],[5028, 5027])).
% 6.49/6.74 tff(5030,plain,
% 6.49/6.74 ($false),
% 6.49/6.74 inference(unit_resolution,[status(thm)],[5029, 391, 133, 665, 5023, 5018])).
% 6.49/6.74 tff(5031,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.74 tff(5032,plain,
% 6.49/6.74 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 6.49/6.74 inference(unit_resolution,[status(thm)],[5031, 5010, 133, 665, 410, 174, 184])).
% 6.49/6.74 tff(5033,plain,
% 6.49/6.74 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 6.49/6.74 inference(unit_resolution,[status(thm)],[1095, 5032, 305])).
% 6.49/6.74 tff(5034,plain,
% 6.49/6.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 6.49/6.74 inference(rewrite,[status(thm)],[])).
% 6.49/6.74 tff(5035,plain,
% 6.49/6.74 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 6.49/6.74 inference(rewrite,[status(thm)],[])).
% 6.49/6.74 tff(5036,plain,
% 6.49/6.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 6.49/6.74 inference(monotonicity,[status(thm)],[5035])).
% 6.49/6.74 tff(5037,plain,
% 6.49/6.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 6.49/6.75 inference(transitivity,[status(thm)],[5036, 5034])).
% 6.49/6.75 tff(5038,plain,
% 6.49/6.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 6.49/6.75 inference(quant_inst,[status(thm)],[])).
% 6.49/6.75 tff(5039,plain,
% 6.49/6.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 6.49/6.75 inference(modus_ponens,[status(thm)],[5038, 5037])).
% 6.49/6.75 tff(5040,plain,
% 6.49/6.75 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5039, 391, 1374, 2641, 328, 5033])).
% 6.49/6.75 tff(5041,plain,
% 6.49/6.75 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[1061, 5040, 4996])).
% 6.49/6.75 tff(5042,plain,
% 6.49/6.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 6.49/6.75 inference(rewrite,[status(thm)],[])).
% 6.49/6.75 tff(5043,plain,
% 6.49/6.75 (((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 6.49/6.75 inference(rewrite,[status(thm)],[])).
% 6.49/6.75 tff(5044,plain,
% 6.49/6.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 6.49/6.75 inference(monotonicity,[status(thm)],[5043])).
% 6.49/6.75 tff(5045,plain,
% 6.49/6.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 6.49/6.75 inference(transitivity,[status(thm)],[5044, 5042])).
% 6.49/6.75 tff(5046,plain,
% 6.49/6.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 6.49/6.75 inference(quant_inst,[status(thm)],[])).
% 6.49/6.75 tff(5047,plain,
% 6.49/6.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 6.49/6.75 inference(modus_ponens,[status(thm)],[5046, 5045])).
% 6.49/6.75 tff(5048,plain,
% 6.49/6.75 (~r(s(s(s(s(elem!1)))), s(z))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5047, 194, 3424, 5041, 3416])).
% 6.49/6.75 tff(5049,plain,
% 6.49/6.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 6.49/6.75 inference(rewrite,[status(thm)],[])).
% 6.49/6.75 tff(5050,plain,
% 6.49/6.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 6.49/6.75 inference(quant_inst,[status(thm)],[])).
% 6.49/6.75 tff(5051,plain,
% 6.49/6.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 6.49/6.75 inference(modus_ponens,[status(thm)],[5050, 5049])).
% 6.49/6.75 tff(5052,plain,
% 6.49/6.75 (~b(s(s(s(s(elem!1)))), s(z))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5051, 391, 1374, 379, 2641, 5033])).
% 6.49/6.75 tff(5053,plain,
% 6.49/6.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 6.49/6.75 inference(rewrite,[status(thm)],[])).
% 6.49/6.75 tff(5054,plain,
% 6.49/6.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 6.49/6.75 inference(quant_inst,[status(thm)],[])).
% 6.49/6.75 tff(5055,plain,
% 6.49/6.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 6.49/6.75 inference(modus_ponens,[status(thm)],[5054, 5053])).
% 6.49/6.75 tff(5056,plain,
% 6.49/6.75 ((s(s(s(s(elem!1)))) = s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5055, 42, 5052])).
% 6.49/6.75 tff(5057,plain,
% 6.49/6.75 (s(s(s(s(elem!1)))) = s(z)),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5056, 5048])).
% 6.49/6.75 tff(5058,plain,
% 6.49/6.75 (s(s(s(s(s(s(z)))))) = s(z)),
% 6.49/6.75 inference(transitivity,[status(thm)],[4981, 5057])).
% 6.49/6.75 tff(5059,assumption,(s(s(s(s(s(s(z)))))) = s(z)), introduced(assumption)).
% 6.49/6.75 tff(5060,plain,
% 6.49/6.75 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 6.49/6.75 inference(monotonicity,[status(thm)],[5059])).
% 6.49/6.75 tff(5061,plain,
% 6.49/6.75 (s(s(s(s(s(z))))) = z),
% 6.49/6.75 inference(transitivity,[status(thm)],[5003, 5060, 112])).
% 6.49/6.75 tff(5062,plain,
% 6.49/6.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 6.49/6.75 inference(quant_inst,[status(thm)],[])).
% 6.49/6.75 tff(5063,plain,
% 6.49/6.75 (~(s(s(s(s(s(z))))) = z)),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5062, 21])).
% 6.49/6.75 tff(5064,plain,
% 6.49/6.75 ($false),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5063, 5061])).
% 6.49/6.75 tff(5065,plain,(~(s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.75 tff(5066,plain,
% 6.49/6.75 ($false),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5065, 5058])).
% 6.49/6.75 tff(5067,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.75 tff(5068,plain,
% 6.49/6.75 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5067, 4975, 4979, 4973, 4965, 310, 133, 665, 410, 174, 184])).
% 6.49/6.75 tff(5069,plain,
% 6.49/6.75 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[4137, 391, 133, 665, 4979, 90])).
% 6.49/6.75 tff(5070,plain,
% 6.49/6.75 ((s(s(s(s(z)))) = s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[2003, 42, 5069])).
% 6.49/6.75 tff(5071,plain,
% 6.49/6.75 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5070, 5068])).
% 6.49/6.75 tff(5072,plain,
% 6.49/6.75 (~b(elem!1, s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[4522, 391, 133, 665, 4979])).
% 6.49/6.75 tff(5073,plain,
% 6.49/6.75 (r(elem!1, s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[1307, 5072, 1457])).
% 6.49/6.75 tff(5074,plain,
% 6.49/6.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.49/6.75 inference(rewrite,[status(thm)],[])).
% 6.49/6.75 tff(5075,plain,
% 6.49/6.75 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.49/6.75 inference(rewrite,[status(thm)],[])).
% 6.49/6.75 tff(5076,plain,
% 6.49/6.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 6.49/6.75 inference(monotonicity,[status(thm)],[5075])).
% 6.49/6.75 tff(5077,plain,
% 6.49/6.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.49/6.75 inference(transitivity,[status(thm)],[5076, 5074])).
% 6.49/6.75 tff(5078,plain,
% 6.49/6.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 6.49/6.75 inference(quant_inst,[status(thm)],[])).
% 6.49/6.75 tff(5079,plain,
% 6.49/6.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 6.49/6.75 inference(modus_ponens,[status(thm)],[5078, 5077])).
% 6.49/6.75 tff(5080,plain,
% 6.49/6.75 (~r(s(s(s(s(z)))), elem!1)),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5079, 194, 4977, 5073, 5071])).
% 6.49/6.75 tff(5081,plain,
% 6.49/6.75 (s(s(s(s(z)))) = elem!1),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[762, 5080, 4963])).
% 6.49/6.75 tff(5082,plain,
% 6.49/6.75 (~b(s(z), s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[3410, 391, 4975, 4965, 4973])).
% 6.49/6.75 tff(5083,plain,
% 6.49/6.75 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[3414, 42, 5082])).
% 6.49/6.75 tff(5084,plain,
% 6.49/6.75 (r(s(z), s(s(elem!1)))),
% 6.49/6.75 inference(unit_resolution,[status(thm)],[5083, 3404])).
% 6.49/6.75 tff(5085,plain,
% 6.49/6.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.49/6.75 inference(rewrite,[status(thm)],[])).
% 6.49/6.75 tff(5086,plain,
% 6.49/6.75 (((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.49/6.76 inference(rewrite,[status(thm)],[])).
% 6.49/6.76 tff(5087,plain,
% 6.49/6.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))))),
% 6.49/6.76 inference(monotonicity,[status(thm)],[5086])).
% 6.49/6.76 tff(5088,plain,
% 6.49/6.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.49/6.76 inference(transitivity,[status(thm)],[5087, 5085])).
% 6.49/6.76 tff(5089,plain,
% 6.49/6.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 6.49/6.76 inference(quant_inst,[status(thm)],[])).
% 6.49/6.76 tff(5090,plain,
% 6.49/6.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))),
% 6.49/6.76 inference(modus_ponens,[status(thm)],[5089, 5088])).
% 6.49/6.76 tff(5091,plain,
% 6.49/6.76 (~r(elem!1, s(z))),
% 6.49/6.76 inference(unit_resolution,[status(thm)],[5090, 194, 4977, 5073, 5084])).
% 6.49/6.76 tff(5092,plain,
% 6.49/6.76 (b(elem!1, s(z))),
% 6.49/6.76 inference(unit_resolution,[status(thm)],[837, 5091, 831])).
% 6.49/6.76 tff(5093,plain,
% 6.49/6.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.49/6.76 inference(rewrite,[status(thm)],[])).
% 6.49/6.76 tff(5094,plain,
% 6.49/6.76 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.49/6.76 inference(rewrite,[status(thm)],[])).
% 6.49/6.76 tff(5095,plain,
% 6.49/6.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 6.49/6.76 inference(monotonicity,[status(thm)],[5094])).
% 6.49/6.76 tff(5096,plain,
% 6.49/6.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.49/6.76 inference(transitivity,[status(thm)],[5095, 5093])).
% 6.49/6.76 tff(5097,plain,
% 6.49/6.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))),
% 6.49/6.76 inference(quant_inst,[status(thm)],[])).
% 6.49/6.76 tff(5098,plain,
% 6.49/6.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 6.49/6.76 inference(modus_ponens,[status(thm)],[5097, 5096])).
% 6.49/6.76 tff(5099,plain,
% 6.49/6.76 (~r(s(z), s(s(s(s(z)))))),
% 6.49/6.76 inference(unit_resolution,[status(thm)],[5098, 194, 4977, 5084, 5071])).
% 6.49/6.76 tff(5100,plain,
% 6.49/6.76 (b(s(z), s(s(s(s(z)))))),
% 6.49/6.76 inference(unit_resolution,[status(thm)],[1230, 5099])).
% 6.49/6.76 tff(5101,plain,
% 6.49/6.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.49/6.76 inference(rewrite,[status(thm)],[])).
% 6.49/6.76 tff(5102,plain,
% 6.49/6.76 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.49/6.76 inference(rewrite,[status(thm)],[])).
% 6.49/6.76 tff(5103,plain,
% 6.49/6.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 6.49/6.76 inference(monotonicity,[status(thm)],[5102])).
% 6.49/6.76 tff(5104,plain,
% 6.49/6.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.49/6.76 inference(transitivity,[status(thm)],[5103, 5101])).
% 6.49/6.76 tff(5105,plain,
% 6.49/6.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 6.49/6.76 inference(quant_inst,[status(thm)],[])).
% 6.49/6.76 tff(5106,plain,
% 6.49/6.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 6.49/6.76 inference(modus_ponens,[status(thm)],[5105, 5104])).
% 6.49/6.76 tff(5107,plain,
% 6.49/6.76 ($false),
% 6.49/6.76 inference(unit_resolution,[status(thm)],[5106, 391, 3823, 1234, 1759, 1233])).
% 6.49/6.76 tff(5108,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.76 tff(5109,plain,
% 6.49/6.76 (~b(s(s(s(s(z)))), s(z))),
% 6.49/6.76 inference(unit_resolution,[status(thm)],[5108, 1234, 3823, 1233])).
% 6.49/6.76 tff(5110,plain,
% 6.49/6.76 (r(s(s(s(s(z)))), s(z))),
% 6.49/6.76 inference(unit_resolution,[status(thm)],[749, 5109])).
% 6.49/6.76 tff(5111,plain,
% 6.49/6.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.49/6.77 inference(rewrite,[status(thm)],[])).
% 6.49/6.77 tff(5112,plain,
% 6.49/6.77 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.49/6.77 inference(rewrite,[status(thm)],[])).
% 6.49/6.77 tff(5113,plain,
% 6.49/6.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 6.49/6.77 inference(monotonicity,[status(thm)],[5112])).
% 6.49/6.77 tff(5114,plain,
% 6.49/6.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.49/6.77 inference(transitivity,[status(thm)],[5113, 5111])).
% 6.49/6.77 tff(5115,plain,
% 6.49/6.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 6.49/6.77 inference(quant_inst,[status(thm)],[])).
% 6.49/6.77 tff(5116,plain,
% 6.49/6.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 6.49/6.77 inference(modus_ponens,[status(thm)],[5115, 5114])).
% 6.49/6.77 tff(5117,plain,
% 6.49/6.77 (~r(s(s(s(s(z)))), z)),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[5116, 194, 722, 182, 5110])).
% 6.49/6.77 tff(5118,plain,
% 6.49/6.77 (b(s(s(s(s(z)))), z)),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[87, 5117])).
% 6.49/6.77 tff(5119,plain,
% 6.49/6.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.49/6.77 inference(rewrite,[status(thm)],[])).
% 6.49/6.77 tff(5120,plain,
% 6.49/6.77 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.49/6.77 inference(rewrite,[status(thm)],[])).
% 6.49/6.77 tff(5121,plain,
% 6.49/6.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 6.49/6.77 inference(monotonicity,[status(thm)],[5120])).
% 6.49/6.77 tff(5122,plain,
% 6.49/6.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.49/6.77 inference(transitivity,[status(thm)],[5121, 5119])).
% 6.49/6.77 tff(5123,plain,
% 6.49/6.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 6.49/6.77 inference(quant_inst,[status(thm)],[])).
% 6.49/6.77 tff(5124,plain,
% 6.49/6.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 6.49/6.77 inference(modus_ponens,[status(thm)],[5123, 5122])).
% 6.49/6.77 tff(5125,plain,
% 6.49/6.77 ($false),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[5124, 391, 133, 3823, 5118, 1234, 1233])).
% 6.49/6.77 tff(5126,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.77 tff(5127,plain,
% 6.49/6.77 (~b(s(s(z)), s(z))),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[5126, 3823, 133, 182, 1234, 722])).
% 6.49/6.77 tff(5128,plain,
% 6.49/6.77 (r(s(s(z)), s(z))),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[3778, 5127])).
% 6.49/6.77 tff(5129,plain,
% 6.49/6.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 6.49/6.77 inference(rewrite,[status(thm)],[])).
% 6.49/6.77 tff(5130,plain,
% 6.49/6.77 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 6.49/6.77 inference(rewrite,[status(thm)],[])).
% 6.49/6.77 tff(5131,plain,
% 6.49/6.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))))),
% 6.49/6.77 inference(monotonicity,[status(thm)],[5130])).
% 6.49/6.77 tff(5132,plain,
% 6.49/6.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 6.49/6.77 inference(transitivity,[status(thm)],[5131, 5129])).
% 6.49/6.77 tff(5133,plain,
% 6.49/6.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 6.49/6.77 inference(quant_inst,[status(thm)],[])).
% 6.49/6.77 tff(5134,plain,
% 6.49/6.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))),
% 6.49/6.77 inference(modus_ponens,[status(thm)],[5133, 5132])).
% 6.49/6.77 tff(5135,plain,
% 6.49/6.77 ($false),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[5134, 391, 133, 3823, 90, 1235, 721])).
% 6.49/6.77 tff(5136,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.77 tff(5137,plain,
% 6.49/6.77 (~b(s(s(z)), z)),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[5136, 3823, 133, 721, 90])).
% 6.49/6.77 tff(5138,plain,
% 6.49/6.77 (r(s(s(z)), z)),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[1211, 5137])).
% 6.49/6.77 tff(5139,plain,
% 6.49/6.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 6.49/6.77 inference(rewrite,[status(thm)],[])).
% 6.49/6.77 tff(5140,plain,
% 6.49/6.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 6.49/6.77 inference(quant_inst,[status(thm)],[])).
% 6.49/6.77 tff(5141,plain,
% 6.49/6.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 6.49/6.77 inference(modus_ponens,[status(thm)],[5140, 5139])).
% 6.49/6.77 tff(5142,plain,
% 6.49/6.77 ($false),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[5141, 194, 184, 182, 5138, 5128])).
% 6.49/6.77 tff(5143,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.77 tff(5144,plain,
% 6.49/6.77 (~b(s(s(z)), s(s(s(s(z)))))),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[5143, 5100, 182, 133, 184, 722, 5092, 90])).
% 6.49/6.77 tff(5145,plain,
% 6.49/6.77 (r(s(s(z)), s(s(s(s(z)))))),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[3652, 5144])).
% 6.49/6.77 tff(5146,plain,
% 6.49/6.77 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), elem!1)),
% 6.49/6.77 inference(monotonicity,[status(thm)],[688])).
% 6.49/6.77 tff(5147,plain,
% 6.49/6.77 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 6.49/6.77 inference(symmetry,[status(thm)],[5146])).
% 6.49/6.77 tff(5148,plain,
% 6.49/6.77 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 6.49/6.77 inference(monotonicity,[status(thm)],[5147])).
% 6.49/6.77 tff(5149,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 6.49/6.77 tff(5150,plain,
% 6.49/6.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 6.49/6.77 inference(modus_ponens,[status(thm)],[5149, 5148])).
% 6.49/6.77 tff(5151,plain,
% 6.49/6.77 ($false),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[1749, 5150])).
% 6.49/6.77 tff(5152,plain,((~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.49/6.77 tff(5153,plain,
% 6.49/6.77 (r(s(s(z)), elem!1)),
% 6.49/6.77 inference(unit_resolution,[status(thm)],[5152, 5145, 5081])).
% 6.49/6.77 tff(5154,plain,
% 6.49/6.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 6.49/6.77 inference(rewrite,[status(thm)],[])).
% 6.49/6.77 tff(5155,plain,
% 6.49/6.77 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 6.49/6.77 inference(rewrite,[status(thm)],[])).
% 6.49/6.77 tff(5156,plain,
% 6.49/6.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1))))),
% 6.49/6.77 inference(monotonicity,[status(thm)],[5155])).
% 6.49/6.77 tff(5157,plain,
% 6.49/6.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 6.49/6.78 inference(transitivity,[status(thm)],[5156, 5154])).
% 6.49/6.78 tff(5158,plain,
% 6.49/6.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 6.49/6.78 inference(quant_inst,[status(thm)],[])).
% 6.49/6.78 tff(5159,plain,
% 6.49/6.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1))),
% 6.49/6.78 inference(modus_ponens,[status(thm)],[5158, 5157])).
% 6.49/6.78 tff(5160,plain,
% 6.49/6.78 (~r(s(s(z)), s(s(s(elem!1))))),
% 6.49/6.78 inference(unit_resolution,[status(thm)],[5159, 194, 4486, 410, 5153])).
% 6.49/6.78 tff(5161,plain,
% 6.49/6.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 6.49/6.78 inference(rewrite,[status(thm)],[])).
% 6.49/6.78 tff(5162,plain,
% 6.49/6.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 6.49/6.78 inference(quant_inst,[status(thm)],[])).
% 6.49/6.78 tff(5163,plain,
% 6.49/6.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 6.49/6.78 inference(modus_ponens,[status(thm)],[5162, 5161])).
% 6.49/6.78 tff(5164,plain,
% 6.49/6.78 (b(s(s(z)), s(s(s(elem!1))))),
% 6.49/6.78 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 5160])).
% 6.49/6.78 tff(5165,plain,
% 6.49/6.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 6.49/6.78 inference(rewrite,[status(thm)],[])).
% 6.49/6.78 tff(5166,plain,
% 6.49/6.78 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 6.49/6.78 inference(rewrite,[status(thm)],[])).
% 6.49/6.78 tff(5167,plain,
% 6.49/6.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 6.49/6.78 inference(monotonicity,[status(thm)],[5166])).
% 6.49/6.78 tff(5168,plain,
% 6.49/6.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 6.49/6.78 inference(transitivity,[status(thm)],[5167, 5165])).
% 6.49/6.78 tff(5169,plain,
% 6.49/6.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 6.49/6.78 inference(quant_inst,[status(thm)],[])).
% 6.49/6.78 tff(5170,plain,
% 6.49/6.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 6.49/6.78 inference(modus_ponens,[status(thm)],[5169, 5168])).
% 6.49/6.78 tff(5171,plain,
% 6.49/6.78 (~r(s(s(elem!1)), s(s(z)))),
% 6.49/6.78 inference(unit_resolution,[status(thm)],[5170, 194, 364, 410, 5153])).
% 6.49/6.78 tff(5172,plain,
% 6.49/6.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 6.49/6.78 inference(rewrite,[status(thm)],[])).
% 6.49/6.78 tff(5173,plain,
% 6.49/6.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 6.49/6.78 inference(quant_inst,[status(thm)],[])).
% 6.49/6.78 tff(5174,plain,
% 6.49/6.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 6.49/6.78 inference(modus_ponens,[status(thm)],[5173, 5172])).
% 6.49/6.78 tff(5175,plain,
% 6.49/6.78 (b(s(s(elem!1)), s(s(z)))),
% 6.49/6.78 inference(unit_resolution,[status(thm)],[5174, 42, 5171, 2689])).
% 6.49/6.78 tff(5176,plain,
% 6.49/6.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.49/6.78 inference(rewrite,[status(thm)],[])).
% 6.49/6.78 tff(5177,plain,
% 6.49/6.78 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.49/6.78 inference(rewrite,[status(thm)],[])).
% 6.49/6.78 tff(5178,plain,
% 6.49/6.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 6.49/6.78 inference(monotonicity,[status(thm)],[5177])).
% 6.49/6.78 tff(5179,plain,
% 6.49/6.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.49/6.78 inference(transitivity,[status(thm)],[5178, 5176])).
% 6.49/6.78 tff(5180,plain,
% 6.49/6.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 6.49/6.78 inference(quant_inst,[status(thm)],[])).
% 6.49/6.78 tff(5181,plain,
% 6.49/6.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 6.49/6.79 inference(modus_ponens,[status(thm)],[5180, 5179])).
% 6.49/6.79 tff(5182,plain,
% 6.49/6.79 ($false),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[5181, 391, 4975, 4979, 4973, 5175, 5164])).
% 6.49/6.79 tff(5183,plain,((~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(elem!1))) = elem!1) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.49/6.79 tff(5184,plain,
% 6.49/6.79 (~r(z, s(z))),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[5183, 4962, 2680, 181, 149, 59, 4946, 4961, 4942, 174, 173, 1293, 288, 151, 4959, 168])).
% 6.49/6.79 tff(5185,plain,
% 6.49/6.79 (b(z, s(z))),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[678, 5184])).
% 6.49/6.79 tff(5186,plain,
% 6.49/6.79 (~r(s(z), elem!1)),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[2379, 4962, 4946, 4764])).
% 6.49/6.79 tff(5187,plain,
% 6.49/6.79 (b(s(z), elem!1)),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[632, 5186, 150])).
% 6.49/6.79 tff(5188,plain,
% 6.49/6.79 ($false),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[4651, 391, 149, 4942, 5187, 5185])).
% 6.49/6.79 tff(5189,plain,((s(s(elem!1)) = elem!1) | (s(z) = elem!1) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), elem!1) | (elem!1 = z) | r(z, elem!1) | b(s(z), z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.79 tff(5190,plain,
% 6.49/6.79 (s(s(elem!1)) = elem!1),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[5189, 91, 174, 168, 2, 80, 150, 10])).
% 6.49/6.79 tff(5191,plain,
% 6.49/6.79 (s(s(s(elem!1))) = s(elem!1)),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[451, 5190])).
% 6.49/6.79 tff(5192,plain,
% 6.49/6.79 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5191])).
% 6.49/6.79 tff(5193,plain,
% 6.49/6.79 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 6.49/6.79 inference(symmetry,[status(thm)],[5192])).
% 6.49/6.79 tff(5194,plain,
% 6.49/6.79 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5191])).
% 6.49/6.79 tff(5195,plain,
% 6.49/6.79 (s(s(s(s(elem!1)))) = elem!1),
% 6.49/6.79 inference(transitivity,[status(thm)],[5194, 5190])).
% 6.49/6.79 tff(5196,plain,
% 6.49/6.79 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(elem!1) = elem!1)),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5195])).
% 6.49/6.79 tff(5197,plain,
% 6.49/6.79 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (elem!1 = s(elem!1))),
% 6.49/6.79 inference(transitivity,[status(thm)],[5196, 160])).
% 6.49/6.79 tff(5198,plain,
% 6.49/6.79 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 6.49/6.79 inference(symmetry,[status(thm)],[5197])).
% 6.49/6.79 tff(5199,plain,
% 6.49/6.79 ((elem!1 = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 6.49/6.79 inference(transitivity,[status(thm)],[5198, 5193])).
% 6.49/6.79 tff(5200,plain,
% 6.49/6.79 ((~(elem!1 = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5199])).
% 6.49/6.79 tff(5201,plain,
% 6.49/6.79 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 6.49/6.79 inference(modus_ponens,[status(thm)],[167, 5200])).
% 6.49/6.79 tff(5202,plain,
% 6.49/6.79 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5190])).
% 6.49/6.79 tff(5203,plain,
% 6.49/6.79 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 6.49/6.79 inference(symmetry,[status(thm)],[5202])).
% 6.49/6.79 tff(5204,plain,
% 6.49/6.79 (b(z, s(s(elem!1)))),
% 6.49/6.79 inference(modus_ponens,[status(thm)],[149, 5203])).
% 6.49/6.79 tff(5205,plain,
% 6.49/6.79 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = elem!1)),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5190])).
% 6.49/6.79 tff(5206,plain,
% 6.49/6.79 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 6.49/6.79 inference(symmetry,[status(thm)],[5205])).
% 6.49/6.79 tff(5207,plain,
% 6.49/6.79 ((s(s(s(elem!1))) = elem!1) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 6.49/6.79 inference(transitivity,[status(thm)],[5206, 268])).
% 6.49/6.79 tff(5208,plain,
% 6.49/6.79 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5207])).
% 6.49/6.79 tff(5209,plain,
% 6.49/6.79 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 6.49/6.79 inference(modus_ponens,[status(thm)],[151, 5208])).
% 6.49/6.79 tff(5210,plain,
% 6.49/6.79 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), elem!1)),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5190])).
% 6.49/6.79 tff(5211,plain,
% 6.49/6.79 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.49/6.79 inference(symmetry,[status(thm)],[5210])).
% 6.49/6.79 tff(5212,plain,
% 6.49/6.79 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.49/6.79 inference(modus_ponens,[status(thm)],[231, 5211])).
% 6.49/6.79 tff(5213,plain,
% 6.49/6.79 ($false),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[4752, 5212, 5209, 2, 59, 174, 151, 168, 5204, 80, 91, 148, 5201])).
% 6.49/6.79 tff(5214,plain,(b(s(z), z) | (elem!1 = z) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), elem!1) | r(z, elem!1) | (s(z) = elem!1) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.79 tff(5215,plain,
% 6.49/6.79 (b(s(z), z)),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[5214, 174, 2, 168, 80, 150, 10])).
% 6.49/6.79 tff(5216,plain,
% 6.49/6.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 6.49/6.79 inference(rewrite,[status(thm)],[])).
% 6.49/6.79 tff(5217,plain,
% 6.49/6.79 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 6.49/6.79 inference(rewrite,[status(thm)],[])).
% 6.49/6.79 tff(5218,plain,
% 6.49/6.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))))),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5217])).
% 6.49/6.79 tff(5219,plain,
% 6.49/6.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 6.49/6.79 inference(transitivity,[status(thm)],[5218, 5216])).
% 6.49/6.79 tff(5220,plain,
% 6.49/6.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 6.49/6.79 inference(quant_inst,[status(thm)],[])).
% 6.49/6.79 tff(5221,plain,
% 6.49/6.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 6.49/6.79 inference(modus_ponens,[status(thm)],[5220, 5219])).
% 6.49/6.79 tff(5222,plain,
% 6.49/6.79 (~b(elem!1, s(z))),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[5221, 391, 149, 4942, 5215])).
% 6.49/6.79 tff(5223,plain,
% 6.49/6.79 (r(elem!1, s(z))),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[837, 5222, 173])).
% 6.49/6.79 tff(5224,plain,
% 6.49/6.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.49/6.79 inference(rewrite,[status(thm)],[])).
% 6.49/6.79 tff(5225,plain,
% 6.49/6.79 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.49/6.79 inference(rewrite,[status(thm)],[])).
% 6.49/6.79 tff(5226,plain,
% 6.49/6.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5225])).
% 6.49/6.79 tff(5227,plain,
% 6.49/6.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.49/6.79 inference(transitivity,[status(thm)],[5226, 5224])).
% 6.49/6.79 tff(5228,plain,
% 6.49/6.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 6.49/6.79 inference(quant_inst,[status(thm)],[])).
% 6.49/6.79 tff(5229,plain,
% 6.49/6.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 6.49/6.79 inference(modus_ponens,[status(thm)],[5228, 5227])).
% 6.49/6.79 tff(5230,plain,
% 6.49/6.79 ($false),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[5229, 391, 133, 665, 644, 590])).
% 6.49/6.79 tff(5231,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.49/6.79 tff(5232,plain,
% 6.49/6.79 (~b(s(z), elem!1)),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[5231, 5215, 4942, 149])).
% 6.49/6.79 tff(5233,plain,
% 6.49/6.79 (r(s(z), elem!1)),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[632, 5232, 150])).
% 6.49/6.79 tff(5234,plain,
% 6.49/6.79 (~b(elem!1, s(z))),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[5221, 391, 133, 665, 590])).
% 6.49/6.79 tff(5235,plain,
% 6.49/6.79 (r(elem!1, s(z))),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[837, 5234, 173])).
% 6.49/6.79 tff(5236,plain,
% 6.49/6.79 (~b(s(z), elem!1)),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[5231, 590, 665, 133])).
% 6.49/6.79 tff(5237,plain,
% 6.49/6.79 (r(s(z), elem!1)),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[632, 5236, 150])).
% 6.49/6.79 tff(5238,plain,
% 6.49/6.79 (r(s(z), elem!1)),
% 6.49/6.79 inference(unit_resolution,[status(thm)],[632, 150, 2829])).
% 6.49/6.79 tff(5239,plain,
% 6.49/6.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 6.49/6.79 inference(rewrite,[status(thm)],[])).
% 6.49/6.79 tff(5240,plain,
% 6.49/6.79 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 6.49/6.79 inference(rewrite,[status(thm)],[])).
% 6.49/6.79 tff(5241,plain,
% 6.49/6.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))))),
% 6.49/6.79 inference(monotonicity,[status(thm)],[5240])).
% 6.49/6.79 tff(5242,plain,
% 6.49/6.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 6.59/6.80 inference(transitivity,[status(thm)],[5241, 5239])).
% 6.59/6.80 tff(5243,plain,
% 6.59/6.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.59/6.80 inference(quant_inst,[status(thm)],[])).
% 6.59/6.80 tff(5244,plain,
% 6.59/6.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))),
% 6.59/6.80 inference(modus_ponens,[status(thm)],[5243, 5242])).
% 6.59/6.80 tff(5245,plain,
% 6.59/6.80 ($false),
% 6.59/6.80 inference(unit_resolution,[status(thm)],[5244, 194, 233, 5238, 232, 838])).
% 6.59/6.80 tff(5246,plain,((s(z) = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.59/6.80 tff(5247,plain,
% 6.59/6.80 (~r(s(z), s(s(s(elem!1))))),
% 6.59/6.80 inference(unit_resolution,[status(thm)],[5246, 5234, 150, 233, 5236])).
% 6.59/6.80 tff(5248,plain,
% 6.59/6.80 (b(s(z), s(s(s(elem!1))))),
% 6.59/6.80 inference(unit_resolution,[status(thm)],[247, 5247])).
% 6.59/6.80 tff(5249,plain,
% 6.59/6.80 ((elem!1 = s(z)) | r(elem!1, s(z))),
% 6.59/6.80 inference(unit_resolution,[status(thm)],[835, 42, 5234])).
% 6.59/6.80 tff(5250,plain,
% 6.59/6.80 (r(elem!1, s(z))),
% 6.59/6.80 inference(unit_resolution,[status(thm)],[5249, 1746])).
% 6.59/6.80 tff(5251,plain,
% 6.59/6.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.59/6.80 inference(rewrite,[status(thm)],[])).
% 6.59/6.80 tff(5252,plain,
% 6.59/6.80 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.59/6.80 inference(rewrite,[status(thm)],[])).
% 6.59/6.80 tff(5253,plain,
% 6.59/6.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 6.59/6.80 inference(monotonicity,[status(thm)],[5252])).
% 6.59/6.80 tff(5254,plain,
% 6.59/6.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.59/6.80 inference(transitivity,[status(thm)],[5253, 5251])).
% 6.59/6.80 tff(5255,plain,
% 6.59/6.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 6.59/6.80 inference(quant_inst,[status(thm)],[])).
% 6.59/6.80 tff(5256,plain,
% 6.59/6.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 6.59/6.80 inference(modus_ponens,[status(thm)],[5255, 5254])).
% 6.59/6.80 tff(5257,plain,
% 6.59/6.80 (~b(s(s(elem!1)), s(elem!1))),
% 6.59/6.80 inference(unit_resolution,[status(thm)],[5256, 391, 133, 665, 973, 2122])).
% 6.59/6.80 tff(5258,plain,
% 6.59/6.80 (r(s(s(elem!1)), s(elem!1))),
% 6.59/6.80 inference(unit_resolution,[status(thm)],[1133, 42, 5257, 285])).
% 6.59/6.80 tff(5259,plain,
% 6.59/6.80 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 6.59/6.80 inference(rewrite,[status(thm)],[])).
% 6.59/6.80 tff(5260,plain,
% 6.59/6.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 6.59/6.80 inference(monotonicity,[status(thm)],[5259])).
% 6.59/6.80 tff(5261,plain,
% 6.59/6.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 6.59/6.80 inference(transitivity,[status(thm)],[5260, 4116])).
% 6.59/6.80 tff(5262,plain,
% 6.59/6.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 6.59/6.80 inference(quant_inst,[status(thm)],[])).
% 6.59/6.80 tff(5263,plain,
% 6.59/6.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 6.59/6.80 inference(modus_ponens,[status(thm)],[5262, 5261])).
% 6.59/6.80 tff(5264,plain,
% 6.59/6.80 (~b(s(s(elem!1)), z)),
% 6.59/6.80 inference(unit_resolution,[status(thm)],[5263, 391, 133, 665, 973])).
% 6.59/6.80 tff(5265,plain,
% 6.59/6.80 (r(s(s(elem!1)), z)),
% 6.59/6.80 inference(unit_resolution,[status(thm)],[2627, 42, 215, 5264])).
% 6.59/6.80 tff(5266,plain,
% 6.59/6.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 6.59/6.80 inference(rewrite,[status(thm)],[])).
% 6.59/6.80 tff(5267,plain,
% 6.59/6.80 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 6.59/6.80 inference(rewrite,[status(thm)],[])).
% 6.59/6.80 tff(5268,plain,
% 6.59/6.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 6.59/6.80 inference(monotonicity,[status(thm)],[5267])).
% 6.59/6.80 tff(5269,plain,
% 6.59/6.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 6.59/6.80 inference(transitivity,[status(thm)],[5268, 5266])).
% 6.59/6.81 tff(5270,plain,
% 6.59/6.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 6.59/6.81 inference(quant_inst,[status(thm)],[])).
% 6.59/6.81 tff(5271,plain,
% 6.59/6.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 6.59/6.81 inference(modus_ponens,[status(thm)],[5270, 5269])).
% 6.59/6.81 tff(5272,plain,
% 6.59/6.81 (~b(z, s(elem!1))),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[5271, 391, 133, 665, 2122])).
% 6.59/6.81 tff(5273,plain,
% 6.59/6.81 (r(z, s(elem!1))),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[566, 5272])).
% 6.59/6.81 tff(5274,plain,
% 6.59/6.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 6.59/6.81 inference(rewrite,[status(thm)],[])).
% 6.59/6.81 tff(5275,plain,
% 6.59/6.81 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 6.59/6.81 inference(rewrite,[status(thm)],[])).
% 6.59/6.81 tff(5276,plain,
% 6.59/6.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1))))),
% 6.59/6.81 inference(monotonicity,[status(thm)],[5275])).
% 6.59/6.81 tff(5277,plain,
% 6.59/6.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 6.59/6.81 inference(transitivity,[status(thm)],[5276, 5274])).
% 6.59/6.81 tff(5278,plain,
% 6.59/6.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 6.59/6.81 inference(quant_inst,[status(thm)],[])).
% 6.59/6.81 tff(5279,plain,
% 6.59/6.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1))),
% 6.59/6.81 inference(modus_ponens,[status(thm)],[5278, 5277])).
% 6.59/6.81 tff(5280,plain,
% 6.59/6.81 (~b(s(elem!1), z)),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[5279, 391, 133, 665, 2122])).
% 6.59/6.81 tff(5281,plain,
% 6.59/6.81 (r(s(elem!1), z)),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[547, 42, 355, 5280])).
% 6.59/6.81 tff(5282,plain,
% 6.59/6.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 6.59/6.81 inference(rewrite,[status(thm)],[])).
% 6.59/6.81 tff(5283,plain,
% 6.59/6.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 6.59/6.81 inference(quant_inst,[status(thm)],[])).
% 6.59/6.81 tff(5284,plain,
% 6.59/6.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 6.59/6.81 inference(modus_ponens,[status(thm)],[5283, 5282])).
% 6.59/6.81 tff(5285,plain,
% 6.59/6.81 ($false),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[5284, 194, 5281, 5273, 5265, 5258])).
% 6.59/6.81 tff(5286,plain,((~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.81 tff(5287,plain,
% 6.59/6.81 (~b(s(s(elem!1)), elem!1)),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[5286, 133, 2122, 665, 285])).
% 6.59/6.81 tff(5288,plain,
% 6.59/6.81 (r(s(s(elem!1)), elem!1)),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[872, 5287, 249])).
% 6.59/6.81 tff(5289,plain,
% 6.59/6.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 6.59/6.81 inference(rewrite,[status(thm)],[])).
% 6.59/6.81 tff(5290,plain,
% 6.59/6.81 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 6.59/6.81 inference(rewrite,[status(thm)],[])).
% 6.59/6.81 tff(5291,plain,
% 6.59/6.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 6.59/6.81 inference(monotonicity,[status(thm)],[5290])).
% 6.59/6.81 tff(5292,plain,
% 6.59/6.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 6.59/6.81 inference(transitivity,[status(thm)],[5291, 5289])).
% 6.59/6.81 tff(5293,plain,
% 6.59/6.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 6.59/6.81 inference(quant_inst,[status(thm)],[])).
% 6.59/6.81 tff(5294,plain,
% 6.59/6.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))),
% 6.59/6.81 inference(modus_ponens,[status(thm)],[5293, 5292])).
% 6.59/6.81 tff(5295,plain,
% 6.59/6.81 (~r(s(z), s(s(elem!1)))),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[5294, 194, 5288, 1484, 5250])).
% 6.59/6.81 tff(5296,plain,
% 6.59/6.81 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[3414, 42, 5295])).
% 6.59/6.81 tff(5297,plain,
% 6.59/6.81 (b(s(z), s(s(elem!1)))),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[5296, 3404])).
% 6.59/6.81 tff(5298,plain,
% 6.59/6.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 6.59/6.81 inference(rewrite,[status(thm)],[])).
% 6.59/6.81 tff(5299,plain,
% 6.59/6.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 6.59/6.81 inference(quant_inst,[status(thm)],[])).
% 6.59/6.81 tff(5300,plain,
% 6.59/6.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 6.59/6.81 inference(modus_ponens,[status(thm)],[5299, 5298])).
% 6.59/6.81 tff(5301,plain,
% 6.59/6.81 (~r(s(s(elem!1)), s(z))),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[5300, 194, 5288, 1484, 5250])).
% 6.59/6.81 tff(5302,plain,
% 6.59/6.81 (b(s(s(elem!1)), s(z))),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[362, 5301])).
% 6.59/6.81 tff(5303,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 6.59/6.81 tff(5304,plain,
% 6.59/6.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.59/6.81 inference(rewrite,[status(thm)],[])).
% 6.59/6.81 tff(5305,plain,
% 6.59/6.81 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.59/6.81 inference(rewrite,[status(thm)],[])).
% 6.59/6.81 tff(5306,plain,
% 6.59/6.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.59/6.81 inference(monotonicity,[status(thm)],[5305])).
% 6.59/6.81 tff(5307,plain,
% 6.59/6.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.59/6.81 inference(transitivity,[status(thm)],[5306, 5304])).
% 6.59/6.81 tff(5308,plain,
% 6.59/6.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 6.59/6.81 inference(quant_inst,[status(thm)],[])).
% 6.59/6.81 tff(5309,plain,
% 6.59/6.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.59/6.81 inference(modus_ponens,[status(thm)],[5308, 5307])).
% 6.59/6.81 tff(5310,plain,
% 6.59/6.81 ($false),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[5309, 391, 381, 3927, 379, 590, 5303])).
% 6.59/6.81 tff(5311,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.81 tff(5312,plain,
% 6.59/6.81 (~b(z, s(s(elem!1)))),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[5311, 5302, 379, 590, 5297])).
% 6.59/6.81 tff(5313,plain,
% 6.59/6.81 (r(z, s(s(elem!1)))),
% 6.59/6.81 inference(unit_resolution,[status(thm)],[324, 5312])).
% 6.59/6.81 tff(5314,plain,
% 6.59/6.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.59/6.82 inference(rewrite,[status(thm)],[])).
% 6.59/6.82 tff(5315,plain,
% 6.59/6.82 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.59/6.82 inference(rewrite,[status(thm)],[])).
% 6.59/6.82 tff(5316,plain,
% 6.59/6.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.59/6.82 inference(monotonicity,[status(thm)],[5315])).
% 6.59/6.82 tff(5317,plain,
% 6.59/6.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.59/6.82 inference(transitivity,[status(thm)],[5316, 5314])).
% 6.59/6.82 tff(5318,plain,
% 6.59/6.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.59/6.82 inference(quant_inst,[status(thm)],[])).
% 6.59/6.82 tff(5319,plain,
% 6.59/6.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.59/6.82 inference(modus_ponens,[status(thm)],[5318, 5317])).
% 6.59/6.82 tff(5320,plain,
% 6.59/6.82 ($false),
% 6.59/6.82 inference(unit_resolution,[status(thm)],[5319, 391, 381, 1374, 379, 5303])).
% 6.59/6.82 tff(5321,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.82 tff(5322,plain,
% 6.59/6.82 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.59/6.82 inference(unit_resolution,[status(thm)],[5321, 5302, 379, 5297])).
% 6.59/6.82 tff(5323,plain,
% 6.59/6.82 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.59/6.82 inference(unit_resolution,[status(thm)],[1370, 5322, 297])).
% 6.59/6.82 tff(5324,plain,
% 6.59/6.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 6.59/6.82 inference(rewrite,[status(thm)],[])).
% 6.59/6.82 tff(5325,plain,
% 6.59/6.82 (((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 6.59/6.82 inference(rewrite,[status(thm)],[])).
% 6.59/6.82 tff(5326,plain,
% 6.59/6.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 6.59/6.82 inference(monotonicity,[status(thm)],[5325])).
% 6.59/6.82 tff(5327,plain,
% 6.59/6.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 6.59/6.82 inference(transitivity,[status(thm)],[5326, 5324])).
% 6.59/6.82 tff(5328,plain,
% 6.59/6.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 6.59/6.82 inference(quant_inst,[status(thm)],[])).
% 6.59/6.82 tff(5329,plain,
% 6.59/6.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 6.59/6.82 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 6.59/6.82 tff(5330,plain,
% 6.59/6.82 ($false),
% 6.59/6.82 inference(unit_resolution,[status(thm)],[5329, 194, 174, 5288, 5323, 5313])).
% 6.59/6.82 tff(5331,plain,((~b(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), elem!1)) | (s(z) = elem!1) | (~b(elem!1, z)) | (s(s(elem!1)) = elem!1) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.82 tff(5332,plain,
% 6.59/6.82 (~b(s(elem!1), elem!1)),
% 6.59/6.82 inference(unit_resolution,[status(thm)],[5331, 288, 174, 133, 590, 5237, 150, 665, 5248, 249, 265])).
% 6.59/6.82 tff(5333,plain,
% 6.59/6.82 (r(s(elem!1), elem!1)),
% 6.59/6.82 inference(unit_resolution,[status(thm)],[2168, 5332, 164])).
% 6.59/6.82 tff(5334,plain,
% 6.59/6.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 6.59/6.82 inference(rewrite,[status(thm)],[])).
% 6.59/6.82 tff(5335,plain,
% 6.59/6.82 (((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 6.59/6.82 inference(rewrite,[status(thm)],[])).
% 6.59/6.82 tff(5336,plain,
% 6.59/6.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 6.59/6.82 inference(monotonicity,[status(thm)],[5335])).
% 6.59/6.82 tff(5337,plain,
% 6.59/6.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 6.59/6.82 inference(transitivity,[status(thm)],[5336, 5334])).
% 6.59/6.82 tff(5338,plain,
% 6.59/6.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 6.59/6.82 inference(quant_inst,[status(thm)],[])).
% 6.59/6.82 tff(5339,plain,
% 6.59/6.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 6.59/6.83 inference(modus_ponens,[status(thm)],[5338, 5337])).
% 6.59/6.83 tff(5340,plain,
% 6.59/6.83 (~r(s(elem!1), s(z))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[5339, 194, 5333, 5237, 5235])).
% 6.59/6.83 tff(5341,plain,
% 6.59/6.83 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[1915, 42, 5340])).
% 6.59/6.83 tff(5342,plain,
% 6.59/6.83 (b(s(elem!1), s(z))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[5341, 1905])).
% 6.59/6.83 tff(5343,plain,
% 6.59/6.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 6.59/6.83 inference(rewrite,[status(thm)],[])).
% 6.59/6.83 tff(5344,plain,
% 6.59/6.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 6.59/6.83 inference(quant_inst,[status(thm)],[])).
% 6.59/6.83 tff(5345,plain,
% 6.59/6.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 6.59/6.83 inference(modus_ponens,[status(thm)],[5344, 5343])).
% 6.59/6.83 tff(5346,plain,
% 6.59/6.83 (~r(s(s(s(elem!1))), s(z))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[5345, 194, 233, 5237, 5235])).
% 6.59/6.83 tff(5347,plain,
% 6.59/6.83 (b(s(s(s(elem!1))), s(z))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[223, 5346])).
% 6.59/6.83 tff(5348,plain,
% 6.59/6.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.59/6.83 inference(rewrite,[status(thm)],[])).
% 6.59/6.83 tff(5349,plain,
% 6.59/6.83 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.59/6.83 inference(rewrite,[status(thm)],[])).
% 6.59/6.83 tff(5350,plain,
% 6.59/6.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.59/6.83 inference(monotonicity,[status(thm)],[5349])).
% 6.59/6.83 tff(5351,plain,
% 6.59/6.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.59/6.83 inference(transitivity,[status(thm)],[5350, 5348])).
% 6.59/6.83 tff(5352,plain,
% 6.59/6.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 6.59/6.83 inference(quant_inst,[status(thm)],[])).
% 6.59/6.83 tff(5353,plain,
% 6.59/6.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.59/6.83 inference(modus_ponens,[status(thm)],[5352, 5351])).
% 6.59/6.83 tff(5354,plain,
% 6.59/6.83 (~b(s(elem!1), s(s(s(elem!1))))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[5353, 391, 5248, 5347, 5342])).
% 6.59/6.83 tff(5355,plain,
% 6.59/6.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.59/6.83 inference(rewrite,[status(thm)],[])).
% 6.59/6.83 tff(5356,plain,
% 6.59/6.83 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), 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)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.59/6.83 inference(rewrite,[status(thm)],[])).
% 6.59/6.83 tff(5357,plain,
% 6.59/6.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 6.59/6.83 inference(monotonicity,[status(thm)],[5356])).
% 6.59/6.83 tff(5358,plain,
% 6.59/6.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.59/6.83 inference(transitivity,[status(thm)],[5357, 5355])).
% 6.59/6.83 tff(5359,plain,
% 6.59/6.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.59/6.83 inference(quant_inst,[status(thm)],[])).
% 6.59/6.83 tff(5360,plain,
% 6.59/6.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 6.59/6.83 inference(modus_ponens,[status(thm)],[5359, 5358])).
% 6.59/6.83 tff(5361,plain,
% 6.59/6.83 (~r(s(elem!1), s(s(s(elem!1))))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[5360, 194, 5333, 233, 5235])).
% 6.59/6.83 tff(5362,plain,
% 6.59/6.83 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[579, 42, 5361])).
% 6.59/6.83 tff(5363,plain,
% 6.59/6.83 (s(elem!1) = s(s(s(elem!1)))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[5362, 5354])).
% 6.59/6.83 tff(5364,plain,
% 6.59/6.83 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 6.59/6.83 inference(monotonicity,[status(thm)],[5363])).
% 6.59/6.83 tff(5365,plain,
% 6.59/6.83 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 6.59/6.83 inference(symmetry,[status(thm)],[5364])).
% 6.59/6.83 tff(5366,plain,
% 6.59/6.83 (s(s(elem!1)) = elem!1),
% 6.59/6.83 inference(transitivity,[status(thm)],[212, 5365, 108])).
% 6.59/6.83 tff(5367,plain,
% 6.59/6.83 ($false),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[249, 5366])).
% 6.59/6.83 tff(5368,plain,((s(s(elem!1)) = elem!1) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(elem!1) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (s(z) = elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.83 tff(5369,plain,
% 6.59/6.83 (s(s(elem!1)) = elem!1),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[5368, 174, 231, 159, 118, 149, 5215, 150, 4942])).
% 6.59/6.83 tff(5370,plain,
% 6.59/6.83 (s(s(s(elem!1))) = s(elem!1)),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[451, 5369])).
% 6.59/6.83 tff(5371,plain,
% 6.59/6.83 (~(s(s(s(s(z)))) = elem!1)),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[717, 5370])).
% 6.59/6.83 tff(5372,plain,
% 6.59/6.83 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 6.59/6.83 inference(monotonicity,[status(thm)],[465])).
% 6.59/6.83 tff(5373,plain,
% 6.59/6.83 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 6.59/6.83 inference(transitivity,[status(thm)],[5372, 2123])).
% 6.59/6.83 tff(5374,plain,
% 6.59/6.83 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 6.59/6.83 inference(monotonicity,[status(thm)],[5373])).
% 6.59/6.83 tff(5375,plain,
% 6.59/6.83 (~(s(elem!1) = s(s(s(s(z)))))),
% 6.59/6.83 inference(modus_ponens,[status(thm)],[3843, 5374])).
% 6.59/6.83 tff(5376,plain,
% 6.59/6.83 ($false),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[1945, 5375])).
% 6.59/6.83 tff(5377,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.83 tff(5378,plain,
% 6.59/6.83 (~(s(elem!1) = s(s(s(s(z)))))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[5377, 5370, 3363])).
% 6.59/6.83 tff(5379,plain,
% 6.59/6.83 (~(s(s(s(s(z)))) = s(elem!1))),
% 6.59/6.83 inference(modus_ponens,[status(thm)],[5378, 2125])).
% 6.59/6.83 tff(5380,plain,
% 6.59/6.83 (r(s(s(s(s(z)))), elem!1)),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[762, 4963, 720])).
% 6.59/6.83 tff(5381,plain,
% 6.59/6.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.59/6.83 inference(rewrite,[status(thm)],[])).
% 6.59/6.83 tff(5382,plain,
% 6.59/6.83 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.59/6.83 inference(rewrite,[status(thm)],[])).
% 6.59/6.83 tff(5383,plain,
% 6.59/6.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 6.59/6.83 inference(monotonicity,[status(thm)],[5382])).
% 6.59/6.83 tff(5384,plain,
% 6.59/6.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.59/6.83 inference(transitivity,[status(thm)],[5383, 5381])).
% 6.59/6.83 tff(5385,plain,
% 6.59/6.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.59/6.83 inference(quant_inst,[status(thm)],[])).
% 6.59/6.83 tff(5386,plain,
% 6.59/6.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 6.59/6.83 inference(modus_ponens,[status(thm)],[5385, 5384])).
% 6.59/6.83 tff(5387,plain,
% 6.59/6.83 (~b(s(z), s(s(s(s(z)))))),
% 6.59/6.83 inference(unit_resolution,[status(thm)],[5386, 391, 133, 665, 90, 590])).
% 6.59/6.84 tff(5388,plain,
% 6.59/6.84 (r(s(z), s(s(s(s(z)))))),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[1230, 5387])).
% 6.59/6.84 tff(5389,plain,
% 6.59/6.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.59/6.84 inference(rewrite,[status(thm)],[])).
% 6.59/6.84 tff(5390,plain,
% 6.59/6.84 (((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.59/6.84 inference(rewrite,[status(thm)],[])).
% 6.59/6.84 tff(5391,plain,
% 6.59/6.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))))),
% 6.59/6.84 inference(monotonicity,[status(thm)],[5390])).
% 6.59/6.84 tff(5392,plain,
% 6.59/6.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.59/6.84 inference(transitivity,[status(thm)],[5391, 5389])).
% 6.59/6.84 tff(5393,plain,
% 6.59/6.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.59/6.84 inference(quant_inst,[status(thm)],[])).
% 6.59/6.84 tff(5394,plain,
% 6.59/6.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))),
% 6.59/6.84 inference(modus_ponens,[status(thm)],[5393, 5392])).
% 6.59/6.84 tff(5395,plain,
% 6.59/6.84 ($false),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[5394, 194, 1484, 847, 2112, 1216])).
% 6.59/6.84 tff(5396,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.84 tff(5397,plain,
% 6.59/6.84 ($false),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[5396, 5388, 5380, 847, 1484])).
% 6.59/6.84 tff(5398,plain,((~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.84 tff(5399,plain,
% 6.59/6.84 (~b(s(s(s(s(z)))), z)),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[5398, 5371, 4942, 149, 5215, 5233, 5223])).
% 6.59/6.84 tff(5400,plain,
% 6.59/6.84 (r(s(s(s(s(z)))), z)),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[87, 5399])).
% 6.59/6.84 tff(5401,plain,
% 6.59/6.84 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 6.59/6.84 inference(monotonicity,[status(thm)],[5370])).
% 6.59/6.84 tff(5402,plain,
% 6.59/6.84 (r(z, s(elem!1))),
% 6.59/6.84 inference(modus_ponens,[status(thm)],[59, 5401])).
% 6.59/6.84 tff(5403,plain,
% 6.59/6.84 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 6.59/6.84 inference(monotonicity,[status(thm)],[5370])).
% 6.59/6.84 tff(5404,plain,
% 6.59/6.84 (r(s(elem!1), z)),
% 6.59/6.84 inference(modus_ponens,[status(thm)],[174, 5403])).
% 6.59/6.84 tff(5405,plain,
% 6.59/6.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 6.59/6.84 inference(rewrite,[status(thm)],[])).
% 6.59/6.84 tff(5406,plain,
% 6.59/6.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 6.59/6.84 inference(quant_inst,[status(thm)],[])).
% 6.59/6.84 tff(5407,plain,
% 6.59/6.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 6.59/6.84 inference(modus_ponens,[status(thm)],[5406, 5405])).
% 6.59/6.84 tff(5408,plain,
% 6.59/6.84 (~r(s(s(s(s(z)))), s(elem!1))),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[5407, 194, 5404, 5402, 5400])).
% 6.59/6.84 tff(5409,plain,
% 6.59/6.84 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[2136, 42, 5408])).
% 6.59/6.84 tff(5410,plain,
% 6.59/6.84 (b(s(s(s(s(z)))), s(elem!1))),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[5409, 5379])).
% 6.59/6.84 tff(5411,plain,
% 6.59/6.84 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 6.59/6.84 inference(monotonicity,[status(thm)],[5370])).
% 6.59/6.84 tff(5412,plain,
% 6.59/6.84 (~r(s(s(s(elem!1))), s(z))),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[5345, 194, 231, 5233, 5223])).
% 6.59/6.84 tff(5413,plain,
% 6.59/6.84 (b(s(s(s(elem!1))), s(z))),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[223, 5412])).
% 6.59/6.84 tff(5414,plain,
% 6.59/6.84 (b(s(elem!1), s(z))),
% 6.59/6.84 inference(modus_ponens,[status(thm)],[5413, 5411])).
% 6.59/6.84 tff(5415,plain,
% 6.59/6.84 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 6.59/6.84 inference(monotonicity,[status(thm)],[5370])).
% 6.59/6.84 tff(5416,plain,
% 6.59/6.84 (~r(s(z), s(s(s(elem!1))))),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[5246, 5222, 150, 231, 5232])).
% 6.59/6.84 tff(5417,plain,
% 6.59/6.84 (b(s(z), s(s(s(elem!1))))),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[247, 5416])).
% 6.59/6.84 tff(5418,plain,
% 6.59/6.84 (b(s(z), s(elem!1))),
% 6.59/6.84 inference(modus_ponens,[status(thm)],[5417, 5415])).
% 6.59/6.84 tff(5419,plain,
% 6.59/6.84 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 6.59/6.84 inference(monotonicity,[status(thm)],[5370])).
% 6.59/6.84 tff(5420,plain,
% 6.59/6.84 (~r(s(z), z)),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[3969, 5400, 59, 3363, 174])).
% 6.59/6.84 tff(5421,plain,
% 6.59/6.84 (r(s(elem!1), elem!1)),
% 6.59/6.84 inference(unit_resolution,[status(thm)],[472, 5370, 231])).
% 6.59/6.84 tff(5422,plain,
% 6.59/6.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.59/6.84 inference(rewrite,[status(thm)],[])).
% 6.59/6.84 tff(5423,plain,
% 6.59/6.84 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.59/6.84 inference(rewrite,[status(thm)],[])).
% 6.59/6.84 tff(5424,plain,
% 6.59/6.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 6.59/6.84 inference(monotonicity,[status(thm)],[5423])).
% 6.59/6.84 tff(5425,plain,
% 6.59/6.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.59/6.84 inference(transitivity,[status(thm)],[5424, 5422])).
% 6.59/6.84 tff(5426,plain,
% 6.59/6.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.59/6.85 inference(quant_inst,[status(thm)],[])).
% 6.59/6.85 tff(5427,plain,
% 6.59/6.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 6.59/6.85 inference(modus_ponens,[status(thm)],[5426, 5425])).
% 6.59/6.85 tff(5428,plain,
% 6.59/6.85 (~r(s(elem!1), s(s(s(elem!1))))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5427, 194, 1628, 174, 59])).
% 6.59/6.85 tff(5429,plain,
% 6.59/6.85 (r(s(z), elem!1)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[632, 2829, 150])).
% 6.59/6.85 tff(5430,plain,
% 6.59/6.85 (r(s(z), elem!1) <=> r(s(z), z)),
% 6.59/6.85 inference(symmetry,[status(thm)],[959])).
% 6.59/6.85 tff(5431,plain,
% 6.59/6.85 (r(s(z), z)),
% 6.59/6.85 inference(modus_ponens,[status(thm)],[1484, 5430])).
% 6.59/6.85 tff(5432,plain,
% 6.59/6.85 ($false),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[175, 5431])).
% 6.59/6.85 tff(5433,plain,((~(z = elem!1)) | r(s(z), z) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.85 tff(5434,plain,
% 6.59/6.85 (~(z = elem!1)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5433, 5429, 175])).
% 6.59/6.85 tff(5435,plain,
% 6.59/6.85 (b(z, elem!1)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[141, 80, 5434])).
% 6.59/6.85 tff(5436,plain,
% 6.59/6.85 (~(s(s(s(elem!1))) = elem!1)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[136, 10, 5435])).
% 6.59/6.85 tff(5437,plain,
% 6.59/6.85 (~(s(elem!1) = elem!1)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[158, 5436])).
% 6.59/6.85 tff(5438,plain,
% 6.59/6.85 (~(elem!1 = s(elem!1))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[166, 5437])).
% 6.59/6.85 tff(5439,plain,
% 6.59/6.85 (~(elem!1 = s(s(s(elem!1))))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[129, 5436])).
% 6.59/6.85 tff(5440,plain,
% 6.59/6.85 (r(elem!1, s(s(s(elem!1))))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[424, 5439, 4028])).
% 6.59/6.85 tff(5441,plain,
% 6.59/6.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 6.59/6.85 inference(rewrite,[status(thm)],[])).
% 6.59/6.85 tff(5442,plain,
% 6.59/6.85 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 6.59/6.85 inference(rewrite,[status(thm)],[])).
% 6.59/6.85 tff(5443,plain,
% 6.59/6.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))))),
% 6.59/6.85 inference(monotonicity,[status(thm)],[5442])).
% 6.59/6.85 tff(5444,plain,
% 6.59/6.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 6.59/6.85 inference(transitivity,[status(thm)],[5443, 5441])).
% 6.59/6.85 tff(5445,plain,
% 6.59/6.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 6.59/6.85 inference(quant_inst,[status(thm)],[])).
% 6.59/6.85 tff(5446,plain,
% 6.59/6.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 6.59/6.85 inference(modus_ponens,[status(thm)],[5445, 5444])).
% 6.59/6.85 tff(5447,plain,
% 6.59/6.85 (~r(s(z), s(elem!1))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5446, 194, 485, 5440, 5429])).
% 6.59/6.85 tff(5448,plain,
% 6.59/6.85 (~(s(z) = s(elem!1))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[117, 5434])).
% 6.59/6.85 tff(5449,plain,
% 6.59/6.85 (b(s(z), s(elem!1))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[602, 42, 5448, 5447])).
% 6.59/6.85 tff(5450,plain,
% 6.59/6.85 (b(s(z), z)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[180, 175])).
% 6.59/6.85 tff(5451,plain,
% 6.59/6.85 (z = elem!1),
% 6.59/6.85 inference(modus_ponens,[status(thm)],[11, 92])).
% 6.59/6.85 tff(5452,plain,
% 6.59/6.85 ($false),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[115, 5451])).
% 6.59/6.85 tff(5453,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.59/6.85 tff(5454,plain,
% 6.59/6.85 (~(elem!1 = z)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5453, 5434])).
% 6.59/6.85 tff(5455,plain,
% 6.59/6.85 (b(elem!1, z)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[526, 5454, 2282])).
% 6.59/6.85 tff(5456,plain,
% 6.59/6.85 (~b(elem!1, s(z))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5221, 391, 5435, 5455, 5450])).
% 6.59/6.85 tff(5457,plain,
% 6.59/6.85 ((elem!1 = s(z)) | r(elem!1, s(z))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[835, 42, 5456])).
% 6.59/6.85 tff(5458,plain,
% 6.59/6.85 (r(elem!1, s(z))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5457, 1746])).
% 6.59/6.85 tff(5459,plain,
% 6.59/6.85 (~(s(elem!1) = s(z))),
% 6.59/6.85 inference(modus_ponens,[status(thm)],[5448, 1904])).
% 6.59/6.85 tff(5460,plain,
% 6.59/6.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 6.59/6.85 inference(rewrite,[status(thm)],[])).
% 6.59/6.85 tff(5461,plain,
% 6.59/6.85 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 6.59/6.85 inference(rewrite,[status(thm)],[])).
% 6.59/6.85 tff(5462,plain,
% 6.59/6.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))))),
% 6.59/6.85 inference(monotonicity,[status(thm)],[5461])).
% 6.59/6.85 tff(5463,plain,
% 6.59/6.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 6.59/6.85 inference(transitivity,[status(thm)],[5462, 5460])).
% 6.59/6.85 tff(5464,plain,
% 6.59/6.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 6.59/6.85 inference(quant_inst,[status(thm)],[])).
% 6.59/6.85 tff(5465,plain,
% 6.59/6.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 6.59/6.85 inference(modus_ponens,[status(thm)],[5464, 5463])).
% 6.59/6.85 tff(5466,plain,
% 6.59/6.85 (~r(s(elem!1), s(z))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5465, 194, 485, 5440, 5429])).
% 6.59/6.85 tff(5467,plain,
% 6.59/6.85 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[1915, 42, 5466])).
% 6.59/6.85 tff(5468,plain,
% 6.59/6.85 (b(s(elem!1), s(z))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5467, 5459])).
% 6.59/6.85 tff(5469,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 6.59/6.85 tff(5470,plain,
% 6.59/6.85 (~(s(s(s(s(z)))) = elem!1)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[717, 465])).
% 6.59/6.85 tff(5471,plain,
% 6.59/6.85 (~b(s(s(s(s(z)))), z)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5398, 5470, 1484, 847, 133, 665, 590])).
% 6.59/6.85 tff(5472,plain,
% 6.59/6.85 (r(s(s(s(s(z)))), z)),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[87, 5471])).
% 6.59/6.85 tff(5473,plain,
% 6.59/6.85 (r(s(z), s(s(elem!1))) <=> r(s(z), elem!1)),
% 6.59/6.85 inference(monotonicity,[status(thm)],[2459])).
% 6.59/6.85 tff(5474,plain,
% 6.59/6.85 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 6.59/6.85 inference(symmetry,[status(thm)],[5473])).
% 6.59/6.85 tff(5475,plain,
% 6.59/6.85 (r(s(z), s(s(elem!1)))),
% 6.59/6.85 inference(modus_ponens,[status(thm)],[1484, 5474])).
% 6.59/6.85 tff(5476,plain,
% 6.59/6.85 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 6.59/6.85 inference(monotonicity,[status(thm)],[2268])).
% 6.59/6.85 tff(5477,plain,
% 6.59/6.85 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 6.59/6.85 inference(symmetry,[status(thm)],[5476])).
% 6.59/6.85 tff(5478,plain,
% 6.59/6.85 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 6.59/6.85 inference(monotonicity,[status(thm)],[5477])).
% 6.59/6.85 tff(5479,plain,
% 6.59/6.85 (~(s(s(s(s(z)))) = s(elem!1))),
% 6.59/6.85 inference(modus_ponens,[status(thm)],[3843, 5478])).
% 6.59/6.85 tff(5480,plain,
% 6.59/6.85 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 6.59/6.85 inference(monotonicity,[status(thm)],[465])).
% 6.59/6.85 tff(5481,plain,
% 6.59/6.85 (r(z, s(elem!1))),
% 6.59/6.85 inference(modus_ponens,[status(thm)],[184, 5480])).
% 6.59/6.85 tff(5482,plain,
% 6.59/6.85 (~r(s(s(s(s(z)))), s(elem!1))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5407, 194, 1628, 5481, 5472])).
% 6.59/6.85 tff(5483,plain,
% 6.59/6.85 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[2136, 42, 5482])).
% 6.59/6.85 tff(5484,plain,
% 6.59/6.85 (b(s(s(s(s(z)))), s(elem!1))),
% 6.59/6.85 inference(unit_resolution,[status(thm)],[5483, 5479])).
% 6.59/6.85 tff(5485,plain,
% 6.59/6.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.59/6.85 inference(rewrite,[status(thm)],[])).
% 6.59/6.85 tff(5486,plain,
% 6.59/6.85 (((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.59/6.85 inference(rewrite,[status(thm)],[])).
% 6.59/6.85 tff(5487,plain,
% 6.59/6.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 6.59/6.85 inference(monotonicity,[status(thm)],[5486])).
% 6.59/6.85 tff(5488,plain,
% 6.59/6.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.59/6.85 inference(transitivity,[status(thm)],[5487, 5485])).
% 6.59/6.85 tff(5489,plain,
% 6.59/6.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.59/6.85 inference(quant_inst,[status(thm)],[])).
% 6.59/6.85 tff(5490,plain,
% 6.59/6.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 6.59/6.86 inference(modus_ponens,[status(thm)],[5489, 5488])).
% 6.59/6.86 tff(5491,plain,
% 6.59/6.86 (~b(s(s(s(s(z)))), s(z))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[5490, 391, 751, 5469, 5484])).
% 6.59/6.86 tff(5492,plain,
% 6.59/6.86 (r(s(s(s(s(z)))), s(z))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[749, 5491])).
% 6.59/6.86 tff(5493,plain,
% 6.59/6.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.59/6.86 inference(rewrite,[status(thm)],[])).
% 6.59/6.86 tff(5494,plain,
% 6.59/6.86 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.59/6.86 inference(rewrite,[status(thm)],[])).
% 6.59/6.86 tff(5495,plain,
% 6.59/6.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 6.59/6.86 inference(monotonicity,[status(thm)],[5494])).
% 6.59/6.86 tff(5496,plain,
% 6.59/6.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.59/6.86 inference(transitivity,[status(thm)],[5495, 5493])).
% 6.59/6.86 tff(5497,plain,
% 6.59/6.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 6.59/6.86 inference(quant_inst,[status(thm)],[])).
% 6.59/6.86 tff(5498,plain,
% 6.59/6.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 6.59/6.86 inference(modus_ponens,[status(thm)],[5497, 5496])).
% 6.59/6.86 tff(5499,plain,
% 6.59/6.86 ($false),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[5498, 194, 722, 2053, 723, 4832])).
% 6.59/6.86 tff(5500,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.86 tff(5501,plain,
% 6.59/6.86 (~r(z, s(z))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[5500, 5492, 5475, 5472])).
% 6.59/6.86 tff(5502,plain,
% 6.59/6.86 (b(z, s(z))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[678, 5501])).
% 6.59/6.86 tff(5503,plain,
% 6.59/6.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.59/6.86 inference(rewrite,[status(thm)],[])).
% 6.59/6.86 tff(5504,plain,
% 6.59/6.86 (((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.59/6.86 inference(rewrite,[status(thm)],[])).
% 6.59/6.86 tff(5505,plain,
% 6.59/6.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 6.59/6.86 inference(monotonicity,[status(thm)],[5504])).
% 6.59/6.86 tff(5506,plain,
% 6.59/6.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.59/6.86 inference(transitivity,[status(thm)],[5505, 5503])).
% 6.59/6.86 tff(5507,plain,
% 6.59/6.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.59/6.86 inference(quant_inst,[status(thm)],[])).
% 6.59/6.86 tff(5508,plain,
% 6.59/6.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 6.59/6.86 inference(modus_ponens,[status(thm)],[5507, 5506])).
% 6.59/6.86 tff(5509,plain,
% 6.59/6.86 (~b(s(z), s(s(s(s(z)))))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[5508, 391, 751, 5469, 5484])).
% 6.59/6.86 tff(5510,plain,
% 6.59/6.86 (r(s(z), s(s(s(s(z)))))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[1230, 5509])).
% 6.59/6.86 tff(5511,plain,
% 6.59/6.86 (~(elem!1 = s(s(s(s(z)))))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[769, 5470])).
% 6.59/6.86 tff(5512,plain,
% 6.59/6.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.59/6.86 inference(rewrite,[status(thm)],[])).
% 6.59/6.86 tff(5513,plain,
% 6.59/6.86 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.59/6.86 inference(rewrite,[status(thm)],[])).
% 6.59/6.86 tff(5514,plain,
% 6.59/6.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 6.59/6.86 inference(monotonicity,[status(thm)],[5513])).
% 6.59/6.86 tff(5515,plain,
% 6.59/6.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.59/6.86 inference(transitivity,[status(thm)],[5514, 5512])).
% 6.59/6.86 tff(5516,plain,
% 6.59/6.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.59/6.86 inference(quant_inst,[status(thm)],[])).
% 6.59/6.86 tff(5517,plain,
% 6.59/6.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 6.59/6.86 inference(modus_ponens,[status(thm)],[5516, 5515])).
% 6.59/6.86 tff(5518,plain,
% 6.59/6.86 (~r(elem!1, s(s(s(s(z)))))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[5517, 194, 1484, 847, 5492])).
% 6.59/6.86 tff(5519,plain,
% 6.59/6.86 (b(elem!1, s(s(s(s(z)))))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[781, 5518, 5511])).
% 6.59/6.86 tff(5520,plain,
% 6.59/6.86 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 6.59/6.86 inference(monotonicity,[status(thm)],[2268])).
% 6.59/6.86 tff(5521,plain,
% 6.59/6.86 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 6.59/6.86 inference(transitivity,[status(thm)],[5520, 3928])).
% 6.59/6.86 tff(5522,plain,
% 6.59/6.86 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 6.59/6.86 inference(symmetry,[status(thm)],[5521])).
% 6.59/6.86 tff(5523,plain,
% 6.59/6.86 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 6.59/6.86 inference(monotonicity,[status(thm)],[5522])).
% 6.59/6.86 tff(5524,plain,
% 6.59/6.86 (~(s(elem!1) = s(s(s(s(z)))))),
% 6.59/6.86 inference(modus_ponens,[status(thm)],[3843, 5523])).
% 6.59/6.86 tff(5525,plain,
% 6.59/6.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.59/6.86 inference(rewrite,[status(thm)],[])).
% 6.59/6.86 tff(5526,plain,
% 6.59/6.86 (((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.59/6.86 inference(rewrite,[status(thm)],[])).
% 6.59/6.86 tff(5527,plain,
% 6.59/6.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 6.59/6.86 inference(monotonicity,[status(thm)],[5526])).
% 6.59/6.86 tff(5528,plain,
% 6.59/6.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.59/6.86 inference(transitivity,[status(thm)],[5527, 5525])).
% 6.59/6.86 tff(5529,plain,
% 6.59/6.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.59/6.86 inference(quant_inst,[status(thm)],[])).
% 6.59/6.86 tff(5530,plain,
% 6.59/6.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 6.59/6.86 inference(modus_ponens,[status(thm)],[5529, 5528])).
% 6.59/6.86 tff(5531,plain,
% 6.59/6.86 (~r(s(elem!1), s(s(s(s(z)))))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[5530, 194, 1628, 5481, 5472])).
% 6.59/6.86 tff(5532,plain,
% 6.59/6.86 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[2142, 42, 5531])).
% 6.59/6.86 tff(5533,plain,
% 6.59/6.86 (b(s(elem!1), s(s(s(s(z)))))),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[5532, 5524])).
% 6.59/6.86 tff(5534,plain,
% 6.59/6.86 (~r(s(s(s(s(z)))), elem!1)),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[5396, 5510, 847, 1484])).
% 6.59/6.86 tff(5535,plain,
% 6.59/6.86 (b(s(s(s(s(z)))), elem!1)),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[762, 5534, 5470])).
% 6.59/6.86 tff(5536,plain,
% 6.59/6.86 (~(s(s(z)) = elem!1)),
% 6.59/6.86 inference(unit_resolution,[status(thm)],[4584, 465, 121])).
% 6.59/6.87 tff(5537,plain,
% 6.59/6.87 (~b(elem!1, s(elem!1))),
% 6.59/6.87 inference(unit_resolution,[status(thm)],[4603, 465, 4028])).
% 6.59/6.87 tff(5538,plain,
% 6.59/6.87 (r(elem!1, s(elem!1))),
% 6.59/6.87 inference(unit_resolution,[status(thm)],[443, 5537, 437])).
% 6.59/6.87 tff(5539,plain,
% 6.59/6.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.59/6.87 inference(rewrite,[status(thm)],[])).
% 6.59/6.87 tff(5540,plain,
% 6.59/6.87 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.59/6.87 inference(rewrite,[status(thm)],[])).
% 6.59/6.87 tff(5541,plain,
% 6.59/6.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))))),
% 6.59/6.87 inference(monotonicity,[status(thm)],[5540])).
% 6.59/6.87 tff(5542,plain,
% 6.59/6.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.59/6.87 inference(transitivity,[status(thm)],[5541, 5539])).
% 6.59/6.87 tff(5543,plain,
% 6.59/6.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.59/6.87 inference(quant_inst,[status(thm)],[])).
% 6.59/6.87 tff(5544,plain,
% 6.59/6.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))),
% 6.59/6.87 inference(modus_ponens,[status(thm)],[5543, 5542])).
% 6.59/6.87 tff(5545,plain,
% 6.59/6.87 (~b(s(s(z)), s(elem!1))),
% 6.59/6.87 inference(unit_resolution,[status(thm)],[5544, 391, 665, 3823, 1652, 4682])).
% 6.59/6.87 tff(5546,plain,
% 6.59/6.87 (r(s(s(z)), s(elem!1))),
% 6.59/6.87 inference(unit_resolution,[status(thm)],[4693, 42, 4690, 5545])).
% 6.59/6.87 tff(5547,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 6.59/6.87 tff(5548,plain,
% 6.59/6.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 6.59/6.87 inference(rewrite,[status(thm)],[])).
% 6.59/6.87 tff(5549,plain,
% 6.59/6.87 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 6.59/6.87 inference(rewrite,[status(thm)],[])).
% 6.59/6.87 tff(5550,plain,
% 6.59/6.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 6.59/6.87 inference(monotonicity,[status(thm)],[5549])).
% 6.59/6.87 tff(5551,plain,
% 6.59/6.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 6.59/6.87 inference(transitivity,[status(thm)],[5550, 5548])).
% 6.59/6.87 tff(5552,plain,
% 6.59/6.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 6.59/6.87 inference(quant_inst,[status(thm)],[])).
% 6.59/6.87 tff(5553,plain,
% 6.59/6.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))),
% 6.59/6.87 inference(modus_ponens,[status(thm)],[5552, 5551])).
% 6.59/6.87 tff(5554,plain,
% 6.59/6.87 (~b(s(s(z)), elem!1)),
% 6.59/6.87 inference(unit_resolution,[status(thm)],[5553, 391, 665, 3823, 2064, 1652])).
% 6.59/6.87 tff(5555,plain,
% 6.59/6.87 (r(s(s(z)), elem!1)),
% 6.59/6.87 inference(unit_resolution,[status(thm)],[4730, 5554, 5547])).
% 6.59/6.87 tff(5556,plain,
% 6.59/6.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 6.59/6.87 inference(rewrite,[status(thm)],[])).
% 6.59/6.87 tff(5557,plain,
% 6.59/6.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 6.59/6.87 inference(quant_inst,[status(thm)],[])).
% 6.59/6.87 tff(5558,plain,
% 6.59/6.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))),
% 6.59/6.87 inference(modus_ponens,[status(thm)],[5557, 5556])).
% 6.59/6.87 tff(5559,plain,
% 6.59/6.87 ($false),
% 6.59/6.87 inference(unit_resolution,[status(thm)],[5558, 194, 485, 2251, 5555, 5546])).
% 6.59/6.87 tff(5560,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(z)) = s(elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.87 tff(5561,plain,
% 6.59/6.87 (~b(s(s(z)), s(s(s(s(z)))))),
% 6.59/6.87 inference(unit_resolution,[status(thm)],[5560, 5538, 485, 2494, 5536, 665, 5535, 5533, 5519])).
% 6.59/6.87 tff(5562,plain,
% 6.59/6.87 (r(s(s(z)), s(s(s(s(z)))))),
% 6.59/6.87 inference(unit_resolution,[status(thm)],[3652, 5561])).
% 6.59/6.87 tff(5563,plain,
% 6.59/6.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 6.59/6.88 inference(rewrite,[status(thm)],[])).
% 6.59/6.88 tff(5564,plain,
% 6.59/6.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 6.59/6.88 inference(quant_inst,[status(thm)],[])).
% 6.59/6.88 tff(5565,plain,
% 6.59/6.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))),
% 6.59/6.88 inference(modus_ponens,[status(thm)],[5564, 5563])).
% 6.59/6.88 tff(5566,plain,
% 6.59/6.88 ($false),
% 6.59/6.88 inference(unit_resolution,[status(thm)],[5565, 194, 1749, 2053, 1216, 2405])).
% 6.59/6.88 tff(5567,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.88 tff(5568,plain,
% 6.59/6.88 (~r(s(s(s(s(z)))), z)),
% 6.59/6.88 inference(unit_resolution,[status(thm)],[5567, 1749, 1216, 2405])).
% 6.59/6.88 tff(5569,plain,
% 6.59/6.88 (b(s(s(s(s(z)))), z)),
% 6.59/6.88 inference(unit_resolution,[status(thm)],[87, 5568])).
% 6.59/6.88 tff(5570,plain,
% 6.59/6.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 6.59/6.88 inference(rewrite,[status(thm)],[])).
% 6.59/6.88 tff(5571,plain,
% 6.59/6.88 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 6.59/6.88 inference(rewrite,[status(thm)],[])).
% 6.59/6.88 tff(5572,plain,
% 6.59/6.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 6.59/6.88 inference(monotonicity,[status(thm)],[5571])).
% 6.59/6.88 tff(5573,plain,
% 6.59/6.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 6.59/6.88 inference(transitivity,[status(thm)],[5572, 5570])).
% 6.59/6.88 tff(5574,plain,
% 6.59/6.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 6.59/6.88 inference(quant_inst,[status(thm)],[])).
% 6.59/6.88 tff(5575,plain,
% 6.59/6.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 6.59/6.88 inference(modus_ponens,[status(thm)],[5574, 5573])).
% 6.59/6.88 tff(5576,plain,
% 6.59/6.88 (~b(s(s(s(s(z)))), s(z))),
% 6.59/6.88 inference(unit_resolution,[status(thm)],[5575, 391, 5569, 664, 590])).
% 6.59/6.88 tff(5577,plain,
% 6.59/6.88 (r(s(s(s(s(z)))), s(z))),
% 6.59/6.88 inference(unit_resolution,[status(thm)],[749, 5576])).
% 6.59/6.88 tff(5578,plain,
% 6.59/6.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 6.59/6.88 inference(rewrite,[status(thm)],[])).
% 6.59/6.88 tff(5579,plain,
% 6.59/6.88 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 6.59/6.88 inference(rewrite,[status(thm)],[])).
% 6.59/6.88 tff(5580,plain,
% 6.59/6.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))))),
% 6.59/6.88 inference(monotonicity,[status(thm)],[5579])).
% 6.59/6.88 tff(5581,plain,
% 6.59/6.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 6.59/6.88 inference(transitivity,[status(thm)],[5580, 5578])).
% 6.59/6.88 tff(5582,plain,
% 6.59/6.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.59/6.88 inference(quant_inst,[status(thm)],[])).
% 6.59/6.88 tff(5583,plain,
% 6.59/6.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))),
% 6.59/6.88 inference(modus_ponens,[status(thm)],[5582, 5581])).
% 6.59/6.88 tff(5584,plain,
% 6.59/6.88 ($false),
% 6.59/6.88 inference(unit_resolution,[status(thm)],[5583, 194, 1749, 1216, 5577, 2405])).
% 6.59/6.88 tff(5585,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.88 tff(5586,plain,
% 6.59/6.88 (~r(s(s(z)), s(z))),
% 6.59/6.88 inference(unit_resolution,[status(thm)],[5585, 5562, 5510, 590, 5502])).
% 6.59/6.88 tff(5587,plain,
% 6.59/6.88 (b(s(s(z)), s(z))),
% 6.59/6.88 inference(unit_resolution,[status(thm)],[3778, 5586])).
% 6.59/6.88 tff(5588,plain,
% 6.59/6.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 6.59/6.88 inference(rewrite,[status(thm)],[])).
% 6.59/6.88 tff(5589,plain,
% 6.59/6.88 (((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 6.59/6.88 inference(rewrite,[status(thm)],[])).
% 6.59/6.88 tff(5590,plain,
% 6.59/6.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 6.59/6.88 inference(monotonicity,[status(thm)],[5589])).
% 6.59/6.89 tff(5591,plain,
% 6.59/6.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 6.59/6.89 inference(transitivity,[status(thm)],[5590, 5588])).
% 6.59/6.89 tff(5592,plain,
% 6.59/6.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 6.59/6.89 inference(quant_inst,[status(thm)],[])).
% 6.59/6.89 tff(5593,plain,
% 6.59/6.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 6.59/6.89 inference(modus_ponens,[status(thm)],[5592, 5591])).
% 6.59/6.89 tff(5594,plain,
% 6.59/6.89 (~b(s(s(z)), z)),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[5593, 391, 751, 5587, 5502, 5469])).
% 6.59/6.89 tff(5595,plain,
% 6.59/6.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 6.59/6.89 inference(rewrite,[status(thm)],[])).
% 6.59/6.89 tff(5596,plain,
% 6.59/6.89 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 6.59/6.89 inference(rewrite,[status(thm)],[])).
% 6.59/6.89 tff(5597,plain,
% 6.59/6.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 6.59/6.89 inference(monotonicity,[status(thm)],[5596])).
% 6.59/6.89 tff(5598,plain,
% 6.59/6.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 6.59/6.89 inference(transitivity,[status(thm)],[5597, 5595])).
% 6.59/6.89 tff(5599,plain,
% 6.59/6.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 6.59/6.89 inference(quant_inst,[status(thm)],[])).
% 6.59/6.89 tff(5600,plain,
% 6.59/6.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 6.59/6.89 inference(modus_ponens,[status(thm)],[5599, 5598])).
% 6.59/6.89 tff(5601,plain,
% 6.59/6.89 (~b(z, s(s(s(s(z)))))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[5600, 391, 133, 665, 5535])).
% 6.59/6.89 tff(5602,plain,
% 6.59/6.89 (r(z, s(s(s(s(z)))))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[800, 5601])).
% 6.59/6.89 tff(5603,plain,
% 6.59/6.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.59/6.89 inference(rewrite,[status(thm)],[])).
% 6.59/6.89 tff(5604,plain,
% 6.59/6.89 (((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.59/6.89 inference(rewrite,[status(thm)],[])).
% 6.59/6.89 tff(5605,plain,
% 6.59/6.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 6.59/6.89 inference(monotonicity,[status(thm)],[5604])).
% 6.59/6.89 tff(5606,plain,
% 6.59/6.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.59/6.89 inference(transitivity,[status(thm)],[5605, 5603])).
% 6.59/6.89 tff(5607,plain,
% 6.59/6.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 6.59/6.89 inference(quant_inst,[status(thm)],[])).
% 6.59/6.89 tff(5608,plain,
% 6.59/6.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 6.59/6.89 inference(modus_ponens,[status(thm)],[5607, 5606])).
% 6.59/6.89 tff(5609,plain,
% 6.59/6.89 (~r(s(s(z)), z)),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[5608, 194, 5562, 5472, 5602])).
% 6.59/6.89 tff(5610,plain,
% 6.59/6.89 ($false),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[1211, 5609, 5594])).
% 6.59/6.89 tff(5611,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (s(z) = s(elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.59/6.89 tff(5612,plain,
% 6.59/6.89 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[5611, 1628, 5468, 5450, 485, 5455, 5448, 5429, 5458, 5435, 3363, 5449, 59, 5438, 4028])).
% 6.59/6.89 tff(5613,plain,
% 6.59/6.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 6.59/6.89 inference(rewrite,[status(thm)],[])).
% 6.59/6.89 tff(5614,plain,
% 6.59/6.89 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 6.59/6.89 inference(rewrite,[status(thm)],[])).
% 6.59/6.89 tff(5615,plain,
% 6.59/6.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 6.59/6.89 inference(monotonicity,[status(thm)],[5614])).
% 6.59/6.89 tff(5616,plain,
% 6.59/6.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 6.59/6.89 inference(transitivity,[status(thm)],[5615, 5613])).
% 6.59/6.89 tff(5617,plain,
% 6.59/6.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 6.59/6.89 inference(quant_inst,[status(thm)],[])).
% 6.59/6.89 tff(5618,plain,
% 6.59/6.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 6.59/6.89 inference(modus_ponens,[status(thm)],[5617, 5616])).
% 6.59/6.89 tff(5619,plain,
% 6.59/6.89 (~r(s(s(s(elem!1))), s(elem!1))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[5618, 194, 1628, 174, 59])).
% 6.59/6.89 tff(5620,plain,
% 6.59/6.89 (b(s(s(s(elem!1))), s(elem!1))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[588, 5612, 5619])).
% 6.59/6.89 tff(5621,plain,
% 6.59/6.89 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 6.59/6.89 inference(monotonicity,[status(thm)],[2602])).
% 6.59/6.89 tff(5622,plain,
% 6.59/6.89 (~(s(elem!1) = s(s(s(elem!1))))),
% 6.59/6.89 inference(modus_ponens,[status(thm)],[279, 5621])).
% 6.59/6.89 tff(5623,plain,
% 6.59/6.89 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[579, 42, 3612])).
% 6.59/6.89 tff(5624,plain,
% 6.59/6.89 (b(s(elem!1), s(s(s(elem!1))))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[5623, 5622])).
% 6.59/6.89 tff(5625,plain,
% 6.59/6.89 (~(s(s(elem!1)) = elem!1)),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[451, 279])).
% 6.59/6.89 tff(5626,plain,
% 6.59/6.89 (~(s(elem!1) = elem!1)),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[1943, 5625])).
% 6.59/6.89 tff(5627,plain,
% 6.59/6.89 (~(elem!1 = s(elem!1))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[166, 5626])).
% 6.59/6.89 tff(5628,plain,
% 6.59/6.89 (~(z = elem!1)),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[5433, 5238, 175])).
% 6.59/6.89 tff(5629,plain,
% 6.59/6.89 (~(s(z) = s(elem!1))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[117, 5628])).
% 6.59/6.89 tff(5630,plain,
% 6.59/6.89 (~(elem!1 = z)),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[5453, 5628])).
% 6.59/6.89 tff(5631,plain,
% 6.59/6.89 (b(elem!1, z)),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[526, 5630, 2282])).
% 6.59/6.89 tff(5632,plain,
% 6.59/6.89 (b(z, elem!1)),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[141, 5628, 80])).
% 6.59/6.89 tff(5633,plain,
% 6.59/6.89 (~b(elem!1, s(z))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[5221, 391, 5632, 5631, 5450])).
% 6.59/6.89 tff(5634,plain,
% 6.59/6.89 ((elem!1 = s(z)) | r(elem!1, s(z))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[835, 42, 5633])).
% 6.59/6.89 tff(5635,plain,
% 6.59/6.89 (r(elem!1, s(z))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[5634, 1746])).
% 6.59/6.89 tff(5636,plain,
% 6.59/6.89 (~(s(s(s(elem!1))) = elem!1)),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[136, 5632, 10])).
% 6.59/6.89 tff(5637,plain,
% 6.59/6.89 (r(elem!1, s(s(s(elem!1))))),
% 6.59/6.89 inference(unit_resolution,[status(thm)],[424, 4028, 4029])).
% 6.59/6.89 tff(5638,plain,
% 6.59/6.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.59/6.89 inference(rewrite,[status(thm)],[])).
% 6.59/6.89 tff(5639,plain,
% 6.59/6.89 (((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.59/6.89 inference(rewrite,[status(thm)],[])).
% 6.69/6.90 tff(5640,plain,
% 6.69/6.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))))),
% 6.69/6.90 inference(monotonicity,[status(thm)],[5639])).
% 6.69/6.90 tff(5641,plain,
% 6.69/6.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.69/6.90 inference(transitivity,[status(thm)],[5640, 5638])).
% 6.69/6.90 tff(5642,plain,
% 6.69/6.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 6.69/6.90 inference(quant_inst,[status(thm)],[])).
% 6.69/6.90 tff(5643,plain,
% 6.69/6.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))),
% 6.69/6.90 inference(modus_ponens,[status(thm)],[5642, 5641])).
% 6.69/6.90 tff(5644,plain,
% 6.69/6.90 ($false),
% 6.69/6.90 inference(unit_resolution,[status(thm)],[5643, 194, 174, 410, 1484, 232])).
% 6.69/6.90 tff(5645,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.90 tff(5646,plain,
% 6.69/6.90 (~r(s(z), s(s(s(elem!1))))),
% 6.69/6.90 inference(unit_resolution,[status(thm)],[5645, 174, 5637, 1484])).
% 6.69/6.90 tff(5647,plain,
% 6.69/6.90 (b(s(z), s(s(s(elem!1))))),
% 6.69/6.90 inference(unit_resolution,[status(thm)],[247, 5646])).
% 6.69/6.90 tff(5648,plain,
% 6.69/6.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.90 inference(rewrite,[status(thm)],[])).
% 6.69/6.90 tff(5649,plain,
% 6.69/6.90 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.90 inference(rewrite,[status(thm)],[])).
% 6.69/6.90 tff(5650,plain,
% 6.69/6.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.69/6.90 inference(monotonicity,[status(thm)],[5649])).
% 6.69/6.90 tff(5651,plain,
% 6.69/6.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.90 inference(transitivity,[status(thm)],[5650, 5648])).
% 6.69/6.90 tff(5652,plain,
% 6.69/6.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))),
% 6.69/6.90 inference(quant_inst,[status(thm)],[])).
% 6.69/6.90 tff(5653,plain,
% 6.69/6.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.69/6.90 inference(modus_ponens,[status(thm)],[5652, 5651])).
% 6.69/6.90 tff(5654,plain,
% 6.69/6.90 (~b(s(elem!1), s(z))),
% 6.69/6.90 inference(unit_resolution,[status(thm)],[5653, 391, 1101, 5647, 5624])).
% 6.69/6.90 tff(5655,plain,
% 6.69/6.90 ((s(elem!1) = s(z)) | r(s(elem!1), s(z))),
% 6.69/6.90 inference(unit_resolution,[status(thm)],[1915, 42, 5654])).
% 6.69/6.90 tff(5656,plain,
% 6.69/6.90 (r(s(elem!1), s(z))),
% 6.69/6.90 inference(unit_resolution,[status(thm)],[5655, 1905])).
% 6.69/6.90 tff(5657,plain,
% 6.69/6.90 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 6.69/6.90 inference(rewrite,[status(thm)],[])).
% 6.69/6.90 tff(5658,plain,
% 6.69/6.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 6.69/6.90 inference(monotonicity,[status(thm)],[5657])).
% 6.69/6.90 tff(5659,plain,
% 6.69/6.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 6.69/6.90 inference(transitivity,[status(thm)],[5658, 5334])).
% 6.69/6.90 tff(5660,plain,
% 6.69/6.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 6.69/6.90 inference(quant_inst,[status(thm)],[])).
% 6.69/6.90 tff(5661,plain,
% 6.69/6.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 6.69/6.90 inference(modus_ponens,[status(thm)],[5660, 5659])).
% 6.69/6.90 tff(5662,plain,
% 6.69/6.90 (~r(s(elem!1), elem!1)),
% 6.69/6.90 inference(unit_resolution,[status(thm)],[5661, 194, 1484, 847, 5656])).
% 6.69/6.90 tff(5663,plain,
% 6.69/6.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 6.69/6.90 inference(rewrite,[status(thm)],[])).
% 6.69/6.90 tff(5664,plain,
% 6.69/6.90 (((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 6.69/6.90 inference(rewrite,[status(thm)],[])).
% 6.69/6.90 tff(5665,plain,
% 6.69/6.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 6.69/6.91 inference(monotonicity,[status(thm)],[5664])).
% 6.69/6.91 tff(5666,plain,
% 6.69/6.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 6.69/6.91 inference(transitivity,[status(thm)],[5665, 5663])).
% 6.69/6.91 tff(5667,plain,
% 6.69/6.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 6.69/6.91 inference(quant_inst,[status(thm)],[])).
% 6.69/6.91 tff(5668,plain,
% 6.69/6.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 6.69/6.91 inference(modus_ponens,[status(thm)],[5667, 5666])).
% 6.69/6.91 tff(5669,plain,
% 6.69/6.91 (~r(elem!1, s(elem!1))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[5668, 194, 1484, 847, 5656])).
% 6.69/6.91 tff(5670,plain,
% 6.69/6.91 (~b(s(s(s(elem!1))), elem!1)),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[2340, 5669, 1101, 5627, 5662])).
% 6.69/6.91 tff(5671,plain,
% 6.69/6.91 (r(s(s(s(elem!1))), elem!1)),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[230, 5670, 127])).
% 6.69/6.91 tff(5672,plain,
% 6.69/6.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 6.69/6.91 inference(rewrite,[status(thm)],[])).
% 6.69/6.91 tff(5673,plain,
% 6.69/6.91 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 6.69/6.91 inference(rewrite,[status(thm)],[])).
% 6.69/6.91 tff(5674,plain,
% 6.69/6.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))))),
% 6.69/6.91 inference(monotonicity,[status(thm)],[5673])).
% 6.69/6.91 tff(5675,plain,
% 6.69/6.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 6.69/6.91 inference(transitivity,[status(thm)],[5674, 5672])).
% 6.69/6.91 tff(5676,plain,
% 6.69/6.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 6.69/6.91 inference(quant_inst,[status(thm)],[])).
% 6.69/6.91 tff(5677,plain,
% 6.69/6.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 6.69/6.91 inference(modus_ponens,[status(thm)],[5676, 5675])).
% 6.69/6.91 tff(5678,plain,
% 6.69/6.91 (~r(s(s(s(elem!1))), s(z))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[5677, 194, 5671, 5637, 1484])).
% 6.69/6.91 tff(5679,plain,
% 6.69/6.91 (b(s(s(s(elem!1))), s(z))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[223, 5678])).
% 6.69/6.91 tff(5680,plain,
% 6.69/6.91 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[281, 279])).
% 6.69/6.91 tff(5681,plain,
% 6.69/6.91 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[272, 5680])).
% 6.69/6.91 tff(5682,plain,
% 6.69/6.91 (~(s(s(elem!1)) = s(elem!1))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[2279, 279])).
% 6.69/6.91 tff(5683,plain,
% 6.69/6.91 (b(s(elem!1), elem!1)),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[2168, 5662, 5626])).
% 6.69/6.91 tff(5684,plain,
% 6.69/6.91 (~b(s(s(elem!1)), elem!1)),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[5286, 5683, 133, 665, 5682])).
% 6.69/6.91 tff(5685,plain,
% 6.69/6.91 (r(s(s(elem!1)), elem!1)),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[872, 5684, 5625])).
% 6.69/6.91 tff(5686,plain,
% 6.69/6.91 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[4039, 5685, 127, 4028, 5670])).
% 6.69/6.91 tff(5687,plain,
% 6.69/6.91 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[1370, 5686, 5681])).
% 6.69/6.91 tff(5688,plain,
% 6.69/6.91 (~r(s(s(elem!1)), s(z))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[2377, 194, 5685, 5637, 1484])).
% 6.69/6.91 tff(5689,plain,
% 6.69/6.91 (b(s(s(elem!1)), s(z))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[362, 5688])).
% 6.69/6.91 tff(5690,plain,
% 6.69/6.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.91 inference(rewrite,[status(thm)],[])).
% 6.69/6.91 tff(5691,plain,
% 6.69/6.91 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(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))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.91 inference(rewrite,[status(thm)],[])).
% 6.69/6.91 tff(5692,plain,
% 6.69/6.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.69/6.91 inference(monotonicity,[status(thm)],[5691])).
% 6.69/6.91 tff(5693,plain,
% 6.69/6.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.91 inference(transitivity,[status(thm)],[5692, 5690])).
% 6.69/6.91 tff(5694,plain,
% 6.69/6.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(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)))))),
% 6.69/6.91 inference(quant_inst,[status(thm)],[])).
% 6.69/6.91 tff(5695,plain,
% 6.69/6.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.69/6.91 inference(modus_ponens,[status(thm)],[5694, 5693])).
% 6.69/6.91 tff(5696,plain,
% 6.69/6.91 ($false),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[5695, 391, 1101, 5689, 5687, 5647, 5679])).
% 6.69/6.91 tff(5697,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), elem!1)) | (s(s(s(elem!1))) = elem!1) | b(elem!1, s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(elem!1, s(z))) | (s(z) = s(elem!1)) | r(s(elem!1), s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.91 tff(5698,plain,
% 6.69/6.91 (~r(s(s(s(elem!1))), z)),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[5697, 4028, 1484, 127, 1101, 133, 665, 847, 121, 3612, 279])).
% 6.69/6.91 tff(5699,plain,
% 6.69/6.91 (b(s(s(s(elem!1))), z)),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[377, 5698])).
% 6.69/6.91 tff(5700,plain,
% 6.69/6.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.91 inference(rewrite,[status(thm)],[])).
% 6.69/6.91 tff(5701,plain,
% 6.69/6.91 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.91 inference(rewrite,[status(thm)],[])).
% 6.69/6.91 tff(5702,plain,
% 6.69/6.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.69/6.91 inference(monotonicity,[status(thm)],[5701])).
% 6.69/6.91 tff(5703,plain,
% 6.69/6.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.91 inference(transitivity,[status(thm)],[5702, 5700])).
% 6.69/6.91 tff(5704,plain,
% 6.69/6.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.91 inference(quant_inst,[status(thm)],[])).
% 6.69/6.91 tff(5705,plain,
% 6.69/6.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 6.69/6.91 inference(modus_ponens,[status(thm)],[5704, 5703])).
% 6.69/6.91 tff(5706,plain,
% 6.69/6.91 (~b(s(z), s(s(s(elem!1))))),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[5705, 391, 133, 665, 5699, 590])).
% 6.69/6.91 tff(5707,plain,
% 6.69/6.91 (~b(s(s(s(elem!1))), elem!1)),
% 6.69/6.91 inference(unit_resolution,[status(thm)],[1514, 391, 133, 665, 5699])).
% 6.69/6.91 tff(5708,plain,
% 6.69/6.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.69/6.92 inference(rewrite,[status(thm)],[])).
% 6.69/6.92 tff(5709,plain,
% 6.69/6.92 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.69/6.92 inference(rewrite,[status(thm)],[])).
% 6.69/6.92 tff(5710,plain,
% 6.69/6.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))))),
% 6.69/6.92 inference(monotonicity,[status(thm)],[5709])).
% 6.69/6.92 tff(5711,plain,
% 6.69/6.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.69/6.92 inference(transitivity,[status(thm)],[5710, 5708])).
% 6.69/6.92 tff(5712,plain,
% 6.69/6.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 6.69/6.92 inference(quant_inst,[status(thm)],[])).
% 6.69/6.92 tff(5713,plain,
% 6.69/6.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))),
% 6.69/6.92 inference(modus_ponens,[status(thm)],[5712, 5711])).
% 6.69/6.92 tff(5714,plain,
% 6.69/6.92 ($false),
% 6.69/6.92 inference(unit_resolution,[status(thm)],[5713, 194, 4031, 4030, 1484, 232])).
% 6.69/6.92 tff(5715,plain,((s(s(s(elem!1))) = elem!1) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.69/6.92 tff(5716,plain,
% 6.69/6.92 (~r(s(z), s(s(s(elem!1))))),
% 6.69/6.92 inference(unit_resolution,[status(thm)],[5715, 5707, 1484, 127, 4028])).
% 6.69/6.92 tff(5717,plain,
% 6.69/6.92 ($false),
% 6.69/6.92 inference(unit_resolution,[status(thm)],[247, 5716, 5706])).
% 6.69/6.92 tff(5718,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(s(z), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(z))) | (s(z) = s(elem!1)) | r(s(elem!1), s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.92 tff(5719,plain,
% 6.69/6.92 (b(elem!1, s(s(s(elem!1))))),
% 6.69/6.92 inference(unit_resolution,[status(thm)],[5718, 5238, 5636, 5632, 5631, 5450, 1101, 5635, 5629, 3612, 279])).
% 6.69/6.92 tff(5720,plain,
% 6.69/6.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(elem!1), s(s(s(elem!1))))))),
% 6.69/6.92 inference(rewrite,[status(thm)],[])).
% 6.69/6.92 tff(5721,plain,
% 6.69/6.92 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(elem!1), s(s(s(elem!1))))))),
% 6.69/6.92 inference(rewrite,[status(thm)],[])).
% 6.69/6.92 tff(5722,plain,
% 6.69/6.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), s(s(s(elem!1)))))))),
% 6.69/6.92 inference(monotonicity,[status(thm)],[5721])).
% 6.69/6.92 tff(5723,plain,
% 6.69/6.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(elem!1), s(s(s(elem!1))))))),
% 6.69/6.92 inference(transitivity,[status(thm)],[5722, 5720])).
% 6.69/6.92 tff(5724,plain,
% 6.69/6.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 6.69/6.92 inference(quant_inst,[status(thm)],[])).
% 6.69/6.92 tff(5725,plain,
% 6.69/6.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(elem!1), s(s(s(elem!1)))))),
% 6.69/6.92 inference(modus_ponens,[status(thm)],[5724, 5723])).
% 6.69/6.92 tff(5726,plain,
% 6.69/6.92 (~b(elem!1, s(elem!1))),
% 6.69/6.92 inference(unit_resolution,[status(thm)],[5725, 391, 1101, 5719, 5624])).
% 6.69/6.92 tff(5727,plain,
% 6.69/6.92 (r(elem!1, s(elem!1))),
% 6.69/6.92 inference(unit_resolution,[status(thm)],[443, 5726, 5627])).
% 6.69/6.92 tff(5728,plain,
% 6.69/6.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 6.69/6.92 inference(rewrite,[status(thm)],[])).
% 6.69/6.92 tff(5729,plain,
% 6.69/6.92 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 6.69/6.92 inference(rewrite,[status(thm)],[])).
% 6.69/6.92 tff(5730,plain,
% 6.69/6.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 6.69/6.92 inference(monotonicity,[status(thm)],[5729])).
% 6.69/6.92 tff(5731,plain,
% 6.69/6.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 6.69/6.93 inference(transitivity,[status(thm)],[5730, 5728])).
% 6.69/6.93 tff(5732,plain,
% 6.69/6.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 6.69/6.93 inference(quant_inst,[status(thm)],[])).
% 6.69/6.93 tff(5733,plain,
% 6.69/6.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 6.69/6.93 inference(modus_ponens,[status(thm)],[5732, 5731])).
% 6.69/6.93 tff(5734,plain,
% 6.69/6.93 (~b(s(elem!1), elem!1)),
% 6.69/6.93 inference(unit_resolution,[status(thm)],[5733, 391, 1101, 5719, 5624])).
% 6.69/6.93 tff(5735,plain,
% 6.69/6.93 (r(s(elem!1), elem!1)),
% 6.69/6.93 inference(unit_resolution,[status(thm)],[2168, 5734, 5626])).
% 6.69/6.93 tff(5736,plain,
% 6.69/6.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 6.69/6.93 inference(rewrite,[status(thm)],[])).
% 6.69/6.93 tff(5737,plain,
% 6.69/6.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 6.69/6.93 inference(quant_inst,[status(thm)],[])).
% 6.69/6.93 tff(5738,plain,
% 6.69/6.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 6.69/6.93 inference(modus_ponens,[status(thm)],[5737, 5736])).
% 6.69/6.93 tff(5739,plain,
% 6.69/6.93 (~r(s(z), s(elem!1))),
% 6.69/6.93 inference(unit_resolution,[status(thm)],[5738, 194, 5735, 5727, 5238])).
% 6.69/6.93 tff(5740,plain,
% 6.69/6.93 (b(s(z), s(elem!1))),
% 6.69/6.93 inference(unit_resolution,[status(thm)],[602, 42, 5629, 5739])).
% 6.69/6.93 tff(5741,plain,
% 6.69/6.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.93 inference(rewrite,[status(thm)],[])).
% 6.69/6.93 tff(5742,plain,
% 6.69/6.93 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.93 inference(rewrite,[status(thm)],[])).
% 6.69/6.93 tff(5743,plain,
% 6.69/6.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.69/6.93 inference(monotonicity,[status(thm)],[5742])).
% 6.69/6.93 tff(5744,plain,
% 6.69/6.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.93 inference(transitivity,[status(thm)],[5743, 5741])).
% 6.69/6.93 tff(5745,plain,
% 6.69/6.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.69/6.93 inference(quant_inst,[status(thm)],[])).
% 6.69/6.93 tff(5746,plain,
% 6.69/6.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 6.69/6.93 inference(modus_ponens,[status(thm)],[5745, 5744])).
% 6.69/6.93 tff(5747,plain,
% 6.69/6.93 (~b(s(z), s(s(s(elem!1))))),
% 6.69/6.93 inference(unit_resolution,[status(thm)],[5746, 391, 1101, 5740, 5624])).
% 6.69/6.93 tff(5748,plain,
% 6.69/6.93 (r(s(z), s(s(s(elem!1))))),
% 6.69/6.93 inference(unit_resolution,[status(thm)],[247, 5747])).
% 6.69/6.93 tff(5749,plain,
% 6.69/6.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 6.69/6.93 inference(rewrite,[status(thm)],[])).
% 6.69/6.93 tff(5750,plain,
% 6.69/6.93 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 6.69/6.93 inference(rewrite,[status(thm)],[])).
% 6.69/6.93 tff(5751,plain,
% 6.69/6.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))))),
% 6.69/6.93 inference(monotonicity,[status(thm)],[5750])).
% 6.69/6.93 tff(5752,plain,
% 6.69/6.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 6.69/6.93 inference(transitivity,[status(thm)],[5751, 5749])).
% 6.69/6.93 tff(5753,plain,
% 6.69/6.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 6.69/6.93 inference(quant_inst,[status(thm)],[])).
% 6.69/6.93 tff(5754,plain,
% 6.69/6.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 6.69/6.93 inference(modus_ponens,[status(thm)],[5753, 5752])).
% 6.69/6.93 tff(5755,plain,
% 6.69/6.93 (~b(s(s(s(elem!1))), s(z))),
% 6.69/6.93 inference(unit_resolution,[status(thm)],[5754, 391, 1101, 5740, 5624])).
% 6.69/6.93 tff(5756,plain,
% 6.69/6.93 (r(s(s(s(elem!1))), s(z))),
% 6.69/6.93 inference(unit_resolution,[status(thm)],[223, 5755])).
% 6.69/6.93 tff(5757,plain,
% 6.69/6.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 6.69/6.93 inference(rewrite,[status(thm)],[])).
% 6.69/6.93 tff(5758,plain,
% 6.69/6.93 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 6.69/6.93 inference(rewrite,[status(thm)],[])).
% 6.69/6.93 tff(5759,plain,
% 6.69/6.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))))),
% 6.69/6.93 inference(monotonicity,[status(thm)],[5758])).
% 6.69/6.93 tff(5760,plain,
% 6.69/6.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 6.69/6.93 inference(transitivity,[status(thm)],[5759, 5757])).
% 6.69/6.93 tff(5761,plain,
% 6.69/6.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 6.69/6.93 inference(quant_inst,[status(thm)],[])).
% 6.69/6.93 tff(5762,plain,
% 6.69/6.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))),
% 6.69/6.93 inference(modus_ponens,[status(thm)],[5761, 5760])).
% 6.69/6.93 tff(5763,plain,
% 6.69/6.93 (~r(s(s(s(elem!1))), elem!1)),
% 6.69/6.93 inference(unit_resolution,[status(thm)],[5762, 194, 5748, 5756, 5635])).
% 6.69/6.93 tff(5764,plain,
% 6.69/6.93 (b(s(s(s(elem!1))), elem!1)),
% 6.69/6.93 inference(unit_resolution,[status(thm)],[230, 5763, 5636])).
% 6.69/6.93 tff(5765,plain,
% 6.69/6.93 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 6.69/6.93 inference(rewrite,[status(thm)],[])).
% 6.69/6.93 tff(5766,plain,
% 6.69/6.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))))),
% 6.69/6.93 inference(monotonicity,[status(thm)],[5765])).
% 6.69/6.93 tff(5767,plain,
% 6.69/6.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 6.69/6.93 inference(transitivity,[status(thm)],[5766, 1509])).
% 6.69/6.94 tff(5768,plain,
% 6.69/6.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 6.69/6.94 inference(quant_inst,[status(thm)],[])).
% 6.69/6.94 tff(5769,plain,
% 6.69/6.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))),
% 6.69/6.94 inference(modus_ponens,[status(thm)],[5768, 5767])).
% 6.69/6.94 tff(5770,plain,
% 6.69/6.94 (~b(s(s(s(elem!1))), z)),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[5769, 391, 5632, 5631, 5764])).
% 6.69/6.94 tff(5771,plain,
% 6.69/6.94 (r(s(s(s(elem!1))), z)),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[377, 5770])).
% 6.69/6.94 tff(5772,plain,
% 6.69/6.94 (~r(s(z), z)),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[1865, 194, 174, 184, 232])).
% 6.69/6.94 tff(5773,plain,
% 6.69/6.94 (b(s(z), z)),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[178, 42, 23, 5772])).
% 6.69/6.94 tff(5774,plain,
% 6.69/6.94 (b(s(s(elem!1)), z)),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[2627, 42, 215, 4502])).
% 6.69/6.94 tff(5775,plain,
% 6.69/6.94 (~r(z, s(s(elem!1)))),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[1448, 194, 174, 184, 1378])).
% 6.69/6.94 tff(5776,plain,
% 6.69/6.94 (b(z, s(s(elem!1)))),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[324, 5775])).
% 6.69/6.94 tff(5777,plain,
% 6.69/6.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.69/6.94 inference(rewrite,[status(thm)],[])).
% 6.69/6.94 tff(5778,plain,
% 6.69/6.94 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.69/6.94 inference(rewrite,[status(thm)],[])).
% 6.69/6.94 tff(5779,plain,
% 6.69/6.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 6.69/6.94 inference(monotonicity,[status(thm)],[5778])).
% 6.69/6.94 tff(5780,plain,
% 6.69/6.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 6.69/6.94 inference(transitivity,[status(thm)],[5779, 5777])).
% 6.69/6.94 tff(5781,plain,
% 6.69/6.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 6.69/6.94 inference(quant_inst,[status(thm)],[])).
% 6.69/6.94 tff(5782,plain,
% 6.69/6.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 6.69/6.94 inference(modus_ponens,[status(thm)],[5781, 5780])).
% 6.69/6.94 tff(5783,plain,
% 6.69/6.94 (~r(s(s(elem!1)), s(z))),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[5782, 194, 174, 232, 1378])).
% 6.69/6.94 tff(5784,plain,
% 6.69/6.94 (b(s(s(elem!1)), s(z))),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[362, 5783])).
% 6.69/6.94 tff(5785,plain,
% 6.69/6.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 6.69/6.94 inference(rewrite,[status(thm)],[])).
% 6.69/6.94 tff(5786,plain,
% 6.69/6.94 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 6.69/6.94 inference(rewrite,[status(thm)],[])).
% 6.69/6.94 tff(5787,plain,
% 6.69/6.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))))),
% 6.69/6.94 inference(monotonicity,[status(thm)],[5786])).
% 6.69/6.94 tff(5788,plain,
% 6.69/6.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 6.69/6.94 inference(transitivity,[status(thm)],[5787, 5785])).
% 6.69/6.94 tff(5789,plain,
% 6.69/6.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 6.69/6.94 inference(quant_inst,[status(thm)],[])).
% 6.69/6.94 tff(5790,plain,
% 6.69/6.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))),
% 6.69/6.94 inference(modus_ponens,[status(thm)],[5789, 5788])).
% 6.69/6.94 tff(5791,plain,
% 6.69/6.94 ($false),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[5790, 391, 5784, 5776, 5774, 5773])).
% 6.69/6.94 tff(5792,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.94 tff(5793,plain,
% 6.69/6.94 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.69/6.94 inference(unit_resolution,[status(thm)],[5792, 5771, 59, 5748])).
% 6.69/6.94 tff(5794,plain,
% 6.69/6.94 (~(s(elem!1) = s(z))),
% 6.69/6.94 inference(modus_ponens,[status(thm)],[5629, 1904])).
% 6.69/6.94 tff(5795,plain,
% 6.69/6.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 6.69/6.94 inference(rewrite,[status(thm)],[])).
% 6.69/6.94 tff(5796,plain,
% 6.69/6.94 (((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 6.69/6.94 inference(rewrite,[status(thm)],[])).
% 6.69/6.94 tff(5797,plain,
% 6.69/6.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))))),
% 6.69/6.95 inference(monotonicity,[status(thm)],[5796])).
% 6.69/6.95 tff(5798,plain,
% 6.69/6.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 6.69/6.95 inference(transitivity,[status(thm)],[5797, 5795])).
% 6.69/6.95 tff(5799,plain,
% 6.69/6.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 6.69/6.95 inference(quant_inst,[status(thm)],[])).
% 6.69/6.95 tff(5800,plain,
% 6.69/6.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 6.69/6.95 inference(modus_ponens,[status(thm)],[5799, 5798])).
% 6.69/6.95 tff(5801,plain,
% 6.69/6.95 (~r(s(elem!1), s(z))),
% 6.69/6.95 inference(unit_resolution,[status(thm)],[5800, 194, 5735, 5727, 5238])).
% 6.69/6.95 tff(5802,plain,
% 6.69/6.95 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 6.69/6.95 inference(unit_resolution,[status(thm)],[1915, 42, 5801])).
% 6.69/6.95 tff(5803,plain,
% 6.69/6.95 (b(s(elem!1), s(z))),
% 6.69/6.95 inference(unit_resolution,[status(thm)],[5802, 5794])).
% 6.69/6.95 tff(5804,plain,
% 6.69/6.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 6.69/6.95 inference(rewrite,[status(thm)],[])).
% 6.69/6.95 tff(5805,plain,
% 6.69/6.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 6.69/6.95 inference(quant_inst,[status(thm)],[])).
% 6.69/6.95 tff(5806,plain,
% 6.69/6.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 6.69/6.95 inference(modus_ponens,[status(thm)],[5805, 5804])).
% 6.69/6.95 tff(5807,plain,
% 6.69/6.95 (~r(s(s(elem!1)), s(elem!1))),
% 6.69/6.95 inference(unit_resolution,[status(thm)],[5806, 194, 485, 2251, 364])).
% 6.69/6.95 tff(5808,plain,
% 6.69/6.95 (b(s(s(elem!1)), s(elem!1))),
% 6.69/6.95 inference(unit_resolution,[status(thm)],[1135, 5807, 285])).
% 6.69/6.95 tff(5809,plain,
% 6.69/6.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 6.69/6.95 inference(rewrite,[status(thm)],[])).
% 6.69/6.95 tff(5810,plain,
% 6.69/6.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 6.69/6.95 inference(quant_inst,[status(thm)],[])).
% 6.69/6.95 tff(5811,plain,
% 6.69/6.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 6.69/6.95 inference(modus_ponens,[status(thm)],[5810, 5809])).
% 6.69/6.95 tff(5812,plain,
% 6.69/6.95 (~r(s(s(elem!1)), s(z))),
% 6.69/6.95 inference(unit_resolution,[status(thm)],[5811, 194, 2251, 364, 1484])).
% 6.69/6.95 tff(5813,plain,
% 6.69/6.95 (b(s(s(elem!1)), s(z))),
% 6.69/6.95 inference(unit_resolution,[status(thm)],[362, 5812])).
% 6.69/6.95 tff(5814,plain,
% 6.69/6.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 6.69/6.95 inference(rewrite,[status(thm)],[])).
% 6.69/6.95 tff(5815,plain,
% 6.69/6.95 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 6.69/6.95 inference(rewrite,[status(thm)],[])).
% 6.69/6.95 tff(5816,plain,
% 6.69/6.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z)))))),
% 6.69/6.95 inference(monotonicity,[status(thm)],[5815])).
% 6.69/6.95 tff(5817,plain,
% 6.69/6.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 6.69/6.95 inference(transitivity,[status(thm)],[5816, 5814])).
% 6.69/6.95 tff(5818,plain,
% 6.69/6.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 6.69/6.95 inference(quant_inst,[status(thm)],[])).
% 6.69/6.95 tff(5819,plain,
% 6.69/6.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z)))),
% 6.69/6.95 inference(modus_ponens,[status(thm)],[5818, 5817])).
% 6.69/6.95 tff(5820,plain,
% 6.69/6.95 ($false),
% 6.69/6.95 inference(unit_resolution,[status(thm)],[5819, 391, 5813, 5808, 751, 1036, 5469])).
% 6.69/6.95 tff(5821,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (s(s(elem!1)) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.95 tff(5822,plain,
% 6.69/6.95 (~r(s(s(elem!1)), elem!1)),
% 6.69/6.95 inference(unit_resolution,[status(thm)],[5821, 5740, 5624, 5803, 5682, 5727, 5238, 5735])).
% 6.69/6.95 tff(5823,plain,
% 6.69/6.95 (b(s(s(elem!1)), elem!1)),
% 6.69/6.95 inference(unit_resolution,[status(thm)],[872, 5822, 5625])).
% 6.69/6.95 tff(5824,plain,
% 6.69/6.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.69/6.95 inference(rewrite,[status(thm)],[])).
% 6.69/6.95 tff(5825,plain,
% 6.69/6.95 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~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)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.69/6.96 inference(rewrite,[status(thm)],[])).
% 6.69/6.96 tff(5826,plain,
% 6.69/6.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 6.69/6.96 inference(monotonicity,[status(thm)],[5825])).
% 6.69/6.96 tff(5827,plain,
% 6.69/6.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.69/6.96 inference(transitivity,[status(thm)],[5826, 5824])).
% 6.69/6.96 tff(5828,plain,
% 6.69/6.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~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))))))),
% 6.69/6.96 inference(quant_inst,[status(thm)],[])).
% 6.69/6.96 tff(5829,plain,
% 6.69/6.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 6.69/6.96 inference(modus_ponens,[status(thm)],[5828, 5827])).
% 6.69/6.96 tff(5830,plain,
% 6.69/6.96 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5829, 391, 5632, 5631, 5764, 5823])).
% 6.69/6.96 tff(5831,plain,
% 6.69/6.96 ($false),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[1354, 42, 5830, 5680, 5793])).
% 6.69/6.96 tff(5832,plain,((s(z) = elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | r(s(elem!1), s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | b(z, s(s(s(elem!1)))) | r(elem!1, z) | r(z, elem!1) | r(s(z), z) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.69/6.96 tff(5833,plain,
% 6.69/6.96 ($false),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5832, 5620, 5612, 175, 80, 10, 2282, 150, 2829, 5428])).
% 6.69/6.96 tff(5834,plain,((~r(s(elem!1), z)) | r(s(z), z) | r(z, elem!1) | b(z, s(s(s(elem!1)))) | r(elem!1, z) | (s(z) = elem!1) | b(s(z), elem!1) | (~r(s(elem!1), elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.96 tff(5835,plain,
% 6.69/6.96 (b(elem!1, s(s(s(elem!1))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5834, 5404, 10, 80, 4941, 150, 5232, 5421, 5420, 174])).
% 6.69/6.96 tff(5836,plain,
% 6.69/6.96 (b(elem!1, s(elem!1))),
% 6.69/6.96 inference(modus_ponens,[status(thm)],[5835, 5419])).
% 6.69/6.96 tff(5837,plain,
% 6.69/6.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.69/6.96 inference(rewrite,[status(thm)],[])).
% 6.69/6.96 tff(5838,plain,
% 6.69/6.96 (((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.69/6.96 inference(rewrite,[status(thm)],[])).
% 6.69/6.96 tff(5839,plain,
% 6.69/6.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 6.69/6.96 inference(monotonicity,[status(thm)],[5838])).
% 6.69/6.96 tff(5840,plain,
% 6.69/6.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 6.69/6.96 inference(transitivity,[status(thm)],[5839, 5837])).
% 6.69/6.96 tff(5841,plain,
% 6.69/6.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.69/6.96 inference(quant_inst,[status(thm)],[])).
% 6.69/6.96 tff(5842,plain,
% 6.69/6.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 6.69/6.96 inference(modus_ponens,[status(thm)],[5841, 5840])).
% 6.69/6.96 tff(5843,plain,
% 6.69/6.96 (~b(s(s(s(s(z)))), elem!1)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5842, 391, 5836, 5418, 5414, 5410])).
% 6.69/6.96 tff(5844,plain,
% 6.69/6.96 (r(s(s(s(s(z)))), elem!1)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[762, 5843, 5371])).
% 6.69/6.96 tff(5845,plain,
% 6.69/6.96 (~b(s(z), s(s(s(s(z)))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5508, 391, 5418, 5414, 5410])).
% 6.69/6.96 tff(5846,plain,
% 6.69/6.96 (r(s(z), s(s(s(s(z)))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[1230, 5845])).
% 6.69/6.96 tff(5847,plain,
% 6.69/6.96 ($false),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5396, 5846, 5844, 5233, 5223])).
% 6.69/6.96 tff(5848,plain,((~r(s(s(s(elem!1))), z)) | b(z, s(s(s(elem!1)))) | r(z, elem!1) | (s(z) = elem!1) | (elem!1 = z) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.69/6.96 tff(5849,plain,
% 6.69/6.96 (~r(s(s(s(elem!1))), z)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5848, 168, 80, 150, 2, 10])).
% 6.69/6.96 tff(5850,plain,
% 6.69/6.96 (b(s(s(s(elem!1))), z)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[377, 5849])).
% 6.69/6.96 tff(5851,plain,
% 6.69/6.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 6.69/6.96 inference(rewrite,[status(thm)],[])).
% 6.69/6.96 tff(5852,plain,
% 6.69/6.96 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 6.69/6.96 inference(rewrite,[status(thm)],[])).
% 6.69/6.96 tff(5853,plain,
% 6.69/6.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))))),
% 6.69/6.96 inference(monotonicity,[status(thm)],[5852])).
% 6.69/6.96 tff(5854,plain,
% 6.69/6.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 6.69/6.96 inference(transitivity,[status(thm)],[5853, 5851])).
% 6.69/6.96 tff(5855,plain,
% 6.69/6.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 6.69/6.96 inference(quant_inst,[status(thm)],[])).
% 6.69/6.96 tff(5856,plain,
% 6.69/6.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))),
% 6.69/6.96 inference(modus_ponens,[status(thm)],[5855, 5854])).
% 6.69/6.96 tff(5857,plain,
% 6.69/6.96 (~b(elem!1, s(s(s(elem!1))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5856, 391, 149, 4942, 5850])).
% 6.69/6.96 tff(5858,plain,
% 6.69/6.96 (r(elem!1, s(s(s(elem!1))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[424, 5857, 148])).
% 6.69/6.96 tff(5859,plain,
% 6.69/6.96 (~r(s(z), z)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[241, 232, 184, 4486])).
% 6.69/6.96 tff(5860,plain,
% 6.69/6.96 (b(s(z), z)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[180, 5859])).
% 6.69/6.96 tff(5861,plain,
% 6.69/6.96 (~r(s(z), elem!1)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5715, 232, 127, 168, 4028])).
% 6.69/6.96 tff(5862,plain,
% 6.69/6.96 (b(s(z), elem!1)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[632, 5861, 150])).
% 6.69/6.96 tff(5863,plain,
% 6.69/6.96 ($false),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5231, 5862, 5860, 665, 133])).
% 6.69/6.96 tff(5864,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(z) = elem!1) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.96 tff(5865,plain,
% 6.69/6.96 (~r(s(z), s(s(s(elem!1))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5864, 4942, 149, 150, 151, 168, 5857, 59])).
% 6.69/6.96 tff(5866,plain,
% 6.69/6.96 (b(s(z), s(s(s(elem!1))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[247, 5865])).
% 6.69/6.96 tff(5867,plain,
% 6.69/6.96 (~b(elem!1, s(s(s(elem!1))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5856, 391, 133, 665, 380])).
% 6.69/6.96 tff(5868,plain,
% 6.69/6.96 (~(s(s(s(elem!1))) = elem!1)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[136, 10, 133])).
% 6.69/6.96 tff(5869,plain,
% 6.69/6.96 (~b(s(s(elem!1)), elem!1)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[4944, 3925, 665, 133])).
% 6.69/6.96 tff(5870,plain,
% 6.69/6.96 (r(s(s(elem!1)), elem!1)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[872, 5869, 249])).
% 6.69/6.96 tff(5871,plain,
% 6.69/6.96 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[4039, 5870, 5868, 5867, 168])).
% 6.69/6.96 tff(5872,plain,
% 6.69/6.96 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[1370, 5871, 288])).
% 6.69/6.96 tff(5873,plain,
% 6.69/6.96 (r(s(s(s(elem!1))), elem!1)),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[230, 168, 5868])).
% 6.69/6.96 tff(5874,plain,
% 6.69/6.96 ($false),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[4971, 194, 233, 364, 410, 1378])).
% 6.69/6.96 tff(5875,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.96 tff(5876,plain,
% 6.69/6.96 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[5875, 5870, 410, 5873])).
% 6.69/6.96 tff(5877,plain,
% 6.69/6.96 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[1356, 5876, 3926])).
% 6.69/6.96 tff(5878,plain,
% 6.69/6.96 ($false),
% 6.69/6.96 inference(unit_resolution,[status(thm)],[4893, 5877, 5872, 380, 3925])).
% 6.69/6.97 tff(5879,plain,((s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (~b(elem!1, z)) | (~b(z, elem!1)) | b(z, s(s(s(elem!1)))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 6.69/6.97 tff(5880,plain,
% 6.69/6.97 (s(s(elem!1)) = elem!1),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5879, 91, 410, 168, 665, 133, 10, 380])).
% 6.69/6.97 tff(5881,plain,
% 6.69/6.97 (s(s(s(elem!1))) = s(elem!1)),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[451, 5880])).
% 6.69/6.97 tff(5882,plain,
% 6.69/6.97 (~(s(elem!1) = s(s(s(s(z)))))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5377, 5881, 3843])).
% 6.69/6.97 tff(5883,plain,
% 6.69/6.97 (~(s(s(s(s(z)))) = s(elem!1))),
% 6.69/6.97 inference(modus_ponens,[status(thm)],[5882, 2125])).
% 6.69/6.97 tff(5884,plain,
% 6.69/6.97 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 6.69/6.97 inference(monotonicity,[status(thm)],[5881])).
% 6.69/6.97 tff(5885,plain,
% 6.69/6.97 (b(s(elem!1), z)),
% 6.69/6.97 inference(modus_ponens,[status(thm)],[380, 5884])).
% 6.69/6.97 tff(5886,plain,
% 6.69/6.97 (~(s(s(s(s(z)))) = elem!1)),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[717, 5881])).
% 6.69/6.97 tff(5887,plain,
% 6.69/6.97 (~(s(elem!1) = elem!1)),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[158, 5868])).
% 6.69/6.97 tff(5888,plain,
% 6.69/6.97 (~(elem!1 = s(elem!1))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[166, 5887])).
% 6.69/6.97 tff(5889,plain,
% 6.69/6.97 (~b(elem!1, s(elem!1))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[4603, 5881, 5867])).
% 6.69/6.97 tff(5890,plain,
% 6.69/6.97 (r(elem!1, s(elem!1))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[443, 5889, 5888])).
% 6.69/6.97 tff(5891,plain,
% 6.69/6.97 (r(s(elem!1), elem!1)),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[472, 5881, 5873])).
% 6.69/6.97 tff(5892,plain,
% 6.69/6.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.69/6.97 inference(rewrite,[status(thm)],[])).
% 6.69/6.97 tff(5893,plain,
% 6.69/6.97 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.69/6.97 inference(rewrite,[status(thm)],[])).
% 6.69/6.97 tff(5894,plain,
% 6.69/6.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 6.69/6.97 inference(monotonicity,[status(thm)],[5893])).
% 6.69/6.97 tff(5895,plain,
% 6.69/6.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.69/6.97 inference(transitivity,[status(thm)],[5894, 5892])).
% 6.69/6.97 tff(5896,plain,
% 6.69/6.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.69/6.97 inference(quant_inst,[status(thm)],[])).
% 6.69/6.97 tff(5897,plain,
% 6.69/6.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 6.69/6.97 inference(modus_ponens,[status(thm)],[5896, 5895])).
% 6.69/6.97 tff(5898,plain,
% 6.69/6.97 (~b(s(elem!1), s(s(s(s(z)))))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5897, 391, 133, 665, 591, 90])).
% 6.69/6.97 tff(5899,plain,
% 6.69/6.97 (r(s(elem!1), s(s(s(s(z)))))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[2142, 42, 5898, 2121])).
% 6.69/6.97 tff(5900,plain,
% 6.69/6.97 ($false),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[4553, 194, 485, 2251, 5380, 5899])).
% 6.69/6.97 tff(5901,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.97 tff(5902,plain,
% 6.69/6.97 (~b(s(s(s(s(z)))), z)),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5901, 5891, 5890, 5882, 5886, 133, 665, 5885])).
% 6.69/6.97 tff(5903,plain,
% 6.69/6.97 (r(s(s(s(s(z)))), z)),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[87, 5902])).
% 6.69/6.97 tff(5904,plain,
% 6.69/6.97 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 6.69/6.97 inference(monotonicity,[status(thm)],[5881])).
% 6.69/6.97 tff(5905,plain,
% 6.69/6.97 (r(z, s(elem!1))),
% 6.69/6.97 inference(modus_ponens,[status(thm)],[59, 5904])).
% 6.69/6.97 tff(5906,assumption,(r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 6.69/6.97 tff(5907,plain,
% 6.69/6.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 6.69/6.97 inference(rewrite,[status(thm)],[])).
% 6.69/6.97 tff(5908,plain,
% 6.69/6.97 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 6.69/6.97 inference(rewrite,[status(thm)],[])).
% 6.69/6.97 tff(5909,plain,
% 6.69/6.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 6.69/6.97 inference(monotonicity,[status(thm)],[5908])).
% 6.69/6.97 tff(5910,plain,
% 6.69/6.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 6.69/6.97 inference(transitivity,[status(thm)],[5909, 5907])).
% 6.69/6.97 tff(5911,plain,
% 6.69/6.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 6.69/6.97 inference(quant_inst,[status(thm)],[])).
% 6.69/6.97 tff(5912,plain,
% 6.69/6.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 6.69/6.97 inference(modus_ponens,[status(thm)],[5911, 5910])).
% 6.69/6.97 tff(5913,plain,
% 6.69/6.97 ($false),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5912, 194, 485, 2144, 2053, 5906])).
% 6.69/6.97 tff(5914,plain,((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.97 tff(5915,plain,
% 6.69/6.97 (~r(s(s(s(s(z)))), s(elem!1))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5914, 5891, 5905, 5903])).
% 6.69/6.97 tff(5916,plain,
% 6.69/6.97 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[2136, 42, 5915])).
% 6.69/6.97 tff(5917,plain,
% 6.69/6.97 (b(s(s(s(s(z)))), s(elem!1))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5916, 5883])).
% 6.69/6.97 tff(5918,plain,
% 6.69/6.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.69/6.97 inference(rewrite,[status(thm)],[])).
% 6.69/6.97 tff(5919,plain,
% 6.69/6.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.69/6.97 inference(quant_inst,[status(thm)],[])).
% 6.69/6.97 tff(5920,plain,
% 6.69/6.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 6.69/6.97 inference(modus_ponens,[status(thm)],[5919, 5918])).
% 6.69/6.97 tff(5921,plain,
% 6.69/6.97 (~r(s(s(s(s(z)))), s(z))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5920, 194, 5905, 181, 5903])).
% 6.69/6.97 tff(5922,plain,
% 6.69/6.97 (b(s(s(s(s(z)))), s(z))),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[749, 5921])).
% 6.69/6.97 tff(5923,plain,
% 6.69/6.97 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 6.69/6.97 inference(monotonicity,[status(thm)],[5881])).
% 6.69/6.97 tff(5924,plain,
% 6.69/6.97 (b(s(z), s(elem!1))),
% 6.69/6.97 inference(modus_ponens,[status(thm)],[379, 5923])).
% 6.69/6.97 tff(5925,plain,
% 6.69/6.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.69/6.97 inference(rewrite,[status(thm)],[])).
% 6.69/6.97 tff(5926,plain,
% 6.69/6.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 6.69/6.97 inference(quant_inst,[status(thm)],[])).
% 6.69/6.97 tff(5927,plain,
% 6.69/6.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))),
% 6.69/6.97 inference(modus_ponens,[status(thm)],[5926, 5925])).
% 6.69/6.97 tff(5928,plain,
% 6.69/6.97 ($false),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5927, 391, 133, 5885, 5924, 5922, 5917])).
% 6.69/6.97 tff(5929,plain,(b(s(z), z) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.97 tff(5930,plain,
% 6.69/6.97 (b(s(z), z)),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5929, 4942, 149, 5866, 5850, 3363, 5858, 168, 10])).
% 6.69/6.97 tff(5931,plain,
% 6.69/6.97 ($false),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5705, 391, 149, 4942, 5850, 5866, 5930])).
% 6.69/6.97 tff(5932,plain,(b(s(s(s(elem!1))), elem!1) | b(z, s(s(s(elem!1)))) | (s(z) = elem!1) | r(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 6.69/6.97 tff(5933,plain,
% 6.69/6.97 (b(s(s(s(elem!1))), elem!1)),
% 6.69/6.97 inference(unit_resolution,[status(thm)],[5932, 150, 10, 80, 2])).
% 6.69/6.97 tff(5934,plain,
% 6.69/6.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 6.69/6.97 inference(rewrite,[status(thm)],[])).
% 6.69/6.98 tff(5935,plain,
% 6.69/6.98 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 6.69/6.98 inference(rewrite,[status(thm)],[])).
% 6.69/6.98 tff(5936,plain,
% 6.69/6.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))))),
% 6.69/6.98 inference(monotonicity,[status(thm)],[5935])).
% 6.69/6.98 tff(5937,plain,
% 6.69/6.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 6.69/6.98 inference(transitivity,[status(thm)],[5936, 5934])).
% 6.69/6.98 tff(5938,plain,
% 6.69/6.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 6.69/6.98 inference(quant_inst,[status(thm)],[])).
% 6.69/6.98 tff(5939,plain,
% 6.69/6.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 6.69/6.98 inference(modus_ponens,[status(thm)],[5938, 5937])).
% 6.69/6.98 tff(5940,plain,
% 6.69/6.98 ($false),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[5939, 194, 530, 184, 847, 182])).
% 6.69/6.98 tff(5941,plain,((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.98 tff(5942,plain,
% 6.69/6.98 (~r(elem!1, s(z))),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[5941, 182, 184, 530])).
% 6.69/6.98 tff(5943,plain,
% 6.69/6.98 (b(elem!1, s(z))),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[837, 5942, 831])).
% 6.69/6.98 tff(5944,plain,
% 6.69/6.98 (~r(s(z), elem!1)),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[1489, 182, 184, 530])).
% 6.69/6.98 tff(5945,plain,
% 6.69/6.98 (~b(s(s(s(elem!1))), z)),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[1505, 5942, 133, 831, 900, 5944])).
% 6.69/6.98 tff(5946,plain,
% 6.69/6.98 (r(s(s(s(elem!1))), z)),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[377, 5945])).
% 6.69/6.98 tff(5947,plain,
% 6.69/6.98 (~r(s(z), s(s(s(elem!1))))),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[1867, 5946, 184, 182])).
% 6.69/6.98 tff(5948,plain,
% 6.69/6.98 (b(s(z), s(s(s(elem!1))))),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[247, 5947])).
% 6.69/6.98 tff(5949,plain,
% 6.69/6.98 (~r(s(s(s(elem!1))), s(z))),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[202, 5946, 184, 182])).
% 6.69/6.98 tff(5950,plain,
% 6.69/6.98 (b(s(s(s(elem!1))), s(z))),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[223, 5949])).
% 6.69/6.98 tff(5951,plain,
% 6.69/6.98 ($false),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[2907, 5950, 5948, 900, 5943])).
% 6.69/6.98 tff(5952,plain,((~r(s(z), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (elem!1 = s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.98 tff(5953,plain,
% 6.69/6.98 (~r(s(z), z)),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[5952, 530, 184, 133, 173, 900])).
% 6.69/6.98 tff(5954,plain,
% 6.69/6.98 (b(s(z), z)),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[180, 5953])).
% 6.69/6.98 tff(5955,plain,
% 6.69/6.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 6.69/6.98 inference(rewrite,[status(thm)],[])).
% 6.69/6.98 tff(5956,plain,
% 6.69/6.98 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 6.69/6.98 inference(rewrite,[status(thm)],[])).
% 6.69/6.98 tff(5957,plain,
% 6.69/6.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 6.69/6.98 inference(monotonicity,[status(thm)],[5956])).
% 6.69/6.98 tff(5958,plain,
% 6.69/6.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 6.69/6.98 inference(transitivity,[status(thm)],[5957, 5955])).
% 6.69/6.98 tff(5959,plain,
% 6.69/6.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 6.69/6.98 inference(quant_inst,[status(thm)],[])).
% 6.69/6.98 tff(5960,plain,
% 6.69/6.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 6.69/6.98 inference(modus_ponens,[status(thm)],[5959, 5958])).
% 6.69/6.98 tff(5961,plain,
% 6.69/6.98 (~r(elem!1, s(s(s(elem!1))))),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[5960, 194, 530, 174, 184])).
% 6.69/6.98 tff(5962,plain,
% 6.69/6.98 (b(elem!1, s(s(s(elem!1))))),
% 6.69/6.98 inference(unit_resolution,[status(thm)],[424, 5961, 1])).
% 6.69/6.98 tff(5963,plain,
% 6.69/6.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 6.69/6.98 inference(rewrite,[status(thm)],[])).
% 6.69/6.98 tff(5964,plain,
% 6.69/6.98 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 6.69/6.98 inference(rewrite,[status(thm)],[])).
% 6.69/6.98 tff(5965,plain,
% 6.69/6.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 6.69/6.98 inference(monotonicity,[status(thm)],[5964])).
% 6.69/6.98 tff(5966,plain,
% 6.69/6.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 6.69/6.98 inference(transitivity,[status(thm)],[5965, 5963])).
% 6.69/6.98 tff(5967,plain,
% 6.69/6.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 6.69/6.98 inference(quant_inst,[status(thm)],[])).
% 6.69/6.98 tff(5968,plain,
% 6.69/6.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 6.69/6.98 inference(modus_ponens,[status(thm)],[5967, 5966])).
% 6.69/6.99 tff(5969,plain,
% 6.69/6.99 ($false),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[5968, 391, 133, 664, 590, 721])).
% 6.69/6.99 tff(5970,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.99 tff(5971,plain,
% 6.69/6.99 (~b(z, s(z))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[5970, 721, 133, 590])).
% 6.69/6.99 tff(5972,plain,
% 6.69/6.99 (r(z, s(z))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[678, 5971])).
% 6.69/6.99 tff(5973,plain,
% 6.69/6.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 6.69/6.99 inference(rewrite,[status(thm)],[])).
% 6.69/6.99 tff(5974,plain,
% 6.69/6.99 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 6.69/6.99 inference(rewrite,[status(thm)],[])).
% 6.69/6.99 tff(5975,plain,
% 6.69/6.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 6.69/6.99 inference(monotonicity,[status(thm)],[5974])).
% 6.69/6.99 tff(5976,plain,
% 6.69/6.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 6.69/6.99 inference(transitivity,[status(thm)],[5975, 5973])).
% 6.69/6.99 tff(5977,plain,
% 6.69/6.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 6.69/6.99 inference(quant_inst,[status(thm)],[])).
% 6.69/6.99 tff(5978,plain,
% 6.69/6.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 6.69/6.99 inference(modus_ponens,[status(thm)],[5977, 5976])).
% 6.69/6.99 tff(5979,plain,
% 6.69/6.99 ($false),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[5978, 194, 174, 184, 232, 722])).
% 6.69/6.99 tff(5980,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.99 tff(5981,plain,
% 6.69/6.99 (~r(s(z), s(s(s(elem!1))))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[5980, 5972, 184, 174])).
% 6.69/6.99 tff(5982,plain,
% 6.69/6.99 (b(s(z), s(s(s(elem!1))))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[247, 5981])).
% 6.69/6.99 tff(5983,plain,
% 6.69/6.99 ($false),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[906, 391, 900, 448, 5982, 721])).
% 6.69/6.99 tff(5984,plain,((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.99 tff(5985,plain,
% 6.69/6.99 (~b(elem!1, s(z))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[5984, 5962, 900, 184, 174, 133, 5954])).
% 6.69/6.99 tff(5986,plain,
% 6.69/6.99 (r(elem!1, s(z))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[837, 5985, 173])).
% 6.69/6.99 tff(5987,plain,
% 6.69/6.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.69/6.99 inference(rewrite,[status(thm)],[])).
% 6.69/6.99 tff(5988,plain,
% 6.69/6.99 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.69/6.99 inference(rewrite,[status(thm)],[])).
% 6.69/6.99 tff(5989,plain,
% 6.69/6.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 6.69/6.99 inference(monotonicity,[status(thm)],[5988])).
% 6.69/6.99 tff(5990,plain,
% 6.69/6.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 6.69/6.99 inference(transitivity,[status(thm)],[5989, 5987])).
% 6.69/6.99 tff(5991,plain,
% 6.69/6.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 6.69/6.99 inference(quant_inst,[status(thm)],[])).
% 6.69/6.99 tff(5992,plain,
% 6.69/6.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 6.69/6.99 inference(modus_ponens,[status(thm)],[5991, 5990])).
% 6.69/6.99 tff(5993,plain,
% 6.69/6.99 ($false),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[5992, 391, 133, 900, 448, 644, 590])).
% 6.69/6.99 tff(5994,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.99 tff(5995,plain,
% 6.69/6.99 (~b(s(z), elem!1)),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[5994, 5962, 900, 133, 5954])).
% 6.69/6.99 tff(5996,plain,
% 6.69/6.99 (r(s(z), elem!1)),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[632, 5995, 150])).
% 6.69/6.99 tff(5997,plain,
% 6.69/6.99 (~r(z, s(z))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[5980, 232, 184, 174])).
% 6.69/6.99 tff(5998,plain,
% 6.69/6.99 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[5792, 232, 184, 174])).
% 6.69/6.99 tff(5999,plain,
% 6.69/6.99 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[1356, 3926, 1350])).
% 6.69/6.99 tff(6000,plain,
% 6.69/6.99 ($false),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[920, 391, 900, 973, 448, 328])).
% 6.69/6.99 tff(6001,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.69/6.99 tff(6002,plain,
% 6.69/6.99 (~b(s(s(elem!1)), elem!1)),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[6001, 5999, 448, 900])).
% 6.69/6.99 tff(6003,plain,
% 6.69/6.99 (r(s(s(elem!1)), elem!1)),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[872, 6002, 249])).
% 6.69/6.99 tff(6004,plain,
% 6.69/6.99 (~r(s(s(elem!1)), s(z))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[1899, 6003, 1484, 847])).
% 6.69/6.99 tff(6005,plain,
% 6.69/6.99 (b(s(s(elem!1)), s(z))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[362, 6004])).
% 6.69/6.99 tff(6006,plain,
% 6.69/6.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 6.69/6.99 inference(rewrite,[status(thm)],[])).
% 6.69/6.99 tff(6007,plain,
% 6.69/6.99 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 6.69/6.99 inference(rewrite,[status(thm)],[])).
% 6.69/6.99 tff(6008,plain,
% 6.69/6.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 6.69/6.99 inference(monotonicity,[status(thm)],[6007])).
% 6.69/6.99 tff(6009,plain,
% 6.69/6.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 6.69/6.99 inference(transitivity,[status(thm)],[6008, 6006])).
% 6.69/6.99 tff(6010,plain,
% 6.69/6.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 6.69/6.99 inference(quant_inst,[status(thm)],[])).
% 6.69/6.99 tff(6011,plain,
% 6.69/6.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z))),
% 6.69/6.99 inference(modus_ponens,[status(thm)],[6010, 6009])).
% 6.69/6.99 tff(6012,plain,
% 6.69/6.99 (~b(z, s(s(elem!1)))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[6011, 391, 133, 6005, 664, 590])).
% 6.69/6.99 tff(6013,plain,
% 6.69/6.99 (r(z, s(s(elem!1)))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[324, 6012])).
% 6.69/6.99 tff(6014,plain,
% 6.69/6.99 (~r(elem!1, s(s(elem!1)))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[2231, 6013, 6003, 530])).
% 6.69/6.99 tff(6015,plain,
% 6.69/6.99 (b(elem!1, s(s(elem!1)))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[1307, 6014, 1293])).
% 6.69/6.99 tff(6016,plain,
% 6.69/6.99 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[372, 6013, 184, 6003])).
% 6.69/6.99 tff(6017,plain,
% 6.69/6.99 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.69/6.99 inference(unit_resolution,[status(thm)],[1370, 6016, 288])).
% 6.69/6.99 tff(6018,plain,
% 6.69/6.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.69/6.99 inference(rewrite,[status(thm)],[])).
% 6.69/6.99 tff(6019,plain,
% 6.69/6.99 (((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(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)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.69/6.99 inference(rewrite,[status(thm)],[])).
% 6.69/6.99 tff(6020,plain,
% 6.69/6.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 6.69/7.00 inference(monotonicity,[status(thm)],[6019])).
% 6.69/7.00 tff(6021,plain,
% 6.69/7.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.69/7.00 inference(transitivity,[status(thm)],[6020, 6018])).
% 6.69/7.00 tff(6022,plain,
% 6.69/7.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 6.69/7.00 inference(quant_inst,[status(thm)],[])).
% 6.69/7.00 tff(6023,plain,
% 6.69/7.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 6.69/7.00 inference(modus_ponens,[status(thm)],[6022, 6021])).
% 6.69/7.00 tff(6024,plain,
% 6.69/7.00 ($false),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[6023, 391, 6005, 900, 6017, 6015, 590])).
% 6.69/7.00 tff(6025,plain,((s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.69/7.00 tff(6026,plain,
% 6.69/7.00 (~b(z, s(z))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[6025, 5998, 590, 530, 184, 133, 1484, 900, 847, 448, 249])).
% 6.69/7.00 tff(6027,plain,
% 6.69/7.00 ($false),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[678, 6026, 5997])).
% 6.69/7.00 tff(6028,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~r(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 6.69/7.00 tff(6029,plain,
% 6.69/7.00 (~r(s(z), s(s(s(elem!1))))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[6028, 249, 530, 184, 133, 1484, 900, 847, 448, 590, 174])).
% 6.69/7.00 tff(6030,plain,
% 6.69/7.00 (b(s(z), s(s(s(elem!1))))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[247, 6029])).
% 6.69/7.00 tff(6031,plain,
% 6.69/7.00 (~r(s(s(elem!1)), s(z))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[1899, 364, 1484, 847])).
% 6.69/7.00 tff(6032,plain,
% 6.69/7.00 (b(s(s(elem!1)), s(z))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[362, 6031])).
% 6.69/7.00 tff(6033,plain,
% 6.69/7.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 6.69/7.00 inference(rewrite,[status(thm)],[])).
% 6.69/7.00 tff(6034,plain,
% 6.69/7.00 (((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 6.69/7.00 inference(rewrite,[status(thm)],[])).
% 6.69/7.00 tff(6035,plain,
% 6.69/7.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 6.69/7.00 inference(monotonicity,[status(thm)],[6034])).
% 6.69/7.00 tff(6036,plain,
% 6.69/7.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 6.69/7.00 inference(transitivity,[status(thm)],[6035, 6033])).
% 6.69/7.00 tff(6037,plain,
% 6.69/7.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 6.69/7.00 inference(quant_inst,[status(thm)],[])).
% 6.69/7.00 tff(6038,plain,
% 6.69/7.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 6.69/7.00 inference(modus_ponens,[status(thm)],[6037, 6036])).
% 6.69/7.00 tff(6039,plain,
% 6.69/7.00 (~r(s(z), s(s(elem!1)))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[6038, 194, 530, 364, 1484])).
% 6.69/7.00 tff(6040,plain,
% 6.69/7.00 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[3414, 42, 6039])).
% 6.69/7.00 tff(6041,plain,
% 6.69/7.00 (b(s(z), s(s(elem!1)))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[6040, 3404])).
% 6.69/7.00 tff(6042,plain,
% 6.69/7.00 (~b(z, s(s(elem!1)))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[5311, 6041, 590, 379, 6032])).
% 6.69/7.00 tff(6043,plain,
% 6.69/7.00 (r(z, s(s(elem!1)))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[324, 6042])).
% 6.69/7.00 tff(6044,plain,
% 6.69/7.00 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[5321, 6041, 379, 6032])).
% 6.69/7.00 tff(6045,plain,
% 6.69/7.00 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[1370, 6044, 297])).
% 6.69/7.00 tff(6046,plain,
% 6.69/7.00 ($false),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[372, 6045, 6043, 184, 364])).
% 6.69/7.00 tff(6047,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.69/7.00 tff(6048,plain,
% 6.69/7.00 (~r(s(s(elem!1)), elem!1)),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[6047, 288, 184, 6030, 590, 530, 1484, 847])).
% 6.69/7.00 tff(6049,plain,
% 6.69/7.00 (b(s(s(elem!1)), elem!1)),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[872, 6048, 249])).
% 6.69/7.00 tff(6050,plain,
% 6.69/7.00 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[6001, 6049, 448, 900])).
% 6.69/7.00 tff(6051,plain,
% 6.69/7.00 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[1356, 6050, 3926])).
% 6.69/7.00 tff(6052,plain,
% 6.69/7.00 (~r(z, s(s(elem!1)))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[1450, 6051, 184, 174])).
% 6.69/7.00 tff(6053,plain,
% 6.69/7.00 (b(z, s(s(elem!1)))),
% 6.69/7.00 inference(unit_resolution,[status(thm)],[324, 6052])).
% 6.69/7.00 tff(6054,plain,
% 6.69/7.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.69/7.00 inference(rewrite,[status(thm)],[])).
% 6.69/7.00 tff(6055,plain,
% 6.69/7.00 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.69/7.01 inference(rewrite,[status(thm)],[])).
% 6.69/7.01 tff(6056,plain,
% 6.69/7.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 6.69/7.01 inference(monotonicity,[status(thm)],[6055])).
% 6.69/7.01 tff(6057,plain,
% 6.69/7.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 6.69/7.01 inference(transitivity,[status(thm)],[6056, 6054])).
% 6.69/7.01 tff(6058,plain,
% 6.69/7.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 6.69/7.01 inference(quant_inst,[status(thm)],[])).
% 6.69/7.01 tff(6059,plain,
% 6.69/7.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 6.69/7.01 inference(modus_ponens,[status(thm)],[6058, 6057])).
% 6.69/7.01 tff(6060,plain,
% 6.69/7.01 ($false),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[6059, 391, 133, 900, 6049, 448, 6053])).
% 6.69/7.01 tff(6061,plain,((s(s(elem!1)) = elem!1) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.69/7.01 tff(6062,plain,
% 6.69/7.01 (s(s(elem!1)) = elem!1),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[6061, 5962, 900, 133, 184, 174, 5954, 530, 5996, 5986])).
% 6.69/7.01 tff(6063,plain,
% 6.69/7.01 (s(s(s(elem!1))) = s(elem!1)),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[451, 6062])).
% 6.69/7.01 tff(6064,plain,
% 6.69/7.01 (~(s(elem!1) = s(s(s(s(z)))))),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[5377, 6063, 3363])).
% 6.69/7.01 tff(6065,plain,
% 6.69/7.01 (~(s(s(s(s(z)))) = elem!1)),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[717, 6063])).
% 6.69/7.01 tff(6066,plain,
% 6.69/7.01 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 6.69/7.01 inference(monotonicity,[status(thm)],[6063])).
% 6.69/7.01 tff(6067,plain,
% 6.69/7.01 (r(z, s(elem!1))),
% 6.69/7.01 inference(modus_ponens,[status(thm)],[184, 6066])).
% 6.69/7.01 tff(6068,plain,
% 6.69/7.01 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 6.69/7.01 inference(monotonicity,[status(thm)],[6063])).
% 6.69/7.01 tff(6069,plain,
% 6.69/7.01 (b(elem!1, s(elem!1))),
% 6.69/7.01 inference(modus_ponens,[status(thm)],[5962, 6068])).
% 6.69/7.01 tff(6070,plain,
% 6.69/7.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.69/7.01 inference(rewrite,[status(thm)],[])).
% 6.69/7.01 tff(6071,plain,
% 6.69/7.01 (((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.69/7.01 inference(rewrite,[status(thm)],[])).
% 6.69/7.01 tff(6072,plain,
% 6.69/7.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))))),
% 6.69/7.01 inference(monotonicity,[status(thm)],[6071])).
% 6.69/7.01 tff(6073,plain,
% 6.69/7.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.69/7.01 inference(transitivity,[status(thm)],[6072, 6070])).
% 6.69/7.01 tff(6074,plain,
% 6.69/7.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 6.69/7.01 inference(quant_inst,[status(thm)],[])).
% 6.69/7.01 tff(6075,plain,
% 6.69/7.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))),
% 6.69/7.01 inference(modus_ponens,[status(thm)],[6074, 6073])).
% 6.69/7.01 tff(6076,plain,
% 6.69/7.01 ($false),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[6075, 194, 530, 1484, 2112, 1216])).
% 6.69/7.01 tff(6077,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.69/7.01 tff(6078,plain,
% 6.69/7.01 (~r(s(z), s(s(s(s(z)))))),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[6077, 2112, 530, 1484])).
% 6.69/7.01 tff(6079,plain,
% 6.69/7.01 (b(s(z), s(s(s(s(z)))))),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[1230, 6078])).
% 6.69/7.01 tff(6080,plain,
% 6.69/7.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 6.69/7.01 inference(rewrite,[status(thm)],[])).
% 6.69/7.01 tff(6081,plain,
% 6.69/7.01 (((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 6.69/7.01 inference(rewrite,[status(thm)],[])).
% 6.69/7.01 tff(6082,plain,
% 6.69/7.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 6.69/7.01 inference(monotonicity,[status(thm)],[6081])).
% 6.69/7.01 tff(6083,plain,
% 6.69/7.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 6.69/7.01 inference(transitivity,[status(thm)],[6082, 6080])).
% 6.69/7.01 tff(6084,plain,
% 6.69/7.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 6.69/7.01 inference(quant_inst,[status(thm)],[])).
% 6.69/7.01 tff(6085,plain,
% 6.69/7.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 6.69/7.01 inference(modus_ponens,[status(thm)],[6084, 6083])).
% 6.69/7.01 tff(6086,plain,
% 6.69/7.01 ($false),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[6085, 194, 530, 2144, 2053, 2112])).
% 6.69/7.01 tff(6087,plain,((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.69/7.01 tff(6088,plain,
% 6.69/7.01 (~r(s(s(s(s(z)))), z)),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[6087, 2112, 2144, 530])).
% 6.69/7.01 tff(6089,plain,
% 6.69/7.01 (b(s(s(s(s(z)))), z)),
% 6.69/7.01 inference(unit_resolution,[status(thm)],[87, 6088])).
% 6.69/7.01 tff(6090,plain,
% 6.69/7.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.69/7.01 inference(rewrite,[status(thm)],[])).
% 6.69/7.01 tff(6091,plain,
% 6.69/7.01 (((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.69/7.02 inference(rewrite,[status(thm)],[])).
% 6.69/7.02 tff(6092,plain,
% 6.69/7.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 6.69/7.02 inference(monotonicity,[status(thm)],[6091])).
% 6.69/7.02 tff(6093,plain,
% 6.69/7.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.69/7.02 inference(transitivity,[status(thm)],[6092, 6090])).
% 6.69/7.02 tff(6094,plain,
% 6.69/7.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 6.69/7.02 inference(quant_inst,[status(thm)],[])).
% 6.69/7.02 tff(6095,plain,
% 6.69/7.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 6.69/7.02 inference(modus_ponens,[status(thm)],[6094, 6093])).
% 6.69/7.02 tff(6096,plain,
% 6.69/7.02 ($false),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[6095, 391, 133, 802, 6089, 6079, 590])).
% 6.69/7.02 tff(6097,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.69/7.02 tff(6098,plain,
% 6.69/7.02 (~r(s(s(s(s(z)))), elem!1)),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[6097, 6069, 133, 5954, 530, 5996, 6067])).
% 6.69/7.02 tff(6099,plain,
% 6.69/7.02 (b(s(s(s(s(z)))), elem!1)),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[762, 6098, 6065])).
% 6.69/7.02 tff(6100,plain,
% 6.69/7.02 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 6.69/7.02 inference(monotonicity,[status(thm)],[6063])).
% 6.69/7.02 tff(6101,plain,
% 6.69/7.02 (b(s(elem!1), elem!1)),
% 6.69/7.02 inference(modus_ponens,[status(thm)],[900, 6100])).
% 6.69/7.02 tff(6102,plain,
% 6.69/7.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(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)))))))),
% 6.69/7.02 inference(rewrite,[status(thm)],[])).
% 6.69/7.02 tff(6103,plain,
% 6.69/7.02 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(elem!1, s(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)))))))),
% 6.69/7.02 inference(rewrite,[status(thm)],[])).
% 6.69/7.02 tff(6104,plain,
% 6.69/7.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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))))))))),
% 6.69/7.02 inference(monotonicity,[status(thm)],[6103])).
% 6.69/7.02 tff(6105,plain,
% 6.69/7.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(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)))))))),
% 6.69/7.02 inference(transitivity,[status(thm)],[6104, 6102])).
% 6.69/7.02 tff(6106,plain,
% 6.69/7.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.69/7.02 inference(quant_inst,[status(thm)],[])).
% 6.69/7.02 tff(6107,plain,
% 6.69/7.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(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))))))),
% 6.69/7.02 inference(modus_ponens,[status(thm)],[6106, 6105])).
% 6.69/7.02 tff(6108,plain,
% 6.69/7.02 (~b(s(elem!1), s(s(s(s(z)))))),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[6107, 391, 6069, 6101, 6099])).
% 6.69/7.02 tff(6109,plain,
% 6.69/7.02 (r(s(elem!1), s(s(s(s(z)))))),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[2142, 42, 6108, 6064])).
% 6.69/7.02 tff(6110,plain,
% 6.69/7.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.69/7.02 inference(rewrite,[status(thm)],[])).
% 6.69/7.02 tff(6111,plain,
% 6.69/7.02 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.69/7.02 inference(rewrite,[status(thm)],[])).
% 6.69/7.02 tff(6112,plain,
% 6.69/7.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 6.69/7.02 inference(monotonicity,[status(thm)],[6111])).
% 6.69/7.02 tff(6113,plain,
% 6.69/7.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.69/7.02 inference(transitivity,[status(thm)],[6112, 6110])).
% 6.69/7.02 tff(6114,plain,
% 6.69/7.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 6.69/7.02 inference(quant_inst,[status(thm)],[])).
% 6.69/7.02 tff(6115,plain,
% 6.69/7.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 6.69/7.02 inference(modus_ponens,[status(thm)],[6114, 6113])).
% 6.69/7.02 tff(6116,plain,
% 6.69/7.02 (~b(s(s(s(s(z)))), z)),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[6115, 391, 133, 6069, 6101, 6099])).
% 6.69/7.02 tff(6117,plain,
% 6.69/7.02 (r(s(s(s(s(z)))), z)),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[87, 6116])).
% 6.69/7.02 tff(6118,plain,
% 6.69/7.02 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 6.69/7.02 inference(monotonicity,[status(thm)],[6063])).
% 6.69/7.02 tff(6119,plain,
% 6.69/7.02 (r(s(elem!1), z)),
% 6.69/7.02 inference(modus_ponens,[status(thm)],[174, 6118])).
% 6.69/7.02 tff(6120,plain,
% 6.69/7.02 ($false),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[5530, 194, 6119, 6067, 6117, 6109])).
% 6.69/7.02 tff(6121,plain,((~r(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(z) = elem!1) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.69/7.02 tff(6122,plain,
% 6.69/7.02 (~r(s(s(s(elem!1))), z)),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[6121, 530, 133, 900, 184, 150, 1])).
% 6.69/7.02 tff(6123,plain,
% 6.69/7.02 (b(s(s(s(elem!1))), z)),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[377, 6122])).
% 6.69/7.02 tff(6124,plain,
% 6.69/7.02 (r(elem!1, s(s(s(elem!1))))),
% 6.69/7.02 inference(unit_resolution,[status(thm)],[424, 4028, 1])).
% 6.69/7.02 tff(6125,plain,
% 6.69/7.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 6.69/7.02 inference(rewrite,[status(thm)],[])).
% 6.69/7.02 tff(6126,plain,
% 6.69/7.02 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 6.69/7.02 inference(rewrite,[status(thm)],[])).
% 6.69/7.02 tff(6127,plain,
% 6.69/7.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 6.69/7.02 inference(monotonicity,[status(thm)],[6126])).
% 6.69/7.02 tff(6128,plain,
% 6.69/7.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 6.82/7.03 inference(transitivity,[status(thm)],[6127, 6125])).
% 6.82/7.03 tff(6129,plain,
% 6.82/7.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 6.82/7.03 inference(quant_inst,[status(thm)],[])).
% 6.82/7.03 tff(6130,plain,
% 6.82/7.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 6.82/7.03 inference(modus_ponens,[status(thm)],[6129, 6128])).
% 6.82/7.03 tff(6131,plain,
% 6.82/7.03 ($false),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6130, 194, 530, 184, 410, 183])).
% 6.82/7.03 tff(6132,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.03 tff(6133,plain,
% 6.82/7.03 (~r(s(s(s(elem!1))), s(z))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6132, 6124, 184, 530])).
% 6.82/7.03 tff(6134,plain,
% 6.82/7.03 (b(s(s(s(elem!1))), s(z))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[223, 6133])).
% 6.82/7.03 tff(6135,plain,
% 6.82/7.03 ($false),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[660, 194, 530, 613, 184, 410])).
% 6.82/7.03 tff(6136,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.03 tff(6137,plain,
% 6.82/7.03 (~r(s(s(s(elem!1))), s(elem!1))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6136, 6124, 184, 530])).
% 6.82/7.03 tff(6138,plain,
% 6.82/7.03 (~b(s(s(s(elem!1))), s(elem!1))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[3554, 1628, 184, 437, 900, 530])).
% 6.82/7.03 tff(6139,plain,
% 6.82/7.03 (s(s(s(elem!1))) = s(elem!1)),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[588, 6138, 1575])).
% 6.82/7.03 tff(6140,plain,
% 6.82/7.03 (b(elem!1, s(elem!1))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[443, 3551, 437])).
% 6.82/7.03 tff(6141,plain,
% 6.82/7.03 ($false),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[4603, 6140, 6139, 4028])).
% 6.82/7.03 tff(6142,plain,((~r(s(elem!1), z)) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.03 tff(6143,plain,
% 6.82/7.03 (~r(s(elem!1), z)),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6142, 6137, 437, 4028, 184, 530, 900])).
% 6.82/7.03 tff(6144,plain,
% 6.82/7.03 (b(s(elem!1), z)),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[549, 6143])).
% 6.82/7.03 tff(6145,plain,
% 6.82/7.03 (r(z, s(elem!1))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[2614, 6144, 184, 6137, 6123])).
% 6.82/7.03 tff(6146,plain,
% 6.82/7.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.82/7.03 inference(rewrite,[status(thm)],[])).
% 6.82/7.03 tff(6147,plain,
% 6.82/7.03 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.82/7.03 inference(rewrite,[status(thm)],[])).
% 6.82/7.03 tff(6148,plain,
% 6.82/7.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 6.82/7.03 inference(monotonicity,[status(thm)],[6147])).
% 6.82/7.03 tff(6149,plain,
% 6.82/7.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 6.82/7.03 inference(transitivity,[status(thm)],[6148, 6146])).
% 6.82/7.03 tff(6150,plain,
% 6.82/7.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 6.82/7.03 inference(quant_inst,[status(thm)],[])).
% 6.82/7.03 tff(6151,plain,
% 6.82/7.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 6.82/7.03 inference(modus_ponens,[status(thm)],[6150, 6149])).
% 6.82/7.03 tff(6152,plain,
% 6.82/7.03 ($false),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6151, 194, 530, 184, 410, 327])).
% 6.82/7.03 tff(6153,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.03 tff(6154,plain,
% 6.82/7.03 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6153, 6124, 184, 530])).
% 6.82/7.03 tff(6155,assumption,(~r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 6.82/7.03 tff(6156,plain,
% 6.82/7.03 (r(elem!1, s(z))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[1505, 1492, 133, 173, 900, 380])).
% 6.82/7.03 tff(6157,plain,
% 6.82/7.03 (b(s(z), elem!1)),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[632, 1492, 150])).
% 6.82/7.03 tff(6158,plain,
% 6.82/7.03 ($false),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[249, 2459])).
% 6.82/7.03 tff(6159,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.82/7.03 tff(6160,plain,
% 6.82/7.03 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6159, 249])).
% 6.82/7.03 tff(6161,plain,
% 6.82/7.03 (b(s(s(s(elem!1))), s(elem!1))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[588, 6160, 1575])).
% 6.82/7.03 tff(6162,plain,
% 6.82/7.03 (~b(elem!1, s(s(elem!1)))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[2248, 6161, 133, 380, 591])).
% 6.82/7.03 tff(6163,plain,
% 6.82/7.03 (r(elem!1, s(s(elem!1)))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[1307, 6162, 1293])).
% 6.82/7.03 tff(6164,plain,
% 6.82/7.03 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[1370, 288, 6155])).
% 6.82/7.03 tff(6165,plain,
% 6.82/7.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~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)))))),
% 6.82/7.03 inference(rewrite,[status(thm)],[])).
% 6.82/7.03 tff(6166,plain,
% 6.82/7.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~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)))))),
% 6.82/7.03 inference(quant_inst,[status(thm)],[])).
% 6.82/7.03 tff(6167,plain,
% 6.82/7.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 6.82/7.03 inference(modus_ponens,[status(thm)],[6166, 6165])).
% 6.82/7.03 tff(6168,plain,
% 6.82/7.03 ($false),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6167, 391, 133, 381, 1374, 1526, 590])).
% 6.82/7.03 tff(6169,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.03 tff(6170,plain,
% 6.82/7.03 (~b(s(s(elem!1)), s(z))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6169, 6164, 133, 1526, 590])).
% 6.82/7.03 tff(6171,plain,
% 6.82/7.03 (r(s(s(elem!1)), s(z))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[362, 6170])).
% 6.82/7.03 tff(6172,plain,
% 6.82/7.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.03 inference(rewrite,[status(thm)],[])).
% 6.82/7.03 tff(6173,plain,
% 6.82/7.03 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.03 inference(rewrite,[status(thm)],[])).
% 6.82/7.03 tff(6174,plain,
% 6.82/7.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))))),
% 6.82/7.03 inference(monotonicity,[status(thm)],[6173])).
% 6.82/7.03 tff(6175,plain,
% 6.82/7.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.03 inference(transitivity,[status(thm)],[6174, 6172])).
% 6.82/7.03 tff(6176,plain,
% 6.82/7.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.03 inference(quant_inst,[status(thm)],[])).
% 6.82/7.03 tff(6177,plain,
% 6.82/7.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))),
% 6.82/7.03 inference(modus_ponens,[status(thm)],[6176, 6175])).
% 6.82/7.03 tff(6178,plain,
% 6.82/7.03 ($false),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6177, 194, 340, 1064, 232, 847])).
% 6.82/7.03 tff(6179,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.03 tff(6180,plain,
% 6.82/7.03 (~r(s(z), s(s(s(elem!1))))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[6179, 6171, 6163, 847])).
% 6.82/7.03 tff(6181,plain,
% 6.82/7.03 (b(s(z), s(s(s(elem!1))))),
% 6.82/7.03 inference(unit_resolution,[status(thm)],[247, 6180])).
% 6.82/7.03 tff(6182,plain,
% 6.82/7.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.03 inference(rewrite,[status(thm)],[])).
% 6.82/7.03 tff(6183,plain,
% 6.82/7.03 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.03 inference(rewrite,[status(thm)],[])).
% 6.82/7.03 tff(6184,plain,
% 6.82/7.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 6.82/7.03 inference(monotonicity,[status(thm)],[6183])).
% 6.82/7.03 tff(6185,plain,
% 6.82/7.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.04 inference(transitivity,[status(thm)],[6184, 6182])).
% 6.82/7.04 tff(6186,plain,
% 6.82/7.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 6.82/7.04 inference(quant_inst,[status(thm)],[])).
% 6.82/7.04 tff(6187,plain,
% 6.82/7.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 6.82/7.04 inference(modus_ponens,[status(thm)],[6186, 6185])).
% 6.82/7.04 tff(6188,plain,
% 6.82/7.04 ($false),
% 6.82/7.04 inference(unit_resolution,[status(thm)],[6187, 194, 530, 340, 326, 1064])).
% 6.82/7.04 tff(6189,plain,((~r(s(s(elem!1)), s(z))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.04 tff(6190,plain,
% 6.82/7.04 (~r(z, s(s(elem!1)))),
% 6.82/7.04 inference(unit_resolution,[status(thm)],[6189, 6171, 6163, 530])).
% 6.82/7.04 tff(6191,plain,
% 6.82/7.04 (b(z, s(s(elem!1)))),
% 6.82/7.04 inference(unit_resolution,[status(thm)],[324, 6190])).
% 6.82/7.04 tff(6192,assumption,(b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 6.82/7.04 tff(6193,plain,
% 6.82/7.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 6.82/7.04 inference(rewrite,[status(thm)],[])).
% 6.82/7.04 tff(6194,plain,
% 6.82/7.04 (((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 6.82/7.04 inference(rewrite,[status(thm)],[])).
% 6.82/7.04 tff(6195,plain,
% 6.82/7.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))))),
% 6.82/7.04 inference(monotonicity,[status(thm)],[6194])).
% 6.82/7.04 tff(6196,plain,
% 6.82/7.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 6.82/7.04 inference(transitivity,[status(thm)],[6195, 6193])).
% 6.82/7.04 tff(6197,plain,
% 6.82/7.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.82/7.04 inference(quant_inst,[status(thm)],[])).
% 6.82/7.04 tff(6198,plain,
% 6.82/7.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))),
% 6.82/7.04 inference(modus_ponens,[status(thm)],[6197, 6196])).
% 6.82/7.04 tff(6199,plain,
% 6.82/7.04 ($false),
% 6.82/7.04 inference(unit_resolution,[status(thm)],[6198, 391, 380, 3927, 379, 590, 6192])).
% 6.82/7.04 tff(6200,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.04 tff(6201,plain,
% 6.82/7.04 (~b(s(s(elem!1)), s(s(z)))),
% 6.82/7.04 inference(unit_resolution,[status(thm)],[6200, 6191, 380, 6181, 590])).
% 6.82/7.04 tff(6202,plain,
% 6.82/7.04 (r(s(s(elem!1)), s(s(z)))),
% 6.82/7.04 inference(unit_resolution,[status(thm)],[5174, 42, 6201, 2689])).
% 6.82/7.04 tff(6203,plain,
% 6.82/7.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.82/7.04 inference(rewrite,[status(thm)],[])).
% 6.82/7.04 tff(6204,plain,
% 6.82/7.04 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.82/7.04 inference(rewrite,[status(thm)],[])).
% 6.82/7.04 tff(6205,plain,
% 6.82/7.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 6.82/7.04 inference(monotonicity,[status(thm)],[6204])).
% 6.82/7.04 tff(6206,plain,
% 6.82/7.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.82/7.04 inference(transitivity,[status(thm)],[6205, 6203])).
% 6.82/7.04 tff(6207,plain,
% 6.82/7.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.82/7.04 inference(quant_inst,[status(thm)],[])).
% 6.82/7.04 tff(6208,plain,
% 6.82/7.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 6.82/7.04 inference(modus_ponens,[status(thm)],[6207, 6206])).
% 6.82/7.04 tff(6209,plain,
% 6.82/7.04 ($false),
% 6.82/7.04 inference(unit_resolution,[status(thm)],[6208, 391, 380, 973, 3927, 1526, 590])).
% 6.82/7.04 tff(6210,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.04 tff(6211,plain,
% 6.82/7.04 (~b(s(s(elem!1)), elem!1)),
% 6.82/7.04 inference(unit_resolution,[status(thm)],[6210, 6191, 380, 1526, 590])).
% 6.82/7.04 tff(6212,plain,
% 6.82/7.04 (r(s(s(elem!1)), elem!1)),
% 6.82/7.04 inference(unit_resolution,[status(thm)],[872, 6211, 249])).
% 6.82/7.04 tff(6213,plain,
% 6.82/7.04 (~r(s(s(s(s(z)))), elem!1)),
% 6.82/7.04 inference(unit_resolution,[status(thm)],[6087, 2053, 2144, 530])).
% 6.82/7.04 tff(6214,plain,
% 6.82/7.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.05 inference(rewrite,[status(thm)],[])).
% 6.82/7.05 tff(6215,plain,
% 6.82/7.05 (((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.05 inference(rewrite,[status(thm)],[])).
% 6.82/7.05 tff(6216,plain,
% 6.82/7.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))))),
% 6.82/7.05 inference(monotonicity,[status(thm)],[6215])).
% 6.82/7.05 tff(6217,plain,
% 6.82/7.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.05 inference(transitivity,[status(thm)],[6216, 6214])).
% 6.82/7.05 tff(6218,plain,
% 6.82/7.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.05 inference(quant_inst,[status(thm)],[])).
% 6.82/7.05 tff(6219,plain,
% 6.82/7.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))),
% 6.82/7.05 inference(modus_ponens,[status(thm)],[6218, 6217])).
% 6.82/7.05 tff(6220,plain,
% 6.82/7.05 (~r(elem!1, s(s(s(s(z)))))),
% 6.82/7.05 inference(unit_resolution,[status(thm)],[6219, 194, 530, 2144, 2053])).
% 6.82/7.05 tff(6221,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 6.82/7.05 tff(6222,plain,
% 6.82/7.05 (b(s(s(s(s(z)))), elem!1)),
% 6.82/7.05 inference(unit_resolution,[status(thm)],[762, 720, 6221])).
% 6.82/7.05 tff(6223,plain,
% 6.82/7.05 (b(elem!1, s(s(s(s(z)))))),
% 6.82/7.05 inference(unit_resolution,[status(thm)],[781, 770, 3222])).
% 6.82/7.05 tff(6224,plain,
% 6.82/7.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.82/7.05 inference(rewrite,[status(thm)],[])).
% 6.82/7.05 tff(6225,plain,
% 6.82/7.05 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.82/7.05 inference(rewrite,[status(thm)],[])).
% 6.82/7.05 tff(6226,plain,
% 6.82/7.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 6.82/7.05 inference(monotonicity,[status(thm)],[6225])).
% 6.82/7.05 tff(6227,plain,
% 6.82/7.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.82/7.05 inference(transitivity,[status(thm)],[6226, 6224])).
% 6.82/7.05 tff(6228,plain,
% 6.82/7.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 6.82/7.05 inference(quant_inst,[status(thm)],[])).
% 6.82/7.05 tff(6229,plain,
% 6.82/7.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 6.82/7.05 inference(modus_ponens,[status(thm)],[6228, 6227])).
% 6.82/7.05 tff(6230,plain,
% 6.82/7.05 ($false),
% 6.82/7.05 inference(unit_resolution,[status(thm)],[6229, 391, 133, 900, 380, 6223, 6222])).
% 6.82/7.05 tff(6231,plain,((s(s(s(s(z)))) = elem!1) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.82/7.05 tff(6232,plain,
% 6.82/7.05 (s(s(s(s(z)))) = elem!1),
% 6.82/7.05 inference(unit_resolution,[status(thm)],[6231, 6220, 900, 380, 133, 6213])).
% 6.82/7.05 tff(6233,plain,
% 6.82/7.05 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 6.82/7.05 inference(monotonicity,[status(thm)],[6232])).
% 6.82/7.05 tff(6234,plain,
% 6.82/7.05 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.82/7.05 inference(symmetry,[status(thm)],[6233])).
% 6.82/7.05 tff(6235,plain,
% 6.82/7.05 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.82/7.05 inference(modus_ponens,[status(thm)],[1064, 6234])).
% 6.82/7.05 tff(6236,assumption,(r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 6.82/7.05 tff(6237,plain,
% 6.82/7.05 (r(s(s(s(s(z)))), s(z)) <=> r(elem!1, s(z))),
% 6.82/7.05 inference(monotonicity,[status(thm)],[6232])).
% 6.82/7.05 tff(6238,plain,
% 6.82/7.05 (r(elem!1, s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 6.82/7.05 inference(symmetry,[status(thm)],[6237])).
% 6.82/7.05 tff(6239,plain,
% 6.82/7.05 (r(s(s(s(s(z)))), s(z))),
% 6.82/7.05 inference(modus_ponens,[status(thm)],[847, 6238])).
% 6.82/7.05 tff(6240,assumption,(r(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 6.82/7.05 tff(6241,plain,
% 6.82/7.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.82/7.05 inference(rewrite,[status(thm)],[])).
% 6.82/7.05 tff(6242,plain,
% 6.82/7.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.82/7.05 inference(quant_inst,[status(thm)],[])).
% 6.82/7.05 tff(6243,plain,
% 6.82/7.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 6.82/7.05 inference(modus_ponens,[status(thm)],[6242, 6241])).
% 6.82/7.05 tff(6244,plain,
% 6.82/7.05 ($false),
% 6.82/7.05 inference(unit_resolution,[status(thm)],[6243, 194, 340, 723, 1747, 6240])).
% 6.82/7.05 tff(6245,plain,((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.05 tff(6246,plain,
% 6.82/7.05 (~r(s(z), s(s(z)))),
% 6.82/7.05 inference(unit_resolution,[status(thm)],[6245, 6235, 340, 6239])).
% 6.82/7.06 tff(6247,plain,
% 6.82/7.06 (b(s(z), s(s(z)))),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[1788, 6246])).
% 6.82/7.06 tff(6248,plain,
% 6.82/7.06 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 6.82/7.06 inference(monotonicity,[status(thm)],[688])).
% 6.82/7.06 tff(6249,plain,
% 6.82/7.06 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(z)))))),
% 6.82/7.06 inference(symmetry,[status(thm)],[6248])).
% 6.82/7.06 tff(6250,plain,
% 6.82/7.06 (b(s(z), s(s(s(s(z)))))),
% 6.82/7.06 inference(modus_ponens,[status(thm)],[644, 6249])).
% 6.82/7.06 tff(6251,plain,
% 6.82/7.06 ($false),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[2881, 6250])).
% 6.82/7.06 tff(6252,plain,((~(s(s(s(s(z)))) = elem!1)) | b(s(z), s(s(s(s(z))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.06 tff(6253,plain,
% 6.82/7.06 (b(s(z), s(s(s(s(z)))))),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[6252, 6232, 644])).
% 6.82/7.06 tff(6254,plain,
% 6.82/7.06 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 6.82/7.06 inference(monotonicity,[status(thm)],[6232])).
% 6.82/7.06 tff(6255,plain,
% 6.82/7.06 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.82/7.06 inference(symmetry,[status(thm)],[6254])).
% 6.82/7.06 tff(6256,plain,
% 6.82/7.06 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.82/7.06 inference(modus_ponens,[status(thm)],[364, 6255])).
% 6.82/7.06 tff(6257,assumption,(r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 6.82/7.06 tff(6258,plain,
% 6.82/7.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.82/7.06 inference(rewrite,[status(thm)],[])).
% 6.82/7.06 tff(6259,plain,
% 6.82/7.06 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.82/7.06 inference(rewrite,[status(thm)],[])).
% 6.82/7.06 tff(6260,plain,
% 6.82/7.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 6.82/7.06 inference(monotonicity,[status(thm)],[6259])).
% 6.82/7.06 tff(6261,plain,
% 6.82/7.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 6.82/7.06 inference(transitivity,[status(thm)],[6260, 6258])).
% 6.82/7.06 tff(6262,plain,
% 6.82/7.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 6.82/7.06 inference(quant_inst,[status(thm)],[])).
% 6.82/7.06 tff(6263,plain,
% 6.82/7.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 6.82/7.06 inference(modus_ponens,[status(thm)],[6262, 6261])).
% 6.82/7.06 tff(6264,plain,
% 6.82/7.06 ($false),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[6263, 194, 1749, 2053, 6257, 6236])).
% 6.82/7.06 tff(6265,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.06 tff(6266,plain,
% 6.82/7.06 (~r(s(s(z)), s(s(s(s(z)))))),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[6265, 6256, 6236, 2053])).
% 6.82/7.06 tff(6267,plain,
% 6.82/7.06 (b(s(s(z)), s(s(s(s(z)))))),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[3652, 6266])).
% 6.82/7.06 tff(6268,plain,
% 6.82/7.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.82/7.06 inference(rewrite,[status(thm)],[])).
% 6.82/7.06 tff(6269,plain,
% 6.82/7.06 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.82/7.06 inference(rewrite,[status(thm)],[])).
% 6.82/7.06 tff(6270,plain,
% 6.82/7.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 6.82/7.06 inference(monotonicity,[status(thm)],[6269])).
% 6.82/7.06 tff(6271,plain,
% 6.82/7.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.82/7.06 inference(transitivity,[status(thm)],[6270, 6268])).
% 6.82/7.06 tff(6272,plain,
% 6.82/7.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.82/7.06 inference(quant_inst,[status(thm)],[])).
% 6.82/7.06 tff(6273,plain,
% 6.82/7.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 6.82/7.06 inference(modus_ponens,[status(thm)],[6272, 6271])).
% 6.82/7.06 tff(6274,plain,
% 6.82/7.06 ($false),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[6273, 391, 3823, 1234, 2439, 3563])).
% 6.82/7.06 tff(6275,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.06 tff(6276,plain,
% 6.82/7.06 (~b(s(s(s(s(z)))), s(s(z)))),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[6275, 6267, 6253, 6247])).
% 6.82/7.06 tff(6277,plain,
% 6.82/7.06 (r(s(s(s(s(z)))), s(s(z)))),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[1714, 6276])).
% 6.82/7.06 tff(6278,plain,
% 6.82/7.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 6.82/7.06 inference(rewrite,[status(thm)],[])).
% 6.82/7.06 tff(6279,plain,
% 6.82/7.06 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 6.82/7.06 inference(rewrite,[status(thm)],[])).
% 6.82/7.06 tff(6280,plain,
% 6.82/7.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 6.82/7.06 inference(monotonicity,[status(thm)],[6279])).
% 6.82/7.06 tff(6281,plain,
% 6.82/7.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 6.82/7.06 inference(transitivity,[status(thm)],[6280, 6278])).
% 6.82/7.06 tff(6282,plain,
% 6.82/7.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.82/7.06 inference(quant_inst,[status(thm)],[])).
% 6.82/7.06 tff(6283,plain,
% 6.82/7.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 6.82/7.06 inference(modus_ponens,[status(thm)],[6282, 6281])).
% 6.82/7.06 tff(6284,plain,
% 6.82/7.06 ($false),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[6283, 194, 1697, 2405, 6240, 6236])).
% 6.82/7.06 tff(6285,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.06 tff(6286,plain,
% 6.82/7.06 (~r(s(s(z)), s(z))),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[6285, 6277, 6236, 6235])).
% 6.82/7.06 tff(6287,plain,
% 6.82/7.06 (b(s(s(z)), s(z))),
% 6.82/7.06 inference(unit_resolution,[status(thm)],[3778, 6286])).
% 6.82/7.06 tff(6288,plain,
% 6.82/7.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 6.82/7.06 inference(rewrite,[status(thm)],[])).
% 6.82/7.06 tff(6289,plain,
% 6.82/7.06 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 6.82/7.06 inference(rewrite,[status(thm)],[])).
% 6.82/7.06 tff(6290,plain,
% 6.82/7.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 6.82/7.06 inference(monotonicity,[status(thm)],[6289])).
% 6.82/7.06 tff(6291,plain,
% 6.82/7.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 6.82/7.06 inference(transitivity,[status(thm)],[6290, 6288])).
% 6.82/7.06 tff(6292,plain,
% 6.82/7.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.82/7.07 inference(quant_inst,[status(thm)],[])).
% 6.82/7.07 tff(6293,plain,
% 6.82/7.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 6.82/7.07 inference(modus_ponens,[status(thm)],[6292, 6291])).
% 6.82/7.07 tff(6294,plain,
% 6.82/7.07 ($false),
% 6.82/7.07 inference(unit_resolution,[status(thm)],[6293, 194, 3557, 1697, 6257, 6236])).
% 6.82/7.07 tff(6295,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.07 tff(6296,plain,
% 6.82/7.07 (~r(s(s(z)), z)),
% 6.82/7.07 inference(unit_resolution,[status(thm)],[6295, 6277, 6236, 6256])).
% 6.82/7.07 tff(6297,plain,
% 6.82/7.07 (b(s(s(z)), z)),
% 6.82/7.07 inference(unit_resolution,[status(thm)],[1211, 6296])).
% 6.82/7.07 tff(6298,plain,
% 6.82/7.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.82/7.07 inference(rewrite,[status(thm)],[])).
% 6.82/7.07 tff(6299,plain,
% 6.82/7.07 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.82/7.07 inference(rewrite,[status(thm)],[])).
% 6.82/7.07 tff(6300,plain,
% 6.82/7.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 6.82/7.07 inference(monotonicity,[status(thm)],[6299])).
% 6.82/7.07 tff(6301,plain,
% 6.82/7.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.82/7.07 inference(transitivity,[status(thm)],[6300, 6298])).
% 6.82/7.07 tff(6302,plain,
% 6.82/7.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.82/7.07 inference(quant_inst,[status(thm)],[])).
% 6.82/7.07 tff(6303,plain,
% 6.82/7.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 6.82/7.07 inference(modus_ponens,[status(thm)],[6302, 6301])).
% 6.82/7.07 tff(6304,plain,
% 6.82/7.07 (~b(s(s(z)), s(s(s(elem!1))))),
% 6.82/7.07 inference(unit_resolution,[status(thm)],[6303, 391, 1526, 6297, 6247, 6287])).
% 6.82/7.07 tff(6305,plain,
% 6.82/7.07 (r(s(s(z)), s(s(s(elem!1))))),
% 6.82/7.07 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 6304])).
% 6.82/7.07 tff(6306,plain,
% 6.82/7.07 (r(s(s(s(s(z)))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 6.82/7.07 inference(monotonicity,[status(thm)],[6232])).
% 6.82/7.07 tff(6307,plain,
% 6.82/7.07 (r(elem!1, s(s(z)))),
% 6.82/7.07 inference(modus_ponens,[status(thm)],[6277, 6306])).
% 6.82/7.07 tff(6308,plain,
% 6.82/7.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 6.82/7.07 inference(rewrite,[status(thm)],[])).
% 6.82/7.07 tff(6309,plain,
% 6.82/7.07 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 6.82/7.07 inference(rewrite,[status(thm)],[])).
% 6.82/7.07 tff(6310,plain,
% 6.82/7.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 6.82/7.07 inference(monotonicity,[status(thm)],[6309])).
% 6.82/7.07 tff(6311,plain,
% 6.82/7.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 6.82/7.07 inference(transitivity,[status(thm)],[6310, 6308])).
% 6.82/7.07 tff(6312,plain,
% 6.82/7.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), elem!1)))),
% 6.82/7.07 inference(quant_inst,[status(thm)],[])).
% 6.82/7.07 tff(6313,plain,
% 6.82/7.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 6.82/7.07 inference(modus_ponens,[status(thm)],[6312, 6311])).
% 6.82/7.07 tff(6314,plain,
% 6.82/7.07 ($false),
% 6.82/7.07 inference(unit_resolution,[status(thm)],[6313, 194, 364, 6307, 6236, 6305])).
% 6.82/7.07 tff(6315,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.07 tff(6316,plain,
% 6.82/7.07 (~r(s(s(s(s(z)))), z)),
% 6.82/7.07 inference(unit_resolution,[status(thm)],[6315, 6212, 6202, 1526, 6171, 6163, 847, 644, 900, 380, 133, 530, 2144])).
% 6.82/7.07 tff(6317,plain,
% 6.82/7.07 (b(s(s(s(s(z)))), z)),
% 6.82/7.07 inference(unit_resolution,[status(thm)],[87, 6316])).
% 6.82/7.07 tff(6318,plain,
% 6.82/7.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 6.82/7.07 inference(rewrite,[status(thm)],[])).
% 6.82/7.07 tff(6319,plain,
% 6.82/7.07 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), 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))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 6.82/7.08 inference(rewrite,[status(thm)],[])).
% 6.82/7.08 tff(6320,plain,
% 6.82/7.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 6.82/7.08 inference(monotonicity,[status(thm)],[6319])).
% 6.82/7.08 tff(6321,plain,
% 6.82/7.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 6.82/7.08 inference(transitivity,[status(thm)],[6320, 6318])).
% 6.82/7.08 tff(6322,plain,
% 6.82/7.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 6.82/7.08 inference(quant_inst,[status(thm)],[])).
% 6.82/7.08 tff(6323,plain,
% 6.82/7.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 6.82/7.08 inference(modus_ponens,[status(thm)],[6322, 6321])).
% 6.82/7.08 tff(6324,plain,
% 6.82/7.08 ($false),
% 6.82/7.08 inference(unit_resolution,[status(thm)],[6323, 391, 380, 1526, 90, 1686, 590])).
% 6.82/7.08 tff(6325,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.08 tff(6326,plain,
% 6.82/7.08 (~b(z, s(s(s(s(z)))))),
% 6.82/7.08 inference(unit_resolution,[status(thm)],[6325, 6317, 1526, 380, 590])).
% 6.82/7.08 tff(6327,plain,
% 6.82/7.08 (r(z, s(s(s(s(z)))))),
% 6.82/7.08 inference(unit_resolution,[status(thm)],[800, 6326])).
% 6.82/7.08 tff(6328,plain,
% 6.82/7.08 (~b(z, s(s(s(s(z)))))),
% 6.82/7.08 inference(unit_resolution,[status(thm)],[6325, 90, 1526, 380, 590])).
% 6.82/7.08 tff(6329,plain,
% 6.82/7.08 (r(z, s(s(s(s(z)))))),
% 6.82/7.08 inference(unit_resolution,[status(thm)],[800, 6328])).
% 6.82/7.08 tff(6330,plain,
% 6.82/7.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.08 inference(rewrite,[status(thm)],[])).
% 6.82/7.08 tff(6331,plain,
% 6.82/7.08 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.08 inference(rewrite,[status(thm)],[])).
% 6.82/7.08 tff(6332,plain,
% 6.82/7.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 6.82/7.08 inference(monotonicity,[status(thm)],[6331])).
% 6.82/7.08 tff(6333,plain,
% 6.82/7.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.08 inference(transitivity,[status(thm)],[6332, 6330])).
% 6.82/7.08 tff(6334,plain,
% 6.82/7.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))),
% 6.82/7.08 inference(quant_inst,[status(thm)],[])).
% 6.82/7.08 tff(6335,plain,
% 6.82/7.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.82/7.08 inference(modus_ponens,[status(thm)],[6334, 6333])).
% 6.82/7.08 tff(6336,plain,
% 6.82/7.08 ($false),
% 6.82/7.08 inference(unit_resolution,[status(thm)],[6335, 194, 530, 2032, 719, 2100])).
% 6.82/7.08 tff(6337,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.08 tff(6338,plain,
% 6.82/7.08 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.82/7.08 inference(unit_resolution,[status(thm)],[6337, 2032, 530, 719])).
% 6.82/7.08 tff(6339,plain,
% 6.82/7.08 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.82/7.08 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 6338])).
% 6.82/7.08 tff(6340,plain,
% 6.82/7.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.08 inference(rewrite,[status(thm)],[])).
% 6.82/7.08 tff(6341,plain,
% 6.82/7.08 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.08 inference(rewrite,[status(thm)],[])).
% 6.82/7.08 tff(6342,plain,
% 6.82/7.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 6.82/7.08 inference(monotonicity,[status(thm)],[6341])).
% 6.82/7.08 tff(6343,plain,
% 6.82/7.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.08 inference(transitivity,[status(thm)],[6342, 6340])).
% 6.82/7.08 tff(6344,plain,
% 6.82/7.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))),
% 6.82/7.08 inference(quant_inst,[status(thm)],[])).
% 6.82/7.08 tff(6345,plain,
% 6.82/7.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 6.82/7.08 inference(modus_ponens,[status(thm)],[6344, 6343])).
% 6.82/7.08 tff(6346,plain,
% 6.82/7.08 ($false),
% 6.82/7.08 inference(unit_resolution,[status(thm)],[6345, 194, 847, 2032, 1216, 723])).
% 6.82/7.08 tff(6347,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.08 tff(6348,plain,
% 6.82/7.08 (~r(s(s(s(s(z)))), s(z))),
% 6.82/7.08 inference(unit_resolution,[status(thm)],[6347, 1216, 2032, 847])).
% 6.82/7.09 tff(6349,plain,
% 6.82/7.09 (b(s(s(s(s(z)))), s(z))),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[749, 6348])).
% 6.82/7.09 tff(6350,plain,
% 6.82/7.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.09 inference(rewrite,[status(thm)],[])).
% 6.82/7.09 tff(6351,plain,
% 6.82/7.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.09 inference(quant_inst,[status(thm)],[])).
% 6.82/7.09 tff(6352,plain,
% 6.82/7.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.82/7.09 inference(modus_ponens,[status(thm)],[6351, 6350])).
% 6.82/7.09 tff(6353,plain,
% 6.82/7.09 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[6352, 391, 133, 1526, 6349, 590])).
% 6.82/7.09 tff(6354,plain,
% 6.82/7.09 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 6353])).
% 6.82/7.09 tff(6355,plain,
% 6.82/7.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.09 inference(rewrite,[status(thm)],[])).
% 6.82/7.09 tff(6356,plain,
% 6.82/7.09 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.09 inference(rewrite,[status(thm)],[])).
% 6.82/7.09 tff(6357,plain,
% 6.82/7.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 6.82/7.09 inference(monotonicity,[status(thm)],[6356])).
% 6.82/7.09 tff(6358,plain,
% 6.82/7.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.09 inference(transitivity,[status(thm)],[6357, 6355])).
% 6.82/7.09 tff(6359,plain,
% 6.82/7.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))),
% 6.82/7.09 inference(quant_inst,[status(thm)],[])).
% 6.82/7.09 tff(6360,plain,
% 6.82/7.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.82/7.09 inference(modus_ponens,[status(thm)],[6359, 6358])).
% 6.82/7.09 tff(6361,plain,
% 6.82/7.09 ($false),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[6360, 194, 847, 2032, 1216, 6354])).
% 6.82/7.09 tff(6362,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.09 tff(6363,plain,
% 6.82/7.09 (~r(s(z), s(s(s(s(z)))))),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[6362, 2032, 847, 3843, 133, 1526, 590])).
% 6.82/7.09 tff(6364,plain,
% 6.82/7.09 (b(s(z), s(s(s(s(z)))))),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[1230, 6363])).
% 6.82/7.09 tff(6365,plain,
% 6.82/7.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.09 inference(rewrite,[status(thm)],[])).
% 6.82/7.09 tff(6366,plain,
% 6.82/7.09 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.09 inference(rewrite,[status(thm)],[])).
% 6.82/7.09 tff(6367,plain,
% 6.82/7.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 6.82/7.09 inference(monotonicity,[status(thm)],[6366])).
% 6.82/7.09 tff(6368,plain,
% 6.82/7.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.09 inference(transitivity,[status(thm)],[6367, 6365])).
% 6.82/7.09 tff(6369,plain,
% 6.82/7.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.82/7.09 inference(quant_inst,[status(thm)],[])).
% 6.82/7.09 tff(6370,plain,
% 6.82/7.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.82/7.09 inference(modus_ponens,[status(thm)],[6369, 6368])).
% 6.82/7.09 tff(6371,plain,
% 6.82/7.09 ($false),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[6370, 391, 1526, 90, 1234, 1759, 3325])).
% 6.82/7.09 tff(6372,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.09 tff(6373,plain,
% 6.82/7.09 (~b(s(s(s(s(z)))), s(z))),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[6372, 6364, 90, 1526, 6339])).
% 6.82/7.09 tff(6374,plain,
% 6.82/7.09 (r(s(s(s(s(z)))), s(z))),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[749, 6373])).
% 6.82/7.09 tff(6375,plain,
% 6.82/7.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.09 inference(rewrite,[status(thm)],[])).
% 6.82/7.09 tff(6376,plain,
% 6.82/7.09 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.09 inference(rewrite,[status(thm)],[])).
% 6.82/7.09 tff(6377,plain,
% 6.82/7.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 6.82/7.09 inference(monotonicity,[status(thm)],[6376])).
% 6.82/7.09 tff(6378,plain,
% 6.82/7.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.09 inference(transitivity,[status(thm)],[6377, 6375])).
% 6.82/7.09 tff(6379,plain,
% 6.82/7.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))),
% 6.82/7.09 inference(quant_inst,[status(thm)],[])).
% 6.82/7.09 tff(6380,plain,
% 6.82/7.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 6.82/7.09 inference(modus_ponens,[status(thm)],[6379, 6378])).
% 6.82/7.09 tff(6381,plain,
% 6.82/7.09 ($false),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[6380, 194, 530, 2032, 6374, 719])).
% 6.82/7.09 tff(6382,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.09 tff(6383,plain,
% 6.82/7.09 (~r(elem!1, s(s(s(s(z)))))),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[6382, 6329, 530, 90, 1526, 3843, 847, 133, 590])).
% 6.82/7.09 tff(6384,plain,
% 6.82/7.09 (s(s(s(s(z)))) = elem!1),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[6231, 6383, 900, 380, 133, 6221])).
% 6.82/7.09 tff(6385,plain,
% 6.82/7.09 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 6.82/7.09 inference(monotonicity,[status(thm)],[6384])).
% 6.82/7.09 tff(6386,plain,
% 6.82/7.09 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 6.82/7.09 inference(symmetry,[status(thm)],[6385])).
% 6.82/7.09 tff(6387,plain,
% 6.82/7.09 ((~b(elem!1, z)) <=> (~b(s(s(s(s(z)))), z))),
% 6.82/7.09 inference(monotonicity,[status(thm)],[6386])).
% 6.82/7.09 tff(6388,plain,
% 6.82/7.09 (~b(s(s(s(s(z)))), z)),
% 6.82/7.09 inference(modus_ponens,[status(thm)],[484, 6387])).
% 6.82/7.09 tff(6389,plain,
% 6.82/7.09 ($false),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[90, 6388])).
% 6.82/7.09 tff(6390,plain,((~b(s(s(s(s(z)))), z)) | b(elem!1, z) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | r(s(s(s(s(z)))), elem!1) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.09 tff(6391,plain,
% 6.82/7.09 (r(s(s(s(s(z)))), elem!1)),
% 6.82/7.09 inference(unit_resolution,[status(thm)],[6390, 6317, 900, 380, 133, 484, 530, 1526, 3843, 847, 590])).
% 6.82/7.09 tff(6392,plain,
% 6.82/7.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.10 inference(rewrite,[status(thm)],[])).
% 6.82/7.10 tff(6393,plain,
% 6.82/7.10 (((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.10 inference(rewrite,[status(thm)],[])).
% 6.82/7.10 tff(6394,plain,
% 6.82/7.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 6.82/7.10 inference(monotonicity,[status(thm)],[6393])).
% 6.82/7.10 tff(6395,plain,
% 6.82/7.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 6.82/7.10 inference(transitivity,[status(thm)],[6394, 6392])).
% 6.82/7.10 tff(6396,plain,
% 6.82/7.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))),
% 6.82/7.10 inference(quant_inst,[status(thm)],[])).
% 6.82/7.10 tff(6397,plain,
% 6.82/7.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 6.82/7.10 inference(modus_ponens,[status(thm)],[6396, 6395])).
% 6.82/7.10 tff(6398,plain,
% 6.82/7.10 ($false),
% 6.82/7.10 inference(unit_resolution,[status(thm)],[6397, 194, 530, 2032, 2112, 719])).
% 6.82/7.10 tff(6399,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.10 tff(6400,plain,
% 6.82/7.10 (~r(elem!1, s(s(s(s(z)))))),
% 6.82/7.10 inference(unit_resolution,[status(thm)],[6399, 6391, 6327, 530])).
% 6.82/7.10 tff(6401,plain,
% 6.82/7.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.10 inference(rewrite,[status(thm)],[])).
% 6.82/7.10 tff(6402,plain,
% 6.82/7.10 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.10 inference(rewrite,[status(thm)],[])).
% 6.82/7.10 tff(6403,plain,
% 6.82/7.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1))))))),
% 6.82/7.10 inference(monotonicity,[status(thm)],[6402])).
% 6.82/7.10 tff(6404,plain,
% 6.82/7.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.10 inference(transitivity,[status(thm)],[6403, 6401])).
% 6.82/7.10 tff(6405,plain,
% 6.82/7.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 6.82/7.10 inference(quant_inst,[status(thm)],[])).
% 6.82/7.10 tff(6406,plain,
% 6.82/7.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1))))),
% 6.82/7.10 inference(modus_ponens,[status(thm)],[6405, 6404])).
% 6.82/7.10 tff(6407,plain,
% 6.82/7.10 ($false),
% 6.82/7.10 inference(unit_resolution,[status(thm)],[6406, 194, 340, 1064, 847, 1216])).
% 6.82/7.10 tff(6408,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.10 tff(6409,plain,
% 6.82/7.10 (~r(s(z), s(s(s(s(z)))))),
% 6.82/7.10 inference(unit_resolution,[status(thm)],[6408, 6171, 6163, 847])).
% 6.82/7.10 tff(6410,plain,
% 6.82/7.10 (b(s(z), s(s(s(s(z)))))),
% 6.82/7.10 inference(unit_resolution,[status(thm)],[1230, 6409])).
% 6.82/7.10 tff(6411,plain,
% 6.82/7.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.82/7.10 inference(rewrite,[status(thm)],[])).
% 6.82/7.10 tff(6412,plain,
% 6.82/7.10 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.82/7.10 inference(rewrite,[status(thm)],[])).
% 6.82/7.10 tff(6413,plain,
% 6.82/7.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 6.82/7.10 inference(monotonicity,[status(thm)],[6412])).
% 6.82/7.10 tff(6414,plain,
% 6.82/7.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.82/7.10 inference(transitivity,[status(thm)],[6413, 6411])).
% 6.82/7.10 tff(6415,plain,
% 6.82/7.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))),
% 6.82/7.10 inference(quant_inst,[status(thm)],[])).
% 6.82/7.10 tff(6416,plain,
% 6.82/7.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 6.82/7.10 inference(modus_ponens,[status(thm)],[6415, 6414])).
% 6.82/7.10 tff(6417,plain,
% 6.82/7.10 ($false),
% 6.82/7.10 inference(unit_resolution,[status(thm)],[6416, 391, 133, 644, 90, 2064, 1234])).
% 6.82/7.10 tff(6418,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.11 tff(6419,plain,
% 6.82/7.11 (~b(elem!1, s(s(s(s(z)))))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6418, 6410, 644, 133, 6317])).
% 6.82/7.11 tff(6420,plain,
% 6.82/7.11 (elem!1 = s(s(s(s(z))))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[781, 6419, 6400])).
% 6.82/7.11 tff(6421,plain,
% 6.82/7.11 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 6.82/7.11 inference(monotonicity,[status(thm)],[6420])).
% 6.82/7.11 tff(6422,plain,
% 6.82/7.11 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 6.82/7.11 inference(symmetry,[status(thm)],[6421])).
% 6.82/7.11 tff(6423,plain,
% 6.82/7.11 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, elem!1))),
% 6.82/7.11 inference(monotonicity,[status(thm)],[6422])).
% 6.82/7.11 tff(6424,plain,
% 6.82/7.11 (~b(z, elem!1)),
% 6.82/7.11 inference(modus_ponens,[status(thm)],[6326, 6423])).
% 6.82/7.11 tff(6425,plain,
% 6.82/7.11 ($false),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[133, 6424])).
% 6.82/7.11 tff(6426,plain,((s(s(elem!1)) = elem!1) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | b(elem!1, z) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(z, s(elem!1))) | (s(s(elem!1)) = s(s(z))) | (~b(s(elem!1), z)) | r(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.11 tff(6427,plain,
% 6.82/7.11 (s(s(elem!1)) = elem!1),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6426, 6157, 133, 6156, 530, 900, 380, 484, 1526, 3363, 590, 2144, 2689, 591, 1575, 6155])).
% 6.82/7.11 tff(6428,plain,
% 6.82/7.11 (s(s(s(elem!1))) = s(elem!1)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[451, 6427])).
% 6.82/7.11 tff(6429,plain,
% 6.82/7.11 (~(s(s(s(s(z)))) = elem!1)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[717, 6428])).
% 6.82/7.11 tff(6430,plain,
% 6.82/7.11 (b(elem!1, s(s(s(s(z)))))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[781, 3222, 770])).
% 6.82/7.11 tff(6431,plain,
% 6.82/7.11 (r(s(s(s(s(z)))), elem!1)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6231, 3222, 900, 380, 133, 720])).
% 6.82/7.11 tff(6432,plain,
% 6.82/7.11 (~r(s(s(s(s(z)))), z)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6087, 6431, 2144, 530])).
% 6.82/7.11 tff(6433,plain,
% 6.82/7.11 (b(s(s(s(s(z)))), z)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[87, 6432])).
% 6.82/7.11 tff(6434,plain,
% 6.82/7.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.82/7.11 inference(rewrite,[status(thm)],[])).
% 6.82/7.11 tff(6435,plain,
% 6.82/7.11 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.82/7.11 inference(rewrite,[status(thm)],[])).
% 6.82/7.11 tff(6436,plain,
% 6.82/7.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 6.82/7.11 inference(monotonicity,[status(thm)],[6435])).
% 6.82/7.11 tff(6437,plain,
% 6.82/7.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.82/7.11 inference(transitivity,[status(thm)],[6436, 6434])).
% 6.82/7.11 tff(6438,plain,
% 6.82/7.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 6.82/7.11 inference(quant_inst,[status(thm)],[])).
% 6.82/7.11 tff(6439,plain,
% 6.82/7.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 6.82/7.11 inference(modus_ponens,[status(thm)],[6438, 6437])).
% 6.82/7.11 tff(6440,plain,
% 6.82/7.11 ($false),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6439, 391, 133, 644, 6433, 6430, 590])).
% 6.82/7.11 tff(6441,plain,(r(elem!1, s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.82/7.11 tff(6442,plain,
% 6.82/7.11 (r(elem!1, s(s(s(s(z)))))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6441, 6157, 133, 590, 2144, 530, 900, 380, 6429])).
% 6.82/7.11 tff(6443,plain,
% 6.82/7.11 ($false),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6219, 194, 530, 2144, 2053, 2032])).
% 6.82/7.11 tff(6444,plain,((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.11 tff(6445,plain,
% 6.82/7.11 (~r(s(s(s(s(z)))), z)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6444, 6442, 2144, 530])).
% 6.82/7.11 tff(6446,plain,
% 6.82/7.11 (b(s(s(s(s(z)))), z)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[87, 6445])).
% 6.82/7.11 tff(6447,plain,
% 6.82/7.11 (~b(z, s(s(s(s(z)))))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6325, 6446, 1526, 380, 590])).
% 6.82/7.11 tff(6448,plain,
% 6.82/7.11 (~r(z, s(s(s(s(z)))))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6382, 6446, 530, 6442, 1526, 3363, 6156, 133, 590])).
% 6.82/7.11 tff(6449,plain,
% 6.82/7.11 ($false),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[800, 6448, 6447])).
% 6.82/7.11 tff(6450,plain,(r(s(z), elem!1) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | b(elem!1, z) | (s(s(elem!1)) = s(s(z))) | (~b(s(elem!1), z)) | r(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(s(elem!1))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.82/7.11 tff(6451,plain,
% 6.82/7.11 (r(s(z), elem!1)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6450, 6134, 530, 133, 5954, 6123, 6145, 900, 484, 2689, 6144, 6137, 6154, 150])).
% 6.82/7.11 tff(6452,plain,
% 6.82/7.11 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[287, 5682])).
% 6.82/7.11 tff(6453,plain,
% 6.82/7.11 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[1370, 6452, 6155])).
% 6.82/7.11 tff(6454,plain,
% 6.82/7.11 (~b(s(s(elem!1)), s(z))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6169, 6453, 133, 1526, 590])).
% 6.82/7.11 tff(6455,plain,
% 6.82/7.11 (r(s(s(elem!1)), s(z))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[362, 6454])).
% 6.82/7.11 tff(6456,plain,
% 6.82/7.11 (~r(s(s(elem!1)), elem!1)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[2379, 6455, 410, 1484])).
% 6.82/7.11 tff(6457,plain,
% 6.82/7.11 (b(s(s(elem!1)), elem!1)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[872, 6456, 5625])).
% 6.82/7.11 tff(6458,plain,
% 6.82/7.11 (b(s(s(s(elem!1))), s(elem!1))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[588, 279, 1575])).
% 6.82/7.11 tff(6459,plain,
% 6.82/7.11 (~b(elem!1, s(s(elem!1)))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[2248, 6458, 133, 380, 591])).
% 6.82/7.11 tff(6460,plain,
% 6.82/7.11 (~(elem!1 = s(s(elem!1)))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[1292, 5625])).
% 6.82/7.11 tff(6461,plain,
% 6.82/7.11 (r(elem!1, s(s(elem!1)))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[1307, 6460, 6459])).
% 6.82/7.11 tff(6462,plain,
% 6.82/7.11 (~r(z, s(s(elem!1)))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6189, 6455, 6461, 530])).
% 6.82/7.11 tff(6463,plain,
% 6.82/7.11 (b(z, s(s(elem!1)))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[324, 6462])).
% 6.82/7.11 tff(6464,plain,
% 6.82/7.11 ($false),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6210, 6463, 6457, 380, 1526, 590])).
% 6.82/7.11 tff(6465,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | r(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(elem!1), z)) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.11 tff(6466,plain,
% 6.82/7.11 (s(s(s(elem!1))) = s(elem!1)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6465, 6134, 6123, 5954, 530, 6124, 6451, 133, 6154, 6144, 6137])).
% 6.82/7.11 tff(6467,plain,
% 6.82/7.11 (~(s(s(s(s(z)))) = elem!1)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[717, 6466])).
% 6.82/7.11 tff(6468,plain,
% 6.82/7.11 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 6.82/7.11 inference(monotonicity,[status(thm)],[6466])).
% 6.82/7.11 tff(6469,plain,
% 6.82/7.11 (b(s(elem!1), elem!1)),
% 6.82/7.11 inference(modus_ponens,[status(thm)],[900, 6468])).
% 6.82/7.11 tff(6470,plain,
% 6.82/7.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.82/7.11 inference(rewrite,[status(thm)],[])).
% 6.82/7.11 tff(6471,plain,
% 6.82/7.11 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.82/7.11 inference(rewrite,[status(thm)],[])).
% 6.82/7.11 tff(6472,plain,
% 6.82/7.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 6.82/7.11 inference(monotonicity,[status(thm)],[6471])).
% 6.82/7.11 tff(6473,plain,
% 6.82/7.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.82/7.11 inference(transitivity,[status(thm)],[6472, 6470])).
% 6.82/7.11 tff(6474,plain,
% 6.82/7.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 6.82/7.11 inference(quant_inst,[status(thm)],[])).
% 6.82/7.11 tff(6475,plain,
% 6.82/7.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 6.82/7.11 inference(modus_ponens,[status(thm)],[6474, 6473])).
% 6.82/7.11 tff(6476,plain,
% 6.82/7.11 ($false),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6475, 391, 133, 591, 2122, 6433, 6430])).
% 6.82/7.11 tff(6477,plain,(r(elem!1, s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.82/7.11 tff(6478,plain,
% 6.82/7.11 (r(elem!1, s(s(s(s(z)))))),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6477, 6144, 133, 6469, 6145, 530, 900, 6123, 6467])).
% 6.82/7.11 tff(6479,plain,
% 6.82/7.11 (~r(s(s(s(s(z)))), z)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[6444, 6478, 6145, 530])).
% 6.82/7.11 tff(6480,plain,
% 6.82/7.11 (b(s(s(s(s(z)))), z)),
% 6.82/7.11 inference(unit_resolution,[status(thm)],[87, 6479])).
% 6.82/7.12 tff(6481,plain,
% 6.82/7.12 (~b(z, s(s(s(s(z)))))),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[6325, 6480, 6134, 6123, 5954])).
% 6.82/7.12 tff(6482,plain,
% 6.82/7.12 (s(s(elem!1)) = elem!1),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[6159, 6466])).
% 6.82/7.12 tff(6483,plain,
% 6.82/7.12 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 6.82/7.12 inference(monotonicity,[status(thm)],[6466])).
% 6.82/7.12 tff(6484,plain,
% 6.82/7.12 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.82/7.12 inference(symmetry,[status(thm)],[6483])).
% 6.82/7.12 tff(6485,plain,
% 6.82/7.12 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 6.82/7.12 inference(monotonicity,[status(thm)],[6482])).
% 6.82/7.12 tff(6486,plain,
% 6.82/7.12 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 6.82/7.12 inference(symmetry,[status(thm)],[6485])).
% 6.82/7.12 tff(6487,plain,
% 6.82/7.12 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.82/7.12 inference(transitivity,[status(thm)],[6486, 6484])).
% 6.82/7.12 tff(6488,plain,
% 6.82/7.12 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.82/7.12 inference(modus_ponens,[status(thm)],[6469, 6487])).
% 6.82/7.12 tff(6489,plain,
% 6.82/7.12 (~b(s(s(elem!1)), s(z))),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[6169, 6488, 133, 6134, 5954])).
% 6.82/7.12 tff(6490,plain,
% 6.82/7.12 (r(s(s(elem!1)), s(z))),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[362, 6489])).
% 6.82/7.12 tff(6491,plain,
% 6.82/7.12 (r(elem!1, s(z))),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[4206, 6490, 6482])).
% 6.82/7.12 tff(6492,plain,
% 6.82/7.12 (~r(z, s(s(s(s(z)))))),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[6382, 6480, 530, 6478, 6134, 3363, 6491, 133, 5954])).
% 6.82/7.12 tff(6493,plain,
% 6.82/7.12 ($false),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[800, 6492, 6481])).
% 6.82/7.12 tff(6494,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | b(elem!1, z) | (s(s(elem!1)) = s(s(z))) | (s(z) = elem!1) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.82/7.12 tff(6495,plain,
% 6.82/7.12 (b(elem!1, s(s(s(elem!1))))),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[6494, 3618, 133, 900, 484, 2680, 150, 184, 437, 1])).
% 6.82/7.12 tff(6496,plain,
% 6.82/7.12 (~r(s(s(s(elem!1))), z)),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[6121, 3618, 133, 900, 184, 150, 1])).
% 6.82/7.12 tff(6497,plain,
% 6.82/7.12 (b(s(s(s(elem!1))), z)),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[377, 6496])).
% 6.82/7.12 tff(6498,plain,
% 6.82/7.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 6.82/7.12 inference(rewrite,[status(thm)],[])).
% 6.82/7.12 tff(6499,plain,
% 6.82/7.12 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 6.82/7.12 inference(rewrite,[status(thm)],[])).
% 6.82/7.12 tff(6500,plain,
% 6.82/7.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))))),
% 6.82/7.12 inference(monotonicity,[status(thm)],[6499])).
% 6.82/7.12 tff(6501,plain,
% 6.82/7.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 6.82/7.12 inference(transitivity,[status(thm)],[6500, 6498])).
% 6.82/7.12 tff(6502,plain,
% 6.82/7.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 6.82/7.12 inference(quant_inst,[status(thm)],[])).
% 6.82/7.12 tff(6503,plain,
% 6.82/7.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))),
% 6.82/7.12 inference(modus_ponens,[status(thm)],[6502, 6501])).
% 6.82/7.12 tff(6504,plain,
% 6.82/7.12 ($false),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[6503, 391, 133, 900, 6497, 6495])).
% 6.82/7.12 tff(6505,plain,(b(elem!1, z) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(z) = elem!1) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 6.82/7.12 tff(6506,plain,
% 6.82/7.12 (b(elem!1, z)),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[6505, 5933, 149, 150, 59, 167, 148, 2])).
% 6.82/7.12 tff(6507,plain,
% 6.82/7.12 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 6.82/7.12 inference(modus_ponens,[status(thm)],[3363, 3930])).
% 6.82/7.12 tff(6508,plain,
% 6.82/7.12 (~b(s(s(s(elem!1))), z)),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[5769, 391, 133, 665, 900])).
% 6.82/7.12 tff(6509,plain,
% 6.82/7.12 (r(s(s(s(elem!1))), z)),
% 6.82/7.12 inference(unit_resolution,[status(thm)],[377, 6508])).
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% 6.82/7.12 tff(6513,plain,
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% 6.82/7.12 tff(6524,plain,
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% 6.82/7.12 inference(unit_resolution,[status(thm)],[287, 6523])).
% 6.82/7.12 tff(6525,plain,
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% 6.82/7.12 inference(unit_resolution,[status(thm)],[3924, 6524, 10, 91])).
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% 6.82/7.12 inference(unit_resolution,[status(thm)],[4944, 6525, 665, 133])).
% 6.82/7.12 tff(6527,plain,
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% 6.82/7.12 inference(unit_resolution,[status(thm)],[872, 6526, 3290])).
% 6.82/7.12 tff(6528,plain,
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% 6.82/7.12 tff(6529,plain,
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% 6.82/7.12 tff(6530,plain,
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% 6.82/7.12 tff(6532,plain,
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% 6.82/7.12 inference(modus_ponens,[status(thm)],[6522, 2670])).
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% 6.82/7.12 tff(6536,plain,
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% 6.82/7.12 tff(6537,plain,
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% 6.82/7.12 inference(modus_ponens,[status(thm)],[592, 6536])).
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% 6.82/7.12 (b(z, s(s(s(s(s(s(z))))))) <=> b(z, s(s(elem!1)))),
% 6.82/7.12 inference(monotonicity,[status(thm)],[2731])).
% 6.82/7.12 tff(6539,plain,
% 6.82/7.12 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(s(z)))))))),
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% 6.82/7.12 tff(6540,plain,
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% 6.82/7.12 inference(modus_ponens,[status(thm)],[3927, 6539])).
% 6.82/7.12 tff(6541,plain,
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% 6.82/7.12 inference(symmetry,[status(thm)],[6541])).
% 6.82/7.12 tff(6543,plain,
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% 6.82/7.12 inference(monotonicity,[status(thm)],[6543])).
% 6.82/7.12 tff(6545,plain,
% 6.82/7.12 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 6.82/7.12 inference(monotonicity,[status(thm)],[6534])).
% 6.82/7.12 tff(6546,plain,
% 6.82/7.12 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 6.82/7.12 inference(symmetry,[status(thm)],[6545])).
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% 6.82/7.12 inference(monotonicity,[status(thm)],[6546])).
% 6.92/7.12 tff(6548,plain,
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% 6.92/7.12 tff(6549,plain,
% 6.92/7.12 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 6.92/7.12 inference(monotonicity,[status(thm)],[6534])).
% 6.92/7.12 tff(6550,plain,
% 6.92/7.12 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 6.92/7.12 inference(symmetry,[status(thm)],[6549])).
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% 6.92/7.12 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 6.92/7.12 inference(monotonicity,[status(thm)],[6550])).
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% 6.92/7.12 inference(monotonicity,[status(thm)],[766])).
% 6.92/7.12 tff(6553,plain,
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% 6.92/7.12 tff(6554,plain,
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% 6.92/7.12 inference(unit_resolution,[status(thm)],[5271, 391, 133, 665, 592, 2122])).
% 6.92/7.12 tff(6555,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.92/7.12 tff(6556,plain,
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% 6.92/7.12 inference(unit_resolution,[status(thm)],[6555, 592, 133, 665])).
% 6.92/7.12 tff(6557,plain,
% 6.92/7.12 (~b(s(elem!1), s(s(s(s(z)))))),
% 6.92/7.12 inference(modus_ponens,[status(thm)],[6556, 6553])).
% 6.92/7.12 tff(6558,plain,
% 6.92/7.12 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 6.92/7.12 inference(modus_ponens,[status(thm)],[6557, 6551])).
% 6.92/7.12 tff(6559,plain,
% 6.92/7.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
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% 6.92/7.12 tff(6560,plain,
% 6.92/7.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 6.92/7.12 inference(quant_inst,[status(thm)],[])).
% 6.92/7.13 tff(6561,plain,
% 6.92/7.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 6.92/7.13 inference(modus_ponens,[status(thm)],[6560, 6559])).
% 6.92/7.13 tff(6562,plain,
% 6.92/7.13 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 6.92/7.13 inference(unit_resolution,[status(thm)],[6561, 42])).
% 6.92/7.13 tff(6563,plain,
% 6.92/7.13 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 6.92/7.13 inference(unit_resolution,[status(thm)],[6562, 6558, 6548])).
% 6.92/7.13 tff(6564,plain,
% 6.92/7.13 (~b(s(s(elem!1)), elem!1)),
% 6.92/7.13 inference(unit_resolution,[status(thm)],[4944, 3927, 665, 133])).
% 6.92/7.13 tff(6565,plain,
% 6.92/7.13 (r(s(s(elem!1)), elem!1)),
% 6.92/7.13 inference(unit_resolution,[status(thm)],[872, 6564, 3290])).
% 6.92/7.13 tff(6566,plain,
% 6.92/7.13 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.92/7.13 inference(modus_ponens,[status(thm)],[6565, 3288])).
% 6.92/7.13 tff(6567,plain,
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% 6.92/7.13 inference(modus_ponens,[status(thm)],[6566, 3287])).
% 6.92/7.13 tff(6568,plain,
% 6.92/7.13 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 6.92/7.13 inference(modus_ponens,[status(thm)],[6567, 2740])).
% 6.92/7.13 tff(6569,plain,
% 6.92/7.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 6.92/7.13 inference(rewrite,[status(thm)],[])).
% 6.92/7.13 tff(6570,plain,
% 6.92/7.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 6.92/7.13 inference(quant_inst,[status(thm)],[])).
% 6.92/7.13 tff(6571,plain,
% 6.92/7.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 6.92/7.13 inference(modus_ponens,[status(thm)],[6570, 6569])).
% 6.92/7.13 tff(6572,plain,
% 6.92/7.13 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 6.92/7.13 inference(unit_resolution,[status(thm)],[6571, 194, 723, 6568, 6563])).
% 6.92/7.13 tff(6573,plain,
% 6.92/7.13 (~r(s(s(elem!1)), s(elem!1))),
% 6.92/7.13 inference(modus_ponens,[status(thm)],[6572, 6544])).
% 6.92/7.13 tff(6574,plain,
% 6.92/7.13 (b(s(s(elem!1)), s(elem!1))),
% 6.92/7.13 inference(unit_resolution,[status(thm)],[1135, 6573, 6523])).
% 6.92/7.13 tff(6575,plain,
% 6.92/7.13 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 6.92/7.13 inference(modus_ponens,[status(thm)],[6574, 6542])).
% 6.92/7.13 tff(6576,plain,
% 6.92/7.13 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(elem!1)))),
% 6.92/7.13 inference(monotonicity,[status(thm)],[6534, 2731])).
% 6.92/7.13 tff(6577,plain,
% 6.92/7.13 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(elem!1))),
% 6.92/7.13 inference(transitivity,[status(thm)],[6576, 1097])).
% 6.92/7.13 tff(6578,plain,
% 6.92/7.13 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))),
% 6.92/7.13 inference(symmetry,[status(thm)],[6577])).
% 6.92/7.13 tff(6579,plain,
% 6.92/7.13 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))))),
% 6.92/7.13 inference(monotonicity,[status(thm)],[6578])).
% 6.92/7.13 tff(6580,plain,
% 6.92/7.13 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))),
% 6.92/7.13 inference(modus_ponens,[status(thm)],[6523, 6579])).
% 6.92/7.13 tff(6581,plain,
% 6.92/7.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 6.92/7.13 inference(rewrite,[status(thm)],[])).
% 6.92/7.13 tff(6582,plain,
% 6.92/7.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 6.92/7.13 inference(quant_inst,[status(thm)],[])).
% 6.92/7.13 tff(6583,plain,
% 6.92/7.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 6.92/7.13 inference(modus_ponens,[status(thm)],[6582, 6581])).
% 6.92/7.13 tff(6584,plain,
% 6.92/7.13 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 6.92/7.13 inference(unit_resolution,[status(thm)],[6583, 194, 723, 6568, 6563])).
% 6.92/7.13 tff(6585,plain,
% 6.92/7.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 6.92/7.13 inference(rewrite,[status(thm)],[])).
% 6.92/7.13 tff(6586,plain,
% 6.92/7.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 6.92/7.13 inference(quant_inst,[status(thm)],[])).
% 6.92/7.13 tff(6587,plain,
% 6.92/7.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 6.92/7.13 inference(modus_ponens,[status(thm)],[6586, 6585])).
% 6.92/7.13 tff(6588,plain,
% 6.92/7.13 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 6.92/7.13 inference(unit_resolution,[status(thm)],[6587, 42, 6584])).
% 6.92/7.13 tff(6589,plain,
% 6.92/7.13 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 6.92/7.13 inference(unit_resolution,[status(thm)],[6588, 6580])).
% 6.92/7.13 tff(6590,plain,
% 6.92/7.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 6.92/7.13 inference(rewrite,[status(thm)],[])).
% 6.92/7.13 tff(6591,plain,
% 6.92/7.13 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 6.92/7.13 inference(rewrite,[status(thm)],[])).
% 6.92/7.13 tff(6592,plain,
% 6.92/7.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 6.92/7.13 inference(monotonicity,[status(thm)],[6591])).
% 6.92/7.13 tff(6593,plain,
% 6.92/7.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 6.92/7.14 inference(transitivity,[status(thm)],[6592, 6590])).
% 6.92/7.14 tff(6594,plain,
% 6.92/7.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 6.92/7.14 inference(quant_inst,[status(thm)],[])).
% 6.92/7.14 tff(6595,plain,
% 6.92/7.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[6594, 6593])).
% 6.92/7.14 tff(6596,plain,
% 6.92/7.14 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[6595, 391, 6589, 6575])).
% 6.92/7.14 tff(6597,plain,
% 6.92/7.14 ($false),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[6596, 6540, 6537])).
% 6.92/7.14 tff(6598,plain,((~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 6.92/7.14 tff(6599,plain,
% 6.92/7.14 (~b(z, s(elem!1))),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[6598, 6525, 766, 6533, 6532, 133, 665])).
% 6.92/7.14 tff(6600,plain,
% 6.92/7.14 (r(z, s(elem!1))),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[566, 6599])).
% 6.92/7.14 tff(6601,plain,
% 6.92/7.14 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[6527, 3288])).
% 6.92/7.14 tff(6602,plain,
% 6.92/7.14 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[6601, 3287])).
% 6.92/7.14 tff(6603,plain,
% 6.92/7.14 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[6602, 2740])).
% 6.92/7.14 tff(6604,plain,
% 6.92/7.14 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(z)))))),
% 6.92/7.14 inference(monotonicity,[status(thm)],[766])).
% 6.92/7.14 tff(6605,plain,
% 6.92/7.14 (r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.92/7.14 inference(monotonicity,[status(thm)],[2731])).
% 6.92/7.14 tff(6606,plain,
% 6.92/7.14 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 6.92/7.14 inference(symmetry,[status(thm)],[6605])).
% 6.92/7.14 tff(6607,plain,
% 6.92/7.14 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[4762, 381, 1526, 379])).
% 6.92/7.14 tff(6608,plain,
% 6.92/7.14 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[1370, 6607, 6524])).
% 6.92/7.14 tff(6609,plain,
% 6.92/7.14 (r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[6608, 6606])).
% 6.92/7.14 tff(6610,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 6.92/7.14 tff(6611,plain,
% 6.92/7.14 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.92/7.14 inference(monotonicity,[status(thm)],[2731])).
% 6.92/7.14 tff(6612,plain,
% 6.92/7.14 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 6.92/7.14 inference(symmetry,[status(thm)],[6611])).
% 6.92/7.14 tff(6613,plain,
% 6.92/7.14 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[281, 3271])).
% 6.92/7.14 tff(6614,plain,
% 6.92/7.14 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.92/7.14 inference(monotonicity,[status(thm)],[2731])).
% 6.92/7.14 tff(6615,plain,
% 6.92/7.14 ((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 6.92/7.14 inference(monotonicity,[status(thm)],[6614])).
% 6.92/7.14 tff(6616,plain,
% 6.92/7.14 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 6.92/7.14 inference(monotonicity,[status(thm)],[2731])).
% 6.92/7.14 tff(6617,plain,
% 6.92/7.14 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 6.92/7.14 inference(symmetry,[status(thm)],[6616])).
% 6.92/7.14 tff(6618,plain,
% 6.92/7.14 (b(s(s(s(s(s(s(z)))))), s(z))),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[381, 6617])).
% 6.92/7.14 tff(6619,plain,
% 6.92/7.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 6.92/7.14 inference(rewrite,[status(thm)],[])).
% 6.92/7.14 tff(6620,plain,
% 6.92/7.14 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 6.92/7.14 inference(rewrite,[status(thm)],[])).
% 6.92/7.14 tff(6621,plain,
% 6.92/7.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 6.92/7.14 inference(monotonicity,[status(thm)],[6620])).
% 6.92/7.14 tff(6622,plain,
% 6.92/7.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 6.92/7.14 inference(transitivity,[status(thm)],[6621, 6619])).
% 6.92/7.14 tff(6623,plain,
% 6.92/7.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 6.92/7.14 inference(quant_inst,[status(thm)],[])).
% 6.92/7.14 tff(6624,plain,
% 6.92/7.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[6623, 6622])).
% 6.92/7.14 tff(6625,plain,
% 6.92/7.14 ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[6624, 391, 379, 1526])).
% 6.92/7.14 tff(6626,plain,
% 6.92/7.14 (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[6625, 6618])).
% 6.92/7.14 tff(6627,plain,
% 6.92/7.14 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[6626, 6615])).
% 6.92/7.14 tff(6628,plain,
% 6.92/7.14 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[1356, 6627, 6613])).
% 6.92/7.14 tff(6629,plain,
% 6.92/7.14 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[6628, 6612])).
% 6.92/7.14 tff(6630,plain,
% 6.92/7.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 6.92/7.14 inference(rewrite,[status(thm)],[])).
% 6.92/7.14 tff(6631,plain,
% 6.92/7.14 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 6.92/7.14 inference(rewrite,[status(thm)],[])).
% 6.92/7.14 tff(6632,plain,
% 6.92/7.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 6.92/7.14 inference(monotonicity,[status(thm)],[6631])).
% 6.92/7.14 tff(6633,plain,
% 6.92/7.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 6.92/7.14 inference(transitivity,[status(thm)],[6632, 6630])).
% 6.92/7.14 tff(6634,plain,
% 6.92/7.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 6.92/7.14 inference(quant_inst,[status(thm)],[])).
% 6.92/7.14 tff(6635,plain,
% 6.92/7.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[6634, 6633])).
% 6.92/7.14 tff(6636,plain,
% 6.92/7.14 (~r(s(s(s(s(s(s(z)))))), z)),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[6635, 194, 174, 184, 6629])).
% 6.92/7.14 tff(6637,plain,
% 6.92/7.14 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 6.92/7.14 inference(quant_inst,[status(thm)],[])).
% 6.92/7.14 tff(6638,plain,
% 6.92/7.14 (~(s(s(s(s(s(s(z)))))) = z)),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[6637, 21])).
% 6.92/7.14 tff(6639,plain,
% 6.92/7.14 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 6.92/7.14 inference(rewrite,[status(thm)],[])).
% 6.92/7.14 tff(6640,plain,
% 6.92/7.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 6.92/7.14 inference(quant_inst,[status(thm)],[])).
% 6.92/7.14 tff(6641,plain,
% 6.92/7.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 6.92/7.14 inference(modus_ponens,[status(thm)],[6640, 6639])).
% 6.92/7.14 tff(6642,plain,
% 6.92/7.14 (b(s(s(s(s(s(s(z)))))), z)),
% 6.92/7.14 inference(unit_resolution,[status(thm)],[6641, 42, 6638, 6636])).
% 6.92/7.14 tff(6643,plain,
% 6.92/7.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 6.92/7.14 inference(rewrite,[status(thm)],[])).
% 6.92/7.14 tff(6644,plain,
% 6.92/7.14 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 6.92/7.15 inference(rewrite,[status(thm)],[])).
% 6.92/7.15 tff(6645,plain,
% 6.92/7.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 6.92/7.15 inference(monotonicity,[status(thm)],[6644])).
% 6.92/7.15 tff(6646,plain,
% 6.92/7.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 6.92/7.15 inference(transitivity,[status(thm)],[6645, 6643])).
% 6.92/7.15 tff(6647,plain,
% 6.92/7.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 6.92/7.15 inference(quant_inst,[status(thm)],[])).
% 6.92/7.15 tff(6648,plain,
% 6.92/7.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 6.92/7.15 inference(modus_ponens,[status(thm)],[6647, 6646])).
% 6.92/7.15 tff(6649,plain,
% 6.92/7.15 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 6.92/7.15 inference(unit_resolution,[status(thm)],[6648, 391, 90, 1686, 6642])).
% 6.92/7.15 tff(6650,plain,
% 6.92/7.15 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 6.92/7.15 inference(rewrite,[status(thm)],[])).
% 6.92/7.15 tff(6651,plain,
% 6.92/7.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 6.92/7.15 inference(quant_inst,[status(thm)],[])).
% 6.92/7.15 tff(6652,plain,
% 6.92/7.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 6.92/7.15 inference(modus_ponens,[status(thm)],[6651, 6650])).
% 6.92/7.15 tff(6653,plain,
% 6.92/7.15 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 6.92/7.15 inference(unit_resolution,[status(thm)],[6652, 42, 4995, 6649])).
% 6.92/7.15 tff(6654,plain,
% 6.92/7.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 6.92/7.15 inference(rewrite,[status(thm)],[])).
% 6.92/7.15 tff(6655,plain,
% 6.92/7.15 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 6.92/7.15 inference(rewrite,[status(thm)],[])).
% 6.92/7.15 tff(6656,plain,
% 6.92/7.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 6.92/7.15 inference(monotonicity,[status(thm)],[6655])).
% 6.92/7.15 tff(6657,plain,
% 6.92/7.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 6.92/7.15 inference(transitivity,[status(thm)],[6656, 6654])).
% 6.92/7.15 tff(6658,plain,
% 6.92/7.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.92/7.15 inference(quant_inst,[status(thm)],[])).
% 6.92/7.15 tff(6659,plain,
% 6.92/7.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 6.92/7.15 inference(modus_ponens,[status(thm)],[6658, 6657])).
% 6.92/7.15 tff(6660,plain,
% 6.92/7.15 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.92/7.15 inference(unit_resolution,[status(thm)],[6659, 194, 6653, 6610, 6609])).
% 6.92/7.15 tff(6661,plain,
% 6.92/7.15 (~r(elem!1, s(s(s(elem!1))))),
% 6.92/7.15 inference(modus_ponens,[status(thm)],[6660, 3277])).
% 6.92/7.15 tff(6662,plain,
% 6.92/7.15 (b(elem!1, s(s(s(elem!1))))),
% 6.92/7.15 inference(unit_resolution,[status(thm)],[424, 6661, 1])).
% 6.92/7.15 tff(6663,plain,
% 6.92/7.15 (~b(s(z), elem!1)),
% 6.92/7.15 inference(unit_resolution,[status(thm)],[4026, 6662, 379, 1526])).
% 6.92/7.15 tff(6664,plain,
% 6.92/7.15 (r(s(z), elem!1)),
% 6.92/7.15 inference(unit_resolution,[status(thm)],[632, 6663, 150])).
% 6.92/7.15 tff(6665,plain,
% 6.92/7.15 (r(s(z), s(s(s(s(z)))))),
% 6.92/7.15 inference(modus_ponens,[status(thm)],[6664, 6604])).
% 6.92/7.15 tff(6666,plain,
% 6.92/7.15 (r(s(s(s(s(z)))), s(z))),
% 6.92/7.15 inference(modus_ponens,[status(thm)],[847, 2670])).
% 6.92/7.15 tff(6667,assumption,(b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 6.92/7.15 tff(6668,plain,
% 6.92/7.15 (r(s(s(z)), elem!1)),
% 6.92/7.15 inference(unit_resolution,[status(thm)],[5152, 1749, 688])).
% 6.92/7.15 tff(6669,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 6.92/7.15 tff(6670,plain,
% 6.92/7.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 6.92/7.15 inference(rewrite,[status(thm)],[])).
% 6.92/7.15 tff(6671,plain,
% 6.92/7.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 6.92/7.15 inference(quant_inst,[status(thm)],[])).
% 6.92/7.15 tff(6672,plain,
% 6.92/7.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 6.92/7.15 inference(modus_ponens,[status(thm)],[6671, 6670])).
% 6.92/7.16 tff(6673,plain,
% 6.92/7.16 ($false),
% 6.92/7.16 inference(unit_resolution,[status(thm)],[6672, 194, 1484, 847, 6669, 2405])).
% 6.92/7.16 tff(6674,plain,((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.92/7.16 tff(6675,plain,
% 6.92/7.16 (~r(s(s(z)), s(z))),
% 6.92/7.16 inference(unit_resolution,[status(thm)],[6674, 6668, 1484, 847])).
% 6.92/7.16 tff(6676,plain,
% 6.92/7.16 (b(s(s(z)), s(z))),
% 6.92/7.16 inference(unit_resolution,[status(thm)],[3778, 6675])).
% 6.92/7.16 tff(6677,plain,
% 6.92/7.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 6.92/7.16 inference(rewrite,[status(thm)],[])).
% 6.92/7.16 tff(6678,plain,
% 6.92/7.16 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 6.92/7.16 inference(rewrite,[status(thm)],[])).
% 6.92/7.16 tff(6679,plain,
% 6.92/7.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 6.92/7.16 inference(monotonicity,[status(thm)],[6678])).
% 6.92/7.16 tff(6680,plain,
% 6.92/7.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 6.92/7.16 inference(transitivity,[status(thm)],[6679, 6677])).
% 6.92/7.16 tff(6681,plain,
% 6.92/7.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 6.92/7.16 inference(quant_inst,[status(thm)],[])).
% 6.92/7.16 tff(6682,plain,
% 6.92/7.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 6.92/7.16 inference(modus_ponens,[status(thm)],[6681, 6680])).
% 6.92/7.16 tff(6683,plain,
% 6.92/7.16 ($false),
% 6.92/7.16 inference(unit_resolution,[status(thm)],[6682, 194, 1749, 1216, 1747, 3297])).
% 6.92/7.16 tff(6684,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 6.92/7.16 tff(6685,plain,
% 6.92/7.16 (~r(s(z), s(s(z)))),
% 6.92/7.16 inference(unit_resolution,[status(thm)],[6684, 1749, 3297, 1216])).
% 6.92/7.16 tff(6686,plain,
% 6.92/7.16 (b(s(z), s(s(z)))),
% 6.92/7.16 inference(unit_resolution,[status(thm)],[1788, 6685])).
% 6.92/7.16 tff(6687,plain,
% 6.92/7.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 6.92/7.16 inference(rewrite,[status(thm)],[])).
% 6.92/7.16 tff(6688,plain,
% 6.92/7.16 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 6.92/7.16 inference(rewrite,[status(thm)],[])).
% 6.92/7.16 tff(6689,plain,
% 6.92/7.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 6.92/7.16 inference(monotonicity,[status(thm)],[6688])).
% 6.92/7.16 tff(6690,plain,
% 6.92/7.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 6.92/7.16 inference(transitivity,[status(thm)],[6689, 6687])).
% 6.92/7.16 tff(6691,plain,
% 6.92/7.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 6.92/7.16 inference(quant_inst,[status(thm)],[])).
% 6.92/7.16 tff(6692,plain,
% 6.92/7.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 6.92/7.16 inference(modus_ponens,[status(thm)],[6691, 6690])).
% 6.92/7.16 tff(6693,plain,
% 6.92/7.16 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 6.92/7.16 inference(unit_resolution,[status(thm)],[6692, 391, 6686, 6676, 6667])).
% 6.92/7.16 tff(6694,plain,
% 6.92/7.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 6.92/7.16 inference(rewrite,[status(thm)],[])).
% 6.92/7.16 tff(6695,plain,
% 6.92/7.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 6.92/7.16 inference(quant_inst,[status(thm)],[])).
% 6.92/7.16 tff(6696,plain,
% 6.92/7.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 6.92/7.16 inference(modus_ponens,[status(thm)],[6695, 6694])).
% 6.92/7.16 tff(6697,plain,
% 6.92/7.16 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 6.92/7.16 inference(unit_resolution,[status(thm)],[6696, 194, 1749, 723, 6610])).
% 6.92/7.16 tff(6698,plain,
% 6.92/7.16 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 6.92/7.16 inference(rewrite,[status(thm)],[])).
% 6.92/7.16 tff(6699,plain,
% 6.92/7.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 6.92/7.16 inference(quant_inst,[status(thm)],[])).
% 6.92/7.17 tff(6700,plain,
% 6.92/7.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 6.92/7.17 inference(modus_ponens,[status(thm)],[6699, 6698])).
% 6.92/7.17 tff(6701,plain,
% 6.92/7.17 ($false),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 6697, 6693])).
% 6.92/7.17 tff(6702,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.92/7.17 tff(6703,plain,
% 6.92/7.17 (~r(s(s(z)), s(s(s(s(z)))))),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[6702, 6618, 6666, 6610, 6664, 847, 6653, 6665, 3270])).
% 6.92/7.17 tff(6704,plain,
% 6.92/7.17 (b(s(s(z)), s(s(s(s(z)))))),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[3652, 6703])).
% 6.92/7.17 tff(6705,plain,
% 6.92/7.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 6.92/7.17 inference(rewrite,[status(thm)],[])).
% 6.92/7.17 tff(6706,plain,
% 6.92/7.17 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 6.92/7.17 inference(rewrite,[status(thm)],[])).
% 6.92/7.17 tff(6707,plain,
% 6.92/7.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 6.92/7.17 inference(monotonicity,[status(thm)],[6706])).
% 6.92/7.17 tff(6708,plain,
% 6.92/7.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 6.92/7.17 inference(transitivity,[status(thm)],[6707, 6705])).
% 6.92/7.17 tff(6709,plain,
% 6.92/7.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.92/7.17 inference(quant_inst,[status(thm)],[])).
% 6.92/7.17 tff(6710,plain,
% 6.92/7.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 6.92/7.17 inference(modus_ponens,[status(thm)],[6709, 6708])).
% 6.92/7.17 tff(6711,plain,
% 6.92/7.17 (~b(s(s(z)), s(s(s(elem!1))))),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[6710, 391, 6704, 90, 1669, 6540])).
% 6.92/7.17 tff(6712,plain,
% 6.92/7.17 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(elem!1))),
% 6.92/7.17 inference(monotonicity,[status(thm)],[6534])).
% 6.92/7.17 tff(6713,plain,
% 6.92/7.17 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(z))))))),
% 6.92/7.17 inference(symmetry,[status(thm)],[6712])).
% 6.92/7.17 tff(6714,plain,
% 6.92/7.17 (r(z, s(s(s(s(s(z))))))),
% 6.92/7.17 inference(modus_ponens,[status(thm)],[2144, 6713])).
% 6.92/7.17 tff(6715,plain,
% 6.92/7.17 (~b(s(s(z)), z)),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[4472, 6704, 90, 1686])).
% 6.92/7.17 tff(6716,plain,
% 6.92/7.17 (r(s(s(z)), z)),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[1211, 6715])).
% 6.92/7.17 tff(6717,plain,
% 6.92/7.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))),
% 6.92/7.17 inference(rewrite,[status(thm)],[])).
% 6.92/7.17 tff(6718,plain,
% 6.92/7.17 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))),
% 6.92/7.17 inference(rewrite,[status(thm)],[])).
% 6.92/7.17 tff(6719,plain,
% 6.92/7.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 6.92/7.17 inference(monotonicity,[status(thm)],[6718])).
% 6.92/7.17 tff(6720,plain,
% 6.92/7.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))))),
% 6.92/7.17 inference(transitivity,[status(thm)],[6719, 6717])).
% 6.92/7.17 tff(6721,plain,
% 6.92/7.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 6.92/7.17 inference(quant_inst,[status(thm)],[])).
% 6.92/7.17 tff(6722,plain,
% 6.92/7.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z)))))))),
% 6.92/7.17 inference(modus_ponens,[status(thm)],[6721, 6720])).
% 6.92/7.17 tff(6723,plain,
% 6.92/7.17 (~r(s(s(z)), s(s(s(elem!1))))),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[6722, 194, 174, 6716, 6714])).
% 6.92/7.17 tff(6724,plain,
% 6.92/7.17 ($false),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 6723, 6711])).
% 6.92/7.17 tff(6725,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, s(elem!1))) | (~(elem!1 = s(s(s(s(z)))))) | (s(z) = elem!1) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.92/7.17 tff(6726,plain,
% 6.92/7.17 (~b(s(s(elem!1)), s(z))),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[6725, 6514, 6511, 6509, 6516, 6603, 6522, 6600, 766, 150, 6520, 6518, 1, 6525, 59])).
% 6.92/7.17 tff(6727,plain,
% 6.92/7.17 (r(s(s(elem!1)), s(z))),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[362, 6726])).
% 6.92/7.17 tff(6728,plain,
% 6.92/7.17 (~r(s(z), elem!1)),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[1899, 6727, 6527, 6522])).
% 6.92/7.17 tff(6729,plain,
% 6.92/7.17 (b(s(z), elem!1)),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[632, 6728, 150])).
% 6.92/7.17 tff(6730,plain,
% 6.92/7.17 (b(s(z), s(s(s(s(z)))))),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[6252, 6729, 3270])).
% 6.92/7.17 tff(6731,plain,
% 6.92/7.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.92/7.17 inference(rewrite,[status(thm)],[])).
% 6.92/7.17 tff(6732,plain,
% 6.92/7.17 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.92/7.17 inference(rewrite,[status(thm)],[])).
% 6.92/7.17 tff(6733,plain,
% 6.92/7.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 6.92/7.17 inference(monotonicity,[status(thm)],[6732])).
% 6.92/7.17 tff(6734,plain,
% 6.92/7.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.92/7.17 inference(transitivity,[status(thm)],[6733, 6731])).
% 6.92/7.17 tff(6735,plain,
% 6.92/7.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.92/7.17 inference(quant_inst,[status(thm)],[])).
% 6.92/7.17 tff(6736,plain,
% 6.92/7.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 6.92/7.17 inference(modus_ponens,[status(thm)],[6735, 6734])).
% 6.92/7.17 tff(6737,plain,
% 6.92/7.17 ($false),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[6736, 391, 6520, 6511, 6730, 6516, 6514])).
% 6.92/7.17 tff(6738,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(z) = elem!1) | (elem!1 = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | b(z, s(s(s(elem!1)))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 6.92/7.17 tff(6739,plain,
% 6.92/7.17 (~(elem!1 = s(s(s(s(z)))))),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[6738, 91, 1, 133, 665, 900, 10, 150])).
% 6.92/7.17 tff(6740,plain,
% 6.92/7.17 (~(s(s(s(s(z)))) = elem!1)),
% 6.92/7.17 inference(modus_ponens,[status(thm)],[6739, 3353])).
% 6.92/7.17 tff(6741,plain,
% 6.92/7.17 (r(s(s(s(s(z)))), elem!1)),
% 6.92/7.17 inference(unit_resolution,[status(thm)],[762, 6740, 6512])).
% 6.92/7.17 tff(6742,plain,
% 6.92/7.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.92/7.18 inference(rewrite,[status(thm)],[])).
% 6.92/7.18 tff(6743,plain,
% 6.92/7.18 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.92/7.18 inference(rewrite,[status(thm)],[])).
% 6.92/7.18 tff(6744,plain,
% 6.92/7.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 6.92/7.18 inference(monotonicity,[status(thm)],[6743])).
% 6.92/7.18 tff(6745,plain,
% 6.92/7.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.92/7.18 inference(transitivity,[status(thm)],[6744, 6742])).
% 6.92/7.18 tff(6746,plain,
% 6.92/7.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.92/7.18 inference(quant_inst,[status(thm)],[])).
% 6.92/7.18 tff(6747,plain,
% 6.92/7.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 6.92/7.18 inference(modus_ponens,[status(thm)],[6746, 6745])).
% 6.92/7.18 tff(6748,plain,
% 6.92/7.18 (~b(elem!1, s(s(s(s(z)))))),
% 6.92/7.18 inference(unit_resolution,[status(thm)],[6747, 391, 133, 665, 6511])).
% 6.92/7.18 tff(6749,plain,
% 6.92/7.18 (r(elem!1, s(s(s(s(z)))))),
% 6.92/7.18 inference(unit_resolution,[status(thm)],[781, 6739, 6748])).
% 6.92/7.18 tff(6750,plain,
% 6.92/7.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.92/7.18 inference(rewrite,[status(thm)],[])).
% 6.92/7.18 tff(6751,plain,
% 6.92/7.18 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.92/7.18 inference(rewrite,[status(thm)],[])).
% 6.92/7.18 tff(6752,plain,
% 6.92/7.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 6.92/7.18 inference(monotonicity,[status(thm)],[6751])).
% 6.92/7.18 tff(6753,plain,
% 6.92/7.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.92/7.18 inference(transitivity,[status(thm)],[6752, 6750])).
% 6.92/7.18 tff(6754,plain,
% 6.92/7.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 6.92/7.18 inference(quant_inst,[status(thm)],[])).
% 6.92/7.18 tff(6755,plain,
% 6.92/7.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 6.92/7.18 inference(modus_ponens,[status(thm)],[6754, 6753])).
% 6.92/7.18 tff(6756,plain,
% 6.92/7.18 ($false),
% 6.92/7.18 inference(unit_resolution,[status(thm)],[6755, 391, 133, 665, 900, 644, 379])).
% 6.92/7.18 tff(6757,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.92/7.18 tff(6758,plain,
% 6.92/7.18 (~b(s(z), elem!1)),
% 6.92/7.18 inference(unit_resolution,[status(thm)],[6757, 6520, 665, 900, 133])).
% 6.92/7.18 tff(6759,plain,
% 6.92/7.18 (r(s(z), elem!1)),
% 6.92/7.18 inference(unit_resolution,[status(thm)],[632, 6758, 150])).
% 6.92/7.18 tff(6760,plain,
% 6.92/7.18 (~r(s(s(s(s(z)))), s(z))),
% 6.92/7.18 inference(unit_resolution,[status(thm)],[2026, 194, 6759, 6749, 6741])).
% 6.92/7.18 tff(6761,plain,
% 6.92/7.18 (b(s(s(s(s(z)))), s(z))),
% 6.92/7.18 inference(unit_resolution,[status(thm)],[749, 6760])).
% 6.92/7.18 tff(6762,plain,
% 6.92/7.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.92/7.18 inference(rewrite,[status(thm)],[])).
% 6.92/7.18 tff(6763,plain,
% 6.92/7.18 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.92/7.18 inference(rewrite,[status(thm)],[])).
% 6.92/7.18 tff(6764,plain,
% 6.92/7.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 6.92/7.18 inference(monotonicity,[status(thm)],[6763])).
% 6.92/7.18 tff(6765,plain,
% 6.92/7.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.92/7.18 inference(transitivity,[status(thm)],[6764, 6762])).
% 6.92/7.18 tff(6766,plain,
% 6.92/7.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.92/7.19 inference(quant_inst,[status(thm)],[])).
% 6.92/7.19 tff(6767,plain,
% 6.92/7.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 6.92/7.19 inference(modus_ponens,[status(thm)],[6766, 6765])).
% 6.92/7.19 tff(6768,plain,
% 6.92/7.19 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[6767, 391, 900, 6520, 6518, 6761])).
% 6.92/7.19 tff(6769,plain,
% 6.92/7.19 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[4313, 42, 6768])).
% 6.92/7.19 tff(6770,plain,
% 6.92/7.19 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[6769, 6507])).
% 6.92/7.19 tff(6771,plain,
% 6.92/7.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.92/7.19 inference(rewrite,[status(thm)],[])).
% 6.92/7.19 tff(6772,plain,
% 6.92/7.19 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.92/7.19 inference(rewrite,[status(thm)],[])).
% 6.92/7.19 tff(6773,plain,
% 6.92/7.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6772])).
% 6.92/7.19 tff(6774,plain,
% 6.92/7.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.92/7.19 inference(transitivity,[status(thm)],[6773, 6771])).
% 6.92/7.19 tff(6775,plain,
% 6.92/7.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 6.92/7.19 inference(quant_inst,[status(thm)],[])).
% 6.92/7.19 tff(6776,plain,
% 6.92/7.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 6.92/7.19 inference(modus_ponens,[status(thm)],[6775, 6774])).
% 6.92/7.19 tff(6777,plain,
% 6.92/7.19 (~r(elem!1, s(s(s(elem!1))))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[6776, 194, 6749, 6741, 6770])).
% 6.92/7.19 tff(6778,plain,
% 6.92/7.19 (b(elem!1, s(s(s(elem!1))))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[424, 6777, 1])).
% 6.92/7.19 tff(6779,plain,
% 6.92/7.19 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[5377, 1945, 3843])).
% 6.92/7.19 tff(6780,plain,
% 6.92/7.19 (~(s(s(elem!1)) = s(elem!1))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[2279, 6779])).
% 6.92/7.19 tff(6781,plain,
% 6.92/7.19 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[1945])).
% 6.92/7.19 tff(6782,plain,
% 6.92/7.19 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 6.92/7.19 inference(symmetry,[status(thm)],[6781])).
% 6.92/7.19 tff(6783,plain,
% 6.92/7.19 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[1945])).
% 6.92/7.19 tff(6784,plain,
% 6.92/7.19 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 6.92/7.19 inference(symmetry,[status(thm)],[6783])).
% 6.92/7.19 tff(6785,plain,
% 6.92/7.19 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6784])).
% 6.92/7.19 tff(6786,plain,
% 6.92/7.19 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 6.92/7.19 inference(transitivity,[status(thm)],[6785, 6782])).
% 6.92/7.19 tff(6787,plain,
% 6.92/7.19 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6786])).
% 6.92/7.19 tff(6788,plain,
% 6.92/7.19 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6784])).
% 6.92/7.19 tff(6789,plain,
% 6.92/7.19 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 6.92/7.19 inference(symmetry,[status(thm)],[6788])).
% 6.92/7.19 tff(6790,plain,
% 6.92/7.19 (~(s(s(elem!1)) = elem!1)),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[451, 6779])).
% 6.92/7.19 tff(6791,plain,
% 6.92/7.19 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[287, 6780])).
% 6.92/7.19 tff(6792,plain,
% 6.92/7.19 (b(z, s(s(elem!1)))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[3924, 6791, 10, 91])).
% 6.92/7.19 tff(6793,plain,
% 6.92/7.19 (~b(s(s(elem!1)), elem!1)),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[4944, 6792, 665, 133])).
% 6.92/7.19 tff(6794,plain,
% 6.92/7.19 (r(s(s(elem!1)), elem!1)),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[872, 6793, 6790])).
% 6.92/7.19 tff(6795,plain,
% 6.92/7.19 (~r(s(s(elem!1)), s(z))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[1899, 6794, 1484, 847])).
% 6.92/7.19 tff(6796,plain,
% 6.92/7.19 (b(s(s(elem!1)), s(z))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[362, 6795])).
% 6.92/7.19 tff(6797,plain,
% 6.92/7.19 (b(s(s(s(s(s(z))))), s(z))),
% 6.92/7.19 inference(modus_ponens,[status(thm)],[6796, 6789])).
% 6.92/7.19 tff(6798,plain,
% 6.92/7.19 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[1945])).
% 6.92/7.19 tff(6799,plain,
% 6.92/7.19 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 6.92/7.19 inference(symmetry,[status(thm)],[6798])).
% 6.92/7.19 tff(6800,plain,
% 6.92/7.19 (s(s(s(z))) = elem!1),
% 6.92/7.19 inference(transitivity,[status(thm)],[693, 6799, 108])).
% 6.92/7.19 tff(6801,plain,
% 6.92/7.19 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6800])).
% 6.92/7.19 tff(6802,plain,
% 6.92/7.19 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 6.92/7.19 inference(symmetry,[status(thm)],[6801])).
% 6.92/7.19 tff(6803,plain,
% 6.92/7.19 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6783])).
% 6.92/7.19 tff(6804,plain,
% 6.92/7.19 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6803])).
% 6.92/7.19 tff(6805,plain,
% 6.92/7.19 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 6.92/7.19 inference(modus_ponens,[status(thm)],[900, 6804])).
% 6.92/7.19 tff(6806,plain,
% 6.92/7.19 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 6.92/7.19 inference(modus_ponens,[status(thm)],[6805, 6802])).
% 6.92/7.19 tff(6807,plain,
% 6.92/7.19 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 6.92/7.19 inference(symmetry,[status(thm)],[6803])).
% 6.92/7.19 tff(6808,plain,
% 6.92/7.19 (b(s(z), s(s(s(s(s(s(z))))))) <=> b(s(z), s(s(s(elem!1))))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6807])).
% 6.92/7.19 tff(6809,plain,
% 6.92/7.19 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(s(s(z)))))))),
% 6.92/7.19 inference(symmetry,[status(thm)],[6808])).
% 6.92/7.19 tff(6810,plain,
% 6.92/7.19 (b(s(z), s(s(s(s(s(s(z)))))))),
% 6.92/7.19 inference(modus_ponens,[status(thm)],[6520, 6809])).
% 6.92/7.19 tff(6811,plain,
% 6.92/7.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 6.92/7.19 inference(rewrite,[status(thm)],[])).
% 6.92/7.19 tff(6812,plain,
% 6.92/7.19 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 6.92/7.19 inference(rewrite,[status(thm)],[])).
% 6.92/7.19 tff(6813,plain,
% 6.92/7.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6812])).
% 6.92/7.19 tff(6814,plain,
% 6.92/7.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 6.92/7.19 inference(transitivity,[status(thm)],[6813, 6811])).
% 6.92/7.19 tff(6815,plain,
% 6.92/7.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 6.92/7.19 inference(quant_inst,[status(thm)],[])).
% 6.92/7.19 tff(6816,plain,
% 6.92/7.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 6.92/7.19 inference(modus_ponens,[status(thm)],[6815, 6814])).
% 6.92/7.19 tff(6817,plain,
% 6.92/7.19 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[6816, 391, 1759])).
% 6.92/7.19 tff(6818,plain,
% 6.92/7.19 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 6.92/7.19 inference(unit_resolution,[status(thm)],[6817, 6810, 6806, 6797])).
% 6.92/7.19 tff(6819,plain,
% 6.92/7.19 (~b(s(s(elem!1)), s(elem!1))),
% 6.92/7.19 inference(modus_ponens,[status(thm)],[6818, 6787])).
% 6.92/7.19 tff(6820,plain,
% 6.92/7.19 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[1945])).
% 6.92/7.19 tff(6821,plain,
% 6.92/7.19 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(elem!1))),
% 6.92/7.19 inference(symmetry,[status(thm)],[6820])).
% 6.92/7.19 tff(6822,plain,
% 6.92/7.19 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6784])).
% 6.92/7.19 tff(6823,plain,
% 6.92/7.19 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(elem!1))),
% 6.92/7.19 inference(transitivity,[status(thm)],[6822, 6821])).
% 6.92/7.19 tff(6824,plain,
% 6.92/7.19 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6823])).
% 6.92/7.19 tff(6825,plain,
% 6.92/7.19 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 6.92/7.19 inference(monotonicity,[status(thm)],[6800])).
% 6.92/7.19 tff(6826,plain,
% 6.92/7.19 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 6.92/7.19 inference(symmetry,[status(thm)],[6825])).
% 6.92/7.19 tff(6827,plain,
% 6.92/7.19 (r(s(s(s(z))), s(z))),
% 6.92/7.19 inference(modus_ponens,[status(thm)],[847, 6826])).
% 6.92/7.19 tff(6828,plain,
% 6.99/7.20 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 6.99/7.20 inference(monotonicity,[status(thm)],[6784, 6800])).
% 6.99/7.20 tff(6829,plain,
% 6.99/7.20 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 6.99/7.20 inference(symmetry,[status(thm)],[6828])).
% 6.99/7.20 tff(6830,plain,
% 6.99/7.20 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 6.99/7.20 inference(modus_ponens,[status(thm)],[6794, 6829])).
% 6.99/7.20 tff(6831,plain,
% 6.99/7.20 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 6.99/7.20 inference(monotonicity,[status(thm)],[6800])).
% 6.99/7.20 tff(6832,plain,
% 6.99/7.20 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 6.99/7.20 inference(symmetry,[status(thm)],[6831])).
% 6.99/7.20 tff(6833,plain,
% 6.99/7.20 (r(s(s(s(s(z)))), s(s(s(z))))),
% 6.99/7.20 inference(modus_ponens,[status(thm)],[2112, 6832])).
% 6.99/7.20 tff(6834,plain,
% 6.99/7.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 6.99/7.20 inference(rewrite,[status(thm)],[])).
% 6.99/7.20 tff(6835,plain,
% 6.99/7.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 6.99/7.20 inference(quant_inst,[status(thm)],[])).
% 6.99/7.20 tff(6836,plain,
% 6.99/7.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 6.99/7.20 inference(modus_ponens,[status(thm)],[6835, 6834])).
% 6.99/7.20 tff(6837,plain,
% 6.99/7.20 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[6836, 194, 6833])).
% 6.99/7.20 tff(6838,plain,
% 6.99/7.20 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[6837, 6830, 6827])).
% 6.99/7.20 tff(6839,plain,
% 6.99/7.20 (~r(s(s(elem!1)), s(elem!1))),
% 6.99/7.20 inference(modus_ponens,[status(thm)],[6838, 6824])).
% 6.99/7.20 tff(6840,plain,
% 6.99/7.20 ($false),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[1135, 6839, 6819, 6780])).
% 6.99/7.20 tff(6841,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | b(z, s(s(s(elem!1)))) | b(s(z), z) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.20 tff(6842,plain,
% 6.99/7.20 (~(s(elem!1) = s(s(s(s(z)))))),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[6841, 6761, 6522, 900, 6741, 6759, 665, 133, 10, 91, 3363])).
% 6.99/7.20 tff(6843,plain,
% 6.99/7.20 (~r(s(elem!1), s(s(s(s(z)))))),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[4341, 194, 485, 847, 2112])).
% 6.99/7.20 tff(6844,plain,
% 6.99/7.20 (b(s(elem!1), s(s(s(s(z)))))),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[2142, 42, 6843, 2121])).
% 6.99/7.20 tff(6845,plain,
% 6.99/7.20 (~r(s(z), s(s(s(s(z)))))),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[5396, 1484, 2112, 847])).
% 6.99/7.20 tff(6846,plain,
% 6.99/7.20 (b(s(z), s(s(s(s(z)))))),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[1230, 6845])).
% 6.99/7.20 tff(6847,plain,
% 6.99/7.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 6.99/7.20 inference(rewrite,[status(thm)],[])).
% 6.99/7.20 tff(6848,plain,
% 6.99/7.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 6.99/7.20 inference(quant_inst,[status(thm)],[])).
% 6.99/7.20 tff(6849,plain,
% 6.99/7.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 6.99/7.20 inference(modus_ponens,[status(thm)],[6848, 6847])).
% 6.99/7.20 tff(6850,plain,
% 6.99/7.20 (~r(s(z), s(elem!1))),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[6849, 194, 485, 1484, 847])).
% 6.99/7.20 tff(6851,plain,
% 6.99/7.20 (b(s(z), s(elem!1))),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[602, 42, 121, 6850])).
% 6.99/7.20 tff(6852,plain,
% 6.99/7.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.99/7.20 inference(rewrite,[status(thm)],[])).
% 6.99/7.20 tff(6853,plain,
% 6.99/7.20 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.99/7.20 inference(rewrite,[status(thm)],[])).
% 6.99/7.20 tff(6854,plain,
% 6.99/7.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 6.99/7.20 inference(monotonicity,[status(thm)],[6853])).
% 6.99/7.20 tff(6855,plain,
% 6.99/7.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 6.99/7.20 inference(transitivity,[status(thm)],[6854, 6852])).
% 6.99/7.20 tff(6856,plain,
% 6.99/7.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))))),
% 6.99/7.20 inference(quant_inst,[status(thm)],[])).
% 6.99/7.20 tff(6857,plain,
% 6.99/7.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 6.99/7.20 inference(modus_ponens,[status(thm)],[6856, 6855])).
% 6.99/7.20 tff(6858,plain,
% 6.99/7.20 ($false),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[6857, 391, 133, 6851, 90, 6846, 6844])).
% 6.99/7.20 tff(6859,plain,((~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.20 tff(6860,plain,
% 6.99/7.20 (~r(s(elem!1), elem!1)),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[6859, 6511, 133, 121, 6842, 6759, 6522, 6741])).
% 6.99/7.20 tff(6861,plain,
% 6.99/7.20 (b(s(elem!1), elem!1)),
% 6.99/7.20 inference(unit_resolution,[status(thm)],[2168, 6860, 5887])).
% 6.99/7.20 tff(6862,plain,
% 6.99/7.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 6.99/7.21 inference(rewrite,[status(thm)],[])).
% 6.99/7.21 tff(6863,plain,
% 6.99/7.21 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), 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))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 6.99/7.21 inference(rewrite,[status(thm)],[])).
% 6.99/7.21 tff(6864,plain,
% 6.99/7.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 6.99/7.21 inference(monotonicity,[status(thm)],[6863])).
% 6.99/7.21 tff(6865,plain,
% 6.99/7.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 6.99/7.21 inference(transitivity,[status(thm)],[6864, 6862])).
% 6.99/7.21 tff(6866,plain,
% 6.99/7.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 6.99/7.21 inference(quant_inst,[status(thm)],[])).
% 6.99/7.21 tff(6867,plain,
% 6.99/7.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 6.99/7.21 inference(modus_ponens,[status(thm)],[6866, 6865])).
% 6.99/7.21 tff(6868,plain,
% 6.99/7.21 ($false),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[6867, 391, 1101, 900, 448, 2122])).
% 6.99/7.21 tff(6869,plain,((~b(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(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.21 tff(6870,plain,
% 6.99/7.21 (~b(s(s(s(elem!1))), s(elem!1))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[6869, 6861, 900, 6778])).
% 6.99/7.21 tff(6871,plain,
% 6.99/7.21 (~b(z, s(elem!1))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[6555, 6861, 133, 665])).
% 6.99/7.21 tff(6872,plain,
% 6.99/7.21 (r(z, s(elem!1))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[566, 6871])).
% 6.99/7.21 tff(6873,plain,
% 6.99/7.21 (r(s(s(s(elem!1))), s(elem!1))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[588, 486, 279])).
% 6.99/7.21 tff(6874,plain,
% 6.99/7.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.99/7.21 inference(rewrite,[status(thm)],[])).
% 6.99/7.21 tff(6875,plain,
% 6.99/7.21 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.99/7.21 inference(rewrite,[status(thm)],[])).
% 6.99/7.21 tff(6876,plain,
% 6.99/7.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 6.99/7.21 inference(monotonicity,[status(thm)],[6875])).
% 6.99/7.21 tff(6877,plain,
% 6.99/7.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 6.99/7.21 inference(transitivity,[status(thm)],[6876, 6874])).
% 6.99/7.21 tff(6878,plain,
% 6.99/7.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 6.99/7.21 inference(quant_inst,[status(thm)],[])).
% 6.99/7.21 tff(6879,plain,
% 6.99/7.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 6.99/7.21 inference(modus_ponens,[status(thm)],[6878, 6877])).
% 6.99/7.21 tff(6880,plain,
% 6.99/7.21 ($false),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[6879, 194, 613, 174, 2144, 604])).
% 6.99/7.21 tff(6881,plain,((~r(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(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.21 tff(6882,plain,
% 6.99/7.21 (~r(s(elem!1), s(s(s(elem!1))))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[6881, 6873, 174, 2144])).
% 6.99/7.21 tff(6883,plain,
% 6.99/7.21 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[579, 42, 6882])).
% 6.99/7.21 tff(6884,plain,
% 6.99/7.21 (b(s(elem!1), s(s(s(elem!1))))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[6883, 5622])).
% 6.99/7.21 tff(6885,plain,
% 6.99/7.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(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))))))),
% 6.99/7.21 inference(rewrite,[status(thm)],[])).
% 6.99/7.21 tff(6886,plain,
% 6.99/7.21 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(s(s(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))))))),
% 6.99/7.21 inference(rewrite,[status(thm)],[])).
% 6.99/7.21 tff(6887,plain,
% 6.99/7.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(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)))))))),
% 6.99/7.21 inference(monotonicity,[status(thm)],[6886])).
% 6.99/7.21 tff(6888,plain,
% 6.99/7.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(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))))))),
% 6.99/7.21 inference(transitivity,[status(thm)],[6887, 6885])).
% 6.99/7.21 tff(6889,plain,
% 6.99/7.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 6.99/7.21 inference(quant_inst,[status(thm)],[])).
% 6.99/7.21 tff(6890,plain,
% 6.99/7.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 6.99/7.21 inference(modus_ponens,[status(thm)],[6889, 6888])).
% 6.99/7.21 tff(6891,plain,
% 6.99/7.21 (~b(s(elem!1), elem!1)),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[6890, 391, 900, 448, 6884])).
% 6.99/7.21 tff(6892,plain,
% 6.99/7.21 (s(elem!1) = elem!1),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[2329, 6891])).
% 6.99/7.21 tff(6893,plain,
% 6.99/7.21 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), elem!1)),
% 6.99/7.21 inference(monotonicity,[status(thm)],[6892])).
% 6.99/7.21 tff(6894,plain,
% 6.99/7.21 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(elem!1))),
% 6.99/7.21 inference(symmetry,[status(thm)],[6893])).
% 6.99/7.21 tff(6895,plain,
% 6.99/7.21 (b(s(s(s(elem!1))), s(elem!1))),
% 6.99/7.21 inference(modus_ponens,[status(thm)],[900, 6894])).
% 6.99/7.21 tff(6896,plain,
% 6.99/7.21 ($false),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[486, 6895])).
% 6.99/7.21 tff(6897,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | r(s(elem!1), elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.21 tff(6898,plain,
% 6.99/7.21 (s(s(s(elem!1))) = s(elem!1)),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[6897, 6872, 6860, 6870, 6509, 6778, 900])).
% 6.99/7.21 tff(6899,plain,
% 6.99/7.21 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 6.99/7.21 inference(monotonicity,[status(thm)],[6898])).
% 6.99/7.21 tff(6900,plain,
% 6.99/7.21 (r(s(elem!1), s(s(s(s(z)))))),
% 6.99/7.21 inference(modus_ponens,[status(thm)],[6770, 6899])).
% 6.99/7.21 tff(6901,plain,
% 6.99/7.21 (~r(s(z), s(s(s(s(z)))))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[5396, 6759, 6741, 6522])).
% 6.99/7.21 tff(6902,plain,
% 6.99/7.21 (b(s(z), s(s(s(s(z)))))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[1230, 6901])).
% 6.99/7.21 tff(6903,plain,
% 6.99/7.21 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[6372, 6761, 6511, 6518, 6902])).
% 6.99/7.21 tff(6904,plain,
% 6.99/7.21 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[2853, 42, 3363, 6903])).
% 6.99/7.21 tff(6905,plain,
% 6.99/7.21 (~r(z, s(s(s(s(z)))))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[4324, 194, 6509, 59, 6904])).
% 6.99/7.21 tff(6906,plain,
% 6.99/7.21 (b(z, s(s(s(s(z)))))),
% 6.99/7.21 inference(unit_resolution,[status(thm)],[800, 6905])).
% 6.99/7.21 tff(6907,plain,
% 6.99/7.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.99/7.21 inference(rewrite,[status(thm)],[])).
% 6.99/7.21 tff(6908,plain,
% 6.99/7.21 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.99/7.21 inference(rewrite,[status(thm)],[])).
% 6.99/7.21 tff(6909,plain,
% 6.99/7.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 6.99/7.22 inference(monotonicity,[status(thm)],[6908])).
% 6.99/7.22 tff(6910,plain,
% 6.99/7.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.99/7.22 inference(transitivity,[status(thm)],[6909, 6907])).
% 6.99/7.22 tff(6911,plain,
% 6.99/7.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 6.99/7.22 inference(quant_inst,[status(thm)],[])).
% 6.99/7.22 tff(6912,plain,
% 6.99/7.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 6.99/7.22 inference(modus_ponens,[status(thm)],[6911, 6910])).
% 6.99/7.22 tff(6913,plain,
% 6.99/7.22 ($false),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[6912, 391, 133, 90, 1234, 1686, 664])).
% 6.99/7.22 tff(6914,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.22 tff(6915,plain,
% 6.99/7.22 (~b(z, s(z))),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[6914, 1686, 90, 1234, 133])).
% 6.99/7.22 tff(6916,plain,
% 6.99/7.22 (r(z, s(z))),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[678, 6915])).
% 6.99/7.22 tff(6917,plain,
% 6.99/7.22 (~b(s(s(z)), z)),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[4472, 3823, 90, 1686])).
% 6.99/7.22 tff(6918,plain,
% 6.99/7.22 (r(s(s(z)), z)),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[1211, 6917])).
% 6.99/7.22 tff(6919,plain,
% 6.99/7.22 (~b(s(s(z)), s(z))),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[5126, 3823, 133, 182, 1234, 6916])).
% 6.99/7.22 tff(6920,plain,
% 6.99/7.22 (r(s(s(z)), s(z))),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[3778, 6919])).
% 6.99/7.22 tff(6921,plain,
% 6.99/7.22 ($false),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[4462, 6920, 6918, 1484, 6916])).
% 6.99/7.22 tff(6922,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.22 tff(6923,plain,
% 6.99/7.22 (~b(s(s(z)), s(s(s(s(z)))))),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[6922, 6759, 133, 181, 6902, 6511, 6906])).
% 6.99/7.22 tff(6924,plain,
% 6.99/7.22 (r(s(s(z)), s(s(s(s(z)))))),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[3652, 6923])).
% 6.99/7.22 tff(6925,plain,
% 6.99/7.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.99/7.22 inference(rewrite,[status(thm)],[])).
% 6.99/7.22 tff(6926,plain,
% 6.99/7.22 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.99/7.22 inference(rewrite,[status(thm)],[])).
% 6.99/7.22 tff(6927,plain,
% 6.99/7.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 6.99/7.22 inference(monotonicity,[status(thm)],[6926])).
% 6.99/7.22 tff(6928,plain,
% 6.99/7.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 6.99/7.22 inference(transitivity,[status(thm)],[6927, 6925])).
% 6.99/7.22 tff(6929,plain,
% 6.99/7.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))),
% 6.99/7.22 inference(quant_inst,[status(thm)],[])).
% 6.99/7.22 tff(6930,plain,
% 6.99/7.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 6.99/7.22 inference(modus_ponens,[status(thm)],[6929, 6928])).
% 6.99/7.22 tff(6931,plain,
% 6.99/7.22 (~r(s(s(z)), s(elem!1))),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[6930, 194, 6924, 6741, 6900])).
% 6.99/7.22 tff(6932,plain,
% 6.99/7.22 (~(s(s(z)) = s(elem!1))),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[2493, 6898])).
% 6.99/7.22 tff(6933,plain,
% 6.99/7.22 (b(s(s(z)), s(elem!1))),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[4693, 42, 6932, 6931])).
% 6.99/7.22 tff(6934,plain,
% 6.99/7.22 (~(s(s(z)) = elem!1)),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[4584, 6898, 121])).
% 6.99/7.22 tff(6935,plain,
% 6.99/7.22 (~r(s(s(z)), elem!1)),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[4725, 194, 6924, 6749, 6741])).
% 6.99/7.22 tff(6936,plain,
% 6.99/7.22 (b(s(s(z)), elem!1)),
% 6.99/7.22 inference(unit_resolution,[status(thm)],[4730, 6935, 6934])).
% 6.99/7.22 tff(6937,plain,
% 6.99/7.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 6.99/7.22 inference(rewrite,[status(thm)],[])).
% 6.99/7.22 tff(6938,plain,
% 6.99/7.22 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 6.99/7.22 inference(rewrite,[status(thm)],[])).
% 6.99/7.22 tff(6939,plain,
% 6.99/7.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))))),
% 6.99/7.22 inference(monotonicity,[status(thm)],[6938])).
% 6.99/7.22 tff(6940,plain,
% 6.99/7.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 6.99/7.22 inference(transitivity,[status(thm)],[6939, 6937])).
% 6.99/7.22 tff(6941,plain,
% 6.99/7.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 6.99/7.23 inference(quant_inst,[status(thm)],[])).
% 6.99/7.23 tff(6942,plain,
% 6.99/7.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))),
% 6.99/7.23 inference(modus_ponens,[status(thm)],[6941, 6940])).
% 6.99/7.23 tff(6943,plain,
% 6.99/7.23 ($false),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[6942, 391, 133, 665, 6861, 6936, 6933])).
% 6.99/7.23 tff(6944,plain,(b(s(z), z) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(z) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | b(z, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 6.99/7.23 tff(6945,plain,
% 6.99/7.23 (b(s(z), z)),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[6944, 6506, 149, 118, 5933, 10, 148, 150])).
% 6.99/7.23 tff(6946,plain,
% 6.99/7.23 (~b(s(z), elem!1)),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[5231, 6945, 6506, 149])).
% 6.99/7.23 tff(6947,plain,
% 6.99/7.23 (r(s(z), elem!1)),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[632, 6946, 150])).
% 6.99/7.23 tff(6948,plain,
% 6.99/7.23 (~b(elem!1, s(z))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[5221, 391, 149, 6506, 6945])).
% 6.99/7.23 tff(6949,plain,
% 6.99/7.23 (r(elem!1, s(z))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[837, 6948, 173])).
% 6.99/7.23 tff(6950,plain,
% 6.99/7.23 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 6.99/7.23 inference(modus_ponens,[status(thm)],[3843, 3930])).
% 6.99/7.23 tff(6951,plain,
% 6.99/7.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.99/7.23 inference(rewrite,[status(thm)],[])).
% 6.99/7.23 tff(6952,plain,
% 6.99/7.23 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.99/7.23 inference(rewrite,[status(thm)],[])).
% 6.99/7.23 tff(6953,plain,
% 6.99/7.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 6.99/7.23 inference(monotonicity,[status(thm)],[6952])).
% 6.99/7.23 tff(6954,plain,
% 6.99/7.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.99/7.23 inference(transitivity,[status(thm)],[6953, 6951])).
% 6.99/7.23 tff(6955,plain,
% 6.99/7.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.99/7.23 inference(quant_inst,[status(thm)],[])).
% 6.99/7.23 tff(6956,plain,
% 6.99/7.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 6.99/7.23 inference(modus_ponens,[status(thm)],[6955, 6954])).
% 6.99/7.23 tff(6957,plain,
% 6.99/7.23 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[6956, 194, 6509, 184, 3447])).
% 6.99/7.23 tff(6958,plain,
% 6.99/7.23 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[4313, 42, 6957])).
% 6.99/7.23 tff(6959,plain,
% 6.99/7.23 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[6958, 6950])).
% 6.99/7.23 tff(6960,plain,
% 6.99/7.23 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[3954, 194, 6509, 184, 3447])).
% 6.99/7.23 tff(6961,plain,
% 6.99/7.23 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 6960])).
% 6.99/7.23 tff(6962,plain,
% 6.99/7.23 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 6.99/7.23 inference(monotonicity,[status(thm)],[688])).
% 6.99/7.23 tff(6963,plain,
% 6.99/7.23 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 6.99/7.23 inference(symmetry,[status(thm)],[6962])).
% 6.99/7.23 tff(6964,plain,
% 6.99/7.23 (b(s(s(s(s(z)))), z)),
% 6.99/7.23 inference(modus_ponens,[status(thm)],[665, 6963])).
% 6.99/7.23 tff(6965,plain,
% 6.99/7.23 ($false),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[3446, 6964])).
% 6.99/7.23 tff(6966,plain,((~(s(s(s(s(z)))) = elem!1)) | b(s(s(s(s(z)))), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.23 tff(6967,plain,
% 6.99/7.23 (~(s(s(s(s(z)))) = elem!1)),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[6966, 3446, 665])).
% 6.99/7.23 tff(6968,plain,
% 6.99/7.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.99/7.23 inference(rewrite,[status(thm)],[])).
% 6.99/7.23 tff(6969,plain,
% 6.99/7.23 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.99/7.23 inference(rewrite,[status(thm)],[])).
% 6.99/7.23 tff(6970,plain,
% 6.99/7.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 6.99/7.23 inference(monotonicity,[status(thm)],[6969])).
% 6.99/7.23 tff(6971,plain,
% 6.99/7.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.99/7.23 inference(transitivity,[status(thm)],[6970, 6968])).
% 6.99/7.23 tff(6972,plain,
% 6.99/7.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.99/7.23 inference(quant_inst,[status(thm)],[])).
% 6.99/7.23 tff(6973,plain,
% 6.99/7.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.99/7.23 inference(modus_ponens,[status(thm)],[6972, 6971])).
% 6.99/7.23 tff(6974,plain,
% 6.99/7.23 ($false),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[6973, 391, 133, 665, 900, 1652, 3325])).
% 6.99/7.23 tff(6975,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.23 tff(6976,plain,
% 6.99/7.23 (~b(s(s(s(s(z)))), elem!1)),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[6975, 6961, 665, 900, 133])).
% 6.99/7.23 tff(6977,plain,
% 6.99/7.23 (r(s(s(s(s(z)))), elem!1)),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[762, 6976, 6967])).
% 6.99/7.23 tff(6978,plain,
% 6.99/7.23 (~r(s(z), s(s(s(s(z)))))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[5396, 6977, 1484, 847])).
% 6.99/7.23 tff(6979,plain,
% 6.99/7.23 (b(s(z), s(s(s(s(z)))))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[1230, 6978])).
% 6.99/7.23 tff(6980,plain,
% 6.99/7.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.99/7.23 inference(rewrite,[status(thm)],[])).
% 6.99/7.23 tff(6981,plain,
% 6.99/7.23 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.99/7.23 inference(rewrite,[status(thm)],[])).
% 6.99/7.23 tff(6982,plain,
% 6.99/7.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 6.99/7.23 inference(monotonicity,[status(thm)],[6981])).
% 6.99/7.23 tff(6983,plain,
% 6.99/7.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.99/7.23 inference(transitivity,[status(thm)],[6982, 6980])).
% 6.99/7.23 tff(6984,plain,
% 6.99/7.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.99/7.23 inference(quant_inst,[status(thm)],[])).
% 6.99/7.23 tff(6985,plain,
% 6.99/7.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 6.99/7.23 inference(modus_ponens,[status(thm)],[6984, 6983])).
% 6.99/7.23 tff(6986,plain,
% 6.99/7.23 (~b(s(z), s(s(s(elem!1))))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[6985, 391, 900, 6979, 6961, 6959])).
% 6.99/7.23 tff(6987,plain,
% 6.99/7.23 (r(s(z), s(s(s(elem!1))))),
% 6.99/7.23 inference(unit_resolution,[status(thm)],[247, 6986])).
% 6.99/7.24 tff(6988,plain,
% 6.99/7.24 (~r(elem!1, s(s(s(elem!1))))),
% 6.99/7.24 inference(unit_resolution,[status(thm)],[5645, 6987, 6509, 1484])).
% 6.99/7.24 tff(6989,plain,
% 6.99/7.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.99/7.24 inference(rewrite,[status(thm)],[])).
% 6.99/7.24 tff(6990,plain,
% 6.99/7.24 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.99/7.24 inference(rewrite,[status(thm)],[])).
% 6.99/7.24 tff(6991,plain,
% 6.99/7.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 6.99/7.24 inference(monotonicity,[status(thm)],[6990])).
% 6.99/7.24 tff(6992,plain,
% 6.99/7.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 6.99/7.24 inference(transitivity,[status(thm)],[6991, 6989])).
% 6.99/7.24 tff(6993,plain,
% 6.99/7.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 6.99/7.24 inference(quant_inst,[status(thm)],[])).
% 6.99/7.24 tff(6994,plain,
% 6.99/7.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 6.99/7.24 inference(modus_ponens,[status(thm)],[6993, 6992])).
% 6.99/7.24 tff(6995,plain,
% 6.99/7.24 (~b(s(s(s(elem!1))), s(z))),
% 6.99/7.24 inference(unit_resolution,[status(thm)],[6994, 391, 900, 6979, 6961, 6959])).
% 6.99/7.24 tff(6996,plain,
% 6.99/7.24 (r(s(s(s(elem!1))), s(z))),
% 6.99/7.24 inference(unit_resolution,[status(thm)],[223, 6995])).
% 6.99/7.24 tff(6997,plain,
% 6.99/7.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.99/7.24 inference(rewrite,[status(thm)],[])).
% 6.99/7.24 tff(6998,plain,
% 6.99/7.24 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.99/7.24 inference(rewrite,[status(thm)],[])).
% 6.99/7.24 tff(6999,plain,
% 6.99/7.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 6.99/7.24 inference(monotonicity,[status(thm)],[6998])).
% 6.99/7.24 tff(7000,plain,
% 6.99/7.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.99/7.24 inference(transitivity,[status(thm)],[6999, 6997])).
% 6.99/7.24 tff(7001,plain,
% 6.99/7.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 6.99/7.24 inference(quant_inst,[status(thm)],[])).
% 6.99/7.24 tff(7002,plain,
% 6.99/7.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.99/7.24 inference(modus_ponens,[status(thm)],[7001, 7000])).
% 6.99/7.24 tff(7003,plain,
% 6.99/7.24 (~b(s(s(s(s(z)))), elem!1)),
% 6.99/7.24 inference(unit_resolution,[status(thm)],[7002, 391, 665, 900, 448, 3325])).
% 6.99/7.24 tff(7004,plain,
% 6.99/7.24 (r(s(s(s(s(z)))), elem!1)),
% 6.99/7.24 inference(unit_resolution,[status(thm)],[762, 720, 7003])).
% 6.99/7.24 tff(7005,plain,
% 6.99/7.24 (~r(s(z), s(s(s(s(z)))))),
% 6.99/7.24 inference(unit_resolution,[status(thm)],[5396, 7004, 1484, 847])).
% 6.99/7.24 tff(7006,plain,
% 6.99/7.24 (b(s(z), s(s(s(s(z)))))),
% 6.99/7.24 inference(unit_resolution,[status(thm)],[1230, 7005])).
% 6.99/7.24 tff(7007,plain,
% 6.99/7.24 (~b(s(z), s(s(s(elem!1))))),
% 6.99/7.24 inference(unit_resolution,[status(thm)],[6985, 391, 900, 7006, 3325, 1669])).
% 6.99/7.24 tff(7008,plain,
% 6.99/7.24 (r(s(z), s(s(s(elem!1))))),
% 6.99/7.24 inference(unit_resolution,[status(thm)],[247, 7007])).
% 6.99/7.24 tff(7009,plain,
% 6.99/7.24 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.99/7.24 inference(unit_resolution,[status(thm)],[5792, 7008, 184, 6509])).
% 6.99/7.24 tff(7010,plain,
% 6.99/7.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.99/7.24 inference(rewrite,[status(thm)],[])).
% 6.99/7.24 tff(7011,plain,
% 6.99/7.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 6.99/7.24 inference(quant_inst,[status(thm)],[])).
% 6.99/7.24 tff(7012,plain,
% 6.99/7.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 6.99/7.25 inference(modus_ponens,[status(thm)],[7011, 7010])).
% 6.99/7.25 tff(7013,plain,
% 6.99/7.25 (~r(s(s(s(s(z)))), s(z))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[7012, 194, 1484, 847, 2112])).
% 6.99/7.25 tff(7014,plain,
% 6.99/7.25 (b(s(s(s(s(z)))), s(z))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[749, 7013])).
% 6.99/7.25 tff(7015,plain,
% 6.99/7.25 (~r(s(z), s(s(s(s(z)))))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[5396, 2112, 1484, 847])).
% 6.99/7.25 tff(7016,plain,
% 6.99/7.25 (b(s(z), s(s(s(s(z)))))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[1230, 7015])).
% 6.99/7.25 tff(7017,plain,
% 6.99/7.25 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[2274, 6850, 232])).
% 6.99/7.25 tff(7018,plain,
% 6.99/7.25 (~(s(s(elem!1)) = elem!1)),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[451, 7017])).
% 6.99/7.25 tff(7019,plain,
% 6.99/7.25 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[281, 7017])).
% 6.99/7.25 tff(7020,plain,
% 6.99/7.25 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[1356, 7019, 1350])).
% 6.99/7.25 tff(7021,plain,
% 6.99/7.25 (~b(s(s(elem!1)), elem!1)),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[6001, 7020, 448, 900])).
% 6.99/7.25 tff(7022,plain,
% 6.99/7.25 (r(s(s(elem!1)), elem!1)),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[872, 7021, 7018])).
% 6.99/7.25 tff(7023,plain,
% 6.99/7.25 (~r(s(s(elem!1)), s(z))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[1899, 7022, 1484, 847])).
% 6.99/7.25 tff(7024,plain,
% 6.99/7.25 (b(s(s(elem!1)), s(z))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[362, 7023])).
% 6.99/7.25 tff(7025,plain,
% 6.99/7.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.99/7.25 inference(rewrite,[status(thm)],[])).
% 6.99/7.25 tff(7026,plain,
% 6.99/7.25 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), 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(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.99/7.25 inference(rewrite,[status(thm)],[])).
% 6.99/7.25 tff(7027,plain,
% 6.99/7.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 6.99/7.25 inference(monotonicity,[status(thm)],[7026])).
% 6.99/7.25 tff(7028,plain,
% 6.99/7.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.99/7.25 inference(transitivity,[status(thm)],[7027, 7025])).
% 6.99/7.25 tff(7029,plain,
% 6.99/7.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.99/7.25 inference(quant_inst,[status(thm)],[])).
% 6.99/7.25 tff(7030,plain,
% 6.99/7.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 6.99/7.25 inference(modus_ponens,[status(thm)],[7029, 7028])).
% 6.99/7.25 tff(7031,plain,
% 6.99/7.25 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[7030, 391, 7024, 7016, 7014])).
% 6.99/7.25 tff(7032,plain,
% 6.99/7.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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)))))))),
% 6.99/7.25 inference(rewrite,[status(thm)],[])).
% 6.99/7.25 tff(7033,plain,
% 6.99/7.25 (((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(elem!1, 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)))))))),
% 6.99/7.25 inference(rewrite,[status(thm)],[])).
% 6.99/7.25 tff(7034,plain,
% 6.99/7.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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))))))))),
% 6.99/7.25 inference(monotonicity,[status(thm)],[7033])).
% 6.99/7.25 tff(7035,plain,
% 6.99/7.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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)))))))),
% 6.99/7.25 inference(transitivity,[status(thm)],[7034, 7032])).
% 6.99/7.25 tff(7036,plain,
% 6.99/7.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 6.99/7.25 inference(quant_inst,[status(thm)],[])).
% 6.99/7.25 tff(7037,plain,
% 6.99/7.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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))))))),
% 6.99/7.25 inference(modus_ponens,[status(thm)],[7036, 7035])).
% 6.99/7.25 tff(7038,plain,
% 6.99/7.25 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[7037, 194, 7022, 847, 2112])).
% 6.99/7.25 tff(7039,plain,
% 6.99/7.25 (s(s(elem!1)) = s(s(s(s(z))))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[1994, 42, 7038, 7031])).
% 6.99/7.25 tff(7040,plain,
% 6.99/7.25 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 6.99/7.25 inference(monotonicity,[status(thm)],[7039])).
% 6.99/7.25 tff(7041,plain,
% 6.99/7.25 (s(elem!1) = s(s(s(z)))),
% 6.99/7.25 inference(transitivity,[status(thm)],[352, 7040, 692])).
% 6.99/7.25 tff(7042,plain,
% 6.99/7.25 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 6.99/7.25 inference(monotonicity,[status(thm)],[7041])).
% 6.99/7.25 tff(7043,plain,
% 6.99/7.25 (~r(s(elem!1), s(z))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[5339, 194, 485, 1484, 847])).
% 6.99/7.25 tff(7044,plain,
% 6.99/7.25 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[1915, 42, 7043])).
% 6.99/7.25 tff(7045,plain,
% 6.99/7.25 (b(s(elem!1), s(z))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[7044, 1905])).
% 6.99/7.25 tff(7046,plain,
% 6.99/7.25 (b(s(s(s(z))), s(z))),
% 6.99/7.25 inference(modus_ponens,[status(thm)],[7045, 7042])).
% 6.99/7.25 tff(7047,plain,
% 6.99/7.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.99/7.25 inference(rewrite,[status(thm)],[])).
% 6.99/7.25 tff(7048,plain,
% 6.99/7.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 6.99/7.25 inference(quant_inst,[status(thm)],[])).
% 6.99/7.25 tff(7049,plain,
% 6.99/7.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 6.99/7.25 inference(modus_ponens,[status(thm)],[7048, 7047])).
% 6.99/7.25 tff(7050,plain,
% 6.99/7.25 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[7049, 194, 7022, 847, 2112])).
% 6.99/7.25 tff(7051,plain,
% 6.99/7.25 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[3469, 391, 7024, 7016, 7014])).
% 6.99/7.25 tff(7052,plain,
% 6.99/7.25 (s(s(s(s(z)))) = s(s(elem!1))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[2003, 42, 7051, 7050])).
% 6.99/7.25 tff(7053,plain,
% 6.99/7.25 (elem!1 = s(s(z))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[1407, 7052])).
% 6.99/7.25 tff(7054,plain,
% 6.99/7.25 (b(z, elem!1) <=> b(z, s(s(z)))),
% 6.99/7.25 inference(monotonicity,[status(thm)],[7053])).
% 6.99/7.25 tff(7055,plain,
% 6.99/7.25 (b(z, s(s(z)))),
% 6.99/7.25 inference(modus_ponens,[status(thm)],[133, 7054])).
% 6.99/7.25 tff(7056,plain,
% 6.99/7.25 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 6.99/7.25 inference(symmetry,[status(thm)],[7040])).
% 6.99/7.25 tff(7057,plain,
% 6.99/7.25 (s(s(s(z))) = s(elem!1)),
% 6.99/7.25 inference(transitivity,[status(thm)],[693, 7056, 259])).
% 6.99/7.25 tff(7058,plain,
% 6.99/7.25 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 6.99/7.25 inference(monotonicity,[status(thm)],[7057])).
% 6.99/7.25 tff(7059,plain,
% 6.99/7.25 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 6.99/7.25 inference(symmetry,[status(thm)],[7058])).
% 6.99/7.25 tff(7060,plain,
% 6.99/7.25 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 6.99/7.25 inference(monotonicity,[status(thm)],[7039])).
% 6.99/7.25 tff(7061,plain,
% 6.99/7.25 (~(s(s(elem!1)) = s(elem!1))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[2279, 7017])).
% 6.99/7.25 tff(7062,plain,
% 6.99/7.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 6.99/7.25 inference(rewrite,[status(thm)],[])).
% 6.99/7.25 tff(7063,plain,
% 6.99/7.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 6.99/7.25 inference(quant_inst,[status(thm)],[])).
% 6.99/7.25 tff(7064,plain,
% 6.99/7.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 6.99/7.25 inference(modus_ponens,[status(thm)],[7063, 7062])).
% 6.99/7.25 tff(7065,plain,
% 6.99/7.25 (~r(s(s(elem!1)), s(elem!1))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[7064, 194, 485, 7022, 847])).
% 6.99/7.25 tff(7066,plain,
% 6.99/7.25 (b(s(s(elem!1)), s(elem!1))),
% 6.99/7.25 inference(unit_resolution,[status(thm)],[1135, 7065, 7061])).
% 6.99/7.25 tff(7067,plain,
% 6.99/7.25 (b(s(s(s(s(z)))), s(elem!1))),
% 6.99/7.25 inference(modus_ponens,[status(thm)],[7066, 7060])).
% 6.99/7.25 tff(7068,plain,
% 6.99/7.25 (b(s(s(s(s(z)))), s(s(s(z))))),
% 6.99/7.25 inference(modus_ponens,[status(thm)],[7067, 7059])).
% 6.99/7.25 tff(7069,plain,
% 6.99/7.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), 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))) | (~b(z, s(s(z)))))),
% 6.99/7.26 inference(rewrite,[status(thm)],[])).
% 6.99/7.26 tff(7070,plain,
% 6.99/7.26 (((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(z), 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))) | (~b(z, s(s(z)))))),
% 6.99/7.26 inference(rewrite,[status(thm)],[])).
% 6.99/7.26 tff(7071,plain,
% 6.99/7.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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))) | (~b(z, s(s(z))))))),
% 6.99/7.26 inference(monotonicity,[status(thm)],[7070])).
% 6.99/7.26 tff(7072,plain,
% 6.99/7.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), 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))) | (~b(z, s(s(z)))))),
% 6.99/7.26 inference(transitivity,[status(thm)],[7071, 7069])).
% 6.99/7.26 tff(7073,plain,
% 6.99/7.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 6.99/7.26 inference(quant_inst,[status(thm)],[])).
% 6.99/7.26 tff(7074,plain,
% 6.99/7.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z))))),
% 6.99/7.26 inference(modus_ponens,[status(thm)],[7073, 7072])).
% 6.99/7.26 tff(7075,plain,
% 6.99/7.26 ($false),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[7074, 391, 7014, 590, 7068, 7055, 7046])).
% 6.99/7.26 tff(7076,plain,((~r(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (s(z) = s(elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.26 tff(7077,plain,
% 6.99/7.26 (~r(s(elem!1), elem!1)),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[7076, 7004, 133, 121, 847, 590, 1484, 448, 900, 7009, 7008])).
% 6.99/7.26 tff(7078,plain,
% 6.99/7.26 (b(s(elem!1), elem!1)),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[2168, 7077, 164])).
% 6.99/7.26 tff(7079,plain,
% 6.99/7.26 (~b(s(s(s(elem!1))), s(elem!1))),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[6869, 7078, 900, 448])).
% 6.99/7.26 tff(7080,plain,
% 6.99/7.26 (~b(z, s(elem!1))),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[6555, 7078, 133, 665])).
% 6.99/7.26 tff(7081,plain,
% 6.99/7.26 (r(z, s(elem!1))),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[566, 7080])).
% 6.99/7.26 tff(7082,plain,
% 6.99/7.26 (s(s(s(elem!1))) = s(elem!1)),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[6897, 7081, 7077, 7079, 6509, 448, 900])).
% 6.99/7.26 tff(7083,plain,
% 6.99/7.26 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 6.99/7.26 inference(monotonicity,[status(thm)],[7082])).
% 6.99/7.26 tff(7084,plain,
% 6.99/7.26 (b(s(elem!1), s(s(s(s(z)))))),
% 6.99/7.26 inference(modus_ponens,[status(thm)],[1669, 7083])).
% 6.99/7.26 tff(7085,plain,
% 6.99/7.26 (~r(s(s(s(s(z)))), s(z))),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[7012, 194, 1484, 847, 7004])).
% 6.99/7.26 tff(7086,plain,
% 6.99/7.26 (b(s(s(s(s(z)))), s(z))),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[749, 7085])).
% 6.99/7.26 tff(7087,plain,
% 6.99/7.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.99/7.26 inference(rewrite,[status(thm)],[])).
% 6.99/7.26 tff(7088,plain,
% 6.99/7.26 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.99/7.26 inference(rewrite,[status(thm)],[])).
% 6.99/7.26 tff(7089,plain,
% 6.99/7.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 6.99/7.26 inference(monotonicity,[status(thm)],[7088])).
% 6.99/7.26 tff(7090,plain,
% 6.99/7.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 6.99/7.26 inference(transitivity,[status(thm)],[7089, 7087])).
% 6.99/7.26 tff(7091,plain,
% 6.99/7.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 6.99/7.26 inference(quant_inst,[status(thm)],[])).
% 6.99/7.26 tff(7092,plain,
% 6.99/7.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 6.99/7.26 inference(modus_ponens,[status(thm)],[7091, 7090])).
% 6.99/7.26 tff(7093,plain,
% 6.99/7.26 (~b(elem!1, s(s(s(s(z)))))),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[7092, 391, 665, 900, 448, 3325])).
% 6.99/7.26 tff(7094,plain,
% 6.99/7.26 (r(elem!1, s(s(s(s(z)))))),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[781, 770, 7093])).
% 6.99/7.26 tff(7095,plain,
% 6.99/7.26 (~r(z, s(z))),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[5980, 7008, 184, 6509])).
% 6.99/7.26 tff(7096,plain,
% 6.99/7.26 (b(z, s(z))),
% 6.99/7.26 inference(unit_resolution,[status(thm)],[678, 7095])).
% 6.99/7.26 tff(7097,plain,
% 6.99/7.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.99/7.26 inference(rewrite,[status(thm)],[])).
% 6.99/7.26 tff(7098,plain,
% 6.99/7.26 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.99/7.26 inference(rewrite,[status(thm)],[])).
% 6.99/7.26 tff(7099,plain,
% 6.99/7.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 6.99/7.27 inference(monotonicity,[status(thm)],[7098])).
% 6.99/7.27 tff(7100,plain,
% 6.99/7.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 6.99/7.27 inference(transitivity,[status(thm)],[7099, 7097])).
% 6.99/7.27 tff(7101,plain,
% 6.99/7.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 6.99/7.27 inference(quant_inst,[status(thm)],[])).
% 6.99/7.27 tff(7102,plain,
% 6.99/7.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 6.99/7.27 inference(modus_ponens,[status(thm)],[7101, 7100])).
% 6.99/7.27 tff(7103,plain,
% 6.99/7.27 (~b(z, s(s(s(s(z)))))),
% 6.99/7.27 inference(unit_resolution,[status(thm)],[7102, 391, 7006, 7086, 7096])).
% 6.99/7.27 tff(7104,plain,
% 6.99/7.27 (r(z, s(s(s(s(z)))))),
% 6.99/7.27 inference(unit_resolution,[status(thm)],[800, 7103])).
% 6.99/7.27 tff(7105,plain,
% 6.99/7.27 (~(s(s(z)) = elem!1)),
% 6.99/7.27 inference(unit_resolution,[status(thm)],[4584, 7082, 121])).
% 6.99/7.27 tff(7106,plain,
% 6.99/7.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 6.99/7.27 inference(rewrite,[status(thm)],[])).
% 6.99/7.27 tff(7107,plain,
% 6.99/7.27 (((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 6.99/7.27 inference(rewrite,[status(thm)],[])).
% 6.99/7.27 tff(7108,plain,
% 6.99/7.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))))),
% 6.99/7.27 inference(monotonicity,[status(thm)],[7107])).
% 6.99/7.27 tff(7109,plain,
% 6.99/7.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 6.99/7.27 inference(transitivity,[status(thm)],[7108, 7106])).
% 6.99/7.27 tff(7110,plain,
% 6.99/7.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 6.99/7.27 inference(quant_inst,[status(thm)],[])).
% 6.99/7.27 tff(7111,plain,
% 6.99/7.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))),
% 6.99/7.27 inference(modus_ponens,[status(thm)],[7110, 7109])).
% 6.99/7.27 tff(7112,plain,
% 6.99/7.27 (~r(s(s(z)), elem!1)),
% 6.99/7.27 inference(unit_resolution,[status(thm)],[7111, 194, 1749, 2053, 2032])).
% 6.99/7.27 tff(7113,plain,
% 6.99/7.27 (b(s(s(z)), elem!1)),
% 6.99/7.27 inference(unit_resolution,[status(thm)],[4730, 7112, 5547])).
% 6.99/7.27 tff(7114,plain,
% 6.99/7.27 (~r(s(s(z)), z)),
% 6.99/7.27 inference(unit_resolution,[status(thm)],[5608, 194, 1749, 2053, 719])).
% 6.99/7.27 tff(7115,plain,
% 6.99/7.27 (b(s(s(z)), z)),
% 6.99/7.27 inference(unit_resolution,[status(thm)],[1211, 7114])).
% 6.99/7.27 tff(7116,plain,
% 6.99/7.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 6.99/7.27 inference(rewrite,[status(thm)],[])).
% 6.99/7.27 tff(7117,plain,
% 6.99/7.27 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 6.99/7.27 inference(rewrite,[status(thm)],[])).
% 6.99/7.27 tff(7118,plain,
% 6.99/7.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 6.99/7.27 inference(monotonicity,[status(thm)],[7117])).
% 6.99/7.27 tff(7119,plain,
% 6.99/7.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 6.99/7.27 inference(transitivity,[status(thm)],[7118, 7116])).
% 6.99/7.27 tff(7120,plain,
% 6.99/7.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 6.99/7.27 inference(quant_inst,[status(thm)],[])).
% 6.99/7.27 tff(7121,plain,
% 6.99/7.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 6.99/7.27 inference(modus_ponens,[status(thm)],[7120, 7119])).
% 6.99/7.27 tff(7122,plain,
% 6.99/7.27 ($false),
% 6.99/7.27 inference(unit_resolution,[status(thm)],[7121, 391, 133, 665, 7115, 7113])).
% 6.99/7.27 tff(7123,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.27 tff(7124,plain,
% 6.99/7.27 (~r(s(s(z)), s(s(s(s(z)))))),
% 6.99/7.27 inference(unit_resolution,[status(thm)],[7123, 7105, 665, 133, 2053, 7104, 7094])).
% 6.99/7.27 tff(7125,plain,
% 6.99/7.27 (b(s(s(z)), s(s(s(s(z)))))),
% 6.99/7.27 inference(unit_resolution,[status(thm)],[3652, 7124])).
% 6.99/7.27 tff(7126,plain,
% 6.99/7.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.99/7.28 inference(rewrite,[status(thm)],[])).
% 6.99/7.28 tff(7127,plain,
% 6.99/7.28 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.99/7.28 inference(rewrite,[status(thm)],[])).
% 6.99/7.28 tff(7128,plain,
% 6.99/7.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))))),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7127])).
% 6.99/7.28 tff(7129,plain,
% 6.99/7.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.99/7.28 inference(transitivity,[status(thm)],[7128, 7126])).
% 6.99/7.28 tff(7130,plain,
% 6.99/7.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 6.99/7.28 inference(quant_inst,[status(thm)],[])).
% 6.99/7.28 tff(7131,plain,
% 6.99/7.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))),
% 6.99/7.28 inference(modus_ponens,[status(thm)],[7130, 7129])).
% 6.99/7.28 tff(7132,plain,
% 6.99/7.28 (~b(s(s(z)), s(elem!1))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[7131, 391, 7125, 7006, 7086, 7084])).
% 6.99/7.28 tff(7133,plain,
% 6.99/7.28 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7082])).
% 6.99/7.28 tff(7134,plain,
% 6.99/7.28 (r(s(elem!1), s(z))),
% 6.99/7.28 inference(modus_ponens,[status(thm)],[183, 7133])).
% 6.99/7.28 tff(7135,plain,
% 6.99/7.28 (~b(s(s(z)), s(z))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[5108, 7125, 7006, 7086])).
% 6.99/7.28 tff(7136,plain,
% 6.99/7.28 (r(s(s(z)), s(z))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[3778, 7135])).
% 6.99/7.28 tff(7137,plain,
% 6.99/7.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 6.99/7.28 inference(rewrite,[status(thm)],[])).
% 6.99/7.28 tff(7138,plain,
% 6.99/7.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 6.99/7.28 inference(quant_inst,[status(thm)],[])).
% 6.99/7.28 tff(7139,plain,
% 6.99/7.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1)))),
% 6.99/7.28 inference(modus_ponens,[status(thm)],[7138, 7137])).
% 6.99/7.28 tff(7140,plain,
% 6.99/7.28 (~r(s(s(z)), s(elem!1))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[7139, 194, 1484, 7136, 7134])).
% 6.99/7.28 tff(7141,plain,
% 6.99/7.28 (~(s(s(z)) = s(elem!1))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[2493, 7082])).
% 6.99/7.28 tff(7142,plain,
% 6.99/7.28 ($false),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[4693, 42, 7141, 7140, 7132])).
% 6.99/7.28 tff(7143,plain,((s(s(s(s(z)))) = elem!1) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (s(z) = s(elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.28 tff(7144,plain,
% 6.99/7.28 (~b(elem!1, s(s(s(elem!1))))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[7143, 6996, 665, 133, 3447, 6959, 1484, 121, 6967, 900, 164, 847, 590, 184, 6961])).
% 6.99/7.28 tff(7145,plain,
% 6.99/7.28 ($false),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[424, 7144, 6988, 1])).
% 6.99/7.28 tff(7146,plain,(b(s(s(s(s(z)))), z) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(z), elem!1)) | (s(z) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.28 tff(7147,plain,
% 6.99/7.28 (b(s(s(s(s(z)))), z)),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[7146, 6506, 148, 149, 6947, 118, 5933, 159, 6949, 6945, 59, 3363])).
% 6.99/7.28 tff(7148,plain,
% 6.99/7.28 (s(s(s(s(z)))) = elem!1),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[5398, 90, 665, 133, 590, 5237, 5235])).
% 6.99/7.28 tff(7149,plain,
% 6.99/7.28 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[717, 7148])).
% 6.99/7.28 tff(7150,plain,
% 6.99/7.28 (~(s(s(elem!1)) = elem!1)),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[451, 7149])).
% 6.99/7.28 tff(7151,plain,
% 6.99/7.28 (~(s(s(elem!1)) = s(elem!1))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[2279, 7149])).
% 6.99/7.28 tff(7152,plain,
% 6.99/7.28 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[287, 7151])).
% 6.99/7.28 tff(7153,plain,
% 6.99/7.28 (~r(z, s(z))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[5980, 232, 184, 6509])).
% 6.99/7.28 tff(7154,plain,
% 6.99/7.28 (b(z, s(z))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[678, 7153])).
% 6.99/7.28 tff(7155,plain,
% 6.99/7.28 (s(s(s(s(z)))) = elem!1),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[5398, 90, 665, 133, 590, 1484, 847])).
% 6.99/7.28 tff(7156,plain,
% 6.99/7.28 (s(s(s(s(s(z))))) = s(elem!1)),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7155])).
% 6.99/7.28 tff(7157,plain,
% 6.99/7.28 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7156])).
% 6.99/7.28 tff(7158,plain,
% 6.99/7.28 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7157])).
% 6.99/7.28 tff(7159,plain,
% 6.99/7.28 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 6.99/7.28 inference(symmetry,[status(thm)],[7158])).
% 6.99/7.28 tff(7160,plain,
% 6.99/7.28 (~(s(s(s(elem!1))) = s(elem!1))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[717, 7155])).
% 6.99/7.28 tff(7161,plain,
% 6.99/7.28 (~(s(s(elem!1)) = elem!1)),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[451, 7160])).
% 6.99/7.28 tff(7162,plain,
% 6.99/7.28 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[281, 7160])).
% 6.99/7.28 tff(7163,plain,
% 6.99/7.28 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[5792, 232, 184, 6509])).
% 6.99/7.28 tff(7164,plain,
% 6.99/7.28 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[1356, 7163, 7162])).
% 6.99/7.28 tff(7165,plain,
% 6.99/7.28 (~b(s(s(elem!1)), elem!1)),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[6001, 7164, 448, 900])).
% 6.99/7.28 tff(7166,plain,
% 6.99/7.28 (r(s(s(elem!1)), elem!1)),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[872, 7165, 7161])).
% 6.99/7.28 tff(7167,plain,
% 6.99/7.28 (~r(s(s(elem!1)), s(z))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[1899, 7166, 1484, 847])).
% 6.99/7.28 tff(7168,plain,
% 6.99/7.28 (b(s(s(elem!1)), s(z))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[362, 7167])).
% 6.99/7.28 tff(7169,plain,
% 6.99/7.28 (b(s(s(s(s(s(s(z)))))), s(z))),
% 6.99/7.28 inference(modus_ponens,[status(thm)],[7168, 7159])).
% 6.99/7.28 tff(7170,plain,
% 6.99/7.28 (r(s(z), s(s(s(s(z))))) <=> r(s(z), elem!1)),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7155])).
% 6.99/7.28 tff(7171,plain,
% 6.99/7.28 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(z)))))),
% 6.99/7.28 inference(symmetry,[status(thm)],[7170])).
% 6.99/7.28 tff(7172,plain,
% 6.99/7.28 (r(s(z), s(s(s(s(z)))))),
% 6.99/7.28 inference(modus_ponens,[status(thm)],[1484, 7171])).
% 6.99/7.28 tff(7173,plain,
% 6.99/7.28 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7155])).
% 6.99/7.28 tff(7174,plain,
% 6.99/7.28 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 6.99/7.28 inference(symmetry,[status(thm)],[7173])).
% 6.99/7.28 tff(7175,plain,
% 6.99/7.28 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7157])).
% 6.99/7.28 tff(7176,plain,
% 6.99/7.28 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 6.99/7.28 inference(symmetry,[status(thm)],[7175])).
% 6.99/7.28 tff(7177,plain,
% 6.99/7.28 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 6.99/7.28 inference(transitivity,[status(thm)],[7176, 7174])).
% 6.99/7.28 tff(7178,plain,
% 6.99/7.28 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 6.99/7.28 inference(modus_ponens,[status(thm)],[7166, 7177])).
% 6.99/7.28 tff(7179,plain,
% 6.99/7.28 (r(s(s(s(s(z)))), s(z)) <=> r(elem!1, s(z))),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7155])).
% 6.99/7.28 tff(7180,plain,
% 6.99/7.28 (r(elem!1, s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 6.99/7.28 inference(symmetry,[status(thm)],[7179])).
% 6.99/7.28 tff(7181,plain,
% 6.99/7.28 (r(s(s(s(s(z)))), s(z))),
% 6.99/7.28 inference(modus_ponens,[status(thm)],[847, 7180])).
% 6.99/7.28 tff(7182,plain,
% 6.99/7.28 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(elem!1)))),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7155, 7157])).
% 6.99/7.28 tff(7183,plain,
% 6.99/7.28 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 6.99/7.28 inference(symmetry,[status(thm)],[7182])).
% 6.99/7.28 tff(7184,plain,
% 6.99/7.28 (~(elem!1 = s(s(elem!1)))),
% 6.99/7.28 inference(unit_resolution,[status(thm)],[1292, 7161])).
% 6.99/7.28 tff(7185,plain,
% 6.99/7.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 6.99/7.28 inference(rewrite,[status(thm)],[])).
% 6.99/7.28 tff(7186,plain,
% 6.99/7.28 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 6.99/7.28 inference(rewrite,[status(thm)],[])).
% 6.99/7.28 tff(7187,plain,
% 6.99/7.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))))),
% 6.99/7.28 inference(monotonicity,[status(thm)],[7186])).
% 6.99/7.28 tff(7188,plain,
% 6.99/7.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 6.99/7.28 inference(transitivity,[status(thm)],[7187, 7185])).
% 6.99/7.28 tff(7189,plain,
% 6.99/7.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 6.99/7.29 inference(quant_inst,[status(thm)],[])).
% 6.99/7.29 tff(7190,plain,
% 6.99/7.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))),
% 6.99/7.29 inference(modus_ponens,[status(thm)],[7189, 7188])).
% 6.99/7.29 tff(7191,plain,
% 6.99/7.29 (~b(elem!1, s(s(elem!1)))),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[7190, 391, 665, 900, 448, 7164])).
% 6.99/7.29 tff(7192,plain,
% 6.99/7.29 (r(elem!1, s(s(elem!1)))),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[1307, 7191, 7184])).
% 6.99/7.29 tff(7193,plain,
% 6.99/7.29 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 6.99/7.29 inference(modus_ponens,[status(thm)],[7192, 7183])).
% 6.99/7.29 tff(7194,plain,
% 6.99/7.29 (~r(s(s(z)), s(s(s(s(z)))))),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[6702, 7193, 7155, 7181, 1484, 847, 7178, 7172, 7169])).
% 6.99/7.29 tff(7195,plain,
% 6.99/7.29 (b(s(s(z)), s(s(s(s(z)))))),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[3652, 7194])).
% 6.99/7.29 tff(7196,plain,
% 6.99/7.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 6.99/7.29 inference(rewrite,[status(thm)],[])).
% 6.99/7.29 tff(7197,plain,
% 6.99/7.29 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 6.99/7.29 inference(rewrite,[status(thm)],[])).
% 6.99/7.29 tff(7198,plain,
% 6.99/7.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))))),
% 6.99/7.29 inference(monotonicity,[status(thm)],[7197])).
% 6.99/7.29 tff(7199,plain,
% 6.99/7.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 6.99/7.29 inference(transitivity,[status(thm)],[7198, 7196])).
% 6.99/7.29 tff(7200,plain,
% 6.99/7.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 6.99/7.29 inference(quant_inst,[status(thm)],[])).
% 6.99/7.29 tff(7201,plain,
% 6.99/7.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))),
% 6.99/7.29 inference(modus_ponens,[status(thm)],[7200, 7199])).
% 6.99/7.29 tff(7202,plain,
% 6.99/7.29 ($false),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[7201, 391, 3823, 90, 1235, 664, 590])).
% 6.99/7.29 tff(7203,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.29 tff(7204,plain,
% 6.99/7.29 (~b(s(s(z)), z)),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[7203, 7195, 590, 90, 7154])).
% 6.99/7.29 tff(7205,plain,
% 6.99/7.29 (r(s(s(z)), z)),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[1211, 7204])).
% 6.99/7.29 tff(7206,plain,
% 6.99/7.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 6.99/7.29 inference(rewrite,[status(thm)],[])).
% 6.99/7.29 tff(7207,plain,
% 6.99/7.29 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 6.99/7.29 inference(rewrite,[status(thm)],[])).
% 6.99/7.29 tff(7208,plain,
% 6.99/7.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 6.99/7.29 inference(monotonicity,[status(thm)],[7207])).
% 6.99/7.29 tff(7209,plain,
% 6.99/7.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 6.99/7.29 inference(transitivity,[status(thm)],[7208, 7206])).
% 6.99/7.29 tff(7210,plain,
% 6.99/7.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 6.99/7.29 inference(quant_inst,[status(thm)],[])).
% 6.99/7.29 tff(7211,plain,
% 6.99/7.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 6.99/7.29 inference(modus_ponens,[status(thm)],[7210, 7209])).
% 6.99/7.29 tff(7212,plain,
% 6.99/7.29 (~r(s(s(z)), s(s(s(elem!1))))),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[7211, 194, 6509, 184, 7205])).
% 6.99/7.29 tff(7213,plain,
% 6.99/7.29 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 6.99/7.29 inference(monotonicity,[status(thm)],[7155])).
% 6.99/7.29 tff(7214,plain,
% 6.99/7.29 (b(s(s(z)), elem!1)),
% 6.99/7.29 inference(modus_ponens,[status(thm)],[7195, 7213])).
% 6.99/7.29 tff(7215,plain,
% 6.99/7.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 6.99/7.29 inference(rewrite,[status(thm)],[])).
% 6.99/7.29 tff(7216,plain,
% 6.99/7.29 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 6.99/7.29 inference(rewrite,[status(thm)],[])).
% 6.99/7.29 tff(7217,plain,
% 6.99/7.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))))),
% 6.99/7.29 inference(monotonicity,[status(thm)],[7216])).
% 6.99/7.29 tff(7218,plain,
% 6.99/7.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 6.99/7.29 inference(transitivity,[status(thm)],[7217, 7215])).
% 6.99/7.29 tff(7219,plain,
% 6.99/7.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 6.99/7.29 inference(quant_inst,[status(thm)],[])).
% 6.99/7.29 tff(7220,plain,
% 6.99/7.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))),
% 6.99/7.29 inference(modus_ponens,[status(thm)],[7219, 7218])).
% 6.99/7.29 tff(7221,plain,
% 6.99/7.29 (~b(s(s(z)), s(s(s(elem!1))))),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[7220, 391, 133, 665, 900, 7214])).
% 6.99/7.29 tff(7222,plain,
% 6.99/7.29 ($false),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 7221, 7212])).
% 6.99/7.29 tff(7223,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 6.99/7.29 tff(7224,plain,
% 6.99/7.29 (~r(s(z), s(s(s(elem!1))))),
% 6.99/7.29 inference(unit_resolution,[status(thm)],[7223, 448, 133, 665, 900, 590, 90, 5237, 5235, 184])).
% 6.99/7.29 tff(7225,plain,
% 6.99/7.29 (b(s(z), s(s(s(elem!1))))),
% 6.99/7.30 inference(unit_resolution,[status(thm)],[247, 7224])).
% 6.99/7.30 tff(7226,plain,
% 6.99/7.30 (~b(s(elem!1), elem!1)),
% 6.99/7.30 inference(unit_resolution,[status(thm)],[5331, 7225, 665, 133, 6509, 590, 150, 5237, 7152, 7150, 7151])).
% 6.99/7.30 tff(7227,plain,
% 6.99/7.30 (r(s(elem!1), elem!1)),
% 6.99/7.30 inference(unit_resolution,[status(thm)],[2168, 7226, 164])).
% 6.99/7.30 tff(7228,plain,
% 6.99/7.30 (~r(s(elem!1), s(z))),
% 6.99/7.30 inference(unit_resolution,[status(thm)],[5339, 194, 7227, 5237, 5235])).
% 6.99/7.30 tff(7229,plain,
% 6.99/7.30 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 6.99/7.30 inference(unit_resolution,[status(thm)],[1915, 42, 7228])).
% 6.99/7.30 tff(7230,plain,
% 6.99/7.30 (b(s(elem!1), s(z))),
% 6.99/7.30 inference(unit_resolution,[status(thm)],[7229, 1905])).
% 6.99/7.30 tff(7231,plain,
% 6.99/7.30 (~r(s(z), s(elem!1))),
% 6.99/7.30 inference(unit_resolution,[status(thm)],[6849, 194, 7227, 5237, 5235])).
% 6.99/7.30 tff(7232,plain,
% 6.99/7.30 (b(s(z), s(elem!1))),
% 6.99/7.30 inference(unit_resolution,[status(thm)],[602, 42, 121, 7231])).
% 6.99/7.30 tff(7233,plain,
% 6.99/7.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.99/7.30 inference(rewrite,[status(thm)],[])).
% 6.99/7.30 tff(7234,plain,
% 6.99/7.30 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))) <=> ((~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 6.99/7.30 inference(rewrite,[status(thm)],[])).
% 6.99/7.30 tff(7235,plain,
% 6.99/7.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 7.09/7.30 inference(monotonicity,[status(thm)],[7234])).
% 7.09/7.30 tff(7236,plain,
% 7.09/7.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 7.09/7.30 inference(transitivity,[status(thm)],[7235, 7233])).
% 7.09/7.30 tff(7237,plain,
% 7.09/7.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 7.09/7.30 inference(quant_inst,[status(thm)],[])).
% 7.09/7.30 tff(7238,plain,
% 7.09/7.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 7.09/7.30 inference(modus_ponens,[status(thm)],[7237, 7236])).
% 7.09/7.30 tff(7239,plain,
% 7.09/7.30 ($false),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[7238, 391, 592, 379, 751, 590, 5469])).
% 7.09/7.30 tff(7240,plain,((~b(z, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.30 tff(7241,plain,
% 7.09/7.30 (~b(z, s(elem!1))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[7240, 7225, 7232, 590, 7230])).
% 7.09/7.30 tff(7242,plain,
% 7.09/7.30 (r(z, s(elem!1))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[566, 7241])).
% 7.09/7.30 tff(7243,plain,
% 7.09/7.30 (~r(z, s(s(elem!1)))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[2178, 2170, 2144, 485])).
% 7.09/7.30 tff(7244,plain,
% 7.09/7.30 (b(z, s(s(elem!1)))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[324, 7243])).
% 7.09/7.30 tff(7245,plain,
% 7.09/7.30 (~b(s(s(elem!1)), elem!1)),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[4944, 7244, 665, 133])).
% 7.09/7.30 tff(7246,plain,
% 7.09/7.30 (r(s(s(elem!1)), elem!1)),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[872, 7245, 249])).
% 7.09/7.30 tff(7247,plain,
% 7.09/7.30 ($false),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[7064, 194, 485, 7246, 2170, 847])).
% 7.09/7.30 tff(7248,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (s(s(elem!1)) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.30 tff(7249,plain,
% 7.09/7.30 (~r(s(s(elem!1)), s(elem!1))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[7248, 7227, 5235, 7150, 665, 133, 7242])).
% 7.09/7.30 tff(7250,plain,
% 7.09/7.30 (b(s(s(elem!1)), s(elem!1))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[1135, 7249, 7151])).
% 7.09/7.30 tff(7251,plain,
% 7.09/7.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 7.09/7.30 inference(rewrite,[status(thm)],[])).
% 7.09/7.30 tff(7252,plain,
% 7.09/7.30 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 7.09/7.30 inference(rewrite,[status(thm)],[])).
% 7.09/7.30 tff(7253,plain,
% 7.09/7.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 7.09/7.30 inference(monotonicity,[status(thm)],[7252])).
% 7.09/7.30 tff(7254,plain,
% 7.09/7.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 7.09/7.30 inference(transitivity,[status(thm)],[7253, 7251])).
% 7.09/7.30 tff(7255,plain,
% 7.09/7.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 7.09/7.30 inference(quant_inst,[status(thm)],[])).
% 7.09/7.30 tff(7256,plain,
% 7.09/7.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 7.09/7.30 inference(modus_ponens,[status(thm)],[7255, 7254])).
% 7.09/7.30 tff(7257,plain,
% 7.09/7.30 (~b(s(s(elem!1)), s(z))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[7256, 391, 7225, 7250, 7232, 7230])).
% 7.09/7.30 tff(7258,plain,
% 7.09/7.30 (r(s(s(elem!1)), s(z))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[362, 7257])).
% 7.09/7.30 tff(7259,plain,
% 7.09/7.30 (~r(s(s(elem!1)), elem!1)),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[1899, 7258, 5237, 5235])).
% 7.09/7.30 tff(7260,plain,
% 7.09/7.30 (~(elem!1 = s(s(elem!1)))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[1292, 7150])).
% 7.09/7.30 tff(7261,plain,
% 7.09/7.30 ((elem!1 = s(z)) | r(elem!1, s(z))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[835, 42, 31])).
% 7.09/7.30 tff(7262,plain,
% 7.09/7.30 (r(elem!1, s(z))),
% 7.09/7.30 inference(unit_resolution,[status(thm)],[7261, 1746])).
% 7.09/7.30 tff(7263,plain,
% 7.09/7.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 7.09/7.30 inference(rewrite,[status(thm)],[])).
% 7.09/7.30 tff(7264,plain,
% 7.09/7.30 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 7.09/7.30 inference(rewrite,[status(thm)],[])).
% 7.09/7.30 tff(7265,plain,
% 7.09/7.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))))),
% 7.09/7.30 inference(monotonicity,[status(thm)],[7264])).
% 7.09/7.30 tff(7266,plain,
% 7.09/7.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 7.09/7.30 inference(transitivity,[status(thm)],[7265, 7263])).
% 7.09/7.30 tff(7267,plain,
% 7.09/7.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 7.09/7.31 inference(quant_inst,[status(thm)],[])).
% 7.09/7.31 tff(7268,plain,
% 7.09/7.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))),
% 7.09/7.31 inference(modus_ponens,[status(thm)],[7267, 7266])).
% 7.09/7.31 tff(7269,plain,
% 7.09/7.31 (~r(elem!1, s(s(elem!1)))),
% 7.09/7.31 inference(unit_resolution,[status(thm)],[7268, 194, 340, 1484, 7262])).
% 7.09/7.31 tff(7270,plain,
% 7.09/7.31 (b(elem!1, s(s(elem!1)))),
% 7.09/7.31 inference(unit_resolution,[status(thm)],[1307, 7269, 1457])).
% 7.09/7.31 tff(7271,plain,
% 7.09/7.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.09/7.31 inference(rewrite,[status(thm)],[])).
% 7.09/7.31 tff(7272,plain,
% 7.09/7.31 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.09/7.31 inference(rewrite,[status(thm)],[])).
% 7.09/7.31 tff(7273,plain,
% 7.09/7.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 7.09/7.31 inference(monotonicity,[status(thm)],[7272])).
% 7.09/7.31 tff(7274,plain,
% 7.09/7.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.09/7.31 inference(transitivity,[status(thm)],[7273, 7271])).
% 7.09/7.31 tff(7275,plain,
% 7.09/7.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.09/7.31 inference(quant_inst,[status(thm)],[])).
% 7.09/7.31 tff(7276,plain,
% 7.09/7.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 7.09/7.31 inference(modus_ponens,[status(thm)],[7275, 7274])).
% 7.09/7.31 tff(7277,plain,
% 7.09/7.31 (~b(s(s(s(s(z)))), elem!1)),
% 7.09/7.31 inference(unit_resolution,[status(thm)],[7276, 391, 665, 973, 3927, 90])).
% 7.09/7.31 tff(7278,plain,
% 7.09/7.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 7.09/7.31 inference(rewrite,[status(thm)],[])).
% 7.09/7.31 tff(7279,plain,
% 7.09/7.31 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 7.09/7.31 inference(rewrite,[status(thm)],[])).
% 7.09/7.31 tff(7280,plain,
% 7.09/7.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 7.09/7.31 inference(monotonicity,[status(thm)],[7279])).
% 7.09/7.31 tff(7281,plain,
% 7.09/7.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 7.09/7.31 inference(transitivity,[status(thm)],[7280, 7278])).
% 7.09/7.31 tff(7282,plain,
% 7.09/7.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 7.09/7.31 inference(quant_inst,[status(thm)],[])).
% 7.09/7.31 tff(7283,plain,
% 7.09/7.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 7.09/7.31 inference(modus_ponens,[status(thm)],[7282, 7281])).
% 7.09/7.31 tff(7284,plain,
% 7.09/7.31 (~b(s(z), s(s(s(s(z)))))),
% 7.09/7.31 inference(unit_resolution,[status(thm)],[7283, 391, 973, 3927, 90, 590])).
% 7.09/7.31 tff(7285,plain,
% 7.09/7.31 (r(s(z), s(s(s(s(z)))))),
% 7.09/7.31 inference(unit_resolution,[status(thm)],[1230, 7284])).
% 7.09/7.31 tff(7286,plain,
% 7.09/7.31 (~r(s(s(s(s(z)))), elem!1)),
% 7.09/7.31 inference(unit_resolution,[status(thm)],[5396, 7262, 7285, 1484])).
% 7.09/7.31 tff(7287,plain,
% 7.09/7.31 (s(s(s(s(z)))) = elem!1),
% 7.09/7.31 inference(unit_resolution,[status(thm)],[762, 7286, 7277])).
% 7.09/7.31 tff(7288,plain,
% 7.09/7.31 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 7.09/7.31 inference(monotonicity,[status(thm)],[7287])).
% 7.09/7.31 tff(7289,plain,
% 7.09/7.31 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.09/7.31 inference(symmetry,[status(thm)],[7288])).
% 7.09/7.31 tff(7290,plain,
% 7.09/7.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 7.09/7.31 inference(rewrite,[status(thm)],[])).
% 7.09/7.31 tff(7291,plain,
% 7.09/7.31 (((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 7.09/7.31 inference(rewrite,[status(thm)],[])).
% 7.09/7.31 tff(7292,plain,
% 7.09/7.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 7.09/7.32 inference(monotonicity,[status(thm)],[7291])).
% 7.09/7.32 tff(7293,plain,
% 7.09/7.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 7.09/7.32 inference(transitivity,[status(thm)],[7292, 7290])).
% 7.09/7.32 tff(7294,plain,
% 7.09/7.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 7.09/7.32 inference(quant_inst,[status(thm)],[])).
% 7.09/7.32 tff(7295,plain,
% 7.09/7.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 7.09/7.32 inference(modus_ponens,[status(thm)],[7294, 7293])).
% 7.09/7.32 tff(7296,plain,
% 7.09/7.32 ($false),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[7295, 391, 665, 973, 3927, 1294])).
% 7.09/7.32 tff(7297,plain,((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.32 tff(7298,plain,
% 7.09/7.32 (~b(elem!1, s(s(elem!1)))),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[7297, 3927, 973, 665])).
% 7.09/7.32 tff(7299,plain,
% 7.09/7.32 (r(elem!1, s(s(elem!1)))),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[1307, 7298, 1457])).
% 7.09/7.32 tff(7300,plain,
% 7.09/7.32 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.09/7.32 inference(modus_ponens,[status(thm)],[7299, 7289])).
% 7.09/7.32 tff(7301,plain,
% 7.09/7.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 7.09/7.32 inference(rewrite,[status(thm)],[])).
% 7.09/7.32 tff(7302,plain,
% 7.09/7.32 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 7.09/7.32 inference(rewrite,[status(thm)],[])).
% 7.09/7.32 tff(7303,plain,
% 7.09/7.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 7.09/7.32 inference(monotonicity,[status(thm)],[7302])).
% 7.09/7.32 tff(7304,plain,
% 7.09/7.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 7.09/7.32 inference(transitivity,[status(thm)],[7303, 7301])).
% 7.09/7.32 tff(7305,plain,
% 7.09/7.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 7.09/7.32 inference(quant_inst,[status(thm)],[])).
% 7.09/7.32 tff(7306,plain,
% 7.09/7.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 7.09/7.32 inference(modus_ponens,[status(thm)],[7305, 7304])).
% 7.09/7.32 tff(7307,plain,
% 7.09/7.32 (~b(s(s(s(s(z)))), s(z))),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[7306, 391, 973, 3927, 90, 590])).
% 7.09/7.32 tff(7308,plain,
% 7.09/7.32 (r(s(s(s(s(z)))), s(z))),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[749, 7307])).
% 7.09/7.32 tff(7309,plain,
% 7.09/7.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.09/7.32 inference(rewrite,[status(thm)],[])).
% 7.09/7.32 tff(7310,plain,
% 7.09/7.32 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.09/7.32 inference(rewrite,[status(thm)],[])).
% 7.09/7.32 tff(7311,plain,
% 7.09/7.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 7.09/7.32 inference(monotonicity,[status(thm)],[7310])).
% 7.09/7.32 tff(7312,plain,
% 7.09/7.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.09/7.32 inference(transitivity,[status(thm)],[7311, 7309])).
% 7.09/7.32 tff(7313,plain,
% 7.09/7.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.09/7.32 inference(quant_inst,[status(thm)],[])).
% 7.09/7.32 tff(7314,plain,
% 7.09/7.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 7.09/7.32 inference(modus_ponens,[status(thm)],[7313, 7312])).
% 7.09/7.32 tff(7315,plain,
% 7.09/7.32 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[7314, 194, 340, 7285, 7308])).
% 7.09/7.32 tff(7316,plain,
% 7.09/7.32 ($false),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[7315, 7300])).
% 7.09/7.32 tff(7317,plain,((~b(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | b(elem!1, s(z)) | (s(z) = elem!1) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.32 tff(7318,plain,
% 7.09/7.32 (~b(z, s(s(elem!1)))),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[7317, 31, 1484, 150, 340, 973, 90, 590, 665, 1457])).
% 7.09/7.32 tff(7319,plain,
% 7.09/7.32 (r(z, s(s(elem!1)))),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[324, 7318])).
% 7.09/7.32 tff(7320,plain,
% 7.09/7.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 7.09/7.32 inference(rewrite,[status(thm)],[])).
% 7.09/7.32 tff(7321,plain,
% 7.09/7.32 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 7.09/7.32 inference(rewrite,[status(thm)],[])).
% 7.09/7.32 tff(7322,plain,
% 7.09/7.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 7.09/7.32 inference(monotonicity,[status(thm)],[7321])).
% 7.09/7.32 tff(7323,plain,
% 7.09/7.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 7.09/7.32 inference(transitivity,[status(thm)],[7322, 7320])).
% 7.09/7.32 tff(7324,plain,
% 7.09/7.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 7.09/7.32 inference(quant_inst,[status(thm)],[])).
% 7.09/7.32 tff(7325,plain,
% 7.09/7.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 7.09/7.32 inference(modus_ponens,[status(thm)],[7324, 7323])).
% 7.09/7.32 tff(7326,plain,
% 7.09/7.32 ($false),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[7325, 194, 340, 174, 327, 326])).
% 7.09/7.32 tff(7327,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.32 tff(7328,plain,
% 7.09/7.32 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[7327, 7319, 174, 340])).
% 7.09/7.32 tff(7329,plain,
% 7.09/7.32 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.09/7.32 inference(unit_resolution,[status(thm)],[1370, 7328, 297])).
% 7.09/7.32 tff(7330,plain,
% 7.09/7.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.09/7.32 inference(rewrite,[status(thm)],[])).
% 7.09/7.32 tff(7331,plain,
% 7.09/7.32 (((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.09/7.32 inference(rewrite,[status(thm)],[])).
% 7.09/7.32 tff(7332,plain,
% 7.09/7.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 7.09/7.33 inference(monotonicity,[status(thm)],[7331])).
% 7.09/7.33 tff(7333,plain,
% 7.09/7.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.09/7.33 inference(transitivity,[status(thm)],[7332, 7330])).
% 7.09/7.33 tff(7334,plain,
% 7.09/7.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 7.09/7.33 inference(quant_inst,[status(thm)],[])).
% 7.09/7.33 tff(7335,plain,
% 7.09/7.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 7.09/7.33 inference(modus_ponens,[status(thm)],[7334, 7333])).
% 7.09/7.33 tff(7336,plain,
% 7.09/7.33 ($false),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[7335, 391, 665, 973, 448, 7329, 7270])).
% 7.09/7.33 tff(7337,plain,(b(elem!1, s(z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (s(z) = elem!1) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.33 tff(7338,plain,
% 7.09/7.33 (~b(s(s(elem!1)), elem!1)),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[7337, 7258, 665, 5234, 7260, 448, 5237, 150, 7152, 6509, 90, 590])).
% 7.09/7.33 tff(7339,plain,
% 7.09/7.33 ($false),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[872, 7338, 7259, 7150])).
% 7.09/7.33 tff(7340,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (s(z) = s(elem!1)) | (s(elem!1) = elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.33 tff(7341,plain,
% 7.09/7.33 (~b(elem!1, s(s(s(elem!1))))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[7340, 6506, 150, 7147, 6945, 149, 118, 159, 5933, 59])).
% 7.09/7.33 tff(7342,plain,
% 7.09/7.33 (r(elem!1, s(s(s(elem!1))))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[424, 7341, 148])).
% 7.09/7.33 tff(7343,plain,
% 7.09/7.33 (s(s(s(s(z)))) = elem!1),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[5398, 7147, 6506, 149, 6945, 6947, 6949])).
% 7.09/7.33 tff(7344,plain,
% 7.09/7.33 (~(s(s(s(elem!1))) = s(elem!1))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[717, 7343])).
% 7.09/7.33 tff(7345,plain,
% 7.09/7.33 (~(s(s(elem!1)) = s(elem!1))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[2279, 7344])).
% 7.09/7.33 tff(7346,plain,
% 7.09/7.33 (~(s(s(elem!1)) = elem!1)),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[451, 7344])).
% 7.09/7.33 tff(7347,plain,
% 7.09/7.33 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[287, 7345])).
% 7.09/7.33 tff(7348,plain,
% 7.09/7.33 (~b(s(s(s(elem!1))), z)),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[5769, 391, 149, 6506, 5933])).
% 7.09/7.33 tff(7349,plain,
% 7.09/7.33 (r(s(s(s(elem!1))), z)),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[377, 7348])).
% 7.09/7.33 tff(7350,plain,
% 7.09/7.33 (~r(s(z), s(s(s(elem!1))))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[5645, 7342, 7349, 6947])).
% 7.09/7.33 tff(7351,plain,
% 7.09/7.33 (b(s(z), s(s(s(elem!1))))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[247, 7350])).
% 7.09/7.33 tff(7352,plain,
% 7.09/7.33 (~b(s(elem!1), elem!1)),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[5331, 7351, 6506, 149, 7349, 6945, 150, 6947, 7347, 7346, 7345])).
% 7.09/7.33 tff(7353,plain,
% 7.09/7.33 (r(s(elem!1), elem!1)),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[2168, 7352, 159])).
% 7.09/7.33 tff(7354,plain,
% 7.09/7.33 (~r(s(z), s(elem!1))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[5446, 194, 7353, 7342, 6947])).
% 7.09/7.33 tff(7355,plain,
% 7.09/7.33 (b(s(z), s(elem!1))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[602, 42, 118, 7354])).
% 7.09/7.33 tff(7356,plain,
% 7.09/7.33 (~(s(elem!1) = s(z))),
% 7.09/7.33 inference(modus_ponens,[status(thm)],[118, 1904])).
% 7.09/7.33 tff(7357,plain,
% 7.09/7.33 (~r(s(elem!1), s(z))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[5465, 194, 7353, 7342, 6947])).
% 7.09/7.33 tff(7358,plain,
% 7.09/7.33 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[1915, 42, 7357])).
% 7.09/7.33 tff(7359,plain,
% 7.09/7.33 (b(s(elem!1), s(z))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[7358, 7356])).
% 7.09/7.33 tff(7360,plain,
% 7.09/7.33 (~b(z, s(elem!1))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[7240, 7359, 7351, 6945, 7355])).
% 7.09/7.33 tff(7361,plain,
% 7.09/7.33 (r(z, s(elem!1))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[566, 7360])).
% 7.09/7.33 tff(7362,plain,
% 7.09/7.33 (~r(elem!1, z)),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[6121, 7349, 149, 5933, 59, 150, 148])).
% 7.09/7.33 tff(7363,plain,
% 7.09/7.33 (r(s(elem!1), elem!1)),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[2168, 5437, 2163])).
% 7.09/7.33 tff(7364,plain,
% 7.09/7.33 (~r(s(elem!1), s(z))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[5465, 194, 7363, 5440, 5429])).
% 7.09/7.33 tff(7365,plain,
% 7.09/7.33 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[1915, 42, 7364])).
% 7.09/7.33 tff(7366,plain,
% 7.09/7.33 (b(s(elem!1), s(z))),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[7365, 5459])).
% 7.09/7.33 tff(7367,plain,
% 7.09/7.33 (~r(s(elem!1), z)),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[5834, 10, 80, 175, 2282, 150, 2829, 7363, 4028, 174])).
% 7.09/7.33 tff(7368,plain,
% 7.09/7.33 (b(s(elem!1), z)),
% 7.09/7.33 inference(unit_resolution,[status(thm)],[549, 7367])).
% 7.09/7.33 tff(7369,plain,
% 7.09/7.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 7.09/7.33 inference(rewrite,[status(thm)],[])).
% 7.09/7.33 tff(7370,plain,
% 7.09/7.33 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 7.09/7.33 inference(rewrite,[status(thm)],[])).
% 7.09/7.33 tff(7371,plain,
% 7.09/7.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 7.09/7.33 inference(monotonicity,[status(thm)],[7370])).
% 7.09/7.33 tff(7372,plain,
% 7.09/7.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 7.09/7.33 inference(transitivity,[status(thm)],[7371, 7369])).
% 7.09/7.33 tff(7373,plain,
% 7.09/7.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 7.09/7.33 inference(quant_inst,[status(thm)],[])).
% 7.09/7.33 tff(7374,plain,
% 7.09/7.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 7.09/7.34 inference(modus_ponens,[status(thm)],[7373, 7372])).
% 7.09/7.34 tff(7375,plain,
% 7.09/7.34 ($false),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[7374, 391, 5435, 5455, 7368, 5450, 7366])).
% 7.09/7.34 tff(7376,plain,(b(z, s(s(s(elem!1)))) | r(z, elem!1) | r(s(z), z) | r(elem!1, z) | (s(z) = elem!1) | b(s(z), elem!1) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.09/7.34 tff(7377,plain,
% 7.09/7.34 (r(s(z), z)),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[7376, 7352, 10, 7349, 150, 7362, 80, 6946, 7341])).
% 7.09/7.34 tff(7378,plain,
% 7.09/7.34 (~r(s(s(s(elem!1))), s(z))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[202, 7377, 59, 7349])).
% 7.09/7.34 tff(7379,plain,
% 7.09/7.34 (b(s(s(s(elem!1))), s(z))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[223, 7378])).
% 7.09/7.34 tff(7380,plain,
% 7.09/7.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 7.09/7.34 inference(rewrite,[status(thm)],[])).
% 7.09/7.34 tff(7381,plain,
% 7.09/7.34 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(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))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 7.09/7.34 inference(rewrite,[status(thm)],[])).
% 7.09/7.34 tff(7382,plain,
% 7.09/7.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 7.09/7.34 inference(monotonicity,[status(thm)],[7381])).
% 7.09/7.34 tff(7383,plain,
% 7.09/7.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 7.09/7.34 inference(transitivity,[status(thm)],[7382, 7380])).
% 7.09/7.34 tff(7384,plain,
% 7.09/7.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 7.09/7.34 inference(quant_inst,[status(thm)],[])).
% 7.09/7.34 tff(7385,plain,
% 7.09/7.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 7.09/7.34 inference(modus_ponens,[status(thm)],[7384, 7383])).
% 7.09/7.34 tff(7386,plain,
% 7.09/7.34 (~b(s(s(s(elem!1))), s(elem!1))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[7385, 391, 5933, 7351, 7379, 7359])).
% 7.09/7.34 tff(7387,plain,
% 7.09/7.34 (r(s(s(s(elem!1))), s(elem!1))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[588, 7386, 7344])).
% 7.09/7.34 tff(7388,plain,
% 7.09/7.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 7.09/7.34 inference(rewrite,[status(thm)],[])).
% 7.09/7.34 tff(7389,plain,
% 7.09/7.34 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 7.09/7.34 inference(rewrite,[status(thm)],[])).
% 7.09/7.34 tff(7390,plain,
% 7.09/7.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 7.09/7.34 inference(monotonicity,[status(thm)],[7389])).
% 7.09/7.34 tff(7391,plain,
% 7.09/7.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 7.09/7.34 inference(transitivity,[status(thm)],[7390, 7388])).
% 7.09/7.34 tff(7392,plain,
% 7.09/7.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 7.09/7.34 inference(quant_inst,[status(thm)],[])).
% 7.09/7.34 tff(7393,plain,
% 7.09/7.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))),
% 7.09/7.34 inference(modus_ponens,[status(thm)],[7392, 7391])).
% 7.09/7.34 tff(7394,plain,
% 7.09/7.34 ($false),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[7393, 194, 7387, 7353, 7349, 7361])).
% 7.09/7.34 tff(7395,plain,((s(z) = elem!1) | b(z, s(s(s(elem!1)))) | r(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 7.09/7.34 tff(7396,plain,
% 7.09/7.34 (s(z) = elem!1),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[7395, 10, 80, 2])).
% 7.09/7.34 tff(7397,plain,
% 7.09/7.34 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 7.09/7.34 inference(monotonicity,[status(thm)],[818])).
% 7.09/7.34 tff(7398,plain,
% 7.09/7.34 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 7.09/7.34 inference(monotonicity,[status(thm)],[812])).
% 7.09/7.34 tff(7399,plain,
% 7.09/7.34 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 7.09/7.34 inference(transitivity,[status(thm)],[7398, 7397])).
% 7.09/7.34 tff(7400,plain,
% 7.09/7.34 (b(z, s(z)) <=> b(z, elem!1)),
% 7.09/7.34 inference(monotonicity,[status(thm)],[812])).
% 7.09/7.34 tff(7401,plain,
% 7.09/7.34 (b(z, elem!1) <=> b(z, s(z))),
% 7.09/7.34 inference(symmetry,[status(thm)],[7400])).
% 7.09/7.34 tff(7402,plain,
% 7.09/7.34 (b(z, s(z))),
% 7.09/7.34 inference(modus_ponens,[status(thm)],[133, 7401])).
% 7.09/7.34 tff(7403,plain,
% 7.09/7.34 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 7.09/7.34 inference(monotonicity,[status(thm)],[812])).
% 7.09/7.34 tff(7404,plain,
% 7.09/7.34 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 7.09/7.34 inference(symmetry,[status(thm)],[7403])).
% 7.09/7.34 tff(7405,plain,
% 7.09/7.34 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 7.09/7.34 inference(monotonicity,[status(thm)],[820])).
% 7.09/7.34 tff(7406,plain,
% 7.09/7.34 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(z)))))),
% 7.09/7.34 inference(symmetry,[status(thm)],[7405])).
% 7.09/7.34 tff(7407,plain,
% 7.09/7.34 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 7.09/7.34 inference(transitivity,[status(thm)],[7406, 7404])).
% 7.09/7.34 tff(7408,plain,
% 7.09/7.34 (~b(s(s(s(elem!1))), s(z))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[3938, 168, 812])).
% 7.09/7.34 tff(7409,plain,
% 7.09/7.34 (r(s(s(s(elem!1))), s(z))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[223, 7408])).
% 7.09/7.34 tff(7410,plain,
% 7.09/7.34 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 7.09/7.34 inference(monotonicity,[status(thm)],[818])).
% 7.09/7.34 tff(7411,plain,
% 7.09/7.34 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 7.09/7.34 inference(monotonicity,[status(thm)],[7410])).
% 7.09/7.34 tff(7412,plain,
% 7.09/7.34 (~(s(s(elem!1)) = s(elem!1))),
% 7.09/7.34 inference(modus_ponens,[status(thm)],[2680, 7411])).
% 7.09/7.34 tff(7413,plain,
% 7.09/7.34 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[287, 7412])).
% 7.09/7.34 tff(7414,plain,
% 7.09/7.34 (b(s(z), z) <=> b(elem!1, z)),
% 7.09/7.34 inference(monotonicity,[status(thm)],[812])).
% 7.09/7.34 tff(7415,plain,
% 7.09/7.34 (b(elem!1, z) <=> b(s(z), z)),
% 7.09/7.34 inference(symmetry,[status(thm)],[7414])).
% 7.09/7.34 tff(7416,plain,
% 7.09/7.34 ((~b(elem!1, z)) <=> (~b(s(z), z))),
% 7.09/7.34 inference(monotonicity,[status(thm)],[7415])).
% 7.09/7.34 tff(7417,plain,
% 7.09/7.34 (~b(s(z), z)),
% 7.09/7.34 inference(modus_ponens,[status(thm)],[484, 7416])).
% 7.09/7.34 tff(7418,plain,
% 7.09/7.34 (~r(elem!1, s(s(s(elem!1))))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[4772, 3618, 233, 59])).
% 7.09/7.34 tff(7419,plain,
% 7.09/7.34 (b(elem!1, s(s(s(elem!1))))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[424, 7418, 1])).
% 7.09/7.34 tff(7420,plain,
% 7.09/7.34 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 7.09/7.34 inference(monotonicity,[status(thm)],[812])).
% 7.09/7.34 tff(7421,plain,
% 7.09/7.34 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 7.09/7.34 inference(monotonicity,[status(thm)],[7420])).
% 7.09/7.34 tff(7422,plain,
% 7.09/7.34 (~(s(s(elem!1)) = elem!1)),
% 7.09/7.34 inference(modus_ponens,[status(thm)],[357, 7421])).
% 7.09/7.34 tff(7423,plain,
% 7.09/7.34 (~r(s(s(s(elem!1))), z)),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[4790, 3618, 233, 59])).
% 7.09/7.34 tff(7424,plain,
% 7.09/7.34 (b(s(s(s(elem!1))), z)),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[377, 7423])).
% 7.09/7.34 tff(7425,plain,
% 7.09/7.34 (b(s(s(elem!1)), elem!1)),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[4905, 7424, 7422, 7419, 3618, 233, 133])).
% 7.09/7.34 tff(7426,plain,
% 7.09/7.34 (~b(z, s(s(elem!1)))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[4912, 391, 133, 7424, 7425, 7419])).
% 7.09/7.34 tff(7427,plain,
% 7.09/7.34 ($false),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[3924, 7426, 7417, 10, 7413])).
% 7.09/7.34 tff(7428,plain,(b(elem!1, z) | b(z, s(s(s(elem!1)))) | (~b(z, elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 7.09/7.34 tff(7429,plain,
% 7.09/7.34 (b(elem!1, z)),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[7428, 5873, 133, 812, 10, 1, 2])).
% 7.09/7.34 tff(7430,plain,
% 7.09/7.34 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 7.09/7.34 inference(monotonicity,[status(thm)],[818])).
% 7.09/7.34 tff(7431,plain,
% 7.09/7.34 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 7.09/7.34 inference(transitivity,[status(thm)],[7430, 582])).
% 7.09/7.34 tff(7432,plain,
% 7.09/7.34 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 7.09/7.34 inference(monotonicity,[status(thm)],[7431])).
% 7.09/7.34 tff(7433,plain,
% 7.09/7.34 (~(s(s(s(elem!1))) = s(elem!1))),
% 7.09/7.34 inference(modus_ponens,[status(thm)],[1397, 7432])).
% 7.09/7.34 tff(7434,plain,
% 7.09/7.34 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[281, 7433])).
% 7.09/7.34 tff(7435,plain,
% 7.09/7.34 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[2686, 7433])).
% 7.09/7.34 tff(7436,plain,
% 7.09/7.34 (~r(s(z), z)),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[202, 174, 184, 183])).
% 7.09/7.34 tff(7437,plain,
% 7.09/7.34 (~(elem!1 = s(elem!1))),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[166, 164])).
% 7.09/7.34 tff(7438,plain,
% 7.09/7.34 (r(s(elem!1), elem!1)),
% 7.09/7.34 inference(unit_resolution,[status(thm)],[2168, 6556, 164])).
% 7.09/7.34 tff(7439,plain,
% 7.09/7.34 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.09/7.34 inference(rewrite,[status(thm)],[])).
% 7.09/7.34 tff(7440,plain,
% 7.09/7.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 7.09/7.35 inference(monotonicity,[status(thm)],[7439])).
% 7.09/7.35 tff(7441,plain,
% 7.09/7.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.09/7.35 inference(transitivity,[status(thm)],[7440, 5422])).
% 7.09/7.35 tff(7442,plain,
% 7.09/7.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 7.09/7.35 inference(quant_inst,[status(thm)],[])).
% 7.09/7.35 tff(7443,plain,
% 7.09/7.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[7442, 7441])).
% 7.09/7.35 tff(7444,plain,
% 7.09/7.35 (~r(s(elem!1), z)),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[7443, 194, 174, 184, 604])).
% 7.09/7.35 tff(7445,plain,
% 7.09/7.35 (b(s(elem!1), z)),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[549, 7444])).
% 7.09/7.35 tff(7446,plain,
% 7.09/7.35 (~b(elem!1, s(elem!1))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[1939, 7445, 665, 592])).
% 7.09/7.35 tff(7447,plain,
% 7.09/7.35 (r(elem!1, s(elem!1))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[443, 7446, 437])).
% 7.09/7.35 tff(7448,plain,
% 7.09/7.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.09/7.35 inference(rewrite,[status(thm)],[])).
% 7.09/7.35 tff(7449,plain,
% 7.09/7.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.09/7.35 inference(quant_inst,[status(thm)],[])).
% 7.09/7.35 tff(7450,plain,
% 7.09/7.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[7449, 7448])).
% 7.09/7.35 tff(7451,plain,
% 7.09/7.35 ($false),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[7450, 194, 485, 233, 7447, 604])).
% 7.09/7.35 tff(7452,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.35 tff(7453,plain,
% 7.09/7.35 (~r(s(elem!1), s(s(s(elem!1))))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[7452, 7438, 233, 7437, 665, 592, 174, 184])).
% 7.09/7.35 tff(7454,plain,
% 7.09/7.35 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 7.09/7.35 inference(monotonicity,[status(thm)],[812])).
% 7.09/7.35 tff(7455,plain,
% 7.09/7.35 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 7.09/7.35 inference(transitivity,[status(thm)],[7454, 3])).
% 7.09/7.35 tff(7456,plain,
% 7.09/7.35 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 7.09/7.35 inference(monotonicity,[status(thm)],[7455])).
% 7.09/7.35 tff(7457,plain,
% 7.09/7.35 (~(s(s(s(elem!1))) = elem!1)),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[217, 7456])).
% 7.09/7.35 tff(7458,plain,
% 7.09/7.35 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[929, 7457])).
% 7.09/7.35 tff(7459,plain,
% 7.09/7.35 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 7.09/7.35 inference(monotonicity,[status(thm)],[818, 820])).
% 7.09/7.35 tff(7460,plain,
% 7.09/7.35 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[3614, 812, 3612])).
% 7.09/7.35 tff(7461,plain,
% 7.09/7.35 (b(s(s(z)), s(s(s(s(z)))))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[3652, 7460])).
% 7.09/7.35 tff(7462,plain,
% 7.09/7.35 (b(s(elem!1), s(s(s(elem!1))))),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[7461, 7459])).
% 7.09/7.35 tff(7463,plain,
% 7.09/7.35 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[272, 270])).
% 7.09/7.35 tff(7464,plain,
% 7.09/7.35 (~(s(elem!1) = elem!1)),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[1943, 249])).
% 7.09/7.35 tff(7465,assumption,(s(s(s(s(elem!1)))) = elem!1), introduced(assumption)).
% 7.09/7.35 tff(7466,plain,
% 7.09/7.35 (elem!1 = s(s(s(s(elem!1))))),
% 7.09/7.35 inference(symmetry,[status(thm)],[7465])).
% 7.09/7.35 tff(7467,plain,
% 7.09/7.35 (s(z) = s(s(s(s(elem!1))))),
% 7.09/7.35 inference(transitivity,[status(thm)],[812, 7466])).
% 7.09/7.35 tff(7468,plain,
% 7.09/7.35 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 7.09/7.35 inference(monotonicity,[status(thm)],[7467])).
% 7.09/7.35 tff(7469,plain,
% 7.09/7.35 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 7.09/7.35 inference(symmetry,[status(thm)],[7468])).
% 7.09/7.35 tff(7470,plain,
% 7.09/7.35 (s(s(s(elem!1))) = z),
% 7.09/7.35 inference(transitivity,[status(thm)],[295, 7469, 112])).
% 7.09/7.35 tff(7471,plain,
% 7.09/7.35 ($false),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[50, 7470])).
% 7.09/7.35 tff(7472,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.35 tff(7473,plain,
% 7.09/7.35 (~(s(s(s(s(elem!1)))) = elem!1)),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[7472, 812])).
% 7.09/7.35 tff(7474,plain,
% 7.09/7.35 ((s(z) = z) <=> (elem!1 = z)),
% 7.09/7.35 inference(monotonicity,[status(thm)],[812])).
% 7.09/7.35 tff(7475,plain,
% 7.09/7.35 ((s(z) = z) <=> (z = elem!1)),
% 7.09/7.35 inference(transitivity,[status(thm)],[7474, 92])).
% 7.09/7.35 tff(7476,plain,
% 7.09/7.35 ((z = elem!1) <=> (s(z) = z)),
% 7.09/7.35 inference(symmetry,[status(thm)],[7475])).
% 7.09/7.35 tff(7477,plain,
% 7.09/7.35 (r(s(z), z)),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[530, 3179])).
% 7.09/7.35 tff(7478,plain,
% 7.09/7.35 ($false),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[175, 7477])).
% 7.09/7.35 tff(7479,plain,((~(s(z) = elem!1)) | r(s(z), z) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.35 tff(7480,plain,
% 7.09/7.35 (~r(elem!1, z)),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[7479, 812, 175])).
% 7.09/7.35 tff(7481,plain,
% 7.09/7.35 (elem!1 = z),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[526, 7480, 484])).
% 7.09/7.35 tff(7482,plain,
% 7.09/7.35 (z = elem!1),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[5453, 7481])).
% 7.09/7.35 tff(7483,plain,
% 7.09/7.35 (s(z) = z),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[7482, 7476])).
% 7.09/7.35 tff(7484,plain,
% 7.09/7.35 ($false),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[23, 7483])).
% 7.09/7.35 tff(7485,plain,((~(s(z) = elem!1)) | b(elem!1, z) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 7.09/7.35 tff(7486,plain,
% 7.09/7.35 (b(elem!1, z)),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[7485, 812, 175])).
% 7.09/7.35 tff(7487,plain,
% 7.09/7.35 (b(z, elem!1)),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[664, 7400])).
% 7.09/7.35 tff(7488,plain,
% 7.09/7.35 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 7.09/7.35 inference(transitivity,[status(thm)],[7455, 4])).
% 7.09/7.35 tff(7489,plain,
% 7.09/7.35 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 7.09/7.35 inference(monotonicity,[status(thm)],[7488])).
% 7.09/7.35 tff(7490,plain,
% 7.09/7.35 (~(elem!1 = s(s(s(elem!1))))),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[217, 7489])).
% 7.09/7.35 tff(7491,plain,
% 7.09/7.35 (r(elem!1, s(s(s(elem!1))))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[424, 4028, 7490])).
% 7.09/7.35 tff(7492,plain,
% 7.09/7.35 (r(s(z), s(s(s(elem!1))))),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[7491, 2565])).
% 7.09/7.35 tff(7493,plain,
% 7.09/7.35 (b(s(elem!1), s(s(s(elem!1))))),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[3823, 7459])).
% 7.09/7.35 tff(7494,plain,
% 7.09/7.35 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 7.09/7.35 inference(monotonicity,[status(thm)],[820])).
% 7.09/7.35 tff(7495,plain,
% 7.09/7.35 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 7.09/7.35 inference(symmetry,[status(thm)],[7494])).
% 7.09/7.35 tff(7496,plain,
% 7.09/7.35 (b(s(s(s(s(z)))), z)),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[380, 7495])).
% 7.09/7.35 tff(7497,plain,
% 7.09/7.35 (~b(s(s(z)), z)),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[7203, 7496, 664, 590, 3823])).
% 7.09/7.35 tff(7498,plain,
% 7.09/7.35 (r(s(s(z)), z)),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[1211, 7497])).
% 7.09/7.35 tff(7499,plain,
% 7.09/7.35 (r(s(elem!1), z)),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[3560, 7498, 812])).
% 7.09/7.35 tff(7500,plain,
% 7.09/7.35 (r(s(s(elem!1)), z)),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[2629, 5264])).
% 7.09/7.35 tff(7501,plain,
% 7.09/7.35 (~b(z, s(s(elem!1)))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[4277, 391, 133, 665, 973])).
% 7.09/7.35 tff(7502,plain,
% 7.09/7.35 (r(z, s(s(elem!1)))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[324, 7501])).
% 7.09/7.35 tff(7503,plain,
% 7.09/7.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 7.09/7.35 inference(rewrite,[status(thm)],[])).
% 7.09/7.35 tff(7504,plain,
% 7.09/7.35 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 7.09/7.35 inference(rewrite,[status(thm)],[])).
% 7.09/7.35 tff(7505,plain,
% 7.09/7.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))))),
% 7.09/7.35 inference(monotonicity,[status(thm)],[7504])).
% 7.09/7.35 tff(7506,plain,
% 7.09/7.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 7.09/7.35 inference(transitivity,[status(thm)],[7505, 7503])).
% 7.09/7.35 tff(7507,plain,
% 7.09/7.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 7.09/7.35 inference(quant_inst,[status(thm)],[])).
% 7.09/7.35 tff(7508,plain,
% 7.09/7.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))),
% 7.09/7.35 inference(modus_ponens,[status(thm)],[7507, 7506])).
% 7.09/7.35 tff(7509,plain,
% 7.09/7.35 (~r(s(s(elem!1)), s(elem!1))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[7508, 194, 1628, 184, 7500])).
% 7.09/7.35 tff(7510,plain,
% 7.09/7.35 (b(s(s(elem!1)), s(elem!1))),
% 7.09/7.35 inference(unit_resolution,[status(thm)],[1135, 7509, 285])).
% 7.09/7.35 tff(7511,plain,
% 7.09/7.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.09/7.35 inference(rewrite,[status(thm)],[])).
% 7.09/7.35 tff(7512,plain,
% 7.09/7.35 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~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))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.09/7.35 inference(rewrite,[status(thm)],[])).
% 7.09/7.35 tff(7513,plain,
% 7.09/7.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 7.09/7.36 inference(monotonicity,[status(thm)],[7512])).
% 7.09/7.36 tff(7514,plain,
% 7.09/7.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.09/7.36 inference(transitivity,[status(thm)],[7513, 7511])).
% 7.09/7.36 tff(7515,plain,
% 7.09/7.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~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)))))),
% 7.09/7.36 inference(quant_inst,[status(thm)],[])).
% 7.09/7.36 tff(7516,plain,
% 7.09/7.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 7.09/7.36 inference(modus_ponens,[status(thm)],[7515, 7514])).
% 7.09/7.36 tff(7517,plain,
% 7.09/7.36 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[7516, 391, 1101, 7510, 1036])).
% 7.09/7.36 tff(7518,plain,
% 7.09/7.36 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[1370, 7517, 297])).
% 7.09/7.36 tff(7519,plain,
% 7.09/7.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 7.09/7.36 inference(rewrite,[status(thm)],[])).
% 7.09/7.36 tff(7520,plain,
% 7.09/7.36 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 7.09/7.36 inference(rewrite,[status(thm)],[])).
% 7.09/7.36 tff(7521,plain,
% 7.09/7.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 7.09/7.36 inference(monotonicity,[status(thm)],[7520])).
% 7.09/7.36 tff(7522,plain,
% 7.09/7.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 7.09/7.36 inference(transitivity,[status(thm)],[7521, 7519])).
% 7.09/7.36 tff(7523,plain,
% 7.09/7.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 7.09/7.36 inference(quant_inst,[status(thm)],[])).
% 7.09/7.36 tff(7524,plain,
% 7.09/7.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 7.09/7.36 inference(modus_ponens,[status(thm)],[7523, 7522])).
% 7.09/7.36 tff(7525,plain,
% 7.09/7.36 ($false),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[7524, 194, 184, 7518, 7502, 7500])).
% 7.09/7.36 tff(7526,plain,((~b(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.36 tff(7527,plain,
% 7.09/7.36 (~b(s(s(elem!1)), elem!1)),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[7526, 7499, 7463, 1101, 7493, 285, 184, 7487, 665])).
% 7.09/7.36 tff(7528,plain,
% 7.09/7.36 (r(s(s(elem!1)), elem!1)),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[872, 7527, 249])).
% 7.09/7.36 tff(7529,plain,
% 7.09/7.36 (~b(s(s(s(elem!1))), elem!1)),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[1514, 391, 7487, 665, 380])).
% 7.09/7.36 tff(7530,plain,
% 7.09/7.36 (r(s(s(s(elem!1))), elem!1)),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[230, 7529, 7457])).
% 7.09/7.36 tff(7531,plain,
% 7.09/7.36 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[4971, 194, 7530, 7528, 7491])).
% 7.09/7.36 tff(7532,plain,
% 7.09/7.36 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[1354, 42, 270, 7531])).
% 7.09/7.36 tff(7533,plain,
% 7.09/7.36 (~b(s(s(elem!1)), s(elem!1))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[1128, 391, 1101, 7532, 7493])).
% 7.09/7.36 tff(7534,plain,
% 7.09/7.36 (r(s(s(elem!1)), s(elem!1))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[1135, 7533, 285])).
% 7.09/7.36 tff(7535,plain,
% 7.09/7.36 (~b(s(elem!1), s(s(elem!1)))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[1107, 391, 1101, 7532, 7493])).
% 7.09/7.36 tff(7536,plain,
% 7.09/7.36 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[1111, 42, 7535])).
% 7.09/7.36 tff(7537,plain,
% 7.09/7.36 (r(s(elem!1), s(s(elem!1)))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[7536, 1100])).
% 7.09/7.36 tff(7538,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 7.09/7.36 tff(7539,plain,
% 7.09/7.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 7.09/7.36 inference(rewrite,[status(thm)],[])).
% 7.09/7.36 tff(7540,plain,
% 7.09/7.36 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 7.09/7.36 inference(rewrite,[status(thm)],[])).
% 7.09/7.36 tff(7541,plain,
% 7.09/7.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 7.09/7.36 inference(monotonicity,[status(thm)],[7540])).
% 7.09/7.36 tff(7542,plain,
% 7.09/7.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 7.09/7.36 inference(transitivity,[status(thm)],[7541, 7539])).
% 7.09/7.36 tff(7543,plain,
% 7.09/7.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 7.09/7.36 inference(quant_inst,[status(thm)],[])).
% 7.09/7.36 tff(7544,plain,
% 7.09/7.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 7.09/7.36 inference(modus_ponens,[status(thm)],[7543, 7542])).
% 7.09/7.36 tff(7545,plain,
% 7.09/7.36 ($false),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[7544, 194, 485, 364, 410, 7538])).
% 7.09/7.36 tff(7546,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.36 tff(7547,plain,
% 7.09/7.36 (~r(s(elem!1), elem!1)),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[7546, 7528, 7491, 7537])).
% 7.09/7.36 tff(7548,plain,
% 7.09/7.36 (b(s(elem!1), elem!1)),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[2168, 7547, 7464])).
% 7.09/7.36 tff(7549,plain,
% 7.09/7.36 (~b(z, s(elem!1))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[6555, 7548, 665, 7487])).
% 7.09/7.36 tff(7550,plain,
% 7.09/7.36 (r(z, s(elem!1))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[566, 7549])).
% 7.09/7.36 tff(7551,plain,
% 7.09/7.36 (~r(z, s(s(elem!1)))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[2307, 194, 7499, 7550, 7534])).
% 7.09/7.36 tff(7552,plain,
% 7.09/7.36 (b(z, s(s(elem!1)))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[324, 7551])).
% 7.09/7.36 tff(7553,plain,
% 7.09/7.36 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[4039, 7528, 7457, 4028, 7529])).
% 7.09/7.36 tff(7554,plain,
% 7.09/7.36 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.09/7.36 inference(unit_resolution,[status(thm)],[1370, 7553, 7463])).
% 7.09/7.36 tff(7555,plain,
% 7.09/7.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.09/7.36 inference(rewrite,[status(thm)],[])).
% 7.09/7.36 tff(7556,plain,
% 7.09/7.36 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.09/7.36 inference(rewrite,[status(thm)],[])).
% 7.09/7.36 tff(7557,plain,
% 7.09/7.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 7.09/7.36 inference(monotonicity,[status(thm)],[7556])).
% 7.09/7.36 tff(7558,plain,
% 7.09/7.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.09/7.36 inference(transitivity,[status(thm)],[7557, 7555])).
% 7.09/7.37 tff(7559,plain,
% 7.09/7.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 7.09/7.37 inference(quant_inst,[status(thm)],[])).
% 7.09/7.37 tff(7560,plain,
% 7.09/7.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 7.09/7.37 inference(modus_ponens,[status(thm)],[7559, 7558])).
% 7.09/7.37 tff(7561,plain,
% 7.09/7.37 ($false),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[7560, 391, 1101, 380, 7554, 7552, 7532])).
% 7.09/7.37 tff(7562,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (s(s(elem!1)) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.37 tff(7563,plain,
% 7.09/7.37 (~b(s(s(s(elem!1))), z)),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[7562, 4028, 665, 285, 270, 1101, 249, 184, 812, 664, 590, 3823])).
% 7.09/7.37 tff(7564,plain,
% 7.09/7.37 (r(s(s(s(elem!1))), z)),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[377, 7563])).
% 7.09/7.37 tff(7565,plain,
% 7.09/7.37 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[5792, 7564, 184, 7492])).
% 7.09/7.37 tff(7566,plain,
% 7.09/7.37 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[299, 7463])).
% 7.09/7.37 tff(7567,plain,
% 7.09/7.37 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[5031, 7564, 665, 7473, 7487, 7491, 184])).
% 7.09/7.37 tff(7568,plain,
% 7.09/7.37 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[1095, 7567, 7566])).
% 7.09/7.37 tff(7569,plain,
% 7.09/7.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.09/7.37 inference(rewrite,[status(thm)],[])).
% 7.09/7.37 tff(7570,plain,
% 7.09/7.37 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.09/7.37 inference(rewrite,[status(thm)],[])).
% 7.09/7.37 tff(7571,plain,
% 7.09/7.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 7.09/7.37 inference(monotonicity,[status(thm)],[7570])).
% 7.09/7.37 tff(7572,plain,
% 7.09/7.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.09/7.37 inference(transitivity,[status(thm)],[7571, 7569])).
% 7.09/7.37 tff(7573,plain,
% 7.09/7.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.09/7.37 inference(quant_inst,[status(thm)],[])).
% 7.09/7.37 tff(7574,plain,
% 7.09/7.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 7.09/7.37 inference(modus_ponens,[status(thm)],[7573, 7572])).
% 7.09/7.37 tff(7575,plain,
% 7.09/7.37 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[7574, 391, 1101, 7568, 7493])).
% 7.09/7.37 tff(7576,plain,
% 7.09/7.37 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[988, 7575, 7458])).
% 7.09/7.37 tff(7577,plain,
% 7.09/7.37 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[1144, 7576, 285, 1035, 1101, 7493, 7568])).
% 7.09/7.37 tff(7578,plain,
% 7.09/7.37 ($false),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[1354, 42, 7577, 270, 7565])).
% 7.09/7.37 tff(7579,plain,(b(elem!1, s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~(s(z) = elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.37 tff(7580,plain,
% 7.09/7.37 (b(elem!1, s(s(s(elem!1))))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[7579, 7486, 285, 1035, 1101, 270, 184, 249, 812, 664, 5450, 7461])).
% 7.09/7.37 tff(7581,plain,
% 7.09/7.37 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 7.09/7.37 inference(monotonicity,[status(thm)],[812])).
% 7.09/7.37 tff(7582,plain,
% 7.09/7.37 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 7.09/7.37 inference(symmetry,[status(thm)],[7581])).
% 7.09/7.37 tff(7583,plain,
% 7.09/7.37 (b(s(z), s(s(s(elem!1))))),
% 7.09/7.37 inference(modus_ponens,[status(thm)],[7580, 7582])).
% 7.09/7.37 tff(7584,plain,
% 7.09/7.37 (~b(s(s(s(elem!1))), z)),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[673, 7583, 7580, 7486, 664])).
% 7.09/7.37 tff(7585,plain,
% 7.09/7.37 (r(s(s(s(elem!1))), z)),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[377, 7584])).
% 7.09/7.37 tff(7586,plain,
% 7.09/7.37 (~(elem!1 = s(elem!1))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[166, 7464])).
% 7.09/7.37 tff(7587,plain,
% 7.09/7.37 (~b(elem!1, s(elem!1))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[5725, 391, 1101, 7580, 7462])).
% 7.09/7.37 tff(7588,plain,
% 7.09/7.37 (r(elem!1, s(elem!1))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[443, 7587, 7586])).
% 7.09/7.37 tff(7589,plain,
% 7.09/7.37 (~b(s(elem!1), elem!1)),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[5733, 391, 1101, 7580, 7462])).
% 7.09/7.37 tff(7590,plain,
% 7.09/7.37 (r(s(elem!1), elem!1)),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[2168, 7589, 7464])).
% 7.09/7.37 tff(7591,plain,
% 7.09/7.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 7.09/7.37 inference(rewrite,[status(thm)],[])).
% 7.09/7.37 tff(7592,plain,
% 7.09/7.37 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 7.09/7.37 inference(rewrite,[status(thm)],[])).
% 7.09/7.37 tff(7593,plain,
% 7.09/7.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 7.09/7.37 inference(monotonicity,[status(thm)],[7592])).
% 7.09/7.37 tff(7594,plain,
% 7.09/7.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 7.09/7.37 inference(transitivity,[status(thm)],[7593, 7591])).
% 7.09/7.37 tff(7595,plain,
% 7.09/7.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 7.09/7.37 inference(quant_inst,[status(thm)],[])).
% 7.09/7.37 tff(7596,plain,
% 7.09/7.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 7.09/7.37 inference(modus_ponens,[status(thm)],[7595, 7594])).
% 7.09/7.37 tff(7597,plain,
% 7.09/7.37 (~r(s(elem!1), s(s(elem!1)))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[7596, 194, 485, 2251, 364])).
% 7.09/7.37 tff(7598,plain,
% 7.09/7.37 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[1111, 42, 7597])).
% 7.09/7.37 tff(7599,plain,
% 7.09/7.37 (b(s(elem!1), s(s(elem!1)))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[7598, 1100])).
% 7.09/7.37 tff(7600,plain,
% 7.09/7.37 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 7.09/7.37 inference(monotonicity,[status(thm)],[820])).
% 7.09/7.37 tff(7601,plain,
% 7.09/7.37 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 7.09/7.37 inference(symmetry,[status(thm)],[7600])).
% 7.09/7.37 tff(7602,plain,
% 7.09/7.37 (r(s(s(s(s(z)))), z)),
% 7.09/7.37 inference(modus_ponens,[status(thm)],[174, 7601])).
% 7.09/7.37 tff(7603,plain,
% 7.09/7.37 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.09/7.37 inference(monotonicity,[status(thm)],[820])).
% 7.09/7.37 tff(7604,plain,
% 7.09/7.37 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.09/7.37 inference(symmetry,[status(thm)],[7603])).
% 7.09/7.37 tff(7605,plain,
% 7.09/7.37 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[7516, 391, 1101, 5808, 1036])).
% 7.09/7.37 tff(7606,plain,
% 7.09/7.37 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.09/7.37 inference(unit_resolution,[status(thm)],[1370, 7605, 7463])).
% 7.09/7.37 tff(7607,plain,
% 7.09/7.37 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.09/7.37 inference(modus_ponens,[status(thm)],[7606, 7604])).
% 7.09/7.37 tff(7608,plain,
% 7.09/7.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.09/7.37 inference(rewrite,[status(thm)],[])).
% 7.09/7.37 tff(7609,plain,
% 7.09/7.37 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.09/7.37 inference(rewrite,[status(thm)],[])).
% 7.09/7.37 tff(7610,plain,
% 7.09/7.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 7.09/7.38 inference(monotonicity,[status(thm)],[7609])).
% 7.09/7.38 tff(7611,plain,
% 7.09/7.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.09/7.38 inference(transitivity,[status(thm)],[7610, 7608])).
% 7.09/7.38 tff(7612,plain,
% 7.09/7.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.09/7.38 inference(quant_inst,[status(thm)],[])).
% 7.09/7.38 tff(7613,plain,
% 7.09/7.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 7.09/7.38 inference(modus_ponens,[status(thm)],[7612, 7611])).
% 7.09/7.38 tff(7614,plain,
% 7.09/7.38 ($false),
% 7.09/7.38 inference(unit_resolution,[status(thm)],[7613, 194, 2053, 719, 6240, 2616])).
% 7.09/7.38 tff(7615,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.38 tff(7616,plain,
% 7.09/7.38 (~r(s(s(elem!1)), z)),
% 7.09/7.38 inference(unit_resolution,[status(thm)],[7615, 7607, 827, 7602])).
% 7.09/7.38 tff(7617,plain,
% 7.09/7.38 (b(s(s(elem!1)), z)),
% 7.09/7.38 inference(unit_resolution,[status(thm)],[2629, 7616])).
% 7.09/7.38 tff(7618,plain,
% 7.09/7.38 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(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)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 7.09/7.38 inference(rewrite,[status(thm)],[])).
% 7.09/7.38 tff(7619,plain,
% 7.09/7.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 7.09/7.38 inference(monotonicity,[status(thm)],[7618])).
% 7.09/7.38 tff(7620,plain,
% 7.09/7.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 7.09/7.38 inference(transitivity,[status(thm)],[7619, 1123])).
% 7.09/7.38 tff(7621,plain,
% 7.09/7.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(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))))))),
% 7.09/7.38 inference(quant_inst,[status(thm)],[])).
% 7.09/7.38 tff(7622,plain,
% 7.09/7.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 7.09/7.38 inference(modus_ponens,[status(thm)],[7621, 7620])).
% 7.09/7.38 tff(7623,plain,
% 7.09/7.38 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.09/7.38 inference(unit_resolution,[status(thm)],[7622, 391, 1101, 5808, 1036])).
% 7.09/7.38 tff(7624,plain,
% 7.09/7.38 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.09/7.38 inference(unit_resolution,[status(thm)],[1354, 42, 7623, 270])).
% 7.09/7.38 tff(7625,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 7.09/7.38 tff(7626,plain,
% 7.09/7.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.09/7.38 inference(rewrite,[status(thm)],[])).
% 7.09/7.38 tff(7627,plain,
% 7.09/7.38 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.09/7.38 inference(rewrite,[status(thm)],[])).
% 7.09/7.38 tff(7628,plain,
% 7.09/7.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 7.09/7.38 inference(monotonicity,[status(thm)],[7627])).
% 7.09/7.38 tff(7629,plain,
% 7.09/7.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.09/7.38 inference(transitivity,[status(thm)],[7628, 7626])).
% 7.09/7.38 tff(7630,plain,
% 7.09/7.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.09/7.38 inference(quant_inst,[status(thm)],[])).
% 7.09/7.38 tff(7631,plain,
% 7.09/7.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 7.09/7.38 inference(modus_ponens,[status(thm)],[7630, 7629])).
% 7.09/7.38 tff(7632,plain,
% 7.09/7.38 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.09/7.38 inference(unit_resolution,[status(thm)],[7631, 391, 1101, 2641, 7625, 975])).
% 7.09/7.38 tff(7633,plain,
% 7.09/7.38 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.09/7.38 inference(unit_resolution,[status(thm)],[1095, 7632, 305])).
% 7.09/7.38 tff(7634,plain,
% 7.09/7.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.09/7.39 inference(rewrite,[status(thm)],[])).
% 7.09/7.39 tff(7635,plain,
% 7.09/7.39 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.09/7.39 inference(rewrite,[status(thm)],[])).
% 7.09/7.39 tff(7636,plain,
% 7.09/7.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 7.09/7.39 inference(monotonicity,[status(thm)],[7635])).
% 7.09/7.39 tff(7637,plain,
% 7.09/7.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.09/7.39 inference(transitivity,[status(thm)],[7636, 7634])).
% 7.09/7.39 tff(7638,plain,
% 7.09/7.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.09/7.39 inference(quant_inst,[status(thm)],[])).
% 7.09/7.39 tff(7639,plain,
% 7.09/7.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 7.09/7.39 inference(modus_ponens,[status(thm)],[7638, 7637])).
% 7.09/7.39 tff(7640,plain,
% 7.09/7.39 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[7639, 391, 2641, 1037, 7625, 975])).
% 7.09/7.39 tff(7641,plain,
% 7.09/7.39 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[1048, 7640, 1035])).
% 7.09/7.39 tff(7642,plain,
% 7.09/7.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.09/7.39 inference(rewrite,[status(thm)],[])).
% 7.09/7.39 tff(7643,plain,
% 7.09/7.39 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.09/7.39 inference(rewrite,[status(thm)],[])).
% 7.09/7.39 tff(7644,plain,
% 7.09/7.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 7.09/7.39 inference(monotonicity,[status(thm)],[7643])).
% 7.09/7.39 tff(7645,plain,
% 7.09/7.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.09/7.39 inference(transitivity,[status(thm)],[7644, 7642])).
% 7.09/7.39 tff(7646,plain,
% 7.09/7.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.09/7.39 inference(quant_inst,[status(thm)],[])).
% 7.09/7.39 tff(7647,plain,
% 7.09/7.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 7.09/7.39 inference(modus_ponens,[status(thm)],[7646, 7645])).
% 7.09/7.39 tff(7648,plain,
% 7.09/7.39 ($false),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[7647, 194, 174, 7641, 7633, 1378])).
% 7.09/7.39 tff(7649,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.09/7.39 tff(7650,plain,
% 7.09/7.39 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[7649, 7624, 174, 1035, 7566, 7617, 5808, 7599, 1101])).
% 7.09/7.39 tff(7651,plain,
% 7.09/7.39 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[988, 7650, 7458])).
% 7.09/7.39 tff(7652,plain,
% 7.09/7.39 (~r(z, s(s(elem!1)))),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[1448, 194, 174, 184, 7624])).
% 7.09/7.39 tff(7653,plain,
% 7.09/7.39 (b(z, s(s(elem!1)))),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[324, 7652])).
% 7.09/7.39 tff(7654,plain,
% 7.09/7.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 7.09/7.39 inference(rewrite,[status(thm)],[])).
% 7.09/7.39 tff(7655,plain,
% 7.09/7.39 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 7.09/7.39 inference(rewrite,[status(thm)],[])).
% 7.09/7.39 tff(7656,plain,
% 7.09/7.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))))),
% 7.09/7.39 inference(monotonicity,[status(thm)],[7655])).
% 7.09/7.39 tff(7657,plain,
% 7.09/7.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 7.09/7.39 inference(transitivity,[status(thm)],[7656, 7654])).
% 7.09/7.39 tff(7658,plain,
% 7.09/7.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 7.09/7.39 inference(quant_inst,[status(thm)],[])).
% 7.09/7.39 tff(7659,plain,
% 7.09/7.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))),
% 7.09/7.39 inference(modus_ponens,[status(thm)],[7658, 7657])).
% 7.09/7.39 tff(7660,plain,
% 7.09/7.39 (~b(z, s(elem!1))),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[7659, 391, 7653, 5808, 7599])).
% 7.09/7.39 tff(7661,plain,
% 7.09/7.39 (r(z, s(elem!1))),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[566, 7660])).
% 7.09/7.39 tff(7662,plain,
% 7.09/7.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.09/7.39 inference(rewrite,[status(thm)],[])).
% 7.09/7.39 tff(7663,plain,
% 7.09/7.39 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.09/7.39 inference(rewrite,[status(thm)],[])).
% 7.09/7.39 tff(7664,plain,
% 7.09/7.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 7.09/7.39 inference(monotonicity,[status(thm)],[7663])).
% 7.09/7.39 tff(7665,plain,
% 7.09/7.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.09/7.39 inference(transitivity,[status(thm)],[7664, 7662])).
% 7.09/7.39 tff(7666,plain,
% 7.09/7.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))),
% 7.09/7.39 inference(quant_inst,[status(thm)],[])).
% 7.09/7.39 tff(7667,plain,
% 7.09/7.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 7.09/7.39 inference(modus_ponens,[status(thm)],[7666, 7665])).
% 7.09/7.39 tff(7668,plain,
% 7.09/7.39 (~r(s(s(s(s(elem!1)))), z)),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[7667, 194, 485, 7661, 7651])).
% 7.09/7.39 tff(7669,plain,
% 7.09/7.39 (b(s(s(s(s(elem!1)))), z)),
% 7.09/7.39 inference(unit_resolution,[status(thm)],[1626, 7668])).
% 7.09/7.39 tff(7670,plain,
% 7.19/7.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.19/7.40 inference(rewrite,[status(thm)],[])).
% 7.19/7.40 tff(7671,plain,
% 7.19/7.40 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.19/7.40 inference(rewrite,[status(thm)],[])).
% 7.19/7.40 tff(7672,plain,
% 7.19/7.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 7.19/7.40 inference(monotonicity,[status(thm)],[7671])).
% 7.19/7.40 tff(7673,plain,
% 7.19/7.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.19/7.40 inference(transitivity,[status(thm)],[7672, 7670])).
% 7.19/7.40 tff(7674,plain,
% 7.19/7.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 7.19/7.40 inference(quant_inst,[status(thm)],[])).
% 7.19/7.40 tff(7675,plain,
% 7.19/7.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 7.19/7.40 inference(modus_ponens,[status(thm)],[7674, 7673])).
% 7.19/7.40 tff(7676,plain,
% 7.19/7.40 (~r(s(s(s(s(elem!1)))), elem!1)),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[7675, 194, 485, 2251, 7651])).
% 7.19/7.40 tff(7677,plain,
% 7.19/7.40 (b(s(s(s(s(elem!1)))), elem!1)),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[1004, 7676, 7473])).
% 7.19/7.40 tff(7678,plain,
% 7.19/7.40 ($false),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[5029, 391, 133, 665, 7677, 7669])).
% 7.19/7.40 tff(7679,plain,((~r(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~(s(z) = elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.40 tff(7680,plain,
% 7.19/7.40 (~r(s(s(elem!1)), elem!1)),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[7679, 7487, 7486, 7590, 7588, 7585, 1035, 1101, 184, 270, 812, 7462, 285])).
% 7.19/7.40 tff(7681,plain,
% 7.19/7.40 (b(s(s(elem!1)), elem!1)),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[872, 7680, 249])).
% 7.19/7.40 tff(7682,plain,
% 7.19/7.40 (~r(s(elem!1), z)),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[7526, 973, 297, 1101, 1036, 285, 184, 133, 665])).
% 7.19/7.40 tff(7683,plain,
% 7.19/7.40 (b(s(elem!1), z)),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[549, 7682])).
% 7.19/7.40 tff(7684,plain,
% 7.19/7.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 7.19/7.40 inference(rewrite,[status(thm)],[])).
% 7.19/7.40 tff(7685,plain,
% 7.19/7.40 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 7.19/7.40 inference(rewrite,[status(thm)],[])).
% 7.19/7.40 tff(7686,plain,
% 7.19/7.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1))))),
% 7.19/7.40 inference(monotonicity,[status(thm)],[7685])).
% 7.19/7.40 tff(7687,plain,
% 7.19/7.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 7.19/7.40 inference(transitivity,[status(thm)],[7686, 7684])).
% 7.19/7.40 tff(7688,plain,
% 7.19/7.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 7.19/7.40 inference(quant_inst,[status(thm)],[])).
% 7.19/7.40 tff(7689,plain,
% 7.19/7.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1))),
% 7.19/7.40 inference(modus_ponens,[status(thm)],[7688, 7687])).
% 7.19/7.40 tff(7690,plain,
% 7.19/7.40 (~b(elem!1, s(elem!1))),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[7689, 391, 133, 665, 7683])).
% 7.19/7.40 tff(7691,plain,
% 7.19/7.40 (r(elem!1, s(elem!1))),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[443, 7690, 7437])).
% 7.19/7.40 tff(7692,plain,
% 7.19/7.40 (~b(s(elem!1), elem!1)),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[5286, 973, 133, 665, 285])).
% 7.19/7.40 tff(7693,plain,
% 7.19/7.40 (r(s(elem!1), elem!1)),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[2168, 7692, 164])).
% 7.19/7.40 tff(7694,plain,
% 7.19/7.40 (~r(s(s(s(s(elem!1)))), elem!1)),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[7675, 194, 7693, 7691, 990])).
% 7.19/7.40 tff(7695,plain,
% 7.19/7.40 (b(s(s(s(s(elem!1)))), elem!1)),
% 7.19/7.40 inference(unit_resolution,[status(thm)],[1004, 7694, 972])).
% 7.19/7.40 tff(7696,plain,
% 7.19/7.40 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.19/7.40 inference(rewrite,[status(thm)],[])).
% 7.19/7.40 tff(7697,plain,
% 7.19/7.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 7.19/7.40 inference(monotonicity,[status(thm)],[7696])).
% 7.19/7.40 tff(7698,plain,
% 7.19/7.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.19/7.40 inference(transitivity,[status(thm)],[7697, 5024])).
% 7.19/7.41 tff(7699,plain,
% 7.19/7.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 7.19/7.41 inference(quant_inst,[status(thm)],[])).
% 7.19/7.41 tff(7700,plain,
% 7.19/7.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 7.19/7.41 inference(modus_ponens,[status(thm)],[7699, 7698])).
% 7.19/7.41 tff(7701,plain,
% 7.19/7.41 (~b(s(s(s(s(elem!1)))), z)),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[7700, 391, 133, 665, 7695])).
% 7.19/7.41 tff(7702,plain,
% 7.19/7.41 (r(s(s(s(s(elem!1)))), z)),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[1626, 7701])).
% 7.19/7.41 tff(7703,plain,
% 7.19/7.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.19/7.41 inference(rewrite,[status(thm)],[])).
% 7.19/7.41 tff(7704,plain,
% 7.19/7.41 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.19/7.41 inference(rewrite,[status(thm)],[])).
% 7.19/7.41 tff(7705,plain,
% 7.19/7.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 7.19/7.41 inference(monotonicity,[status(thm)],[7704])).
% 7.19/7.41 tff(7706,plain,
% 7.19/7.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.19/7.41 inference(transitivity,[status(thm)],[7705, 7703])).
% 7.19/7.41 tff(7707,plain,
% 7.19/7.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.19/7.41 inference(quant_inst,[status(thm)],[])).
% 7.19/7.41 tff(7708,plain,
% 7.19/7.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 7.19/7.41 inference(modus_ponens,[status(thm)],[7707, 7706])).
% 7.19/7.41 tff(7709,plain,
% 7.19/7.41 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[7708, 391, 133, 665, 973, 7695])).
% 7.19/7.41 tff(7710,plain,
% 7.19/7.41 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[1048, 7709, 1035])).
% 7.19/7.41 tff(7711,plain,
% 7.19/7.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.19/7.41 inference(rewrite,[status(thm)],[])).
% 7.19/7.41 tff(7712,plain,
% 7.19/7.41 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.19/7.41 inference(rewrite,[status(thm)],[])).
% 7.19/7.41 tff(7713,plain,
% 7.19/7.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 7.19/7.41 inference(monotonicity,[status(thm)],[7712])).
% 7.19/7.41 tff(7714,plain,
% 7.19/7.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.19/7.41 inference(transitivity,[status(thm)],[7713, 7711])).
% 7.19/7.41 tff(7715,plain,
% 7.19/7.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 7.19/7.41 inference(quant_inst,[status(thm)],[])).
% 7.19/7.41 tff(7716,plain,
% 7.19/7.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 7.19/7.41 inference(modus_ponens,[status(thm)],[7715, 7714])).
% 7.19/7.41 tff(7717,plain,
% 7.19/7.41 ($false),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[7716, 194, 184, 7710, 7702, 7500])).
% 7.19/7.41 tff(7718,plain,((~b(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (s(elem!1) = elem!1) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.41 tff(7719,plain,
% 7.19/7.41 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[7718, 7681, 1035, 7487, 7486, 7473, 184, 7464, 7463, 1101, 7462, 285])).
% 7.19/7.41 tff(7720,plain,
% 7.19/7.41 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[988, 7719, 7458])).
% 7.19/7.41 tff(7721,plain,
% 7.19/7.41 (~r(s(elem!1), z)),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[7526, 7681, 7463, 1101, 7462, 285, 184, 7487, 7486])).
% 7.19/7.41 tff(7722,plain,
% 7.19/7.41 (b(s(elem!1), z)),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[549, 7721])).
% 7.19/7.41 tff(7723,plain,
% 7.19/7.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.19/7.41 inference(rewrite,[status(thm)],[])).
% 7.19/7.41 tff(7724,plain,
% 7.19/7.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.19/7.41 inference(quant_inst,[status(thm)],[])).
% 7.19/7.41 tff(7725,plain,
% 7.19/7.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 7.19/7.41 inference(modus_ponens,[status(thm)],[7724, 7723])).
% 7.19/7.41 tff(7726,plain,
% 7.19/7.41 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[7725, 391, 7487, 1101, 7722, 7720])).
% 7.19/7.41 tff(7727,plain,
% 7.19/7.41 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[1095, 7726, 7566])).
% 7.19/7.41 tff(7728,plain,
% 7.19/7.41 (~r(s(s(s(s(elem!1)))), z)),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[5016, 194, 7585, 184, 7727])).
% 7.19/7.41 tff(7729,plain,
% 7.19/7.41 (b(s(s(s(s(elem!1)))), z)),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[1626, 7728])).
% 7.19/7.41 tff(7730,plain,
% 7.19/7.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.19/7.41 inference(rewrite,[status(thm)],[])).
% 7.19/7.41 tff(7731,plain,
% 7.19/7.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.19/7.41 inference(quant_inst,[status(thm)],[])).
% 7.19/7.41 tff(7732,plain,
% 7.19/7.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 7.19/7.41 inference(modus_ponens,[status(thm)],[7731, 7730])).
% 7.19/7.41 tff(7733,plain,
% 7.19/7.41 ($false),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[7732, 391, 7487, 7486, 7722, 7729, 7720])).
% 7.19/7.41 tff(7734,plain,((~(s(z) = elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1)) | (s(s(elem!1)) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | r(s(elem!1), s(s(s(elem!1)))) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 7.19/7.41 tff(7735,plain,
% 7.19/7.41 (~b(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[7734, 7453, 184, 175, 7402, 7435, 7434, 7422, 285, 812])).
% 7.19/7.41 tff(7736,plain,
% 7.19/7.41 (r(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.41 inference(unit_resolution,[status(thm)],[588, 7735, 7433])).
% 7.19/7.41 tff(7737,plain,
% 7.19/7.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 7.19/7.41 inference(rewrite,[status(thm)],[])).
% 7.19/7.41 tff(7738,plain,
% 7.19/7.41 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), 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(s(elem!1), elem!1)))),
% 7.19/7.41 inference(rewrite,[status(thm)],[])).
% 7.19/7.41 tff(7739,plain,
% 7.19/7.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 7.19/7.42 inference(monotonicity,[status(thm)],[7738])).
% 7.19/7.42 tff(7740,plain,
% 7.19/7.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 7.19/7.42 inference(transitivity,[status(thm)],[7739, 7737])).
% 7.19/7.42 tff(7741,plain,
% 7.19/7.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 7.19/7.42 inference(quant_inst,[status(thm)],[])).
% 7.19/7.42 tff(7742,plain,
% 7.19/7.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1))),
% 7.19/7.42 inference(modus_ponens,[status(thm)],[7741, 7740])).
% 7.19/7.42 tff(7743,plain,
% 7.19/7.42 ($false),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7742, 194, 613, 485, 233, 2251])).
% 7.19/7.42 tff(7744,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.42 tff(7745,plain,
% 7.19/7.42 (~r(elem!1, s(elem!1))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7744, 7736, 7438, 233])).
% 7.19/7.42 tff(7746,plain,
% 7.19/7.42 (b(elem!1, s(elem!1))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[443, 7745, 7437])).
% 7.19/7.42 tff(7747,plain,
% 7.19/7.42 (~b(s(elem!1), z)),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[1939, 7746, 665, 592])).
% 7.19/7.42 tff(7748,plain,
% 7.19/7.42 (r(s(elem!1), z)),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[549, 7747])).
% 7.19/7.42 tff(7749,plain,
% 7.19/7.42 ($false),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[5618, 194, 7736, 7748, 174, 184])).
% 7.19/7.42 tff(7750,plain,((~b(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | r(s(z), z) | (s(s(elem!1)) = s(elem!1)) | (~(s(z) = elem!1)) | (s(elem!1) = elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.42 tff(7751,plain,
% 7.19/7.42 (~b(z, s(elem!1))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7750, 174, 184, 665, 233, 7436, 285, 812, 164, 133])).
% 7.19/7.42 tff(7752,plain,
% 7.19/7.42 (r(z, s(elem!1))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[566, 7751])).
% 7.19/7.42 tff(7753,plain,
% 7.19/7.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.42 inference(rewrite,[status(thm)],[])).
% 7.19/7.42 tff(7754,plain,
% 7.19/7.42 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.42 inference(rewrite,[status(thm)],[])).
% 7.19/7.42 tff(7755,plain,
% 7.19/7.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 7.19/7.42 inference(monotonicity,[status(thm)],[7754])).
% 7.19/7.42 tff(7756,plain,
% 7.19/7.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.42 inference(transitivity,[status(thm)],[7755, 7753])).
% 7.19/7.42 tff(7757,plain,
% 7.19/7.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.42 inference(quant_inst,[status(thm)],[])).
% 7.19/7.42 tff(7758,plain,
% 7.19/7.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 7.19/7.42 inference(modus_ponens,[status(thm)],[7757, 7756])).
% 7.19/7.42 tff(7759,plain,
% 7.19/7.42 ($false),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7758, 194, 1628, 174, 2144, 604])).
% 7.19/7.42 tff(7760,plain,((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.42 tff(7761,plain,
% 7.19/7.42 (~r(s(elem!1), s(s(s(elem!1))))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7760, 1628, 2144, 174])).
% 7.19/7.42 tff(7762,plain,
% 7.19/7.42 (~b(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7734, 7761, 184, 175, 664, 7435, 7434, 7422, 285, 812])).
% 7.19/7.42 tff(7763,plain,
% 7.19/7.42 (r(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[588, 7762, 7433])).
% 7.19/7.42 tff(7764,plain,
% 7.19/7.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 7.19/7.42 inference(rewrite,[status(thm)],[])).
% 7.19/7.42 tff(7765,plain,
% 7.19/7.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 7.19/7.42 inference(quant_inst,[status(thm)],[])).
% 7.19/7.42 tff(7766,plain,
% 7.19/7.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 7.19/7.42 inference(modus_ponens,[status(thm)],[7765, 7764])).
% 7.19/7.42 tff(7767,plain,
% 7.19/7.42 ($false),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7766, 194, 7763, 1628, 174, 2144])).
% 7.19/7.42 tff(7768,plain,((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | r(s(z), z) | (~b(z, s(z))) | (s(s(elem!1)) = s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.42 tff(7769,plain,
% 7.19/7.42 (~r(s(elem!1), z)),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7768, 174, 7752, 184, 7436, 7402, 285, 812])).
% 7.19/7.42 tff(7770,plain,
% 7.19/7.42 (b(s(elem!1), z)),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[549, 7769])).
% 7.19/7.42 tff(7771,plain,
% 7.19/7.42 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 7.19/7.42 inference(rewrite,[status(thm)],[])).
% 7.19/7.42 tff(7772,plain,
% 7.19/7.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1))))),
% 7.19/7.42 inference(monotonicity,[status(thm)],[7771])).
% 7.19/7.42 tff(7773,plain,
% 7.19/7.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 7.19/7.42 inference(transitivity,[status(thm)],[7772, 5274])).
% 7.19/7.42 tff(7774,plain,
% 7.19/7.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 7.19/7.42 inference(quant_inst,[status(thm)],[])).
% 7.19/7.42 tff(7775,plain,
% 7.19/7.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1))),
% 7.19/7.42 inference(modus_ponens,[status(thm)],[7774, 7773])).
% 7.19/7.42 tff(7776,plain,
% 7.19/7.42 ($false),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7775, 391, 133, 665, 591, 2122])).
% 7.19/7.42 tff(7777,plain,((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.42 tff(7778,plain,
% 7.19/7.42 (~b(s(elem!1), elem!1)),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7777, 7770, 665, 133])).
% 7.19/7.42 tff(7779,plain,
% 7.19/7.42 (r(s(elem!1), elem!1)),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[2168, 7778, 164])).
% 7.19/7.42 tff(7780,plain,
% 7.19/7.42 (~b(elem!1, s(elem!1))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7689, 391, 133, 665, 7770])).
% 7.19/7.42 tff(7781,plain,
% 7.19/7.42 (r(elem!1, s(elem!1))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[443, 7780, 7437])).
% 7.19/7.42 tff(7782,plain,
% 7.19/7.42 (~r(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7744, 7781, 7779, 233])).
% 7.19/7.42 tff(7783,plain,
% 7.19/7.42 (b(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[588, 7782, 7433])).
% 7.19/7.42 tff(7784,plain,
% 7.19/7.42 (r(s(elem!1), s(s(s(elem!1))))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7734, 7783, 184, 7436, 7402, 7435, 7434, 7422, 285, 812])).
% 7.19/7.42 tff(7785,plain,
% 7.19/7.42 ($false),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7450, 194, 7779, 233, 7781, 7784])).
% 7.19/7.42 tff(7786,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1)) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(elem!1) = elem!1) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.42 tff(7787,plain,
% 7.19/7.42 (~r(s(s(s(elem!1))), z)),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7786, 5873, 59, 7412, 812, 133, 7429, 5887, 7409])).
% 7.19/7.42 tff(7788,plain,
% 7.19/7.42 (b(s(s(s(elem!1))), z)),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[377, 7787])).
% 7.19/7.42 tff(7789,plain,
% 7.19/7.42 (~b(elem!1, s(s(s(elem!1))))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[5856, 391, 133, 7429, 7788])).
% 7.19/7.42 tff(7790,plain,
% 7.19/7.42 (r(elem!1, s(s(s(elem!1))))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[424, 7789, 1])).
% 7.19/7.42 tff(7791,plain,
% 7.19/7.42 (r(s(z), s(s(s(s(z)))))),
% 7.19/7.42 inference(modus_ponens,[status(thm)],[7790, 7407])).
% 7.19/7.42 tff(7792,plain,
% 7.19/7.42 (b(s(z), z)),
% 7.19/7.42 inference(modus_ponens,[status(thm)],[7429, 7415])).
% 7.19/7.42 tff(7793,plain,
% 7.19/7.42 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 7.19/7.42 inference(monotonicity,[status(thm)],[7582])).
% 7.19/7.42 tff(7794,plain,
% 7.19/7.42 (~b(s(z), s(s(s(elem!1))))),
% 7.19/7.42 inference(modus_ponens,[status(thm)],[4028, 7793])).
% 7.19/7.42 tff(7795,plain,
% 7.19/7.42 ($false),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[379, 7794])).
% 7.19/7.42 tff(7796,plain,((~(s(z) = elem!1)) | (~b(s(z), s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.42 tff(7797,plain,
% 7.19/7.42 (~b(s(z), s(s(s(elem!1))))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[7796, 7789, 812])).
% 7.19/7.42 tff(7798,plain,
% 7.19/7.42 (r(s(z), s(s(s(elem!1))))),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[247, 7797])).
% 7.19/7.42 tff(7799,plain,
% 7.19/7.42 (~r(s(z), z)),
% 7.19/7.42 inference(unit_resolution,[status(thm)],[3499, 7798, 59, 7409])).
% 7.19/7.42 tff(7800,plain,
% 7.19/7.42 (~b(z, s(elem!1))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[6555, 2122, 133, 665])).
% 7.19/7.43 tff(7801,plain,
% 7.19/7.43 (r(z, s(elem!1))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[566, 7800])).
% 7.19/7.43 tff(7802,plain,
% 7.19/7.43 (~b(s(elem!1), z)),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7777, 2122, 665, 133])).
% 7.19/7.43 tff(7803,plain,
% 7.19/7.43 (r(s(elem!1), z)),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[549, 7802])).
% 7.19/7.43 tff(7804,plain,
% 7.19/7.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.43 inference(rewrite,[status(thm)],[])).
% 7.19/7.43 tff(7805,plain,
% 7.19/7.43 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.43 inference(rewrite,[status(thm)],[])).
% 7.19/7.43 tff(7806,plain,
% 7.19/7.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 7.19/7.43 inference(monotonicity,[status(thm)],[7805])).
% 7.19/7.43 tff(7807,plain,
% 7.19/7.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.43 inference(transitivity,[status(thm)],[7806, 7804])).
% 7.19/7.43 tff(7808,plain,
% 7.19/7.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 7.19/7.43 inference(quant_inst,[status(thm)],[])).
% 7.19/7.43 tff(7809,plain,
% 7.19/7.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 7.19/7.43 inference(modus_ponens,[status(thm)],[7808, 7807])).
% 7.19/7.43 tff(7810,plain,
% 7.19/7.43 ($false),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7809, 194, 1628, 233, 184, 604])).
% 7.19/7.43 tff(7811,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.43 tff(7812,plain,
% 7.19/7.43 (~r(s(elem!1), s(s(s(elem!1))))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7811, 7803, 233, 184])).
% 7.19/7.43 tff(7813,plain,
% 7.19/7.43 (~b(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7734, 7812, 184, 175, 7402, 7435, 7434, 7422, 285, 812])).
% 7.19/7.43 tff(7814,plain,
% 7.19/7.43 (r(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[588, 7813, 7433])).
% 7.19/7.43 tff(7815,plain,
% 7.19/7.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 7.19/7.43 inference(rewrite,[status(thm)],[])).
% 7.19/7.43 tff(7816,plain,
% 7.19/7.43 (((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 7.19/7.43 inference(rewrite,[status(thm)],[])).
% 7.19/7.43 tff(7817,plain,
% 7.19/7.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 7.19/7.43 inference(monotonicity,[status(thm)],[7816])).
% 7.19/7.43 tff(7818,plain,
% 7.19/7.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 7.19/7.43 inference(transitivity,[status(thm)],[7817, 7815])).
% 7.19/7.43 tff(7819,plain,
% 7.19/7.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 7.19/7.43 inference(quant_inst,[status(thm)],[])).
% 7.19/7.43 tff(7820,plain,
% 7.19/7.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))),
% 7.19/7.43 inference(modus_ponens,[status(thm)],[7819, 7818])).
% 7.19/7.43 tff(7821,plain,
% 7.19/7.43 ($false),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7820, 194, 7814, 7803, 7801, 184])).
% 7.19/7.43 tff(7822,plain,((~b(s(elem!1), elem!1)) | (~r(z, s(s(s(elem!1))))) | r(s(z), z) | (s(s(elem!1)) = s(elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.43 tff(7823,plain,
% 7.19/7.43 (~b(s(elem!1), elem!1)),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7822, 7799, 59, 7412, 812, 5873, 7429, 133])).
% 7.19/7.43 tff(7824,plain,
% 7.19/7.43 (r(s(elem!1), elem!1)),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[2168, 7823, 5887])).
% 7.19/7.43 tff(7825,plain,
% 7.19/7.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.19/7.43 inference(rewrite,[status(thm)],[])).
% 7.19/7.43 tff(7826,plain,
% 7.19/7.43 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.19/7.43 inference(rewrite,[status(thm)],[])).
% 7.19/7.43 tff(7827,plain,
% 7.19/7.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 7.19/7.43 inference(monotonicity,[status(thm)],[7826])).
% 7.19/7.43 tff(7828,plain,
% 7.19/7.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.19/7.43 inference(transitivity,[status(thm)],[7827, 7825])).
% 7.19/7.43 tff(7829,plain,
% 7.19/7.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 7.19/7.43 inference(quant_inst,[status(thm)],[])).
% 7.19/7.43 tff(7830,plain,
% 7.19/7.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 7.19/7.43 inference(modus_ponens,[status(thm)],[7829, 7828])).
% 7.19/7.43 tff(7831,plain,
% 7.19/7.43 ($false),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7830, 194, 613, 485, 233, 410])).
% 7.19/7.43 tff(7832,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.43 tff(7833,plain,
% 7.19/7.43 (~r(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7832, 7824, 5873, 7790])).
% 7.19/7.43 tff(7834,plain,
% 7.19/7.43 (b(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[588, 7833, 7433])).
% 7.19/7.43 tff(7835,plain,
% 7.19/7.43 (~b(s(s(z)), s(s(s(s(z)))))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7579, 7834, 812, 7429, 7412, 7434, 7435, 7422, 59, 7402, 7792, 7789])).
% 7.19/7.43 tff(7836,plain,
% 7.19/7.43 (r(s(s(z)), s(s(s(s(z)))))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[3652, 7835])).
% 7.19/7.43 tff(7837,plain,
% 7.19/7.43 (~r(s(s(z)), s(z))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[5585, 7836, 7792, 7791, 7402])).
% 7.19/7.43 tff(7838,plain,
% 7.19/7.43 (b(s(s(z)), s(z))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[3778, 7837])).
% 7.19/7.43 tff(7839,plain,
% 7.19/7.43 (b(s(elem!1), elem!1)),
% 7.19/7.43 inference(modus_ponens,[status(thm)],[7838, 7399])).
% 7.19/7.43 tff(7840,plain,
% 7.19/7.43 ($false),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7823, 7839])).
% 7.19/7.43 tff(7841,plain,(b(s(s(s(elem!1))), elem!1) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 7.19/7.43 tff(7842,plain,
% 7.19/7.43 (b(s(s(s(elem!1))), elem!1)),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7841, 7396, 149, 148, 10, 2])).
% 7.19/7.43 tff(7843,plain,
% 7.19/7.43 (b(z, s(s(elem!1)))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[3924, 7417, 10, 7413])).
% 7.19/7.43 tff(7844,plain,
% 7.19/7.43 (r(s(z), z)),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7485, 484, 812])).
% 7.19/7.43 tff(7845,plain,
% 7.19/7.43 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(s(z)))), elem!1))),
% 7.19/7.43 inference(monotonicity,[status(thm)],[822])).
% 7.19/7.43 tff(7846,plain,
% 7.19/7.43 (~r(s(s(s(elem!1))), elem!1)),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7428, 484, 133, 812, 10, 1, 2])).
% 7.19/7.43 tff(7847,plain,
% 7.19/7.43 (~r(s(s(s(s(z)))), elem!1)),
% 7.19/7.43 inference(modus_ponens,[status(thm)],[7846, 7845])).
% 7.19/7.43 tff(7848,plain,
% 7.19/7.43 (b(s(s(s(elem!1))), elem!1)),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[7841, 812, 133, 1, 10, 2])).
% 7.19/7.43 tff(7849,plain,
% 7.19/7.43 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(elem!1))))),
% 7.19/7.43 inference(transitivity,[status(thm)],[7405, 2565])).
% 7.19/7.43 tff(7850,plain,
% 7.19/7.43 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 7.19/7.43 inference(monotonicity,[status(thm)],[812])).
% 7.19/7.43 tff(7851,plain,
% 7.19/7.43 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 7.19/7.43 inference(transitivity,[status(thm)],[7850, 765])).
% 7.19/7.43 tff(7852,plain,
% 7.19/7.43 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 7.19/7.43 inference(monotonicity,[status(thm)],[7851])).
% 7.19/7.43 tff(7853,plain,
% 7.19/7.43 (~(s(s(s(s(z)))) = elem!1)),
% 7.19/7.43 inference(modus_ponens,[status(thm)],[743, 7852])).
% 7.19/7.43 tff(7854,plain,
% 7.19/7.43 (r(elem!1, s(s(s(s(z)))))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[6231, 380, 900, 6221, 133, 7853])).
% 7.19/7.43 tff(7855,plain,
% 7.19/7.43 (r(s(z), s(s(s(elem!1))))),
% 7.19/7.43 inference(modus_ponens,[status(thm)],[7854, 7849])).
% 7.19/7.43 tff(7856,plain,
% 7.19/7.43 (~r(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[641, 7855, 184, 182])).
% 7.19/7.43 tff(7857,plain,
% 7.19/7.43 (b(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[588, 7856, 7433])).
% 7.19/7.43 tff(7858,plain,
% 7.19/7.43 (~r(s(elem!1), z)),
% 7.19/7.43 inference(unit_resolution,[status(thm)],[3554, 7857, 184, 437, 900, 530])).
% 7.19/7.44 tff(7859,plain,
% 7.19/7.44 (b(s(elem!1), z)),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[549, 7858])).
% 7.19/7.44 tff(7860,plain,
% 7.19/7.44 (r(z, s(elem!1))),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[2614, 7859, 184, 380, 7856])).
% 7.19/7.44 tff(7861,plain,
% 7.19/7.44 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 7.19/7.44 inference(monotonicity,[status(thm)],[819])).
% 7.19/7.44 tff(7862,plain,
% 7.19/7.44 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 7.19/7.44 inference(symmetry,[status(thm)],[7861])).
% 7.19/7.44 tff(7863,plain,
% 7.19/7.44 (b(z, s(s(s(z))))),
% 7.19/7.44 inference(modus_ponens,[status(thm)],[3927, 7862])).
% 7.19/7.44 tff(7864,plain,
% 7.19/7.44 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 7.19/7.44 inference(monotonicity,[status(thm)],[819])).
% 7.19/7.44 tff(7865,plain,
% 7.19/7.44 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 7.19/7.44 inference(symmetry,[status(thm)],[7864])).
% 7.19/7.44 tff(7866,plain,
% 7.19/7.44 (elem!1 = s(z)),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[1495, 812])).
% 7.19/7.44 tff(7867,plain,
% 7.19/7.44 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[337, 7855, 184, 182])).
% 7.19/7.44 tff(7868,plain,
% 7.19/7.44 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[1370, 7867, 297])).
% 7.19/7.44 tff(7869,plain,
% 7.19/7.44 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[3482, 7868, 7866])).
% 7.19/7.44 tff(7870,plain,
% 7.19/7.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 7.19/7.44 inference(modus_ponens,[status(thm)],[7869, 7865])).
% 7.19/7.44 tff(7871,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 7.19/7.44 tff(7872,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 7.19/7.44 tff(7873,plain,
% 7.19/7.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 7.19/7.44 inference(rewrite,[status(thm)],[])).
% 7.19/7.44 tff(7874,plain,
% 7.19/7.44 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 7.19/7.44 inference(rewrite,[status(thm)],[])).
% 7.19/7.44 tff(7875,plain,
% 7.19/7.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 7.19/7.44 inference(monotonicity,[status(thm)],[7874])).
% 7.19/7.44 tff(7876,plain,
% 7.19/7.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 7.19/7.44 inference(transitivity,[status(thm)],[7875, 7873])).
% 7.19/7.44 tff(7877,plain,
% 7.19/7.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 7.19/7.44 inference(quant_inst,[status(thm)],[])).
% 7.19/7.44 tff(7878,plain,
% 7.19/7.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 7.19/7.44 inference(modus_ponens,[status(thm)],[7877, 7876])).
% 7.19/7.44 tff(7879,plain,
% 7.19/7.44 ($false),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[7878, 391, 90, 7872, 7871, 1685])).
% 7.19/7.44 tff(7880,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.44 tff(7881,plain,
% 7.19/7.44 (~b(s(s(s(z))), z)),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[7880, 7870, 7863, 7496])).
% 7.19/7.44 tff(7882,plain,
% 7.19/7.44 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 7.19/7.44 inference(monotonicity,[status(thm)],[819])).
% 7.19/7.44 tff(7883,plain,
% 7.19/7.44 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 7.19/7.44 inference(symmetry,[status(thm)],[7882])).
% 7.19/7.44 tff(7884,plain,
% 7.19/7.44 (b(s(s(s(z))), z)),
% 7.19/7.44 inference(modus_ponens,[status(thm)],[2641, 7883])).
% 7.19/7.44 tff(7885,plain,
% 7.19/7.44 ($false),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[1678, 7884])).
% 7.19/7.44 tff(7886,plain,((~b(s(s(elem!1)), z)) | b(s(s(s(z))), z) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.44 tff(7887,plain,
% 7.19/7.44 (~b(s(s(elem!1)), z)),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[7886, 7881, 812])).
% 7.19/7.44 tff(7888,plain,
% 7.19/7.44 (r(s(s(elem!1)), z)),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[2629, 7887])).
% 7.19/7.44 tff(7889,plain,
% 7.19/7.44 (~r(s(s(elem!1)), s(z))),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[2621, 7888, 182, 7860])).
% 7.19/7.44 tff(7890,plain,
% 7.19/7.44 (b(s(s(elem!1)), s(z))),
% 7.19/7.44 inference(unit_resolution,[status(thm)],[362, 7889])).
% 7.19/7.44 tff(7891,plain,
% 7.19/7.44 (b(s(s(elem!1)), elem!1)),
% 7.19/7.44 inference(modus_ponens,[status(thm)],[7890, 1458])).
% 7.19/7.44 tff(7892,plain,
% 7.19/7.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.19/7.44 inference(rewrite,[status(thm)],[])).
% 7.19/7.44 tff(7893,plain,
% 7.19/7.44 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.19/7.44 inference(rewrite,[status(thm)],[])).
% 7.19/7.44 tff(7894,plain,
% 7.19/7.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1))))),
% 7.19/7.44 inference(monotonicity,[status(thm)],[7893])).
% 7.19/7.44 tff(7895,plain,
% 7.19/7.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.19/7.44 inference(transitivity,[status(thm)],[7894, 7892])).
% 7.19/7.44 tff(7896,plain,
% 7.19/7.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 7.19/7.44 inference(quant_inst,[status(thm)],[])).
% 7.19/7.44 tff(7897,plain,
% 7.19/7.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1))),
% 7.19/7.45 inference(modus_ponens,[status(thm)],[7896, 7895])).
% 7.19/7.45 tff(7898,plain,
% 7.19/7.45 ($false),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[7897, 391, 7857, 380, 7891, 3927, 7859])).
% 7.19/7.45 tff(7899,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(s(z)))), elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.45 tff(7900,plain,
% 7.19/7.45 (~b(s(s(s(elem!1))), z)),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[7899, 7843, 812, 7844, 59, 5888, 7848, 3618, 7413, 7847, 133])).
% 7.19/7.45 tff(7901,plain,
% 7.19/7.45 (r(s(s(s(elem!1))), z)),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[377, 7900])).
% 7.19/7.45 tff(7902,plain,
% 7.19/7.45 (~r(s(z), s(s(s(elem!1))))),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[1867, 7901, 59, 7844])).
% 7.19/7.45 tff(7903,plain,
% 7.19/7.45 (b(s(z), s(s(s(elem!1))))),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[247, 7902])).
% 7.19/7.45 tff(7904,plain,
% 7.19/7.45 (b(elem!1, s(s(s(elem!1))))),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[7796, 7903, 812])).
% 7.19/7.45 tff(7905,plain,
% 7.19/7.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 7.19/7.45 inference(rewrite,[status(thm)],[])).
% 7.19/7.45 tff(7906,plain,
% 7.19/7.45 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 7.19/7.45 inference(rewrite,[status(thm)],[])).
% 7.19/7.45 tff(7907,plain,
% 7.19/7.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 7.19/7.45 inference(monotonicity,[status(thm)],[7906])).
% 7.19/7.45 tff(7908,plain,
% 7.19/7.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 7.19/7.45 inference(transitivity,[status(thm)],[7907, 7905])).
% 7.19/7.45 tff(7909,plain,
% 7.19/7.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 7.19/7.45 inference(quant_inst,[status(thm)],[])).
% 7.19/7.45 tff(7910,plain,
% 7.19/7.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 7.19/7.45 inference(modus_ponens,[status(thm)],[7909, 7908])).
% 7.19/7.45 tff(7911,plain,
% 7.19/7.45 ($false),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[7910, 391, 133, 1101, 973, 448, 3927])).
% 7.19/7.45 tff(7912,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.45 tff(7913,plain,
% 7.19/7.45 (~b(s(s(elem!1)), elem!1)),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[7912, 1101, 133, 448, 3927])).
% 7.19/7.45 tff(7914,plain,
% 7.19/7.45 (r(s(s(elem!1)), elem!1)),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[872, 7913, 249])).
% 7.19/7.45 tff(7915,plain,
% 7.19/7.45 (~b(s(elem!1), elem!1)),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[6869, 1101, 900, 448])).
% 7.19/7.45 tff(7916,plain,
% 7.19/7.45 (r(s(elem!1), elem!1)),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[2168, 7915, 164])).
% 7.19/7.45 tff(7917,plain,
% 7.19/7.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 7.19/7.45 inference(rewrite,[status(thm)],[])).
% 7.19/7.45 tff(7918,plain,
% 7.19/7.45 (((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 7.19/7.45 inference(rewrite,[status(thm)],[])).
% 7.19/7.45 tff(7919,plain,
% 7.19/7.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 7.19/7.45 inference(monotonicity,[status(thm)],[7918])).
% 7.19/7.45 tff(7920,plain,
% 7.19/7.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 7.19/7.45 inference(transitivity,[status(thm)],[7919, 7917])).
% 7.19/7.45 tff(7921,plain,
% 7.19/7.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 7.19/7.45 inference(quant_inst,[status(thm)],[])).
% 7.19/7.45 tff(7922,plain,
% 7.19/7.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 7.19/7.45 inference(modus_ponens,[status(thm)],[7921, 7920])).
% 7.19/7.45 tff(7923,plain,
% 7.19/7.45 (~r(s(elem!1), s(s(elem!1)))),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[7922, 194, 530, 7916, 7914])).
% 7.19/7.45 tff(7924,plain,
% 7.19/7.45 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[1111, 42, 7923])).
% 7.19/7.45 tff(7925,plain,
% 7.19/7.45 (b(s(elem!1), s(s(elem!1)))),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[7924, 1100])).
% 7.19/7.45 tff(7926,plain,
% 7.19/7.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 7.19/7.45 inference(rewrite,[status(thm)],[])).
% 7.19/7.45 tff(7927,plain,
% 7.19/7.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 7.19/7.45 inference(quant_inst,[status(thm)],[])).
% 7.19/7.45 tff(7928,plain,
% 7.19/7.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 7.19/7.45 inference(modus_ponens,[status(thm)],[7927, 7926])).
% 7.19/7.45 tff(7929,plain,
% 7.19/7.45 ($false),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[7928, 194, 530, 485, 364, 2170])).
% 7.19/7.45 tff(7930,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.45 tff(7931,plain,
% 7.19/7.45 (~r(s(s(elem!1)), s(elem!1))),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[7930, 7914, 530, 7916])).
% 7.19/7.45 tff(7932,plain,
% 7.19/7.45 (b(s(s(elem!1)), s(elem!1))),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[1135, 7931, 285])).
% 7.19/7.45 tff(7933,plain,
% 7.19/7.45 (~r(s(elem!1), z)),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[3554, 1101, 184, 7437, 900, 530])).
% 7.19/7.45 tff(7934,plain,
% 7.19/7.45 (b(s(elem!1), z)),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[549, 7933])).
% 7.19/7.45 tff(7935,plain,
% 7.19/7.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 7.19/7.45 inference(rewrite,[status(thm)],[])).
% 7.19/7.45 tff(7936,plain,
% 7.19/7.45 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 7.19/7.45 inference(rewrite,[status(thm)],[])).
% 7.19/7.45 tff(7937,plain,
% 7.19/7.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 7.19/7.45 inference(monotonicity,[status(thm)],[7936])).
% 7.19/7.45 tff(7938,plain,
% 7.19/7.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 7.19/7.45 inference(transitivity,[status(thm)],[7937, 7935])).
% 7.19/7.45 tff(7939,plain,
% 7.19/7.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 7.19/7.45 inference(quant_inst,[status(thm)],[])).
% 7.19/7.45 tff(7940,plain,
% 7.19/7.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 7.19/7.45 inference(modus_ponens,[status(thm)],[7939, 7938])).
% 7.19/7.45 tff(7941,plain,
% 7.19/7.45 ($false),
% 7.19/7.45 inference(unit_resolution,[status(thm)],[7940, 391, 3927, 7934, 7932, 7925])).
% 7.19/7.45 tff(7942,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~r(elem!1, z)) | (s(s(elem!1)) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(elem!1) = elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.46 tff(7943,plain,
% 7.19/7.46 (~b(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.46 inference(unit_resolution,[status(thm)],[7942, 7843, 7412, 3618, 7422, 133, 7904, 5887, 7848, 59])).
% 7.19/7.46 tff(7944,plain,
% 7.19/7.46 (r(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.46 inference(unit_resolution,[status(thm)],[588, 7943, 7433])).
% 7.19/7.46 tff(7945,plain,
% 7.19/7.46 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 7.19/7.46 inference(symmetry,[status(thm)],[820])).
% 7.19/7.46 tff(7946,plain,
% 7.19/7.46 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 7.19/7.46 inference(monotonicity,[status(thm)],[7945])).
% 7.19/7.46 tff(7947,plain,
% 7.19/7.46 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 7.19/7.46 inference(symmetry,[status(thm)],[7946])).
% 7.19/7.46 tff(7948,plain,
% 7.19/7.46 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 7.19/7.46 inference(monotonicity,[status(thm)],[818])).
% 7.19/7.46 tff(7949,plain,
% 7.19/7.46 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 7.19/7.46 inference(transitivity,[status(thm)],[7948, 7947])).
% 7.19/7.46 tff(7950,plain,
% 7.19/7.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.46 inference(rewrite,[status(thm)],[])).
% 7.19/7.46 tff(7951,plain,
% 7.19/7.46 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.46 inference(rewrite,[status(thm)],[])).
% 7.19/7.46 tff(7952,plain,
% 7.19/7.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 7.19/7.46 inference(monotonicity,[status(thm)],[7951])).
% 7.19/7.46 tff(7953,plain,
% 7.19/7.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.46 inference(transitivity,[status(thm)],[7952, 7950])).
% 7.19/7.46 tff(7954,plain,
% 7.19/7.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 7.19/7.46 inference(quant_inst,[status(thm)],[])).
% 7.19/7.46 tff(7955,plain,
% 7.19/7.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 7.19/7.46 inference(modus_ponens,[status(thm)],[7954, 7953])).
% 7.19/7.46 tff(7956,plain,
% 7.19/7.46 ($false),
% 7.19/7.46 inference(unit_resolution,[status(thm)],[7955, 194, 613, 1628, 184, 604])).
% 7.19/7.46 tff(7957,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.46 tff(7958,plain,
% 7.19/7.46 (~r(s(elem!1), s(s(s(elem!1))))),
% 7.19/7.46 inference(unit_resolution,[status(thm)],[7957, 1628, 613, 184])).
% 7.19/7.46 tff(7959,plain,
% 7.19/7.46 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.19/7.46 inference(unit_resolution,[status(thm)],[3614, 7958, 812])).
% 7.19/7.46 tff(7960,plain,
% 7.19/7.46 (b(s(s(z)), s(s(s(s(z)))))),
% 7.19/7.46 inference(unit_resolution,[status(thm)],[3652, 7959])).
% 7.19/7.46 tff(7961,plain,
% 7.19/7.46 (b(s(elem!1), s(s(s(elem!1))))),
% 7.19/7.46 inference(modus_ponens,[status(thm)],[7960, 7949])).
% 7.19/7.46 tff(7962,plain,
% 7.19/7.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.46 inference(rewrite,[status(thm)],[])).
% 7.19/7.46 tff(7963,plain,
% 7.19/7.46 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.46 inference(rewrite,[status(thm)],[])).
% 7.19/7.46 tff(7964,plain,
% 7.19/7.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 7.19/7.46 inference(monotonicity,[status(thm)],[7963])).
% 7.19/7.46 tff(7965,plain,
% 7.19/7.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 7.19/7.46 inference(transitivity,[status(thm)],[7964, 7962])).
% 7.19/7.46 tff(7966,plain,
% 7.19/7.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 7.19/7.46 inference(quant_inst,[status(thm)],[])).
% 7.19/7.46 tff(7967,plain,
% 7.19/7.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 7.19/7.46 inference(modus_ponens,[status(thm)],[7966, 7965])).
% 7.19/7.46 tff(7968,plain,
% 7.19/7.46 ($false),
% 7.19/7.46 inference(unit_resolution,[status(thm)],[7967, 391, 900, 448, 6140, 7961])).
% 7.19/7.46 tff(7969,plain,((~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.46 tff(7970,plain,
% 7.19/7.46 (~r(s(elem!1), z)),
% 7.19/7.46 inference(unit_resolution,[status(thm)],[7969, 7904, 7848, 812, 7944, 59, 5888, 3618])).
% 7.19/7.46 tff(7971,plain,
% 7.19/7.46 (b(s(elem!1), z)),
% 7.19/7.46 inference(unit_resolution,[status(thm)],[549, 7970])).
% 7.19/7.46 tff(7972,plain,
% 7.19/7.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 7.19/7.46 inference(rewrite,[status(thm)],[])).
% 7.19/7.46 tff(7973,plain,
% 7.19/7.46 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 7.19/7.47 inference(rewrite,[status(thm)],[])).
% 7.19/7.47 tff(7974,plain,
% 7.19/7.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1))))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[7973])).
% 7.19/7.47 tff(7975,plain,
% 7.19/7.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 7.19/7.47 inference(transitivity,[status(thm)],[7974, 7972])).
% 7.19/7.47 tff(7976,plain,
% 7.19/7.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 7.19/7.47 inference(quant_inst,[status(thm)],[])).
% 7.19/7.47 tff(7977,plain,
% 7.19/7.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1))),
% 7.19/7.47 inference(modus_ponens,[status(thm)],[7976, 7975])).
% 7.19/7.47 tff(7978,plain,
% 7.19/7.47 ($false),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[7977, 391, 133, 900, 448, 591, 2122])).
% 7.19/7.47 tff(7979,plain,((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.47 tff(7980,plain,
% 7.19/7.47 (~b(s(elem!1), elem!1)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[7979, 7904, 7848, 133, 7971])).
% 7.19/7.47 tff(7981,plain,
% 7.19/7.47 (r(s(elem!1), elem!1)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[2168, 7980, 5887])).
% 7.19/7.47 tff(7982,plain,
% 7.19/7.47 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[820])).
% 7.19/7.47 tff(7983,plain,
% 7.19/7.47 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 7.19/7.47 inference(symmetry,[status(thm)],[7982])).
% 7.19/7.47 tff(7984,plain,
% 7.19/7.47 (r(s(s(s(s(z)))), s(elem!1))),
% 7.19/7.47 inference(modus_ponens,[status(thm)],[7944, 7983])).
% 7.19/7.47 tff(7985,plain,
% 7.19/7.47 (r(s(s(s(s(z)))), z)),
% 7.19/7.47 inference(modus_ponens,[status(thm)],[7901, 7601])).
% 7.19/7.47 tff(7986,plain,
% 7.19/7.47 (~r(z, s(elem!1))),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[5914, 7981, 7985, 7984])).
% 7.19/7.47 tff(7987,plain,
% 7.19/7.47 (b(z, s(elem!1))),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[566, 7986])).
% 7.19/7.47 tff(7988,plain,
% 7.19/7.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 7.19/7.47 inference(rewrite,[status(thm)],[])).
% 7.19/7.47 tff(7989,plain,
% 7.19/7.47 (((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 7.19/7.47 inference(rewrite,[status(thm)],[])).
% 7.19/7.47 tff(7990,plain,
% 7.19/7.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[7989])).
% 7.19/7.47 tff(7991,plain,
% 7.19/7.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 7.19/7.47 inference(transitivity,[status(thm)],[7990, 7988])).
% 7.19/7.47 tff(7992,plain,
% 7.19/7.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 7.19/7.47 inference(quant_inst,[status(thm)],[])).
% 7.19/7.47 tff(7993,plain,
% 7.19/7.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 7.19/7.47 inference(modus_ponens,[status(thm)],[7992, 7991])).
% 7.19/7.47 tff(7994,plain,
% 7.19/7.47 ($false),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[7993, 391, 133, 3927, 592, 591, 1037])).
% 7.19/7.47 tff(7995,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.47 tff(7996,plain,
% 7.19/7.47 (~b(s(s(elem!1)), s(elem!1))),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[7995, 7987, 7843, 133, 7971])).
% 7.19/7.47 tff(7997,plain,
% 7.19/7.47 (r(s(s(elem!1)), s(elem!1))),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[1135, 7996, 7412])).
% 7.19/7.47 tff(7998,plain,
% 7.19/7.47 (~r(s(s(elem!1)), elem!1)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[7930, 7997, 3618, 7981])).
% 7.19/7.47 tff(7999,plain,
% 7.19/7.47 (b(s(s(elem!1)), elem!1)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[872, 7998, 7422])).
% 7.19/7.47 tff(8000,plain,
% 7.19/7.47 ($false),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[6059, 391, 133, 7848, 7999, 7904, 7843])).
% 7.19/7.47 tff(8001,plain,(b(elem!1, z) | (~b(z, elem!1)) | (~(s(z) = elem!1)) | b(z, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 7.19/7.47 tff(8002,plain,
% 7.19/7.47 (b(elem!1, z)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[8001, 7396, 149, 10, 148, 2])).
% 7.19/7.47 tff(8003,plain,
% 7.19/7.47 (~b(s(s(s(elem!1))), z)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[5769, 391, 149, 8002, 7842])).
% 7.19/7.47 tff(8004,plain,
% 7.19/7.47 (r(s(s(s(elem!1))), z)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[377, 8003])).
% 7.19/7.47 tff(8005,plain,
% 7.19/7.47 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 7.19/7.47 inference(monotonicity,[status(thm)],[7396])).
% 7.19/7.47 tff(8006,plain,
% 7.19/7.47 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[8005])).
% 7.19/7.47 tff(8007,plain,
% 7.19/7.47 (~(s(s(elem!1)) = elem!1)),
% 7.19/7.47 inference(modus_ponens,[status(thm)],[357, 8006])).
% 7.19/7.47 tff(8008,plain,
% 7.19/7.47 (s(s(z)) = s(elem!1)),
% 7.19/7.47 inference(monotonicity,[status(thm)],[7396])).
% 7.19/7.47 tff(8009,plain,
% 7.19/7.47 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[8008])).
% 7.19/7.47 tff(8010,plain,
% 7.19/7.47 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[8009])).
% 7.19/7.47 tff(8011,plain,
% 7.19/7.47 (~(s(s(elem!1)) = s(elem!1))),
% 7.19/7.47 inference(modus_ponens,[status(thm)],[2680, 8010])).
% 7.19/7.47 tff(8012,plain,
% 7.19/7.47 (b(z, s(z)) <=> b(z, elem!1)),
% 7.19/7.47 inference(monotonicity,[status(thm)],[7396])).
% 7.19/7.47 tff(8013,plain,
% 7.19/7.47 (b(z, elem!1) <=> b(z, s(z))),
% 7.19/7.47 inference(symmetry,[status(thm)],[8012])).
% 7.19/7.47 tff(8014,plain,
% 7.19/7.47 (b(z, s(z))),
% 7.19/7.47 inference(modus_ponens,[status(thm)],[149, 8013])).
% 7.19/7.47 tff(8015,plain,
% 7.19/7.47 (~r(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[5618, 194, 1628, 174, 184])).
% 7.19/7.47 tff(8016,plain,
% 7.19/7.47 (b(s(s(s(elem!1))), s(elem!1))),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[588, 8015, 7433])).
% 7.19/7.47 tff(8017,plain,
% 7.19/7.47 (~r(elem!1, z)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[3554, 8016, 184, 437, 900, 1628])).
% 7.19/7.47 tff(8018,plain,
% 7.19/7.47 (~r(s(z), z)),
% 7.19/7.47 inference(modus_ponens,[status(thm)],[8017, 3180])).
% 7.19/7.47 tff(8019,plain,
% 7.19/7.47 (~r(s(elem!1), s(s(s(elem!1))))),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[5427, 194, 1628, 174, 184])).
% 7.19/7.47 tff(8020,plain,
% 7.19/7.47 (r(s(z), z)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[7734, 8016, 184, 8019, 664, 7435, 7434, 7422, 285, 812])).
% 7.19/7.47 tff(8021,plain,
% 7.19/7.47 ($false),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[8020, 8018])).
% 7.19/7.47 tff(8022,plain,((~r(s(elem!1), z)) | (~(s(z) = elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(elem!1)) | (elem!1 = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.47 tff(8023,plain,
% 7.19/7.47 (~r(s(elem!1), z)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[8022, 7396, 59, 8014, 8011, 167, 7842, 8004])).
% 7.19/7.47 tff(8024,plain,
% 7.19/7.47 (b(s(elem!1), z)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[549, 8023])).
% 7.19/7.47 tff(8025,plain,
% 7.19/7.47 (~b(s(elem!1), elem!1)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[7777, 8024, 8002, 149])).
% 7.19/7.47 tff(8026,plain,
% 7.19/7.47 (r(s(elem!1), elem!1)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[2168, 8025, 159])).
% 7.19/7.47 tff(8027,plain,
% 7.19/7.47 (s(s(s(z))) = s(s(elem!1))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[8008])).
% 7.19/7.47 tff(8028,plain,
% 7.19/7.47 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[8027])).
% 7.19/7.47 tff(8029,plain,
% 7.19/7.47 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[8028])).
% 7.19/7.47 tff(8030,plain,
% 7.19/7.47 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(elem!1)))))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[8029])).
% 7.19/7.47 tff(8031,plain,
% 7.19/7.47 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 7.19/7.47 inference(symmetry,[status(thm)],[8030])).
% 7.19/7.47 tff(8032,plain,
% 7.19/7.47 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 7.19/7.47 inference(monotonicity,[status(thm)],[8031])).
% 7.19/7.47 tff(8033,plain,
% 7.19/7.47 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 7.19/7.47 inference(symmetry,[status(thm)],[8032])).
% 7.19/7.47 tff(8034,plain,
% 7.19/7.47 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 7.19/7.47 inference(monotonicity,[status(thm)],[7396])).
% 7.19/7.47 tff(8035,plain,
% 7.19/7.47 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 7.19/7.47 inference(monotonicity,[status(thm)],[8034])).
% 7.19/7.47 tff(8036,plain,
% 7.19/7.47 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 7.19/7.47 inference(modus_ponens,[status(thm)],[5065, 8035])).
% 7.19/7.47 tff(8037,plain,
% 7.19/7.47 (elem!1 = s(z)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[1495, 7396])).
% 7.19/7.47 tff(8038,plain,
% 7.19/7.47 (b(s(s(s(s(z)))), elem!1)),
% 7.19/7.47 inference(unit_resolution,[status(thm)],[1563, 7842, 8037])).
% 7.19/7.47 tff(8039,plain,
% 7.19/7.47 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 7.19/7.47 inference(monotonicity,[status(thm)],[8028])).
% 7.19/7.47 tff(8040,plain,
% 7.19/7.47 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 7.19/7.47 inference(symmetry,[status(thm)],[8039])).
% 7.19/7.47 tff(8041,plain,
% 7.19/7.47 (r(s(s(s(s(z)))), z)),
% 7.19/7.47 inference(modus_ponens,[status(thm)],[8004, 8040])).
% 7.19/7.47 tff(8042,assumption,(b(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 7.19/7.47 tff(8043,plain,
% 7.19/7.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 7.19/7.48 inference(rewrite,[status(thm)],[])).
% 7.19/7.48 tff(8044,plain,
% 7.19/7.48 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 7.19/7.48 inference(rewrite,[status(thm)],[])).
% 7.19/7.48 tff(8045,plain,
% 7.19/7.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 7.19/7.48 inference(monotonicity,[status(thm)],[8044])).
% 7.19/7.48 tff(8046,plain,
% 7.19/7.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 7.19/7.48 inference(transitivity,[status(thm)],[8045, 8043])).
% 7.19/7.48 tff(8047,plain,
% 7.19/7.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 7.19/7.48 inference(quant_inst,[status(thm)],[])).
% 7.19/7.48 tff(8048,plain,
% 7.19/7.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z))),
% 7.19/7.48 inference(modus_ponens,[status(thm)],[8047, 8046])).
% 7.19/7.48 tff(8049,plain,
% 7.19/7.48 (~b(s(s(s(s(s(s(z)))))), z)),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[8048, 391, 133, 665, 8042])).
% 7.19/7.48 tff(8050,plain,
% 7.19/7.48 (r(s(s(s(s(s(s(z)))))), z)),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[6641, 42, 6638, 8049])).
% 7.19/7.48 tff(8051,plain,
% 7.19/7.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 7.19/7.48 inference(rewrite,[status(thm)],[])).
% 7.19/7.48 tff(8052,plain,
% 7.19/7.48 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 7.19/7.48 inference(rewrite,[status(thm)],[])).
% 7.19/7.48 tff(8053,plain,
% 7.19/7.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 7.19/7.48 inference(monotonicity,[status(thm)],[8052])).
% 7.19/7.48 tff(8054,plain,
% 7.19/7.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 7.19/7.48 inference(transitivity,[status(thm)],[8053, 8051])).
% 7.19/7.48 tff(8055,plain,
% 7.19/7.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 7.19/7.48 inference(quant_inst,[status(thm)],[])).
% 7.19/7.48 tff(8056,plain,
% 7.19/7.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 7.19/7.48 inference(modus_ponens,[status(thm)],[8055, 8054])).
% 7.19/7.48 tff(8057,plain,
% 7.19/7.48 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[8056, 391, 133, 665, 1652, 8042])).
% 7.19/7.48 tff(8058,plain,
% 7.19/7.48 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[6652, 42, 4995, 8057])).
% 7.19/7.48 tff(8059,plain,
% 7.19/7.48 (~b(z, s(s(s(s(z)))))),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[5600, 391, 133, 665, 1652])).
% 7.19/7.48 tff(8060,plain,
% 7.19/7.48 (r(z, s(s(s(s(z)))))),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[800, 8059])).
% 7.19/7.48 tff(8061,plain,
% 7.19/7.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 7.19/7.48 inference(rewrite,[status(thm)],[])).
% 7.19/7.48 tff(8062,plain,
% 7.19/7.48 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 7.19/7.48 inference(rewrite,[status(thm)],[])).
% 7.19/7.48 tff(8063,plain,
% 7.19/7.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 7.19/7.48 inference(monotonicity,[status(thm)],[8062])).
% 7.19/7.48 tff(8064,plain,
% 7.19/7.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 7.19/7.48 inference(transitivity,[status(thm)],[8063, 8061])).
% 7.19/7.48 tff(8065,plain,
% 7.19/7.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 7.19/7.48 inference(quant_inst,[status(thm)],[])).
% 7.19/7.48 tff(8066,plain,
% 7.19/7.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 7.19/7.48 inference(modus_ponens,[status(thm)],[8065, 8064])).
% 7.19/7.48 tff(8067,plain,
% 7.19/7.48 ($false),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[8066, 194, 2053, 8060, 8058, 8050])).
% 7.19/7.48 tff(8068,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.48 tff(8069,plain,
% 7.19/7.48 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[8068, 8041, 149, 8038, 8002])).
% 7.19/7.48 tff(8070,plain,
% 7.19/7.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))),
% 7.19/7.48 inference(rewrite,[status(thm)],[])).
% 7.19/7.48 tff(8071,plain,
% 7.19/7.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))),
% 7.19/7.48 inference(quant_inst,[status(thm)],[])).
% 7.19/7.48 tff(8072,plain,
% 7.19/7.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 7.19/7.48 inference(modus_ponens,[status(thm)],[8071, 8070])).
% 7.19/7.48 tff(8073,plain,
% 7.19/7.48 ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[8072, 42])).
% 7.19/7.48 tff(8074,plain,
% 7.19/7.48 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[8073, 8069, 8036])).
% 7.19/7.48 tff(8075,plain,
% 7.19/7.48 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 7.19/7.48 inference(modus_ponens,[status(thm)],[8074, 8033])).
% 7.19/7.48 tff(8076,plain,
% 7.19/7.48 (~b(elem!1, s(elem!1))),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[7689, 391, 149, 8002, 8024])).
% 7.19/7.48 tff(8077,plain,
% 7.19/7.48 (r(elem!1, s(elem!1))),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[443, 8076, 167])).
% 7.19/7.48 tff(8078,plain,
% 7.19/7.48 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 7.19/7.48 inference(commutativity,[status(thm)],[])).
% 7.19/7.48 tff(8079,plain,
% 7.19/7.48 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 7.19/7.48 inference(monotonicity,[status(thm)],[820])).
% 7.19/7.48 tff(8080,plain,
% 7.19/7.48 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(elem!1)))))),
% 7.19/7.48 inference(monotonicity,[status(thm)],[8079])).
% 7.19/7.48 tff(8081,plain,
% 7.19/7.48 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 7.19/7.48 inference(symmetry,[status(thm)],[8080])).
% 7.19/7.48 tff(8082,plain,
% 7.19/7.48 (s(s(elem!1)) = s(s(s(z)))),
% 7.19/7.48 inference(symmetry,[status(thm)],[819])).
% 7.19/7.48 tff(8083,plain,
% 7.19/7.48 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 7.19/7.48 inference(monotonicity,[status(thm)],[8082, 8081])).
% 7.19/7.48 tff(8084,plain,
% 7.19/7.48 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 7.19/7.48 inference(transitivity,[status(thm)],[8083, 8078])).
% 7.19/7.48 tff(8085,plain,
% 7.19/7.48 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 7.19/7.48 inference(symmetry,[status(thm)],[8084])).
% 7.19/7.48 tff(8086,plain,
% 7.19/7.48 ((~(s(s(s(s(s(s(z)))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))),
% 7.19/7.48 inference(monotonicity,[status(thm)],[8085])).
% 7.19/7.48 tff(8087,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(z)))), introduced(assumption)).
% 7.19/7.48 tff(8088,plain,
% 7.19/7.48 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(z))))),
% 7.19/7.48 inference(monotonicity,[status(thm)],[8087])).
% 7.19/7.48 tff(8089,plain,
% 7.19/7.48 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 7.19/7.48 inference(symmetry,[status(thm)],[8088])).
% 7.19/7.48 tff(8090,plain,
% 7.19/7.48 (s(s(z)) = s(s(s(s(s(z)))))),
% 7.19/7.48 inference(transitivity,[status(thm)],[710, 8089, 4988])).
% 7.19/7.48 tff(8091,plain,
% 7.19/7.48 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 7.19/7.48 inference(monotonicity,[status(thm)],[8090])).
% 7.19/7.48 tff(8092,plain,
% 7.19/7.48 (s(z) = s(s(s(s(z))))),
% 7.19/7.48 inference(transitivity,[status(thm)],[706, 8091, 4986])).
% 7.19/7.48 tff(8093,plain,
% 7.19/7.48 ($false),
% 7.19/7.48 inference(unit_resolution,[status(thm)],[743, 8092])).
% 7.19/7.48 tff(8094,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.48 tff(8095,plain,
% 7.19/7.48 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 7.19/7.48 inference(modus_ponens,[status(thm)],[8094, 8086])).
% 7.19/7.49 tff(8096,plain,
% 7.19/7.49 (s(elem!1) = s(s(z))),
% 7.19/7.49 inference(symmetry,[status(thm)],[818])).
% 7.19/7.49 tff(8097,plain,
% 7.19/7.49 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 7.19/7.49 inference(monotonicity,[status(thm)],[8081, 8096])).
% 7.19/7.49 tff(8098,plain,
% 7.19/7.49 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 7.19/7.49 inference(symmetry,[status(thm)],[8097])).
% 7.19/7.49 tff(8099,plain,
% 7.19/7.49 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 7.19/7.49 inference(monotonicity,[status(thm)],[8098])).
% 7.19/7.49 tff(8100,plain,
% 7.19/7.49 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 7.19/7.49 inference(modus_ponens,[status(thm)],[5009, 8099])).
% 7.19/7.49 tff(8101,assumption,(r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 7.19/7.49 tff(8102,plain,
% 7.19/7.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 7.19/7.49 inference(rewrite,[status(thm)],[])).
% 7.19/7.49 tff(8103,plain,
% 7.19/7.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 7.19/7.49 inference(quant_inst,[status(thm)],[])).
% 7.19/7.49 tff(8104,plain,
% 7.19/7.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 7.19/7.49 inference(modus_ponens,[status(thm)],[8103, 8102])).
% 7.19/7.49 tff(8105,plain,
% 7.19/7.49 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[8104, 194, 485, 2251, 8101])).
% 7.19/7.49 tff(8106,plain,
% 7.19/7.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 7.19/7.49 inference(rewrite,[status(thm)],[])).
% 7.19/7.49 tff(8107,plain,
% 7.19/7.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 7.19/7.49 inference(quant_inst,[status(thm)],[])).
% 7.19/7.49 tff(8108,plain,
% 7.19/7.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 7.19/7.49 inference(modus_ponens,[status(thm)],[8107, 8106])).
% 7.19/7.49 tff(8109,plain,
% 7.19/7.49 ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[8108, 42, 8105])).
% 7.19/7.49 tff(8110,plain,
% 7.19/7.49 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[8109, 8100])).
% 7.19/7.49 tff(8111,plain,
% 7.19/7.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 7.19/7.49 inference(rewrite,[status(thm)],[])).
% 7.19/7.49 tff(8112,plain,
% 7.19/7.49 (((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(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(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 7.19/7.49 inference(rewrite,[status(thm)],[])).
% 7.19/7.49 tff(8113,plain,
% 7.19/7.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 7.19/7.49 inference(monotonicity,[status(thm)],[8112])).
% 7.19/7.49 tff(8114,plain,
% 7.19/7.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 7.19/7.49 inference(transitivity,[status(thm)],[8113, 8111])).
% 7.19/7.49 tff(8115,plain,
% 7.19/7.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 7.19/7.49 inference(quant_inst,[status(thm)],[])).
% 7.19/7.49 tff(8116,plain,
% 7.19/7.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 7.19/7.49 inference(modus_ponens,[status(thm)],[8115, 8114])).
% 7.19/7.49 tff(8117,plain,
% 7.19/7.49 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[8116, 391, 133, 591, 5808, 8110])).
% 7.19/7.49 tff(8118,plain,
% 7.19/7.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 7.19/7.49 inference(rewrite,[status(thm)],[])).
% 7.19/7.49 tff(8119,plain,
% 7.19/7.49 (((~r(elem!1, s(elem!1))) | (~r(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(elem!1)))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 7.19/7.49 inference(rewrite,[status(thm)],[])).
% 7.19/7.49 tff(8120,plain,
% 7.19/7.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(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(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 7.19/7.49 inference(monotonicity,[status(thm)],[8119])).
% 7.19/7.49 tff(8121,plain,
% 7.19/7.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(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(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 7.19/7.49 inference(transitivity,[status(thm)],[8120, 8118])).
% 7.19/7.49 tff(8122,plain,
% 7.19/7.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(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(elem!1))))))))),
% 7.19/7.49 inference(quant_inst,[status(thm)],[])).
% 7.19/7.49 tff(8123,plain,
% 7.19/7.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 7.19/7.49 inference(modus_ponens,[status(thm)],[8122, 8121])).
% 7.19/7.49 tff(8124,plain,
% 7.19/7.49 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[8123, 194, 2251, 364, 8101])).
% 7.19/7.49 tff(8125,plain,
% 7.19/7.49 (((~![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)))))))) <=> ((~![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)))))))),
% 7.19/7.49 inference(rewrite,[status(thm)],[])).
% 7.19/7.49 tff(8126,plain,
% 7.19/7.49 ((~![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)))))))),
% 7.19/7.49 inference(quant_inst,[status(thm)],[])).
% 7.19/7.49 tff(8127,plain,
% 7.19/7.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 7.19/7.49 inference(modus_ponens,[status(thm)],[8126, 8125])).
% 7.19/7.49 tff(8128,plain,
% 7.19/7.49 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[8127, 42, 8124])).
% 7.19/7.49 tff(8129,plain,
% 7.19/7.49 ($false),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[8128, 8117, 8095])).
% 7.19/7.49 tff(8130,plain,((~r(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~(s(z) = elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.19/7.49 tff(8131,plain,
% 7.19/7.49 (~r(s(s(elem!1)), elem!1)),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[8130, 8024, 149, 7396, 8011, 8077, 8075, 8026])).
% 7.19/7.49 tff(8132,plain,
% 7.19/7.49 (b(s(s(elem!1)), elem!1)),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[872, 8131, 8007])).
% 7.19/7.49 tff(8133,plain,
% 7.19/7.49 (~b(z, s(s(elem!1)))),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[4944, 8132, 8002, 149])).
% 7.19/7.49 tff(8134,plain,
% 7.19/7.49 (r(z, s(s(elem!1)))),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[324, 8133])).
% 7.19/7.49 tff(8135,plain,
% 7.19/7.49 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 7.19/7.49 inference(monotonicity,[status(thm)],[8008])).
% 7.19/7.49 tff(8136,plain,
% 7.19/7.49 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 7.19/7.49 inference(transitivity,[status(thm)],[8135, 582])).
% 7.19/7.49 tff(8137,plain,
% 7.19/7.49 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 7.19/7.49 inference(monotonicity,[status(thm)],[8136])).
% 7.19/7.49 tff(8138,plain,
% 7.19/7.49 (~(s(s(s(elem!1))) = s(elem!1))),
% 7.19/7.49 inference(modus_ponens,[status(thm)],[1397, 8137])).
% 7.19/7.49 tff(8139,plain,
% 7.19/7.49 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 7.19/7.49 inference(unit_resolution,[status(thm)],[281, 8138])).
% 7.19/7.49 tff(8140,plain,
% 7.19/7.49 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 7.19/7.49 inference(symmetry,[status(thm)],[8028])).
% 7.19/7.49 tff(8141,plain,
% 7.19/7.49 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 7.19/7.49 inference(monotonicity,[status(thm)],[8140, 8031])).
% 7.19/7.49 tff(8142,plain,
% 7.19/7.49 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 7.19/7.49 inference(symmetry,[status(thm)],[8141])).
% 7.19/7.49 tff(8143,plain,
% 7.19/7.49 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))))),
% 7.19/7.49 inference(monotonicity,[status(thm)],[8142])).
% 7.19/7.49 tff(8144,plain,
% 7.19/7.49 (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 7.29/7.50 inference(modus_ponens,[status(thm)],[4995, 8143])).
% 7.29/7.50 tff(8145,plain,
% 7.29/7.50 (s(elem!1) = s(s(z))),
% 7.29/7.50 inference(symmetry,[status(thm)],[8008])).
% 7.29/7.50 tff(8146,plain,
% 7.29/7.50 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 7.29/7.50 inference(monotonicity,[status(thm)],[8031, 8145])).
% 7.29/7.50 tff(8147,plain,
% 7.29/7.50 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 7.29/7.50 inference(symmetry,[status(thm)],[8146])).
% 7.29/7.50 tff(8148,plain,
% 7.29/7.50 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 7.29/7.50 inference(monotonicity,[status(thm)],[8147])).
% 7.29/7.50 tff(8149,plain,
% 7.29/7.50 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 7.29/7.50 inference(modus_ponens,[status(thm)],[5009, 8148])).
% 7.29/7.50 tff(8150,plain,
% 7.29/7.50 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 7.29/7.50 inference(unit_resolution,[status(thm)],[8104, 194, 8026, 8077, 8075])).
% 7.29/7.50 tff(8151,plain,
% 7.29/7.50 ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 7.29/7.50 inference(unit_resolution,[status(thm)],[8108, 42, 8150])).
% 7.29/7.50 tff(8152,plain,
% 7.29/7.50 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 7.29/7.50 inference(unit_resolution,[status(thm)],[8151, 8149])).
% 7.29/7.50 tff(8153,assumption,(b(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 7.29/7.50 tff(8154,assumption,(b(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 7.29/7.50 tff(8155,plain,
% 7.29/7.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 7.29/7.50 inference(rewrite,[status(thm)],[])).
% 7.29/7.50 tff(8156,plain,
% 7.29/7.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 7.29/7.50 inference(quant_inst,[status(thm)],[])).
% 7.29/7.50 tff(8157,plain,
% 7.29/7.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 7.29/7.50 inference(modus_ponens,[status(thm)],[8156, 8155])).
% 7.29/7.50 tff(8158,plain,
% 7.29/7.50 ($false),
% 7.29/7.50 inference(unit_resolution,[status(thm)],[8157, 391, 133, 665, 591, 8154, 8153])).
% 7.29/7.50 tff(8159,plain,((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.50 tff(8160,plain,
% 7.29/7.50 (~b(s(s(s(s(s(elem!1))))), z)),
% 7.29/7.50 inference(unit_resolution,[status(thm)],[8159, 8002, 149, 8024, 8152])).
% 7.29/7.50 tff(8161,plain,
% 7.29/7.50 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 7.29/7.50 inference(quant_inst,[status(thm)],[])).
% 7.29/7.50 tff(8162,plain,
% 7.29/7.50 (~(s(s(s(s(s(elem!1))))) = z)),
% 7.29/7.50 inference(unit_resolution,[status(thm)],[8161, 21])).
% 7.29/7.50 tff(8163,plain,
% 7.29/7.50 (((~![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))),
% 7.29/7.50 inference(rewrite,[status(thm)],[])).
% 7.29/7.50 tff(8164,plain,
% 7.29/7.50 ((~![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))),
% 7.29/7.50 inference(quant_inst,[status(thm)],[])).
% 7.29/7.50 tff(8165,plain,
% 7.29/7.50 ((~![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)),
% 7.29/7.50 inference(modus_ponens,[status(thm)],[8164, 8163])).
% 7.29/7.50 tff(8166,plain,
% 7.29/7.50 (r(s(s(s(s(s(elem!1))))), z)),
% 7.29/7.50 inference(unit_resolution,[status(thm)],[8165, 42, 8162, 8160])).
% 7.29/7.50 tff(8167,plain,
% 7.29/7.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 7.29/7.50 inference(rewrite,[status(thm)],[])).
% 7.29/7.50 tff(8168,plain,
% 7.29/7.50 (((~r(z, s(s(s(elem!1))))) | (~r(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(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 7.29/7.50 inference(rewrite,[status(thm)],[])).
% 7.29/7.50 tff(8169,plain,
% 7.29/7.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(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(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))))),
% 7.29/7.50 inference(monotonicity,[status(thm)],[8168])).
% 7.29/7.50 tff(8170,plain,
% 7.29/7.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(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(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 7.29/7.50 inference(transitivity,[status(thm)],[8169, 8167])).
% 7.29/7.50 tff(8171,plain,
% 7.29/7.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(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(elem!1))))))))),
% 7.29/7.50 inference(quant_inst,[status(thm)],[])).
% 7.29/7.50 tff(8172,plain,
% 7.29/7.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))),
% 7.29/7.50 inference(modus_ponens,[status(thm)],[8171, 8170])).
% 7.29/7.50 tff(8173,plain,
% 7.29/7.50 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 7.29/7.50 inference(unit_resolution,[status(thm)],[8172, 194, 8004, 59, 8166])).
% 7.29/7.50 tff(8174,plain,
% 7.29/7.50 (((~![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)))))))),
% 7.29/7.50 inference(rewrite,[status(thm)],[])).
% 7.29/7.50 tff(8175,plain,
% 7.29/7.50 ((~![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)))))))),
% 7.29/7.50 inference(quant_inst,[status(thm)],[])).
% 7.29/7.50 tff(8176,plain,
% 7.29/7.50 ((~![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))))))),
% 7.29/7.50 inference(modus_ponens,[status(thm)],[8175, 8174])).
% 7.29/7.50 tff(8177,plain,
% 7.29/7.50 ((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))))))),
% 7.29/7.50 inference(unit_resolution,[status(thm)],[8176, 42, 8173])).
% 7.29/7.50 tff(8178,plain,
% 7.29/7.50 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 7.29/7.50 inference(unit_resolution,[status(thm)],[8177, 8144])).
% 7.29/7.50 tff(8179,plain,
% 7.29/7.50 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 7.29/7.51 inference(commutativity,[status(thm)],[])).
% 7.29/7.51 tff(8180,plain,
% 7.29/7.51 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 7.29/7.51 inference(monotonicity,[status(thm)],[8031, 8140])).
% 7.29/7.51 tff(8181,plain,
% 7.29/7.51 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 7.29/7.51 inference(transitivity,[status(thm)],[8180, 8179])).
% 7.29/7.51 tff(8182,plain,
% 7.29/7.51 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 7.29/7.51 inference(symmetry,[status(thm)],[8181])).
% 7.29/7.51 tff(8183,plain,
% 7.29/7.51 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 7.29/7.51 inference(monotonicity,[status(thm)],[8182])).
% 7.29/7.51 tff(8184,plain,
% 7.29/7.51 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 7.29/7.51 inference(modus_ponens,[status(thm)],[4995, 8183])).
% 7.29/7.51 tff(8185,plain,
% 7.29/7.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(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(elem!1))))))),
% 7.29/7.51 inference(rewrite,[status(thm)],[])).
% 7.29/7.51 tff(8186,plain,
% 7.29/7.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(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(elem!1))))))),
% 7.29/7.51 inference(quant_inst,[status(thm)],[])).
% 7.29/7.51 tff(8187,plain,
% 7.29/7.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(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(elem!1)))))),
% 7.29/7.51 inference(modus_ponens,[status(thm)],[8186, 8185])).
% 7.29/7.51 tff(8188,plain,
% 7.29/7.51 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 7.29/7.51 inference(unit_resolution,[status(thm)],[8187, 194, 8004, 59, 8166])).
% 7.29/7.51 tff(8189,plain,
% 7.29/7.51 (((~![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)))))),
% 7.29/7.51 inference(rewrite,[status(thm)],[])).
% 7.29/7.51 tff(8190,plain,
% 7.29/7.51 ((~![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)))))),
% 7.29/7.51 inference(quant_inst,[status(thm)],[])).
% 7.29/7.51 tff(8191,plain,
% 7.29/7.51 ((~![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))))),
% 7.29/7.51 inference(modus_ponens,[status(thm)],[8190, 8189])).
% 7.29/7.51 tff(8192,plain,
% 7.29/7.51 ((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))))),
% 7.29/7.51 inference(unit_resolution,[status(thm)],[8191, 42, 8188])).
% 7.29/7.51 tff(8193,plain,
% 7.29/7.51 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 7.29/7.51 inference(unit_resolution,[status(thm)],[8192, 8184])).
% 7.29/7.51 tff(8194,plain,
% 7.29/7.51 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 7.29/7.51 inference(commutativity,[status(thm)],[])).
% 7.29/7.51 tff(8195,plain,
% 7.29/7.51 ((s(elem!1) = s(s(s(s(s(elem!1)))))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 7.29/7.51 inference(monotonicity,[status(thm)],[8145, 8031])).
% 7.29/7.51 tff(8196,plain,
% 7.29/7.51 ((s(elem!1) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 7.29/7.51 inference(transitivity,[status(thm)],[8195, 8194])).
% 7.29/7.51 tff(8197,plain,
% 7.29/7.51 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 7.29/7.51 inference(symmetry,[status(thm)],[8196])).
% 7.29/7.51 tff(8198,plain,
% 7.29/7.51 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(s(elem!1)))))))),
% 7.29/7.51 inference(monotonicity,[status(thm)],[8197])).
% 7.29/7.51 tff(8199,plain,
% 7.29/7.51 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 7.29/7.51 inference(modus_ponens,[status(thm)],[5009, 8198])).
% 7.29/7.51 tff(8200,plain,
% 7.29/7.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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))))))))),
% 7.29/7.51 inference(rewrite,[status(thm)],[])).
% 7.29/7.51 tff(8201,plain,
% 7.29/7.51 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, 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))))))))),
% 7.29/7.51 inference(rewrite,[status(thm)],[])).
% 7.29/7.51 tff(8202,plain,
% 7.29/7.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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)))))))))),
% 7.29/7.51 inference(monotonicity,[status(thm)],[8201])).
% 7.29/7.51 tff(8203,plain,
% 7.29/7.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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))))))))),
% 7.29/7.51 inference(transitivity,[status(thm)],[8202, 8200])).
% 7.29/7.51 tff(8204,plain,
% 7.29/7.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 7.29/7.51 inference(quant_inst,[status(thm)],[])).
% 7.29/7.51 tff(8205,plain,
% 7.29/7.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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)))))))),
% 7.29/7.51 inference(modus_ponens,[status(thm)],[8204, 8203])).
% 7.29/7.51 tff(8206,plain,
% 7.29/7.51 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 7.29/7.51 inference(unit_resolution,[status(thm)],[8205, 194, 8026, 8077, 8075])).
% 7.29/7.51 tff(8207,plain,
% 7.29/7.51 (((~![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)))))))),
% 7.29/7.51 inference(rewrite,[status(thm)],[])).
% 7.29/7.51 tff(8208,plain,
% 7.29/7.51 ((~![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)))))))),
% 7.29/7.51 inference(quant_inst,[status(thm)],[])).
% 7.29/7.51 tff(8209,plain,
% 7.29/7.51 ((~![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))))))),
% 7.29/7.51 inference(modus_ponens,[status(thm)],[8208, 8207])).
% 7.29/7.51 tff(8210,plain,
% 7.29/7.51 ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 7.29/7.51 inference(unit_resolution,[status(thm)],[8209, 42, 8206])).
% 7.29/7.51 tff(8211,plain,
% 7.29/7.51 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 7.29/7.51 inference(unit_resolution,[status(thm)],[8210, 8199])).
% 7.29/7.51 tff(8212,plain,
% 7.29/7.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 7.29/7.51 inference(rewrite,[status(thm)],[])).
% 7.29/7.51 tff(8213,plain,
% 7.29/7.51 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(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(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 7.29/7.51 inference(rewrite,[status(thm)],[])).
% 7.29/7.51 tff(8214,plain,
% 7.29/7.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 7.29/7.51 inference(monotonicity,[status(thm)],[8213])).
% 7.29/7.51 tff(8215,plain,
% 7.29/7.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 7.29/7.51 inference(transitivity,[status(thm)],[8214, 8212])).
% 7.29/7.51 tff(8216,plain,
% 7.29/7.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(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))))),
% 7.29/7.51 inference(quant_inst,[status(thm)],[])).
% 7.29/7.51 tff(8217,plain,
% 7.29/7.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 7.29/7.51 inference(modus_ponens,[status(thm)],[8216, 8215])).
% 7.29/7.51 tff(8218,plain,
% 7.29/7.51 (~b(s(s(s(elem!1))), s(elem!1))),
% 7.29/7.51 inference(unit_resolution,[status(thm)],[8217, 391, 7842, 8211, 8193, 8178])).
% 7.29/7.51 tff(8219,plain,
% 7.29/7.51 (r(s(s(s(elem!1))), s(elem!1))),
% 7.29/7.51 inference(unit_resolution,[status(thm)],[588, 8218, 8138])).
% 7.29/7.51 tff(8220,plain,
% 7.29/7.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.29/7.52 inference(rewrite,[status(thm)],[])).
% 7.29/7.52 tff(8221,plain,
% 7.29/7.52 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.29/7.52 inference(rewrite,[status(thm)],[])).
% 7.29/7.52 tff(8222,plain,
% 7.29/7.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8221])).
% 7.29/7.52 tff(8223,plain,
% 7.29/7.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.29/7.52 inference(transitivity,[status(thm)],[8222, 8220])).
% 7.29/7.52 tff(8224,plain,
% 7.29/7.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.29/7.52 inference(quant_inst,[status(thm)],[])).
% 7.29/7.52 tff(8225,plain,
% 7.29/7.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[8224, 8223])).
% 7.29/7.52 tff(8226,plain,
% 7.29/7.52 (~r(elem!1, s(s(s(elem!1))))),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[8225, 194, 8219, 8026, 8077])).
% 7.29/7.52 tff(8227,plain,
% 7.29/7.52 (b(elem!1, s(s(s(elem!1))))),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[424, 8226, 148])).
% 7.29/7.52 tff(8228,plain,
% 7.29/7.52 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[6001, 8132, 7842, 8227])).
% 7.29/7.52 tff(8229,plain,
% 7.29/7.52 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[1356, 8228, 8139])).
% 7.29/7.52 tff(8230,plain,
% 7.29/7.52 ($false),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[1450, 8229, 8134, 59, 8004])).
% 7.29/7.52 tff(8231,plain,(b(z, s(s(s(elem!1)))) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.29/7.52 tff(8232,plain,
% 7.29/7.52 (r(z, elem!1)),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[8231, 2, 10])).
% 7.29/7.52 tff(8233,plain,
% 7.29/7.52 (~r(elem!1, s(z))),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[5941, 3618, 59, 181])).
% 7.29/7.52 tff(8234,plain,
% 7.29/7.52 (elem!1 = s(z)),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[837, 8233, 31])).
% 7.29/7.52 tff(8235,plain,
% 7.29/7.52 (s(elem!1) = s(s(z))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8234])).
% 7.29/7.52 tff(8236,plain,
% 7.29/7.52 (s(s(elem!1)) = s(s(s(z)))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8235])).
% 7.29/7.52 tff(8237,plain,
% 7.29/7.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8236])).
% 7.29/7.52 tff(8238,plain,
% 7.29/7.52 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8237])).
% 7.29/7.52 tff(8239,plain,
% 7.29/7.52 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(s(z)))), z))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8238])).
% 7.29/7.52 tff(8240,plain,
% 7.29/7.52 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8234])).
% 7.29/7.52 tff(8241,plain,
% 7.29/7.52 ((s(s(s(elem!1))) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 7.29/7.52 inference(transitivity,[status(thm)],[8240, 204])).
% 7.29/7.52 tff(8242,plain,
% 7.29/7.52 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 7.29/7.52 inference(symmetry,[status(thm)],[8241])).
% 7.29/7.52 tff(8243,plain,
% 7.29/7.52 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8242])).
% 7.29/7.52 tff(8244,plain,
% 7.29/7.52 (~(s(s(s(elem!1))) = elem!1)),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[217, 8243])).
% 7.29/7.52 tff(8245,plain,
% 7.29/7.52 ((s(s(s(elem!1))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 7.29/7.52 inference(monotonicity,[status(thm)],[266])).
% 7.29/7.52 tff(8246,plain,
% 7.29/7.52 ((s(s(elem!1)) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 7.29/7.52 inference(symmetry,[status(thm)],[8245])).
% 7.29/7.52 tff(8247,plain,
% 7.29/7.52 (s(s(elem!1)) = s(elem!1)),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[287, 266])).
% 7.29/7.52 tff(8248,plain,
% 7.29/7.52 (s(s(elem!1)) = elem!1),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[264, 8247])).
% 7.29/7.52 tff(8249,plain,
% 7.29/7.52 (s(s(s(elem!1))) = elem!1),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[8248, 8246])).
% 7.29/7.52 tff(8250,plain,
% 7.29/7.52 ($false),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[127, 8249])).
% 7.29/7.52 tff(8251,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.29/7.52 tff(8252,plain,
% 7.29/7.52 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[8251, 8244])).
% 7.29/7.52 tff(8253,plain,
% 7.29/7.52 (b(z, s(s(elem!1)))),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[3924, 8252, 10, 91])).
% 7.29/7.52 tff(8254,plain,
% 7.29/7.52 (~r(elem!1, s(z))),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[5941, 3618, 59, 182])).
% 7.29/7.52 tff(8255,plain,
% 7.29/7.52 (elem!1 = s(z)),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[837, 8254, 31])).
% 7.29/7.52 tff(8256,plain,
% 7.29/7.52 (s(elem!1) = s(s(z))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8255])).
% 7.29/7.52 tff(8257,plain,
% 7.29/7.52 (s(s(elem!1)) = s(s(s(z)))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8256])).
% 7.29/7.52 tff(8258,plain,
% 7.29/7.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8257])).
% 7.29/7.52 tff(8259,plain,
% 7.29/7.52 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8258, 8257])).
% 7.29/7.52 tff(8260,plain,
% 7.29/7.52 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8255])).
% 7.29/7.52 tff(8261,plain,
% 7.29/7.52 ((s(s(s(elem!1))) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 7.29/7.52 inference(transitivity,[status(thm)],[8260, 204])).
% 7.29/7.52 tff(8262,plain,
% 7.29/7.52 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 7.29/7.52 inference(symmetry,[status(thm)],[8261])).
% 7.29/7.52 tff(8263,plain,
% 7.29/7.52 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8262])).
% 7.29/7.52 tff(8264,plain,
% 7.29/7.52 (~(s(s(s(elem!1))) = elem!1)),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[217, 8263])).
% 7.29/7.52 tff(8265,plain,
% 7.29/7.52 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[8251, 8264])).
% 7.29/7.52 tff(8266,plain,
% 7.29/7.52 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8258])).
% 7.29/7.52 tff(8267,plain,
% 7.29/7.52 (r(z, s(s(s(s(z)))))),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[59, 8266])).
% 7.29/7.52 tff(8268,plain,
% 7.29/7.52 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8258])).
% 7.29/7.52 tff(8269,plain,
% 7.29/7.52 (b(s(s(s(s(z)))), z)),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[380, 8268])).
% 7.29/7.52 tff(8270,plain,
% 7.29/7.52 (s(s(z)) = s(elem!1)),
% 7.29/7.52 inference(symmetry,[status(thm)],[8256])).
% 7.29/7.52 tff(8271,plain,
% 7.29/7.52 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8270])).
% 7.29/7.52 tff(8272,plain,
% 7.29/7.52 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8271])).
% 7.29/7.52 tff(8273,plain,
% 7.29/7.52 (~(s(s(elem!1)) = s(elem!1))),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[2680, 8272])).
% 7.29/7.52 tff(8274,plain,
% 7.29/7.52 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 7.29/7.52 inference(transitivity,[status(thm)],[8271, 1098])).
% 7.29/7.52 tff(8275,plain,
% 7.29/7.52 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8274])).
% 7.29/7.52 tff(8276,plain,
% 7.29/7.52 (~(s(elem!1) = s(s(elem!1)))),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[2680, 8275])).
% 7.29/7.52 tff(8277,plain,
% 7.29/7.52 ((elem!1 = s(elem!1)) <=> (s(z) = s(elem!1))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8255])).
% 7.29/7.52 tff(8278,plain,
% 7.29/7.52 ((s(z) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 7.29/7.52 inference(symmetry,[status(thm)],[8277])).
% 7.29/7.52 tff(8279,plain,
% 7.29/7.52 ((s(z) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 7.29/7.52 inference(transitivity,[status(thm)],[8278, 161])).
% 7.29/7.52 tff(8280,plain,
% 7.29/7.52 ((~(s(z) = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8279])).
% 7.29/7.52 tff(8281,plain,
% 7.29/7.52 (~(s(elem!1) = elem!1)),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[118, 8280])).
% 7.29/7.52 tff(8282,plain,
% 7.29/7.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 7.29/7.52 inference(rewrite,[status(thm)],[])).
% 7.29/7.52 tff(8283,plain,
% 7.29/7.52 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 7.29/7.52 inference(rewrite,[status(thm)],[])).
% 7.29/7.52 tff(8284,plain,
% 7.29/7.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z))))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8283])).
% 7.29/7.52 tff(8285,plain,
% 7.29/7.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 7.29/7.52 inference(transitivity,[status(thm)],[8284, 8282])).
% 7.29/7.52 tff(8286,plain,
% 7.29/7.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 7.29/7.52 inference(quant_inst,[status(thm)],[])).
% 7.29/7.52 tff(8287,plain,
% 7.29/7.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z))),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[8286, 8285])).
% 7.29/7.52 tff(8288,plain,
% 7.29/7.52 ($false),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[8287, 194, 411, 530, 233, 184])).
% 7.29/7.52 tff(8289,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.52 tff(8290,plain,
% 7.29/7.52 (~r(s(s(s(elem!1))), elem!1)),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[8289, 3618, 59, 8232])).
% 7.29/7.52 tff(8291,plain,
% 7.29/7.52 (b(s(s(s(elem!1))), elem!1)),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[230, 8264, 8290])).
% 7.29/7.52 tff(8292,plain,
% 7.29/7.52 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8258])).
% 7.29/7.52 tff(8293,plain,
% 7.29/7.52 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(s(s(s(z)))), s(z)))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8292])).
% 7.29/7.52 tff(8294,plain,
% 7.29/7.52 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8255])).
% 7.29/7.52 tff(8295,plain,
% 7.29/7.52 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), s(z)))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8294])).
% 7.29/7.52 tff(8296,plain,
% 7.29/7.52 (~r(s(s(s(elem!1))), s(z))),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[8290, 8295])).
% 7.29/7.52 tff(8297,plain,
% 7.29/7.52 (~r(s(s(s(s(z)))), s(z))),
% 7.29/7.52 inference(modus_ponens,[status(thm)],[8296, 8293])).
% 7.29/7.52 tff(8298,plain,
% 7.29/7.52 (b(s(s(s(s(z)))), s(z))),
% 7.29/7.52 inference(unit_resolution,[status(thm)],[749, 8297])).
% 7.29/7.52 tff(8299,plain,
% 7.29/7.52 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 7.29/7.52 inference(monotonicity,[status(thm)],[8256])).
% 7.29/7.52 tff(8300,plain,
% 7.29/7.52 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 7.29/7.52 inference(symmetry,[status(thm)],[8299])).
% 7.29/7.53 tff(8301,plain,
% 7.29/7.53 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8258])).
% 7.29/7.53 tff(8302,plain,
% 7.29/7.53 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 7.29/7.53 inference(symmetry,[status(thm)],[8301])).
% 7.29/7.53 tff(8303,plain,
% 7.29/7.53 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 7.29/7.53 inference(transitivity,[status(thm)],[8302, 8300])).
% 7.29/7.53 tff(8304,plain,
% 7.29/7.53 (s(z) = elem!1),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[172, 8255])).
% 7.29/7.53 tff(8305,plain,
% 7.29/7.53 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 7.29/7.53 inference(transitivity,[status(thm)],[8262, 4])).
% 7.29/7.53 tff(8306,plain,
% 7.29/7.53 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8305])).
% 7.29/7.53 tff(8307,plain,
% 7.29/7.53 (~(elem!1 = s(s(s(elem!1))))),
% 7.29/7.53 inference(modus_ponens,[status(thm)],[217, 8306])).
% 7.29/7.53 tff(8308,plain,
% 7.29/7.53 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[169])).
% 7.29/7.53 tff(8309,plain,
% 7.29/7.53 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 7.29/7.53 inference(symmetry,[status(thm)],[8308])).
% 7.29/7.53 tff(8310,plain,
% 7.29/7.53 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8309])).
% 7.29/7.53 tff(8311,plain,
% 7.29/7.53 (~b(s(z), s(s(s(elem!1))))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[2884, 169, 2881])).
% 7.29/7.53 tff(8312,plain,
% 7.29/7.53 (~b(elem!1, s(s(s(elem!1))))),
% 7.29/7.53 inference(modus_ponens,[status(thm)],[8311, 8310])).
% 7.29/7.53 tff(8313,plain,
% 7.29/7.53 ($false),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[448, 8312])).
% 7.29/7.53 tff(8314,plain,((~(elem!1 = s(z))) | (~b(elem!1, s(s(s(elem!1))))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.53 tff(8315,plain,
% 7.29/7.53 (~b(elem!1, s(s(s(elem!1))))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[8314, 2881, 8255])).
% 7.29/7.53 tff(8316,plain,
% 7.29/7.53 (r(elem!1, s(s(s(elem!1))))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[424, 8315, 8307])).
% 7.29/7.53 tff(8317,plain,
% 7.29/7.53 (~r(s(s(s(elem!1))), s(elem!1))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[6136, 8316, 59, 3618])).
% 7.29/7.53 tff(8318,plain,
% 7.29/7.53 (b(s(s(s(elem!1))), s(z))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[223, 8296])).
% 7.29/7.53 tff(8319,plain,
% 7.29/7.53 (~b(s(z), s(s(s(elem!1))))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[2884, 2881, 8255])).
% 7.29/7.53 tff(8320,plain,
% 7.29/7.53 (r(s(z), s(s(s(elem!1))))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[247, 8319])).
% 7.29/7.53 tff(8321,plain,
% 7.29/7.53 (~r(s(elem!1), z)),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[2594, 8320, 8232, 8318, 182, 8317, 118])).
% 7.29/7.53 tff(8322,plain,
% 7.29/7.53 (b(s(elem!1), z)),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[549, 8321])).
% 7.29/7.53 tff(8323,plain,
% 7.29/7.53 (r(z, s(elem!1))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[2614, 8322, 380, 8317, 59])).
% 7.29/7.53 tff(8324,plain,
% 7.29/7.53 ((~(s(z) = s(elem!1))) <=> (~(elem!1 = s(elem!1)))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8278])).
% 7.29/7.53 tff(8325,plain,
% 7.29/7.53 (~(elem!1 = s(elem!1))),
% 7.29/7.53 inference(modus_ponens,[status(thm)],[118, 8324])).
% 7.29/7.53 tff(8326,plain,
% 7.29/7.53 (r(z, elem!1) <=> r(z, s(z))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8255])).
% 7.29/7.53 tff(8327,plain,
% 7.29/7.53 (r(z, s(z))),
% 7.29/7.53 inference(modus_ponens,[status(thm)],[8232, 8326])).
% 7.29/7.53 tff(8328,plain,
% 7.29/7.53 (~r(elem!1, s(z))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[845, 182, 722, 411])).
% 7.29/7.53 tff(8329,assumption,(~b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 7.29/7.53 tff(8330,plain,
% 7.29/7.53 (elem!1 = s(z)),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[837, 8328, 31])).
% 7.29/7.53 tff(8331,plain,
% 7.29/7.53 (~b(s(z), s(s(s(elem!1))))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[2884, 8330, 2881])).
% 7.29/7.53 tff(8332,plain,
% 7.29/7.53 (r(s(z), s(s(s(elem!1))))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[247, 8331])).
% 7.29/7.53 tff(8333,plain,
% 7.29/7.53 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[337, 8332, 184, 182])).
% 7.29/7.53 tff(8334,plain,
% 7.29/7.53 (s(s(s(elem!1))) = s(s(elem!1))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[1370, 8333, 8329])).
% 7.29/7.53 tff(8335,plain,
% 7.29/7.53 (s(s(elem!1)) = s(elem!1)),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[287, 8334])).
% 7.29/7.53 tff(8336,plain,
% 7.29/7.53 (s(s(elem!1)) = elem!1),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[264, 8335])).
% 7.29/7.53 tff(8337,plain,
% 7.29/7.53 (s(elem!1) = s(s(s(elem!1)))),
% 7.29/7.53 inference(symmetry,[status(thm)],[282])).
% 7.29/7.53 tff(8338,plain,
% 7.29/7.53 (s(elem!1) = s(s(elem!1))),
% 7.29/7.53 inference(transitivity,[status(thm)],[8337, 266])).
% 7.29/7.53 tff(8339,plain,
% 7.29/7.53 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8338])).
% 7.29/7.53 tff(8340,plain,
% 7.29/7.53 (elem!1 = s(s(elem!1))),
% 7.29/7.53 inference(transitivity,[status(thm)],[261, 8339, 259, 8337, 266])).
% 7.29/7.53 tff(8341,plain,
% 7.29/7.53 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8340])).
% 7.29/7.53 tff(8342,plain,
% 7.29/7.53 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 7.29/7.53 inference(symmetry,[status(thm)],[8341])).
% 7.29/7.53 tff(8343,plain,
% 7.29/7.53 (b(elem!1, s(z))),
% 7.29/7.53 inference(modus_ponens,[status(thm)],[381, 8342])).
% 7.29/7.53 tff(8344,plain,
% 7.29/7.53 ($false),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[31, 8343])).
% 7.29/7.53 tff(8345,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | b(elem!1, s(z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.53 tff(8346,plain,
% 7.29/7.53 (~b(s(s(elem!1)), s(z))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[8345, 8334, 31])).
% 7.29/7.53 tff(8347,plain,
% 7.29/7.53 (r(s(s(elem!1)), s(z))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[362, 8346])).
% 7.29/7.53 tff(8348,plain,
% 7.29/7.53 ($false),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[4206, 8347, 8336, 8328])).
% 7.29/7.53 tff(8349,plain,((~r(s(z), z)) | b(elem!1, s(z)) | b(s(s(s(elem!1))), s(s(elem!1))) | (~r(z, s(s(s(elem!1))))) | b(s(z), s(s(s(s(z))))) | (~r(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.53 tff(8350,plain,
% 7.29/7.53 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[8349, 2881, 8327, 182, 59, 31, 8232])).
% 7.29/7.53 tff(8351,plain,
% 7.29/7.53 (s(z) = elem!1),
% 7.29/7.53 inference(symmetry,[status(thm)],[8255])).
% 7.29/7.53 tff(8352,plain,
% 7.29/7.53 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8351])).
% 7.29/7.53 tff(8353,plain,
% 7.29/7.53 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8352])).
% 7.29/7.53 tff(8354,plain,
% 7.29/7.53 (~(s(s(elem!1)) = elem!1)),
% 7.29/7.53 inference(modus_ponens,[status(thm)],[357, 8353])).
% 7.29/7.53 tff(8355,plain,
% 7.29/7.53 (~r(s(z), elem!1)),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[1489, 3618, 59, 182])).
% 7.29/7.53 tff(8356,plain,
% 7.29/7.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 7.29/7.53 inference(rewrite,[status(thm)],[])).
% 7.29/7.53 tff(8357,plain,
% 7.29/7.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 7.29/7.53 inference(quant_inst,[status(thm)],[])).
% 7.29/7.53 tff(8358,plain,
% 7.29/7.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))),
% 7.29/7.53 inference(modus_ponens,[status(thm)],[8357, 8356])).
% 7.29/7.53 tff(8359,plain,
% 7.29/7.53 ($false),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[8358, 194, 411, 530, 364, 2616])).
% 7.29/7.53 tff(8360,plain,((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.53 tff(8361,plain,
% 7.29/7.53 (~r(s(s(elem!1)), z)),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[8360, 1482, 364, 8232])).
% 7.29/7.53 tff(8362,plain,
% 7.29/7.53 (b(s(s(elem!1)), z)),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[2629, 8361])).
% 7.29/7.53 tff(8363,plain,
% 7.29/7.53 (~r(z, s(s(elem!1)))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[867, 1482, 364, 8232])).
% 7.29/7.53 tff(8364,plain,
% 7.29/7.53 (b(z, s(s(elem!1)))),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[324, 8363])).
% 7.29/7.53 tff(8365,plain,
% 7.29/7.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.29/7.53 inference(rewrite,[status(thm)],[])).
% 7.29/7.53 tff(8366,plain,
% 7.29/7.53 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.29/7.53 inference(rewrite,[status(thm)],[])).
% 7.29/7.53 tff(8367,plain,
% 7.29/7.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8366])).
% 7.29/7.53 tff(8368,plain,
% 7.29/7.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.29/7.53 inference(transitivity,[status(thm)],[8367, 8365])).
% 7.29/7.53 tff(8369,plain,
% 7.29/7.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 7.29/7.53 inference(quant_inst,[status(thm)],[])).
% 7.29/7.53 tff(8370,plain,
% 7.29/7.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 7.29/7.53 inference(modus_ponens,[status(thm)],[8369, 8368])).
% 7.29/7.53 tff(8371,plain,
% 7.29/7.53 (~b(s(s(s(elem!1))), z)),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[8370, 391, 1374, 8364, 8362])).
% 7.29/7.53 tff(8372,plain,
% 7.29/7.53 (r(s(s(s(elem!1))), z)),
% 7.29/7.53 inference(unit_resolution,[status(thm)],[377, 8371])).
% 7.29/7.53 tff(8373,plain,
% 7.29/7.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.29/7.53 inference(rewrite,[status(thm)],[])).
% 7.29/7.53 tff(8374,plain,
% 7.29/7.53 (((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.29/7.53 inference(rewrite,[status(thm)],[])).
% 7.29/7.53 tff(8375,plain,
% 7.29/7.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 7.29/7.53 inference(monotonicity,[status(thm)],[8374])).
% 7.29/7.53 tff(8376,plain,
% 7.29/7.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.29/7.54 inference(transitivity,[status(thm)],[8375, 8373])).
% 7.29/7.54 tff(8377,plain,
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% 7.29/7.54 inference(quant_inst,[status(thm)],[])).
% 7.29/7.54 tff(8378,plain,
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% 7.29/7.54 inference(modus_ponens,[status(thm)],[8377, 8376])).
% 7.29/7.54 tff(8379,plain,
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% 7.29/7.54 inference(unit_resolution,[status(thm)],[8378, 194, 411, 174, 184, 410])).
% 7.29/7.54 tff(8380,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.54 tff(8381,plain,
% 7.29/7.54 (~r(elem!1, s(s(s(elem!1))))),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[8380, 8372, 59, 8232])).
% 7.29/7.54 tff(8382,plain,
% 7.29/7.54 (elem!1 = s(s(s(elem!1)))),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[424, 8381, 4028])).
% 7.29/7.54 tff(8383,plain,
% 7.29/7.54 (s(elem!1) = s(s(s(s(elem!1))))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8382])).
% 7.29/7.54 tff(8384,plain,
% 7.29/7.54 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8383])).
% 7.29/7.54 tff(8385,plain,
% 7.29/7.54 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 7.29/7.54 inference(symmetry,[status(thm)],[8384])).
% 7.29/7.54 tff(8386,plain,
% 7.29/7.54 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8385])).
% 7.29/7.54 tff(8387,plain,
% 7.29/7.54 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 7.29/7.54 inference(symmetry,[status(thm)],[8386])).
% 7.29/7.54 tff(8388,plain,
% 7.29/7.54 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8385])).
% 7.29/7.54 tff(8389,plain,
% 7.29/7.54 ((~b(s(s(s(s(s(elem!1))))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8388])).
% 7.29/7.54 tff(8390,plain,
% 7.29/7.54 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(elem!1)))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8385])).
% 7.29/7.54 tff(8391,plain,
% 7.29/7.54 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 7.29/7.54 inference(symmetry,[status(thm)],[8390])).
% 7.29/7.54 tff(8392,plain,
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% 7.29/7.54 inference(modus_ponens,[status(thm)],[8364, 8391])).
% 7.29/7.54 tff(8393,plain,
% 7.29/7.54 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(elem!1))))), z)),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8384])).
% 7.29/7.54 tff(8394,plain,
% 7.29/7.54 (b(s(s(s(s(s(elem!1))))), z)),
% 7.29/7.54 inference(modus_ponens,[status(thm)],[8362, 8393])).
% 7.29/7.54 tff(8395,plain,
% 7.29/7.54 (s(s(s(elem!1))) = elem!1),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[129, 8382])).
% 7.29/7.54 tff(8396,plain,
% 7.29/7.54 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 7.29/7.54 inference(symmetry,[status(thm)],[3707])).
% 7.29/7.54 tff(8397,plain,
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% 7.29/7.54 inference(monotonicity,[status(thm)],[8396])).
% 7.29/7.54 tff(8398,plain,
% 7.29/7.54 (~b(s(s(s(elem!1))), s(z))),
% 7.29/7.54 inference(modus_ponens,[status(thm)],[31, 8397])).
% 7.29/7.54 tff(8399,plain,
% 7.29/7.54 ($false),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[1526, 8398])).
% 7.29/7.54 tff(8400,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.54 tff(8401,plain,
% 7.29/7.54 (~b(s(s(s(elem!1))), s(z))),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[8400, 8395, 31])).
% 7.29/7.54 tff(8402,plain,
% 7.29/7.54 (r(s(s(s(elem!1))), s(z))),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[223, 8401])).
% 7.29/7.54 tff(8403,plain,
% 7.29/7.54 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[5])).
% 7.29/7.54 tff(8404,plain,
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% 7.29/7.54 inference(modus_ponens,[status(thm)],[183, 8403])).
% 7.29/7.54 tff(8405,plain,
% 7.29/7.54 ($false),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[832, 8404])).
% 7.29/7.54 tff(8406,plain,((~r(s(s(s(elem!1))), s(z))) | r(elem!1, s(z)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.54 tff(8407,plain,
% 7.29/7.54 (r(elem!1, s(z))),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[8406, 8402, 8395])).
% 7.29/7.54 tff(8408,plain,
% 7.29/7.54 (~(elem!1 = z)),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[3205, 91, 1492])).
% 7.29/7.54 tff(8409,plain,
% 7.29/7.54 (~r(elem!1, z)),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[5941, 181, 184, 847])).
% 7.29/7.54 tff(8410,plain,
% 7.29/7.54 ($false),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[526, 8409, 8408, 484])).
% 7.29/7.54 tff(8411,plain,(b(s(z), z) | b(elem!1, z) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.29/7.54 tff(8412,plain,
% 7.29/7.54 (b(s(z), z)),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[8411, 8407, 59, 484, 1492])).
% 7.29/7.54 tff(8413,plain,
% 7.29/7.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 7.29/7.54 inference(rewrite,[status(thm)],[])).
% 7.29/7.54 tff(8414,plain,
% 7.29/7.54 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), 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(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 7.29/7.54 inference(rewrite,[status(thm)],[])).
% 7.29/7.54 tff(8415,plain,
% 7.29/7.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8414])).
% 7.29/7.54 tff(8416,plain,
% 7.29/7.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 7.29/7.54 inference(transitivity,[status(thm)],[8415, 8413])).
% 7.29/7.54 tff(8417,plain,
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% 7.29/7.54 inference(quant_inst,[status(thm)],[])).
% 7.29/7.54 tff(8418,plain,
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% 7.29/7.54 inference(modus_ponens,[status(thm)],[8417, 8416])).
% 7.29/7.54 tff(8419,plain,
% 7.29/7.54 ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[8418, 391, 8412, 8394])).
% 7.29/7.54 tff(8420,plain,
% 7.29/7.54 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[8419, 8392])).
% 7.29/7.54 tff(8421,plain,
% 7.29/7.54 (~b(s(s(elem!1)), s(z))),
% 7.29/7.54 inference(modus_ponens,[status(thm)],[8420, 8389])).
% 7.29/7.54 tff(8422,plain,
% 7.29/7.54 (r(s(s(elem!1)), s(z))),
% 7.29/7.54 inference(unit_resolution,[status(thm)],[362, 8421])).
% 7.29/7.54 tff(8423,plain,
% 7.29/7.54 (r(s(s(s(s(s(elem!1))))), s(z))),
% 7.29/7.54 inference(modus_ponens,[status(thm)],[8422, 8387])).
% 7.29/7.54 tff(8424,plain,
% 7.29/7.54 (s(s(s(elem!1))) = elem!1),
% 7.29/7.54 inference(symmetry,[status(thm)],[8382])).
% 7.29/7.54 tff(8425,plain,
% 7.29/7.54 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8424])).
% 7.29/7.54 tff(8426,plain,
% 7.29/7.54 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 7.29/7.54 inference(symmetry,[status(thm)],[8425])).
% 7.29/7.54 tff(8427,plain,
% 7.29/7.54 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8385, 8382])).
% 7.29/7.54 tff(8428,plain,
% 7.29/7.54 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 7.29/7.54 inference(symmetry,[status(thm)],[8427])).
% 7.29/7.54 tff(8429,plain,
% 7.29/7.54 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8382])).
% 7.29/7.54 tff(8430,plain,
% 7.29/7.54 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.29/7.54 inference(modus_ponens,[status(thm)],[364, 8429])).
% 7.29/7.54 tff(8431,plain,
% 7.29/7.54 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 7.29/7.54 inference(modus_ponens,[status(thm)],[8430, 8428])).
% 7.29/7.54 tff(8432,plain,
% 7.29/7.54 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 7.29/7.54 inference(modus_ponens,[status(thm)],[8431, 8426])).
% 7.29/7.54 tff(8433,plain,
% 7.29/7.54 ((s(z) = s(s(s(s(s(elem!1)))))) <=> (s(z) = s(s(elem!1)))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8385])).
% 7.29/7.54 tff(8434,plain,
% 7.29/7.54 ((s(z) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = s(z))),
% 7.29/7.54 inference(transitivity,[status(thm)],[8433, 3401])).
% 7.29/7.54 tff(8435,plain,
% 7.29/7.54 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(s(s(s(elem!1))))))),
% 7.29/7.54 inference(symmetry,[status(thm)],[8434])).
% 7.29/7.54 tff(8436,plain,
% 7.29/7.54 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(s(s(s(elem!1)))))))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8435])).
% 7.29/7.54 tff(8437,plain,
% 7.29/7.54 (~(s(z) = s(s(s(s(s(elem!1))))))),
% 7.29/7.54 inference(modus_ponens,[status(thm)],[357, 8436])).
% 7.29/7.54 tff(8438,plain,
% 7.29/7.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 7.29/7.54 inference(rewrite,[status(thm)],[])).
% 7.29/7.54 tff(8439,plain,
% 7.29/7.54 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 7.29/7.54 inference(rewrite,[status(thm)],[])).
% 7.29/7.54 tff(8440,plain,
% 7.29/7.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 7.29/7.54 inference(monotonicity,[status(thm)],[8439])).
% 7.29/7.54 tff(8441,plain,
% 7.29/7.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 7.29/7.54 inference(transitivity,[status(thm)],[8440, 8438])).
% 7.29/7.54 tff(8442,plain,
% 7.29/7.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 7.29/7.55 inference(quant_inst,[status(thm)],[])).
% 7.29/7.55 tff(8443,plain,
% 7.29/7.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 7.29/7.55 inference(modus_ponens,[status(thm)],[8442, 8441])).
% 7.29/7.55 tff(8444,plain,
% 7.29/7.55 ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 7.29/7.55 inference(unit_resolution,[status(thm)],[8443, 391, 8412, 8394])).
% 7.29/7.55 tff(8445,plain,
% 7.29/7.55 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 7.29/7.55 inference(unit_resolution,[status(thm)],[8444, 8392])).
% 7.29/7.55 tff(8446,plain,
% 7.29/7.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), 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(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))))),
% 7.29/7.55 inference(rewrite,[status(thm)],[])).
% 7.29/7.55 tff(8447,plain,
% 7.29/7.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))))),
% 7.29/7.55 inference(quant_inst,[status(thm)],[])).
% 7.29/7.55 tff(8448,plain,
% 7.29/7.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 7.29/7.55 inference(modus_ponens,[status(thm)],[8447, 8446])).
% 7.29/7.55 tff(8449,plain,
% 7.29/7.55 ((s(z) = s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 7.29/7.55 inference(unit_resolution,[status(thm)],[8448, 42, 8445])).
% 7.29/7.55 tff(8450,plain,
% 7.29/7.55 (r(s(z), s(s(s(s(s(elem!1))))))),
% 7.29/7.55 inference(unit_resolution,[status(thm)],[8449, 8437])).
% 7.29/7.55 tff(8451,plain,
% 7.29/7.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 7.29/7.55 inference(rewrite,[status(thm)],[])).
% 7.29/7.55 tff(8452,plain,
% 7.29/7.55 (((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 7.29/7.55 inference(rewrite,[status(thm)],[])).
% 7.29/7.55 tff(8453,plain,
% 7.29/7.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 7.29/7.55 inference(monotonicity,[status(thm)],[8452])).
% 7.29/7.55 tff(8454,plain,
% 7.29/7.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 7.29/7.55 inference(transitivity,[status(thm)],[8453, 8451])).
% 7.29/7.55 tff(8455,plain,
% 7.29/7.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 7.29/7.55 inference(quant_inst,[status(thm)],[])).
% 7.29/7.55 tff(8456,plain,
% 7.29/7.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 7.29/7.55 inference(modus_ponens,[status(thm)],[8455, 8454])).
% 7.29/7.55 tff(8457,plain,
% 7.29/7.55 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 7.29/7.55 inference(unit_resolution,[status(thm)],[8456, 194, 8402, 8450])).
% 7.29/7.55 tff(8458,plain,
% 7.29/7.55 ($false),
% 7.29/7.55 inference(unit_resolution,[status(thm)],[8457, 8432, 8423])).
% 7.29/7.55 tff(8459,plain,((elem!1 = z) | (~r(s(s(elem!1)), elem!1)) | b(elem!1, z) | r(s(z), elem!1) | b(elem!1, s(z)) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.55 tff(8460,plain,
% 7.29/7.55 (~r(s(s(elem!1)), elem!1)),
% 7.29/7.55 inference(unit_resolution,[status(thm)],[8459, 8350, 10, 2, 484, 31, 8355, 8315])).
% 7.29/7.55 tff(8461,plain,
% 7.29/7.55 (b(s(s(elem!1)), elem!1)),
% 7.29/7.55 inference(unit_resolution,[status(thm)],[872, 8460, 8354])).
% 7.29/7.55 tff(8462,plain,
% 7.29/7.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.29/7.55 inference(rewrite,[status(thm)],[])).
% 7.29/7.55 tff(8463,plain,
% 7.29/7.55 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.29/7.55 inference(rewrite,[status(thm)],[])).
% 7.29/7.55 tff(8464,plain,
% 7.29/7.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 7.29/7.55 inference(monotonicity,[status(thm)],[8463])).
% 7.29/7.55 tff(8465,plain,
% 7.29/7.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.29/7.55 inference(transitivity,[status(thm)],[8464, 8462])).
% 7.29/7.55 tff(8466,plain,
% 7.29/7.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 7.29/7.55 inference(quant_inst,[status(thm)],[])).
% 7.29/7.55 tff(8467,plain,
% 7.29/7.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[8466, 8465])).
% 7.29/7.56 tff(8468,plain,
% 7.29/7.56 ($false),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8467, 391, 380, 973, 1374, 3927, 802])).
% 7.29/7.56 tff(8469,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.56 tff(8470,plain,
% 7.29/7.56 (~b(elem!1, s(elem!1))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8469, 8461, 3927, 380, 8350])).
% 7.29/7.56 tff(8471,plain,
% 7.29/7.56 (r(elem!1, s(elem!1))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[443, 8470, 8325])).
% 7.29/7.56 tff(8472,plain,
% 7.29/7.56 (~r(s(elem!1), s(s(s(elem!1))))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[3626, 8471, 3618, 8323])).
% 7.29/7.56 tff(8473,plain,
% 7.29/7.56 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[3614, 8472, 8304])).
% 7.29/7.56 tff(8474,plain,
% 7.29/7.56 (b(s(s(z)), s(s(s(s(z)))))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[3652, 8473])).
% 7.29/7.56 tff(8475,plain,
% 7.29/7.56 (b(s(elem!1), s(s(s(elem!1))))),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[8474, 8303])).
% 7.29/7.56 tff(8476,plain,
% 7.29/7.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.29/7.56 inference(rewrite,[status(thm)],[])).
% 7.29/7.56 tff(8477,plain,
% 7.29/7.56 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.29/7.56 inference(rewrite,[status(thm)],[])).
% 7.29/7.56 tff(8478,plain,
% 7.29/7.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1))))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[8477])).
% 7.29/7.56 tff(8479,plain,
% 7.29/7.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.29/7.56 inference(transitivity,[status(thm)],[8478, 8476])).
% 7.29/7.56 tff(8480,plain,
% 7.29/7.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 7.29/7.56 inference(quant_inst,[status(thm)],[])).
% 7.29/7.56 tff(8481,plain,
% 7.29/7.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1))),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[8480, 8479])).
% 7.29/7.56 tff(8482,plain,
% 7.29/7.56 ($false),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8481, 391, 380, 973, 3927, 591, 1036])).
% 7.29/7.56 tff(8483,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.56 tff(8484,plain,
% 7.29/7.56 (~b(s(elem!1), s(s(s(elem!1))))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8483, 8322, 380, 8461, 3927])).
% 7.29/7.56 tff(8485,plain,
% 7.29/7.56 ($false),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8484, 8475])).
% 7.29/7.56 tff(8486,plain,(b(s(z), s(s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~r(s(z), z)) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.56 tff(8487,plain,
% 7.29/7.56 (b(s(z), s(s(s(s(z)))))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8486, 380, 3927, 182, 10, 2, 484, 31])).
% 7.29/7.56 tff(8488,plain,
% 7.29/7.56 ((elem!1 = s(s(z))) <=> (s(z) = s(s(z)))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[8255])).
% 7.29/7.56 tff(8489,plain,
% 7.29/7.56 ((s(z) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 7.29/7.56 inference(symmetry,[status(thm)],[8488])).
% 7.29/7.56 tff(8490,plain,
% 7.29/7.56 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[8489])).
% 7.29/7.56 tff(8491,plain,
% 7.29/7.56 (~(elem!1 = s(s(z)))),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[1783, 8490])).
% 7.29/7.56 tff(8492,plain,
% 7.29/7.56 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 7.29/7.56 inference(symmetry,[status(thm)],[698])).
% 7.29/7.56 tff(8493,plain,
% 7.29/7.56 ((s(z) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 7.29/7.56 inference(transitivity,[status(thm)],[8489, 8492])).
% 7.29/7.56 tff(8494,plain,
% 7.29/7.56 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[8493])).
% 7.29/7.56 tff(8495,plain,
% 7.29/7.56 (~(s(s(z)) = elem!1)),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[1783, 8494])).
% 7.29/7.56 tff(8496,plain,
% 7.29/7.56 (~b(s(s(z)), s(z))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[5108, 3823, 1759, 1234])).
% 7.29/7.56 tff(8497,plain,
% 7.29/7.56 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 7.29/7.56 inference(symmetry,[status(thm)],[7398])).
% 7.29/7.56 tff(8498,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 7.29/7.56 tff(8499,plain,
% 7.29/7.56 (b(s(s(z)), s(z))),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[8498, 8497])).
% 7.29/7.56 tff(8500,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 7.29/7.56 tff(8501,plain,
% 7.29/7.56 ($false),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8500, 8499])).
% 7.29/7.56 tff(8502,plain,((~(s(z) = elem!1)) | b(s(s(z)), s(z)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.56 tff(8503,plain,
% 7.29/7.56 (~b(s(s(z)), elem!1)),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8502, 8496, 812])).
% 7.29/7.56 tff(8504,plain,
% 7.29/7.56 (r(s(s(z)), elem!1)),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[4730, 8503, 5547])).
% 7.29/7.56 tff(8505,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 7.29/7.56 tff(8506,plain,
% 7.29/7.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 7.29/7.56 inference(rewrite,[status(thm)],[])).
% 7.29/7.56 tff(8507,plain,
% 7.29/7.56 (((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 7.29/7.56 inference(rewrite,[status(thm)],[])).
% 7.29/7.56 tff(8508,plain,
% 7.29/7.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[8507])).
% 7.29/7.56 tff(8509,plain,
% 7.29/7.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 7.29/7.56 inference(transitivity,[status(thm)],[8508, 8506])).
% 7.29/7.56 tff(8510,plain,
% 7.29/7.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))),
% 7.29/7.56 inference(quant_inst,[status(thm)],[])).
% 7.29/7.56 tff(8511,plain,
% 7.29/7.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1))),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[8510, 8509])).
% 7.29/7.56 tff(8512,plain,
% 7.29/7.56 ($false),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8511, 194, 411, 530, 6669, 8505])).
% 7.29/7.56 tff(8513,plain,((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.56 tff(8514,plain,
% 7.29/7.56 (~r(z, s(s(z)))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8513, 8504, 530, 411])).
% 7.29/7.56 tff(8515,plain,
% 7.29/7.56 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[818])).
% 7.29/7.56 tff(8516,plain,
% 7.29/7.56 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 7.29/7.56 inference(symmetry,[status(thm)],[8515])).
% 7.29/7.56 tff(8517,plain,
% 7.29/7.56 (r(z, s(s(z)))),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[2144, 8516])).
% 7.29/7.56 tff(8518,assumption,(~r(z, s(s(z)))), introduced(assumption)).
% 7.29/7.56 tff(8519,plain,
% 7.29/7.56 ($false),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8518, 8517])).
% 7.29/7.56 tff(8520,plain,((~r(z, s(elem!1))) | r(z, s(s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.56 tff(8521,plain,
% 7.29/7.56 (~r(z, s(elem!1))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8520, 8514, 812])).
% 7.29/7.56 tff(8522,plain,
% 7.29/7.56 (b(z, s(elem!1))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[566, 8521])).
% 7.29/7.56 tff(8523,plain,
% 7.29/7.56 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[818])).
% 7.29/7.56 tff(8524,plain,
% 7.29/7.56 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 7.29/7.56 inference(symmetry,[status(thm)],[8523])).
% 7.29/7.56 tff(8525,plain,
% 7.29/7.56 (b(z, s(s(z)))),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[592, 8524])).
% 7.29/7.56 tff(8526,plain,
% 7.29/7.56 ($false),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[3373, 8525])).
% 7.29/7.56 tff(8527,plain,((~b(z, s(elem!1))) | b(z, s(s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.56 tff(8528,plain,
% 7.29/7.56 (b(z, s(s(z)))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8527, 8522, 812])).
% 7.29/7.56 tff(8529,plain,
% 7.29/7.56 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[820])).
% 7.29/7.56 tff(8530,plain,
% 7.29/7.56 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(z)))))),
% 7.29/7.56 inference(symmetry,[status(thm)],[8529])).
% 7.29/7.56 tff(8531,plain,
% 7.29/7.56 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[8530])).
% 7.29/7.56 tff(8532,plain,
% 7.29/7.56 (~b(elem!1, s(s(s(s(z)))))),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[4028, 8531])).
% 7.29/7.56 tff(8533,plain,
% 7.29/7.56 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[812])).
% 7.29/7.56 tff(8534,plain,
% 7.29/7.56 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 7.29/7.56 inference(symmetry,[status(thm)],[8533])).
% 7.29/7.56 tff(8535,plain,
% 7.29/7.56 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(s(z), s(s(s(s(z))))))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[8534])).
% 7.29/7.56 tff(8536,assumption,(~b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 7.29/7.56 tff(8537,plain,
% 7.29/7.56 (~b(s(z), s(s(s(s(z)))))),
% 7.29/7.56 inference(modus_ponens,[status(thm)],[8536, 8535])).
% 7.29/7.56 tff(8538,plain,
% 7.29/7.56 ($false),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[1234, 8537])).
% 7.29/7.56 tff(8539,plain,((~(s(z) = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.56 tff(8540,plain,
% 7.29/7.56 (b(elem!1, s(s(s(s(z)))))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8539, 812, 1234])).
% 7.29/7.56 tff(8541,plain,
% 7.29/7.56 ($false),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8540, 8532])).
% 7.29/7.56 tff(8542,plain,((~(s(z) = elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.56 tff(8543,plain,
% 7.29/7.56 (b(elem!1, s(s(s(elem!1))))),
% 7.29/7.56 inference(unit_resolution,[status(thm)],[8542, 1234, 812])).
% 7.29/7.56 tff(8544,plain,
% 7.29/7.56 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 7.29/7.56 inference(monotonicity,[status(thm)],[818])).
% 7.29/7.56 tff(8545,plain,
% 7.29/7.56 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 7.29/7.57 inference(symmetry,[status(thm)],[8544])).
% 7.29/7.57 tff(8546,plain,
% 7.29/7.57 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 7.29/7.57 inference(monotonicity,[status(thm)],[820])).
% 7.29/7.57 tff(8547,plain,
% 7.29/7.57 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 7.29/7.57 inference(transitivity,[status(thm)],[7948, 8546, 8545])).
% 7.29/7.57 tff(8548,plain,
% 7.29/7.57 (b(s(s(z)), s(s(s(elem!1))))),
% 7.29/7.57 inference(modus_ponens,[status(thm)],[3823, 8547])).
% 7.29/7.57 tff(8549,assumption,(~b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 7.29/7.57 tff(8550,plain,
% 7.29/7.57 ($false),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[8549, 8548])).
% 7.29/7.57 tff(8551,plain,((~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.57 tff(8552,plain,
% 7.29/7.57 (b(s(s(z)), s(s(s(elem!1))))),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[8551, 3823, 812])).
% 7.29/7.57 tff(8553,assumption,(b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 7.29/7.57 tff(8554,plain,
% 7.29/7.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 7.29/7.57 inference(rewrite,[status(thm)],[])).
% 7.29/7.57 tff(8555,plain,
% 7.29/7.57 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 7.29/7.57 inference(rewrite,[status(thm)],[])).
% 7.29/7.57 tff(8556,plain,
% 7.29/7.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 7.29/7.57 inference(monotonicity,[status(thm)],[8555])).
% 7.29/7.57 tff(8557,plain,
% 7.29/7.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 7.29/7.57 inference(transitivity,[status(thm)],[8556, 8554])).
% 7.29/7.57 tff(8558,plain,
% 7.29/7.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))))),
% 7.29/7.57 inference(quant_inst,[status(thm)],[])).
% 7.29/7.57 tff(8559,plain,
% 7.29/7.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 7.29/7.57 inference(modus_ponens,[status(thm)],[8558, 8557])).
% 7.29/7.57 tff(8560,plain,
% 7.29/7.57 ($false),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[8559, 391, 448, 1526, 3369, 1234, 8553])).
% 7.29/7.57 tff(8561,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.57 tff(8562,plain,
% 7.29/7.57 (~b(elem!1, s(s(z)))),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[8561, 8552, 1526, 1234, 8543])).
% 7.29/7.57 tff(8563,plain,
% 7.29/7.57 (r(elem!1, s(s(z)))),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[3394, 8562, 1405])).
% 7.29/7.57 tff(8564,plain,
% 7.29/7.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 7.29/7.57 inference(rewrite,[status(thm)],[])).
% 7.29/7.57 tff(8565,plain,
% 7.29/7.57 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 7.29/7.57 inference(rewrite,[status(thm)],[])).
% 7.29/7.57 tff(8566,plain,
% 7.29/7.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))))),
% 7.29/7.57 inference(monotonicity,[status(thm)],[8565])).
% 7.29/7.57 tff(8567,plain,
% 7.29/7.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 7.29/7.57 inference(transitivity,[status(thm)],[8566, 8564])).
% 7.29/7.57 tff(8568,plain,
% 7.29/7.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))),
% 7.29/7.57 inference(quant_inst,[status(thm)],[])).
% 7.29/7.57 tff(8569,plain,
% 7.29/7.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))),
% 7.29/7.57 inference(modus_ponens,[status(thm)],[8568, 8567])).
% 7.29/7.57 tff(8570,plain,
% 7.29/7.57 ((~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[8569, 194])).
% 7.29/7.57 tff(8571,plain,
% 7.29/7.57 (~r(s(s(z)), z)),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[8570, 8563, 530, 719])).
% 7.29/7.57 tff(8572,plain,
% 7.29/7.57 (b(s(s(z)), z)),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[1211, 8571])).
% 7.29/7.57 tff(8573,plain,
% 7.29/7.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 7.29/7.57 inference(rewrite,[status(thm)],[])).
% 7.29/7.57 tff(8574,plain,
% 7.29/7.57 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 7.29/7.57 inference(rewrite,[status(thm)],[])).
% 7.29/7.57 tff(8575,plain,
% 7.29/7.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))))),
% 7.29/7.57 inference(monotonicity,[status(thm)],[8574])).
% 7.29/7.57 tff(8576,plain,
% 7.29/7.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 7.29/7.57 inference(transitivity,[status(thm)],[8575, 8573])).
% 7.29/7.57 tff(8577,plain,
% 7.29/7.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 7.29/7.57 inference(quant_inst,[status(thm)],[])).
% 7.29/7.57 tff(8578,plain,
% 7.29/7.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))),
% 7.29/7.57 inference(modus_ponens,[status(thm)],[8577, 8576])).
% 7.29/7.57 tff(8579,plain,
% 7.29/7.57 ($false),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[8578, 391, 3823, 90, 8572, 8528])).
% 7.29/7.57 tff(8580,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~(s(z) = elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (elem!1 = s(s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.57 tff(8581,plain,
% 7.29/7.57 (~b(s(s(z)), s(s(s(s(z)))))),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[8580, 8269, 8304, 3618, 8232, 8267, 8495, 8491, 8318, 8487, 8298])).
% 7.29/7.57 tff(8582,plain,
% 7.29/7.57 (r(s(s(z)), s(s(s(s(z)))))),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[3652, 8581])).
% 7.29/7.57 tff(8583,plain,
% 7.29/7.57 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 7.29/7.57 inference(commutativity,[status(thm)],[])).
% 7.29/7.57 tff(8584,plain,
% 7.29/7.57 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 7.29/7.57 inference(monotonicity,[status(thm)],[1552])).
% 7.29/7.57 tff(8585,plain,
% 7.29/7.57 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 7.29/7.57 inference(monotonicity,[status(thm)],[8584, 1551])).
% 7.29/7.57 tff(8586,plain,
% 7.29/7.57 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 7.29/7.57 inference(transitivity,[status(thm)],[8585, 8583])).
% 7.29/7.57 tff(8587,plain,
% 7.29/7.57 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 7.29/7.57 inference(symmetry,[status(thm)],[8586])).
% 7.29/7.57 tff(8588,plain,
% 7.29/7.57 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 7.29/7.57 inference(monotonicity,[status(thm)],[8587])).
% 7.29/7.57 tff(8589,assumption,(s(s(s(z))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 7.29/7.57 tff(8590,plain,
% 7.29/7.57 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 7.29/7.57 inference(monotonicity,[status(thm)],[8589])).
% 7.29/7.57 tff(8591,plain,
% 7.29/7.57 (s(s(z)) = s(s(s(s(z))))),
% 7.29/7.57 inference(transitivity,[status(thm)],[710, 8590, 4986])).
% 7.29/7.57 tff(8592,plain,
% 7.29/7.57 ($false),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[714, 8591])).
% 7.29/7.57 tff(8593,plain,(~(s(s(s(z))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.57 tff(8594,plain,
% 7.29/7.57 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 7.29/7.57 inference(modus_ponens,[status(thm)],[8593, 8588])).
% 7.29/7.57 tff(8595,plain,
% 7.29/7.57 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 7.29/7.57 inference(monotonicity,[status(thm)],[170])).
% 7.29/7.57 tff(8596,plain,
% 7.29/7.57 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 7.29/7.57 inference(monotonicity,[status(thm)],[8595])).
% 7.29/7.57 tff(8597,plain,
% 7.29/7.57 (~(s(s(elem!1)) = elem!1)),
% 7.29/7.57 inference(modus_ponens,[status(thm)],[357, 8596])).
% 7.29/7.57 tff(8598,plain,
% 7.29/7.57 (s(z) = elem!1),
% 7.29/7.57 inference(unit_resolution,[status(thm)],[172, 169])).
% 7.29/7.57 tff(8599,plain,
% 7.29/7.57 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 7.29/7.57 inference(monotonicity,[status(thm)],[1551])).
% 7.29/7.57 tff(8600,plain,
% 7.29/7.57 (b(z, s(s(s(z))))),
% 7.29/7.57 inference(modus_ponens,[status(thm)],[3927, 8599])).
% 7.29/7.57 tff(8601,plain,
% 7.29/7.57 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 7.29/7.58 inference(monotonicity,[status(thm)],[1552, 1551])).
% 7.29/7.58 tff(8602,plain,
% 7.29/7.58 (r(s(s(s(s(z)))), s(s(s(z))))),
% 7.29/7.58 inference(modus_ponens,[status(thm)],[327, 8601])).
% 7.29/7.58 tff(8603,plain,
% 7.29/7.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.29/7.58 inference(rewrite,[status(thm)],[])).
% 7.29/7.58 tff(8604,plain,
% 7.29/7.58 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.29/7.58 inference(rewrite,[status(thm)],[])).
% 7.29/7.58 tff(8605,plain,
% 7.29/7.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 7.29/7.58 inference(monotonicity,[status(thm)],[8604])).
% 7.29/7.58 tff(8606,plain,
% 7.29/7.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.29/7.58 inference(transitivity,[status(thm)],[8605, 8603])).
% 7.29/7.58 tff(8607,plain,
% 7.29/7.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 7.29/7.58 inference(quant_inst,[status(thm)],[])).
% 7.29/7.58 tff(8608,plain,
% 7.29/7.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 7.29/7.58 inference(modus_ponens,[status(thm)],[8607, 8606])).
% 7.29/7.58 tff(8609,plain,
% 7.29/7.58 (~r(s(s(z)), z)),
% 7.29/7.58 inference(unit_resolution,[status(thm)],[8608, 194, 1749, 719, 8602])).
% 7.29/7.58 tff(8610,plain,
% 7.29/7.58 (b(s(s(z)), z)),
% 7.29/7.58 inference(unit_resolution,[status(thm)],[1211, 8609])).
% 7.29/7.58 tff(8611,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 7.29/7.58 tff(8612,plain,
% 7.29/7.58 (r(s(elem!1), s(s(s(elem!1))))),
% 7.29/7.58 inference(unit_resolution,[status(thm)],[3614, 1749, 8598])).
% 7.29/7.58 tff(8613,plain,
% 7.29/7.58 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(z)))),
% 7.29/7.58 inference(monotonicity,[status(thm)],[1550])).
% 7.29/7.58 tff(8614,plain,
% 7.29/7.58 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 7.29/7.58 inference(symmetry,[status(thm)],[8613])).
% 7.29/7.58 tff(8615,plain,
% 7.29/7.58 (s(s(s(z))) = s(s(elem!1))),
% 7.29/7.58 inference(symmetry,[status(thm)],[1551])).
% 7.29/7.58 tff(8616,plain,
% 7.29/7.58 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 7.29/7.58 inference(monotonicity,[status(thm)],[8615])).
% 7.29/7.58 tff(8617,plain,
% 7.29/7.58 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 7.29/7.58 inference(transitivity,[status(thm)],[8616, 8614])).
% 7.29/7.58 tff(8618,plain,
% 7.29/7.58 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 7.29/7.58 inference(monotonicity,[status(thm)],[8617])).
% 7.29/7.58 tff(8619,plain,
% 7.29/7.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 7.29/7.58 inference(rewrite,[status(thm)],[])).
% 7.29/7.58 tff(8620,plain,
% 7.29/7.58 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 7.29/7.58 inference(rewrite,[status(thm)],[])).
% 7.29/7.58 tff(8621,plain,
% 7.29/7.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 7.29/7.58 inference(monotonicity,[status(thm)],[8620])).
% 7.29/7.58 tff(8622,plain,
% 7.29/7.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 7.29/7.58 inference(transitivity,[status(thm)],[8621, 8619])).
% 7.29/7.58 tff(8623,plain,
% 7.29/7.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 7.29/7.58 inference(quant_inst,[status(thm)],[])).
% 7.29/7.58 tff(8624,plain,
% 7.29/7.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 7.29/7.58 inference(modus_ponens,[status(thm)],[8623, 8622])).
% 7.29/7.58 tff(8625,plain,
% 7.29/7.58 (~b(s(s(s(z))), s(s(z)))),
% 7.29/7.58 inference(unit_resolution,[status(thm)],[8624, 391, 1235, 7871, 1685])).
% 7.29/7.58 tff(8626,plain,
% 7.29/7.58 (~b(s(s(elem!1)), s(elem!1))),
% 7.29/7.58 inference(modus_ponens,[status(thm)],[8625, 8618])).
% 7.29/7.58 tff(8627,plain,
% 7.29/7.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 7.29/7.58 inference(rewrite,[status(thm)],[])).
% 7.29/7.58 tff(8628,plain,
% 7.29/7.58 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 7.29/7.58 inference(rewrite,[status(thm)],[])).
% 7.29/7.58 tff(8629,plain,
% 7.29/7.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 7.29/7.58 inference(monotonicity,[status(thm)],[8628])).
% 7.29/7.58 tff(8630,plain,
% 7.29/7.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 7.29/7.58 inference(transitivity,[status(thm)],[8629, 8627])).
% 7.29/7.59 tff(8631,plain,
% 7.29/7.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 7.29/7.59 inference(quant_inst,[status(thm)],[])).
% 7.29/7.59 tff(8632,plain,
% 7.29/7.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 7.29/7.59 inference(modus_ponens,[status(thm)],[8631, 8630])).
% 7.29/7.59 tff(8633,plain,
% 7.29/7.59 (~b(s(s(z)), s(s(s(z))))),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[8632, 391, 1235, 7871, 1685])).
% 7.29/7.59 tff(8634,plain,
% 7.29/7.59 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 7.29/7.59 inference(monotonicity,[status(thm)],[818, 819])).
% 7.29/7.59 tff(8635,plain,
% 7.29/7.59 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 7.29/7.59 inference(monotonicity,[status(thm)],[8634])).
% 7.29/7.59 tff(8636,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 7.29/7.59 tff(8637,plain,
% 7.29/7.59 (~b(s(elem!1), s(s(elem!1)))),
% 7.29/7.59 inference(modus_ponens,[status(thm)],[8636, 8635])).
% 7.29/7.59 tff(8638,plain,
% 7.29/7.59 ($false),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[7625, 8637])).
% 7.29/7.59 tff(8639,plain,(b(s(s(z)), s(s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.59 tff(8640,plain,
% 7.29/7.59 (~b(s(elem!1), s(s(elem!1)))),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[8639, 8633, 8598])).
% 7.29/7.59 tff(8641,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 7.29/7.59 tff(8642,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 7.29/7.59 tff(8643,plain,
% 7.29/7.59 ($false),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[1111, 42, 8642, 8641, 8611])).
% 7.29/7.59 tff(8644,plain,(b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.59 tff(8645,plain,
% 7.29/7.59 (r(s(elem!1), s(s(elem!1)))),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[8644, 8640, 8611])).
% 7.29/7.59 tff(8646,plain,
% 7.29/7.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.29/7.59 inference(rewrite,[status(thm)],[])).
% 7.29/7.59 tff(8647,plain,
% 7.29/7.59 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.29/7.59 inference(rewrite,[status(thm)],[])).
% 7.29/7.59 tff(8648,plain,
% 7.29/7.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 7.29/7.59 inference(monotonicity,[status(thm)],[8647])).
% 7.29/7.59 tff(8649,plain,
% 7.29/7.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.29/7.59 inference(transitivity,[status(thm)],[8648, 8646])).
% 7.29/7.59 tff(8650,plain,
% 7.29/7.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.29/7.59 inference(quant_inst,[status(thm)],[])).
% 7.29/7.59 tff(8651,plain,
% 7.29/7.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 7.29/7.59 inference(modus_ponens,[status(thm)],[8650, 8649])).
% 7.29/7.59 tff(8652,plain,
% 7.29/7.59 ($false),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[8651, 194, 327, 604, 2170, 7538])).
% 7.29/7.59 tff(8653,plain,((~r(s(s(s(elem!1))), 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(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.59 tff(8654,plain,
% 7.29/7.59 (~r(s(s(elem!1)), s(elem!1))),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[8653, 8645, 327, 604])).
% 7.29/7.59 tff(8655,plain,
% 7.29/7.59 (b(s(s(elem!1)), s(elem!1))),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[1135, 8654, 285])).
% 7.29/7.59 tff(8656,plain,
% 7.29/7.59 ($false),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[8655, 8626])).
% 7.29/7.59 tff(8657,plain,((~b(s(s(s(z))), z)) | (~(elem!1 = s(z))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.59 tff(8658,plain,
% 7.29/7.59 (~b(s(s(s(z))), z)),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[8657, 8612, 285, 327, 169, 8611, 8610, 8600])).
% 7.29/7.59 tff(8659,plain,
% 7.29/7.59 (~b(s(s(elem!1)), z)),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[7886, 8658, 8598])).
% 7.29/7.59 tff(8660,plain,
% 7.29/7.59 (r(s(s(elem!1)), z)),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[2629, 8659])).
% 7.29/7.59 tff(8661,plain,
% 7.29/7.59 (~r(s(s(elem!1)), elem!1)),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[8360, 8660, 411, 530])).
% 7.29/7.59 tff(8662,plain,
% 7.29/7.59 (b(s(s(elem!1)), elem!1)),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[872, 8661, 8597])).
% 7.29/7.59 tff(8663,plain,
% 7.29/7.59 (b(elem!1, s(s(s(elem!1))))),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[8542, 1234, 8598])).
% 7.29/7.59 tff(8664,plain,
% 7.29/7.59 (~(s(s(s(s(elem!1)))) = elem!1)),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[7472, 8598])).
% 7.29/7.59 tff(8665,plain,
% 7.29/7.59 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 7.29/7.59 inference(commutativity,[status(thm)],[])).
% 7.29/7.59 tff(8666,plain,
% 7.29/7.59 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 7.29/7.59 inference(symmetry,[status(thm)],[8665])).
% 7.29/7.59 tff(8667,plain,
% 7.29/7.59 (s(s(z)) = s(elem!1)),
% 7.29/7.59 inference(symmetry,[status(thm)],[1550])).
% 7.29/7.59 tff(8668,plain,
% 7.29/7.59 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 7.29/7.59 inference(symmetry,[status(thm)],[8584])).
% 7.29/7.59 tff(8669,plain,
% 7.29/7.59 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 7.29/7.59 inference(monotonicity,[status(thm)],[8668, 8667])).
% 7.29/7.59 tff(8670,plain,
% 7.29/7.59 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 7.29/7.59 inference(transitivity,[status(thm)],[8669, 8665])).
% 7.29/7.59 tff(8671,plain,
% 7.29/7.59 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 7.29/7.59 inference(transitivity,[status(thm)],[8670, 8666])).
% 7.29/7.59 tff(8672,plain,
% 7.29/7.59 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 7.29/7.59 inference(monotonicity,[status(thm)],[8671])).
% 7.29/7.59 tff(8673,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 7.29/7.59 tff(8674,plain,
% 7.29/7.59 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 7.29/7.59 inference(monotonicity,[status(thm)],[8673])).
% 7.29/7.59 tff(8675,plain,
% 7.29/7.59 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 7.29/7.59 inference(symmetry,[status(thm)],[8674])).
% 7.29/7.59 tff(8676,plain,
% 7.29/7.59 (s(z) = s(s(s(s(z))))),
% 7.29/7.59 inference(transitivity,[status(thm)],[706, 8675, 4986])).
% 7.29/7.59 tff(8677,plain,
% 7.29/7.59 ($false),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[743, 8676])).
% 7.29/7.59 tff(8678,plain,(~(s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.29/7.59 tff(8679,plain,
% 7.29/7.59 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 7.29/7.59 inference(modus_ponens,[status(thm)],[8678, 8672])).
% 7.29/7.59 tff(8680,plain,
% 7.29/7.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 7.29/7.59 inference(rewrite,[status(thm)],[])).
% 7.29/7.59 tff(8681,plain,
% 7.29/7.59 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 7.29/7.59 inference(rewrite,[status(thm)],[])).
% 7.29/7.59 tff(8682,plain,
% 7.29/7.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 7.29/7.59 inference(monotonicity,[status(thm)],[8681])).
% 7.29/7.59 tff(8683,plain,
% 7.29/7.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 7.29/7.59 inference(transitivity,[status(thm)],[8682, 8680])).
% 7.29/7.59 tff(8684,plain,
% 7.29/7.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 7.29/7.59 inference(quant_inst,[status(thm)],[])).
% 7.29/7.59 tff(8685,plain,
% 7.29/7.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 7.29/7.59 inference(modus_ponens,[status(thm)],[8684, 8683])).
% 7.29/7.59 tff(8686,plain,
% 7.29/7.59 (~b(s(s(elem!1)), s(elem!1))),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[8685, 391, 900, 973, 448, 2122])).
% 7.29/7.59 tff(8687,plain,
% 7.29/7.59 (r(s(s(elem!1)), s(elem!1))),
% 7.29/7.59 inference(unit_resolution,[status(thm)],[1135, 8686, 285])).
% 7.29/7.59 tff(8688,plain,
% 7.29/7.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 7.29/7.59 inference(rewrite,[status(thm)],[])).
% 7.29/7.59 tff(8689,plain,
% 7.29/7.59 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 7.38/7.60 inference(rewrite,[status(thm)],[])).
% 7.38/7.60 tff(8690,plain,
% 7.38/7.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 7.38/7.60 inference(monotonicity,[status(thm)],[8689])).
% 7.38/7.60 tff(8691,plain,
% 7.38/7.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 7.38/7.60 inference(transitivity,[status(thm)],[8690, 8688])).
% 7.38/7.60 tff(8692,plain,
% 7.38/7.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 7.38/7.60 inference(quant_inst,[status(thm)],[])).
% 7.38/7.60 tff(8693,plain,
% 7.38/7.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 7.38/7.60 inference(modus_ponens,[status(thm)],[8692, 8691])).
% 7.38/7.60 tff(8694,plain,
% 7.38/7.60 (~b(s(elem!1), s(s(elem!1)))),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[8693, 391, 900, 973, 448, 2122])).
% 7.38/7.60 tff(8695,plain,
% 7.38/7.60 (r(s(elem!1), s(s(elem!1)))),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[8644, 8694, 8611])).
% 7.38/7.60 tff(8696,plain,
% 7.38/7.60 ($false),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[8653, 8695, 8687, 327, 604])).
% 7.38/7.60 tff(8697,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.60 tff(8698,plain,
% 7.38/7.60 (~b(s(elem!1), elem!1)),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[8697, 8662, 900, 8611, 285, 8663, 8612, 327])).
% 7.38/7.60 tff(8699,plain,
% 7.38/7.60 (r(s(elem!1), elem!1)),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[2168, 8698, 164])).
% 7.38/7.60 tff(8700,plain,
% 7.38/7.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.38/7.60 inference(rewrite,[status(thm)],[])).
% 7.38/7.60 tff(8701,plain,
% 7.38/7.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.38/7.60 inference(quant_inst,[status(thm)],[])).
% 7.38/7.60 tff(8702,plain,
% 7.38/7.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 7.38/7.60 inference(modus_ponens,[status(thm)],[8701, 8700])).
% 7.38/7.60 tff(8703,plain,
% 7.38/7.60 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[8702, 194, 530, 485, 991])).
% 7.38/7.60 tff(8704,plain,
% 7.38/7.60 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[988, 8703, 957])).
% 7.38/7.60 tff(8705,plain,
% 7.38/7.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 7.38/7.60 inference(rewrite,[status(thm)],[])).
% 7.38/7.60 tff(8706,plain,
% 7.38/7.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 7.38/7.60 inference(quant_inst,[status(thm)],[])).
% 7.38/7.60 tff(8707,plain,
% 7.38/7.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 7.38/7.60 inference(modus_ponens,[status(thm)],[8706, 8705])).
% 7.38/7.60 tff(8708,plain,
% 7.38/7.60 (~r(s(s(s(s(elem!1)))), z)),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[8707, 194, 411, 530, 991])).
% 7.38/7.60 tff(8709,plain,
% 7.38/7.60 (b(s(s(s(s(elem!1)))), z)),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[1626, 8708])).
% 7.38/7.60 tff(8710,plain,
% 7.38/7.60 (~r(s(elem!1), z)),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[541, 485, 530, 411])).
% 7.38/7.60 tff(8711,plain,
% 7.38/7.60 (b(s(elem!1), z)),
% 7.38/7.60 inference(unit_resolution,[status(thm)],[547, 42, 355, 8710])).
% 7.38/7.60 tff(8712,plain,
% 7.38/7.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.38/7.60 inference(rewrite,[status(thm)],[])).
% 7.38/7.60 tff(8713,plain,
% 7.38/7.60 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.38/7.60 inference(rewrite,[status(thm)],[])).
% 7.38/7.60 tff(8714,plain,
% 7.38/7.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 7.38/7.60 inference(monotonicity,[status(thm)],[8713])).
% 7.38/7.60 tff(8715,plain,
% 7.38/7.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.38/7.60 inference(transitivity,[status(thm)],[8714, 8712])).
% 7.38/7.60 tff(8716,plain,
% 7.38/7.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.38/7.61 inference(quant_inst,[status(thm)],[])).
% 7.38/7.61 tff(8717,plain,
% 7.38/7.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 7.38/7.61 inference(modus_ponens,[status(thm)],[8716, 8715])).
% 7.38/7.61 tff(8718,plain,
% 7.38/7.61 ($false),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[8717, 391, 973, 3927, 8711, 8709, 8704])).
% 7.38/7.61 tff(8719,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.61 tff(8720,plain,
% 7.38/7.61 (~r(s(s(s(s(elem!1)))), elem!1)),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[8719, 8699, 411, 8679, 3927, 8662, 530])).
% 7.38/7.61 tff(8721,plain,
% 7.38/7.61 (b(s(s(s(s(elem!1)))), elem!1)),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[1004, 8720, 8664])).
% 7.38/7.61 tff(8722,plain,
% 7.38/7.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.38/7.61 inference(rewrite,[status(thm)],[])).
% 7.38/7.61 tff(8723,plain,
% 7.38/7.61 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.38/7.61 inference(rewrite,[status(thm)],[])).
% 7.38/7.61 tff(8724,plain,
% 7.38/7.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 7.38/7.61 inference(monotonicity,[status(thm)],[8723])).
% 7.38/7.61 tff(8725,plain,
% 7.38/7.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.38/7.61 inference(transitivity,[status(thm)],[8724, 8722])).
% 7.38/7.61 tff(8726,plain,
% 7.38/7.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 7.38/7.61 inference(quant_inst,[status(thm)],[])).
% 7.38/7.61 tff(8727,plain,
% 7.38/7.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 7.38/7.61 inference(modus_ponens,[status(thm)],[8726, 8725])).
% 7.38/7.61 tff(8728,plain,
% 7.38/7.61 ($false),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[8727, 391, 900, 973, 448, 1733, 2698])).
% 7.38/7.61 tff(8729,plain,((~b(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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.61 tff(8730,plain,
% 7.38/7.61 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[8729, 8721, 900, 8663, 8662])).
% 7.38/7.61 tff(8731,plain,
% 7.38/7.61 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[1061, 8730, 8594])).
% 7.38/7.61 tff(8732,plain,
% 7.38/7.61 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 7.38/7.61 inference(monotonicity,[status(thm)],[8668, 8615])).
% 7.38/7.61 tff(8733,plain,
% 7.38/7.61 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 7.38/7.61 inference(symmetry,[status(thm)],[8732])).
% 7.38/7.61 tff(8734,plain,
% 7.38/7.61 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 7.38/7.61 inference(modus_ponens,[status(thm)],[1177, 8733])).
% 7.38/7.61 tff(8735,assumption,(~r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 7.38/7.61 tff(8736,plain,
% 7.38/7.61 ($false),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[8735, 8734])).
% 7.38/7.61 tff(8737,plain,(r(s(s(s(s(s(z))))), s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.61 tff(8738,plain,
% 7.38/7.61 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[8737, 8731, 169])).
% 7.38/7.61 tff(8739,plain,
% 7.38/7.61 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 7.38/7.61 inference(monotonicity,[status(thm)],[8584, 169])).
% 7.38/7.61 tff(8740,plain,
% 7.38/7.61 (b(s(s(s(s(s(z))))), s(z))),
% 7.38/7.61 inference(modus_ponens,[status(thm)],[8721, 8739])).
% 7.38/7.61 tff(8741,plain,
% 7.38/7.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 7.38/7.61 inference(rewrite,[status(thm)],[])).
% 7.38/7.61 tff(8742,plain,
% 7.38/7.61 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 7.38/7.61 inference(rewrite,[status(thm)],[])).
% 7.38/7.61 tff(8743,plain,
% 7.38/7.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 7.38/7.61 inference(monotonicity,[status(thm)],[8742])).
% 7.38/7.61 tff(8744,plain,
% 7.38/7.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 7.38/7.61 inference(transitivity,[status(thm)],[8743, 8741])).
% 7.38/7.61 tff(8745,plain,
% 7.38/7.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 7.38/7.61 inference(quant_inst,[status(thm)],[])).
% 7.38/7.61 tff(8746,plain,
% 7.38/7.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 7.38/7.61 inference(modus_ponens,[status(thm)],[8745, 8744])).
% 7.38/7.61 tff(8747,plain,
% 7.38/7.61 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[8746, 391, 90, 1234, 1759, 8740])).
% 7.38/7.61 tff(8748,assumption,(~r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 7.38/7.61 tff(8749,assumption,(s(s(s(s(z)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 7.38/7.61 tff(8750,plain,
% 7.38/7.61 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 7.38/7.61 inference(symmetry,[status(thm)],[8749])).
% 7.38/7.61 tff(8751,plain,
% 7.38/7.61 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))),
% 7.38/7.61 inference(monotonicity,[status(thm)],[8750])).
% 7.38/7.61 tff(8752,plain,
% 7.38/7.61 (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))),
% 7.38/7.61 inference(symmetry,[status(thm)],[8751])).
% 7.38/7.61 tff(8753,plain,
% 7.38/7.61 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 7.38/7.61 inference(transitivity,[status(thm)],[8749, 8752])).
% 7.38/7.61 tff(8754,plain,
% 7.38/7.61 ($false),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[4995, 8753])).
% 7.38/7.61 tff(8755,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.61 tff(8756,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 7.38/7.61 tff(8757,plain,
% 7.38/7.61 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 7.38/7.61 inference(rewrite,[status(thm)],[])).
% 7.38/7.61 tff(8758,plain,
% 7.38/7.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 7.38/7.61 inference(quant_inst,[status(thm)],[])).
% 7.38/7.61 tff(8759,plain,
% 7.38/7.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 7.38/7.61 inference(modus_ponens,[status(thm)],[8758, 8757])).
% 7.38/7.61 tff(8760,plain,
% 7.38/7.61 ($false),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[8759, 42, 8756, 8755, 8748])).
% 7.38/7.61 tff(8761,plain,(b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.61 tff(8762,plain,
% 7.38/7.61 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[8761, 8747])).
% 7.38/7.61 tff(8763,plain,
% 7.38/7.61 (((~![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))),
% 7.38/7.61 inference(rewrite,[status(thm)],[])).
% 7.38/7.61 tff(8764,plain,
% 7.38/7.61 ((~![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))),
% 7.38/7.61 inference(quant_inst,[status(thm)],[])).
% 7.38/7.61 tff(8765,plain,
% 7.38/7.61 ((~![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)),
% 7.38/7.61 inference(modus_ponens,[status(thm)],[8764, 8763])).
% 7.38/7.61 tff(8766,plain,
% 7.38/7.61 (r(s(s(s(z))), z)),
% 7.38/7.61 inference(unit_resolution,[status(thm)],[8765, 42, 741, 8658])).
% 7.38/7.61 tff(8767,plain,
% 7.38/7.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 7.38/7.62 inference(rewrite,[status(thm)],[])).
% 7.38/7.62 tff(8768,plain,
% 7.38/7.62 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 7.38/7.62 inference(rewrite,[status(thm)],[])).
% 7.38/7.62 tff(8769,plain,
% 7.38/7.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8768])).
% 7.38/7.62 tff(8770,plain,
% 7.38/7.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 7.38/7.62 inference(transitivity,[status(thm)],[8769, 8767])).
% 7.38/7.62 tff(8771,plain,
% 7.38/7.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 7.38/7.62 inference(quant_inst,[status(thm)],[])).
% 7.38/7.62 tff(8772,plain,
% 7.38/7.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[8771, 8770])).
% 7.38/7.62 tff(8773,plain,
% 7.38/7.62 ($false),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8772, 194, 8766, 8602, 8762, 8738])).
% 7.38/7.62 tff(8774,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~r(elem!1, z)) | (s(elem!1) = elem!1) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.62 tff(8775,plain,
% 7.38/7.62 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8774, 8582, 8487, 8298, 8255, 8291, 8232, 3927, 3618, 8281, 8276, 8273, 8269, 8267])).
% 7.38/7.62 tff(8776,plain,
% 7.38/7.62 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[1370, 8775, 8265])).
% 7.38/7.62 tff(8777,plain,
% 7.38/7.62 (b(s(s(s(s(z)))), s(s(s(z))))),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[8776, 8259])).
% 7.38/7.62 tff(8778,plain,
% 7.38/7.62 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8257])).
% 7.38/7.62 tff(8779,plain,
% 7.38/7.62 (b(z, s(s(s(z))))),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[3927, 8778])).
% 7.38/7.62 tff(8780,plain,
% 7.38/7.62 (~b(s(s(elem!1)), s(z))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[3263, 8776, 8487, 8298, 8318])).
% 7.38/7.62 tff(8781,plain,
% 7.38/7.62 (r(s(s(elem!1)), s(z))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[362, 8780])).
% 7.38/7.62 tff(8782,plain,
% 7.38/7.62 (~r(s(s(elem!1)), z)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[4103, 8781, 8327, 182])).
% 7.38/7.62 tff(8783,plain,
% 7.38/7.62 (b(s(s(elem!1)), z)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[2629, 8782])).
% 7.38/7.62 tff(8784,plain,
% 7.38/7.62 (b(s(s(s(z))), z)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[7886, 8783, 8304])).
% 7.38/7.62 tff(8785,plain,
% 7.38/7.62 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[7880, 8784, 8779, 8269])).
% 7.38/7.62 tff(8786,plain,
% 7.38/7.62 ($false),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8785, 8777])).
% 7.38/7.62 tff(8787,plain,((~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.62 tff(8788,plain,
% 7.38/7.62 (~b(s(s(s(elem!1))), z)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8787, 8253, 181, 10, 2, 484, 31])).
% 7.38/7.62 tff(8789,plain,
% 7.38/7.62 (~b(s(s(s(s(z)))), z)),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[8788, 8239])).
% 7.38/7.62 tff(8790,plain,
% 7.38/7.62 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8234])).
% 7.38/7.62 tff(8791,plain,
% 7.38/7.62 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), s(z)))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8790])).
% 7.38/7.62 tff(8792,plain,
% 7.38/7.62 (~r(s(s(s(elem!1))), s(z))),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[8290, 8791])).
% 7.38/7.62 tff(8793,plain,
% 7.38/7.62 (b(elem!1, elem!1) <=> b(s(z), s(z))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[169, 169])).
% 7.38/7.62 tff(8794,plain,
% 7.38/7.62 (b(s(z), s(z)) <=> b(elem!1, elem!1)),
% 7.38/7.62 inference(symmetry,[status(thm)],[8793])).
% 7.38/7.62 tff(8795,plain,
% 7.38/7.62 (b(s(z), elem!1) <=> b(s(z), s(z))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[169])).
% 7.38/7.62 tff(8796,plain,
% 7.38/7.62 (b(s(z), s(z)) <=> b(s(z), elem!1)),
% 7.38/7.62 inference(symmetry,[status(thm)],[8795])).
% 7.38/7.62 tff(8797,plain,
% 7.38/7.62 ((~b(s(z), s(z))) <=> (~b(s(z), elem!1))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8796])).
% 7.38/7.62 tff(8798,assumption,(~b(s(z), s(z))), introduced(assumption)).
% 7.38/7.62 tff(8799,plain,
% 7.38/7.62 (~b(s(z), elem!1)),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[8798, 8797])).
% 7.38/7.62 tff(8800,plain,
% 7.38/7.62 ($false),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[644, 8799])).
% 7.38/7.62 tff(8801,plain,((~(elem!1 = s(z))) | (~b(s(z), elem!1)) | b(s(z), s(z))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.62 tff(8802,plain,
% 7.38/7.62 (b(s(z), s(z))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8801, 169, 644])).
% 7.38/7.62 tff(8803,plain,
% 7.38/7.62 (b(elem!1, elem!1)),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[8802, 8794])).
% 7.38/7.62 tff(8804,plain,
% 7.38/7.62 ($false),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[4741, 8803])).
% 7.38/7.62 tff(8805,plain,((~(elem!1 = s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.62 tff(8806,plain,
% 7.38/7.62 (~b(s(z), elem!1)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8805, 8234])).
% 7.38/7.62 tff(8807,plain,
% 7.38/7.62 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 7.38/7.62 inference(transitivity,[status(thm)],[8242, 4])).
% 7.38/7.62 tff(8808,plain,
% 7.38/7.62 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8807])).
% 7.38/7.62 tff(8809,plain,
% 7.38/7.62 (~(elem!1 = s(s(s(elem!1))))),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[217, 8808])).
% 7.38/7.62 tff(8810,plain,
% 7.38/7.62 (r(s(s(s(elem!1))), z)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[377, 8788])).
% 7.38/7.62 tff(8811,plain,
% 7.38/7.62 (~r(elem!1, s(s(s(elem!1))))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8380, 8810, 59, 8232])).
% 7.38/7.62 tff(8812,plain,
% 7.38/7.62 (b(elem!1, s(s(s(elem!1))))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[424, 8811, 8809])).
% 7.38/7.62 tff(8813,plain,
% 7.38/7.62 (b(s(z), s(s(s(s(z)))))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8314, 8812, 8234])).
% 7.38/7.62 tff(8814,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 7.38/7.62 tff(8815,plain,
% 7.38/7.62 (b(s(s(s(elem!1))), s(z))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[223, 8814])).
% 7.38/7.62 tff(8816,plain,
% 7.38/7.62 (elem!1 = z),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8231, 80, 10])).
% 7.38/7.62 tff(8817,plain,
% 7.38/7.62 (b(s(z), elem!1) <=> b(s(z), z)),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8816])).
% 7.38/7.62 tff(8818,plain,
% 7.38/7.62 ((~b(s(z), elem!1)) <=> (~b(s(z), z))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8817])).
% 7.38/7.62 tff(8819,plain,
% 7.38/7.62 (~b(s(z), z)),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[2829, 8818])).
% 7.38/7.62 tff(8820,plain,
% 7.38/7.62 (r(s(z), z)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[178, 42, 23, 8819])).
% 7.38/7.62 tff(8821,plain,
% 7.38/7.62 (b(elem!1, s(z)) <=> b(z, s(z))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8816])).
% 7.38/7.62 tff(8822,plain,
% 7.38/7.62 (b(z, s(z)) <=> b(elem!1, s(z))),
% 7.38/7.62 inference(symmetry,[status(thm)],[8821])).
% 7.38/7.62 tff(8823,plain,
% 7.38/7.62 (s(elem!1) = s(z)),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8816])).
% 7.38/7.62 tff(8824,plain,
% 7.38/7.62 (b(z, s(elem!1)) <=> b(z, s(z))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8823])).
% 7.38/7.62 tff(8825,plain,
% 7.38/7.62 (b(z, s(elem!1)) <=> b(elem!1, s(z))),
% 7.38/7.62 inference(transitivity,[status(thm)],[8824, 8822])).
% 7.38/7.62 tff(8826,plain,
% 7.38/7.62 (r(elem!1, s(z)) <=> r(z, s(z))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[11])).
% 7.38/7.62 tff(8827,plain,
% 7.38/7.62 (r(z, s(z)) <=> r(elem!1, s(z))),
% 7.38/7.62 inference(symmetry,[status(thm)],[8826])).
% 7.38/7.62 tff(8828,plain,
% 7.38/7.62 (r(z, s(elem!1)) <=> r(z, s(z))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[488])).
% 7.38/7.62 tff(8829,plain,
% 7.38/7.62 (r(z, s(elem!1)) <=> r(elem!1, s(z))),
% 7.38/7.62 inference(transitivity,[status(thm)],[8828, 8827])).
% 7.38/7.62 tff(8830,plain,
% 7.38/7.62 (r(elem!1, s(z))),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[2144, 8829])).
% 7.38/7.62 tff(8831,plain,
% 7.38/7.62 ($false),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[832, 8830])).
% 7.38/7.62 tff(8832,plain,((~r(z, s(elem!1))) | r(elem!1, s(z)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.62 tff(8833,plain,
% 7.38/7.62 (~r(z, s(elem!1))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8832, 8816, 832])).
% 7.38/7.62 tff(8834,plain,
% 7.38/7.62 (b(z, s(elem!1))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[566, 8833])).
% 7.38/7.62 tff(8835,plain,
% 7.38/7.62 (b(elem!1, s(z))),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[8834, 8825])).
% 7.38/7.62 tff(8836,plain,
% 7.38/7.62 ((s(z) = elem!1) <=> (s(z) = z)),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8816])).
% 7.38/7.62 tff(8837,plain,
% 7.38/7.62 ((s(z) = z) <=> (s(z) = elem!1)),
% 7.38/7.62 inference(symmetry,[status(thm)],[8836])).
% 7.38/7.62 tff(8838,plain,
% 7.38/7.62 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8837])).
% 7.38/7.62 tff(8839,plain,
% 7.38/7.62 (~(s(z) = elem!1)),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[23, 8838])).
% 7.38/7.62 tff(8840,plain,
% 7.38/7.62 (r(s(z), elem!1)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[632, 8839, 2829])).
% 7.38/7.62 tff(8841,plain,
% 7.38/7.62 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[11])).
% 7.38/7.62 tff(8842,plain,
% 7.38/7.62 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 7.38/7.62 inference(symmetry,[status(thm)],[8841])).
% 7.38/7.62 tff(8843,plain,
% 7.38/7.62 ((~b(z, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[8842])).
% 7.38/7.62 tff(8844,plain,
% 7.38/7.62 (~b(elem!1, s(s(s(elem!1))))),
% 7.38/7.62 inference(modus_ponens,[status(thm)],[10, 8843])).
% 7.38/7.62 tff(8845,plain,
% 7.38/7.62 ($false),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[448, 8844])).
% 7.38/7.62 tff(8846,plain,((~(elem!1 = z)) | (~b(elem!1, s(s(s(elem!1))))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.62 tff(8847,plain,
% 7.38/7.62 (~b(elem!1, s(s(s(elem!1))))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8846, 8816, 10])).
% 7.38/7.62 tff(8848,plain,
% 7.38/7.62 (r(s(s(s(elem!1))), elem!1)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[230, 9, 168])).
% 7.38/7.62 tff(8849,plain,
% 7.38/7.62 (r(elem!1, s(s(s(elem!1))))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[424, 1, 4028])).
% 7.38/7.62 tff(8850,plain,
% 7.38/7.62 (~r(z, elem!1)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[419, 8848, 59, 8849])).
% 7.38/7.62 tff(8851,plain,
% 7.38/7.62 (elem!1 = z),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[7395, 8850, 10, 150])).
% 7.38/7.62 tff(8852,plain,
% 7.38/7.62 (r(s(s(s(elem!1))), z)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[406, 8851, 8848])).
% 7.38/7.62 tff(8853,plain,
% 7.38/7.62 (z = elem!1),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[5453, 8851])).
% 7.38/7.62 tff(8854,plain,
% 7.38/7.62 (r(s(z), z)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[5433, 8853, 1484])).
% 7.38/7.62 tff(8855,plain,
% 7.38/7.62 ($false),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[3969, 8854, 8852, 2053, 59, 3363])).
% 7.38/7.62 tff(8856,plain,((elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | b(z, s(s(s(elem!1)))) | (s(z) = elem!1) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.62 tff(8857,plain,
% 7.38/7.62 (b(s(s(s(elem!1))), elem!1)),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[8856, 8839, 3447, 10, 1439, 8847, 8840])).
% 7.38/7.62 tff(8858,plain,
% 7.38/7.62 (~b(s(z), s(s(s(elem!1))))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[2907, 8857, 1526, 8835])).
% 7.38/7.62 tff(8859,plain,
% 7.38/7.62 (r(s(z), s(s(s(elem!1))))),
% 7.38/7.62 inference(unit_resolution,[status(thm)],[247, 8858])).
% 7.38/7.62 tff(8860,plain,
% 7.38/7.62 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 7.38/7.62 inference(monotonicity,[status(thm)],[491])).
% 7.38/7.62 tff(8861,plain,
% 7.38/7.62 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 7.38/7.62 inference(symmetry,[status(thm)],[8860])).
% 7.38/7.63 tff(8862,plain,
% 7.38/7.63 (s(s(s(z))) = s(s(s(s(z))))),
% 7.38/7.63 inference(transitivity,[status(thm)],[491, 290, 8861])).
% 7.38/7.63 tff(8863,plain,
% 7.38/7.63 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8862])).
% 7.38/7.63 tff(8864,plain,
% 7.38/7.63 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(z))))),
% 7.38/7.63 inference(symmetry,[status(thm)],[8863])).
% 7.38/7.63 tff(8865,plain,
% 7.38/7.63 (s(s(s(elem!1))) = s(s(elem!1))),
% 7.38/7.63 inference(transitivity,[status(thm)],[490, 693, 8864, 685, 2980])).
% 7.38/7.63 tff(8866,plain,
% 7.38/7.63 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[2980, 491])).
% 7.38/7.63 tff(8867,plain,
% 7.38/7.63 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 7.38/7.63 inference(transitivity,[status(thm)],[8866, 267])).
% 7.38/7.63 tff(8868,plain,
% 7.38/7.63 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8867])).
% 7.38/7.63 tff(8869,plain,
% 7.38/7.63 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 7.38/7.63 inference(transitivity,[status(thm)],[8867, 268])).
% 7.38/7.63 tff(8870,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 7.38/7.63 tff(8871,plain,
% 7.38/7.63 (s(s(elem!1)) = s(s(s(elem!1)))),
% 7.38/7.63 inference(modus_ponens,[status(thm)],[8870, 8869])).
% 7.38/7.63 tff(8872,plain,
% 7.38/7.63 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(z))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[488])).
% 7.38/7.63 tff(8873,plain,
% 7.38/7.63 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 7.38/7.63 inference(transitivity,[status(thm)],[8872, 204])).
% 7.38/7.63 tff(8874,plain,
% 7.38/7.63 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 7.38/7.63 inference(symmetry,[status(thm)],[8873])).
% 7.38/7.63 tff(8875,plain,
% 7.38/7.63 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8874])).
% 7.38/7.63 tff(8876,plain,
% 7.38/7.63 (~(s(s(s(elem!1))) = s(elem!1))),
% 7.38/7.63 inference(modus_ponens,[status(thm)],[217, 8875])).
% 7.38/7.63 tff(8877,plain,
% 7.38/7.63 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[281, 8876])).
% 7.38/7.63 tff(8878,plain,
% 7.38/7.63 ($false),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[8877, 8871])).
% 7.38/7.63 tff(8879,plain,((~(s(s(z)) = s(s(s(z))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.63 tff(8880,plain,
% 7.38/7.63 (~(s(s(z)) = s(s(s(z))))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[8879, 11])).
% 7.38/7.63 tff(8881,plain,
% 7.38/7.63 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.38/7.63 inference(modus_ponens,[status(thm)],[8880, 8868])).
% 7.38/7.63 tff(8882,plain,
% 7.38/7.63 ($false),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[8881, 8865])).
% 7.38/7.63 tff(8883,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.63 tff(8884,plain,
% 7.38/7.63 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[8883, 8816])).
% 7.38/7.63 tff(8885,plain,
% 7.38/7.63 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[307, 8884])).
% 7.38/7.63 tff(8886,plain,
% 7.38/7.63 (b(s(elem!1), z) <=> b(s(z), z)),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8823])).
% 7.38/7.63 tff(8887,plain,
% 7.38/7.63 (b(s(z), z) <=> b(s(elem!1), z)),
% 7.38/7.63 inference(symmetry,[status(thm)],[8886])).
% 7.38/7.63 tff(8888,plain,
% 7.38/7.63 ((~b(s(z), z)) <=> (~b(s(elem!1), z))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8887])).
% 7.38/7.63 tff(8889,plain,
% 7.38/7.63 (~b(s(elem!1), z)),
% 7.38/7.63 inference(modus_ponens,[status(thm)],[8819, 8888])).
% 7.38/7.63 tff(8890,plain,
% 7.38/7.63 (r(s(elem!1), z)),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[549, 8889])).
% 7.38/7.63 tff(8891,plain,
% 7.38/7.63 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8816])).
% 7.38/7.63 tff(8892,plain,
% 7.38/7.63 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 7.38/7.63 inference(symmetry,[status(thm)],[8891])).
% 7.38/7.63 tff(8893,plain,
% 7.38/7.63 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(s(z)))), elem!1))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8892])).
% 7.38/7.63 tff(8894,plain,
% 7.38/7.63 (~b(s(s(s(s(z)))), elem!1)),
% 7.38/7.63 inference(modus_ponens,[status(thm)],[3446, 8893])).
% 7.38/7.63 tff(8895,plain,
% 7.38/7.63 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8823])).
% 7.38/7.63 tff(8896,plain,
% 7.38/7.63 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 7.38/7.63 inference(symmetry,[status(thm)],[8895])).
% 7.38/7.63 tff(8897,plain,
% 7.38/7.63 (b(s(s(s(elem!1))), s(elem!1))),
% 7.38/7.63 inference(modus_ponens,[status(thm)],[1526, 8896])).
% 7.38/7.63 tff(8898,plain,
% 7.38/7.63 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8816])).
% 7.38/7.63 tff(8899,plain,
% 7.38/7.63 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 7.38/7.63 inference(symmetry,[status(thm)],[8898])).
% 7.38/7.63 tff(8900,plain,
% 7.38/7.63 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 7.38/7.63 inference(transitivity,[status(thm)],[8887, 8899])).
% 7.38/7.63 tff(8901,plain,
% 7.38/7.63 ((~b(s(z), z)) <=> (~b(s(elem!1), elem!1))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8900])).
% 7.38/7.63 tff(8902,plain,
% 7.38/7.63 (~b(s(elem!1), elem!1)),
% 7.38/7.63 inference(modus_ponens,[status(thm)],[8819, 8901])).
% 7.38/7.63 tff(8903,plain,
% 7.38/7.63 (r(s(elem!1), elem!1)),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[2168, 8902, 2204])).
% 7.38/7.63 tff(8904,plain,
% 7.38/7.63 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[1648, 8903, 8816, 8897, 59, 1442, 8894, 8890])).
% 7.38/7.63 tff(8905,plain,
% 7.38/7.63 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[1164, 8904, 8885])).
% 7.38/7.63 tff(8906,plain,
% 7.38/7.63 ($false),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[1546, 8905, 8859, 59, 8820])).
% 7.38/7.63 tff(8907,plain,(r(z, elem!1) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(s(s(elem!1)))) | b(s(z), elem!1) | b(s(s(s(s(z)))), z) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.63 tff(8908,plain,
% 7.38/7.63 (r(z, elem!1)),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[8907, 832, 10, 2829, 3446, 8815])).
% 7.38/7.63 tff(8909,assumption,(z = s(s(z))), introduced(assumption)).
% 7.38/7.63 tff(8910,plain,
% 7.38/7.63 (s(s(z)) = z),
% 7.38/7.63 inference(symmetry,[status(thm)],[8909])).
% 7.38/7.63 tff(8911,plain,
% 7.38/7.63 ($false),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[1207, 8910])).
% 7.38/7.63 tff(8912,plain,(~(z = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.63 tff(8913,plain,
% 7.38/7.63 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(s(z))))))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[6249])).
% 7.38/7.63 tff(8914,plain,
% 7.38/7.63 (~b(s(z), s(s(s(s(z)))))),
% 7.38/7.63 inference(modus_ponens,[status(thm)],[2829, 8913])).
% 7.38/7.63 tff(8915,plain,
% 7.38/7.63 ($false),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[1234, 8914])).
% 7.38/7.63 tff(8916,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.38/7.63 tff(8917,plain,
% 7.38/7.63 (~(s(s(s(s(z)))) = elem!1)),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[8916, 2829, 1234])).
% 7.38/7.63 tff(8918,plain,
% 7.38/7.63 (b(elem!1, s(z))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[837, 173, 832])).
% 7.38/7.63 tff(8919,plain,
% 7.38/7.63 (~(elem!1 = s(s(s(s(z)))))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[769, 8917])).
% 7.38/7.63 tff(8920,plain,
% 7.38/7.63 (~r(s(s(s(s(z)))), s(z))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[3243, 182, 2053, 411])).
% 7.38/7.63 tff(8921,plain,
% 7.38/7.63 (b(s(s(s(s(z)))), s(z))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[749, 8920])).
% 7.38/7.63 tff(8922,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 7.38/7.63 tff(8923,plain,
% 7.38/7.63 (~r(elem!1, s(s(s(s(z)))))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[2040, 182, 1484, 411])).
% 7.38/7.63 tff(8924,plain,
% 7.38/7.63 (b(elem!1, s(s(s(s(z)))))),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[781, 8923, 8922])).
% 7.38/7.63 tff(8925,plain,
% 7.38/7.63 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.63 inference(rewrite,[status(thm)],[])).
% 7.38/7.63 tff(8926,plain,
% 7.38/7.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8925])).
% 7.38/7.63 tff(8927,plain,
% 7.38/7.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.63 inference(transitivity,[status(thm)],[8926, 2083])).
% 7.38/7.63 tff(8928,plain,
% 7.38/7.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 7.38/7.63 inference(quant_inst,[status(thm)],[])).
% 7.38/7.63 tff(8929,plain,
% 7.38/7.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.38/7.63 inference(modus_ponens,[status(thm)],[8928, 8927])).
% 7.38/7.63 tff(8930,plain,
% 7.38/7.63 ($false),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[8929, 391, 8924, 1234, 8921, 721])).
% 7.38/7.63 tff(8931,plain,((~r(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.63 tff(8932,plain,
% 7.38/7.63 (~r(s(z), z)),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[8931, 8918, 1234, 8919, 2053, 411, 5238])).
% 7.38/7.63 tff(8933,plain,
% 7.38/7.63 (b(s(z), z)),
% 7.38/7.63 inference(unit_resolution,[status(thm)],[180, 8932])).
% 7.38/7.63 tff(8934,plain,
% 7.38/7.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 7.38/7.63 inference(rewrite,[status(thm)],[])).
% 7.38/7.63 tff(8935,plain,
% 7.38/7.63 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 7.38/7.63 inference(rewrite,[status(thm)],[])).
% 7.38/7.63 tff(8936,plain,
% 7.38/7.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 7.38/7.63 inference(monotonicity,[status(thm)],[8935])).
% 7.38/7.63 tff(8937,plain,
% 7.38/7.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 7.38/7.63 inference(transitivity,[status(thm)],[8936, 8934])).
% 7.38/7.63 tff(8938,plain,
% 7.38/7.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 7.38/7.63 inference(quant_inst,[status(thm)],[])).
% 7.38/7.63 tff(8939,plain,
% 7.38/7.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 7.38/7.64 inference(modus_ponens,[status(thm)],[8938, 8937])).
% 7.38/7.64 tff(8940,plain,
% 7.38/7.64 (~b(elem!1, s(s(s(elem!1))))),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[8939, 391, 1526, 1686, 590, 721])).
% 7.38/7.64 tff(8941,plain,
% 7.38/7.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 7.38/7.64 inference(rewrite,[status(thm)],[])).
% 7.38/7.64 tff(8942,plain,
% 7.38/7.64 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 7.38/7.64 inference(rewrite,[status(thm)],[])).
% 7.38/7.64 tff(8943,plain,
% 7.38/7.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 7.38/7.64 inference(monotonicity,[status(thm)],[8942])).
% 7.38/7.64 tff(8944,plain,
% 7.38/7.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 7.38/7.64 inference(transitivity,[status(thm)],[8943, 8941])).
% 7.38/7.64 tff(8945,plain,
% 7.38/7.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 7.38/7.64 inference(quant_inst,[status(thm)],[])).
% 7.38/7.64 tff(8946,plain,
% 7.38/7.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 7.38/7.64 inference(modus_ponens,[status(thm)],[8945, 8944])).
% 7.38/7.64 tff(8947,plain,
% 7.38/7.64 (~b(s(s(s(elem!1))), elem!1)),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[8946, 391, 1526, 1686, 590, 721])).
% 7.38/7.64 tff(8948,plain,
% 7.38/7.64 ($false),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[8856, 8947, 8940, 2053, 10, 150, 1, 1484])).
% 7.38/7.64 tff(8949,plain,((~b(s(z), z)) | (~r(s(s(s(s(z)))), z)) | b(z, s(s(s(elem!1)))) | (s(z) = elem!1) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.64 tff(8950,plain,
% 7.38/7.64 (~b(z, s(s(s(s(z)))))),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[8949, 1, 10, 150, 2053, 5238, 8815, 8933, 8918])).
% 7.38/7.64 tff(8951,plain,
% 7.38/7.64 (r(z, s(s(s(s(z)))))),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[800, 8950])).
% 7.38/7.64 tff(8952,plain,
% 7.38/7.64 (~b(s(s(s(s(z)))), s(z))),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[2097, 8951, 1234, 8917, 8918, 411])).
% 7.38/7.64 tff(8953,plain,
% 7.38/7.64 (r(s(s(s(s(z)))), s(z))),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[749, 8952])).
% 7.38/7.64 tff(8954,plain,
% 7.38/7.64 (b(s(s(s(elem!1))), elem!1)),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[8856, 4028, 2053, 10, 1, 150, 1484])).
% 7.38/7.64 tff(8955,plain,
% 7.38/7.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.64 inference(rewrite,[status(thm)],[])).
% 7.38/7.64 tff(8956,plain,
% 7.38/7.64 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(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))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.64 inference(rewrite,[status(thm)],[])).
% 7.38/7.64 tff(8957,plain,
% 7.38/7.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 7.38/7.64 inference(monotonicity,[status(thm)],[8956])).
% 7.38/7.64 tff(8958,plain,
% 7.38/7.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.64 inference(transitivity,[status(thm)],[8957, 8955])).
% 7.38/7.64 tff(8959,plain,
% 7.38/7.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 7.38/7.64 inference(quant_inst,[status(thm)],[])).
% 7.38/7.64 tff(8960,plain,
% 7.38/7.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 7.38/7.64 inference(modus_ponens,[status(thm)],[8959, 8958])).
% 7.38/7.64 tff(8961,plain,
% 7.38/7.64 ($false),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[8960, 391, 900, 1526, 1652, 1234, 721])).
% 7.38/7.64 tff(8962,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.64 tff(8963,plain,
% 7.38/7.64 (~b(s(s(s(s(z)))), elem!1)),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[8962, 8954, 1526, 1234, 8918])).
% 7.38/7.64 tff(8964,plain,
% 7.38/7.64 (r(s(s(s(s(z)))), elem!1)),
% 7.38/7.64 inference(unit_resolution,[status(thm)],[762, 8963, 720])).
% 7.38/7.64 tff(8965,plain,
% 7.38/7.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 7.38/7.64 inference(rewrite,[status(thm)],[])).
% 7.38/7.64 tff(8966,plain,
% 7.38/7.64 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 7.38/7.65 inference(rewrite,[status(thm)],[])).
% 7.38/7.65 tff(8967,plain,
% 7.38/7.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))))),
% 7.38/7.65 inference(monotonicity,[status(thm)],[8966])).
% 7.38/7.65 tff(8968,plain,
% 7.38/7.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 7.38/7.65 inference(transitivity,[status(thm)],[8967, 8965])).
% 7.38/7.65 tff(8969,plain,
% 7.38/7.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 7.38/7.65 inference(quant_inst,[status(thm)],[])).
% 7.38/7.65 tff(8970,plain,
% 7.38/7.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))),
% 7.38/7.65 inference(modus_ponens,[status(thm)],[8969, 8968])).
% 7.38/7.65 tff(8971,plain,
% 7.38/7.65 ($false),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[8970, 194, 411, 410, 2112, 719])).
% 7.38/7.65 tff(8972,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.65 tff(8973,plain,
% 7.38/7.65 (~r(z, elem!1)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[8972, 8849, 719, 2112])).
% 7.38/7.65 tff(8974,plain,
% 7.38/7.65 (elem!1 = z),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[7395, 8973, 10, 150])).
% 7.38/7.65 tff(8975,plain,
% 7.38/7.65 (z = elem!1),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[5453, 8974])).
% 7.38/7.65 tff(8976,plain,
% 7.38/7.65 (r(s(z), z)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[5433, 8975, 1484])).
% 7.38/7.65 tff(8977,plain,
% 7.38/7.65 (~r(s(s(s(elem!1))), z)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[3969, 8976, 2053, 59, 3363])).
% 7.38/7.65 tff(8978,plain,
% 7.38/7.65 (b(s(s(s(elem!1))), z)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[377, 8977])).
% 7.38/7.65 tff(8979,plain,
% 7.38/7.65 (~r(z, s(elem!1))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[8832, 8974, 832])).
% 7.38/7.65 tff(8980,plain,
% 7.38/7.65 (~r(s(s(s(elem!1))), elem!1)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[406, 8977, 8974])).
% 7.38/7.65 tff(8981,plain,
% 7.38/7.65 (b(s(s(s(elem!1))), elem!1)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[230, 8980, 9])).
% 7.38/7.65 tff(8982,plain,
% 7.38/7.65 (~b(s(z), s(s(s(elem!1))))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[2907, 8981, 1526, 8918])).
% 7.38/7.65 tff(8983,plain,
% 7.38/7.65 (r(s(z), s(s(s(elem!1))))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[247, 8982])).
% 7.38/7.65 tff(8984,plain,
% 7.38/7.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[641, 8983, 59, 8976])).
% 7.38/7.65 tff(8985,plain,
% 7.38/7.65 (~b(s(elem!1), z)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[2614, 8984, 59, 8979, 8978])).
% 7.38/7.65 tff(8986,plain,
% 7.38/7.65 (r(s(elem!1), z)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[549, 8985])).
% 7.38/7.65 tff(8987,plain,
% 7.38/7.65 (~r(elem!1, s(elem!1))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[2288, 8974, 8979])).
% 7.38/7.65 tff(8988,plain,
% 7.38/7.65 (b(elem!1, s(elem!1))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[443, 8987, 427])).
% 7.38/7.65 tff(8989,plain,
% 7.38/7.65 (~(s(s(s(elem!1))) = s(elem!1))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[4603, 8988, 4028])).
% 7.38/7.65 tff(8990,plain,
% 7.38/7.65 (b(s(s(s(elem!1))), s(elem!1))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[588, 8984, 8989])).
% 7.38/7.65 tff(8991,plain,
% 7.38/7.65 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[1546, 8983, 59, 8976])).
% 7.38/7.65 tff(8992,plain,
% 7.38/7.65 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[1164, 8991, 1373])).
% 7.38/7.65 tff(8993,plain,
% 7.38/7.65 (r(s(elem!1), elem!1)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[2340, 8990, 8987, 427, 8981])).
% 7.38/7.65 tff(8994,plain,
% 7.38/7.65 ($false),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[1648, 8993, 8992, 8974, 8990, 59, 930, 1549, 8986])).
% 7.38/7.65 tff(8995,plain,((elem!1 = s(s(s(elem!1)))) | b(s(s(s(s(z)))), elem!1) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | r(elem!1, s(z)) | b(z, s(s(s(elem!1)))) | (s(z) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.65 tff(8996,plain,
% 7.38/7.65 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[8995, 8963, 1, 1526, 4028, 2053, 1484, 832, 10, 150, 719, 8964])).
% 7.38/7.65 tff(8997,plain,
% 7.38/7.65 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[307, 8996])).
% 7.38/7.65 tff(8998,plain,
% 7.38/7.65 (~r(z, elem!1)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[8972, 8964, 719, 6124])).
% 7.38/7.65 tff(8999,plain,
% 7.38/7.65 (elem!1 = z),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[7395, 8998, 10, 150])).
% 7.38/7.65 tff(9000,plain,
% 7.38/7.65 ($false),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[8883, 8999, 8997])).
% 7.38/7.65 tff(9001,plain,(b(elem!1, s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | (s(z) = elem!1) | (~r(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | r(elem!1, s(z)) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.65 tff(9002,plain,
% 7.38/7.65 (b(elem!1, s(s(s(elem!1))))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[9001, 8951, 10, 1, 150, 8815, 2053, 5238, 832, 8917, 1234])).
% 7.38/7.65 tff(9003,plain,
% 7.38/7.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.65 inference(rewrite,[status(thm)],[])).
% 7.38/7.65 tff(9004,plain,
% 7.38/7.65 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.65 inference(rewrite,[status(thm)],[])).
% 7.38/7.65 tff(9005,plain,
% 7.38/7.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.38/7.65 inference(monotonicity,[status(thm)],[9004])).
% 7.38/7.65 tff(9006,plain,
% 7.38/7.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.65 inference(transitivity,[status(thm)],[9005, 9003])).
% 7.38/7.65 tff(9007,plain,
% 7.38/7.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 7.38/7.65 inference(quant_inst,[status(thm)],[])).
% 7.38/7.65 tff(9008,plain,
% 7.38/7.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 7.38/7.65 inference(modus_ponens,[status(thm)],[9007, 9006])).
% 7.38/7.65 tff(9009,plain,
% 7.38/7.65 ($false),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[9008, 391, 448, 1526, 1234, 3563, 721])).
% 7.38/7.65 tff(9010,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.65 tff(9011,plain,
% 7.38/7.65 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[9010, 9002, 8815, 1234, 8918])).
% 7.38/7.65 tff(9012,plain,
% 7.38/7.65 (r(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[1714, 9011])).
% 7.38/7.65 tff(9013,plain,
% 7.38/7.65 (b(elem!1, s(s(s(elem!1))))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[9001, 150, 10, 719, 1, 1526, 2053, 5238, 832, 8917, 1234])).
% 7.38/7.65 tff(9014,plain,
% 7.38/7.65 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[9010, 9013, 1526, 1234, 8918])).
% 7.38/7.65 tff(9015,plain,
% 7.38/7.65 (r(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[1714, 9014])).
% 7.38/7.65 tff(9016,plain,
% 7.38/7.65 (~(elem!1 = z)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[8846, 9013, 10])).
% 7.38/7.65 tff(9017,plain,
% 7.38/7.65 (r(z, elem!1)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[8231, 9016, 10])).
% 7.38/7.65 tff(9018,plain,
% 7.38/7.65 (~b(s(s(s(s(z)))), s(z))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[2097, 9017, 1234, 8917, 719, 8918])).
% 7.38/7.65 tff(9019,plain,
% 7.38/7.65 (r(s(s(s(s(z)))), s(z))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[749, 9018])).
% 7.38/7.65 tff(9020,plain,
% 7.38/7.65 (~r(s(s(z)), s(z))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[2429, 9019, 5238, 9015])).
% 7.38/7.65 tff(9021,plain,
% 7.38/7.65 (b(s(s(z)), s(z))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[3778, 9020])).
% 7.38/7.65 tff(9022,plain,
% 7.38/7.65 (~r(s(z), z)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[3243, 9019, 2053, 9017])).
% 7.38/7.65 tff(9023,plain,
% 7.38/7.65 (b(s(z), z)),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[180, 9022])).
% 7.38/7.65 tff(9024,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 7.38/7.65 tff(9025,plain,
% 7.38/7.65 (s(elem!1) = s(s(s(z)))),
% 7.38/7.65 inference(monotonicity,[status(thm)],[3584])).
% 7.38/7.65 tff(9026,plain,
% 7.38/7.65 (s(s(elem!1)) = s(s(s(s(z))))),
% 7.38/7.65 inference(monotonicity,[status(thm)],[9025])).
% 7.38/7.65 tff(9027,plain,
% 7.38/7.65 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 7.38/7.65 inference(monotonicity,[status(thm)],[9026])).
% 7.38/7.65 tff(9028,plain,
% 7.38/7.65 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 7.38/7.65 inference(symmetry,[status(thm)],[9027])).
% 7.38/7.65 tff(9029,plain,
% 7.38/7.65 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 7.38/7.65 inference(monotonicity,[status(thm)],[9028])).
% 7.38/7.65 tff(9030,plain,
% 7.38/7.65 (~b(s(s(elem!1)), s(z))),
% 7.38/7.65 inference(modus_ponens,[status(thm)],[9024, 9029])).
% 7.38/7.65 tff(9031,plain,
% 7.38/7.65 ($false),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[381, 9030])).
% 7.38/7.65 tff(9032,plain,((~(elem!1 = s(s(z)))) | (~b(s(s(elem!1)), s(z))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.65 tff(9033,plain,
% 7.38/7.65 (~b(s(s(elem!1)), s(z))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[9032, 3584, 9024])).
% 7.38/7.65 tff(9034,plain,
% 7.38/7.65 (r(s(s(elem!1)), s(z))),
% 7.38/7.65 inference(unit_resolution,[status(thm)],[362, 9033])).
% 7.38/7.65 tff(9035,plain,
% 7.38/7.65 (r(s(s(elem!1)), z) <=> r(s(s(s(s(z)))), z)),
% 7.38/7.65 inference(monotonicity,[status(thm)],[9026])).
% 7.38/7.65 tff(9036,plain,
% 7.38/7.65 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 7.38/7.65 inference(symmetry,[status(thm)],[9035])).
% 7.38/7.65 tff(9037,plain,
% 7.38/7.65 (r(s(s(elem!1)), z)),
% 7.38/7.65 inference(modus_ponens,[status(thm)],[2053, 9036])).
% 7.38/7.65 tff(9038,plain,
% 7.38/7.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(z)))))),
% 7.38/7.66 inference(rewrite,[status(thm)],[])).
% 7.38/7.66 tff(9039,plain,
% 7.38/7.66 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(z)))))),
% 7.38/7.66 inference(rewrite,[status(thm)],[])).
% 7.38/7.66 tff(9040,plain,
% 7.38/7.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(z))))))),
% 7.38/7.66 inference(monotonicity,[status(thm)],[9039])).
% 7.38/7.66 tff(9041,plain,
% 7.38/7.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(z)))))),
% 7.38/7.66 inference(transitivity,[status(thm)],[9040, 9038])).
% 7.38/7.66 tff(9042,plain,
% 7.38/7.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 7.38/7.66 inference(quant_inst,[status(thm)],[])).
% 7.38/7.66 tff(9043,plain,
% 7.38/7.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(z))))),
% 7.38/7.66 inference(modus_ponens,[status(thm)],[9042, 9041])).
% 7.38/7.66 tff(9044,plain,
% 7.38/7.66 ($false),
% 7.38/7.66 inference(unit_resolution,[status(thm)],[9043, 194, 340, 722, 1747, 2616])).
% 7.38/7.66 tff(9045,plain,((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.66 tff(9046,plain,
% 7.38/7.66 (~r(z, s(z))),
% 7.38/7.66 inference(unit_resolution,[status(thm)],[9045, 9037, 1747, 9034])).
% 7.38/7.66 tff(9047,plain,
% 7.38/7.66 (b(z, s(z))),
% 7.38/7.66 inference(unit_resolution,[status(thm)],[678, 9046])).
% 7.38/7.66 tff(9048,plain,
% 7.38/7.66 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 7.38/7.66 inference(monotonicity,[status(thm)],[3584])).
% 7.38/7.66 tff(9049,plain,
% 7.38/7.66 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 7.38/7.66 inference(symmetry,[status(thm)],[9048])).
% 7.38/7.66 tff(9050,plain,
% 7.38/7.66 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.66 inference(monotonicity,[status(thm)],[9026])).
% 7.38/7.66 tff(9051,plain,
% 7.38/7.66 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 7.38/7.66 inference(symmetry,[status(thm)],[9050])).
% 7.38/7.66 tff(9052,plain,
% 7.38/7.66 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 7.38/7.66 inference(transitivity,[status(thm)],[9051, 9049])).
% 7.38/7.66 tff(9053,plain,
% 7.38/7.66 (r(s(s(elem!1)), elem!1)),
% 7.38/7.66 inference(modus_ponens,[status(thm)],[1697, 9052])).
% 7.38/7.66 tff(9054,plain,
% 7.38/7.66 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(z)))))),
% 7.38/7.66 inference(monotonicity,[status(thm)],[9026])).
% 7.38/7.66 tff(9055,plain,
% 7.38/7.66 (r(z, s(s(s(s(z))))) <=> r(z, s(s(elem!1)))),
% 7.38/7.66 inference(symmetry,[status(thm)],[9054])).
% 7.38/7.66 tff(9056,plain,
% 7.38/7.66 (r(z, s(s(elem!1)))),
% 7.38/7.66 inference(modus_ponens,[status(thm)],[719, 9055])).
% 7.38/7.66 tff(9057,plain,
% 7.38/7.66 (~r(elem!1, z)),
% 7.38/7.66 inference(unit_resolution,[status(thm)],[867, 9056, 9053, 411])).
% 7.38/7.66 tff(9058,plain,
% 7.38/7.66 (b(elem!1, z)),
% 7.38/7.66 inference(unit_resolution,[status(thm)],[526, 9057, 2])).
% 7.38/7.66 tff(9059,plain,
% 7.38/7.66 (b(s(s(z)), z)),
% 7.38/7.66 inference(modus_ponens,[status(thm)],[9058, 3585])).
% 7.38/7.66 tff(9060,plain,
% 7.38/7.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 7.38/7.66 inference(rewrite,[status(thm)],[])).
% 7.38/7.66 tff(9061,plain,
% 7.38/7.66 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 7.38/7.66 inference(rewrite,[status(thm)],[])).
% 7.38/7.66 tff(9062,plain,
% 7.38/7.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 7.38/7.66 inference(monotonicity,[status(thm)],[9061])).
% 7.38/7.66 tff(9063,plain,
% 7.38/7.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 7.38/7.66 inference(transitivity,[status(thm)],[9062, 9060])).
% 7.38/7.66 tff(9064,plain,
% 7.38/7.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 7.38/7.66 inference(quant_inst,[status(thm)],[])).
% 7.38/7.66 tff(9065,plain,
% 7.38/7.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 7.38/7.66 inference(modus_ponens,[status(thm)],[9064, 9063])).
% 7.38/7.66 tff(9066,plain,
% 7.38/7.66 ($false),
% 7.38/7.66 inference(unit_resolution,[status(thm)],[9065, 391, 9059, 1233, 9047, 590])).
% 7.38/7.66 tff(9067,plain,((~(elem!1 = s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (elem!1 = z) | (~r(s(z), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.66 tff(9068,plain,
% 7.38/7.66 (~(elem!1 = s(s(z)))),
% 7.38/7.66 inference(unit_resolution,[status(thm)],[9067, 9021, 9023, 9016, 1747, 9017, 9015, 2053, 719, 9018])).
% 7.38/7.66 tff(9069,plain,
% 7.38/7.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.38/7.66 inference(rewrite,[status(thm)],[])).
% 7.38/7.66 tff(9070,plain,
% 7.38/7.66 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.38/7.66 inference(rewrite,[status(thm)],[])).
% 7.38/7.66 tff(9071,plain,
% 7.38/7.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 7.38/7.66 inference(monotonicity,[status(thm)],[9070])).
% 7.38/7.66 tff(9072,plain,
% 7.38/7.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.38/7.67 inference(transitivity,[status(thm)],[9071, 9069])).
% 7.38/7.67 tff(9073,plain,
% 7.38/7.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 7.38/7.67 inference(quant_inst,[status(thm)],[])).
% 7.38/7.67 tff(9074,plain,
% 7.38/7.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 7.38/7.67 inference(modus_ponens,[status(thm)],[9073, 9072])).
% 7.38/7.67 tff(9075,plain,
% 7.38/7.67 ($false),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[9074, 194, 1749, 723, 1747, 1697])).
% 7.38/7.67 tff(9076,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.67 tff(9077,plain,
% 7.38/7.67 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[9076, 9019, 1747, 9015])).
% 7.38/7.67 tff(9078,plain,
% 7.38/7.67 (b(s(s(z)), s(s(s(s(z)))))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[3652, 9077])).
% 7.38/7.67 tff(9079,plain,
% 7.38/7.67 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[1407, 9068])).
% 7.38/7.67 tff(9080,plain,
% 7.38/7.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 7.38/7.67 inference(rewrite,[status(thm)],[])).
% 7.38/7.67 tff(9081,plain,
% 7.38/7.67 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 7.38/7.67 inference(rewrite,[status(thm)],[])).
% 7.38/7.67 tff(9082,plain,
% 7.38/7.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 7.38/7.67 inference(monotonicity,[status(thm)],[9081])).
% 7.38/7.67 tff(9083,plain,
% 7.38/7.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 7.38/7.67 inference(transitivity,[status(thm)],[9082, 9080])).
% 7.38/7.67 tff(9084,plain,
% 7.38/7.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 7.38/7.67 inference(quant_inst,[status(thm)],[])).
% 7.38/7.67 tff(9085,plain,
% 7.38/7.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 7.38/7.67 inference(modus_ponens,[status(thm)],[9084, 9083])).
% 7.38/7.67 tff(9086,plain,
% 7.38/7.67 ($false),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[9085, 391, 448, 3927, 1526, 590, 721])).
% 7.38/7.67 tff(9087,plain,((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.67 tff(9088,plain,
% 7.38/7.67 (~b(z, s(s(elem!1)))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[9087, 9013, 1526, 9023, 8918])).
% 7.38/7.67 tff(9089,plain,
% 7.38/7.67 (r(z, s(s(elem!1)))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[324, 9088])).
% 7.38/7.67 tff(9090,plain,
% 7.38/7.67 (~(s(s(elem!1)) = elem!1)),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[4206, 340, 832])).
% 7.38/7.67 tff(9091,plain,
% 7.38/7.67 (~(elem!1 = s(s(elem!1)))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[1292, 9090])).
% 7.38/7.67 tff(9092,plain,
% 7.38/7.67 (~b(elem!1, s(s(elem!1)))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[2824, 340, 719, 721, 720, 1234, 1484, 1983, 411])).
% 7.38/7.67 tff(9093,plain,
% 7.38/7.67 (~r(elem!1, s(s(elem!1)))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[2549, 340, 411, 326])).
% 7.38/7.67 tff(9094,plain,
% 7.38/7.67 ($false),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[1307, 9093, 9092, 9091])).
% 7.38/7.67 tff(9095,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = s(s(elem!1))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.67 tff(9096,plain,
% 7.38/7.67 (~r(s(s(elem!1)), s(z))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[9095, 9017, 9089, 719, 8918, 8917, 1234, 5238, 9079, 832])).
% 7.38/7.67 tff(9097,plain,
% 7.38/7.67 (b(s(s(elem!1)), s(z))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[362, 9096])).
% 7.38/7.67 tff(9098,plain,
% 7.38/7.67 (r(s(s(s(s(z)))), elem!1)),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[762, 1549, 720])).
% 7.38/7.67 tff(9099,plain,
% 7.38/7.67 (~b(s(s(s(s(z)))), s(z))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[2097, 411, 1234, 720, 719, 8918])).
% 7.38/7.67 tff(9100,plain,
% 7.38/7.67 (r(s(s(s(s(z)))), s(z))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[749, 9099])).
% 7.38/7.67 tff(9101,plain,
% 7.38/7.67 (r(elem!1, s(s(s(s(z)))))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[781, 8922, 8536])).
% 7.38/7.67 tff(9102,plain,
% 7.38/7.67 ($false),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[2026, 194, 1484, 2032, 2112, 723])).
% 7.38/7.67 tff(9103,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.67 tff(9104,plain,
% 7.38/7.67 (~r(s(s(s(s(z)))), elem!1)),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[9103, 9101, 1484, 723])).
% 7.38/7.67 tff(9105,plain,
% 7.38/7.67 (s(s(s(s(z)))) = elem!1),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[762, 9104, 1549])).
% 7.38/7.67 tff(9106,plain,
% 7.38/7.67 (elem!1 = s(s(s(s(z))))),
% 7.38/7.67 inference(modus_ponens,[status(thm)],[9105, 764])).
% 7.38/7.67 tff(9107,plain,
% 7.38/7.67 ($false),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[8922, 9106])).
% 7.38/7.67 tff(9108,plain,((elem!1 = s(s(s(s(z))))) | b(s(s(s(s(z)))), elem!1) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.67 tff(9109,plain,
% 7.38/7.67 (b(elem!1, s(s(s(s(z)))))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[9108, 1549, 723, 1484, 770])).
% 7.38/7.67 tff(9110,plain,
% 7.38/7.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(z)))))),
% 7.38/7.67 inference(rewrite,[status(thm)],[])).
% 7.38/7.67 tff(9111,plain,
% 7.38/7.67 (((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(z)))))),
% 7.38/7.67 inference(rewrite,[status(thm)],[])).
% 7.38/7.67 tff(9112,plain,
% 7.38/7.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(z))))))),
% 7.38/7.67 inference(monotonicity,[status(thm)],[9111])).
% 7.38/7.67 tff(9113,plain,
% 7.38/7.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(z)))))),
% 7.38/7.67 inference(transitivity,[status(thm)],[9112, 9110])).
% 7.38/7.67 tff(9114,plain,
% 7.38/7.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 7.38/7.67 inference(quant_inst,[status(thm)],[])).
% 7.38/7.67 tff(9115,plain,
% 7.38/7.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(z))))),
% 7.38/7.67 inference(modus_ponens,[status(thm)],[9114, 9113])).
% 7.38/7.67 tff(9116,plain,
% 7.38/7.67 ($false),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[9115, 194, 1484, 1748, 2112, 723])).
% 7.38/7.67 tff(9117,plain,((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.67 tff(9118,plain,
% 7.38/7.67 (~r(elem!1, s(s(z)))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[9117, 9098, 1484, 723])).
% 7.38/7.67 tff(9119,plain,
% 7.38/7.67 (b(elem!1, s(s(z)))),
% 7.38/7.67 inference(unit_resolution,[status(thm)],[3394, 9118, 1405])).
% 7.38/7.67 tff(9120,plain,
% 7.38/7.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 7.38/7.67 inference(rewrite,[status(thm)],[])).
% 7.38/7.67 tff(9121,plain,
% 7.38/7.67 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 7.38/7.67 inference(rewrite,[status(thm)],[])).
% 7.38/7.67 tff(9122,plain,
% 7.38/7.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 7.38/7.67 inference(monotonicity,[status(thm)],[9121])).
% 7.38/7.67 tff(9123,plain,
% 7.38/7.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 7.38/7.67 inference(transitivity,[status(thm)],[9122, 9120])).
% 7.38/7.67 tff(9124,plain,
% 7.38/7.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 7.38/7.68 inference(quant_inst,[status(thm)],[])).
% 7.38/7.68 tff(9125,plain,
% 7.38/7.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 7.38/7.68 inference(modus_ponens,[status(thm)],[9124, 9123])).
% 7.38/7.68 tff(9126,plain,
% 7.38/7.68 ($false),
% 7.38/7.68 inference(unit_resolution,[status(thm)],[9125, 391, 3823, 2064, 3369, 3563])).
% 7.38/7.68 tff(9127,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.68 tff(9128,plain,
% 7.38/7.68 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.68 inference(unit_resolution,[status(thm)],[9127, 9119, 3823, 9109])).
% 7.38/7.68 tff(9129,plain,
% 7.38/7.68 (r(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.68 inference(unit_resolution,[status(thm)],[1714, 9128])).
% 7.38/7.68 tff(9130,assumption,(r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 7.38/7.68 tff(9131,plain,
% 7.38/7.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.38/7.68 inference(rewrite,[status(thm)],[])).
% 7.38/7.68 tff(9132,plain,
% 7.38/7.68 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.38/7.68 inference(rewrite,[status(thm)],[])).
% 7.38/7.68 tff(9133,plain,
% 7.38/7.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 7.38/7.68 inference(monotonicity,[status(thm)],[9132])).
% 7.38/7.68 tff(9134,plain,
% 7.38/7.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.38/7.68 inference(transitivity,[status(thm)],[9133, 9131])).
% 7.38/7.68 tff(9135,plain,
% 7.38/7.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 7.38/7.68 inference(quant_inst,[status(thm)],[])).
% 7.38/7.68 tff(9136,plain,
% 7.38/7.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 7.38/7.68 inference(modus_ponens,[status(thm)],[9135, 9134])).
% 7.38/7.68 tff(9137,plain,
% 7.38/7.68 ($false),
% 7.38/7.68 inference(unit_resolution,[status(thm)],[9136, 194, 723, 1747, 1697, 9130])).
% 7.38/7.68 tff(9138,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.68 tff(9139,plain,
% 7.38/7.68 (~r(s(s(z)), s(s(s(elem!1))))),
% 7.38/7.68 inference(unit_resolution,[status(thm)],[9138, 9129, 1747, 723])).
% 7.38/7.68 tff(9140,plain,
% 7.38/7.68 (b(s(s(z)), s(s(s(elem!1))))),
% 7.38/7.68 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 9139])).
% 7.38/7.68 tff(9141,plain,
% 7.38/7.68 (~b(elem!1, s(s(s(elem!1))))),
% 7.38/7.68 inference(unit_resolution,[status(thm)],[8561, 9119, 1526, 1234, 9140])).
% 7.38/7.68 tff(9142,plain,
% 7.38/7.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 7.38/7.68 inference(rewrite,[status(thm)],[])).
% 7.38/7.68 tff(9143,plain,
% 7.38/7.68 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 7.38/7.68 inference(rewrite,[status(thm)],[])).
% 7.38/7.68 tff(9144,plain,
% 7.38/7.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))))),
% 7.38/7.68 inference(monotonicity,[status(thm)],[9143])).
% 7.38/7.68 tff(9145,plain,
% 7.38/7.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 7.38/7.68 inference(transitivity,[status(thm)],[9144, 9142])).
% 7.38/7.68 tff(9146,plain,
% 7.38/7.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.38/7.68 inference(quant_inst,[status(thm)],[])).
% 7.38/7.68 tff(9147,plain,
% 7.38/7.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))),
% 7.38/7.68 inference(modus_ponens,[status(thm)],[9146, 9145])).
% 7.38/7.68 tff(9148,plain,
% 7.38/7.68 ($false),
% 7.38/7.68 inference(unit_resolution,[status(thm)],[9147, 194, 1484, 1749, 723, 2405])).
% 7.38/7.68 tff(9149,plain,((~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.68 tff(9150,plain,
% 7.38/7.68 (~r(s(s(z)), s(z))),
% 7.38/7.68 inference(unit_resolution,[status(thm)],[9149, 1749, 1484, 723])).
% 7.38/7.68 tff(9151,plain,
% 7.38/7.68 (b(s(s(z)), s(z))),
% 7.38/7.68 inference(unit_resolution,[status(thm)],[3778, 9150])).
% 7.38/7.68 tff(9152,plain,
% 7.38/7.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.68 inference(rewrite,[status(thm)],[])).
% 7.38/7.68 tff(9153,plain,
% 7.38/7.68 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.68 inference(rewrite,[status(thm)],[])).
% 7.38/7.68 tff(9154,plain,
% 7.38/7.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.38/7.68 inference(monotonicity,[status(thm)],[9153])).
% 7.38/7.69 tff(9155,plain,
% 7.38/7.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.69 inference(transitivity,[status(thm)],[9154, 9152])).
% 7.38/7.69 tff(9156,plain,
% 7.38/7.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))),
% 7.38/7.69 inference(quant_inst,[status(thm)],[])).
% 7.38/7.69 tff(9157,plain,
% 7.38/7.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.38/7.69 inference(modus_ponens,[status(thm)],[9156, 9155])).
% 7.38/7.69 tff(9158,plain,
% 7.38/7.69 ($false),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[9157, 391, 3369, 1234, 2439, 1233, 721])).
% 7.38/7.69 tff(9159,plain,((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.69 tff(9160,plain,
% 7.38/7.69 (~b(s(z), s(s(z)))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[9159, 9151, 1234, 3369, 721])).
% 7.38/7.69 tff(9161,plain,
% 7.38/7.69 (r(s(z), s(s(z)))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[1788, 9160])).
% 7.38/7.69 tff(9162,plain,
% 7.38/7.69 (~r(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[9076, 1749, 723, 9161])).
% 7.38/7.69 tff(9163,plain,
% 7.38/7.69 (b(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[1714, 9162])).
% 7.38/7.69 tff(9164,plain,
% 7.38/7.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.69 inference(rewrite,[status(thm)],[])).
% 7.38/7.69 tff(9165,plain,
% 7.38/7.69 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.69 inference(rewrite,[status(thm)],[])).
% 7.38/7.69 tff(9166,plain,
% 7.38/7.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[9165])).
% 7.38/7.69 tff(9167,plain,
% 7.38/7.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.38/7.69 inference(transitivity,[status(thm)],[9166, 9164])).
% 7.38/7.69 tff(9168,plain,
% 7.38/7.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 7.38/7.69 inference(quant_inst,[status(thm)],[])).
% 7.38/7.69 tff(9169,plain,
% 7.38/7.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.38/7.69 inference(modus_ponens,[status(thm)],[9168, 9167])).
% 7.38/7.69 tff(9170,plain,
% 7.38/7.69 ($false),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[9169, 391, 2064, 3369, 1234, 9163, 9151])).
% 7.38/7.69 tff(9171,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.69 tff(9172,plain,
% 7.38/7.69 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[9171, 721, 723, 1234, 2064, 3369, 1484])).
% 7.38/7.69 tff(9173,plain,
% 7.38/7.69 (b(s(s(z)), s(s(s(s(z)))))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[3652, 9172])).
% 7.38/7.69 tff(9174,plain,
% 7.38/7.69 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[9127, 9173, 2064, 3369])).
% 7.38/7.69 tff(9175,plain,
% 7.38/7.69 (r(s(s(s(s(z)))), s(s(z)))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[1714, 9174])).
% 7.38/7.69 tff(9176,plain,
% 7.38/7.69 (~r(s(s(z)), s(z))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[2429, 9175, 1484, 723])).
% 7.38/7.69 tff(9177,plain,
% 7.38/7.69 (b(s(s(z)), s(z))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[3778, 9176])).
% 7.38/7.69 tff(9178,plain,
% 7.38/7.69 (~b(s(z), s(s(z)))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[9159, 9177, 3369, 1234, 721])).
% 7.38/7.69 tff(9179,plain,
% 7.38/7.69 (r(s(z), s(s(z)))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[1788, 9178])).
% 7.38/7.69 tff(9180,plain,
% 7.38/7.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.38/7.69 inference(rewrite,[status(thm)],[])).
% 7.38/7.69 tff(9181,plain,
% 7.38/7.69 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.38/7.69 inference(rewrite,[status(thm)],[])).
% 7.38/7.69 tff(9182,plain,
% 7.38/7.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[9181])).
% 7.38/7.69 tff(9183,plain,
% 7.38/7.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.38/7.69 inference(transitivity,[status(thm)],[9182, 9180])).
% 7.38/7.69 tff(9184,plain,
% 7.38/7.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 7.38/7.69 inference(quant_inst,[status(thm)],[])).
% 7.38/7.69 tff(9185,plain,
% 7.38/7.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 7.38/7.69 inference(modus_ponens,[status(thm)],[9184, 9183])).
% 7.38/7.69 tff(9186,plain,
% 7.38/7.69 ($false),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[9185, 194, 3557, 723, 9179, 9175])).
% 7.38/7.69 tff(9187,plain,((~b(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.69 tff(9188,plain,
% 7.38/7.69 (~r(s(s(z)), z)),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[9187, 9119, 1234, 723, 8918, 1484, 9109])).
% 7.38/7.69 tff(9189,plain,
% 7.38/7.69 (b(s(s(z)), z)),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[1211, 9188])).
% 7.38/7.69 tff(9190,plain,
% 7.38/7.69 (~r(s(s(z)), s(z))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[2429, 9129, 1484, 723])).
% 7.38/7.69 tff(9191,plain,
% 7.38/7.69 (b(s(s(z)), s(z))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[3778, 9190])).
% 7.38/7.69 tff(9192,plain,
% 7.38/7.69 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(elem!1))))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[283])).
% 7.38/7.69 tff(9193,plain,
% 7.38/7.69 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(elem!1)))),
% 7.38/7.69 inference(symmetry,[status(thm)],[9192])).
% 7.38/7.69 tff(9194,plain,
% 7.38/7.69 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[283])).
% 7.38/7.69 tff(9195,plain,
% 7.38/7.69 ((~r(s(z), s(s(elem!1)))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[9194])).
% 7.38/7.69 tff(9196,plain,
% 7.38/7.69 (~b(s(s(s(s(z)))), s(z))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[5108, 3823, 1234, 1233])).
% 7.38/7.69 tff(9197,plain,
% 7.38/7.69 (r(s(s(s(s(z)))), s(z))),
% 7.38/7.69 inference(unit_resolution,[status(thm)],[749, 9196])).
% 7.38/7.69 tff(9198,plain,
% 7.38/7.69 ((z = s(z)) <=> (s(z) = z)),
% 7.38/7.69 inference(commutativity,[status(thm)],[])).
% 7.38/7.69 tff(9199,plain,
% 7.38/7.69 ((s(z) = z) <=> (z = s(z))),
% 7.38/7.69 inference(symmetry,[status(thm)],[9198])).
% 7.38/7.69 tff(9200,plain,
% 7.38/7.69 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[9199])).
% 7.38/7.69 tff(9201,plain,
% 7.38/7.69 (~(z = s(z))),
% 7.38/7.69 inference(modus_ponens,[status(thm)],[23, 9200])).
% 7.38/7.69 tff(9202,plain,
% 7.38/7.69 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[283])).
% 7.38/7.69 tff(9203,plain,
% 7.38/7.69 (s(elem!1) = s(s(elem!1))),
% 7.38/7.69 inference(transitivity,[status(thm)],[352, 9202, 211])).
% 7.38/7.69 tff(9204,plain,
% 7.38/7.69 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(elem!1)))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[9203])).
% 7.38/7.69 tff(9205,plain,
% 7.38/7.69 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = elem!1)),
% 7.38/7.69 inference(transitivity,[status(thm)],[9204, 250])).
% 7.38/7.69 tff(9206,plain,
% 7.38/7.69 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(elem!1))),
% 7.38/7.69 inference(symmetry,[status(thm)],[9205])).
% 7.38/7.69 tff(9207,plain,
% 7.38/7.69 ((s(s(elem!1)) = elem!1) <=> (s(elem!1) = elem!1)),
% 7.38/7.69 inference(transitivity,[status(thm)],[9206, 161])).
% 7.38/7.69 tff(9208,plain,
% 7.38/7.69 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[9203])).
% 7.38/7.69 tff(9209,plain,
% 7.38/7.69 (inj_0(s(s(elem!1))) = inj_0(s(elem!1))),
% 7.38/7.69 inference(symmetry,[status(thm)],[9208])).
% 7.38/7.69 tff(9210,plain,
% 7.38/7.69 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 7.38/7.69 inference(symmetry,[status(thm)],[9202])).
% 7.38/7.69 tff(9211,plain,
% 7.38/7.69 (s(s(elem!1)) = elem!1),
% 7.38/7.69 inference(transitivity,[status(thm)],[212, 9210, 9209, 108])).
% 7.38/7.69 tff(9212,plain,
% 7.38/7.69 (s(elem!1) = elem!1),
% 7.38/7.69 inference(modus_ponens,[status(thm)],[9211, 9207])).
% 7.38/7.69 tff(9213,plain,
% 7.38/7.69 (elem!1 = s(elem!1)),
% 7.38/7.69 inference(symmetry,[status(thm)],[152])).
% 7.38/7.69 tff(9214,plain,
% 7.38/7.69 (s(s(s(s(z)))) = s(elem!1)),
% 7.38/7.69 inference(transitivity,[status(thm)],[688, 9213])).
% 7.38/7.69 tff(9215,plain,
% 7.38/7.69 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[9214])).
% 7.38/7.69 tff(9216,plain,
% 7.38/7.69 (s(s(s(z))) = s(elem!1)),
% 7.38/7.69 inference(transitivity,[status(thm)],[693, 9215, 108, 9213])).
% 7.38/7.69 tff(9217,plain,
% 7.38/7.69 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[9216])).
% 7.38/7.69 tff(9218,plain,
% 7.38/7.69 (s(s(z)) = s(elem!1)),
% 7.38/7.69 inference(transitivity,[status(thm)],[710, 9217, 108, 9213])).
% 7.38/7.69 tff(9219,plain,
% 7.38/7.69 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 7.38/7.69 inference(monotonicity,[status(thm)],[9218])).
% 7.38/7.69 tff(9220,plain,
% 7.38/7.69 (s(z) = elem!1),
% 7.38/7.69 inference(transitivity,[status(thm)],[706, 9219, 108])).
% 7.38/7.69 tff(9221,plain,
% 7.48/7.70 (s(s(elem!1)) = elem!1),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[1943, 152])).
% 7.48/7.70 tff(9222,plain,
% 7.48/7.70 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9221])).
% 7.48/7.70 tff(9223,plain,
% 7.48/7.70 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 7.48/7.70 inference(transitivity,[status(thm)],[9222, 474])).
% 7.48/7.70 tff(9224,plain,
% 7.48/7.70 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9223])).
% 7.48/7.70 tff(9225,plain,
% 7.48/7.70 (~(s(z) = elem!1)),
% 7.48/7.70 inference(modus_ponens,[status(thm)],[357, 9224])).
% 7.48/7.70 tff(9226,plain,
% 7.48/7.70 ($false),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9225, 9220])).
% 7.48/7.70 tff(9227,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.70 tff(9228,plain,
% 7.48/7.70 (~(s(s(s(s(z)))) = elem!1)),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9227, 9212])).
% 7.48/7.70 tff(9229,plain,
% 7.48/7.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.48/7.70 inference(rewrite,[status(thm)],[])).
% 7.48/7.70 tff(9230,plain,
% 7.48/7.70 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.48/7.70 inference(rewrite,[status(thm)],[])).
% 7.48/7.70 tff(9231,plain,
% 7.48/7.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9230])).
% 7.48/7.70 tff(9232,plain,
% 7.48/7.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.48/7.70 inference(transitivity,[status(thm)],[9231, 9229])).
% 7.48/7.70 tff(9233,plain,
% 7.48/7.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 7.48/7.70 inference(quant_inst,[status(thm)],[])).
% 7.48/7.70 tff(9234,plain,
% 7.48/7.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.48/7.70 inference(modus_ponens,[status(thm)],[9233, 9232])).
% 7.48/7.70 tff(9235,plain,
% 7.48/7.70 ($false),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9234, 391, 381, 3823, 1234, 1233, 1232])).
% 7.48/7.70 tff(9236,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.70 tff(9237,plain,
% 7.48/7.70 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9236, 381, 1234, 1233, 3823])).
% 7.48/7.70 tff(9238,plain,
% 7.48/7.70 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9211])).
% 7.48/7.70 tff(9239,plain,
% 7.48/7.70 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.70 inference(symmetry,[status(thm)],[9238])).
% 7.48/7.70 tff(9240,plain,
% 7.48/7.70 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.70 inference(modus_ponens,[status(thm)],[1652, 9239])).
% 7.48/7.70 tff(9241,plain,
% 7.48/7.70 ($false),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[3478, 9240])).
% 7.48/7.70 tff(9242,plain,((~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(z)))), s(s(elem!1))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.70 tff(9243,plain,
% 7.48/7.70 (~b(s(s(s(s(z)))), elem!1)),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9242, 9237, 266])).
% 7.48/7.70 tff(9244,plain,
% 7.48/7.70 (r(s(s(s(s(z)))), elem!1)),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[762, 9243, 9228])).
% 7.48/7.70 tff(9245,plain,
% 7.48/7.70 (r(s(s(elem!1)), s(s(z))) <=> r(elem!1, s(s(z)))),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9211])).
% 7.48/7.70 tff(9246,plain,
% 7.48/7.70 (r(elem!1, s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 7.48/7.70 inference(symmetry,[status(thm)],[9245])).
% 7.48/7.70 tff(9247,plain,
% 7.48/7.70 (s(s(z)) = elem!1),
% 7.48/7.70 inference(symmetry,[status(thm)],[3584])).
% 7.48/7.70 tff(9248,plain,
% 7.48/7.70 (s(s(z)) = s(s(elem!1))),
% 7.48/7.70 inference(transitivity,[status(thm)],[9247, 261, 9208, 9202, 211])).
% 7.48/7.70 tff(9249,plain,
% 7.48/7.70 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9248])).
% 7.48/7.70 tff(9250,plain,
% 7.48/7.70 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 7.48/7.70 inference(symmetry,[status(thm)],[9249])).
% 7.48/7.70 tff(9251,plain,
% 7.48/7.70 (s(s(elem!1)) = s(z)),
% 7.48/7.70 inference(transitivity,[status(thm)],[212, 9210, 9250, 705])).
% 7.48/7.70 tff(9252,plain,
% 7.48/7.70 ($false),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[357, 9251])).
% 7.48/7.70 tff(9253,plain,((~(elem!1 = s(s(z)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.70 tff(9254,plain,
% 7.48/7.70 (~(elem!1 = s(s(z)))),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9253, 266])).
% 7.48/7.70 tff(9255,plain,
% 7.48/7.70 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9211])).
% 7.48/7.70 tff(9256,plain,
% 7.48/7.70 ((~b(s(s(elem!1)), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9255])).
% 7.48/7.70 tff(9257,plain,
% 7.48/7.70 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(elem!1)))),
% 7.48/7.70 inference(symmetry,[status(thm)],[9194])).
% 7.48/7.70 tff(9258,plain,
% 7.48/7.70 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9211])).
% 7.48/7.70 tff(9259,plain,
% 7.48/7.70 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.70 inference(symmetry,[status(thm)],[9258])).
% 7.48/7.70 tff(9260,plain,
% 7.48/7.70 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.70 inference(modus_ponens,[status(thm)],[2112, 9259])).
% 7.48/7.70 tff(9261,plain,
% 7.48/7.70 ($false),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[3950, 9260])).
% 7.48/7.70 tff(9262,plain,(r(s(s(s(s(z)))), s(s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.70 tff(9263,plain,
% 7.48/7.70 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9262, 2112, 266])).
% 7.48/7.70 tff(9264,plain,
% 7.48/7.70 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 7.48/7.70 inference(symmetry,[status(thm)],[9255])).
% 7.48/7.70 tff(9265,plain,
% 7.48/7.70 (r(s(s(elem!1)), s(s(z)))),
% 7.48/7.70 inference(modus_ponens,[status(thm)],[1748, 9246])).
% 7.48/7.70 tff(9266,plain,
% 7.48/7.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.70 inference(rewrite,[status(thm)],[])).
% 7.48/7.70 tff(9267,plain,
% 7.48/7.70 (((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.70 inference(rewrite,[status(thm)],[])).
% 7.48/7.70 tff(9268,plain,
% 7.48/7.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9267])).
% 7.48/7.70 tff(9269,plain,
% 7.48/7.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.70 inference(transitivity,[status(thm)],[9268, 9266])).
% 7.48/7.70 tff(9270,plain,
% 7.48/7.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))),
% 7.48/7.70 inference(quant_inst,[status(thm)],[])).
% 7.48/7.70 tff(9271,plain,
% 7.48/7.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 7.48/7.70 inference(modus_ponens,[status(thm)],[9270, 9269])).
% 7.48/7.70 tff(9272,plain,
% 7.48/7.70 (~r(s(s(elem!1)), s(s(z)))),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9271, 194, 326, 2053, 6240])).
% 7.48/7.70 tff(9273,plain,
% 7.48/7.70 ($false),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9272, 9265])).
% 7.48/7.70 tff(9274,plain,((~r(elem!1, s(s(z)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.70 tff(9275,plain,
% 7.48/7.70 (~r(elem!1, s(s(z)))),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9274, 326, 6240, 2053, 266])).
% 7.48/7.70 tff(9276,plain,
% 7.48/7.70 (b(elem!1, s(s(z)))),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[3394, 9275, 9254])).
% 7.48/7.70 tff(9277,plain,
% 7.48/7.70 (b(s(s(elem!1)), s(s(z)))),
% 7.48/7.70 inference(modus_ponens,[status(thm)],[9276, 9264])).
% 7.48/7.70 tff(9278,plain,
% 7.48/7.70 (r(s(s(elem!1)), z) <=> r(s(s(s(elem!1))), z)),
% 7.48/7.70 inference(monotonicity,[status(thm)],[283])).
% 7.48/7.70 tff(9279,plain,
% 7.48/7.70 ((~r(s(s(elem!1)), z)) <=> (~r(s(s(s(elem!1))), z))),
% 7.48/7.70 inference(monotonicity,[status(thm)],[9278])).
% 7.48/7.70 tff(9280,plain,
% 7.48/7.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.70 inference(rewrite,[status(thm)],[])).
% 7.48/7.70 tff(9281,plain,
% 7.48/7.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.70 inference(quant_inst,[status(thm)],[])).
% 7.48/7.70 tff(9282,plain,
% 7.48/7.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 7.48/7.70 inference(modus_ponens,[status(thm)],[9281, 9280])).
% 7.48/7.70 tff(9283,plain,
% 7.48/7.70 ($false),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9282, 194, 326, 2053, 6240, 2616])).
% 7.48/7.70 tff(9284,plain,((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.70 tff(9285,plain,
% 7.48/7.70 (~r(s(s(elem!1)), z)),
% 7.48/7.70 inference(unit_resolution,[status(thm)],[9284, 326, 2053, 6240])).
% 7.48/7.71 tff(9286,plain,
% 7.48/7.71 (~r(s(s(s(elem!1))), z)),
% 7.48/7.71 inference(modus_ponens,[status(thm)],[9285, 9279])).
% 7.48/7.71 tff(9287,plain,
% 7.48/7.71 (b(s(s(s(elem!1))), z)),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[377, 9286])).
% 7.48/7.71 tff(9288,plain,
% 7.48/7.71 (b(s(s(s(elem!1))), z) <=> b(s(s(elem!1)), z)),
% 7.48/7.71 inference(monotonicity,[status(thm)],[266])).
% 7.48/7.71 tff(9289,plain,
% 7.48/7.71 (b(s(s(elem!1)), z)),
% 7.48/7.71 inference(modus_ponens,[status(thm)],[380, 9288])).
% 7.48/7.71 tff(9290,plain,
% 7.48/7.71 ($false),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[2624, 9289])).
% 7.48/7.71 tff(9291,plain,((~b(s(s(s(elem!1))), z)) | b(s(s(elem!1)), z) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.71 tff(9292,plain,
% 7.48/7.71 (b(s(s(elem!1)), z)),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[9291, 9287, 266])).
% 7.48/7.71 tff(9293,plain,
% 7.48/7.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.71 inference(rewrite,[status(thm)],[])).
% 7.48/7.71 tff(9294,plain,
% 7.48/7.71 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.71 inference(rewrite,[status(thm)],[])).
% 7.48/7.71 tff(9295,plain,
% 7.48/7.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z))))))),
% 7.48/7.71 inference(monotonicity,[status(thm)],[9294])).
% 7.48/7.71 tff(9296,plain,
% 7.48/7.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.71 inference(transitivity,[status(thm)],[9295, 9293])).
% 7.48/7.71 tff(9297,plain,
% 7.48/7.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.71 inference(quant_inst,[status(thm)],[])).
% 7.48/7.71 tff(9298,plain,
% 7.48/7.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z))))),
% 7.48/7.71 inference(modus_ponens,[status(thm)],[9297, 9296])).
% 7.48/7.71 tff(9299,plain,
% 7.48/7.71 (~b(s(s(elem!1)), s(s(z)))),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[9298, 391, 9292, 1235, 1234, 664])).
% 7.48/7.71 tff(9300,plain,
% 7.48/7.71 ($false),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[9299, 9277])).
% 7.48/7.71 tff(9301,plain,((~r(z, s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.71 tff(9302,plain,
% 7.48/7.71 (~r(z, s(s(elem!1)))),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[9301, 664, 1235, 1234, 266, 2053, 9263])).
% 7.48/7.71 tff(9303,plain,
% 7.48/7.71 (b(z, s(s(elem!1)))),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[324, 9302])).
% 7.48/7.71 tff(9304,plain,
% 7.48/7.71 (b(s(z), s(s(elem!1)))),
% 7.48/7.71 inference(modus_ponens,[status(thm)],[379, 9193])).
% 7.48/7.71 tff(9305,plain,
% 7.48/7.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 7.48/7.71 inference(rewrite,[status(thm)],[])).
% 7.48/7.71 tff(9306,plain,
% 7.48/7.71 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 7.48/7.71 inference(rewrite,[status(thm)],[])).
% 7.48/7.71 tff(9307,plain,
% 7.48/7.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1))))))),
% 7.48/7.71 inference(monotonicity,[status(thm)],[9306])).
% 7.48/7.71 tff(9308,plain,
% 7.48/7.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 7.48/7.71 inference(transitivity,[status(thm)],[9307, 9305])).
% 7.48/7.71 tff(9309,plain,
% 7.48/7.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 7.48/7.71 inference(quant_inst,[status(thm)],[])).
% 7.48/7.71 tff(9310,plain,
% 7.48/7.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1))))),
% 7.48/7.71 inference(modus_ponens,[status(thm)],[9309, 9308])).
% 7.48/7.71 tff(9311,plain,
% 7.48/7.71 (~b(s(z), s(s(elem!1)))),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[9310, 391, 381, 3927, 664])).
% 7.48/7.71 tff(9312,plain,
% 7.48/7.71 ($false),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[9311, 9304])).
% 7.48/7.71 tff(9313,plain,((~b(s(z), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.71 tff(9314,plain,
% 7.48/7.71 (~b(s(z), s(s(s(elem!1))))),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[9313, 9303, 381, 266, 664])).
% 7.48/7.71 tff(9315,plain,
% 7.48/7.71 (r(s(z), s(s(s(elem!1))))),
% 7.48/7.71 inference(unit_resolution,[status(thm)],[247, 9314])).
% 7.48/7.71 tff(9316,plain,
% 7.48/7.71 (r(s(z), s(s(elem!1)))),
% 7.48/7.71 inference(modus_ponens,[status(thm)],[9315, 9257])).
% 7.48/7.71 tff(9317,plain,
% 7.48/7.71 (r(s(s(s(elem!1))), z) <=> r(s(s(elem!1)), z)),
% 7.48/7.71 inference(symmetry,[status(thm)],[9278])).
% 7.48/7.71 tff(9318,plain,
% 7.48/7.71 (r(s(s(elem!1)), z)),
% 7.48/7.71 inference(modus_ponens,[status(thm)],[174, 9317])).
% 7.48/7.71 tff(9319,plain,
% 7.48/7.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.71 inference(rewrite,[status(thm)],[])).
% 7.48/7.71 tff(9320,plain,
% 7.48/7.71 (((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.72 inference(rewrite,[status(thm)],[])).
% 7.48/7.72 tff(9321,plain,
% 7.48/7.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 7.48/7.72 inference(monotonicity,[status(thm)],[9320])).
% 7.48/7.72 tff(9322,plain,
% 7.48/7.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.72 inference(transitivity,[status(thm)],[9321, 9319])).
% 7.48/7.72 tff(9323,plain,
% 7.48/7.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))),
% 7.48/7.72 inference(quant_inst,[status(thm)],[])).
% 7.48/7.72 tff(9324,plain,
% 7.48/7.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 7.48/7.72 inference(modus_ponens,[status(thm)],[9323, 9322])).
% 7.48/7.72 tff(9325,plain,
% 7.48/7.72 ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9324, 194, 723, 4832])).
% 7.48/7.72 tff(9326,plain,
% 7.48/7.72 ($false),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9325, 9260, 9318])).
% 7.48/7.72 tff(9327,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.72 tff(9328,plain,
% 7.48/7.72 (~r(s(s(s(elem!1))), z)),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9327, 9316, 2112, 266, 723])).
% 7.48/7.72 tff(9329,plain,
% 7.48/7.72 (b(s(s(s(elem!1))), z)),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[377, 9328])).
% 7.48/7.72 tff(9330,plain,
% 7.48/7.72 (b(s(s(elem!1)), z)),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9291, 9329, 266])).
% 7.48/7.72 tff(9331,plain,
% 7.48/7.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.72 inference(rewrite,[status(thm)],[])).
% 7.48/7.72 tff(9332,plain,
% 7.48/7.72 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.72 inference(rewrite,[status(thm)],[])).
% 7.48/7.72 tff(9333,plain,
% 7.48/7.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 7.48/7.72 inference(monotonicity,[status(thm)],[9332])).
% 7.48/7.72 tff(9334,plain,
% 7.48/7.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.72 inference(transitivity,[status(thm)],[9333, 9331])).
% 7.48/7.72 tff(9335,plain,
% 7.48/7.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.72 inference(quant_inst,[status(thm)],[])).
% 7.48/7.72 tff(9336,plain,
% 7.48/7.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 7.48/7.72 inference(modus_ponens,[status(thm)],[9335, 9334])).
% 7.48/7.72 tff(9337,plain,
% 7.48/7.72 (~b(s(s(elem!1)), s(s(z)))),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9336, 391, 381, 9303, 9330, 1235])).
% 7.48/7.72 tff(9338,plain,
% 7.48/7.72 (~b(elem!1, s(s(z)))),
% 7.48/7.72 inference(modus_ponens,[status(thm)],[9337, 9256])).
% 7.48/7.72 tff(9339,plain,
% 7.48/7.72 (r(elem!1, s(s(z)))),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[3394, 9338, 9254])).
% 7.48/7.72 tff(9340,plain,
% 7.48/7.72 (r(s(s(elem!1)), s(s(z)))),
% 7.48/7.72 inference(modus_ponens,[status(thm)],[9339, 9246])).
% 7.48/7.72 tff(9341,plain,
% 7.48/7.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.72 inference(rewrite,[status(thm)],[])).
% 7.48/7.72 tff(9342,plain,
% 7.48/7.72 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.72 inference(rewrite,[status(thm)],[])).
% 7.48/7.72 tff(9343,plain,
% 7.48/7.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 7.48/7.72 inference(monotonicity,[status(thm)],[9342])).
% 7.48/7.72 tff(9344,plain,
% 7.48/7.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.72 inference(transitivity,[status(thm)],[9343, 9341])).
% 7.48/7.72 tff(9345,plain,
% 7.48/7.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))),
% 7.48/7.72 inference(quant_inst,[status(thm)],[])).
% 7.48/7.72 tff(9346,plain,
% 7.48/7.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 7.48/7.72 inference(modus_ponens,[status(thm)],[9345, 9344])).
% 7.48/7.72 tff(9347,plain,
% 7.48/7.72 (~r(s(s(elem!1)), s(s(z)))),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9346, 194, 723, 9316, 9263])).
% 7.48/7.72 tff(9348,plain,
% 7.48/7.72 ($false),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9347, 9340])).
% 7.48/7.72 tff(9349,plain,((~b(z, s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.72 tff(9350,plain,
% 7.48/7.72 (~b(z, s(z))),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9349, 381, 9197, 266, 1235, 9244, 1234, 2053])).
% 7.48/7.72 tff(9351,plain,
% 7.48/7.72 ((z = s(z)) | r(z, s(z))),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[45, 42, 9350])).
% 7.48/7.72 tff(9352,plain,
% 7.48/7.72 (r(z, s(z))),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9351, 9201])).
% 7.48/7.72 tff(9353,plain,
% 7.48/7.72 (~r(s(z), s(s(elem!1)))),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[5500, 9352, 2053, 9197])).
% 7.48/7.72 tff(9354,plain,
% 7.48/7.72 (~r(s(z), s(s(s(elem!1))))),
% 7.48/7.72 inference(modus_ponens,[status(thm)],[9353, 9195])).
% 7.48/7.72 tff(9355,plain,
% 7.48/7.72 (b(s(z), s(s(s(elem!1))))),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[247, 9354])).
% 7.48/7.72 tff(9356,plain,
% 7.48/7.72 (b(s(z), s(s(elem!1)))),
% 7.48/7.72 inference(modus_ponens,[status(thm)],[9355, 9193])).
% 7.48/7.72 tff(9357,plain,
% 7.48/7.72 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9262, 9244, 266])).
% 7.48/7.72 tff(9358,plain,
% 7.48/7.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.72 inference(rewrite,[status(thm)],[])).
% 7.48/7.72 tff(9359,plain,
% 7.48/7.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.48/7.72 inference(quant_inst,[status(thm)],[])).
% 7.48/7.72 tff(9360,plain,
% 7.48/7.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 7.48/7.72 inference(modus_ponens,[status(thm)],[9359, 9358])).
% 7.48/7.72 tff(9361,plain,
% 7.48/7.72 ($false),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9360, 194, 722, 2053, 6240, 2616])).
% 7.48/7.72 tff(9362,plain,((~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.72 tff(9363,plain,
% 7.48/7.72 (~r(s(s(elem!1)), z)),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9362, 9352, 2053, 9357])).
% 7.48/7.72 tff(9364,plain,
% 7.48/7.72 (~r(s(s(s(elem!1))), z)),
% 7.48/7.72 inference(modus_ponens,[status(thm)],[9363, 9279])).
% 7.48/7.72 tff(9365,plain,
% 7.48/7.72 (b(s(s(s(elem!1))), z)),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[377, 9364])).
% 7.48/7.72 tff(9366,plain,
% 7.48/7.72 (b(s(s(elem!1)), z)),
% 7.48/7.72 inference(unit_resolution,[status(thm)],[9291, 9365, 266])).
% 7.48/7.72 tff(9367,plain,
% 7.48/7.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.48/7.72 inference(rewrite,[status(thm)],[])).
% 7.48/7.72 tff(9368,plain,
% 7.48/7.72 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.48/7.72 inference(rewrite,[status(thm)],[])).
% 7.48/7.72 tff(9369,plain,
% 7.48/7.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.48/7.73 inference(monotonicity,[status(thm)],[9368])).
% 7.48/7.73 tff(9370,plain,
% 7.48/7.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.48/7.73 inference(transitivity,[status(thm)],[9369, 9367])).
% 7.48/7.73 tff(9371,plain,
% 7.48/7.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 7.48/7.73 inference(quant_inst,[status(thm)],[])).
% 7.48/7.73 tff(9372,plain,
% 7.48/7.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.48/7.73 inference(modus_ponens,[status(thm)],[9371, 9370])).
% 7.48/7.73 tff(9373,plain,
% 7.48/7.73 ($false),
% 7.48/7.73 inference(unit_resolution,[status(thm)],[9372, 391, 3823, 1234, 3563, 1233])).
% 7.48/7.73 tff(9374,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.73 tff(9375,plain,
% 7.48/7.73 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.48/7.73 inference(unit_resolution,[status(thm)],[9374, 3823, 1234, 1233])).
% 7.48/7.73 tff(9376,plain,
% 7.48/7.73 (r(s(s(s(s(z)))), s(s(z)))),
% 7.48/7.73 inference(unit_resolution,[status(thm)],[1714, 9375])).
% 7.48/7.73 tff(9377,plain,
% 7.48/7.73 (~b(s(s(elem!1)), s(s(z)))),
% 7.48/7.73 inference(unit_resolution,[status(thm)],[9336, 391, 381, 3927, 2641, 1235])).
% 7.48/7.73 tff(9378,plain,
% 7.48/7.73 (~b(elem!1, s(s(z)))),
% 7.48/7.73 inference(modus_ponens,[status(thm)],[9377, 9256])).
% 7.48/7.73 tff(9379,plain,
% 7.48/7.73 (r(elem!1, s(s(z)))),
% 7.48/7.73 inference(unit_resolution,[status(thm)],[3394, 9378, 9254])).
% 7.48/7.73 tff(9380,plain,
% 7.48/7.73 (r(s(s(elem!1)), s(s(z)))),
% 7.48/7.73 inference(modus_ponens,[status(thm)],[9379, 9246])).
% 7.48/7.73 tff(9381,plain,
% 7.48/7.73 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), elem!1)),
% 7.48/7.73 inference(monotonicity,[status(thm)],[9211])).
% 7.48/7.73 tff(9382,plain,
% 7.48/7.73 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(elem!1)))),
% 7.48/7.73 inference(symmetry,[status(thm)],[9381])).
% 7.48/7.73 tff(9383,plain,
% 7.48/7.73 ((~(elem!1 = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 7.48/7.73 inference(monotonicity,[status(thm)],[8492])).
% 7.48/7.73 tff(9384,plain,
% 7.48/7.73 (~(s(s(z)) = elem!1)),
% 7.48/7.73 inference(modus_ponens,[status(thm)],[9254, 9383])).
% 7.48/7.73 tff(9385,plain,
% 7.48/7.73 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 7.48/7.73 inference(monotonicity,[status(thm)],[9211])).
% 7.48/7.73 tff(9386,plain,
% 7.48/7.73 ((~b(s(s(z)), s(s(elem!1)))) <=> (~b(s(s(z)), elem!1))),
% 7.48/7.73 inference(monotonicity,[status(thm)],[9385])).
% 7.48/7.73 tff(9387,plain,
% 7.48/7.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 7.48/7.73 inference(rewrite,[status(thm)],[])).
% 7.48/7.73 tff(9388,plain,
% 7.48/7.73 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 7.48/7.73 inference(rewrite,[status(thm)],[])).
% 7.48/7.73 tff(9389,plain,
% 7.48/7.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))))),
% 7.48/7.73 inference(monotonicity,[status(thm)],[9388])).
% 7.48/7.73 tff(9390,plain,
% 7.48/7.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 7.48/7.73 inference(transitivity,[status(thm)],[9389, 9387])).
% 7.48/7.73 tff(9391,plain,
% 7.48/7.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 7.48/7.73 inference(quant_inst,[status(thm)],[])).
% 7.48/7.73 tff(9392,plain,
% 7.48/7.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))),
% 7.48/7.73 inference(modus_ponens,[status(thm)],[9391, 9390])).
% 7.48/7.73 tff(9393,plain,
% 7.48/7.73 (~b(s(s(z)), s(s(elem!1)))),
% 7.48/7.73 inference(unit_resolution,[status(thm)],[9392, 391, 381, 3927, 2641, 1235])).
% 7.48/7.73 tff(9394,plain,
% 7.48/7.73 (~b(s(s(z)), elem!1)),
% 7.48/7.73 inference(modus_ponens,[status(thm)],[9393, 9386])).
% 7.48/7.73 tff(9395,plain,
% 7.48/7.73 (r(s(s(z)), elem!1)),
% 7.48/7.73 inference(unit_resolution,[status(thm)],[4730, 9394, 9384])).
% 7.48/7.73 tff(9396,plain,
% 7.48/7.73 (r(s(s(z)), s(s(elem!1)))),
% 7.48/7.73 inference(modus_ponens,[status(thm)],[9395, 9382])).
% 7.48/7.73 tff(9397,plain,
% 7.48/7.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.48/7.73 inference(rewrite,[status(thm)],[])).
% 7.48/7.73 tff(9398,plain,
% 7.48/7.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.48/7.73 inference(quant_inst,[status(thm)],[])).
% 7.48/7.73 tff(9399,plain,
% 7.48/7.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 7.48/7.73 inference(modus_ponens,[status(thm)],[9398, 9397])).
% 7.48/7.73 tff(9400,plain,
% 7.48/7.73 ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))),
% 7.48/7.73 inference(unit_resolution,[status(thm)],[9399, 194, 1697, 6240])).
% 7.48/7.73 tff(9401,plain,
% 7.48/7.73 ($false),
% 7.48/7.73 inference(unit_resolution,[status(thm)],[9400, 9396, 9380])).
% 7.48/7.73 tff(9402,plain,((~b(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.73 tff(9403,plain,
% 7.48/7.73 (~b(z, s(s(elem!1)))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[9402, 9357, 9376, 266, 381, 9366, 1235])).
% 7.48/7.74 tff(9404,plain,
% 7.48/7.74 (r(z, s(s(elem!1)))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[324, 9403])).
% 7.48/7.74 tff(9405,plain,
% 7.48/7.74 (~r(elem!1, s(s(z)))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[9274, 9404, 9357, 2053, 266])).
% 7.48/7.74 tff(9406,plain,
% 7.48/7.74 (b(elem!1, s(s(z)))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[3394, 9405, 9254])).
% 7.48/7.74 tff(9407,plain,
% 7.48/7.74 (b(s(s(elem!1)), s(s(z)))),
% 7.48/7.74 inference(modus_ponens,[status(thm)],[9406, 9264])).
% 7.48/7.74 tff(9408,plain,
% 7.48/7.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.74 inference(rewrite,[status(thm)],[])).
% 7.48/7.74 tff(9409,plain,
% 7.48/7.74 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.74 inference(rewrite,[status(thm)],[])).
% 7.48/7.74 tff(9410,plain,
% 7.48/7.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9409])).
% 7.48/7.74 tff(9411,plain,
% 7.48/7.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.74 inference(transitivity,[status(thm)],[9410, 9408])).
% 7.48/7.74 tff(9412,plain,
% 7.48/7.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.48/7.74 inference(quant_inst,[status(thm)],[])).
% 7.48/7.74 tff(9413,plain,
% 7.48/7.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 7.48/7.74 inference(modus_ponens,[status(thm)],[9412, 9411])).
% 7.48/7.74 tff(9414,plain,
% 7.48/7.74 ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[9413, 391, 381, 1233])).
% 7.48/7.74 tff(9415,plain,
% 7.48/7.74 ($false),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[9414, 9407, 9356])).
% 7.48/7.74 tff(9416,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.74 tff(9417,plain,
% 7.48/7.74 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[9416, 9191, 3823, 381, 1234, 2053, 9189])).
% 7.48/7.74 tff(9418,plain,
% 7.48/7.74 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[299, 9417])).
% 7.48/7.74 tff(9419,plain,
% 7.48/7.74 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[307, 9418])).
% 7.48/7.74 tff(9420,plain,
% 7.48/7.74 (elem!1 = s(s(s(elem!1)))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[8995, 1549, 9419, 1526, 9141, 2053, 1484, 832, 10, 150, 719, 9098])).
% 7.48/7.74 tff(9421,plain,
% 7.48/7.74 (s(elem!1) = s(s(s(s(elem!1))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9420])).
% 7.48/7.74 tff(9422,plain,
% 7.48/7.74 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9421])).
% 7.48/7.74 tff(9423,plain,
% 7.48/7.74 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 7.48/7.74 inference(symmetry,[status(thm)],[9422])).
% 7.48/7.74 tff(9424,plain,
% 7.48/7.74 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9423])).
% 7.48/7.74 tff(9425,plain,
% 7.48/7.74 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 7.48/7.74 inference(symmetry,[status(thm)],[9424])).
% 7.48/7.74 tff(9426,plain,
% 7.48/7.74 (b(s(s(s(s(s(elem!1))))), s(z))),
% 7.48/7.74 inference(modus_ponens,[status(thm)],[381, 9425])).
% 7.48/7.74 tff(9427,plain,
% 7.48/7.74 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(elem!1)))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9423])).
% 7.48/7.74 tff(9428,plain,
% 7.48/7.74 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 7.48/7.74 inference(symmetry,[status(thm)],[9427])).
% 7.48/7.74 tff(9429,plain,
% 7.48/7.74 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[1407, 1405])).
% 7.48/7.74 tff(9430,plain,
% 7.48/7.74 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[9236, 9191, 1234, 381, 3823])).
% 7.48/7.74 tff(9431,plain,
% 7.48/7.74 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[3067])).
% 7.48/7.74 tff(9432,plain,
% 7.48/7.74 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 7.48/7.74 inference(symmetry,[status(thm)],[9431])).
% 7.48/7.74 tff(9433,plain,
% 7.48/7.74 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9432])).
% 7.48/7.74 tff(9434,plain,
% 7.48/7.74 (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 7.48/7.74 inference(modus_ponens,[status(thm)],[1983, 9433])).
% 7.48/7.74 tff(9435,plain,
% 7.48/7.74 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[3067])).
% 7.48/7.74 tff(9436,plain,
% 7.48/7.74 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 7.48/7.74 inference(symmetry,[status(thm)],[9435])).
% 7.48/7.74 tff(9437,plain,
% 7.48/7.74 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9436])).
% 7.48/7.74 tff(9438,plain,
% 7.48/7.74 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 7.48/7.74 inference(modus_ponens,[status(thm)],[3478, 9437])).
% 7.48/7.74 tff(9439,assumption,(~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 7.48/7.74 tff(9440,plain,
% 7.48/7.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(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(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 7.48/7.74 inference(rewrite,[status(thm)],[])).
% 7.48/7.74 tff(9441,plain,
% 7.48/7.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 7.48/7.74 inference(quant_inst,[status(thm)],[])).
% 7.48/7.74 tff(9442,plain,
% 7.48/7.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 7.48/7.74 inference(modus_ponens,[status(thm)],[9441, 9440])).
% 7.48/7.74 tff(9443,plain,
% 7.48/7.74 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[9442, 42, 9439])).
% 7.48/7.74 tff(9444,plain,
% 7.48/7.74 ($false),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[9443, 9438, 9434])).
% 7.48/7.74 tff(9445,plain,(r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(elem!1))) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.74 tff(9446,plain,
% 7.48/7.74 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[9445, 9420, 9430, 9429])).
% 7.48/7.74 tff(9447,plain,
% 7.48/7.74 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9422])).
% 7.48/7.74 tff(9448,plain,
% 7.48/7.74 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9420])).
% 7.48/7.74 tff(9449,plain,
% 7.48/7.74 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 7.48/7.74 inference(transitivity,[status(thm)],[9448, 9447])).
% 7.48/7.74 tff(9450,plain,
% 7.48/7.74 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9420])).
% 7.48/7.74 tff(9451,plain,
% 7.48/7.74 ((s(s(elem!1)) = elem!1) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 7.48/7.74 inference(transitivity,[status(thm)],[9450, 267])).
% 7.48/7.74 tff(9452,plain,
% 7.48/7.74 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 7.48/7.74 inference(symmetry,[status(thm)],[9451])).
% 7.48/7.74 tff(9453,plain,
% 7.48/7.74 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9452])).
% 7.48/7.74 tff(9454,plain,
% 7.48/7.74 (~(s(s(elem!1)) = elem!1)),
% 7.48/7.74 inference(modus_ponens,[status(thm)],[9417, 9453])).
% 7.48/7.74 tff(9455,plain,
% 7.48/7.74 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9420])).
% 7.48/7.74 tff(9456,plain,
% 7.48/7.74 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 7.48/7.74 inference(symmetry,[status(thm)],[9455])).
% 7.48/7.74 tff(9457,plain,
% 7.48/7.74 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9423])).
% 7.48/7.74 tff(9458,plain,
% 7.48/7.74 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 7.48/7.74 inference(transitivity,[status(thm)],[9457, 9456])).
% 7.48/7.74 tff(9459,plain,
% 7.48/7.74 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), elem!1))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9458])).
% 7.48/7.74 tff(9460,plain,
% 7.48/7.74 (r(z, elem!1)),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[147, 9420, 10])).
% 7.48/7.74 tff(9461,plain,
% 7.48/7.74 (~r(s(z), z)),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[3243, 9460, 2053, 723])).
% 7.48/7.74 tff(9462,plain,
% 7.48/7.74 (~(z = elem!1)),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[5433, 9461, 1484])).
% 7.48/7.74 tff(9463,plain,
% 7.48/7.74 (~(s(z) = s(elem!1))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[117, 9462])).
% 7.48/7.74 tff(9464,plain,
% 7.48/7.74 (~(s(s(elem!1)) = s(s(z)))),
% 7.48/7.74 inference(unit_resolution,[status(thm)],[1962, 9463])).
% 7.48/7.74 tff(9465,plain,
% 7.48/7.74 ((s(s(s(s(s(elem!1))))) = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[3067])).
% 7.48/7.74 tff(9466,plain,
% 7.48/7.74 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(z)))),
% 7.48/7.74 inference(symmetry,[status(thm)],[9465])).
% 7.48/7.74 tff(9467,plain,
% 7.48/7.74 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(z))))),
% 7.48/7.74 inference(monotonicity,[status(thm)],[9466])).
% 7.48/7.74 tff(9468,plain,
% 7.48/7.74 (~(s(s(s(s(s(elem!1))))) = s(s(z)))),
% 7.48/7.74 inference(modus_ponens,[status(thm)],[2689, 9467])).
% 7.48/7.74 tff(9469,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 7.48/7.74 tff(9470,plain,
% 7.48/7.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z)))))),
% 7.48/7.74 inference(rewrite,[status(thm)],[])).
% 7.48/7.74 tff(9471,plain,
% 7.48/7.74 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(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(s(z))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z)))))),
% 7.48/7.74 inference(rewrite,[status(thm)],[])).
% 7.48/7.74 tff(9472,plain,
% 7.48/7.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z))))))),
% 7.48/7.75 inference(monotonicity,[status(thm)],[9471])).
% 7.48/7.75 tff(9473,plain,
% 7.48/7.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z)))))),
% 7.48/7.75 inference(transitivity,[status(thm)],[9472, 9470])).
% 7.48/7.75 tff(9474,plain,
% 7.48/7.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(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(s(z)))))),
% 7.48/7.75 inference(quant_inst,[status(thm)],[])).
% 7.48/7.75 tff(9475,plain,
% 7.48/7.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z))))),
% 7.48/7.75 inference(modus_ponens,[status(thm)],[9474, 9473])).
% 7.48/7.75 tff(9476,plain,
% 7.48/7.75 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 7.48/7.75 inference(unit_resolution,[status(thm)],[9475, 391, 1526, 1234, 8553, 9469])).
% 7.48/7.75 tff(9477,plain,
% 7.48/7.75 (((~![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))))),
% 7.48/7.75 inference(rewrite,[status(thm)],[])).
% 7.48/7.75 tff(9478,plain,
% 7.48/7.75 ((~![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))))),
% 7.48/7.75 inference(quant_inst,[status(thm)],[])).
% 7.48/7.75 tff(9479,plain,
% 7.48/7.75 ((~![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)))),
% 7.48/7.75 inference(modus_ponens,[status(thm)],[9478, 9477])).
% 7.48/7.75 tff(9480,plain,
% 7.48/7.75 ((s(s(s(s(s(elem!1))))) = s(s(z))) | r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 7.48/7.75 inference(unit_resolution,[status(thm)],[9479, 42, 9476])).
% 7.48/7.75 tff(9481,plain,
% 7.48/7.75 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 7.48/7.75 inference(unit_resolution,[status(thm)],[9480, 9468])).
% 7.48/7.75 tff(9482,plain,
% 7.48/7.75 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 7.48/7.75 inference(commutativity,[status(thm)],[])).
% 7.48/7.75 tff(9483,plain,
% 7.48/7.75 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(z)) = s(s(elem!1)))),
% 7.48/7.75 inference(monotonicity,[status(thm)],[3067])).
% 7.48/7.75 tff(9484,plain,
% 7.48/7.75 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = s(s(z)))),
% 7.48/7.75 inference(transitivity,[status(thm)],[9483, 9482])).
% 7.48/7.75 tff(9485,plain,
% 7.48/7.75 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(elem!1))))))),
% 7.48/7.75 inference(symmetry,[status(thm)],[9484])).
% 7.48/7.75 tff(9486,plain,
% 7.48/7.75 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(elem!1)))))))),
% 7.48/7.75 inference(monotonicity,[status(thm)],[9485])).
% 7.48/7.75 tff(9487,plain,
% 7.48/7.75 (~(s(s(z)) = s(s(s(s(s(elem!1))))))),
% 7.48/7.75 inference(modus_ponens,[status(thm)],[2689, 9486])).
% 7.48/7.75 tff(9488,plain,
% 7.48/7.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 7.48/7.75 inference(rewrite,[status(thm)],[])).
% 7.48/7.75 tff(9489,plain,
% 7.48/7.75 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 7.48/7.75 inference(rewrite,[status(thm)],[])).
% 7.48/7.75 tff(9490,plain,
% 7.48/7.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 7.48/7.75 inference(monotonicity,[status(thm)],[9489])).
% 7.48/7.75 tff(9491,plain,
% 7.48/7.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 7.48/7.75 inference(transitivity,[status(thm)],[9490, 9488])).
% 7.48/7.75 tff(9492,plain,
% 7.48/7.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 7.48/7.75 inference(quant_inst,[status(thm)],[])).
% 7.48/7.75 tff(9493,plain,
% 7.48/7.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 7.48/7.75 inference(modus_ponens,[status(thm)],[9492, 9491])).
% 7.48/7.75 tff(9494,plain,
% 7.48/7.75 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 7.48/7.75 inference(unit_resolution,[status(thm)],[9493, 391, 1526, 1234, 8553, 9469])).
% 7.48/7.75 tff(9495,plain,
% 7.48/7.75 (((~![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)))))))),
% 7.48/7.75 inference(rewrite,[status(thm)],[])).
% 7.48/7.75 tff(9496,plain,
% 7.48/7.75 ((~![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)))))))),
% 7.48/7.75 inference(quant_inst,[status(thm)],[])).
% 7.48/7.75 tff(9497,plain,
% 7.48/7.75 ((~![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))))))),
% 7.48/7.76 inference(modus_ponens,[status(thm)],[9496, 9495])).
% 7.48/7.76 tff(9498,plain,
% 7.48/7.76 ((s(s(z)) = s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[9497, 42, 9494])).
% 7.48/7.76 tff(9499,plain,
% 7.48/7.76 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[9498, 9487])).
% 7.48/7.76 tff(9500,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 7.48/7.76 tff(9501,plain,
% 7.48/7.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(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(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(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(z)), s(s(s(s(s(elem!1))))))))),
% 7.48/7.76 inference(rewrite,[status(thm)],[])).
% 7.48/7.76 tff(9502,plain,
% 7.48/7.76 (((~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(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(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(z)), s(s(s(s(s(elem!1))))))))),
% 7.48/7.76 inference(rewrite,[status(thm)],[])).
% 7.48/7.76 tff(9503,plain,
% 7.48/7.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(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(z)), s(s(s(s(s(elem!1)))))))))),
% 7.48/7.76 inference(monotonicity,[status(thm)],[9502])).
% 7.48/7.76 tff(9504,plain,
% 7.48/7.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(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(z)), s(s(s(s(s(elem!1))))))))),
% 7.48/7.76 inference(transitivity,[status(thm)],[9503, 9501])).
% 7.48/7.76 tff(9505,plain,
% 7.48/7.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.48/7.76 inference(quant_inst,[status(thm)],[])).
% 7.48/7.76 tff(9506,plain,
% 7.48/7.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 7.48/7.76 inference(modus_ponens,[status(thm)],[9505, 9504])).
% 7.48/7.76 tff(9507,plain,
% 7.48/7.76 ($false),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[9506, 194, 1697, 9500, 9499, 9481])).
% 7.48/7.76 tff(9508,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = s(s(z))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(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(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.76 tff(9509,plain,
% 7.48/7.76 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[9508, 9464, 9140, 9446, 9420, 1526, 1234, 9129])).
% 7.48/7.76 tff(9510,plain,
% 7.48/7.76 (~b(s(s(elem!1)), elem!1)),
% 7.48/7.76 inference(modus_ponens,[status(thm)],[9509, 9459])).
% 7.48/7.76 tff(9511,plain,
% 7.48/7.76 (r(s(s(elem!1)), elem!1)),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[872, 9510, 9454])).
% 7.48/7.76 tff(9512,plain,
% 7.48/7.76 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 7.48/7.76 inference(modus_ponens,[status(thm)],[9511, 9449])).
% 7.48/7.76 tff(9513,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 7.48/7.76 tff(9514,plain,
% 7.48/7.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 7.48/7.76 inference(rewrite,[status(thm)],[])).
% 7.48/7.76 tff(9515,plain,
% 7.48/7.76 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 7.48/7.76 inference(rewrite,[status(thm)],[])).
% 7.48/7.76 tff(9516,plain,
% 7.48/7.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 7.48/7.76 inference(monotonicity,[status(thm)],[9515])).
% 7.48/7.76 tff(9517,plain,
% 7.48/7.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 7.48/7.76 inference(transitivity,[status(thm)],[9516, 9514])).
% 7.48/7.76 tff(9518,plain,
% 7.48/7.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))),
% 7.48/7.76 inference(quant_inst,[status(thm)],[])).
% 7.48/7.76 tff(9519,plain,
% 7.48/7.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 7.48/7.76 inference(modus_ponens,[status(thm)],[9518, 9517])).
% 7.48/7.76 tff(9520,plain,
% 7.48/7.76 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[9519, 194, 2053, 9500])).
% 7.48/7.76 tff(9521,plain,
% 7.48/7.76 ($false),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[9520, 3073, 9513])).
% 7.48/7.76 tff(9522,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.76 tff(9523,plain,
% 7.48/7.76 (~r(z, s(s(elem!1)))),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[9522, 9512, 9446, 9420, 2053])).
% 7.48/7.76 tff(9524,plain,
% 7.48/7.76 (b(z, s(s(elem!1)))),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[324, 9523])).
% 7.48/7.76 tff(9525,plain,
% 7.48/7.76 (b(z, s(s(s(s(s(elem!1))))))),
% 7.48/7.76 inference(modus_ponens,[status(thm)],[9524, 9428])).
% 7.48/7.76 tff(9526,plain,
% 7.48/7.76 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.48/7.76 inference(monotonicity,[status(thm)],[9423])).
% 7.48/7.76 tff(9527,plain,
% 7.48/7.76 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 7.48/7.76 inference(symmetry,[status(thm)],[9526])).
% 7.48/7.76 tff(9528,plain,
% 7.48/7.76 (s(s(s(elem!1))) = elem!1),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[129, 9420])).
% 7.48/7.76 tff(9529,plain,
% 7.48/7.76 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[2694, 9528, 1549])).
% 7.48/7.76 tff(9530,plain,
% 7.48/7.76 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.48/7.76 inference(monotonicity,[status(thm)],[3067])).
% 7.48/7.76 tff(9531,plain,
% 7.48/7.76 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 7.48/7.76 inference(symmetry,[status(thm)],[9530])).
% 7.48/7.76 tff(9532,plain,
% 7.48/7.76 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 7.48/7.76 inference(modus_ponens,[status(thm)],[327, 9531])).
% 7.48/7.76 tff(9533,plain,
% 7.48/7.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 7.48/7.76 inference(rewrite,[status(thm)],[])).
% 7.48/7.76 tff(9534,plain,
% 7.48/7.76 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 7.48/7.76 inference(rewrite,[status(thm)],[])).
% 7.48/7.76 tff(9535,plain,
% 7.48/7.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 7.48/7.76 inference(monotonicity,[status(thm)],[9534])).
% 7.48/7.76 tff(9536,plain,
% 7.48/7.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 7.48/7.76 inference(transitivity,[status(thm)],[9535, 9533])).
% 7.48/7.76 tff(9537,plain,
% 7.48/7.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 7.48/7.76 inference(quant_inst,[status(thm)],[])).
% 7.48/7.76 tff(9538,plain,
% 7.48/7.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 7.48/7.76 inference(modus_ponens,[status(thm)],[9537, 9536])).
% 7.48/7.76 tff(9539,plain,
% 7.48/7.76 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[9538, 194, 184, 2053, 2100])).
% 7.48/7.76 tff(9540,plain,
% 7.48/7.76 ($false),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[9539, 9532])).
% 7.48/7.76 tff(9541,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.76 tff(9542,plain,
% 7.48/7.76 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[9541, 9529, 59, 2053, 9420])).
% 7.48/7.76 tff(9543,plain,
% 7.48/7.76 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.48/7.76 inference(unit_resolution,[status(thm)],[1370, 9542, 9417])).
% 7.48/7.76 tff(9544,plain,
% 7.48/7.76 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 7.48/7.76 inference(modus_ponens,[status(thm)],[9543, 9527])).
% 7.48/7.77 tff(9545,plain,
% 7.48/7.77 (~(elem!1 = z)),
% 7.48/7.77 inference(unit_resolution,[status(thm)],[5453, 9462])).
% 7.48/7.77 tff(9546,plain,
% 7.48/7.77 (b(elem!1, z)),
% 7.48/7.77 inference(unit_resolution,[status(thm)],[526, 9545, 2282])).
% 7.48/7.77 tff(9547,plain,
% 7.48/7.77 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 7.48/7.77 inference(monotonicity,[status(thm)],[125])).
% 7.48/7.77 tff(9548,plain,
% 7.48/7.77 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 7.48/7.77 inference(symmetry,[status(thm)],[9547])).
% 7.48/7.77 tff(9549,plain,
% 7.48/7.77 ((~b(s(s(s(elem!1))), z)) <=> (~b(elem!1, z))),
% 7.48/7.77 inference(monotonicity,[status(thm)],[9548])).
% 7.48/7.77 tff(9550,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 7.48/7.77 tff(9551,plain,
% 7.48/7.77 (~b(elem!1, z)),
% 7.48/7.77 inference(modus_ponens,[status(thm)],[9550, 9549])).
% 7.48/7.77 tff(9552,plain,
% 7.48/7.77 ($false),
% 7.48/7.77 inference(unit_resolution,[status(thm)],[665, 9551])).
% 7.48/7.77 tff(9553,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(elem!1, z)) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 7.48/7.77 tff(9554,plain,
% 7.48/7.77 (b(s(s(s(elem!1))), z)),
% 7.48/7.77 inference(unit_resolution,[status(thm)],[9553, 9546, 9420])).
% 7.48/7.77 tff(9555,plain,
% 7.48/7.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 7.48/7.77 inference(rewrite,[status(thm)],[])).
% 7.48/7.77 tff(9556,plain,
% 7.48/7.77 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, 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))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 7.48/7.77 inference(rewrite,[status(thm)],[])).
% 7.48/7.77 tff(9557,plain,
% 7.48/7.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, 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))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 7.48/7.77 inference(monotonicity,[status(thm)],[9556])).
% 7.48/7.77 tff(9558,plain,
% 7.48/7.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, 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))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 7.48/7.77 inference(transitivity,[status(thm)],[9557, 9555])).
% 7.48/7.77 tff(9559,plain,
% 7.48/7.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, 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))), z)))),
% 7.48/7.77 inference(quant_inst,[status(thm)],[])).
% 7.48/7.77 tff(9560,plain,
% 7.48/7.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 7.48/7.77 inference(modus_ponens,[status(thm)],[9559, 9558])).
% 7.48/7.77 tff(9561,plain,
% 7.48/7.77 ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 7.48/7.77 inference(unit_resolution,[status(thm)],[9560, 391, 9554, 1234, 9544])).
% 7.48/7.77 tff(9562,plain,
% 7.48/7.77 ($false),
% 7.48/7.77 inference(unit_resolution,[status(thm)],[9561, 9525, 9426])).
% 7.48/7.77 tff(9563,plain,(b(s(s(s(s(z)))), elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | r(elem!1, z) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | b(z, s(s(s(elem!1)))) | r(elem!1, s(z)) | (s(z) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(z))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.48/7.77 tff(9564,plain,
% 7.48/7.77 (r(elem!1, z)),
% 7.48/7.77 inference(unit_resolution,[status(thm)],[9563, 1549, 1484, 2053, 1526, 9100, 1234, 381, 10, 832, 150, 719, 1747, 3823, 1405, 720])).
% 7.48/7.77 tff(9565,plain,
% 7.48/7.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 7.48/7.77 inference(rewrite,[status(thm)],[])).
% 7.48/7.77 tff(9566,plain,
% 7.48/7.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 7.48/7.77 inference(quant_inst,[status(thm)],[])).
% 7.48/7.77 tff(9567,plain,
% 7.48/7.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 7.48/7.77 inference(modus_ponens,[status(thm)],[9566, 9565])).
% 7.48/7.77 tff(9568,plain,
% 7.48/7.77 ($false),
% 7.48/7.77 inference(unit_resolution,[status(thm)],[9567, 194, 411, 9564, 2053, 9098])).
% 7.48/7.77 tff(9569,plain,(b(s(s(s(s(z)))), elem!1) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | b(z, s(s(s(elem!1)))) | r(elem!1, s(z)) | (s(z) = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(z))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.48/7.77 tff(9570,plain,
% 7.48/7.77 (b(s(s(s(s(z)))), elem!1)),
% 7.48/7.77 inference(unit_resolution,[status(thm)],[9569, 9017, 2053, 5238, 1526, 1234, 9097, 10, 832, 150, 719, 1747, 9078, 9068, 8917])).
% 7.48/7.77 tff(9571,plain,
% 7.48/7.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.48/7.77 inference(rewrite,[status(thm)],[])).
% 7.48/7.77 tff(9572,plain,
% 7.48/7.77 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.48/7.77 inference(rewrite,[status(thm)],[])).
% 7.48/7.77 tff(9573,plain,
% 7.48/7.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9572])).
% 7.48/7.78 tff(9574,plain,
% 7.48/7.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.48/7.78 inference(transitivity,[status(thm)],[9573, 9571])).
% 7.48/7.78 tff(9575,plain,
% 7.48/7.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 7.48/7.78 inference(quant_inst,[status(thm)],[])).
% 7.48/7.78 tff(9576,plain,
% 7.48/7.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[9575, 9574])).
% 7.48/7.78 tff(9577,plain,
% 7.48/7.78 ($false),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[9576, 391, 9013, 9078, 9570, 1234, 9021])).
% 7.48/7.78 tff(9578,plain,((s(z) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(s(s(elem!1)))) | r(elem!1, s(z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (elem!1 = s(s(s(elem!1)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.48/7.78 tff(9579,plain,
% 7.48/7.78 (s(z) = elem!1),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[9578, 1, 2053, 8815, 10, 832, 719, 1747, 1234, 2829])).
% 7.48/7.78 tff(9580,plain,
% 7.48/7.78 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9579])).
% 7.48/7.78 tff(9581,plain,
% 7.48/7.78 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9580])).
% 7.48/7.78 tff(9582,plain,
% 7.48/7.78 (~(s(s(elem!1)) = elem!1)),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[357, 9581])).
% 7.48/7.78 tff(9583,plain,
% 7.48/7.78 (~(s(s(elem!1)) = s(elem!1))),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[264, 9582])).
% 7.48/7.78 tff(9584,plain,
% 7.48/7.78 (r(z, s(z)) <=> r(z, elem!1)),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9579])).
% 7.48/7.78 tff(9585,plain,
% 7.48/7.78 (r(z, elem!1) <=> r(z, s(z))),
% 7.48/7.78 inference(symmetry,[status(thm)],[9584])).
% 7.48/7.78 tff(9586,plain,
% 7.48/7.78 ((s(z) = z) <=> (elem!1 = z)),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9579])).
% 7.48/7.78 tff(9587,plain,
% 7.48/7.78 ((s(z) = z) <=> (z = elem!1)),
% 7.48/7.78 inference(transitivity,[status(thm)],[9586, 92])).
% 7.48/7.78 tff(9588,plain,
% 7.48/7.78 ((s(z) = z) <=> (elem!1 = z)),
% 7.48/7.78 inference(transitivity,[status(thm)],[9587, 93])).
% 7.48/7.78 tff(9589,plain,
% 7.48/7.78 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9588])).
% 7.48/7.78 tff(9590,plain,
% 7.48/7.78 (~(elem!1 = z)),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[23, 9589])).
% 7.48/7.78 tff(9591,plain,
% 7.48/7.78 (r(z, elem!1)),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[8231, 9590, 10])).
% 7.48/7.78 tff(9592,plain,
% 7.48/7.78 (r(z, s(z))),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[9591, 9585])).
% 7.48/7.78 tff(9593,plain,
% 7.48/7.78 (s(s(z)) = s(elem!1)),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9579])).
% 7.48/7.78 tff(9594,plain,
% 7.48/7.78 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9593])).
% 7.48/7.78 tff(9595,plain,
% 7.48/7.78 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9579])).
% 7.48/7.78 tff(9596,plain,
% 7.48/7.78 (r(elem!1, s(s(z)))),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[1747, 9595])).
% 7.48/7.78 tff(9597,plain,
% 7.48/7.78 (r(elem!1, s(elem!1))),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[9596, 9594])).
% 7.48/7.78 tff(9598,plain,
% 7.48/7.78 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[7945])).
% 7.48/7.78 tff(9599,plain,
% 7.48/7.78 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[820])).
% 7.48/7.78 tff(9600,plain,
% 7.48/7.78 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.48/7.78 inference(symmetry,[status(thm)],[9599])).
% 7.48/7.78 tff(9601,plain,
% 7.48/7.78 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9600])).
% 7.48/7.78 tff(9602,plain,
% 7.48/7.78 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[463, 9601])).
% 7.48/7.78 tff(9603,plain,
% 7.48/7.78 (elem!1 = s(s(s(elem!1)))),
% 7.48/7.78 inference(transitivity,[status(thm)],[261, 8339, 259, 8337])).
% 7.48/7.78 tff(9604,plain,
% 7.48/7.78 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9603])).
% 7.48/7.78 tff(9605,plain,
% 7.48/7.78 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[2064, 9604])).
% 7.48/7.78 tff(9606,assumption,(~b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 7.48/7.78 tff(9607,plain,
% 7.48/7.78 ($false),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[9606, 9605])).
% 7.48/7.78 tff(9608,plain,((~b(elem!1, s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.78 tff(9609,plain,
% 7.48/7.78 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[9608, 9602, 8540])).
% 7.48/7.78 tff(9610,plain,
% 7.48/7.78 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 7.48/7.78 inference(monotonicity,[status(thm)],[812])).
% 7.48/7.78 tff(9611,plain,
% 7.48/7.78 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 7.48/7.78 inference(symmetry,[status(thm)],[9610])).
% 7.48/7.78 tff(9612,plain,
% 7.48/7.78 (b(s(s(s(s(z)))), s(z))),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[1652, 9611])).
% 7.48/7.78 tff(9613,plain,
% 7.48/7.78 ($false),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[9024, 9612])).
% 7.48/7.78 tff(9614,plain,((~(s(z) = elem!1)) | b(s(s(s(s(z)))), s(z)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.78 tff(9615,plain,
% 7.48/7.78 (~b(s(s(s(s(z)))), elem!1)),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[9614, 812, 9024])).
% 7.48/7.78 tff(9616,plain,
% 7.48/7.78 (b(s(s(s(elem!1))), elem!1)),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[3938, 812, 1526])).
% 7.48/7.78 tff(9617,plain,
% 7.48/7.78 ($false),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[1563, 9616, 7866, 9615])).
% 7.48/7.78 tff(9618,plain,((~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.78 tff(9619,plain,
% 7.48/7.78 (b(s(s(s(s(z)))), s(z))),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[9618, 812, 1526])).
% 7.48/7.78 tff(9620,plain,
% 7.48/7.78 (r(s(elem!1), s(s(s(elem!1))))),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[3614, 1749, 812])).
% 7.48/7.78 tff(9621,plain,
% 7.48/7.78 (r(s(s(s(elem!1))), z)),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[2053, 7600])).
% 7.48/7.78 tff(9622,plain,
% 7.48/7.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.48/7.78 inference(rewrite,[status(thm)],[])).
% 7.48/7.78 tff(9623,plain,
% 7.48/7.78 (((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.48/7.78 inference(rewrite,[status(thm)],[])).
% 7.48/7.78 tff(9624,plain,
% 7.48/7.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9623])).
% 7.48/7.78 tff(9625,plain,
% 7.48/7.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.48/7.78 inference(transitivity,[status(thm)],[9624, 9622])).
% 7.48/7.78 tff(9626,plain,
% 7.48/7.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 7.48/7.78 inference(quant_inst,[status(thm)],[])).
% 7.48/7.78 tff(9627,plain,
% 7.48/7.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[9626, 9625])).
% 7.48/7.78 tff(9628,plain,
% 7.48/7.78 (~r(z, s(elem!1))),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[9627, 194, 9621, 184, 9620])).
% 7.48/7.78 tff(9629,plain,
% 7.48/7.78 (b(z, s(elem!1))),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[566, 9628])).
% 7.48/7.78 tff(9630,plain,
% 7.48/7.78 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 7.48/7.78 inference(monotonicity,[status(thm)],[818])).
% 7.48/7.78 tff(9631,plain,
% 7.48/7.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.48/7.78 inference(rewrite,[status(thm)],[])).
% 7.48/7.78 tff(9632,plain,
% 7.48/7.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.48/7.78 inference(quant_inst,[status(thm)],[])).
% 7.48/7.78 tff(9633,plain,
% 7.48/7.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[9632, 9631])).
% 7.48/7.78 tff(9634,plain,
% 7.48/7.78 ($false),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[9633, 194, 1749, 722, 2053, 3557])).
% 7.48/7.78 tff(9635,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.78 tff(9636,plain,
% 7.48/7.78 (~r(s(s(z)), z)),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[9635, 1749, 2053, 815])).
% 7.48/7.78 tff(9637,plain,
% 7.48/7.78 (b(s(s(z)), z)),
% 7.48/7.78 inference(unit_resolution,[status(thm)],[1211, 9636])).
% 7.48/7.78 tff(9638,plain,
% 7.48/7.78 (b(s(elem!1), z)),
% 7.48/7.78 inference(modus_ponens,[status(thm)],[9637, 9630])).
% 7.48/7.78 tff(9639,plain,
% 7.48/7.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 7.48/7.78 inference(rewrite,[status(thm)],[])).
% 7.48/7.78 tff(9640,plain,
% 7.48/7.78 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 7.48/7.78 inference(rewrite,[status(thm)],[])).
% 7.48/7.78 tff(9641,plain,
% 7.48/7.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))))),
% 7.48/7.78 inference(monotonicity,[status(thm)],[9640])).
% 7.48/7.79 tff(9642,plain,
% 7.48/7.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 7.48/7.79 inference(transitivity,[status(thm)],[9641, 9639])).
% 7.48/7.79 tff(9643,plain,
% 7.48/7.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 7.48/7.79 inference(quant_inst,[status(thm)],[])).
% 7.48/7.79 tff(9644,plain,
% 7.48/7.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))),
% 7.48/7.79 inference(modus_ponens,[status(thm)],[9643, 9642])).
% 7.48/7.79 tff(9645,plain,
% 7.48/7.79 (~b(s(elem!1), elem!1)),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[9644, 391, 665, 9629, 9638])).
% 7.48/7.79 tff(9646,plain,
% 7.48/7.79 (r(s(elem!1), elem!1)),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[2168, 9645, 164])).
% 7.48/7.79 tff(9647,plain,
% 7.48/7.79 (~(s(s(elem!1)) = s(elem!1))),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[264, 7422])).
% 7.48/7.79 tff(9648,plain,
% 7.48/7.79 (r(s(s(elem!1)), elem!1)),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[2220, 340, 812])).
% 7.48/7.79 tff(9649,plain,
% 7.48/7.79 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 7.48/7.79 inference(transitivity,[status(thm)],[7420, 2206])).
% 7.48/7.79 tff(9650,plain,
% 7.48/7.79 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 7.48/7.79 inference(monotonicity,[status(thm)],[9649])).
% 7.48/7.79 tff(9651,plain,
% 7.48/7.79 (~(elem!1 = s(s(elem!1)))),
% 7.48/7.79 inference(modus_ponens,[status(thm)],[357, 9650])).
% 7.48/7.79 tff(9652,plain,
% 7.48/7.79 (~r(s(s(elem!1)), z)),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[9045, 340, 1747, 815])).
% 7.48/7.79 tff(9653,plain,
% 7.48/7.79 (b(s(s(elem!1)), z)),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[2629, 9652])).
% 7.48/7.79 tff(9654,plain,
% 7.48/7.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 7.48/7.79 inference(rewrite,[status(thm)],[])).
% 7.48/7.79 tff(9655,plain,
% 7.48/7.79 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 7.48/7.79 inference(rewrite,[status(thm)],[])).
% 7.48/7.79 tff(9656,plain,
% 7.48/7.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1)))))),
% 7.48/7.79 inference(monotonicity,[status(thm)],[9655])).
% 7.48/7.79 tff(9657,plain,
% 7.48/7.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 7.48/7.79 inference(transitivity,[status(thm)],[9656, 9654])).
% 7.48/7.79 tff(9658,plain,
% 7.48/7.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 7.48/7.79 inference(quant_inst,[status(thm)],[])).
% 7.48/7.79 tff(9659,plain,
% 7.48/7.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1)))),
% 7.48/7.79 inference(modus_ponens,[status(thm)],[9658, 9657])).
% 7.48/7.79 tff(9660,plain,
% 7.48/7.79 ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1)))),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[9659, 391])).
% 7.48/7.79 tff(9661,plain,
% 7.48/7.79 (~b(elem!1, s(s(elem!1)))),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[9660, 9653, 665, 591, 592])).
% 7.48/7.79 tff(9662,plain,
% 7.48/7.79 (r(elem!1, s(s(elem!1)))),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[1307, 9661, 9651])).
% 7.48/7.79 tff(9663,plain,
% 7.48/7.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(elem!1)))))),
% 7.48/7.79 inference(rewrite,[status(thm)],[])).
% 7.48/7.79 tff(9664,plain,
% 7.48/7.79 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(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)) | (~r(elem!1, s(s(elem!1)))))),
% 7.48/7.79 inference(rewrite,[status(thm)],[])).
% 7.48/7.79 tff(9665,plain,
% 7.48/7.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(elem!1))))))),
% 7.48/7.79 inference(monotonicity,[status(thm)],[9664])).
% 7.48/7.79 tff(9666,plain,
% 7.48/7.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(elem!1)))))),
% 7.48/7.79 inference(transitivity,[status(thm)],[9665, 9663])).
% 7.48/7.79 tff(9667,plain,
% 7.48/7.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 7.48/7.79 inference(quant_inst,[status(thm)],[])).
% 7.48/7.79 tff(9668,plain,
% 7.48/7.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 7.48/7.79 inference(modus_ponens,[status(thm)],[9667, 9666])).
% 7.48/7.79 tff(9669,plain,
% 7.48/7.79 ($false),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[9668, 194, 485, 364, 1064, 2170])).
% 7.48/7.79 tff(9670,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.79 tff(9671,plain,
% 7.48/7.79 (~r(s(s(elem!1)), s(elem!1))),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[9670, 9662, 485, 9648])).
% 7.48/7.79 tff(9672,plain,
% 7.48/7.79 (b(s(s(elem!1)), s(elem!1))),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[1135, 9671, 9647])).
% 7.48/7.79 tff(9673,plain,
% 7.48/7.79 (~r(z, s(s(elem!1)))),
% 7.48/7.79 inference(unit_resolution,[status(thm)],[2549, 9662, 411, 340])).
% 7.48/7.80 tff(9674,plain,
% 7.48/7.80 (b(z, s(s(elem!1)))),
% 7.48/7.80 inference(unit_resolution,[status(thm)],[324, 9673])).
% 7.48/7.80 tff(9675,plain,
% 7.48/7.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 7.48/7.80 inference(rewrite,[status(thm)],[])).
% 7.48/7.80 tff(9676,plain,
% 7.48/7.80 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 7.48/7.80 inference(rewrite,[status(thm)],[])).
% 7.48/7.80 tff(9677,plain,
% 7.48/7.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))))),
% 7.48/7.80 inference(monotonicity,[status(thm)],[9676])).
% 7.48/7.80 tff(9678,plain,
% 7.48/7.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 7.48/7.80 inference(transitivity,[status(thm)],[9677, 9675])).
% 7.48/7.80 tff(9679,plain,
% 7.48/7.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 7.48/7.80 inference(quant_inst,[status(thm)],[])).
% 7.48/7.80 tff(9680,plain,
% 7.48/7.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))),
% 7.48/7.80 inference(modus_ponens,[status(thm)],[9679, 9678])).
% 7.48/7.80 tff(9681,plain,
% 7.48/7.80 ($false),
% 7.48/7.80 inference(unit_resolution,[status(thm)],[9680, 391, 9674, 591, 9653, 9672])).
% 7.48/7.80 tff(9682,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~r(s(z), s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.48/7.80 tff(9683,plain,
% 7.48/7.80 (~r(s(s(elem!1)), s(z))),
% 7.48/7.80 inference(unit_resolution,[status(thm)],[9682, 9638, 9646, 411, 665, 9629, 1747, 812])).
% 7.48/7.80 tff(9684,plain,
% 7.48/7.80 (b(s(s(elem!1)), s(z))),
% 7.48/7.80 inference(unit_resolution,[status(thm)],[362, 9683])).
% 7.48/7.80 tff(9685,plain,
% 7.48/7.80 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.48/7.80 inference(unit_resolution,[status(thm)],[3263, 9684, 1526, 1234, 9619])).
% 7.48/7.80 tff(9686,plain,
% 7.48/7.80 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.48/7.80 inference(unit_resolution,[status(thm)],[1370, 9685, 9609])).
% 7.48/7.80 tff(9687,plain,
% 7.48/7.80 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.48/7.80 inference(modus_ponens,[status(thm)],[9686, 9598])).
% 7.48/7.80 tff(9688,plain,
% 7.48/7.80 (~r(s(s(elem!1)), z)),
% 7.48/7.80 inference(unit_resolution,[status(thm)],[7615, 9687, 2053, 719])).
% 7.48/7.80 tff(9689,plain,
% 7.48/7.80 (b(s(s(elem!1)), z)),
% 7.48/7.80 inference(unit_resolution,[status(thm)],[2629, 9688])).
% 7.48/7.80 tff(9690,plain,
% 7.48/7.80 (b(s(s(elem!1)), elem!1)),
% 7.48/7.80 inference(modus_ponens,[status(thm)],[9684, 1458])).
% 7.48/7.80 tff(9691,plain,
% 7.48/7.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.80 inference(rewrite,[status(thm)],[])).
% 7.58/7.80 tff(9692,plain,
% 7.58/7.80 (((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~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)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.80 inference(rewrite,[status(thm)],[])).
% 7.58/7.80 tff(9693,plain,
% 7.58/7.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 7.58/7.80 inference(monotonicity,[status(thm)],[9692])).
% 7.58/7.80 tff(9694,plain,
% 7.58/7.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.80 inference(transitivity,[status(thm)],[9693, 9691])).
% 7.58/7.80 tff(9695,plain,
% 7.58/7.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~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))))))),
% 7.58/7.80 inference(quant_inst,[status(thm)],[])).
% 7.58/7.80 tff(9696,plain,
% 7.58/7.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 7.58/7.80 inference(modus_ponens,[status(thm)],[9695, 9694])).
% 7.58/7.80 tff(9697,plain,
% 7.58/7.80 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.58/7.80 inference(unit_resolution,[status(thm)],[9696, 391, 665, 9616, 9690, 9629])).
% 7.58/7.80 tff(9698,plain,
% 7.58/7.80 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.58/7.80 inference(unit_resolution,[status(thm)],[1356, 9697, 7434])).
% 7.58/7.80 tff(9699,plain,
% 7.58/7.80 (~r(z, s(s(elem!1)))),
% 7.58/7.80 inference(unit_resolution,[status(thm)],[1450, 9698, 184, 9621])).
% 7.58/7.80 tff(9700,plain,
% 7.58/7.80 (b(z, s(s(elem!1)))),
% 7.58/7.80 inference(unit_resolution,[status(thm)],[324, 9699])).
% 7.58/7.80 tff(9701,plain,
% 7.58/7.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.80 inference(rewrite,[status(thm)],[])).
% 7.58/7.80 tff(9702,plain,
% 7.58/7.80 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.80 inference(rewrite,[status(thm)],[])).
% 7.58/7.80 tff(9703,plain,
% 7.58/7.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 7.58/7.80 inference(monotonicity,[status(thm)],[9702])).
% 7.58/7.80 tff(9704,plain,
% 7.58/7.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.80 inference(transitivity,[status(thm)],[9703, 9701])).
% 7.58/7.80 tff(9705,plain,
% 7.58/7.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.80 inference(quant_inst,[status(thm)],[])).
% 7.58/7.80 tff(9706,plain,
% 7.58/7.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 7.58/7.80 inference(modus_ponens,[status(thm)],[9705, 9704])).
% 7.58/7.80 tff(9707,plain,
% 7.58/7.80 ($false),
% 7.58/7.80 inference(unit_resolution,[status(thm)],[9706, 391, 665, 9690, 9700, 9689])).
% 7.58/7.80 tff(9708,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.58/7.80 tff(9709,plain,
% 7.58/7.80 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.80 inference(unit_resolution,[status(thm)],[9708, 665, 184, 2053, 719, 812, 1526, 1234, 411, 1747, 164])).
% 7.58/7.80 tff(9710,plain,
% 7.58/7.80 (b(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.80 inference(unit_resolution,[status(thm)],[3652, 9709])).
% 7.58/7.80 tff(9711,plain,
% 7.58/7.80 (~b(s(s(z)), s(z))),
% 7.58/7.80 inference(unit_resolution,[status(thm)],[5108, 9710, 1234, 9619])).
% 7.58/7.80 tff(9712,plain,
% 7.58/7.80 (r(s(s(z)), s(z))),
% 7.58/7.80 inference(unit_resolution,[status(thm)],[3778, 9711])).
% 7.58/7.80 tff(9713,plain,
% 7.58/7.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 7.58/7.80 inference(rewrite,[status(thm)],[])).
% 7.58/7.80 tff(9714,plain,
% 7.58/7.80 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 7.58/7.80 inference(rewrite,[status(thm)],[])).
% 7.58/7.80 tff(9715,plain,
% 7.58/7.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 7.58/7.80 inference(monotonicity,[status(thm)],[9714])).
% 7.58/7.80 tff(9716,plain,
% 7.58/7.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 7.58/7.80 inference(transitivity,[status(thm)],[9715, 9713])).
% 7.58/7.80 tff(9717,plain,
% 7.58/7.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 7.58/7.81 inference(quant_inst,[status(thm)],[])).
% 7.58/7.81 tff(9718,plain,
% 7.58/7.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[9717, 9716])).
% 7.58/7.81 tff(9719,plain,
% 7.58/7.81 ($false),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9718, 194, 722, 1747, 2405, 8505])).
% 7.58/7.81 tff(9720,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.81 tff(9721,plain,
% 7.58/7.81 (~r(z, s(s(z)))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9720, 9712, 1747, 815])).
% 7.58/7.81 tff(9722,plain,
% 7.58/7.81 (~r(z, s(elem!1))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[8520, 9721, 812])).
% 7.58/7.81 tff(9723,plain,
% 7.58/7.81 (b(z, s(elem!1))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[566, 9722])).
% 7.58/7.81 tff(9724,plain,
% 7.58/7.81 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 7.58/7.81 inference(monotonicity,[status(thm)],[818])).
% 7.58/7.81 tff(9725,plain,
% 7.58/7.81 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 7.58/7.81 inference(monotonicity,[status(thm)],[812])).
% 7.58/7.81 tff(9726,plain,
% 7.58/7.81 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 7.58/7.81 inference(transitivity,[status(thm)],[9725, 9724])).
% 7.58/7.81 tff(9727,plain,
% 7.58/7.81 (r(s(elem!1), elem!1)),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[2405, 9726])).
% 7.58/7.81 tff(9728,plain,
% 7.58/7.81 ($false),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[469, 9727])).
% 7.58/7.81 tff(9729,plain,((~r(s(s(z)), s(z))) | r(s(elem!1), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.81 tff(9730,plain,
% 7.58/7.81 (r(s(elem!1), elem!1)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9729, 9712, 812])).
% 7.58/7.81 tff(9731,plain,
% 7.58/7.81 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 7.58/7.81 inference(monotonicity,[status(thm)],[818])).
% 7.58/7.81 tff(9732,plain,
% 7.58/7.81 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 7.58/7.81 inference(monotonicity,[status(thm)],[812])).
% 7.58/7.81 tff(9733,plain,
% 7.58/7.81 (r(elem!1, s(s(z)))),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[1747, 9732])).
% 7.58/7.81 tff(9734,plain,
% 7.58/7.81 (r(elem!1, s(elem!1))),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[9733, 9731])).
% 7.58/7.81 tff(9735,plain,
% 7.58/7.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)))),
% 7.58/7.81 inference(rewrite,[status(thm)],[])).
% 7.58/7.81 tff(9736,plain,
% 7.58/7.81 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)))),
% 7.58/7.81 inference(rewrite,[status(thm)],[])).
% 7.58/7.81 tff(9737,plain,
% 7.58/7.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))))),
% 7.58/7.81 inference(monotonicity,[status(thm)],[9736])).
% 7.58/7.81 tff(9738,plain,
% 7.58/7.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)))),
% 7.58/7.81 inference(transitivity,[status(thm)],[9737, 9735])).
% 7.58/7.81 tff(9739,plain,
% 7.58/7.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 7.58/7.81 inference(quant_inst,[status(thm)],[])).
% 7.58/7.81 tff(9740,plain,
% 7.58/7.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[9739, 9738])).
% 7.58/7.81 tff(9741,plain,
% 7.58/7.81 (~r(s(elem!1), z)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9740, 194, 411, 9730, 9734])).
% 7.58/7.81 tff(9742,plain,
% 7.58/7.81 (b(s(elem!1), z)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[549, 9741])).
% 7.58/7.81 tff(9743,plain,
% 7.58/7.81 (~r(s(s(elem!1)), s(z))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9682, 9742, 9730, 411, 665, 9723, 1747, 812])).
% 7.58/7.81 tff(9744,plain,
% 7.58/7.81 (b(s(s(elem!1)), s(z))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[362, 9743])).
% 7.58/7.81 tff(9745,plain,
% 7.58/7.81 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[3263, 9744, 1526, 1234, 9619])).
% 7.58/7.81 tff(9746,plain,
% 7.58/7.81 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[1370, 9745, 9609])).
% 7.58/7.81 tff(9747,plain,
% 7.58/7.81 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[9746, 9598])).
% 7.58/7.81 tff(9748,plain,
% 7.58/7.81 (~r(s(s(elem!1)), z)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[7615, 9747, 2053, 719])).
% 7.58/7.81 tff(9749,plain,
% 7.58/7.81 (b(s(s(elem!1)), z)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[2629, 9748])).
% 7.58/7.81 tff(9750,plain,
% 7.58/7.81 (b(s(s(elem!1)), elem!1)),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[9744, 1458])).
% 7.58/7.81 tff(9751,plain,
% 7.58/7.81 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9696, 391, 665, 9616, 9750, 9723])).
% 7.58/7.81 tff(9752,plain,
% 7.58/7.81 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[1356, 9751, 7434])).
% 7.58/7.81 tff(9753,plain,
% 7.58/7.81 (~r(z, s(s(elem!1)))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[1450, 9752, 184, 9621])).
% 7.58/7.81 tff(9754,plain,
% 7.58/7.81 (b(z, s(s(elem!1)))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[324, 9753])).
% 7.58/7.81 tff(9755,plain,
% 7.58/7.81 ($false),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9706, 391, 665, 9750, 9754, 9749])).
% 7.58/7.81 tff(9756,plain,((~b(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.58/7.81 tff(9757,plain,
% 7.58/7.81 (~b(elem!1, z)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9756, 9579, 2053, 719, 59, 8815, 1234, 9591, 1747, 426])).
% 7.58/7.81 tff(9758,plain,
% 7.58/7.81 (r(elem!1, z)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[526, 9757, 9590])).
% 7.58/7.81 tff(9759,plain,
% 7.58/7.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 7.58/7.81 inference(rewrite,[status(thm)],[])).
% 7.58/7.81 tff(9760,plain,
% 7.58/7.81 (((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 7.58/7.81 inference(rewrite,[status(thm)],[])).
% 7.58/7.81 tff(9761,plain,
% 7.58/7.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z))))),
% 7.58/7.81 inference(monotonicity,[status(thm)],[9760])).
% 7.58/7.81 tff(9762,plain,
% 7.58/7.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 7.58/7.81 inference(transitivity,[status(thm)],[9761, 9759])).
% 7.58/7.81 tff(9763,plain,
% 7.58/7.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 7.58/7.81 inference(quant_inst,[status(thm)],[])).
% 7.58/7.81 tff(9764,plain,
% 7.58/7.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z))),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[9763, 9762])).
% 7.58/7.81 tff(9765,plain,
% 7.58/7.81 ($false),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9764, 194, 411, 530, 1628, 2251])).
% 7.58/7.81 tff(9766,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.81 tff(9767,plain,
% 7.58/7.81 (~r(s(elem!1), z)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9766, 9758, 9597, 9591])).
% 7.58/7.81 tff(9768,plain,
% 7.58/7.81 (b(s(elem!1), z)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[549, 9767])).
% 7.58/7.81 tff(9769,plain,
% 7.58/7.81 (b(elem!1, s(s(s(s(z)))))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[8539, 9579, 1234])).
% 7.58/7.81 tff(9770,plain,
% 7.58/7.81 (s(s(s(z))) = s(s(elem!1))),
% 7.58/7.81 inference(monotonicity,[status(thm)],[9593])).
% 7.58/7.81 tff(9771,plain,
% 7.58/7.81 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 7.58/7.81 inference(monotonicity,[status(thm)],[9770])).
% 7.58/7.81 tff(9772,plain,
% 7.58/7.81 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 7.58/7.81 inference(monotonicity,[status(thm)],[9771])).
% 7.58/7.81 tff(9773,plain,
% 7.58/7.81 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.58/7.81 inference(symmetry,[status(thm)],[9772])).
% 7.58/7.81 tff(9774,plain,
% 7.58/7.81 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.58/7.81 inference(monotonicity,[status(thm)],[9773])).
% 7.58/7.81 tff(9775,plain,
% 7.58/7.81 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[463, 9774])).
% 7.58/7.81 tff(9776,plain,
% 7.58/7.81 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[9608, 9775, 9769])).
% 7.58/7.81 tff(9777,plain,
% 7.58/7.81 (b(s(z), z) <=> b(elem!1, z)),
% 7.58/7.81 inference(monotonicity,[status(thm)],[9579])).
% 7.58/7.81 tff(9778,plain,
% 7.58/7.81 (b(elem!1, z) <=> b(s(z), z)),
% 7.58/7.81 inference(symmetry,[status(thm)],[9777])).
% 7.58/7.81 tff(9779,plain,
% 7.58/7.81 ((~b(elem!1, z)) <=> (~b(s(z), z))),
% 7.58/7.81 inference(monotonicity,[status(thm)],[9778])).
% 7.58/7.81 tff(9780,plain,
% 7.58/7.81 (~b(s(z), z)),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[9757, 9779])).
% 7.58/7.81 tff(9781,plain,
% 7.58/7.81 (b(z, s(s(elem!1)))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[3924, 9780, 10, 9776])).
% 7.58/7.81 tff(9782,plain,
% 7.58/7.81 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 7.58/7.81 inference(monotonicity,[status(thm)],[9579])).
% 7.58/7.81 tff(9783,plain,
% 7.58/7.81 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 7.58/7.81 inference(monotonicity,[status(thm)],[9782])).
% 7.58/7.81 tff(9784,plain,
% 7.58/7.81 (~r(s(s(s(elem!1))), elem!1)),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[8814, 9783])).
% 7.58/7.81 tff(9785,plain,
% 7.58/7.81 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 7.58/7.81 inference(transitivity,[status(thm)],[7948, 8546])).
% 7.58/7.81 tff(9786,plain,
% 7.58/7.81 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[3263, 381, 1526, 1234, 9619])).
% 7.58/7.81 tff(9787,plain,
% 7.58/7.81 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[1370, 9786, 9609])).
% 7.58/7.81 tff(9788,plain,
% 7.58/7.81 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.58/7.81 inference(modus_ponens,[status(thm)],[9787, 9598])).
% 7.58/7.81 tff(9789,plain,
% 7.58/7.81 (~r(s(s(elem!1)), z)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[7615, 9788, 2053, 719])).
% 7.58/7.81 tff(9790,plain,
% 7.58/7.81 (b(s(s(elem!1)), z)),
% 7.58/7.81 inference(unit_resolution,[status(thm)],[2629, 9789])).
% 7.58/7.81 tff(9791,plain,
% 7.58/7.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.82 inference(rewrite,[status(thm)],[])).
% 7.58/7.82 tff(9792,plain,
% 7.58/7.82 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.82 inference(rewrite,[status(thm)],[])).
% 7.58/7.82 tff(9793,plain,
% 7.58/7.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 7.58/7.82 inference(monotonicity,[status(thm)],[9792])).
% 7.58/7.82 tff(9794,plain,
% 7.58/7.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.82 inference(transitivity,[status(thm)],[9793, 9791])).
% 7.58/7.82 tff(9795,plain,
% 7.58/7.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 7.58/7.82 inference(quant_inst,[status(thm)],[])).
% 7.58/7.82 tff(9796,plain,
% 7.58/7.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 7.58/7.82 inference(modus_ponens,[status(thm)],[9795, 9794])).
% 7.58/7.82 tff(9797,plain,
% 7.58/7.82 (~b(s(s(elem!1)), s(elem!1))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[9796, 391, 1459, 3927, 591, 9790])).
% 7.58/7.82 tff(9798,plain,
% 7.58/7.82 (r(s(s(elem!1)), s(elem!1))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[1135, 9797, 9647])).
% 7.58/7.82 tff(9799,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 7.58/7.82 tff(9800,plain,
% 7.58/7.82 (s(s(elem!1)) = s(elem!1)),
% 7.58/7.82 inference(symmetry,[status(thm)],[9799])).
% 7.58/7.82 tff(9801,plain,
% 7.58/7.82 ($false),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[285, 9800])).
% 7.58/7.82 tff(9802,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.82 tff(9803,plain,
% 7.58/7.82 (~(s(elem!1) = s(s(elem!1)))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[9802, 9647])).
% 7.58/7.82 tff(9804,plain,
% 7.58/7.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.82 inference(rewrite,[status(thm)],[])).
% 7.58/7.82 tff(9805,plain,
% 7.58/7.82 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.82 inference(rewrite,[status(thm)],[])).
% 7.58/7.82 tff(9806,plain,
% 7.58/7.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 7.58/7.82 inference(monotonicity,[status(thm)],[9805])).
% 7.58/7.82 tff(9807,plain,
% 7.58/7.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.82 inference(transitivity,[status(thm)],[9806, 9804])).
% 7.58/7.82 tff(9808,plain,
% 7.58/7.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 7.58/7.82 inference(quant_inst,[status(thm)],[])).
% 7.58/7.82 tff(9809,plain,
% 7.58/7.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 7.58/7.82 inference(modus_ponens,[status(thm)],[9808, 9807])).
% 7.58/7.82 tff(9810,plain,
% 7.58/7.82 (~b(s(elem!1), s(s(elem!1)))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[9809, 391, 1459, 3927, 591, 9790])).
% 7.58/7.82 tff(9811,plain,
% 7.58/7.82 (r(s(elem!1), s(s(elem!1)))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[8644, 9810, 9803])).
% 7.58/7.82 tff(9812,plain,
% 7.58/7.82 (~r(s(elem!1), s(s(s(elem!1))))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[8653, 9811, 9787, 9798])).
% 7.58/7.82 tff(9813,plain,
% 7.58/7.82 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[3614, 9812, 812])).
% 7.58/7.82 tff(9814,plain,
% 7.58/7.82 (b(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[3652, 9813])).
% 7.58/7.82 tff(9815,plain,
% 7.58/7.82 (b(s(elem!1), s(s(s(elem!1))))),
% 7.58/7.82 inference(modus_ponens,[status(thm)],[9814, 9785])).
% 7.58/7.82 tff(9816,plain,
% 7.58/7.82 (b(elem!1, s(s(s(elem!1))))),
% 7.58/7.82 inference(modus_ponens,[status(thm)],[8540, 8529])).
% 7.58/7.82 tff(9817,plain,
% 7.58/7.82 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[920, 391, 9616, 1459, 9816])).
% 7.58/7.82 tff(9818,plain,
% 7.58/7.82 (r(s(elem!1), elem!1)),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[2168, 5626, 2163])).
% 7.58/7.82 tff(9819,plain,
% 7.58/7.82 ((~(elem!1 = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 7.58/7.82 inference(monotonicity,[status(thm)],[3])).
% 7.58/7.82 tff(9820,plain,
% 7.58/7.82 (r(s(s(elem!1)), s(elem!1))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[1135, 5682, 1031])).
% 7.58/7.82 tff(9821,plain,
% 7.58/7.82 (~r(s(s(elem!1)), elem!1)),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[7930, 9818, 530, 9820])).
% 7.58/7.82 tff(9822,plain,
% 7.58/7.82 (b(s(s(elem!1)), elem!1)),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[872, 9821, 5625])).
% 7.58/7.82 tff(9823,plain,
% 7.58/7.82 (~(elem!1 = s(s(s(elem!1))))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[1887, 9822, 1351])).
% 7.58/7.82 tff(9824,plain,
% 7.58/7.82 (~(s(s(s(elem!1))) = elem!1)),
% 7.58/7.82 inference(modus_ponens,[status(thm)],[9823, 9819])).
% 7.58/7.82 tff(9825,plain,
% 7.58/7.82 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[929, 9824])).
% 7.58/7.82 tff(9826,plain,
% 7.58/7.82 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[1354, 42, 1351, 5680])).
% 7.58/7.82 tff(9827,plain,
% 7.58/7.82 (~r(z, s(s(elem!1)))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[1448, 194, 174, 184, 9826])).
% 7.58/7.82 tff(9828,plain,
% 7.58/7.82 (b(z, s(s(elem!1)))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[324, 9827])).
% 7.58/7.82 tff(9829,plain,
% 7.58/7.82 (~r(s(s(s(s(elem!1)))), elem!1)),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[8719, 9822, 9828, 9825, 530, 9818, 411])).
% 7.58/7.82 tff(9830,plain,
% 7.58/7.82 (~r(s(z), s(s(s(elem!1))))),
% 7.58/7.82 inference(unit_resolution,[status(thm)],[5792, 9826, 174, 184])).
% 7.58/7.83 tff(9831,plain,
% 7.58/7.83 (b(s(z), s(s(s(elem!1))))),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[247, 9830])).
% 7.58/7.83 tff(9832,plain,
% 7.58/7.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.58/7.83 inference(rewrite,[status(thm)],[])).
% 7.58/7.83 tff(9833,plain,
% 7.58/7.83 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.58/7.83 inference(rewrite,[status(thm)],[])).
% 7.58/7.83 tff(9834,plain,
% 7.58/7.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 7.58/7.83 inference(monotonicity,[status(thm)],[9833])).
% 7.58/7.83 tff(9835,plain,
% 7.58/7.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.58/7.83 inference(transitivity,[status(thm)],[9834, 9832])).
% 7.58/7.83 tff(9836,plain,
% 7.58/7.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.58/7.83 inference(quant_inst,[status(thm)],[])).
% 7.58/7.83 tff(9837,plain,
% 7.58/7.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 7.58/7.83 inference(modus_ponens,[status(thm)],[9836, 9835])).
% 7.58/7.83 tff(9838,plain,
% 7.58/7.83 (~r(elem!1, s(s(s(elem!1))))),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[9837, 194, 411, 530, 174])).
% 7.58/7.83 tff(9839,plain,
% 7.58/7.83 (b(elem!1, s(s(s(elem!1))))),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[424, 9823, 9838])).
% 7.58/7.83 tff(9840,plain,
% 7.58/7.83 (b(s(s(s(elem!1))), elem!1)),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[230, 9824, 225])).
% 7.58/7.83 tff(9841,plain,
% 7.58/7.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 7.58/7.83 inference(rewrite,[status(thm)],[])).
% 7.58/7.83 tff(9842,plain,
% 7.58/7.83 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 7.58/7.83 inference(rewrite,[status(thm)],[])).
% 7.58/7.83 tff(9843,plain,
% 7.58/7.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 7.58/7.83 inference(monotonicity,[status(thm)],[9842])).
% 7.58/7.83 tff(9844,plain,
% 7.58/7.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 7.58/7.83 inference(transitivity,[status(thm)],[9843, 9841])).
% 7.58/7.83 tff(9845,plain,
% 7.58/7.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 7.58/7.83 inference(quant_inst,[status(thm)],[])).
% 7.58/7.83 tff(9846,plain,
% 7.58/7.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 7.58/7.83 inference(modus_ponens,[status(thm)],[9845, 9844])).
% 7.58/7.83 tff(9847,plain,
% 7.58/7.83 (~b(s(z), elem!1)),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[9846, 391, 9840, 9839, 9831])).
% 7.58/7.83 tff(9848,plain,
% 7.58/7.83 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 7.58/7.83 inference(monotonicity,[status(thm)],[94])).
% 7.58/7.83 tff(9849,plain,
% 7.58/7.83 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 7.58/7.83 inference(symmetry,[status(thm)],[9848])).
% 7.58/7.83 tff(9850,plain,
% 7.58/7.83 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), z))),
% 7.58/7.83 inference(monotonicity,[status(thm)],[9849])).
% 7.58/7.83 tff(9851,plain,
% 7.58/7.83 (~r(s(s(s(elem!1))), z)),
% 7.58/7.83 inference(modus_ponens,[status(thm)],[225, 9850])).
% 7.58/7.83 tff(9852,plain,
% 7.58/7.83 ($false),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[174, 9851])).
% 7.58/7.83 tff(9853,plain,((~(z = elem!1)) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.58/7.83 tff(9854,plain,
% 7.58/7.83 (~(z = elem!1)),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[9853, 225, 174])).
% 7.58/7.83 tff(9855,plain,
% 7.58/7.83 (~(s(z) = s(elem!1))),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[117, 9854])).
% 7.58/7.83 tff(9856,plain,
% 7.58/7.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 7.58/7.83 inference(rewrite,[status(thm)],[])).
% 7.58/7.83 tff(9857,plain,
% 7.58/7.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 7.58/7.83 inference(quant_inst,[status(thm)],[])).
% 7.58/7.83 tff(9858,plain,
% 7.58/7.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 7.58/7.83 inference(modus_ponens,[status(thm)],[9857, 9856])).
% 7.58/7.83 tff(9859,plain,
% 7.58/7.83 (~r(s(z), z)),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[9858, 194, 411, 530, 1484])).
% 7.58/7.83 tff(9860,plain,
% 7.58/7.83 (b(s(z), z)),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[178, 42, 23, 9859])).
% 7.58/7.83 tff(9861,plain,
% 7.58/7.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 7.58/7.83 inference(rewrite,[status(thm)],[])).
% 7.58/7.83 tff(9862,plain,
% 7.58/7.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 7.58/7.83 inference(quant_inst,[status(thm)],[])).
% 7.58/7.83 tff(9863,plain,
% 7.58/7.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 7.58/7.83 inference(modus_ponens,[status(thm)],[9862, 9861])).
% 7.58/7.83 tff(9864,plain,
% 7.58/7.83 (~r(s(z), s(elem!1))),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[9863, 194, 530, 485, 1484])).
% 7.58/7.83 tff(9865,plain,
% 7.58/7.83 (b(s(z), s(elem!1))),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[602, 42, 121, 9864])).
% 7.58/7.83 tff(9866,plain,
% 7.58/7.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.83 inference(rewrite,[status(thm)],[])).
% 7.58/7.83 tff(9867,plain,
% 7.58/7.83 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.83 inference(rewrite,[status(thm)],[])).
% 7.58/7.83 tff(9868,plain,
% 7.58/7.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1))))),
% 7.58/7.83 inference(monotonicity,[status(thm)],[9867])).
% 7.58/7.83 tff(9869,plain,
% 7.58/7.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)))),
% 7.58/7.83 inference(transitivity,[status(thm)],[9868, 9866])).
% 7.58/7.83 tff(9870,plain,
% 7.58/7.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 7.58/7.83 inference(quant_inst,[status(thm)],[])).
% 7.58/7.83 tff(9871,plain,
% 7.58/7.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1))),
% 7.58/7.83 inference(modus_ponens,[status(thm)],[9870, 9869])).
% 7.58/7.83 tff(9872,plain,
% 7.58/7.83 ($false),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[9871, 391, 973, 3927, 8711, 9865, 9860])).
% 7.58/7.83 tff(9873,plain,((~r(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (s(z) = s(elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.83 tff(9874,plain,
% 7.58/7.83 (~r(s(z), elem!1)),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[9873, 9822, 9828, 9855, 530, 9818, 411])).
% 7.58/7.83 tff(9875,plain,
% 7.58/7.83 (s(z) = elem!1),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[632, 9874, 9847])).
% 7.58/7.83 tff(9876,plain,
% 7.58/7.83 (~(s(s(s(s(elem!1)))) = elem!1)),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[7472, 9875])).
% 7.58/7.83 tff(9877,plain,
% 7.58/7.83 (b(s(s(s(s(elem!1)))), elem!1)),
% 7.58/7.83 inference(unit_resolution,[status(thm)],[1004, 9876, 9829])).
% 7.58/7.83 tff(9878,plain,
% 7.58/7.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.58/7.84 inference(rewrite,[status(thm)],[])).
% 7.58/7.84 tff(9879,plain,
% 7.58/7.84 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.58/7.84 inference(rewrite,[status(thm)],[])).
% 7.58/7.84 tff(9880,plain,
% 7.58/7.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 7.58/7.84 inference(monotonicity,[status(thm)],[9879])).
% 7.58/7.84 tff(9881,plain,
% 7.58/7.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.58/7.84 inference(transitivity,[status(thm)],[9880, 9878])).
% 7.58/7.84 tff(9882,plain,
% 7.58/7.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.58/7.84 inference(quant_inst,[status(thm)],[])).
% 7.58/7.84 tff(9883,plain,
% 7.58/7.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 7.58/7.84 inference(modus_ponens,[status(thm)],[9882, 9881])).
% 7.58/7.84 tff(9884,plain,
% 7.58/7.84 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[9883, 391, 9840, 9839, 9877])).
% 7.58/7.84 tff(9885,plain,
% 7.58/7.84 (~(s(elem!1) = s(s(elem!1)))),
% 7.58/7.84 inference(modus_ponens,[status(thm)],[5682, 1099])).
% 7.58/7.84 tff(9886,plain,
% 7.58/7.84 (~r(s(s(elem!1)), z)),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[4501, 194, 174, 184, 9826])).
% 7.58/7.84 tff(9887,plain,
% 7.58/7.84 (b(s(s(elem!1)), z)),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[2627, 42, 215, 9886])).
% 7.58/7.84 tff(9888,plain,
% 7.58/7.84 (~r(s(elem!1), z)),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[541, 9818, 530, 411])).
% 7.58/7.84 tff(9889,plain,
% 7.58/7.84 (b(s(elem!1), z)),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[547, 42, 355, 9888])).
% 7.58/7.84 tff(9890,plain,
% 7.58/7.84 (~b(s(elem!1), s(s(elem!1)))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[9809, 391, 9822, 9828, 9889, 9887])).
% 7.58/7.84 tff(9891,plain,
% 7.58/7.84 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[1111, 42, 9890])).
% 7.58/7.84 tff(9892,plain,
% 7.58/7.84 (r(s(elem!1), s(s(elem!1)))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[9891, 9885])).
% 7.58/7.84 tff(9893,plain,
% 7.58/7.84 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[8727, 391, 9840, 9822, 9839, 9877])).
% 7.58/7.84 tff(9894,plain,
% 7.58/7.84 ((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 7.58/7.84 inference(monotonicity,[status(thm)],[1020])).
% 7.58/7.84 tff(9895,plain,
% 7.58/7.84 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[2686, 279])).
% 7.58/7.84 tff(9896,plain,
% 7.58/7.84 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 7.58/7.84 inference(modus_ponens,[status(thm)],[9895, 9894])).
% 7.58/7.84 tff(9897,plain,
% 7.58/7.84 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[1061, 9896, 9893])).
% 7.58/7.84 tff(9898,plain,
% 7.58/7.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.58/7.84 inference(rewrite,[status(thm)],[])).
% 7.58/7.84 tff(9899,plain,
% 7.58/7.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.58/7.84 inference(quant_inst,[status(thm)],[])).
% 7.58/7.84 tff(9900,plain,
% 7.58/7.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 7.58/7.84 inference(modus_ponens,[status(thm)],[9899, 9898])).
% 7.58/7.84 tff(9901,plain,
% 7.58/7.84 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[9900, 194, 9820, 9897, 9892])).
% 7.58/7.84 tff(9902,plain,
% 7.58/7.84 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[988, 9901, 9825])).
% 7.58/7.84 tff(9903,plain,
% 7.58/7.84 (~r(z, s(elem!1))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[556, 194, 411, 530, 9818])).
% 7.58/7.84 tff(9904,plain,
% 7.58/7.84 (b(z, s(elem!1))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[566, 9903])).
% 7.58/7.84 tff(9905,plain,
% 7.58/7.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.58/7.84 inference(rewrite,[status(thm)],[])).
% 7.58/7.84 tff(9906,plain,
% 7.58/7.84 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.58/7.84 inference(rewrite,[status(thm)],[])).
% 7.58/7.84 tff(9907,plain,
% 7.58/7.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 7.58/7.84 inference(monotonicity,[status(thm)],[9906])).
% 7.58/7.84 tff(9908,plain,
% 7.58/7.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.58/7.84 inference(transitivity,[status(thm)],[9907, 9905])).
% 7.58/7.84 tff(9909,plain,
% 7.58/7.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))),
% 7.58/7.84 inference(quant_inst,[status(thm)],[])).
% 7.58/7.84 tff(9910,plain,
% 7.58/7.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 7.58/7.84 inference(modus_ponens,[status(thm)],[9909, 9908])).
% 7.58/7.84 tff(9911,plain,
% 7.58/7.84 (~b(s(s(s(s(elem!1)))), z)),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[9910, 391, 9828, 9904, 9889, 9902])).
% 7.58/7.84 tff(9912,plain,
% 7.58/7.84 (r(s(s(s(s(elem!1)))), z)),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[1626, 9911])).
% 7.58/7.84 tff(9913,plain,
% 7.58/7.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.58/7.84 inference(rewrite,[status(thm)],[])).
% 7.58/7.84 tff(9914,plain,
% 7.58/7.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.58/7.84 inference(quant_inst,[status(thm)],[])).
% 7.58/7.84 tff(9915,plain,
% 7.58/7.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 7.58/7.84 inference(modus_ponens,[status(thm)],[9914, 9913])).
% 7.58/7.84 tff(9916,plain,
% 7.58/7.84 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[9915, 194, 411, 174, 9912])).
% 7.58/7.84 tff(9917,plain,
% 7.58/7.84 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[1095, 9916, 9884])).
% 7.58/7.84 tff(9918,plain,
% 7.58/7.84 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 7.58/7.84 inference(monotonicity,[status(thm)],[9917])).
% 7.58/7.84 tff(9919,plain,
% 7.58/7.84 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 7.58/7.84 inference(symmetry,[status(thm)],[9918])).
% 7.58/7.84 tff(9920,plain,
% 7.58/7.84 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 7.58/7.84 inference(symmetry,[status(thm)],[9917])).
% 7.58/7.84 tff(9921,plain,
% 7.58/7.84 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 7.58/7.84 inference(monotonicity,[status(thm)],[9920])).
% 7.58/7.84 tff(9922,plain,
% 7.58/7.84 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(elem!1))))),
% 7.58/7.84 inference(symmetry,[status(thm)],[9921])).
% 7.58/7.84 tff(9923,plain,
% 7.58/7.84 (s(s(s(elem!1))) = s(s(elem!1))),
% 7.58/7.84 inference(transitivity,[status(thm)],[295, 9922, 211])).
% 7.58/7.84 tff(9924,plain,
% 7.58/7.84 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 7.58/7.84 inference(modus_ponens,[status(thm)],[9923, 9919])).
% 7.58/7.84 tff(9925,plain,
% 7.58/7.84 ($false),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[9896, 9924])).
% 7.58/7.84 tff(9926,plain,((s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), elem!1) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(elem!1), elem!1) | b(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.84 tff(9927,plain,
% 7.58/7.84 (b(s(elem!1), elem!1)),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[9926, 9797, 184, 530, 411, 225, 7433, 9621, 9817])).
% 7.58/7.84 tff(9928,plain,
% 7.58/7.84 ($false),
% 7.58/7.84 inference(unit_resolution,[status(thm)],[6890, 391, 9616, 9816, 9927, 9815])).
% 7.58/7.84 tff(9929,plain,((~b(s(s(elem!1)), s(z))) | (~(s(z) = elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(z, elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.85 tff(9930,plain,
% 7.58/7.85 (~b(s(s(elem!1)), s(z))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[9929, 9579, 59, 9758, 9591, 9784, 9781, 9768, 2053, 719, 8815, 1234])).
% 7.58/7.85 tff(9931,plain,
% 7.58/7.85 (r(s(s(elem!1)), s(z))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[362, 9930])).
% 7.58/7.85 tff(9932,plain,
% 7.58/7.85 (~r(s(s(elem!1)), z)),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[9045, 9931, 1747, 9592])).
% 7.58/7.85 tff(9933,plain,
% 7.58/7.85 (b(s(s(elem!1)), z)),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[2629, 9932])).
% 7.58/7.85 tff(9934,plain,
% 7.58/7.85 (~b(s(s(elem!1)), s(elem!1))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[9680, 391, 9781, 9768, 9933])).
% 7.58/7.85 tff(9935,plain,
% 7.58/7.85 (r(s(s(elem!1)), s(elem!1))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[1135, 9934, 9583])).
% 7.58/7.85 tff(9936,plain,
% 7.58/7.85 (b(s(s(s(s(z)))), s(z))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[9618, 9579, 8815])).
% 7.58/7.85 tff(9937,plain,
% 7.58/7.85 (r(s(s(elem!1)), elem!1)),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[2220, 9931, 9579])).
% 7.58/7.85 tff(9938,plain,
% 7.58/7.85 (~r(s(elem!1), elem!1)),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[7930, 9935, 9758, 9937])).
% 7.58/7.85 tff(9939,plain,
% 7.58/7.85 (~r(s(s(z)), s(z))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[9729, 9938, 9579])).
% 7.58/7.85 tff(9940,plain,
% 7.58/7.85 (b(s(s(z)), s(z))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[3778, 9939])).
% 7.58/7.85 tff(9941,plain,
% 7.58/7.85 (~b(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[5108, 9940, 1234, 9936])).
% 7.58/7.85 tff(9942,plain,
% 7.58/7.85 (r(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[3652, 9941])).
% 7.58/7.85 tff(9943,plain,
% 7.58/7.85 (r(s(elem!1), s(s(s(elem!1))))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[3614, 9942, 9579])).
% 7.58/7.85 tff(9944,plain,
% 7.58/7.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.58/7.85 inference(rewrite,[status(thm)],[])).
% 7.58/7.85 tff(9945,plain,
% 7.58/7.85 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(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)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.58/7.85 inference(rewrite,[status(thm)],[])).
% 7.58/7.85 tff(9946,plain,
% 7.58/7.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 7.58/7.85 inference(monotonicity,[status(thm)],[9945])).
% 7.58/7.85 tff(9947,plain,
% 7.58/7.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.58/7.85 inference(transitivity,[status(thm)],[9946, 9944])).
% 7.58/7.85 tff(9948,plain,
% 7.58/7.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 7.58/7.85 inference(quant_inst,[status(thm)],[])).
% 7.58/7.85 tff(9949,plain,
% 7.58/7.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 7.58/7.85 inference(modus_ponens,[status(thm)],[9948, 9947])).
% 7.58/7.85 tff(9950,plain,
% 7.58/7.85 ($false),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[9949, 194, 9597, 9937, 9943, 9935])).
% 7.58/7.85 tff(9951,plain,((elem!1 = s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | b(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(z)) | r(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.58/7.85 tff(9952,plain,
% 7.58/7.85 (~r(s(z), s(s(z)))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[9951, 8951, 1, 2053, 1234, 10, 8814, 832, 2829])).
% 7.58/7.85 tff(9953,plain,
% 7.58/7.85 (b(s(z), s(s(z)))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[1788, 9952])).
% 7.58/7.85 tff(9954,plain,
% 7.58/7.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 7.58/7.85 inference(rewrite,[status(thm)],[])).
% 7.58/7.85 tff(9955,plain,
% 7.58/7.85 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 7.58/7.85 inference(rewrite,[status(thm)],[])).
% 7.58/7.85 tff(9956,plain,
% 7.58/7.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 7.58/7.85 inference(monotonicity,[status(thm)],[9955])).
% 7.58/7.85 tff(9957,plain,
% 7.58/7.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 7.58/7.85 inference(transitivity,[status(thm)],[9956, 9954])).
% 7.58/7.85 tff(9958,plain,
% 7.58/7.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 7.58/7.85 inference(quant_inst,[status(thm)],[])).
% 7.58/7.85 tff(9959,plain,
% 7.58/7.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 7.58/7.85 inference(modus_ponens,[status(thm)],[9958, 9957])).
% 7.58/7.85 tff(9960,plain,
% 7.58/7.85 ($false),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[9959, 391, 448, 1526, 2439, 1233, 721])).
% 7.58/7.85 tff(9961,plain,((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.85 tff(9962,plain,
% 7.58/7.85 (~b(s(s(z)), s(z))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[9961, 9002, 9953, 8918, 8815])).
% 7.58/7.85 tff(9963,plain,
% 7.58/7.85 (r(s(s(z)), s(z))),
% 7.58/7.85 inference(unit_resolution,[status(thm)],[3778, 9962])).
% 7.58/7.86 tff(9964,plain,
% 7.58/7.86 ($false),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[2429, 9963, 9012, 8953, 5238])).
% 7.58/7.86 tff(9965,plain,((elem!1 = s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | b(z, s(s(s(elem!1)))) | (s(z) = elem!1) | (~r(s(s(s(s(z)))), z)) | r(elem!1, s(z)) | r(s(s(s(elem!1))), s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.58/7.86 tff(9966,plain,
% 7.58/7.86 (elem!1 = s(s(s(elem!1)))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[9965, 150, 411, 10, 1234, 2053, 832, 8814, 2829])).
% 7.58/7.86 tff(9967,plain,
% 7.58/7.86 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 7.58/7.86 inference(monotonicity,[status(thm)],[125])).
% 7.58/7.86 tff(9968,plain,
% 7.58/7.86 (r(s(z), s(s(s(elem!1))))),
% 7.58/7.86 inference(modus_ponens,[status(thm)],[1484, 9967])).
% 7.58/7.86 tff(9969,plain,
% 7.58/7.86 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.58/7.86 inference(monotonicity,[status(thm)],[125])).
% 7.58/7.86 tff(9970,plain,
% 7.58/7.86 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.58/7.86 inference(modus_ponens,[status(thm)],[1652, 9969])).
% 7.58/7.86 tff(9971,plain,
% 7.58/7.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.86 inference(rewrite,[status(thm)],[])).
% 7.58/7.86 tff(9972,plain,
% 7.58/7.86 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.86 inference(rewrite,[status(thm)],[])).
% 7.58/7.86 tff(9973,plain,
% 7.58/7.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.58/7.86 inference(monotonicity,[status(thm)],[9972])).
% 7.58/7.86 tff(9974,plain,
% 7.58/7.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.86 inference(transitivity,[status(thm)],[9973, 9971])).
% 7.58/7.86 tff(9975,plain,
% 7.58/7.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 7.58/7.86 inference(quant_inst,[status(thm)],[])).
% 7.58/7.86 tff(9976,plain,
% 7.58/7.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 7.58/7.86 inference(modus_ponens,[status(thm)],[9975, 9974])).
% 7.58/7.86 tff(9977,plain,
% 7.58/7.86 ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[9976, 391])).
% 7.58/7.86 tff(9978,plain,
% 7.58/7.86 (~b(z, s(z))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[9977, 1652, 1234, 1686, 721])).
% 7.58/7.86 tff(9979,plain,
% 7.58/7.86 (r(z, s(z))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[678, 9978])).
% 7.58/7.86 tff(9980,plain,
% 7.58/7.86 (~r(s(s(s(elem!1))), z)),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[5980, 9979, 184, 232])).
% 7.58/7.86 tff(9981,plain,
% 7.58/7.86 (b(s(s(s(elem!1))), z)),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[377, 9980])).
% 7.58/7.86 tff(9982,plain,
% 7.58/7.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 7.58/7.86 inference(rewrite,[status(thm)],[])).
% 7.58/7.86 tff(9983,plain,
% 7.58/7.86 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 7.58/7.86 inference(rewrite,[status(thm)],[])).
% 7.58/7.86 tff(9984,plain,
% 7.58/7.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 7.58/7.86 inference(monotonicity,[status(thm)],[9983])).
% 7.58/7.86 tff(9985,plain,
% 7.58/7.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 7.58/7.86 inference(transitivity,[status(thm)],[9984, 9982])).
% 7.58/7.86 tff(9986,plain,
% 7.58/7.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 7.58/7.86 inference(quant_inst,[status(thm)],[])).
% 7.58/7.86 tff(9987,plain,
% 7.58/7.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 7.58/7.86 inference(modus_ponens,[status(thm)],[9986, 9985])).
% 7.58/7.86 tff(9988,plain,
% 7.58/7.86 ($false),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[9987, 391, 9981, 1234, 1686, 590, 9970])).
% 7.58/7.86 tff(9989,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.86 tff(9990,plain,
% 7.58/7.86 (~b(s(s(s(s(z)))), elem!1)),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[9989, 1686, 1234, 590, 125, 184, 9968, 721])).
% 7.58/7.86 tff(9991,plain,
% 7.58/7.86 (r(s(s(s(s(z)))), elem!1)),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[762, 9990, 720])).
% 7.58/7.86 tff(9992,plain,
% 7.58/7.86 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[9171, 9119, 9109, 721, 723, 1234, 1484])).
% 7.58/7.86 tff(9993,plain,
% 7.58/7.86 (b(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[3652, 9992])).
% 7.58/7.86 tff(9994,plain,
% 7.58/7.86 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[6275, 9993, 1234, 2439])).
% 7.58/7.86 tff(9995,plain,
% 7.58/7.86 (~b(s(s(z)), s(z))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[9159, 9119, 1234, 721, 2439])).
% 7.58/7.86 tff(9996,plain,
% 7.58/7.86 (r(s(s(z)), s(z))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[3778, 9995])).
% 7.58/7.86 tff(9997,plain,
% 7.58/7.86 (~r(s(s(s(s(z)))), s(s(z)))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[2429, 9996, 723, 1484])).
% 7.58/7.86 tff(9998,plain,
% 7.58/7.86 ($false),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[1714, 9997, 9994])).
% 7.58/7.86 tff(9999,plain,(b(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (elem!1 = s(s(z))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.58/7.86 tff(10000,plain,
% 7.58/7.86 (~r(s(s(s(s(z)))), s(z))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[9999, 2439, 1484, 1234, 1549, 721, 1405, 720])).
% 7.58/7.86 tff(10001,plain,
% 7.58/7.86 (b(s(s(s(s(z)))), s(z))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[749, 10000])).
% 7.58/7.86 tff(10002,plain,
% 7.58/7.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.86 inference(rewrite,[status(thm)],[])).
% 7.58/7.86 tff(10003,plain,
% 7.58/7.86 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.86 inference(rewrite,[status(thm)],[])).
% 7.58/7.86 tff(10004,plain,
% 7.58/7.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.58/7.86 inference(monotonicity,[status(thm)],[10003])).
% 7.58/7.86 tff(10005,plain,
% 7.58/7.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.86 inference(transitivity,[status(thm)],[10004, 10002])).
% 7.58/7.86 tff(10006,plain,
% 7.58/7.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 7.58/7.86 inference(quant_inst,[status(thm)],[])).
% 7.58/7.86 tff(10007,plain,
% 7.58/7.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.58/7.86 inference(modus_ponens,[status(thm)],[10006, 10005])).
% 7.58/7.86 tff(10008,plain,
% 7.58/7.86 ($false),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[10007, 391, 1234, 10001, 2439, 1686, 590])).
% 7.58/7.86 tff(10009,plain,((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(s(z), elem!1)) | b(s(s(s(s(z)))), elem!1) | (~b(elem!1, s(z))) | (elem!1 = s(s(z))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.58/7.86 tff(10010,plain,
% 7.58/7.86 (~b(s(z), s(s(z)))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[10009, 1686, 1234, 590, 1484, 9990, 721, 3820, 720])).
% 7.58/7.86 tff(10011,plain,
% 7.58/7.86 (r(s(z), s(s(z)))),
% 7.58/7.86 inference(unit_resolution,[status(thm)],[1788, 10010])).
% 7.58/7.86 tff(10012,plain,
% 7.58/7.87 (~r(elem!1, s(s(z)))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[9117, 723, 1484, 2112])).
% 7.58/7.87 tff(10013,plain,
% 7.58/7.87 (b(elem!1, s(s(z)))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[3394, 10012, 3820])).
% 7.58/7.87 tff(10014,plain,
% 7.58/7.87 (b(s(s(s(elem!1))), s(s(z)))),
% 7.58/7.87 inference(modus_ponens,[status(thm)],[10013, 3815])).
% 7.58/7.87 tff(10015,plain,
% 7.58/7.87 (b(elem!1, s(s(s(s(z)))))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[9108, 723, 1549, 1484, 8922])).
% 7.58/7.87 tff(10016,plain,
% 7.58/7.87 (~b(elem!1, s(s(z)))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[9171, 1749, 2064, 721, 723, 1234, 1484])).
% 7.58/7.87 tff(10017,plain,
% 7.58/7.87 (r(elem!1, s(s(z)))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[3394, 10016, 3820])).
% 7.58/7.87 tff(10018,plain,
% 7.58/7.87 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 7.58/7.87 inference(monotonicity,[status(thm)],[125])).
% 7.58/7.87 tff(10019,plain,
% 7.58/7.87 (r(s(s(s(elem!1))), s(s(z)))),
% 7.58/7.87 inference(modus_ponens,[status(thm)],[1748, 10018])).
% 7.58/7.87 tff(10020,assumption,(~r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 7.58/7.87 tff(10021,plain,
% 7.58/7.87 ($false),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[10020, 10019])).
% 7.58/7.87 tff(10022,plain,((~r(elem!1, s(s(z)))) | r(s(s(s(elem!1))), s(s(z))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.87 tff(10023,plain,
% 7.58/7.87 (r(s(s(s(elem!1))), s(s(z)))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[10022, 10017, 125])).
% 7.58/7.87 tff(10024,plain,
% 7.58/7.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.58/7.87 inference(rewrite,[status(thm)],[])).
% 7.58/7.87 tff(10025,plain,
% 7.58/7.87 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.58/7.87 inference(rewrite,[status(thm)],[])).
% 7.58/7.87 tff(10026,plain,
% 7.58/7.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 7.58/7.87 inference(monotonicity,[status(thm)],[10025])).
% 7.58/7.87 tff(10027,plain,
% 7.58/7.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.58/7.87 inference(transitivity,[status(thm)],[10026, 10024])).
% 7.58/7.87 tff(10028,plain,
% 7.58/7.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 7.58/7.87 inference(quant_inst,[status(thm)],[])).
% 7.58/7.87 tff(10029,plain,
% 7.58/7.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 7.58/7.87 inference(modus_ponens,[status(thm)],[10028, 10027])).
% 7.58/7.87 tff(10030,plain,
% 7.58/7.87 ($false),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[10029, 194, 9968, 1749, 1747, 10023])).
% 7.58/7.87 tff(10031,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.87 tff(10032,plain,
% 7.58/7.87 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[10031, 10015, 125, 1747, 721, 723, 1234, 1484])).
% 7.58/7.87 tff(10033,plain,
% 7.58/7.87 (b(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[3652, 10032])).
% 7.58/7.87 tff(10034,plain,
% 7.58/7.87 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[9127, 10033, 10015, 10013])).
% 7.58/7.87 tff(10035,plain,
% 7.58/7.87 (r(s(s(s(s(z)))), s(s(z)))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[1714, 10034])).
% 7.58/7.87 tff(10036,plain,
% 7.58/7.87 (~r(s(s(z)), s(z))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[2429, 10035, 723, 1484])).
% 7.58/7.87 tff(10037,plain,
% 7.58/7.87 (b(s(s(z)), s(z))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[3778, 10036])).
% 7.58/7.87 tff(10038,plain,
% 7.58/7.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 7.58/7.87 inference(rewrite,[status(thm)],[])).
% 7.58/7.87 tff(10039,plain,
% 7.58/7.87 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 7.58/7.87 inference(rewrite,[status(thm)],[])).
% 7.58/7.87 tff(10040,plain,
% 7.58/7.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 7.58/7.87 inference(monotonicity,[status(thm)],[10039])).
% 7.58/7.87 tff(10041,plain,
% 7.58/7.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 7.58/7.87 inference(transitivity,[status(thm)],[10040, 10038])).
% 7.58/7.87 tff(10042,plain,
% 7.58/7.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 7.58/7.87 inference(quant_inst,[status(thm)],[])).
% 7.58/7.87 tff(10043,plain,
% 7.58/7.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 7.58/7.87 inference(modus_ponens,[status(thm)],[10042, 10041])).
% 7.58/7.87 tff(10044,plain,
% 7.58/7.87 (~b(s(s(s(elem!1))), s(s(z)))),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[10043, 391, 1526, 1686, 10037, 590])).
% 7.58/7.87 tff(10045,plain,
% 7.58/7.87 ($false),
% 7.58/7.87 inference(unit_resolution,[status(thm)],[10044, 10014])).
% 7.58/7.87 tff(10046,plain,((~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(z)))), elem!1) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.88 tff(10047,plain,
% 7.58/7.88 (~r(s(s(s(s(z)))), s(z))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[10046, 1686, 1526, 125, 590, 1484, 10011, 721, 1234, 9991, 9990, 770])).
% 7.58/7.88 tff(10048,plain,
% 7.58/7.88 (b(s(s(s(s(z)))), s(z))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[749, 10047])).
% 7.58/7.88 tff(10049,plain,
% 7.58/7.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.88 inference(rewrite,[status(thm)],[])).
% 7.58/7.88 tff(10050,plain,
% 7.58/7.88 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.88 inference(rewrite,[status(thm)],[])).
% 7.58/7.88 tff(10051,plain,
% 7.58/7.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10050])).
% 7.58/7.88 tff(10052,plain,
% 7.58/7.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.88 inference(transitivity,[status(thm)],[10051, 10049])).
% 7.58/7.88 tff(10053,plain,
% 7.58/7.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 7.58/7.88 inference(quant_inst,[status(thm)],[])).
% 7.58/7.88 tff(10054,plain,
% 7.58/7.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.58/7.88 inference(modus_ponens,[status(thm)],[10053, 10052])).
% 7.58/7.88 tff(10055,plain,
% 7.58/7.88 ($false),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[10054, 391, 1234, 10048, 1686, 590])).
% 7.58/7.88 tff(10056,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.88 tff(10057,plain,
% 7.58/7.88 (~b(z, s(s(s(s(z)))))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[10056, 8933, 1234, 8815, 9966, 5238, 8918, 8917, 59])).
% 7.58/7.88 tff(10058,plain,
% 7.58/7.88 (r(z, s(s(s(s(z)))))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[800, 10057])).
% 7.58/7.88 tff(10059,plain,
% 7.58/7.88 (~b(s(s(s(s(z)))), s(z))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[2097, 10058, 1234, 8917, 8918, 411])).
% 7.58/7.88 tff(10060,plain,
% 7.58/7.88 (r(s(s(s(s(z)))), s(z))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[749, 10059])).
% 7.58/7.88 tff(10061,plain,
% 7.58/7.88 (s(s(s(elem!1))) = elem!1),
% 7.58/7.88 inference(symmetry,[status(thm)],[9966])).
% 7.58/7.88 tff(10062,plain,
% 7.58/7.88 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10061])).
% 7.58/7.88 tff(10063,plain,
% 7.58/7.88 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 7.58/7.88 inference(transitivity,[status(thm)],[10062, 698])).
% 7.58/7.88 tff(10064,plain,
% 7.58/7.88 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10063])).
% 7.58/7.88 tff(10065,plain,
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% 7.58/7.88 inference(modus_ponens,[status(thm)],[1397, 10064])).
% 7.58/7.88 tff(10066,plain,
% 7.58/7.88 (elem!1 = s(s(s(elem!1)))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[9951, 719, 1747, 2053, 1234, 10, 8814, 832, 2829])).
% 7.58/7.88 tff(10067,plain,
% 7.58/7.88 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10066])).
% 7.58/7.88 tff(10068,plain,
% 7.58/7.88 (s(s(s(elem!1))) = elem!1),
% 7.58/7.88 inference(symmetry,[status(thm)],[10066])).
% 7.58/7.88 tff(10069,plain,
% 7.58/7.88 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10068])).
% 7.58/7.88 tff(10070,plain,
% 7.58/7.88 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 7.58/7.88 inference(transitivity,[status(thm)],[10069, 698])).
% 7.58/7.88 tff(10071,plain,
% 7.58/7.88 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10070])).
% 7.58/7.88 tff(10072,plain,
% 7.58/7.88 (~(elem!1 = s(s(z)))),
% 7.58/7.88 inference(modus_ponens,[status(thm)],[1397, 10071])).
% 7.58/7.88 tff(10073,plain,
% 7.58/7.88 (r(z, elem!1)),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[147, 10066, 10])).
% 7.58/7.88 tff(10074,plain,
% 7.58/7.88 (s(s(s(elem!1))) = elem!1),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[129, 10066])).
% 7.58/7.88 tff(10075,plain,
% 7.58/7.88 (b(elem!1, s(z))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[8400, 10074, 8815])).
% 7.58/7.88 tff(10076,plain,
% 7.58/7.88 (~b(s(s(s(s(z)))), s(z))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[2097, 10075, 1234, 8917, 719, 10073])).
% 7.58/7.88 tff(10077,plain,
% 7.58/7.88 (~(s(z) = elem!1)),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[9618, 10076, 8815])).
% 7.58/7.88 tff(10078,plain,
% 7.58/7.88 (r(s(z), elem!1)),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[632, 10077, 2829])).
% 7.58/7.88 tff(10079,plain,
% 7.58/7.88 (r(s(s(s(s(z)))), s(z))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[749, 10076])).
% 7.58/7.88 tff(10080,plain,
% 7.58/7.88 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10066])).
% 7.58/7.88 tff(10081,plain,
% 7.58/7.88 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 7.58/7.88 inference(symmetry,[status(thm)],[10080])).
% 7.58/7.88 tff(10082,plain,
% 7.58/7.88 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10081])).
% 7.58/7.88 tff(10083,plain,
% 7.58/7.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.58/7.88 inference(rewrite,[status(thm)],[])).
% 7.58/7.88 tff(10084,plain,
% 7.58/7.88 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.58/7.88 inference(rewrite,[status(thm)],[])).
% 7.58/7.88 tff(10085,plain,
% 7.58/7.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10084])).
% 7.58/7.88 tff(10086,plain,
% 7.58/7.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.58/7.88 inference(transitivity,[status(thm)],[10085, 10083])).
% 7.58/7.88 tff(10087,plain,
% 7.58/7.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))))),
% 7.58/7.88 inference(quant_inst,[status(thm)],[])).
% 7.58/7.88 tff(10088,plain,
% 7.58/7.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.58/7.88 inference(modus_ponens,[status(thm)],[10087, 10086])).
% 7.58/7.88 tff(10089,plain,
% 7.58/7.88 ($false),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[10088, 194, 184, 2053, 719, 4317])).
% 7.58/7.88 tff(10090,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.88 tff(10091,plain,
% 7.58/7.88 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[10090, 719, 2053, 59])).
% 7.58/7.88 tff(10092,plain,
% 7.58/7.88 (~r(elem!1, s(s(s(s(z)))))),
% 7.58/7.88 inference(modus_ponens,[status(thm)],[10091, 10082])).
% 7.58/7.88 tff(10093,plain,
% 7.58/7.88 (b(elem!1, s(s(s(s(z)))))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[781, 10092, 8919])).
% 7.58/7.88 tff(10094,plain,
% 7.58/7.88 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[10031, 10066, 1747, 10093, 10075, 10079, 1234, 10078])).
% 7.58/7.88 tff(10095,plain,
% 7.58/7.88 (b(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.88 inference(unit_resolution,[status(thm)],[3652, 10094])).
% 7.58/7.88 tff(10096,plain,
% 7.58/7.88 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10066])).
% 7.58/7.88 tff(10097,plain,
% 7.58/7.88 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), elem!1)),
% 7.58/7.88 inference(symmetry,[status(thm)],[10096])).
% 7.58/7.88 tff(10098,plain,
% 7.58/7.88 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10097])).
% 7.58/7.88 tff(10099,plain,
% 7.58/7.88 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10066])).
% 7.58/7.88 tff(10100,plain,
% 7.58/7.88 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.58/7.88 inference(modus_ponens,[status(thm)],[10093, 10099])).
% 7.58/7.88 tff(10101,plain,
% 7.58/7.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.58/7.88 inference(rewrite,[status(thm)],[])).
% 7.58/7.88 tff(10102,plain,
% 7.58/7.88 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.58/7.88 inference(rewrite,[status(thm)],[])).
% 7.58/7.88 tff(10103,plain,
% 7.58/7.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.58/7.88 inference(monotonicity,[status(thm)],[10102])).
% 7.58/7.88 tff(10104,plain,
% 7.58/7.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.58/7.89 inference(transitivity,[status(thm)],[10103, 10101])).
% 7.58/7.89 tff(10105,plain,
% 7.58/7.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 7.58/7.89 inference(quant_inst,[status(thm)],[])).
% 7.58/7.89 tff(10106,plain,
% 7.58/7.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.58/7.89 inference(modus_ponens,[status(thm)],[10105, 10104])).
% 7.58/7.89 tff(10107,plain,
% 7.58/7.89 ($false),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[10106, 391, 1526, 1234, 3325, 1669])).
% 7.58/7.89 tff(10108,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.89 tff(10109,plain,
% 7.58/7.89 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[10108, 10100, 1234, 8815])).
% 7.58/7.89 tff(10110,plain,
% 7.58/7.89 (~b(s(s(s(s(z)))), elem!1)),
% 7.58/7.89 inference(modus_ponens,[status(thm)],[10109, 10098])).
% 7.58/7.89 tff(10111,plain,
% 7.58/7.89 (~b(s(s(elem!1)), s(z))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[9569, 10110, 2053, 10073, 8815, 1234, 10078, 10, 832, 10077, 719, 1747, 10095, 10072, 8917])).
% 7.58/7.89 tff(10112,plain,
% 7.58/7.89 (r(s(s(elem!1)), s(z))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[362, 10111])).
% 7.58/7.89 tff(10113,plain,
% 7.58/7.89 (~(s(s(elem!1)) = elem!1)),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[4206, 10112, 832])).
% 7.58/7.89 tff(10114,plain,
% 7.58/7.89 (~(elem!1 = s(s(elem!1)))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[1292, 10113])).
% 7.58/7.89 tff(10115,plain,
% 7.58/7.89 (~b(elem!1, s(s(elem!1)))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[2817, 10112, 10066, 1234, 10073, 10075, 10078, 719])).
% 7.58/7.89 tff(10116,plain,
% 7.58/7.89 (r(elem!1, s(s(elem!1)))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[1307, 10115, 10114])).
% 7.58/7.89 tff(10117,plain,
% 7.58/7.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.58/7.89 inference(modus_ponens,[status(thm)],[10116, 10067])).
% 7.58/7.89 tff(10118,plain,
% 7.58/7.89 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[2849, 10077])).
% 7.58/7.89 tff(10119,plain,
% 7.58/7.89 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[2853, 42, 10118, 10109])).
% 7.58/7.89 tff(10120,plain,
% 7.58/7.89 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[9541, 10119, 59, 2053, 10066])).
% 7.58/7.89 tff(10121,plain,
% 7.58/7.89 ($false),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[10120, 10117])).
% 7.58/7.89 tff(10122,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | r(elem!1, s(z)) | (~r(s(s(s(s(z)))), z)) | b(z, s(s(s(elem!1)))) | (~r(s(z), s(s(z)))) | b(s(z), elem!1) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.89 tff(10123,plain,
% 7.58/7.89 (~r(s(z), s(s(z)))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[10122, 10058, 832, 2053, 10, 1234, 2829, 8814])).
% 7.58/7.89 tff(10124,plain,
% 7.58/7.89 (b(s(z), s(s(z)))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[1788, 10123])).
% 7.58/7.89 tff(10125,plain,
% 7.58/7.89 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[6275, 3823, 1234, 2439])).
% 7.58/7.89 tff(10126,plain,
% 7.58/7.89 (r(s(s(s(s(z)))), s(s(z)))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[1714, 10125])).
% 7.58/7.89 tff(10127,plain,
% 7.58/7.89 (~r(s(s(z)), s(z))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[2429, 10126, 723, 5238])).
% 7.58/7.89 tff(10128,plain,
% 7.58/7.89 (b(s(s(z)), s(z))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[3778, 10127])).
% 7.58/7.89 tff(10129,plain,
% 7.58/7.89 (~r(s(s(z)), s(z))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[2429, 5238, 1697, 723])).
% 7.58/7.89 tff(10130,plain,
% 7.58/7.89 (b(s(s(z)), s(z))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[3778, 10129])).
% 7.58/7.89 tff(10131,plain,
% 7.58/7.89 (~r(s(s(s(s(z)))), elem!1)),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[9117, 5238, 1748, 723])).
% 7.58/7.89 tff(10132,plain,
% 7.58/7.89 (b(s(s(s(s(z)))), elem!1)),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[762, 10131, 8917])).
% 7.58/7.89 tff(10133,plain,
% 7.58/7.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.89 inference(rewrite,[status(thm)],[])).
% 7.58/7.89 tff(10134,plain,
% 7.58/7.89 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.89 inference(rewrite,[status(thm)],[])).
% 7.58/7.89 tff(10135,plain,
% 7.58/7.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.58/7.89 inference(monotonicity,[status(thm)],[10134])).
% 7.58/7.89 tff(10136,plain,
% 7.58/7.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.58/7.89 inference(transitivity,[status(thm)],[10135, 10133])).
% 7.58/7.89 tff(10137,plain,
% 7.58/7.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 7.58/7.89 inference(quant_inst,[status(thm)],[])).
% 7.58/7.89 tff(10138,plain,
% 7.58/7.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.58/7.89 inference(modus_ponens,[status(thm)],[10137, 10136])).
% 7.58/7.89 tff(10139,plain,
% 7.58/7.89 ($false),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[10138, 391, 3823, 10132, 1234, 10130, 8918])).
% 7.58/7.89 tff(10140,plain,((s(z) = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(z)))) | r(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.58/7.89 tff(10141,plain,
% 7.58/7.89 (~r(elem!1, s(s(z)))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[10140, 10126, 1234, 150, 3823, 723, 832, 2829])).
% 7.58/7.89 tff(10142,plain,
% 7.58/7.89 (b(elem!1, s(s(z)))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[3394, 10141, 1405])).
% 7.58/7.89 tff(10143,plain,
% 7.58/7.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 7.58/7.89 inference(rewrite,[status(thm)],[])).
% 7.58/7.89 tff(10144,plain,
% 7.58/7.89 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 7.58/7.89 inference(rewrite,[status(thm)],[])).
% 7.58/7.89 tff(10145,plain,
% 7.58/7.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 7.58/7.89 inference(monotonicity,[status(thm)],[10144])).
% 7.58/7.89 tff(10146,plain,
% 7.58/7.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 7.58/7.89 inference(transitivity,[status(thm)],[10145, 10143])).
% 7.58/7.89 tff(10147,plain,
% 7.58/7.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 7.58/7.89 inference(quant_inst,[status(thm)],[])).
% 7.58/7.89 tff(10148,plain,
% 7.58/7.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 7.58/7.89 inference(modus_ponens,[status(thm)],[10147, 10146])).
% 7.58/7.89 tff(10149,plain,
% 7.58/7.89 ($false),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[10148, 391, 3369, 2439, 1233, 721])).
% 7.58/7.89 tff(10150,plain,((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.58/7.89 tff(10151,plain,
% 7.58/7.89 ($false),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[10150, 10142, 10128, 8918, 2439])).
% 7.58/7.89 tff(10152,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (elem!1 = s(s(z))) | (~b(s(z), s(s(s(s(z)))))) | (s(z) = elem!1) | (~r(s(s(s(s(z)))), s(z))) | r(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.58/7.89 tff(10153,plain,
% 7.58/7.89 (~b(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[10152, 10124, 10065, 1234, 150, 10060, 832, 2829])).
% 7.58/7.89 tff(10154,plain,
% 7.58/7.89 (r(s(s(z)), s(s(s(s(z)))))),
% 7.58/7.89 inference(unit_resolution,[status(thm)],[3652, 10153])).
% 7.58/7.89 tff(10155,plain,
% 7.58/7.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.58/7.89 inference(rewrite,[status(thm)],[])).
% 7.58/7.89 tff(10156,plain,
% 7.58/7.89 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.58/7.89 inference(rewrite,[status(thm)],[])).
% 7.58/7.89 tff(10157,plain,
% 7.58/7.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 7.58/7.89 inference(monotonicity,[status(thm)],[10156])).
% 7.58/7.89 tff(10158,plain,
% 7.69/7.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.69/7.90 inference(transitivity,[status(thm)],[10157, 10155])).
% 7.69/7.90 tff(10159,plain,
% 7.69/7.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 7.69/7.90 inference(quant_inst,[status(thm)],[])).
% 7.69/7.90 tff(10160,plain,
% 7.69/7.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 7.69/7.90 inference(modus_ponens,[status(thm)],[10159, 10158])).
% 7.69/7.90 tff(10161,plain,
% 7.69/7.90 (~r(z, s(s(z)))),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[10160, 194, 10154, 2053, 10058])).
% 7.69/7.90 tff(10162,plain,
% 7.69/7.90 (((~![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))))),
% 7.69/7.90 inference(rewrite,[status(thm)],[])).
% 7.69/7.90 tff(10163,plain,
% 7.69/7.90 ((~![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))))),
% 7.69/7.90 inference(quant_inst,[status(thm)],[])).
% 7.69/7.90 tff(10164,plain,
% 7.69/7.90 ((~![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)))),
% 7.69/7.90 inference(modus_ponens,[status(thm)],[10163, 10162])).
% 7.69/7.90 tff(10165,plain,
% 7.69/7.90 (b(z, s(s(z)))),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[10164, 42, 10161, 8912])).
% 7.69/7.90 tff(10166,plain,
% 7.69/7.90 (~r(s(s(z)), s(z))),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[9149, 10154, 5238, 10060])).
% 7.69/7.90 tff(10167,plain,
% 7.69/7.90 (b(s(s(z)), s(z))),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[3778, 10166])).
% 7.69/7.90 tff(10168,plain,
% 7.69/7.90 (~b(elem!1, s(s(z)))),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[10150, 10167, 8918, 10124])).
% 7.69/7.90 tff(10169,plain,
% 7.69/7.90 (r(elem!1, s(s(z)))),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[3394, 10168, 10065])).
% 7.69/7.90 tff(10170,plain,
% 7.69/7.90 (r(s(s(s(elem!1))), s(s(z)))),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[10022, 10169, 9966])).
% 7.69/7.90 tff(10171,plain,
% 7.69/7.90 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 7.69/7.90 inference(monotonicity,[status(thm)],[9966])).
% 7.69/7.90 tff(10172,plain,
% 7.69/7.90 (r(s(z), s(s(s(elem!1))))),
% 7.69/7.90 inference(modus_ponens,[status(thm)],[5238, 10171])).
% 7.69/7.90 tff(10173,plain,
% 7.69/7.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.69/7.90 inference(rewrite,[status(thm)],[])).
% 7.69/7.90 tff(10174,plain,
% 7.69/7.90 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.69/7.90 inference(rewrite,[status(thm)],[])).
% 7.69/7.90 tff(10175,plain,
% 7.69/7.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 7.69/7.90 inference(monotonicity,[status(thm)],[10174])).
% 7.69/7.90 tff(10176,plain,
% 7.69/7.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.69/7.90 inference(transitivity,[status(thm)],[10175, 10173])).
% 7.69/7.90 tff(10177,plain,
% 7.69/7.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 7.69/7.90 inference(quant_inst,[status(thm)],[])).
% 7.69/7.90 tff(10178,plain,
% 7.69/7.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 7.69/7.90 inference(modus_ponens,[status(thm)],[10177, 10176])).
% 7.69/7.90 tff(10179,plain,
% 7.69/7.90 (~r(z, s(z))),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[10178, 194, 59, 10172, 10170])).
% 7.69/7.90 tff(10180,plain,
% 7.69/7.90 (b(z, s(z))),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[678, 10179])).
% 7.69/7.90 tff(10181,plain,
% 7.69/7.90 (~r(s(s(z)), z)),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[5608, 194, 10154, 2053, 10058])).
% 7.69/7.90 tff(10182,plain,
% 7.69/7.90 (b(s(s(z)), z)),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[1211, 10181])).
% 7.69/7.90 tff(10183,plain,
% 7.69/7.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 7.69/7.90 inference(rewrite,[status(thm)],[])).
% 7.69/7.90 tff(10184,plain,
% 7.69/7.90 (((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 7.69/7.90 inference(rewrite,[status(thm)],[])).
% 7.69/7.90 tff(10185,plain,
% 7.69/7.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 7.69/7.90 inference(monotonicity,[status(thm)],[10184])).
% 7.69/7.90 tff(10186,plain,
% 7.69/7.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 7.69/7.90 inference(transitivity,[status(thm)],[10185, 10183])).
% 7.69/7.90 tff(10187,plain,
% 7.69/7.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 7.69/7.90 inference(quant_inst,[status(thm)],[])).
% 7.69/7.90 tff(10188,plain,
% 7.69/7.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 7.69/7.90 inference(modus_ponens,[status(thm)],[10187, 10186])).
% 7.69/7.90 tff(10189,plain,
% 7.69/7.90 ($false),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[10188, 391, 10182, 10124, 10180, 10165])).
% 7.69/7.90 tff(10190,plain,((s(z) = elem!1) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | r(elem!1, s(z)) | b(s(z), elem!1) | (~r(z, elem!1)) | b(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.90 tff(10191,plain,
% 7.69/7.90 (s(z) = elem!1),
% 7.69/7.90 inference(unit_resolution,[status(thm)],[10190, 832, 1234, 3447, 2829, 8908, 10, 8814])).
% 7.69/7.91 tff(10192,plain,
% 7.69/7.91 (s(s(z)) = s(elem!1)),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10191])).
% 7.69/7.91 tff(10193,plain,
% 7.69/7.91 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10192])).
% 7.69/7.91 tff(10194,plain,
% 7.69/7.91 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10191])).
% 7.69/7.91 tff(10195,plain,
% 7.69/7.91 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 7.69/7.91 inference(transitivity,[status(thm)],[10194, 10193])).
% 7.69/7.91 tff(10196,plain,
% 7.69/7.91 (s(s(s(z))) = s(s(elem!1))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10192])).
% 7.69/7.91 tff(10197,plain,
% 7.69/7.91 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10196])).
% 7.69/7.91 tff(10198,plain,
% 7.69/7.91 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(elem!1))))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10197])).
% 7.69/7.91 tff(10199,plain,
% 7.69/7.91 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 7.69/7.91 inference(symmetry,[status(thm)],[10198])).
% 7.69/7.91 tff(10200,plain,
% 7.69/7.91 (r(z, s(s(s(s(z)))))),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[59, 10199])).
% 7.69/7.91 tff(10201,plain,
% 7.69/7.91 (~r(s(z), s(s(z)))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[10122, 10200, 832, 3447, 10, 1234, 2829, 8814])).
% 7.69/7.91 tff(10202,plain,
% 7.69/7.91 (b(s(z), s(s(z)))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[1788, 10201])).
% 7.69/7.91 tff(10203,plain,
% 7.69/7.91 (b(elem!1, s(elem!1))),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[10202, 10195])).
% 7.69/7.91 tff(10204,plain,
% 7.69/7.91 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10191])).
% 7.69/7.91 tff(10205,plain,
% 7.69/7.91 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10204])).
% 7.69/7.91 tff(10206,plain,
% 7.69/7.91 (~r(s(s(s(elem!1))), elem!1)),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[8814, 10205])).
% 7.69/7.91 tff(10207,plain,
% 7.69/7.91 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10197])).
% 7.69/7.91 tff(10208,plain,
% 7.69/7.91 (b(elem!1, s(s(s(s(z)))))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[8539, 10191, 1234])).
% 7.69/7.91 tff(10209,plain,
% 7.69/7.91 (b(elem!1, s(s(s(elem!1))))),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[10208, 10207])).
% 7.69/7.91 tff(10210,plain,
% 7.69/7.91 (b(elem!1, s(s(z)))),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[10202, 10194])).
% 7.69/7.91 tff(10211,plain,
% 7.69/7.91 (~b(s(s(z)), s(s(s(elem!1))))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[8561, 10210, 8815, 1234, 10209])).
% 7.69/7.91 tff(10212,plain,
% 7.69/7.91 (~b(s(s(z)), s(s(s(s(z)))))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[8551, 10211, 10191])).
% 7.69/7.91 tff(10213,plain,
% 7.69/7.91 (r(s(s(z)), s(s(s(s(z)))))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[3652, 10212])).
% 7.69/7.91 tff(10214,plain,
% 7.69/7.91 (r(s(elem!1), s(s(s(elem!1))))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[3614, 10213, 10191])).
% 7.69/7.91 tff(10215,plain,
% 7.69/7.91 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10192])).
% 7.69/7.91 tff(10216,plain,
% 7.69/7.91 (r(z, s(z)) <=> r(z, elem!1)),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10191])).
% 7.69/7.91 tff(10217,plain,
% 7.69/7.91 (r(z, elem!1) <=> r(z, s(z))),
% 7.69/7.91 inference(symmetry,[status(thm)],[10216])).
% 7.69/7.91 tff(10218,plain,
% 7.69/7.91 (r(z, s(z))),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[8908, 10217])).
% 7.69/7.91 tff(10219,plain,
% 7.69/7.91 (~r(s(s(z)), z)),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[9635, 10213, 3447, 10218])).
% 7.69/7.91 tff(10220,plain,
% 7.69/7.91 (b(s(s(z)), z)),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[1211, 10219])).
% 7.69/7.91 tff(10221,plain,
% 7.69/7.91 (b(s(elem!1), z)),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[10220, 10215])).
% 7.69/7.91 tff(10222,plain,
% 7.69/7.91 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10197])).
% 7.69/7.91 tff(10223,plain,
% 7.69/7.91 (r(s(s(s(elem!1))), z)),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[3447, 10222])).
% 7.69/7.91 tff(10224,plain,
% 7.69/7.91 (~r(z, s(elem!1))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[9627, 194, 10223, 59, 10214])).
% 7.69/7.91 tff(10225,plain,
% 7.69/7.91 (b(z, s(elem!1))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[566, 10224])).
% 7.69/7.91 tff(10226,plain,
% 7.69/7.91 (~b(elem!1, z)),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[1939, 10225, 10221, 10203])).
% 7.69/7.91 tff(10227,plain,
% 7.69/7.91 (r(s(z), z)),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[7485, 10226, 10191])).
% 7.69/7.91 tff(10228,plain,
% 7.69/7.91 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[2711, 7435])).
% 7.69/7.91 tff(10229,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.91 inference(rewrite,[status(thm)],[])).
% 7.69/7.91 tff(10230,plain,
% 7.69/7.91 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.91 inference(rewrite,[status(thm)],[])).
% 7.69/7.91 tff(10231,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10230])).
% 7.69/7.91 tff(10232,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.91 inference(transitivity,[status(thm)],[10231, 10229])).
% 7.69/7.91 tff(10233,plain,
% 7.69/7.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 7.69/7.91 inference(quant_inst,[status(thm)],[])).
% 7.69/7.91 tff(10234,plain,
% 7.69/7.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[10233, 10232])).
% 7.69/7.91 tff(10235,plain,
% 7.69/7.91 (~r(s(z), s(s(s(s(z)))))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[10234, 194, 182, 2053, 719])).
% 7.69/7.91 tff(10236,plain,
% 7.69/7.91 (b(s(z), s(s(s(s(z)))))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[1230, 10235])).
% 7.69/7.91 tff(10237,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.91 inference(rewrite,[status(thm)],[])).
% 7.69/7.91 tff(10238,plain,
% 7.69/7.91 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.91 inference(rewrite,[status(thm)],[])).
% 7.69/7.91 tff(10239,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10238])).
% 7.69/7.91 tff(10240,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.91 inference(transitivity,[status(thm)],[10239, 10237])).
% 7.69/7.91 tff(10241,plain,
% 7.69/7.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 7.69/7.91 inference(quant_inst,[status(thm)],[])).
% 7.69/7.91 tff(10242,plain,
% 7.69/7.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[10241, 10240])).
% 7.69/7.91 tff(10243,plain,
% 7.69/7.91 (~r(s(s(s(s(z)))), s(z))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[10242, 194, 182, 2053, 719])).
% 7.69/7.91 tff(10244,plain,
% 7.69/7.91 (b(s(s(s(s(z)))), s(z))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[749, 10243])).
% 7.69/7.91 tff(10245,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 7.69/7.91 inference(rewrite,[status(thm)],[])).
% 7.69/7.91 tff(10246,plain,
% 7.69/7.91 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 7.69/7.91 inference(rewrite,[status(thm)],[])).
% 7.69/7.91 tff(10247,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10246])).
% 7.69/7.91 tff(10248,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 7.69/7.91 inference(transitivity,[status(thm)],[10247, 10245])).
% 7.69/7.91 tff(10249,plain,
% 7.69/7.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 7.69/7.91 inference(quant_inst,[status(thm)],[])).
% 7.69/7.91 tff(10250,plain,
% 7.69/7.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 7.69/7.91 inference(modus_ponens,[status(thm)],[10249, 10248])).
% 7.69/7.91 tff(10251,plain,
% 7.69/7.91 (~r(s(s(z)), s(z))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[10250, 194, 182, 3557, 719])).
% 7.69/7.91 tff(10252,plain,
% 7.69/7.91 (b(s(s(z)), s(z))),
% 7.69/7.91 inference(unit_resolution,[status(thm)],[3778, 10251])).
% 7.69/7.91 tff(10253,plain,
% 7.69/7.91 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.69/7.91 inference(rewrite,[status(thm)],[])).
% 7.69/7.91 tff(10254,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 7.69/7.91 inference(monotonicity,[status(thm)],[10253])).
% 7.69/7.91 tff(10255,plain,
% 7.69/7.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.69/7.92 inference(transitivity,[status(thm)],[10254, 5603])).
% 7.69/7.92 tff(10256,plain,
% 7.69/7.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.69/7.92 inference(quant_inst,[status(thm)],[])).
% 7.69/7.92 tff(10257,plain,
% 7.69/7.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 7.69/7.92 inference(modus_ponens,[status(thm)],[10256, 10255])).
% 7.69/7.92 tff(10258,plain,
% 7.69/7.92 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.69/7.92 inference(unit_resolution,[status(thm)],[10257, 194, 2053, 3557, 719])).
% 7.69/7.92 tff(10259,plain,
% 7.69/7.92 (b(s(s(z)), s(s(s(s(z)))))),
% 7.69/7.92 inference(unit_resolution,[status(thm)],[3652, 10258])).
% 7.69/7.92 tff(10260,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[5108, 10259, 10252, 10244, 10236])).
% 7.69/7.92 tff(10261,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.92 tff(10262,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[10261, 182, 2053, 827])).
% 7.69/7.92 tff(10263,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[1211, 10262])).
% 7.69/7.92 tff(10264,plain,
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% 7.69/7.92 inference(modus_ponens,[status(thm)],[10263, 9630])).
% 7.69/7.92 tff(10265,plain,
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% 7.69/7.92 inference(transitivity,[status(thm)],[7475, 93])).
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% 7.69/7.92 inference(monotonicity,[status(thm)],[10265])).
% 7.69/7.92 tff(10267,plain,
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% 7.69/7.92 inference(modus_ponens,[status(thm)],[23, 10266])).
% 7.69/7.92 tff(10268,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[9627, 194, 9621, 184, 604])).
% 7.69/7.92 tff(10269,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[566, 10268])).
% 7.69/7.92 tff(10270,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[1939, 10269, 10264, 802])).
% 7.69/7.92 tff(10271,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[526, 10270, 10267])).
% 7.69/7.92 tff(10272,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[9929, 10271, 184, 812, 411, 225, 3927, 10264, 2053, 827, 1526, 1234])).
% 7.69/7.92 tff(10273,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[362, 10272])).
% 7.69/7.92 tff(10274,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[4103, 10273, 182, 815])).
% 7.69/7.92 tff(10275,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[2629, 10274])).
% 7.69/7.92 tff(10276,plain,
% 7.69/7.92 (~b(s(s(elem!1)), s(elem!1))),
% 7.69/7.92 inference(unit_resolution,[status(thm)],[9680, 391, 3927, 10264, 10275])).
% 7.69/7.92 tff(10277,plain,
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% 7.69/7.92 tff(10278,plain,
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% 7.69/7.92 tff(10279,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[8962, 10278, 1526, 1234, 9616])).
% 7.69/7.92 tff(10280,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[8400, 10279, 1526])).
% 7.69/7.92 tff(10281,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[158, 10280])).
% 7.69/7.92 tff(10282,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[2220, 10273, 812])).
% 7.69/7.92 tff(10283,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[7930, 10277, 10271, 10282])).
% 7.69/7.92 tff(10284,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[2168, 10283, 10281])).
% 7.69/7.92 tff(10285,plain,
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% 7.69/7.92 inference(unit_resolution,[status(thm)],[6869, 10284, 9816, 9616])).
% 7.69/7.92 tff(10286,plain,
% 7.69/7.92 (r(s(s(s(elem!1))), s(elem!1))),
% 7.69/7.92 inference(unit_resolution,[status(thm)],[588, 10285, 7433])).
% 7.69/7.92 tff(10287,plain,
% 7.69/7.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.69/7.92 inference(rewrite,[status(thm)],[])).
% 7.69/7.92 tff(10288,plain,
% 7.69/7.92 (((~r(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)))))) <=> ((~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))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.69/7.92 inference(rewrite,[status(thm)],[])).
% 7.69/7.92 tff(10289,plain,
% 7.69/7.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 7.69/7.92 inference(monotonicity,[status(thm)],[10288])).
% 7.69/7.92 tff(10290,plain,
% 7.69/7.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 7.69/7.92 inference(transitivity,[status(thm)],[10289, 10287])).
% 7.69/7.92 tff(10291,plain,
% 7.69/7.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))),
% 7.69/7.92 inference(quant_inst,[status(thm)],[])).
% 7.69/7.92 tff(10292,plain,
% 7.69/7.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 7.69/7.92 inference(modus_ponens,[status(thm)],[10291, 10290])).
% 7.69/7.92 tff(10293,plain,
% 7.69/7.92 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.69/7.92 inference(unit_resolution,[status(thm)],[10292, 194, 10286, 604, 10277])).
% 7.69/7.92 tff(10294,plain,
% 7.69/7.92 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.69/7.92 inference(unit_resolution,[status(thm)],[1356, 10293, 7434])).
% 7.69/7.92 tff(10295,plain,
% 7.69/7.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 7.69/7.92 inference(rewrite,[status(thm)],[])).
% 7.69/7.92 tff(10296,plain,
% 7.69/7.92 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 7.69/7.92 inference(rewrite,[status(thm)],[])).
% 7.69/7.92 tff(10297,plain,
% 7.69/7.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))))),
% 7.69/7.92 inference(monotonicity,[status(thm)],[10296])).
% 7.69/7.92 tff(10298,plain,
% 7.69/7.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 7.69/7.92 inference(transitivity,[status(thm)],[10297, 10295])).
% 7.69/7.92 tff(10299,plain,
% 7.69/7.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 7.69/7.92 inference(quant_inst,[status(thm)],[])).
% 7.69/7.92 tff(10300,plain,
% 7.69/7.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))),
% 7.69/7.92 inference(modus_ponens,[status(thm)],[10299, 10298])).
% 7.69/7.92 tff(10301,plain,
% 7.69/7.92 (~b(elem!1, s(s(elem!1)))),
% 7.69/7.92 inference(unit_resolution,[status(thm)],[10300, 391, 9616, 9816, 10294])).
% 7.69/7.92 tff(10302,plain,
% 7.69/7.92 (r(elem!1, s(s(elem!1)))),
% 7.69/7.92 inference(unit_resolution,[status(thm)],[1307, 10301, 9651])).
% 7.69/7.92 tff(10303,plain,
% 7.69/7.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 7.69/7.92 inference(rewrite,[status(thm)],[])).
% 7.69/7.92 tff(10304,plain,
% 7.69/7.92 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 7.69/7.92 inference(rewrite,[status(thm)],[])).
% 7.69/7.92 tff(10305,plain,
% 7.69/7.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 7.69/7.92 inference(monotonicity,[status(thm)],[10304])).
% 7.69/7.92 tff(10306,plain,
% 7.69/7.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 7.69/7.92 inference(transitivity,[status(thm)],[10305, 10303])).
% 7.69/7.92 tff(10307,plain,
% 7.69/7.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 7.69/7.93 inference(quant_inst,[status(thm)],[])).
% 7.69/7.93 tff(10308,plain,
% 7.69/7.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 7.69/7.93 inference(modus_ponens,[status(thm)],[10307, 10306])).
% 7.69/7.93 tff(10309,plain,
% 7.69/7.93 (~b(s(elem!1), s(s(elem!1)))),
% 7.69/7.93 inference(unit_resolution,[status(thm)],[10308, 391, 3927, 10264, 10275])).
% 7.69/7.93 tff(10310,plain,
% 7.69/7.93 (r(s(elem!1), s(s(elem!1)))),
% 7.69/7.93 inference(unit_resolution,[status(thm)],[8644, 10309, 9803])).
% 7.69/7.93 tff(10311,plain,
% 7.69/7.93 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 7.69/7.93 inference(unit_resolution,[status(thm)],[929, 10280])).
% 7.69/7.93 tff(10312,plain,
% 7.69/7.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.69/7.93 inference(rewrite,[status(thm)],[])).
% 7.69/7.93 tff(10313,plain,
% 7.69/7.93 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.69/7.93 inference(rewrite,[status(thm)],[])).
% 7.69/7.93 tff(10314,plain,
% 7.69/7.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 7.69/7.93 inference(monotonicity,[status(thm)],[10313])).
% 7.69/7.93 tff(10315,plain,
% 7.69/7.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.69/7.93 inference(transitivity,[status(thm)],[10314, 10312])).
% 7.69/7.93 tff(10316,plain,
% 7.69/7.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.69/7.93 inference(quant_inst,[status(thm)],[])).
% 7.69/7.93 tff(10317,plain,
% 7.69/7.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 7.69/7.93 inference(modus_ponens,[status(thm)],[10316, 10315])).
% 7.69/7.93 tff(10318,plain,
% 7.69/7.93 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 7.69/7.93 inference(unit_resolution,[status(thm)],[10317, 194, 364, 1177, 7538])).
% 7.69/7.93 tff(10319,plain,
% 7.69/7.93 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 7.69/7.93 inference(unit_resolution,[status(thm)],[988, 10318, 957])).
% 7.69/7.93 tff(10320,plain,
% 7.69/7.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 7.69/7.93 inference(rewrite,[status(thm)],[])).
% 7.69/7.93 tff(10321,plain,
% 7.69/7.93 (((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 7.69/7.93 inference(rewrite,[status(thm)],[])).
% 7.69/7.93 tff(10322,plain,
% 7.69/7.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 7.69/7.93 inference(monotonicity,[status(thm)],[10321])).
% 7.69/7.93 tff(10323,plain,
% 7.69/7.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 7.69/7.93 inference(transitivity,[status(thm)],[10322, 10320])).
% 7.69/7.93 tff(10324,plain,
% 7.69/7.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 7.69/7.93 inference(quant_inst,[status(thm)],[])).
% 7.69/7.93 tff(10325,plain,
% 7.69/7.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 7.69/7.93 inference(modus_ponens,[status(thm)],[10324, 10323])).
% 7.69/7.93 tff(10326,plain,
% 7.69/7.93 (~r(s(s(s(s(elem!1)))), elem!1)),
% 7.69/7.93 inference(unit_resolution,[status(thm)],[10325, 194, 364, 1064, 1177])).
% 7.69/7.93 tff(10327,plain,
% 7.69/7.93 (b(s(s(s(s(elem!1)))), elem!1)),
% 7.69/7.93 inference(unit_resolution,[status(thm)],[1004, 10326, 972])).
% 7.69/7.93 tff(10328,plain,
% 7.69/7.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.69/7.93 inference(rewrite,[status(thm)],[])).
% 7.69/7.93 tff(10329,plain,
% 7.69/7.93 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.69/7.93 inference(rewrite,[status(thm)],[])).
% 7.69/7.93 tff(10330,plain,
% 7.69/7.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 7.69/7.94 inference(monotonicity,[status(thm)],[10329])).
% 7.69/7.94 tff(10331,plain,
% 7.69/7.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 7.69/7.94 inference(transitivity,[status(thm)],[10330, 10328])).
% 7.69/7.94 tff(10332,plain,
% 7.69/7.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 7.69/7.94 inference(quant_inst,[status(thm)],[])).
% 7.69/7.94 tff(10333,plain,
% 7.69/7.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 7.69/7.94 inference(modus_ponens,[status(thm)],[10332, 10331])).
% 7.69/7.94 tff(10334,plain,
% 7.69/7.94 ($false),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[10333, 391, 900, 448, 2122, 10327, 10319])).
% 7.69/7.94 tff(10335,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.94 tff(10336,plain,
% 7.69/7.94 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[10335, 10284, 9816, 9616, 10311, 7473, 10282, 10310, 10302])).
% 7.69/7.94 tff(10337,plain,
% 7.69/7.94 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[1061, 10336, 10228])).
% 7.69/7.94 tff(10338,plain,
% 7.69/7.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 7.69/7.94 inference(rewrite,[status(thm)],[])).
% 7.69/7.94 tff(10339,plain,
% 7.69/7.94 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 7.69/7.94 inference(rewrite,[status(thm)],[])).
% 7.69/7.94 tff(10340,plain,
% 7.69/7.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))))),
% 7.69/7.94 inference(monotonicity,[status(thm)],[10339])).
% 7.69/7.94 tff(10341,plain,
% 7.69/7.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 7.69/7.94 inference(transitivity,[status(thm)],[10340, 10338])).
% 7.69/7.94 tff(10342,plain,
% 7.69/7.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 7.69/7.94 inference(quant_inst,[status(thm)],[])).
% 7.69/7.94 tff(10343,plain,
% 7.69/7.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))),
% 7.69/7.94 inference(modus_ponens,[status(thm)],[10342, 10341])).
% 7.69/7.94 tff(10344,plain,
% 7.69/7.94 (~b(s(s(s(s(elem!1)))), z)),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[10343, 391, 3927, 10275, 10337])).
% 7.69/7.94 tff(10345,plain,
% 7.69/7.94 (r(s(s(s(s(elem!1)))), z)),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[1626, 10344])).
% 7.69/7.94 tff(10346,plain,
% 7.69/7.94 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[299, 9609])).
% 7.69/7.94 tff(10347,plain,
% 7.69/7.94 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[8653, 10310, 604, 10277])).
% 7.69/7.94 tff(10348,plain,
% 7.69/7.94 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[1370, 10347, 9609])).
% 7.69/7.94 tff(10349,plain,
% 7.69/7.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.69/7.94 inference(rewrite,[status(thm)],[])).
% 7.69/7.94 tff(10350,plain,
% 7.69/7.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.69/7.94 inference(quant_inst,[status(thm)],[])).
% 7.69/7.94 tff(10351,plain,
% 7.69/7.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 7.69/7.94 inference(modus_ponens,[status(thm)],[10350, 10349])).
% 7.69/7.94 tff(10352,plain,
% 7.69/7.94 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[10351, 391, 10348, 3927, 10275, 10337])).
% 7.69/7.94 tff(10353,plain,
% 7.69/7.94 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[1095, 10352, 10346])).
% 7.69/7.94 tff(10354,plain,
% 7.69/7.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.69/7.94 inference(rewrite,[status(thm)],[])).
% 7.69/7.94 tff(10355,plain,
% 7.69/7.94 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.69/7.94 inference(rewrite,[status(thm)],[])).
% 7.69/7.94 tff(10356,plain,
% 7.69/7.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 7.69/7.94 inference(monotonicity,[status(thm)],[10355])).
% 7.69/7.94 tff(10357,plain,
% 7.69/7.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 7.69/7.94 inference(transitivity,[status(thm)],[10356, 10354])).
% 7.69/7.94 tff(10358,plain,
% 7.69/7.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 7.69/7.94 inference(quant_inst,[status(thm)],[])).
% 7.69/7.94 tff(10359,plain,
% 7.69/7.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 7.69/7.94 inference(modus_ponens,[status(thm)],[10358, 10357])).
% 7.69/7.94 tff(10360,plain,
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% 7.69/7.94 inference(unit_resolution,[status(thm)],[10359, 194, 10286, 184, 10353, 10345])).
% 7.69/7.94 tff(10361,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(z), z)) | (~r(z, elem!1)) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.94 tff(10362,plain,
% 7.69/7.94 (~b(z, s(s(elem!1)))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[10361, 10227, 59, 10191, 10214, 8908, 10206, 3447, 8815, 1234, 10203])).
% 7.69/7.94 tff(10363,plain,
% 7.69/7.94 (r(z, s(s(elem!1)))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[324, 10362])).
% 7.69/7.94 tff(10364,plain,
% 7.69/7.94 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 7.69/7.94 inference(monotonicity,[status(thm)],[10191])).
% 7.69/7.94 tff(10365,plain,
% 7.69/7.94 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 7.69/7.94 inference(symmetry,[status(thm)],[10364])).
% 7.69/7.94 tff(10366,plain,
% 7.69/7.94 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(elem!1))))),
% 7.69/7.94 inference(transitivity,[status(thm)],[10207, 10365])).
% 7.69/7.94 tff(10367,plain,
% 7.69/7.94 (b(s(z), s(s(s(elem!1))))),
% 7.69/7.94 inference(modus_ponens,[status(thm)],[10208, 10366])).
% 7.69/7.94 tff(10368,plain,
% 7.69/7.94 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 7.69/7.94 inference(monotonicity,[status(thm)],[10197])).
% 7.69/7.94 tff(10369,plain,
% 7.69/7.94 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.69/7.94 inference(symmetry,[status(thm)],[10368])).
% 7.69/7.94 tff(10370,plain,
% 7.69/7.94 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.69/7.94 inference(monotonicity,[status(thm)],[10369])).
% 7.69/7.94 tff(10371,plain,
% 7.69/7.94 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.69/7.94 inference(modus_ponens,[status(thm)],[463, 10370])).
% 7.69/7.94 tff(10372,plain,
% 7.69/7.94 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[9608, 10371, 10208])).
% 7.69/7.94 tff(10373,plain,
% 7.69/7.94 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[1365, 10363, 10, 10227, 10372])).
% 7.69/7.94 tff(10374,plain,
% 7.69/7.94 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.69/7.94 inference(unit_resolution,[status(thm)],[1370, 10373, 10372])).
% 7.69/7.94 tff(10375,plain,
% 7.69/7.94 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 7.69/7.95 inference(monotonicity,[status(thm)],[10192])).
% 7.69/7.95 tff(10376,plain,
% 7.69/7.95 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 7.69/7.95 inference(transitivity,[status(thm)],[10375, 582])).
% 7.69/7.95 tff(10377,plain,
% 7.69/7.95 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 7.69/7.95 inference(monotonicity,[status(thm)],[10376])).
% 7.69/7.95 tff(10378,plain,
% 7.69/7.95 (~(s(s(s(elem!1))) = s(elem!1))),
% 7.69/7.95 inference(modus_ponens,[status(thm)],[1397, 10377])).
% 7.69/7.95 tff(10379,plain,
% 7.69/7.95 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[281, 10378])).
% 7.69/7.95 tff(10380,plain,
% 7.69/7.95 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[1450, 10363, 59, 10223])).
% 7.69/7.95 tff(10381,plain,
% 7.69/7.95 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[1356, 10380, 10379])).
% 7.69/7.95 tff(10382,plain,
% 7.69/7.95 ($false),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[3432, 10381, 10374, 10227, 10367, 10363])).
% 7.69/7.95 tff(10383,plain,(r(elem!1, s(z)) | b(z, s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | b(s(z), elem!1) | r(s(s(s(elem!1))), s(z)) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 7.69/7.95 tff(10384,plain,
% 7.69/7.95 (b(s(s(s(s(z)))), z)),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[10383, 8813, 8806, 10, 8792, 8233])).
% 7.69/7.95 tff(10385,plain,
% 7.69/7.95 ($false),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[10384, 8789])).
% 7.69/7.95 tff(10386,plain,(b(elem!1, z) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, s(z)) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 7.69/7.95 tff(10387,plain,
% 7.69/7.95 (b(elem!1, z)),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[10386, 91, 2, 31, 10])).
% 7.69/7.95 tff(10388,plain,
% 7.69/7.95 (b(s(z), z)),
% 7.69/7.95 inference(modus_ponens,[status(thm)],[665, 7415])).
% 7.69/7.95 tff(10389,plain,
% 7.69/7.95 ($false),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[91, 10388])).
% 7.69/7.95 tff(10390,plain,((~(s(z) = elem!1)) | b(s(z), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.95 tff(10391,plain,
% 7.69/7.95 (~(s(z) = elem!1)),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[10390, 91, 10387])).
% 7.69/7.95 tff(10392,plain,
% 7.69/7.95 (~(elem!1 = s(z))),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[172, 10391])).
% 7.69/7.95 tff(10393,plain,
% 7.69/7.95 (r(elem!1, s(z))),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[837, 10392, 31])).
% 7.69/7.95 tff(10394,plain,
% 7.69/7.95 (b(z, s(z))),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[678, 846])).
% 7.69/7.95 tff(10395,plain,
% 7.69/7.95 (~r(s(s(s(s(z)))), z)),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[2061, 2913, 182, 411])).
% 7.69/7.95 tff(10396,plain,
% 7.69/7.95 (b(s(s(s(s(z)))), z)),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[87, 10395])).
% 7.69/7.95 tff(10397,plain,
% 7.69/7.95 (~r(s(z), elem!1)),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[2475, 838, 411, 182])).
% 7.69/7.95 tff(10398,plain,
% 7.69/7.95 (b(s(z), elem!1)),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[632, 10397, 150])).
% 7.69/7.95 tff(10399,plain,
% 7.69/7.95 (~(s(s(s(s(z)))) = elem!1)),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[6252, 10398, 2881])).
% 7.69/7.95 tff(10400,plain,
% 7.69/7.95 (~(elem!1 = s(s(s(s(z)))))),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[769, 10399])).
% 7.69/7.95 tff(10401,plain,
% 7.69/7.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 7.69/7.95 inference(rewrite,[status(thm)],[])).
% 7.69/7.95 tff(10402,plain,
% 7.69/7.95 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 7.69/7.95 inference(rewrite,[status(thm)],[])).
% 7.69/7.95 tff(10403,plain,
% 7.69/7.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 7.69/7.95 inference(monotonicity,[status(thm)],[10402])).
% 7.69/7.95 tff(10404,plain,
% 7.69/7.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 7.69/7.95 inference(transitivity,[status(thm)],[10403, 10401])).
% 7.69/7.95 tff(10405,plain,
% 7.69/7.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 7.69/7.95 inference(quant_inst,[status(thm)],[])).
% 7.69/7.95 tff(10406,plain,
% 7.69/7.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 7.69/7.95 inference(modus_ponens,[status(thm)],[10405, 10404])).
% 7.69/7.95 tff(10407,plain,
% 7.69/7.95 ($false),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[10406, 194, 411, 847, 2053, 2112])).
% 7.69/7.95 tff(10408,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.95 tff(10409,plain,
% 7.69/7.95 (~r(s(s(s(s(z)))), z)),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[10408, 2112, 847, 411])).
% 7.69/7.95 tff(10410,plain,
% 7.69/7.95 (b(s(s(s(s(z)))), z)),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[87, 10409])).
% 7.69/7.95 tff(10411,plain,
% 7.69/7.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.95 inference(rewrite,[status(thm)],[])).
% 7.69/7.95 tff(10412,plain,
% 7.69/7.95 (((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.95 inference(rewrite,[status(thm)],[])).
% 7.69/7.95 tff(10413,plain,
% 7.69/7.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))))),
% 7.69/7.95 inference(monotonicity,[status(thm)],[10412])).
% 7.69/7.95 tff(10414,plain,
% 7.69/7.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.95 inference(transitivity,[status(thm)],[10413, 10411])).
% 7.69/7.95 tff(10415,plain,
% 7.69/7.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.95 inference(quant_inst,[status(thm)],[])).
% 7.69/7.95 tff(10416,plain,
% 7.69/7.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))),
% 7.69/7.95 inference(modus_ponens,[status(thm)],[10415, 10414])).
% 7.69/7.95 tff(10417,plain,
% 7.69/7.95 ($false),
% 7.69/7.95 inference(unit_resolution,[status(thm)],[10416, 194, 411, 847, 2112, 719])).
% 7.69/7.95 tff(10418,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.95 tff(10419,plain,
% 7.69/7.96 (~r(z, s(s(s(s(z)))))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[10418, 2112, 847, 411])).
% 7.69/7.96 tff(10420,plain,
% 7.69/7.96 (b(z, s(s(s(s(z)))))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[800, 10419])).
% 7.69/7.96 tff(10421,plain,
% 7.69/7.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.96 inference(rewrite,[status(thm)],[])).
% 7.69/7.96 tff(10422,plain,
% 7.69/7.96 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.96 inference(rewrite,[status(thm)],[])).
% 7.69/7.96 tff(10423,plain,
% 7.69/7.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.69/7.96 inference(monotonicity,[status(thm)],[10422])).
% 7.69/7.96 tff(10424,plain,
% 7.69/7.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.96 inference(transitivity,[status(thm)],[10423, 10421])).
% 7.69/7.96 tff(10425,plain,
% 7.69/7.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 7.69/7.96 inference(quant_inst,[status(thm)],[])).
% 7.69/7.96 tff(10426,plain,
% 7.69/7.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 7.69/7.96 inference(modus_ponens,[status(thm)],[10425, 10424])).
% 7.69/7.96 tff(10427,plain,
% 7.69/7.96 (~b(z, s(z))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[10426, 391, 90, 1234, 1686])).
% 7.69/7.96 tff(10428,plain,
% 7.69/7.96 (r(z, s(z))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[678, 10427])).
% 7.69/7.96 tff(10429,plain,
% 7.69/7.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.96 inference(rewrite,[status(thm)],[])).
% 7.69/7.96 tff(10430,plain,
% 7.69/7.96 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.96 inference(rewrite,[status(thm)],[])).
% 7.69/7.96 tff(10431,plain,
% 7.69/7.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.69/7.96 inference(monotonicity,[status(thm)],[10430])).
% 7.69/7.96 tff(10432,plain,
% 7.69/7.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.96 inference(transitivity,[status(thm)],[10431, 10429])).
% 7.69/7.96 tff(10433,plain,
% 7.69/7.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 7.69/7.96 inference(quant_inst,[status(thm)],[])).
% 7.69/7.96 tff(10434,plain,
% 7.69/7.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 7.69/7.96 inference(modus_ponens,[status(thm)],[10433, 10432])).
% 7.69/7.96 tff(10435,plain,
% 7.69/7.96 (~b(s(z), z)),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[10434, 391, 90, 1234, 1686])).
% 7.69/7.96 tff(10436,plain,
% 7.69/7.96 (r(s(z), z)),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[180, 10435])).
% 7.69/7.96 tff(10437,plain,
% 7.69/7.96 ($false),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[845, 10436, 10428, 847, 411])).
% 7.69/7.96 tff(10438,plain,((~b(z, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.96 tff(10439,plain,
% 7.69/7.96 (~b(s(z), s(s(s(s(z)))))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[10438, 10420, 411, 847, 10410])).
% 7.69/7.96 tff(10440,plain,
% 7.69/7.96 (r(s(z), s(s(s(s(z)))))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[1230, 10439])).
% 7.69/7.96 tff(10441,plain,
% 7.69/7.96 (~b(elem!1, s(s(s(s(z)))))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[3234, 10420, 665, 10410])).
% 7.69/7.96 tff(10442,plain,
% 7.69/7.96 (r(elem!1, s(s(s(s(z)))))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[781, 10441, 8922])).
% 7.69/7.96 tff(10443,plain,
% 7.69/7.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.69/7.96 inference(rewrite,[status(thm)],[])).
% 7.69/7.96 tff(10444,plain,
% 7.69/7.96 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.69/7.96 inference(rewrite,[status(thm)],[])).
% 7.69/7.96 tff(10445,plain,
% 7.69/7.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 7.69/7.96 inference(monotonicity,[status(thm)],[10444])).
% 7.69/7.96 tff(10446,plain,
% 7.69/7.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.69/7.96 inference(transitivity,[status(thm)],[10445, 10443])).
% 7.69/7.96 tff(10447,plain,
% 7.69/7.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))),
% 7.69/7.96 inference(quant_inst,[status(thm)],[])).
% 7.69/7.96 tff(10448,plain,
% 7.69/7.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 7.69/7.96 inference(modus_ponens,[status(thm)],[10447, 10446])).
% 7.69/7.96 tff(10449,plain,
% 7.69/7.96 ($false),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[10448, 194, 847, 10442, 2112, 10440])).
% 7.69/7.96 tff(10450,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(s(z))))) | (~r(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.96 tff(10451,plain,
% 7.69/7.96 (~r(s(s(s(s(z)))), elem!1)),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[10450, 10400, 411, 838, 665])).
% 7.69/7.96 tff(10452,plain,
% 7.69/7.96 (b(s(s(s(s(z)))), elem!1)),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[762, 10451, 10399])).
% 7.69/7.96 tff(10453,plain,
% 7.69/7.96 (~b(z, s(s(s(s(z)))))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[4246, 10452, 665, 10396])).
% 7.69/7.96 tff(10454,plain,
% 7.69/7.96 (r(z, s(s(s(s(z)))))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[800, 10453])).
% 7.69/7.96 tff(10455,plain,
% 7.69/7.96 (~r(s(s(s(s(z)))), s(z))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[1224, 10454, 182, 2913])).
% 7.69/7.96 tff(10456,plain,
% 7.69/7.96 (b(s(s(s(s(z)))), s(z))),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[749, 10455])).
% 7.69/7.96 tff(10457,plain,
% 7.69/7.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/7.96 inference(rewrite,[status(thm)],[])).
% 7.69/7.96 tff(10458,plain,
% 7.69/7.96 (((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/7.96 inference(rewrite,[status(thm)],[])).
% 7.69/7.96 tff(10459,plain,
% 7.69/7.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 7.69/7.96 inference(monotonicity,[status(thm)],[10458])).
% 7.69/7.96 tff(10460,plain,
% 7.69/7.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/7.96 inference(transitivity,[status(thm)],[10459, 10457])).
% 7.69/7.96 tff(10461,plain,
% 7.69/7.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 7.69/7.96 inference(quant_inst,[status(thm)],[])).
% 7.69/7.96 tff(10462,plain,
% 7.69/7.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 7.69/7.96 inference(modus_ponens,[status(thm)],[10461, 10460])).
% 7.69/7.96 tff(10463,plain,
% 7.69/7.96 ($false),
% 7.69/7.96 inference(unit_resolution,[status(thm)],[10462, 391, 665, 10398, 10396, 10456, 10394])).
% 7.69/7.97 tff(10464,plain,((s(z) = elem!1) | (~b(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)) | b(s(z), s(s(s(s(z))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.97 tff(10465,plain,
% 7.69/7.97 (b(s(z), s(s(s(s(z)))))),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[10464, 10391, 181, 8232, 10387, 31])).
% 7.69/7.97 tff(10466,plain,
% 7.69/7.97 (~r(s(z), elem!1)),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[2475, 10393, 8232, 181])).
% 7.69/7.97 tff(10467,plain,
% 7.69/7.97 (b(s(z), elem!1)),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[632, 10466, 10391])).
% 7.69/7.97 tff(10468,plain,
% 7.69/7.97 (~r(z, s(z))),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[845, 847, 182, 411])).
% 7.69/7.97 tff(10469,plain,
% 7.69/7.97 (b(z, s(z))),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[678, 10468])).
% 7.69/7.97 tff(10470,plain,
% 7.69/7.97 (~r(s(s(s(s(z)))), s(z))),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[3243, 3447, 182, 411])).
% 7.69/7.97 tff(10471,plain,
% 7.69/7.97 (b(s(s(s(s(z)))), s(z))),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[749, 10470])).
% 7.69/7.97 tff(10472,plain,
% 7.69/7.97 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.97 inference(rewrite,[status(thm)],[])).
% 7.69/7.97 tff(10473,plain,
% 7.69/7.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.69/7.97 inference(monotonicity,[status(thm)],[10472])).
% 7.69/7.97 tff(10474,plain,
% 7.69/7.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.97 inference(transitivity,[status(thm)],[10473, 7097])).
% 7.69/7.97 tff(10475,plain,
% 7.69/7.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 7.69/7.97 inference(quant_inst,[status(thm)],[])).
% 7.69/7.97 tff(10476,plain,
% 7.69/7.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.69/7.97 inference(modus_ponens,[status(thm)],[10475, 10474])).
% 7.69/7.97 tff(10477,plain,
% 7.69/7.97 ($false),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[10476, 391, 1234, 1759, 1686, 664])).
% 7.69/7.97 tff(10478,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.97 tff(10479,plain,
% 7.69/7.97 (~b(z, s(s(s(s(z)))))),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[10478, 10471, 1234, 10469])).
% 7.69/7.97 tff(10480,plain,
% 7.69/7.97 (r(z, s(s(s(s(z)))))),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[800, 10479])).
% 7.69/7.97 tff(10481,plain,
% 7.69/7.97 (~(elem!1 = s(s(s(s(z)))))),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[769, 6967])).
% 7.69/7.97 tff(10482,plain,
% 7.69/7.97 (~r(s(s(s(s(z)))), elem!1)),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[10408, 3447, 847, 411])).
% 7.69/7.97 tff(10483,plain,
% 7.69/7.97 (b(s(s(s(s(z)))), elem!1)),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[762, 10482, 6967])).
% 7.69/7.97 tff(10484,plain,
% 7.69/7.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.97 inference(rewrite,[status(thm)],[])).
% 7.69/7.97 tff(10485,plain,
% 7.69/7.97 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.97 inference(rewrite,[status(thm)],[])).
% 7.69/7.97 tff(10486,plain,
% 7.69/7.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 7.69/7.97 inference(monotonicity,[status(thm)],[10485])).
% 7.69/7.97 tff(10487,plain,
% 7.69/7.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 7.69/7.97 inference(transitivity,[status(thm)],[10486, 10484])).
% 7.69/7.97 tff(10488,plain,
% 7.69/7.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))),
% 7.69/7.97 inference(quant_inst,[status(thm)],[])).
% 7.69/7.97 tff(10489,plain,
% 7.69/7.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 7.69/7.97 inference(modus_ponens,[status(thm)],[10488, 10487])).
% 7.69/7.97 tff(10490,plain,
% 7.69/7.97 ($false),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[10489, 391, 665, 644, 2064, 1652, 1234])).
% 7.69/7.97 tff(10491,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.97 tff(10492,plain,
% 7.69/7.97 (~b(elem!1, s(s(s(s(z)))))),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[10491, 10483, 665, 1234, 644])).
% 7.69/7.97 tff(10493,plain,
% 7.69/7.97 (r(elem!1, s(s(s(s(z)))))),
% 7.69/7.97 inference(unit_resolution,[status(thm)],[781, 10492, 10481])).
% 7.69/7.97 tff(10494,plain,
% 7.69/7.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.69/7.97 inference(rewrite,[status(thm)],[])).
% 7.69/7.97 tff(10495,plain,
% 7.69/7.97 (((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.69/7.97 inference(rewrite,[status(thm)],[])).
% 7.69/7.97 tff(10496,plain,
% 7.69/7.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 7.69/7.98 inference(monotonicity,[status(thm)],[10495])).
% 7.69/7.98 tff(10497,plain,
% 7.69/7.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.69/7.98 inference(transitivity,[status(thm)],[10496, 10494])).
% 7.69/7.98 tff(10498,plain,
% 7.69/7.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))),
% 7.69/7.98 inference(quant_inst,[status(thm)],[])).
% 7.69/7.98 tff(10499,plain,
% 7.69/7.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 7.69/7.98 inference(modus_ponens,[status(thm)],[10498, 10497])).
% 7.69/7.98 tff(10500,plain,
% 7.69/7.98 ($false),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[10499, 194, 411, 3447, 10493, 10480])).
% 7.69/7.98 tff(10501,plain,(b(s(s(s(s(z)))), z) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.98 tff(10502,plain,
% 7.69/7.98 (b(s(s(s(s(z)))), z)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[10501, 10387, 8232, 10465, 10467, 10393, 181])).
% 7.69/7.98 tff(10503,plain,
% 7.69/7.98 (~b(z, s(s(s(s(z)))))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[10438, 10502, 10465, 8232, 10393])).
% 7.69/7.98 tff(10504,plain,
% 7.69/7.98 (r(z, s(s(s(s(z)))))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[800, 10503])).
% 7.69/7.98 tff(10505,plain,
% 7.69/7.98 (~r(s(s(s(s(z)))), elem!1)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[10418, 10504, 10393, 8232])).
% 7.69/7.98 tff(10506,plain,
% 7.69/7.98 (~r(z, s(z))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[845, 10393, 181, 8232])).
% 7.69/7.98 tff(10507,plain,
% 7.69/7.98 (b(z, s(z))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[678, 10506])).
% 7.69/7.98 tff(10508,plain,
% 7.69/7.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.69/7.98 inference(rewrite,[status(thm)],[])).
% 7.69/7.98 tff(10509,plain,
% 7.69/7.98 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.69/7.98 inference(rewrite,[status(thm)],[])).
% 7.69/7.98 tff(10510,plain,
% 7.69/7.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 7.69/7.98 inference(monotonicity,[status(thm)],[10509])).
% 7.69/7.98 tff(10511,plain,
% 7.69/7.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.69/7.98 inference(transitivity,[status(thm)],[10510, 10508])).
% 7.69/7.98 tff(10512,plain,
% 7.69/7.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.69/7.98 inference(quant_inst,[status(thm)],[])).
% 7.69/7.98 tff(10513,plain,
% 7.69/7.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 7.69/7.98 inference(modus_ponens,[status(thm)],[10512, 10511])).
% 7.69/7.98 tff(10514,plain,
% 7.69/7.98 (~b(s(s(s(s(z)))), elem!1)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[10513, 391, 10387, 10467, 10502, 10507])).
% 7.69/7.98 tff(10515,plain,
% 7.69/7.98 (s(s(s(s(z)))) = elem!1),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[762, 10514, 10505])).
% 7.69/7.98 tff(10516,plain,
% 7.69/7.98 (~(s(s(s(elem!1))) = elem!1)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[1436, 10515])).
% 7.69/7.98 tff(10517,plain,
% 7.69/7.98 (~(elem!1 = s(s(s(elem!1))))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[129, 10516])).
% 7.69/7.98 tff(10518,plain,
% 7.69/7.98 ($false),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[419, 8848, 8849, 184, 411])).
% 7.69/7.98 tff(10519,plain,((elem!1 = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.98 tff(10520,plain,
% 7.69/7.98 (b(s(s(s(elem!1))), elem!1)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[10519, 4028, 184, 411, 1])).
% 7.69/7.98 tff(10521,plain,
% 7.69/7.98 (~r(s(s(s(elem!1))), z)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[8380, 6124, 184, 411])).
% 7.69/7.98 tff(10522,plain,
% 7.69/7.98 (b(s(s(s(elem!1))), z)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[377, 10521])).
% 7.69/7.98 tff(10523,plain,
% 7.69/7.98 (~b(s(s(s(elem!1))), s(z))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[2522, 10522, 182, 644, 10520, 665, 411, 831])).
% 7.69/7.98 tff(10524,plain,
% 7.69/7.98 (r(s(s(s(elem!1))), s(z))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[223, 10523])).
% 7.69/7.98 tff(10525,plain,
% 7.69/7.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 7.69/7.98 inference(rewrite,[status(thm)],[])).
% 7.69/7.98 tff(10526,plain,
% 7.69/7.98 (((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 7.69/7.98 inference(rewrite,[status(thm)],[])).
% 7.69/7.98 tff(10527,plain,
% 7.69/7.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 7.69/7.98 inference(monotonicity,[status(thm)],[10526])).
% 7.69/7.98 tff(10528,plain,
% 7.69/7.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 7.69/7.98 inference(transitivity,[status(thm)],[10527, 10525])).
% 7.69/7.98 tff(10529,plain,
% 7.69/7.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 7.69/7.98 inference(quant_inst,[status(thm)],[])).
% 7.69/7.98 tff(10530,plain,
% 7.69/7.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 7.69/7.98 inference(modus_ponens,[status(thm)],[10529, 10528])).
% 7.69/7.98 tff(10531,plain,
% 7.69/7.98 ($false),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[10530, 194, 411, 184, 6124, 10524])).
% 7.69/7.98 tff(10532,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (elem!1 = s(z)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.98 tff(10533,plain,
% 7.69/7.98 (b(elem!1, s(s(s(elem!1))))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[10532, 181, 59, 8232, 10467, 10387, 10392, 10517])).
% 7.69/7.98 tff(10534,plain,
% 7.69/7.98 (~b(s(s(s(elem!1))), z)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[673, 379, 664, 448, 665])).
% 7.69/7.98 tff(10535,plain,
% 7.69/7.98 (r(s(s(s(elem!1))), z)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[377, 10534])).
% 7.69/7.98 tff(10536,plain,
% 7.69/7.98 (~b(s(s(s(elem!1))), s(z))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[4026, 379, 644, 448])).
% 7.69/7.98 tff(10537,plain,
% 7.69/7.98 (r(s(s(s(elem!1))), s(z))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[223, 10536])).
% 7.69/7.98 tff(10538,plain,
% 7.69/7.98 ($false),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[202, 10537, 10535, 184, 182])).
% 7.69/7.98 tff(10539,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.98 tff(10540,plain,
% 7.69/7.98 (~b(s(z), s(s(s(elem!1))))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[10539, 181, 59, 10467, 10533, 10507, 10387])).
% 7.69/7.98 tff(10541,plain,
% 7.69/7.98 (r(s(z), s(s(s(elem!1))))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[247, 10540])).
% 7.69/7.98 tff(10542,plain,
% 7.69/7.98 (~r(s(s(s(elem!1))), elem!1)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[241, 10541, 59, 181])).
% 7.69/7.98 tff(10543,plain,
% 7.69/7.98 (b(s(s(s(elem!1))), elem!1)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[230, 10542, 10516])).
% 7.69/7.98 tff(10544,plain,
% 7.69/7.98 (~r(s(s(s(elem!1))), z)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[1867, 10541, 59, 181])).
% 7.69/7.98 tff(10545,plain,
% 7.69/7.98 (b(s(s(s(elem!1))), z)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[377, 10544])).
% 7.69/7.98 tff(10546,plain,
% 7.69/7.98 (~r(s(s(s(elem!1))), s(z))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[3499, 10541, 59, 181])).
% 7.69/7.98 tff(10547,plain,
% 7.69/7.98 (b(s(s(s(elem!1))), s(z))),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[223, 10546])).
% 7.69/7.98 tff(10548,plain,
% 7.69/7.98 ($false),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[2522, 10547, 10545, 181, 10467, 10543, 10387, 8232, 10392])).
% 7.69/7.98 tff(10549,plain,(b(s(z), z) | b(elem!1, s(z)) | (elem!1 = z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.98 tff(10550,plain,
% 7.69/7.98 (b(s(z), z)),
% 7.69/7.98 inference(unit_resolution,[status(thm)],[10549, 31, 2, 10])).
% 7.69/7.98 tff(10551,plain,
% 7.69/7.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 7.69/7.98 inference(rewrite,[status(thm)],[])).
% 7.69/7.98 tff(10552,plain,
% 7.69/7.98 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 7.69/7.98 inference(rewrite,[status(thm)],[])).
% 7.69/7.98 tff(10553,plain,
% 7.69/7.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 7.69/7.98 inference(monotonicity,[status(thm)],[10552])).
% 7.69/7.98 tff(10554,plain,
% 7.69/7.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 7.69/7.99 inference(transitivity,[status(thm)],[10553, 10551])).
% 7.69/7.99 tff(10555,plain,
% 7.69/7.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 7.69/7.99 inference(quant_inst,[status(thm)],[])).
% 7.69/7.99 tff(10556,plain,
% 7.69/7.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 7.69/7.99 inference(modus_ponens,[status(thm)],[10555, 10554])).
% 7.69/7.99 tff(10557,plain,
% 7.69/7.99 ($false),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[10556, 194, 722, 182, 2053, 1216])).
% 7.69/7.99 tff(10558,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.99 tff(10559,plain,
% 7.69/7.99 (~r(s(z), z)),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[10558, 722, 2053, 1216])).
% 7.69/7.99 tff(10560,plain,
% 7.69/7.99 (b(s(z), z)),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[180, 10559])).
% 7.69/7.99 tff(10561,plain,
% 7.69/7.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.99 inference(rewrite,[status(thm)],[])).
% 7.69/7.99 tff(10562,plain,
% 7.69/7.99 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.99 inference(rewrite,[status(thm)],[])).
% 7.69/7.99 tff(10563,plain,
% 7.69/7.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 7.69/7.99 inference(monotonicity,[status(thm)],[10562])).
% 7.69/7.99 tff(10564,plain,
% 7.69/7.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/7.99 inference(transitivity,[status(thm)],[10563, 10561])).
% 7.69/7.99 tff(10565,plain,
% 7.69/7.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 7.69/7.99 inference(quant_inst,[status(thm)],[])).
% 7.69/7.99 tff(10566,plain,
% 7.69/7.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 7.69/7.99 inference(modus_ponens,[status(thm)],[10565, 10564])).
% 7.69/7.99 tff(10567,plain,
% 7.69/7.99 ($false),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[10566, 194, 722, 2053, 1216, 719])).
% 7.69/7.99 tff(10568,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.99 tff(10569,plain,
% 7.69/7.99 (~r(z, s(s(s(s(z)))))),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[10568, 722, 2053, 1216])).
% 7.69/7.99 tff(10570,plain,
% 7.69/7.99 (b(z, s(s(s(s(z)))))),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[800, 10569])).
% 7.69/7.99 tff(10571,plain,
% 7.69/7.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.69/7.99 inference(rewrite,[status(thm)],[])).
% 7.69/7.99 tff(10572,plain,
% 7.69/7.99 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.69/7.99 inference(rewrite,[status(thm)],[])).
% 7.69/7.99 tff(10573,plain,
% 7.69/7.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 7.69/7.99 inference(monotonicity,[status(thm)],[10572])).
% 7.69/7.99 tff(10574,plain,
% 7.69/7.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.69/7.99 inference(transitivity,[status(thm)],[10573, 10571])).
% 7.69/7.99 tff(10575,plain,
% 7.69/7.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 7.69/7.99 inference(quant_inst,[status(thm)],[])).
% 7.69/7.99 tff(10576,plain,
% 7.69/7.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 7.69/7.99 inference(modus_ponens,[status(thm)],[10575, 10574])).
% 7.69/7.99 tff(10577,plain,
% 7.69/7.99 ($false),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[10576, 194, 722, 2053, 1216, 723])).
% 7.69/7.99 tff(10578,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.69/7.99 tff(10579,plain,
% 7.69/7.99 (~r(s(s(s(s(z)))), s(z))),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[10578, 722, 2053, 1216])).
% 7.69/7.99 tff(10580,plain,
% 7.69/7.99 (b(s(s(s(s(z)))), s(z))),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[749, 10579])).
% 7.69/7.99 tff(10581,plain,
% 7.69/7.99 (~r(s(s(z)), s(z))),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[5567, 1749, 2053, 1216])).
% 7.69/7.99 tff(10582,plain,
% 7.69/7.99 (b(s(s(z)), s(z))),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[3778, 10581])).
% 7.69/7.99 tff(10583,plain,
% 7.69/7.99 (~r(s(s(z)), z)),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[9635, 1749, 2053, 722])).
% 7.69/7.99 tff(10584,plain,
% 7.69/7.99 (b(s(s(z)), z)),
% 7.69/7.99 inference(unit_resolution,[status(thm)],[1211, 10583])).
% 7.69/7.99 tff(10585,plain,
% 7.69/7.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/7.99 inference(rewrite,[status(thm)],[])).
% 7.69/7.99 tff(10586,plain,
% 7.69/7.99 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/7.99 inference(rewrite,[status(thm)],[])).
% 7.69/7.99 tff(10587,plain,
% 7.69/7.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 7.69/8.00 inference(monotonicity,[status(thm)],[10586])).
% 7.69/8.00 tff(10588,plain,
% 7.69/8.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/8.00 inference(transitivity,[status(thm)],[10587, 10585])).
% 7.69/8.00 tff(10589,plain,
% 7.69/8.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 7.69/8.00 inference(quant_inst,[status(thm)],[])).
% 7.69/8.00 tff(10590,plain,
% 7.69/8.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 7.69/8.00 inference(modus_ponens,[status(thm)],[10589, 10588])).
% 7.69/8.00 tff(10591,plain,
% 7.69/8.00 ($false),
% 7.69/8.00 inference(unit_resolution,[status(thm)],[10590, 391, 10584, 10580, 10570, 10582, 10560])).
% 7.69/8.00 tff(10592,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.69/8.00 tff(10593,plain,
% 7.69/8.00 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.69/8.00 inference(unit_resolution,[status(thm)],[10592, 722, 2053, 1216])).
% 7.69/8.00 tff(10594,plain,
% 7.69/8.00 (b(s(s(z)), s(s(s(s(z)))))),
% 7.69/8.00 inference(unit_resolution,[status(thm)],[3652, 10593])).
% 7.69/8.00 tff(10595,plain,
% 7.69/8.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/8.00 inference(rewrite,[status(thm)],[])).
% 7.69/8.00 tff(10596,plain,
% 7.69/8.00 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/8.00 inference(rewrite,[status(thm)],[])).
% 7.69/8.00 tff(10597,plain,
% 7.69/8.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 7.69/8.00 inference(monotonicity,[status(thm)],[10596])).
% 7.69/8.00 tff(10598,plain,
% 7.69/8.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/8.00 inference(transitivity,[status(thm)],[10597, 10595])).
% 7.69/8.00 tff(10599,plain,
% 7.69/8.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 7.69/8.00 inference(quant_inst,[status(thm)],[])).
% 7.69/8.00 tff(10600,plain,
% 7.69/8.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 7.69/8.00 inference(modus_ponens,[status(thm)],[10599, 10598])).
% 7.69/8.00 tff(10601,plain,
% 7.69/8.00 (~b(s(s(z)), z)),
% 7.69/8.00 inference(unit_resolution,[status(thm)],[10600, 391, 10594, 10580, 10570, 10560])).
% 7.69/8.00 tff(10602,plain,
% 7.69/8.00 (r(s(s(z)), z)),
% 7.69/8.00 inference(unit_resolution,[status(thm)],[1211, 10601])).
% 7.69/8.00 tff(10603,plain,
% 7.69/8.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 7.69/8.00 inference(rewrite,[status(thm)],[])).
% 7.69/8.00 tff(10604,plain,
% 7.69/8.00 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 7.69/8.00 inference(rewrite,[status(thm)],[])).
% 7.69/8.00 tff(10605,plain,
% 7.69/8.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 7.69/8.00 inference(monotonicity,[status(thm)],[10604])).
% 7.69/8.00 tff(10606,plain,
% 7.69/8.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 7.69/8.00 inference(transitivity,[status(thm)],[10605, 10603])).
% 7.69/8.00 tff(10607,plain,
% 7.69/8.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 7.69/8.00 inference(quant_inst,[status(thm)],[])).
% 7.69/8.00 tff(10608,plain,
% 7.69/8.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 7.69/8.00 inference(modus_ponens,[status(thm)],[10607, 10606])).
% 7.69/8.00 tff(10609,plain,
% 7.69/8.00 ($false),
% 7.69/8.00 inference(unit_resolution,[status(thm)],[10608, 194, 722, 3557, 1216, 2405])).
% 7.69/8.00 tff(10610,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.69/8.00 tff(10611,plain,
% 7.69/8.00 (~r(s(s(z)), s(z))),
% 7.69/8.00 inference(unit_resolution,[status(thm)],[10610, 10602, 1216, 722])).
% 7.69/8.00 tff(10612,plain,
% 7.69/8.00 (b(s(s(z)), s(z))),
% 7.69/8.00 inference(unit_resolution,[status(thm)],[3778, 10611])).
% 7.69/8.00 tff(10613,plain,
% 7.69/8.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/8.00 inference(rewrite,[status(thm)],[])).
% 7.69/8.00 tff(10614,plain,
% 7.69/8.00 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/8.01 inference(rewrite,[status(thm)],[])).
% 7.69/8.01 tff(10615,plain,
% 7.69/8.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 7.69/8.01 inference(monotonicity,[status(thm)],[10614])).
% 7.69/8.01 tff(10616,plain,
% 7.69/8.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.69/8.01 inference(transitivity,[status(thm)],[10615, 10613])).
% 7.69/8.01 tff(10617,plain,
% 7.69/8.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 7.69/8.01 inference(quant_inst,[status(thm)],[])).
% 7.69/8.01 tff(10618,plain,
% 7.69/8.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 7.69/8.01 inference(modus_ponens,[status(thm)],[10617, 10616])).
% 7.69/8.01 tff(10619,plain,
% 7.69/8.01 ($false),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[10618, 391, 10594, 10580, 10570, 10612, 10560])).
% 7.69/8.01 tff(10620,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 7.69/8.01 tff(10621,plain,
% 7.69/8.01 (~r(z, s(z))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[10620, 3447, 2913])).
% 7.69/8.01 tff(10622,plain,
% 7.69/8.01 (b(z, s(z))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[678, 10621])).
% 7.69/8.01 tff(10623,plain,
% 7.69/8.01 (~(s(s(s(elem!1))) = elem!1)),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[8400, 1526, 31])).
% 7.69/8.01 tff(10624,plain,
% 7.69/8.01 (~(elem!1 = s(s(s(elem!1))))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[129, 10623])).
% 7.69/8.01 tff(10625,plain,
% 7.69/8.01 (r(elem!1, s(s(s(elem!1))))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[424, 10624, 4028])).
% 7.69/8.01 tff(10626,plain,
% 7.69/8.01 (~r(s(s(s(elem!1))), z)),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[8380, 10625, 411, 184])).
% 7.69/8.01 tff(10627,plain,
% 7.69/8.01 (b(s(s(s(elem!1))), z)),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[377, 10626])).
% 7.69/8.01 tff(10628,plain,
% 7.69/8.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 7.69/8.01 inference(rewrite,[status(thm)],[])).
% 7.69/8.01 tff(10629,plain,
% 7.69/8.01 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 7.69/8.01 inference(rewrite,[status(thm)],[])).
% 7.69/8.01 tff(10630,plain,
% 7.69/8.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 7.69/8.01 inference(monotonicity,[status(thm)],[10629])).
% 7.69/8.01 tff(10631,plain,
% 7.69/8.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 7.69/8.01 inference(transitivity,[status(thm)],[10630, 10628])).
% 7.69/8.01 tff(10632,plain,
% 7.69/8.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 7.69/8.01 inference(quant_inst,[status(thm)],[])).
% 7.69/8.01 tff(10633,plain,
% 7.69/8.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 7.69/8.01 inference(modus_ponens,[status(thm)],[10632, 10631])).
% 7.69/8.01 tff(10634,plain,
% 7.69/8.01 ($false),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[10633, 391, 10627, 1526, 664, 590])).
% 7.69/8.01 tff(10635,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 7.69/8.01 tff(10636,plain,
% 7.69/8.01 (~b(s(s(s(elem!1))), s(z))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[10635, 10622, 8232, 59, 10550, 4028, 31])).
% 7.69/8.01 tff(10637,plain,
% 7.69/8.01 (r(s(s(s(elem!1))), s(z))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[223, 10636])).
% 7.69/8.01 tff(10638,plain,
% 7.69/8.01 (~r(elem!1, s(s(s(elem!1))))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[6132, 10637, 59, 3618])).
% 7.69/8.01 tff(10639,plain,
% 7.69/8.01 (elem!1 = s(s(s(elem!1)))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[424, 10638, 4028])).
% 7.69/8.01 tff(10640,plain,
% 7.69/8.01 (s(s(s(elem!1))) = elem!1),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[129, 10639])).
% 7.69/8.01 tff(10641,plain,
% 7.69/8.01 (r(s(s(s(elem!1))), z)),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[533, 10640, 3618])).
% 7.69/8.01 tff(10642,plain,
% 7.69/8.01 (~r(z, s(z))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[10620, 2913, 3447])).
% 7.69/8.01 tff(10643,plain,
% 7.69/8.01 (b(z, s(z))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[678, 10642])).
% 7.69/8.01 tff(10644,assumption,(~b(z, s(s(s(s(z)))))), introduced(assumption)).
% 7.69/8.01 tff(10645,plain,
% 7.69/8.01 (r(z, s(s(s(s(z)))))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[800, 10644])).
% 7.69/8.01 tff(10646,plain,
% 7.69/8.01 (r(s(s(s(s(z)))), s(z))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[749, 9024])).
% 7.69/8.01 tff(10647,plain,
% 7.69/8.01 (((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/8.01 inference(rewrite,[status(thm)],[])).
% 7.69/8.01 tff(10648,plain,
% 7.69/8.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 7.69/8.01 inference(monotonicity,[status(thm)],[10647])).
% 7.69/8.01 tff(10649,plain,
% 7.69/8.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 7.69/8.01 inference(transitivity,[status(thm)],[10648, 10229])).
% 7.69/8.01 tff(10650,plain,
% 7.69/8.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 7.69/8.01 inference(quant_inst,[status(thm)],[])).
% 7.69/8.01 tff(10651,plain,
% 7.69/8.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 7.69/8.01 inference(modus_ponens,[status(thm)],[10650, 10649])).
% 7.69/8.01 tff(10652,plain,
% 7.69/8.01 (~r(s(z), z)),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[10651, 194, 3447, 2913, 719])).
% 7.69/8.01 tff(10653,plain,
% 7.69/8.01 (b(s(z), z)),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[180, 10652])).
% 7.69/8.01 tff(10654,plain,
% 7.69/8.01 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 7.69/8.01 inference(rewrite,[status(thm)],[])).
% 7.69/8.01 tff(10655,plain,
% 7.69/8.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 7.69/8.01 inference(monotonicity,[status(thm)],[10654])).
% 7.69/8.01 tff(10656,plain,
% 7.69/8.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 7.69/8.01 inference(transitivity,[status(thm)],[10655, 9060])).
% 7.69/8.01 tff(10657,plain,
% 7.69/8.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 7.69/8.01 inference(quant_inst,[status(thm)],[])).
% 7.69/8.01 tff(10658,plain,
% 7.69/8.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 7.69/8.01 inference(modus_ponens,[status(thm)],[10657, 10656])).
% 7.69/8.01 tff(10659,plain,
% 7.69/8.01 (~b(s(s(z)), s(z))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[10658, 391, 1235, 10643, 10653])).
% 7.69/8.01 tff(10660,plain,
% 7.69/8.01 (r(s(s(z)), s(z))),
% 7.69/8.01 inference(unit_resolution,[status(thm)],[3778, 10659])).
% 7.69/8.01 tff(10661,plain,
% 7.69/8.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 7.69/8.01 inference(rewrite,[status(thm)],[])).
% 7.69/8.01 tff(10662,plain,
% 7.69/8.01 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 7.69/8.01 inference(rewrite,[status(thm)],[])).
% 7.69/8.01 tff(10663,plain,
% 7.69/8.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 7.69/8.01 inference(monotonicity,[status(thm)],[10662])).
% 7.69/8.01 tff(10664,plain,
% 7.69/8.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 7.69/8.02 inference(transitivity,[status(thm)],[10663, 10661])).
% 7.69/8.02 tff(10665,plain,
% 7.69/8.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 7.69/8.02 inference(quant_inst,[status(thm)],[])).
% 7.69/8.02 tff(10666,plain,
% 7.69/8.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 7.69/8.02 inference(modus_ponens,[status(thm)],[10665, 10664])).
% 7.69/8.02 tff(10667,plain,
% 7.69/8.02 (~b(s(z), s(s(z)))),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[10666, 391, 1235, 10643, 10653])).
% 7.69/8.02 tff(10668,plain,
% 7.69/8.02 (r(s(z), s(s(z)))),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[1788, 10667])).
% 7.69/8.02 tff(10669,plain,
% 7.69/8.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.69/8.02 inference(rewrite,[status(thm)],[])).
% 7.69/8.02 tff(10670,plain,
% 7.69/8.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.69/8.02 inference(quant_inst,[status(thm)],[])).
% 7.69/8.02 tff(10671,plain,
% 7.69/8.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 7.69/8.02 inference(modus_ponens,[status(thm)],[10670, 10669])).
% 7.69/8.02 tff(10672,plain,
% 7.69/8.02 ($false),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[10671, 194, 723, 1747, 1697, 2405])).
% 7.69/8.02 tff(10673,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 7.69/8.02 tff(10674,plain,
% 7.69/8.02 (~r(s(s(s(s(z)))), s(s(z)))),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[10673, 10646, 10668, 10660])).
% 7.69/8.02 tff(10675,plain,
% 7.69/8.02 (b(s(s(s(s(z)))), s(s(z)))),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[1714, 10674])).
% 7.69/8.02 tff(10676,plain,
% 7.69/8.02 (~r(s(z), z)),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[10651, 194, 2053, 1216, 719])).
% 7.69/8.02 tff(10677,plain,
% 7.69/8.02 (b(s(z), z)),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[180, 10676])).
% 7.69/8.02 tff(10678,plain,
% 7.69/8.02 (~r(z, s(z))),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[10620, 1216, 2053])).
% 7.69/8.02 tff(10679,plain,
% 7.69/8.02 (b(z, s(z))),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[678, 10678])).
% 7.69/8.02 tff(10680,plain,
% 7.69/8.02 (~(elem!1 = z)),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[5453, 115])).
% 7.69/8.02 tff(10681,plain,
% 7.69/8.02 (b(z, s(s(s(elem!1))))),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[8231, 80, 10680])).
% 7.69/8.02 tff(10682,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 7.69/8.02 tff(10683,plain,
% 7.69/8.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 7.69/8.02 inference(rewrite,[status(thm)],[])).
% 7.69/8.02 tff(10684,plain,
% 7.69/8.02 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 7.69/8.02 inference(rewrite,[status(thm)],[])).
% 7.69/8.02 tff(10685,plain,
% 7.69/8.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 7.69/8.02 inference(monotonicity,[status(thm)],[10684])).
% 7.69/8.02 tff(10686,plain,
% 7.69/8.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 7.69/8.02 inference(transitivity,[status(thm)],[10685, 10683])).
% 7.69/8.02 tff(10687,plain,
% 7.69/8.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 7.69/8.02 inference(quant_inst,[status(thm)],[])).
% 7.69/8.02 tff(10688,plain,
% 7.69/8.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 7.69/8.02 inference(modus_ponens,[status(thm)],[10687, 10686])).
% 7.69/8.02 tff(10689,plain,
% 7.69/8.02 ($false),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[10688, 391, 10682, 1526, 664, 590])).
% 7.69/8.02 tff(10690,plain,((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.69/8.02 tff(10691,plain,
% 7.69/8.02 (~b(s(s(s(elem!1))), s(z))),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[10690, 10681, 10679, 10677])).
% 7.69/8.02 tff(10692,plain,
% 7.69/8.02 (r(s(s(s(elem!1))), s(z))),
% 7.69/8.02 inference(unit_resolution,[status(thm)],[223, 10691])).
% 7.69/8.02 tff(10693,plain,
% 7.69/8.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 7.69/8.02 inference(rewrite,[status(thm)],[])).
% 7.69/8.02 tff(10694,plain,
% 7.69/8.02 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 7.69/8.02 inference(rewrite,[status(thm)],[])).
% 7.69/8.02 tff(10695,plain,
% 7.69/8.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 7.69/8.02 inference(monotonicity,[status(thm)],[10694])).
% 7.69/8.02 tff(10696,plain,
% 7.69/8.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 7.82/8.03 inference(transitivity,[status(thm)],[10695, 10693])).
% 7.82/8.03 tff(10697,plain,
% 7.82/8.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 7.82/8.03 inference(quant_inst,[status(thm)],[])).
% 7.82/8.03 tff(10698,plain,
% 7.82/8.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 7.82/8.03 inference(modus_ponens,[status(thm)],[10697, 10696])).
% 7.82/8.03 tff(10699,plain,
% 7.82/8.03 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[10698, 194, 10692, 1216, 10646])).
% 7.82/8.03 tff(10700,plain,
% 7.82/8.03 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 7.82/8.03 inference(commutativity,[status(thm)],[])).
% 7.82/8.03 tff(10701,plain,
% 7.82/8.03 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 7.82/8.03 inference(symmetry,[status(thm)],[10700])).
% 7.82/8.03 tff(10702,plain,
% 7.82/8.03 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 7.82/8.03 inference(monotonicity,[status(thm)],[10701])).
% 7.82/8.03 tff(10703,plain,
% 7.82/8.03 (~(s(s(s(elem!1))) = s(s(z)))),
% 7.82/8.03 inference(modus_ponens,[status(thm)],[1397, 10702])).
% 7.82/8.03 tff(10704,plain,
% 7.82/8.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.03 inference(rewrite,[status(thm)],[])).
% 7.82/8.03 tff(10705,plain,
% 7.82/8.03 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.03 inference(rewrite,[status(thm)],[])).
% 7.82/8.03 tff(10706,plain,
% 7.82/8.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 7.82/8.03 inference(monotonicity,[status(thm)],[10705])).
% 7.82/8.03 tff(10707,plain,
% 7.82/8.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.03 inference(transitivity,[status(thm)],[10706, 10704])).
% 7.82/8.03 tff(10708,plain,
% 7.82/8.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.03 inference(quant_inst,[status(thm)],[])).
% 7.82/8.03 tff(10709,plain,
% 7.82/8.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 7.82/8.03 inference(modus_ponens,[status(thm)],[10708, 10707])).
% 7.82/8.03 tff(10710,plain,
% 7.82/8.03 (~r(s(s(s(elem!1))), s(s(z)))),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[10709, 194, 10692, 1216, 2405])).
% 7.82/8.03 tff(10711,plain,
% 7.82/8.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 7.82/8.03 inference(rewrite,[status(thm)],[])).
% 7.82/8.03 tff(10712,plain,
% 7.82/8.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 7.82/8.03 inference(quant_inst,[status(thm)],[])).
% 7.82/8.03 tff(10713,plain,
% 7.82/8.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 7.82/8.03 inference(modus_ponens,[status(thm)],[10712, 10711])).
% 7.82/8.03 tff(10714,plain,
% 7.82/8.03 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[10713, 42, 10710])).
% 7.82/8.03 tff(10715,plain,
% 7.82/8.03 (b(s(s(s(elem!1))), s(s(z)))),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[10714, 10703])).
% 7.82/8.03 tff(10716,plain,
% 7.82/8.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.03 inference(rewrite,[status(thm)],[])).
% 7.82/8.03 tff(10717,plain,
% 7.82/8.03 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.03 inference(rewrite,[status(thm)],[])).
% 7.82/8.03 tff(10718,plain,
% 7.82/8.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 7.82/8.03 inference(monotonicity,[status(thm)],[10717])).
% 7.82/8.03 tff(10719,plain,
% 7.82/8.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.03 inference(transitivity,[status(thm)],[10718, 10716])).
% 7.82/8.03 tff(10720,plain,
% 7.82/8.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 7.82/8.03 inference(quant_inst,[status(thm)],[])).
% 7.82/8.03 tff(10721,plain,
% 7.82/8.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 7.82/8.03 inference(modus_ponens,[status(thm)],[10720, 10719])).
% 7.82/8.03 tff(10722,plain,
% 7.82/8.03 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[10721, 391, 3823, 3563, 10715])).
% 7.82/8.03 tff(10723,plain,
% 7.82/8.03 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[2853, 42, 10699])).
% 7.82/8.03 tff(10724,plain,
% 7.82/8.03 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[10723, 10722])).
% 7.82/8.03 tff(10725,plain,
% 7.82/8.03 (s(z) = elem!1),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[2849, 10724])).
% 7.82/8.03 tff(10726,plain,
% 7.82/8.03 (~b(s(s(s(s(z)))), elem!1)),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[9614, 10725, 9024])).
% 7.82/8.03 tff(10727,plain,
% 7.82/8.03 (~(s(s(s(elem!1))) = elem!1)),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[2694, 10726, 10699])).
% 7.82/8.03 tff(10728,plain,
% 7.82/8.03 (~(elem!1 = s(s(s(elem!1))))),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[129, 10727])).
% 7.82/8.03 tff(10729,plain,
% 7.82/8.03 (b(z, elem!1)),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[141, 80, 115])).
% 7.82/8.03 tff(10730,plain,
% 7.82/8.03 (~(s(elem!1) = elem!1)),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[158, 10727])).
% 7.82/8.03 tff(10731,plain,
% 7.82/8.03 (r(z, s(s(s(elem!1))))),
% 7.82/8.03 inference(modus_ponens,[status(thm)],[719, 825])).
% 7.82/8.03 tff(10732,plain,
% 7.82/8.03 ($false),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[53, 10731])).
% 7.82/8.03 tff(10733,plain,((~r(z, s(s(s(s(z)))))) | r(z, s(s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.03 tff(10734,plain,
% 7.82/8.03 (r(z, s(s(s(elem!1))))),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[10733, 10725, 719])).
% 7.82/8.03 tff(10735,plain,
% 7.82/8.03 (b(elem!1, z)),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[7485, 10725, 10676])).
% 7.82/8.03 tff(10736,plain,
% 7.82/8.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 7.82/8.03 inference(rewrite,[status(thm)],[])).
% 7.82/8.03 tff(10737,plain,
% 7.82/8.03 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 7.82/8.03 inference(rewrite,[status(thm)],[])).
% 7.82/8.03 tff(10738,plain,
% 7.82/8.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1))))),
% 7.82/8.03 inference(monotonicity,[status(thm)],[10737])).
% 7.82/8.03 tff(10739,plain,
% 7.82/8.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 7.82/8.03 inference(transitivity,[status(thm)],[10738, 10736])).
% 7.82/8.03 tff(10740,plain,
% 7.82/8.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 7.82/8.03 inference(quant_inst,[status(thm)],[])).
% 7.82/8.03 tff(10741,plain,
% 7.82/8.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1))),
% 7.82/8.03 inference(modus_ponens,[status(thm)],[10740, 10739])).
% 7.82/8.03 tff(10742,plain,
% 7.82/8.03 ($false),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[10741, 391, 133, 665, 900, 10682])).
% 7.82/8.03 tff(10743,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.03 tff(10744,plain,
% 7.82/8.03 (~b(s(s(s(elem!1))), elem!1)),
% 7.82/8.03 inference(unit_resolution,[status(thm)],[10743, 10735, 10681, 10729])).
% 7.82/8.04 tff(10745,plain,
% 7.82/8.04 (r(s(s(s(elem!1))), elem!1)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[230, 10727, 10744])).
% 7.82/8.04 tff(10746,plain,
% 7.82/8.04 ((s(z) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 7.82/8.04 inference(monotonicity,[status(thm)],[812])).
% 7.82/8.04 tff(10747,plain,
% 7.82/8.04 ((s(z) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 7.82/8.04 inference(transitivity,[status(thm)],[10746, 8492])).
% 7.82/8.04 tff(10748,plain,
% 7.82/8.04 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 7.82/8.04 inference(monotonicity,[status(thm)],[10747])).
% 7.82/8.04 tff(10749,plain,
% 7.82/8.04 (~(s(s(z)) = elem!1)),
% 7.82/8.04 inference(modus_ponens,[status(thm)],[1783, 10748])).
% 7.82/8.04 tff(10750,plain,
% 7.82/8.04 (r(elem!1, s(s(s(s(z)))))),
% 7.82/8.04 inference(modus_ponens,[status(thm)],[6124, 7406])).
% 7.82/8.04 tff(10751,plain,
% 7.82/8.04 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[7123, 10750, 665, 133, 10749, 827, 2053])).
% 7.82/8.04 tff(10752,plain,
% 7.82/8.04 (b(s(s(z)), s(s(s(s(z)))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[3652, 10751])).
% 7.82/8.04 tff(10753,plain,
% 7.82/8.04 (~b(s(s(s(elem!1))), s(elem!1))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[7579, 10752, 812, 665, 285, 7434, 7435, 7422, 184, 7402, 10388, 4028])).
% 7.82/8.04 tff(10754,plain,
% 7.82/8.04 (r(s(s(s(elem!1))), s(elem!1))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[588, 10753, 7433])).
% 7.82/8.04 tff(10755,plain,
% 7.82/8.04 (~r(s(elem!1), elem!1)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[7832, 10754, 233, 6124])).
% 7.82/8.04 tff(10756,plain,
% 7.82/8.04 (b(s(elem!1), elem!1)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[2168, 10755, 164])).
% 7.82/8.04 tff(10757,plain,
% 7.82/8.04 (~b(z, s(elem!1))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[6555, 10756, 133, 665])).
% 7.82/8.04 tff(10758,plain,
% 7.82/8.04 (r(z, s(elem!1))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[566, 10757])).
% 7.82/8.04 tff(10759,plain,
% 7.82/8.04 (~b(s(elem!1), z)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[5279, 391, 133, 665, 10756])).
% 7.82/8.04 tff(10760,plain,
% 7.82/8.04 (r(s(elem!1), z)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[549, 10759])).
% 7.82/8.04 tff(10761,plain,
% 7.82/8.04 ($false),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[7766, 194, 10754, 10760, 9621, 10758])).
% 7.82/8.04 tff(10762,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(elem!1) = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.04 tff(10763,plain,
% 7.82/8.04 (s(s(elem!1)) = s(elem!1)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10762, 10745, 2053, 4028, 10725, 10735, 10734, 10730, 10729, 10728])).
% 7.82/8.04 tff(10764,plain,
% 7.82/8.04 (s(s(elem!1)) = elem!1),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[264, 10763])).
% 7.82/8.04 tff(10765,plain,
% 7.82/8.04 (~b(s(s(elem!1)), s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[912, 10764, 31])).
% 7.82/8.04 tff(10766,plain,
% 7.82/8.04 (~b(s(z), s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[7796, 10725, 4028])).
% 7.82/8.04 tff(10767,plain,
% 7.82/8.04 (r(s(z), s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[247, 10766])).
% 7.82/8.04 tff(10768,plain,
% 7.82/8.04 (r(elem!1, s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[2570, 10767, 10725])).
% 7.82/8.04 tff(10769,plain,
% 7.82/8.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.82/8.04 inference(rewrite,[status(thm)],[])).
% 7.82/8.04 tff(10770,plain,
% 7.82/8.04 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.82/8.04 inference(rewrite,[status(thm)],[])).
% 7.82/8.04 tff(10771,plain,
% 7.82/8.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 7.82/8.04 inference(monotonicity,[status(thm)],[10770])).
% 7.82/8.04 tff(10772,plain,
% 7.82/8.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.82/8.04 inference(transitivity,[status(thm)],[10771, 10769])).
% 7.82/8.04 tff(10773,plain,
% 7.82/8.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 7.82/8.04 inference(quant_inst,[status(thm)],[])).
% 7.82/8.04 tff(10774,plain,
% 7.82/8.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 7.82/8.04 inference(modus_ponens,[status(thm)],[10773, 10772])).
% 7.82/8.04 tff(10775,plain,
% 7.82/8.04 ($false),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10774, 194, 410, 183, 847, 1216])).
% 7.82/8.04 tff(10776,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.04 tff(10777,plain,
% 7.82/8.04 (~r(elem!1, s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10776, 10768, 1216, 10692])).
% 7.82/8.04 tff(10778,plain,
% 7.82/8.04 (~r(s(s(elem!1)), s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[4206, 10764, 10777])).
% 7.82/8.04 tff(10779,plain,
% 7.82/8.04 ($false),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[362, 10778, 10765])).
% 7.82/8.04 tff(10780,plain,(r(z, elem!1) | b(elem!1, s(z)) | (~r(s(s(s(s(z)))), z)) | b(elem!1, s(s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.82/8.04 tff(10781,plain,
% 7.82/8.04 (r(z, elem!1)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10780, 4028, 2053, 31, 1216, 9024, 719, 3823, 3563, 2405, 115])).
% 7.82/8.04 tff(10782,plain,
% 7.82/8.04 (b(z, s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[58, 53])).
% 7.82/8.04 tff(10783,plain,
% 7.82/8.04 (~b(s(s(s(elem!1))), s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10690, 10782, 664, 590])).
% 7.82/8.04 tff(10784,plain,
% 7.82/8.04 (r(s(s(s(elem!1))), s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[223, 10783])).
% 7.82/8.04 tff(10785,plain,
% 7.82/8.04 (~(s(z) = elem!1)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10733, 53, 719])).
% 7.82/8.04 tff(10786,plain,
% 7.82/8.04 (~(elem!1 = s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[172, 10785])).
% 7.82/8.04 tff(10787,plain,
% 7.82/8.04 (r(elem!1, s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[837, 10786, 31])).
% 7.82/8.04 tff(10788,plain,
% 7.82/8.04 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 7.82/8.04 inference(monotonicity,[status(thm)],[5])).
% 7.82/8.04 tff(10789,plain,
% 7.82/8.04 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 7.82/8.04 inference(symmetry,[status(thm)],[10788])).
% 7.82/8.04 tff(10790,plain,
% 7.82/8.04 (r(z, s(s(s(elem!1))))),
% 7.82/8.04 inference(modus_ponens,[status(thm)],[411, 10789])).
% 7.82/8.04 tff(10791,plain,
% 7.82/8.04 ($false),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[53, 10790])).
% 7.82/8.04 tff(10792,plain,((~(s(s(s(elem!1))) = elem!1)) | r(z, s(s(s(elem!1)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.04 tff(10793,plain,
% 7.82/8.04 (~(s(s(s(elem!1))) = elem!1)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10792, 53, 411])).
% 7.82/8.04 tff(10794,plain,
% 7.82/8.04 (~(elem!1 = s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[129, 10793])).
% 7.82/8.04 tff(10795,plain,
% 7.82/8.04 (r(elem!1, s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[424, 10794, 4028])).
% 7.82/8.04 tff(10796,plain,
% 7.82/8.04 ($false),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10776, 10795, 10787, 1216, 10784])).
% 7.82/8.04 tff(10797,plain,(r(z, s(s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.04 tff(10798,plain,
% 7.82/8.04 (r(z, s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10797, 4028, 1216, 31, 10679, 10677, 10781, 719])).
% 7.82/8.04 tff(10799,plain,
% 7.82/8.04 (~b(s(s(s(elem!1))), s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10635, 10781, 10677, 10679, 10798, 4028, 31])).
% 7.82/8.04 tff(10800,plain,
% 7.82/8.04 (r(s(s(s(elem!1))), s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[223, 10799])).
% 7.82/8.04 tff(10801,plain,
% 7.82/8.04 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10698, 194, 10800, 1216, 10646])).
% 7.82/8.04 tff(10802,plain,
% 7.82/8.04 (~r(s(s(s(elem!1))), s(s(z)))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10709, 194, 10800, 1216, 2405])).
% 7.82/8.04 tff(10803,plain,
% 7.82/8.04 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10713, 42, 10802])).
% 7.82/8.04 tff(10804,plain,
% 7.82/8.04 (b(s(s(s(elem!1))), s(s(z)))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10803, 10703])).
% 7.82/8.04 tff(10805,plain,
% 7.82/8.04 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10721, 391, 3823, 3563, 10804])).
% 7.82/8.04 tff(10806,plain,
% 7.82/8.04 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[2853, 42, 10801])).
% 7.82/8.04 tff(10807,plain,
% 7.82/8.04 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10806, 10805])).
% 7.82/8.04 tff(10808,plain,
% 7.82/8.04 (s(z) = elem!1),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[2849, 10807])).
% 7.82/8.04 tff(10809,plain,
% 7.82/8.04 (~b(s(s(s(s(z)))), elem!1)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[9614, 10808, 9024])).
% 7.82/8.04 tff(10810,plain,
% 7.82/8.04 (~(s(s(s(elem!1))) = elem!1)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[2694, 10809, 10801])).
% 7.82/8.04 tff(10811,plain,
% 7.82/8.04 (elem!1 = s(z)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[1495, 10808])).
% 7.82/8.04 tff(10812,plain,
% 7.82/8.04 (~b(s(s(s(elem!1))), elem!1)),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[1563, 10809, 10811])).
% 7.82/8.04 tff(10813,plain,
% 7.82/8.04 (elem!1 = s(s(s(elem!1)))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10519, 10812, 4028, 10781, 10798])).
% 7.82/8.04 tff(10814,plain,
% 7.82/8.04 ($false),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[129, 10813, 10810])).
% 7.82/8.04 tff(10815,plain,(b(elem!1, s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | b(elem!1, s(z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.82/8.04 tff(10816,plain,
% 7.82/8.04 (b(elem!1, s(s(s(elem!1))))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[10815, 9024, 3823, 10675, 2913, 10660, 31, 719, 3447, 115])).
% 7.82/8.04 tff(10817,plain,
% 7.82/8.04 (~(elem!1 = s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[8314, 10816, 2881])).
% 7.82/8.04 tff(10818,plain,
% 7.82/8.04 (r(elem!1, s(z))),
% 7.82/8.04 inference(unit_resolution,[status(thm)],[837, 10817, 31])).
% 7.82/8.04 tff(10819,plain,
% 7.82/8.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.82/8.04 inference(rewrite,[status(thm)],[])).
% 7.82/8.04 tff(10820,plain,
% 7.82/8.04 (((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.82/8.04 inference(rewrite,[status(thm)],[])).
% 7.82/8.04 tff(10821,plain,
% 7.82/8.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 7.82/8.05 inference(monotonicity,[status(thm)],[10820])).
% 7.82/8.05 tff(10822,plain,
% 7.82/8.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.82/8.05 inference(transitivity,[status(thm)],[10821, 10819])).
% 7.82/8.05 tff(10823,plain,
% 7.82/8.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 7.82/8.05 inference(quant_inst,[status(thm)],[])).
% 7.82/8.05 tff(10824,plain,
% 7.82/8.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 7.82/8.05 inference(modus_ponens,[status(thm)],[10823, 10822])).
% 7.82/8.05 tff(10825,plain,
% 7.82/8.05 (~r(s(s(s(s(z)))), elem!1)),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[10824, 194, 10818, 2913, 10646])).
% 7.82/8.05 tff(10826,plain,
% 7.82/8.05 (~r(elem!1, s(s(s(s(z)))))),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[6347, 10818, 2913, 10646])).
% 7.82/8.05 tff(10827,plain,
% 7.82/8.05 (~(s(z) = elem!1)),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[1495, 10817])).
% 7.82/8.05 tff(10828,plain,
% 7.82/8.05 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[2849, 10827])).
% 7.82/8.05 tff(10829,plain,
% 7.82/8.05 (~b(s(s(z)), s(z))),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[10658, 391, 1235, 664, 590])).
% 7.82/8.05 tff(10830,plain,
% 7.82/8.05 (r(s(s(z)), s(z))),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[3778, 10829])).
% 7.82/8.05 tff(10831,plain,
% 7.82/8.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 7.82/8.05 inference(rewrite,[status(thm)],[])).
% 7.82/8.05 tff(10832,plain,
% 7.82/8.05 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 7.82/8.05 inference(rewrite,[status(thm)],[])).
% 7.82/8.05 tff(10833,plain,
% 7.82/8.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))))),
% 7.82/8.05 inference(monotonicity,[status(thm)],[10832])).
% 7.82/8.05 tff(10834,plain,
% 7.82/8.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 7.82/8.05 inference(transitivity,[status(thm)],[10833, 10831])).
% 7.82/8.05 tff(10835,plain,
% 7.82/8.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 7.82/8.05 inference(quant_inst,[status(thm)],[])).
% 7.82/8.05 tff(10836,plain,
% 7.82/8.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))),
% 7.82/8.05 inference(modus_ponens,[status(thm)],[10835, 10834])).
% 7.82/8.05 tff(10837,plain,
% 7.82/8.05 (~r(elem!1, s(s(z)))),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[10836, 194, 847, 1216, 10830])).
% 7.82/8.05 tff(10838,plain,
% 7.82/8.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 7.82/8.05 inference(rewrite,[status(thm)],[])).
% 7.82/8.05 tff(10839,plain,
% 7.82/8.05 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 7.82/8.05 inference(rewrite,[status(thm)],[])).
% 7.82/8.05 tff(10840,plain,
% 7.82/8.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1))))),
% 7.82/8.05 inference(monotonicity,[status(thm)],[10839])).
% 7.82/8.05 tff(10841,plain,
% 7.82/8.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 7.82/8.05 inference(transitivity,[status(thm)],[10840, 10838])).
% 7.82/8.05 tff(10842,plain,
% 7.82/8.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 7.82/8.05 inference(quant_inst,[status(thm)],[])).
% 7.82/8.05 tff(10843,plain,
% 7.82/8.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1))),
% 7.82/8.05 inference(modus_ponens,[status(thm)],[10842, 10841])).
% 7.82/8.05 tff(10844,plain,
% 7.82/8.05 ($false),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[10843, 391, 133, 900, 10682, 448])).
% 7.82/8.05 tff(10845,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.05 tff(10846,plain,
% 7.82/8.05 (~b(s(s(s(elem!1))), elem!1)),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[10845, 10681, 448, 10729])).
% 7.82/8.05 tff(10847,plain,
% 7.82/8.05 (~b(s(s(s(elem!1))), s(z))),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[10690, 10681, 664, 590])).
% 7.82/8.05 tff(10848,plain,
% 7.82/8.05 (r(s(s(s(elem!1))), s(z))),
% 7.82/8.05 inference(unit_resolution,[status(thm)],[223, 10847])).
% 7.82/8.05 tff(10849,plain,
% 7.82/8.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.82/8.05 inference(rewrite,[status(thm)],[])).
% 7.82/8.05 tff(10850,plain,
% 7.82/8.05 (((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(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))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.82/8.06 inference(rewrite,[status(thm)],[])).
% 7.82/8.06 tff(10851,plain,
% 7.82/8.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(z), s(s(s(s(z))))))))),
% 7.82/8.06 inference(monotonicity,[status(thm)],[10850])).
% 7.82/8.06 tff(10852,plain,
% 7.82/8.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.82/8.06 inference(transitivity,[status(thm)],[10851, 10849])).
% 7.82/8.06 tff(10853,plain,
% 7.82/8.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 7.82/8.06 inference(quant_inst,[status(thm)],[])).
% 7.82/8.06 tff(10854,plain,
% 7.82/8.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 7.82/8.06 inference(modus_ponens,[status(thm)],[10853, 10852])).
% 7.82/8.06 tff(10855,plain,
% 7.82/8.06 ($false),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[10854, 194, 233, 183, 847, 1216])).
% 7.82/8.06 tff(10856,plain,((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.06 tff(10857,plain,
% 7.82/8.06 (~r(s(s(s(elem!1))), elem!1)),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[10856, 10848, 1216, 847])).
% 7.82/8.06 tff(10858,plain,
% 7.82/8.06 (s(s(s(elem!1))) = elem!1),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[230, 10857, 10846])).
% 7.82/8.06 tff(10859,plain,
% 7.82/8.06 (~(s(s(s(s(z)))) = elem!1)),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[1436, 10858])).
% 7.82/8.06 tff(10860,plain,
% 7.82/8.06 (~(elem!1 = s(s(s(s(z)))))),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[769, 10859])).
% 7.82/8.06 tff(10861,plain,
% 7.82/8.06 (b(elem!1, s(s(s(s(z)))))),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[781, 10860, 3222])).
% 7.82/8.06 tff(10862,plain,
% 7.82/8.06 (~b(elem!1, s(s(z)))),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[9127, 10861, 3563, 3823])).
% 7.82/8.06 tff(10863,plain,
% 7.82/8.06 (b(s(s(s(s(z)))), elem!1)),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[762, 10859, 6221])).
% 7.82/8.06 tff(10864,plain,
% 7.82/8.06 ($false),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[5600, 391, 133, 665, 1652, 1686])).
% 7.82/8.06 tff(10865,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.06 tff(10866,plain,
% 7.82/8.06 (~b(z, s(s(s(s(z)))))),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[10865, 1652, 665, 133])).
% 7.82/8.06 tff(10867,plain,
% 7.82/8.06 (r(z, s(s(s(s(z)))))),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[800, 10866])).
% 7.82/8.06 tff(10868,plain,
% 7.82/8.06 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.82/8.06 inference(rewrite,[status(thm)],[])).
% 7.82/8.06 tff(10869,plain,
% 7.82/8.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 7.82/8.06 inference(monotonicity,[status(thm)],[10868])).
% 7.82/8.06 tff(10870,plain,
% 7.82/8.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.82/8.06 inference(transitivity,[status(thm)],[10869, 4081])).
% 7.82/8.06 tff(10871,plain,
% 7.82/8.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 7.82/8.06 inference(quant_inst,[status(thm)],[])).
% 7.82/8.06 tff(10872,plain,
% 7.82/8.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 7.82/8.06 inference(modus_ponens,[status(thm)],[10871, 10870])).
% 7.82/8.06 tff(10873,plain,
% 7.82/8.06 (~b(s(s(s(s(z)))), z)),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[10872, 391, 133, 665, 1652])).
% 7.82/8.06 tff(10874,plain,
% 7.82/8.06 (r(s(s(s(s(z)))), z)),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[87, 10873])).
% 7.82/8.06 tff(10875,plain,
% 7.82/8.06 ($false),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[5856, 391, 133, 665, 380, 448])).
% 7.82/8.06 tff(10876,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.06 tff(10877,plain,
% 7.82/8.06 (~b(s(s(s(elem!1))), z)),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[10876, 448, 665, 133])).
% 7.82/8.06 tff(10878,plain,
% 7.82/8.06 (r(s(s(s(elem!1))), z)),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[377, 10877])).
% 7.82/8.06 tff(10879,plain,
% 7.82/8.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.06 inference(rewrite,[status(thm)],[])).
% 7.82/8.06 tff(10880,plain,
% 7.82/8.06 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.06 inference(rewrite,[status(thm)],[])).
% 7.82/8.06 tff(10881,plain,
% 7.82/8.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.82/8.06 inference(monotonicity,[status(thm)],[10880])).
% 7.82/8.06 tff(10882,plain,
% 7.82/8.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.06 inference(transitivity,[status(thm)],[10881, 10879])).
% 7.82/8.06 tff(10883,plain,
% 7.82/8.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.06 inference(quant_inst,[status(thm)],[])).
% 7.82/8.06 tff(10884,plain,
% 7.82/8.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.82/8.06 inference(modus_ponens,[status(thm)],[10883, 10882])).
% 7.82/8.06 tff(10885,plain,
% 7.82/8.06 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[10884, 194, 10878, 10874, 10867])).
% 7.82/8.06 tff(10886,plain,
% 7.82/8.06 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[4313, 42, 10885])).
% 7.82/8.06 tff(10887,plain,
% 7.82/8.06 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[10886, 6950])).
% 7.82/8.06 tff(10888,plain,
% 7.82/8.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.06 inference(rewrite,[status(thm)],[])).
% 7.82/8.06 tff(10889,plain,
% 7.82/8.06 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.06 inference(rewrite,[status(thm)],[])).
% 7.82/8.06 tff(10890,plain,
% 7.82/8.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.82/8.06 inference(monotonicity,[status(thm)],[10889])).
% 7.82/8.06 tff(10891,plain,
% 7.82/8.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.06 inference(transitivity,[status(thm)],[10890, 10888])).
% 7.82/8.06 tff(10892,plain,
% 7.82/8.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 7.82/8.06 inference(quant_inst,[status(thm)],[])).
% 7.82/8.06 tff(10893,plain,
% 7.82/8.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.82/8.06 inference(modus_ponens,[status(thm)],[10892, 10891])).
% 7.82/8.06 tff(10894,plain,
% 7.82/8.06 ($false),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[10893, 391, 665, 10682, 448, 1652, 10887])).
% 7.82/8.06 tff(10895,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.06 tff(10896,plain,
% 7.82/8.06 (~b(elem!1, z)),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[10895, 10863, 448, 10729, 10681, 3843])).
% 7.82/8.06 tff(10897,plain,
% 7.82/8.06 (~(elem!1 = s(s(z)))),
% 7.82/8.06 inference(unit_resolution,[status(thm)],[3589, 10896, 1235])).
% 7.82/8.07 tff(10898,plain,
% 7.82/8.07 ($false),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[3394, 10897, 10862, 10837])).
% 7.82/8.07 tff(10899,plain,(r(z, elem!1) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.82/8.07 tff(10900,plain,
% 7.82/8.07 (r(z, elem!1)),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10899, 10675, 1235, 3823, 10816, 10828, 10826, 10825, 2913, 10818, 10643, 10653, 115])).
% 7.82/8.07 tff(10901,plain,
% 7.82/8.07 (~(elem!1 = s(z))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[8314, 448, 2881])).
% 7.82/8.07 tff(10902,plain,
% 7.82/8.07 (~(s(z) = elem!1)),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[1495, 10901])).
% 7.82/8.07 tff(10903,plain,
% 7.82/8.07 (~r(elem!1, s(s(z)))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10836, 194, 847, 2913, 10830])).
% 7.82/8.07 tff(10904,plain,
% 7.82/8.07 (~r(s(s(s(elem!1))), elem!1)),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10856, 10784, 2913, 847])).
% 7.82/8.07 tff(10905,plain,
% 7.82/8.07 (b(s(s(s(elem!1))), elem!1)),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[230, 10904, 10793])).
% 7.82/8.07 tff(10906,plain,
% 7.82/8.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 7.82/8.07 inference(rewrite,[status(thm)],[])).
% 7.82/8.07 tff(10907,plain,
% 7.82/8.07 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 7.82/8.07 inference(rewrite,[status(thm)],[])).
% 7.82/8.07 tff(10908,plain,
% 7.82/8.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 7.82/8.07 inference(monotonicity,[status(thm)],[10907])).
% 7.82/8.07 tff(10909,plain,
% 7.82/8.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 7.82/8.07 inference(transitivity,[status(thm)],[10908, 10906])).
% 7.82/8.07 tff(10910,plain,
% 7.82/8.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 7.82/8.07 inference(quant_inst,[status(thm)],[])).
% 7.82/8.07 tff(10911,plain,
% 7.82/8.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 7.82/8.07 inference(modus_ponens,[status(thm)],[10910, 10909])).
% 7.82/8.07 tff(10912,plain,
% 7.82/8.07 (~b(elem!1, z)),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10911, 391, 10905, 10782, 448])).
% 7.82/8.07 tff(10913,plain,
% 7.82/8.07 (~(elem!1 = s(s(z)))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[3589, 10912, 1235])).
% 7.82/8.07 tff(10914,plain,
% 7.82/8.07 (b(elem!1, s(s(z)))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[3394, 10913, 10903])).
% 7.82/8.07 tff(10915,plain,
% 7.82/8.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.07 inference(rewrite,[status(thm)],[])).
% 7.82/8.07 tff(10916,plain,
% 7.82/8.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.07 inference(quant_inst,[status(thm)],[])).
% 7.82/8.07 tff(10917,plain,
% 7.82/8.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 7.82/8.07 inference(modus_ponens,[status(thm)],[10916, 10915])).
% 7.82/8.07 tff(10918,plain,
% 7.82/8.07 (~r(s(s(s(elem!1))), s(s(z)))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10917, 194, 1484, 183, 2405])).
% 7.82/8.07 tff(10919,plain,
% 7.82/8.07 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10713, 42, 10918])).
% 7.82/8.07 tff(10920,plain,
% 7.82/8.07 (b(s(s(s(elem!1))), s(s(z)))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10919, 10703])).
% 7.82/8.07 tff(10921,plain,
% 7.82/8.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.82/8.07 inference(rewrite,[status(thm)],[])).
% 7.82/8.07 tff(10922,plain,
% 7.82/8.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.82/8.07 inference(quant_inst,[status(thm)],[])).
% 7.82/8.07 tff(10923,plain,
% 7.82/8.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 7.82/8.07 inference(modus_ponens,[status(thm)],[10922, 10921])).
% 7.82/8.07 tff(10924,plain,
% 7.82/8.07 (~r(s(s(z)), s(s(s(elem!1))))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10923, 194, 1484, 183, 2405])).
% 7.82/8.07 tff(10925,plain,
% 7.82/8.07 (b(s(s(z)), s(s(s(elem!1))))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 10924])).
% 7.82/8.07 tff(10926,plain,
% 7.82/8.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.07 inference(rewrite,[status(thm)],[])).
% 7.82/8.07 tff(10927,plain,
% 7.82/8.07 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.07 inference(rewrite,[status(thm)],[])).
% 7.82/8.07 tff(10928,plain,
% 7.82/8.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 7.82/8.07 inference(monotonicity,[status(thm)],[10927])).
% 7.82/8.07 tff(10929,plain,
% 7.82/8.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 7.82/8.07 inference(transitivity,[status(thm)],[10928, 10926])).
% 7.82/8.07 tff(10930,plain,
% 7.82/8.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 7.82/8.07 inference(quant_inst,[status(thm)],[])).
% 7.82/8.07 tff(10931,plain,
% 7.82/8.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 7.82/8.07 inference(modus_ponens,[status(thm)],[10930, 10929])).
% 7.82/8.07 tff(10932,plain,
% 7.82/8.07 ($false),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10931, 391, 448, 3369, 10925, 10920])).
% 7.82/8.07 tff(10933,plain,((~r(s(s(z)), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.07 tff(10934,plain,
% 7.82/8.07 (~r(s(z), elem!1)),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10933, 10914, 448, 10784, 10830])).
% 7.82/8.07 tff(10935,plain,
% 7.82/8.07 (~r(elem!1, s(s(s(s(z)))))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[6347, 847, 2913, 723])).
% 7.82/8.07 tff(10936,plain,
% 7.82/8.07 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[2849, 10902])).
% 7.82/8.07 tff(10937,assumption,(s(s(s(elem!1))) = s(s(s(s(z))))), introduced(assumption)).
% 7.82/8.07 tff(10938,plain,
% 7.82/8.07 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 7.82/8.07 inference(symmetry,[status(thm)],[10937])).
% 7.82/8.07 tff(10939,plain,
% 7.82/8.07 ($false),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[3843, 10938])).
% 7.82/8.07 tff(10940,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.07 tff(10941,plain,
% 7.82/8.07 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 7.82/8.07 inference(unit_resolution,[status(thm)],[10940, 10936])).
% 7.82/8.07 tff(10942,plain,
% 7.82/8.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.07 inference(rewrite,[status(thm)],[])).
% 7.82/8.07 tff(10943,plain,
% 7.82/8.07 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.07 inference(rewrite,[status(thm)],[])).
% 7.82/8.07 tff(10944,plain,
% 7.82/8.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.82/8.08 inference(monotonicity,[status(thm)],[10943])).
% 7.82/8.08 tff(10945,plain,
% 7.82/8.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.08 inference(transitivity,[status(thm)],[10944, 10942])).
% 7.82/8.08 tff(10946,plain,
% 7.82/8.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.08 inference(quant_inst,[status(thm)],[])).
% 7.82/8.08 tff(10947,plain,
% 7.82/8.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.82/8.08 inference(modus_ponens,[status(thm)],[10946, 10945])).
% 7.82/8.08 tff(10948,plain,
% 7.82/8.08 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[10947, 194, 10784, 2913, 723])).
% 7.82/8.08 tff(10949,plain,
% 7.82/8.08 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[4313, 42, 10948, 10941])).
% 7.82/8.08 tff(10950,plain,
% 7.82/8.08 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[10698, 194, 10784, 2913, 723])).
% 7.82/8.08 tff(10951,plain,
% 7.82/8.08 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[2853, 42, 10936, 10950])).
% 7.82/8.08 tff(10952,plain,
% 7.82/8.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.08 inference(rewrite,[status(thm)],[])).
% 7.82/8.08 tff(10953,plain,
% 7.82/8.08 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.08 inference(rewrite,[status(thm)],[])).
% 7.82/8.08 tff(10954,plain,
% 7.82/8.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.82/8.08 inference(monotonicity,[status(thm)],[10953])).
% 7.82/8.08 tff(10955,plain,
% 7.82/8.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.08 inference(transitivity,[status(thm)],[10954, 10952])).
% 7.82/8.08 tff(10956,plain,
% 7.82/8.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 7.82/8.08 inference(quant_inst,[status(thm)],[])).
% 7.82/8.08 tff(10957,plain,
% 7.82/8.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.82/8.08 inference(modus_ponens,[status(thm)],[10956, 10955])).
% 7.82/8.08 tff(10958,plain,
% 7.82/8.08 ($false),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[10957, 391, 900, 2064, 3325, 1669])).
% 7.82/8.08 tff(10959,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.08 tff(10960,plain,
% 7.82/8.08 (~b(elem!1, s(s(s(s(z)))))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[10959, 10951, 10905, 10949])).
% 7.82/8.08 tff(10961,plain,
% 7.82/8.08 (elem!1 = s(s(s(s(z))))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[781, 10960, 10935])).
% 7.82/8.08 tff(10962,plain,
% 7.82/8.08 (s(s(s(s(z)))) = elem!1),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[769, 10961])).
% 7.82/8.08 tff(10963,plain,
% 7.82/8.08 (~b(s(z), elem!1)),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[6252, 10962, 2881])).
% 7.82/8.08 tff(10964,plain,
% 7.82/8.08 ($false),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[632, 10963, 10934, 10902])).
% 7.82/8.08 tff(10965,plain,(r(z, s(s(s(elem!1)))) | b(s(z), s(s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.08 tff(10966,plain,
% 7.82/8.08 (r(z, s(s(s(elem!1))))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[10965, 10816, 2881, 1235, 10646, 10818, 10643, 10653, 10900])).
% 7.82/8.08 tff(10967,plain,
% 7.82/8.08 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[10090, 10966, 3447, 719])).
% 7.82/8.08 tff(10968,plain,
% 7.82/8.08 (~(s(z) = s(elem!1))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[117, 115])).
% 7.82/8.08 tff(10969,plain,
% 7.82/8.08 (~r(elem!1, s(s(z)))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[10836, 194, 847, 2913, 2405])).
% 7.82/8.08 tff(10970,assumption,(~r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 7.82/8.08 tff(10971,plain,
% 7.82/8.08 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.82/8.08 inference(unit_resolution,[status(thm)],[4313, 42, 10970, 10941])).
% 7.82/8.08 tff(10972,plain,
% 7.82/8.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.08 inference(rewrite,[status(thm)],[])).
% 7.82/8.08 tff(10973,plain,
% 7.82/8.08 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.08 inference(rewrite,[status(thm)],[])).
% 7.82/8.08 tff(10974,plain,
% 7.82/8.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.82/8.08 inference(monotonicity,[status(thm)],[10973])).
% 7.82/8.09 tff(10975,plain,
% 7.82/8.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.09 inference(transitivity,[status(thm)],[10974, 10972])).
% 7.82/8.09 tff(10976,plain,
% 7.82/8.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 7.82/8.09 inference(quant_inst,[status(thm)],[])).
% 7.82/8.09 tff(10977,plain,
% 7.82/8.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.82/8.09 inference(modus_ponens,[status(thm)],[10976, 10975])).
% 7.82/8.09 tff(10978,plain,
% 7.82/8.09 (~b(s(s(z)), s(s(s(elem!1))))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[10977, 391, 3823, 3563, 10971])).
% 7.82/8.09 tff(10979,plain,
% 7.82/8.09 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 7.82/8.09 inference(monotonicity,[status(thm)],[3584])).
% 7.82/8.09 tff(10980,plain,
% 7.82/8.09 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 7.82/8.09 inference(symmetry,[status(thm)],[10979])).
% 7.82/8.09 tff(10981,plain,
% 7.82/8.09 ((~b(s(s(z)), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 7.82/8.09 inference(monotonicity,[status(thm)],[10980])).
% 7.82/8.09 tff(10982,plain,
% 7.82/8.09 (~b(elem!1, s(s(s(elem!1))))),
% 7.82/8.09 inference(modus_ponens,[status(thm)],[8549, 10981])).
% 7.82/8.09 tff(10983,plain,
% 7.82/8.09 ($false),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[448, 10982])).
% 7.82/8.09 tff(10984,plain,((~(elem!1 = s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | b(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.09 tff(10985,plain,
% 7.82/8.09 (~(elem!1 = s(s(z)))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[10984, 10978, 448])).
% 7.82/8.09 tff(10986,plain,
% 7.82/8.09 (b(elem!1, s(s(z)))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[3394, 10985, 10969])).
% 7.82/8.09 tff(10987,plain,
% 7.82/8.09 (~b(elem!1, s(s(s(s(z)))))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[9127, 10986, 3563, 3823])).
% 7.82/8.09 tff(10988,plain,
% 7.82/8.09 (elem!1 = s(s(s(s(z))))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[781, 10987, 10935])).
% 7.82/8.09 tff(10989,plain,
% 7.82/8.09 (s(elem!1) = s(s(s(s(s(z)))))),
% 7.82/8.09 inference(monotonicity,[status(thm)],[10988])).
% 7.82/8.09 tff(10990,plain,
% 7.82/8.09 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 7.82/8.09 inference(monotonicity,[status(thm)],[10989])).
% 7.82/8.09 tff(10991,plain,
% 7.82/8.09 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 7.82/8.09 inference(monotonicity,[status(thm)],[10990])).
% 7.82/8.09 tff(10992,plain,
% 7.82/8.09 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 7.82/8.09 inference(monotonicity,[status(thm)],[10988])).
% 7.82/8.09 tff(10993,plain,
% 7.82/8.09 (~r(s(s(s(s(z)))), elem!1)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[10824, 194, 847, 2913, 723])).
% 7.82/8.09 tff(10994,plain,
% 7.82/8.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 7.82/8.09 inference(rewrite,[status(thm)],[])).
% 7.82/8.09 tff(10995,plain,
% 7.82/8.09 (((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 7.82/8.09 inference(rewrite,[status(thm)],[])).
% 7.82/8.09 tff(10996,plain,
% 7.82/8.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))))),
% 7.82/8.09 inference(monotonicity,[status(thm)],[10995])).
% 7.82/8.09 tff(10997,plain,
% 7.82/8.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 7.82/8.09 inference(transitivity,[status(thm)],[10996, 10994])).
% 7.82/8.09 tff(10998,plain,
% 7.82/8.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 7.82/8.09 inference(quant_inst,[status(thm)],[])).
% 7.82/8.09 tff(10999,plain,
% 7.82/8.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 7.82/8.09 inference(modus_ponens,[status(thm)],[10998, 10997])).
% 7.82/8.09 tff(11000,plain,
% 7.82/8.09 (~r(s(s(z)), elem!1)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[10999, 194, 847, 2913, 2405])).
% 7.82/8.09 tff(11001,plain,
% 7.82/8.09 (elem!1 = s(s(z))),
% 7.82/8.09 inference(modus_ponens,[status(thm)],[4579, 698])).
% 7.82/8.09 tff(11002,plain,
% 7.82/8.09 ($false),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[1405, 11001])).
% 7.82/8.09 tff(11003,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.09 tff(11004,plain,
% 7.82/8.09 (~(s(s(z)) = elem!1)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[11003, 10985])).
% 7.82/8.09 tff(11005,plain,
% 7.82/8.09 (b(s(s(z)), elem!1)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[4730, 11004, 11000])).
% 7.82/8.09 tff(11006,plain,
% 7.82/8.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 7.82/8.09 inference(rewrite,[status(thm)],[])).
% 7.82/8.09 tff(11007,plain,
% 7.82/8.09 (((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 7.82/8.09 inference(rewrite,[status(thm)],[])).
% 7.82/8.09 tff(11008,plain,
% 7.82/8.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 7.82/8.09 inference(monotonicity,[status(thm)],[11007])).
% 7.82/8.09 tff(11009,plain,
% 7.82/8.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 7.82/8.09 inference(transitivity,[status(thm)],[11008, 11006])).
% 7.82/8.09 tff(11010,plain,
% 7.82/8.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 7.82/8.09 inference(quant_inst,[status(thm)],[])).
% 7.82/8.09 tff(11011,plain,
% 7.82/8.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 7.82/8.09 inference(modus_ponens,[status(thm)],[11010, 11009])).
% 7.82/8.09 tff(11012,plain,
% 7.82/8.09 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[11011, 391])).
% 7.82/8.09 tff(11013,plain,
% 7.82/8.09 (~b(s(s(s(s(z)))), elem!1)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[11012, 11005, 3563, 10986])).
% 7.82/8.09 tff(11014,plain,
% 7.82/8.09 (s(s(s(s(z)))) = elem!1),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[762, 11013, 10993])).
% 7.82/8.09 tff(11015,plain,
% 7.82/8.09 (~(s(s(s(elem!1))) = s(elem!1))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[717, 11014])).
% 7.82/8.09 tff(11016,plain,
% 7.82/8.09 (~(s(s(elem!1)) = elem!1)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[451, 11015])).
% 7.82/8.09 tff(11017,plain,
% 7.82/8.09 (~r(s(s(s(elem!1))), elem!1)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[10856, 183, 2913, 847])).
% 7.82/8.09 tff(11018,plain,
% 7.82/8.09 (b(s(s(s(elem!1))), elem!1)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[230, 11017, 127])).
% 7.82/8.09 tff(11019,plain,
% 7.82/8.09 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[10698, 194, 183, 2913, 723])).
% 7.82/8.09 tff(11020,plain,
% 7.82/8.09 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[2853, 42, 10936, 11019])).
% 7.82/8.09 tff(11021,plain,
% 7.82/8.09 (~b(elem!1, s(s(s(s(z)))))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[10959, 11020, 11018, 10971])).
% 7.82/8.09 tff(11022,plain,
% 7.82/8.09 (elem!1 = s(s(s(s(z))))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[781, 11021, 10935])).
% 7.82/8.09 tff(11023,plain,
% 7.82/8.09 (s(s(s(s(z)))) = elem!1),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[769, 11022])).
% 7.82/8.09 tff(11024,plain,
% 7.82/8.09 (b(s(s(s(s(z)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 7.82/8.09 inference(monotonicity,[status(thm)],[688])).
% 7.82/8.09 tff(11025,plain,
% 7.82/8.09 (b(elem!1, s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 7.82/8.09 inference(symmetry,[status(thm)],[11024])).
% 7.82/8.09 tff(11026,plain,
% 7.82/8.09 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 7.82/8.09 inference(monotonicity,[status(thm)],[11025])).
% 7.82/8.09 tff(11027,plain,
% 7.82/8.09 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.82/8.09 inference(modus_ponens,[status(thm)],[3583, 11026])).
% 7.82/8.09 tff(11028,plain,
% 7.82/8.09 ($false),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[3563, 11027])).
% 7.82/8.09 tff(11029,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.09 tff(11030,plain,
% 7.82/8.09 (b(elem!1, s(s(z)))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[11029, 11023, 3563])).
% 7.82/8.09 tff(11031,plain,
% 7.82/8.09 (~b(s(z), elem!1)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[6252, 11023, 2881])).
% 7.82/8.09 tff(11032,plain,
% 7.82/8.09 (r(s(z), elem!1)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[632, 11031, 10902])).
% 7.82/8.09 tff(11033,plain,
% 7.82/8.09 ($false),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[10933, 11032, 11030, 448, 183, 2405])).
% 7.82/8.09 tff(11034,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(s(z), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.09 tff(11035,plain,
% 7.82/8.09 (~r(s(s(s(elem!1))), s(z))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[11034, 127, 2405, 3563, 2881, 10970, 723, 448, 847])).
% 7.82/8.09 tff(11036,plain,
% 7.82/8.09 (b(s(s(s(elem!1))), s(z))),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[223, 11035])).
% 7.82/8.09 tff(11037,plain,
% 7.82/8.09 (~b(s(s(s(elem!1))), z)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[10633, 391, 11036, 10643, 590])).
% 7.82/8.09 tff(11038,plain,
% 7.82/8.09 (r(s(s(s(elem!1))), z)),
% 7.82/8.09 inference(unit_resolution,[status(thm)],[377, 11037])).
% 7.82/8.10 tff(11039,assumption,(~r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 7.82/8.10 tff(11040,plain,
% 7.82/8.10 ($false),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 8549, 11039])).
% 7.82/8.10 tff(11041,plain,(b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.10 tff(11042,plain,
% 7.82/8.10 (r(s(s(z)), s(s(s(elem!1))))),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[11041, 10978])).
% 7.82/8.10 tff(11043,plain,
% 7.82/8.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.82/8.10 inference(rewrite,[status(thm)],[])).
% 7.82/8.10 tff(11044,plain,
% 7.82/8.10 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.82/8.10 inference(rewrite,[status(thm)],[])).
% 7.82/8.10 tff(11045,plain,
% 7.82/8.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 7.82/8.10 inference(monotonicity,[status(thm)],[11044])).
% 7.82/8.10 tff(11046,plain,
% 7.82/8.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.82/8.10 inference(transitivity,[status(thm)],[11045, 11043])).
% 7.82/8.10 tff(11047,plain,
% 7.82/8.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 7.82/8.10 inference(quant_inst,[status(thm)],[])).
% 7.82/8.10 tff(11048,plain,
% 7.82/8.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 7.82/8.10 inference(modus_ponens,[status(thm)],[11047, 11046])).
% 7.82/8.10 tff(11049,plain,
% 7.82/8.10 ($false),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[11048, 194, 174, 232, 2405, 9130])).
% 7.82/8.10 tff(11050,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.82/8.10 tff(11051,plain,
% 7.82/8.10 (~r(s(z), s(s(s(elem!1))))),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[11050, 11042, 2405, 11038])).
% 7.82/8.10 tff(11052,plain,
% 7.82/8.10 (b(s(z), s(s(s(elem!1))))),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[247, 11051])).
% 7.82/8.10 tff(11053,plain,
% 7.82/8.10 (~b(s(z), elem!1)),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[4026, 11052, 448, 11036])).
% 7.82/8.10 tff(11054,plain,
% 7.82/8.10 (r(s(z), elem!1)),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[632, 11053, 10902])).
% 7.82/8.10 tff(11055,plain,
% 7.82/8.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.10 inference(rewrite,[status(thm)],[])).
% 7.82/8.10 tff(11056,plain,
% 7.82/8.10 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.10 inference(rewrite,[status(thm)],[])).
% 7.82/8.10 tff(11057,plain,
% 7.82/8.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.82/8.10 inference(monotonicity,[status(thm)],[11056])).
% 7.82/8.10 tff(11058,plain,
% 7.82/8.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.10 inference(transitivity,[status(thm)],[11057, 11055])).
% 7.82/8.10 tff(11059,plain,
% 7.82/8.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.10 inference(quant_inst,[status(thm)],[])).
% 7.82/8.10 tff(11060,plain,
% 7.82/8.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.82/8.10 inference(modus_ponens,[status(thm)],[11059, 11058])).
% 7.82/8.10 tff(11061,plain,
% 7.82/8.10 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[11060, 194, 411, 174, 3447])).
% 7.82/8.10 tff(11062,plain,
% 7.82/8.10 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[4313, 42, 11061])).
% 7.82/8.10 tff(11063,plain,
% 7.82/8.10 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[11062, 6507])).
% 7.82/8.10 tff(11064,plain,
% 7.82/8.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 7.82/8.10 inference(rewrite,[status(thm)],[])).
% 7.82/8.10 tff(11065,plain,
% 7.82/8.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 7.82/8.10 inference(quant_inst,[status(thm)],[])).
% 7.82/8.10 tff(11066,plain,
% 7.82/8.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 7.82/8.10 inference(modus_ponens,[status(thm)],[11065, 11064])).
% 7.82/8.10 tff(11067,plain,
% 7.82/8.10 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[11066, 194, 411, 174, 3447])).
% 7.82/8.10 tff(11068,plain,
% 7.82/8.10 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.82/8.10 inference(unit_resolution,[status(thm)],[2853, 42, 3363, 11067])).
% 7.82/8.10 tff(11069,plain,
% 7.82/8.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.11 inference(rewrite,[status(thm)],[])).
% 7.82/8.11 tff(11070,plain,
% 7.82/8.11 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.11 inference(rewrite,[status(thm)],[])).
% 7.82/8.11 tff(11071,plain,
% 7.82/8.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.82/8.11 inference(monotonicity,[status(thm)],[11070])).
% 7.82/8.11 tff(11072,plain,
% 7.82/8.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.11 inference(transitivity,[status(thm)],[11071, 11069])).
% 7.82/8.11 tff(11073,plain,
% 7.82/8.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 7.82/8.11 inference(quant_inst,[status(thm)],[])).
% 7.82/8.11 tff(11074,plain,
% 7.82/8.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.82/8.11 inference(modus_ponens,[status(thm)],[11073, 11072])).
% 7.82/8.11 tff(11075,plain,
% 7.82/8.11 (~b(s(s(s(s(z)))), elem!1)),
% 7.82/8.11 inference(unit_resolution,[status(thm)],[11074, 391, 448, 11068, 11063])).
% 7.82/8.11 tff(11076,plain,
% 7.82/8.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.11 inference(rewrite,[status(thm)],[])).
% 7.82/8.11 tff(11077,plain,
% 7.82/8.11 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.11 inference(rewrite,[status(thm)],[])).
% 7.82/8.11 tff(11078,plain,
% 7.82/8.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.82/8.11 inference(monotonicity,[status(thm)],[11077])).
% 7.82/8.11 tff(11079,plain,
% 7.82/8.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.11 inference(transitivity,[status(thm)],[11078, 11076])).
% 7.82/8.11 tff(11080,plain,
% 7.82/8.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.82/8.11 inference(quant_inst,[status(thm)],[])).
% 7.82/8.11 tff(11081,plain,
% 7.82/8.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.82/8.11 inference(modus_ponens,[status(thm)],[11080, 11079])).
% 7.82/8.11 tff(11082,plain,
% 7.82/8.11 (~b(s(z), s(s(s(s(z)))))),
% 7.82/8.11 inference(unit_resolution,[status(thm)],[11081, 391, 379, 11068, 11063])).
% 7.82/8.11 tff(11083,plain,
% 7.82/8.11 (r(s(z), s(s(s(s(z)))))),
% 7.82/8.11 inference(unit_resolution,[status(thm)],[1230, 11082])).
% 7.82/8.11 tff(11084,plain,
% 7.82/8.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.11 inference(rewrite,[status(thm)],[])).
% 7.82/8.11 tff(11085,plain,
% 7.82/8.11 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.11 inference(rewrite,[status(thm)],[])).
% 7.82/8.11 tff(11086,plain,
% 7.82/8.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.82/8.11 inference(monotonicity,[status(thm)],[11085])).
% 7.82/8.11 tff(11087,plain,
% 7.82/8.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.82/8.11 inference(transitivity,[status(thm)],[11086, 11084])).
% 7.82/8.11 tff(11088,plain,
% 7.82/8.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 7.82/8.11 inference(quant_inst,[status(thm)],[])).
% 7.82/8.11 tff(11089,plain,
% 7.82/8.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.82/8.11 inference(modus_ponens,[status(thm)],[11088, 11087])).
% 7.82/8.11 tff(11090,plain,
% 7.82/8.11 (~b(elem!1, s(z))),
% 7.82/8.11 inference(unit_resolution,[status(thm)],[11089, 391, 448, 379, 11068, 11063])).
% 7.82/8.11 tff(11091,plain,
% 7.82/8.11 ((elem!1 = s(z)) | r(elem!1, s(z))),
% 7.82/8.11 inference(unit_resolution,[status(thm)],[835, 42, 11090])).
% 7.82/8.11 tff(11092,plain,
% 7.82/8.11 (r(elem!1, s(z))),
% 7.82/8.11 inference(unit_resolution,[status(thm)],[11091, 1746])).
% 7.82/8.11 tff(11093,plain,
% 7.82/8.11 (~r(s(s(s(s(z)))), elem!1)),
% 7.82/8.11 inference(unit_resolution,[status(thm)],[5396, 11092, 11083, 1484])).
% 7.82/8.11 tff(11094,plain,
% 7.82/8.11 (s(s(s(s(z)))) = elem!1),
% 7.82/8.11 inference(unit_resolution,[status(thm)],[762, 11093, 11075])).
% 7.82/8.11 tff(11095,plain,
% 7.82/8.11 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 7.82/8.11 inference(monotonicity,[status(thm)],[11094])).
% 7.82/8.11 tff(11096,plain,
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% 7.82/8.12 inference(modus_ponens,[status(thm)],[11112, 11111])).
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% 7.82/8.12 inference(monotonicity,[status(thm)],[11118, 11117])).
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% 7.82/8.12 inference(monotonicity,[status(thm)],[11142])).
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% 7.92/8.12 tff(11147,plain,
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% 7.92/8.12 tff(11148,plain,((s(s(s(elem!1))) = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(elem!1, s(z))) | (elem!1 = z) | b(s(s(s(s(z)))), z) | (~r(s(s(z)), s(z))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.12 tff(11149,plain,
% 7.92/8.12 (s(s(s(elem!1))) = elem!1),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[11148, 10675, 3823, 10816, 10900, 10968, 10966, 10653, 10818, 10680, 3446, 10660, 10967, 2881, 10646])).
% 7.92/8.12 tff(11150,plain,
% 7.92/8.12 (~b(s(s(s(elem!1))), s(z))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[8400, 11149, 31])).
% 7.92/8.12 tff(11151,plain,
% 7.92/8.12 (r(s(s(s(elem!1))), s(z))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[223, 11150])).
% 7.92/8.12 tff(11152,plain,
% 7.92/8.12 (~r(elem!1, s(s(z)))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[10836, 194, 10818, 2913, 10660])).
% 7.92/8.12 tff(11153,plain,
% 7.92/8.12 (~(s(s(s(s(z)))) = elem!1)),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[1436, 11149])).
% 7.92/8.12 tff(11154,plain,
% 7.92/8.12 (~(elem!1 = s(s(s(s(z)))))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[769, 11153])).
% 7.92/8.12 tff(11155,plain,
% 7.92/8.12 (b(elem!1, s(s(s(s(z)))))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[781, 11154, 10826])).
% 7.92/8.12 tff(11156,plain,
% 7.92/8.12 (~b(elem!1, s(s(z)))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[9127, 11155, 10675, 3823])).
% 7.92/8.12 tff(11157,plain,
% 7.92/8.12 (elem!1 = s(s(z))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[3394, 11156, 11152])).
% 7.92/8.12 tff(11158,plain,
% 7.92/8.12 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[9253, 11157])).
% 7.92/8.12 tff(11159,plain,
% 7.92/8.12 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[1370, 11158, 8329])).
% 7.92/8.12 tff(11160,plain,
% 7.92/8.12 (~b(s(s(elem!1)), s(z))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[9032, 11157, 9024])).
% 7.92/8.12 tff(11161,plain,
% 7.92/8.12 (r(s(s(elem!1)), s(z))),
% 7.92/8.12 inference(unit_resolution,[status(thm)],[362, 11160])).
% 7.92/8.12 tff(11162,plain,
% 7.92/8.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.92/8.12 inference(rewrite,[status(thm)],[])).
% 7.92/8.12 tff(11163,plain,
% 7.92/8.12 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.92/8.12 inference(rewrite,[status(thm)],[])).
% 7.92/8.12 tff(11164,plain,
% 7.92/8.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 7.92/8.12 inference(monotonicity,[status(thm)],[11163])).
% 7.92/8.12 tff(11165,plain,
% 7.92/8.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.92/8.13 inference(transitivity,[status(thm)],[11164, 11162])).
% 7.92/8.13 tff(11166,plain,
% 7.92/8.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 7.92/8.13 inference(quant_inst,[status(thm)],[])).
% 7.92/8.13 tff(11167,plain,
% 7.92/8.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 7.92/8.13 inference(modus_ponens,[status(thm)],[11166, 11165])).
% 7.92/8.13 tff(11168,plain,
% 7.92/8.13 ($false),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[11167, 194, 340, 327, 183, 1216])).
% 7.92/8.13 tff(11169,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.13 tff(11170,plain,
% 7.92/8.13 ($false),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[11169, 11161, 11159, 2913, 11151])).
% 7.92/8.13 tff(11171,plain,(b(s(s(s(s(z)))), s(z)) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(z)) | b(s(s(s(s(z)))), z) | b(s(z), s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.92/8.13 tff(11172,plain,
% 7.92/8.13 (b(s(s(s(s(z)))), s(z))),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[11171, 1235, 3823, 31, 3446, 2881, 719, 8329, 115])).
% 7.92/8.13 tff(11173,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 7.92/8.13 tff(11174,plain,
% 7.92/8.13 (r(s(s(s(elem!1))), s(z))),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[223, 11173])).
% 7.92/8.13 tff(11175,plain,
% 7.92/8.13 (b(s(s(s(elem!1))), s(z))),
% 7.92/8.13 inference(modus_ponens,[status(thm)],[1759, 1554])).
% 7.92/8.13 tff(11176,plain,
% 7.92/8.13 ($false),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[11173, 11175])).
% 7.92/8.13 tff(11177,plain,((~(elem!1 = s(z))) | b(s(s(s(elem!1))), s(z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.13 tff(11178,plain,
% 7.92/8.13 (~(elem!1 = s(z))),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[11177, 11173, 1759])).
% 7.92/8.13 tff(11179,plain,
% 7.92/8.13 (r(elem!1, s(z))),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[837, 11178, 31])).
% 7.92/8.13 tff(11180,plain,
% 7.92/8.13 (~r(elem!1, s(s(s(elem!1))))),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[10776, 11179, 1216, 11174])).
% 7.92/8.13 tff(11181,plain,
% 7.92/8.13 (elem!1 = s(s(s(elem!1)))),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[424, 11180, 4028])).
% 7.92/8.13 tff(11182,plain,
% 7.92/8.13 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.92/8.13 inference(monotonicity,[status(thm)],[11181])).
% 7.92/8.13 tff(11183,plain,
% 7.92/8.13 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 7.92/8.13 inference(monotonicity,[status(thm)],[688])).
% 7.92/8.13 tff(11184,plain,
% 7.92/8.13 (b(elem!1, s(z))),
% 7.92/8.13 inference(modus_ponens,[status(thm)],[1759, 11183])).
% 7.92/8.13 tff(11185,plain,
% 7.92/8.13 ($false),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[31, 11184])).
% 7.92/8.13 tff(11186,plain,((~b(s(s(s(s(z)))), s(z))) | b(elem!1, s(z)) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.13 tff(11187,plain,
% 7.92/8.13 (~(s(s(s(s(z)))) = elem!1)),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[11186, 1759, 31])).
% 7.92/8.13 tff(11188,plain,
% 7.92/8.13 (~(elem!1 = s(s(s(s(z)))))),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[769, 11187])).
% 7.92/8.13 tff(11189,plain,
% 7.92/8.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.92/8.13 inference(rewrite,[status(thm)],[])).
% 7.92/8.13 tff(11190,plain,
% 7.92/8.13 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.92/8.13 inference(rewrite,[status(thm)],[])).
% 7.92/8.13 tff(11191,plain,
% 7.92/8.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 7.92/8.13 inference(monotonicity,[status(thm)],[11190])).
% 7.92/8.13 tff(11192,plain,
% 7.92/8.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.92/8.13 inference(transitivity,[status(thm)],[11191, 11189])).
% 7.92/8.13 tff(11193,plain,
% 7.92/8.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))),
% 7.92/8.13 inference(quant_inst,[status(thm)],[])).
% 7.92/8.13 tff(11194,plain,
% 7.92/8.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 7.92/8.13 inference(modus_ponens,[status(thm)],[11193, 11192])).
% 7.92/8.13 tff(11195,plain,
% 7.92/8.13 ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[11194, 194])).
% 7.92/8.13 tff(11196,plain,
% 7.92/8.13 (~r(elem!1, s(s(s(s(z)))))),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[11195, 11179, 2053, 1216])).
% 7.92/8.13 tff(11197,plain,
% 7.92/8.13 (b(elem!1, s(s(s(s(z)))))),
% 7.92/8.13 inference(unit_resolution,[status(thm)],[781, 11196, 11188])).
% 7.92/8.13 tff(11198,plain,
% 7.92/8.13 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.92/8.13 inference(modus_ponens,[status(thm)],[11197, 11182])).
% 7.92/8.13 tff(11199,plain,
% 7.92/8.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.92/8.13 inference(rewrite,[status(thm)],[])).
% 7.92/8.13 tff(11200,plain,
% 7.92/8.13 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.92/8.13 inference(rewrite,[status(thm)],[])).
% 7.92/8.13 tff(11201,plain,
% 7.92/8.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.92/8.13 inference(monotonicity,[status(thm)],[11200])).
% 7.92/8.13 tff(11202,plain,
% 7.92/8.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.92/8.14 inference(transitivity,[status(thm)],[11201, 11199])).
% 7.92/8.14 tff(11203,plain,
% 7.92/8.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 7.92/8.14 inference(quant_inst,[status(thm)],[])).
% 7.92/8.14 tff(11204,plain,
% 7.92/8.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.92/8.14 inference(modus_ponens,[status(thm)],[11203, 11202])).
% 7.92/8.14 tff(11205,plain,
% 7.92/8.14 (~b(s(s(z)), s(s(s(elem!1))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[11204, 391, 3823, 1759, 590, 11198])).
% 7.92/8.14 tff(11206,plain,
% 7.92/8.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.92/8.14 inference(rewrite,[status(thm)],[])).
% 7.92/8.14 tff(11207,plain,
% 7.92/8.14 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.92/8.14 inference(rewrite,[status(thm)],[])).
% 7.92/8.14 tff(11208,plain,
% 7.92/8.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 7.92/8.14 inference(monotonicity,[status(thm)],[11207])).
% 7.92/8.14 tff(11209,plain,
% 7.92/8.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.92/8.14 inference(transitivity,[status(thm)],[11208, 11206])).
% 7.92/8.14 tff(11210,plain,
% 7.92/8.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.92/8.14 inference(quant_inst,[status(thm)],[])).
% 7.92/8.14 tff(11211,plain,
% 7.92/8.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 7.92/8.14 inference(modus_ponens,[status(thm)],[11210, 11209])).
% 7.92/8.14 tff(11212,plain,
% 7.92/8.14 (~r(s(s(z)), s(s(s(elem!1))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[11211, 194, 11174, 1216, 2405])).
% 7.92/8.14 tff(11213,plain,
% 7.92/8.14 ($false),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[11041, 11212, 11205])).
% 7.92/8.14 tff(11214,plain,(b(s(s(s(elem!1))), s(z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.14 tff(11215,plain,
% 7.92/8.14 (b(s(s(s(elem!1))), s(z))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[11214, 4028, 2405, 3823, 1759, 590, 1216, 2053, 31])).
% 7.92/8.14 tff(11216,plain,
% 7.92/8.14 (~b(z, s(s(s(elem!1))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[10690, 11215, 10679, 590])).
% 7.92/8.14 tff(11217,plain,
% 7.92/8.14 (r(z, s(s(s(elem!1))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[58, 11216])).
% 7.92/8.14 tff(11218,plain,
% 7.92/8.14 (r(z, elem!1)),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[8231, 11216, 2])).
% 7.92/8.14 tff(11219,plain,
% 7.92/8.14 ($false),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[10635, 11218, 11217, 590, 10679, 4028, 11215, 31])).
% 7.92/8.14 tff(11220,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(z), z)) | b(elem!1, s(z)) | (elem!1 = z) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.14 tff(11221,plain,
% 7.92/8.14 (b(elem!1, s(s(s(elem!1))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[11220, 10660, 31, 10680, 10653, 3823, 11172, 2913, 3447])).
% 7.92/8.14 tff(11222,plain,
% 7.92/8.14 (~(elem!1 = s(z))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[8314, 11221, 2881])).
% 7.92/8.14 tff(11223,plain,
% 7.92/8.14 (~(s(z) = elem!1)),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[1495, 11222])).
% 7.92/8.14 tff(11224,plain,
% 7.92/8.14 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[2849, 11223])).
% 7.92/8.14 tff(11225,plain,
% 7.92/8.14 (~(s(s(s(s(z)))) = elem!1)),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[11186, 11172, 31])).
% 7.92/8.14 tff(11226,plain,
% 7.92/8.14 (~(elem!1 = s(s(s(s(z)))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[769, 11225])).
% 7.92/8.14 tff(11227,plain,
% 7.92/8.14 (r(elem!1, s(z))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[837, 11222, 31])).
% 7.92/8.14 tff(11228,plain,
% 7.92/8.14 (~r(elem!1, s(s(s(s(z)))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[11195, 11227, 3447, 2913])).
% 7.92/8.14 tff(11229,plain,
% 7.92/8.14 (b(elem!1, s(s(s(s(z)))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[781, 11228, 11226])).
% 7.92/8.14 tff(11230,plain,
% 7.92/8.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.92/8.14 inference(rewrite,[status(thm)],[])).
% 7.92/8.14 tff(11231,plain,
% 7.92/8.14 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.92/8.14 inference(rewrite,[status(thm)],[])).
% 7.92/8.14 tff(11232,plain,
% 7.92/8.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 7.92/8.14 inference(monotonicity,[status(thm)],[11231])).
% 7.92/8.14 tff(11233,plain,
% 7.92/8.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.92/8.14 inference(transitivity,[status(thm)],[11232, 11230])).
% 7.92/8.14 tff(11234,plain,
% 7.92/8.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 7.92/8.14 inference(quant_inst,[status(thm)],[])).
% 7.92/8.14 tff(11235,plain,
% 7.92/8.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 7.92/8.14 inference(modus_ponens,[status(thm)],[11234, 11233])).
% 7.92/8.14 tff(11236,plain,
% 7.92/8.14 (~b(elem!1, s(s(z)))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[11235, 391, 3823, 11229, 11172, 10653])).
% 7.92/8.14 tff(11237,plain,
% 7.92/8.14 (~r(elem!1, s(s(z)))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[10836, 194, 11227, 2913, 10660])).
% 7.92/8.14 tff(11238,plain,
% 7.92/8.14 (elem!1 = s(s(z))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[3394, 11237, 11236])).
% 7.92/8.14 tff(11239,plain,
% 7.92/8.14 (s(elem!1) = s(s(s(z)))),
% 7.92/8.14 inference(monotonicity,[status(thm)],[11238])).
% 7.92/8.14 tff(11240,plain,
% 7.92/8.14 (s(s(elem!1)) = s(s(s(s(z))))),
% 7.92/8.14 inference(monotonicity,[status(thm)],[11239])).
% 7.92/8.14 tff(11241,plain,
% 7.92/8.14 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.92/8.14 inference(monotonicity,[status(thm)],[11240])).
% 7.92/8.14 tff(11242,plain,
% 7.92/8.14 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[9253, 11238])).
% 7.92/8.14 tff(11243,plain,
% 7.92/8.14 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[1370, 11242, 8329])).
% 7.92/8.14 tff(11244,plain,
% 7.92/8.14 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.92/8.14 inference(modus_ponens,[status(thm)],[11243, 11241])).
% 7.92/8.14 tff(11245,plain,
% 7.92/8.14 (~r(z, s(s(s(elem!1))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[10090, 11244, 3447, 719])).
% 7.92/8.14 tff(11246,plain,
% 7.92/8.14 (b(z, s(s(s(elem!1))))),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[58, 11245])).
% 7.92/8.14 tff(11247,plain,
% 7.92/8.14 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 7.92/8.14 inference(monotonicity,[status(thm)],[3584])).
% 7.92/8.14 tff(11248,plain,
% 7.92/8.14 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 7.92/8.14 inference(symmetry,[status(thm)],[11247])).
% 7.92/8.14 tff(11249,plain,
% 7.92/8.14 ((~b(s(z), s(s(z)))) <=> (~b(s(z), elem!1))),
% 7.92/8.14 inference(monotonicity,[status(thm)],[11248])).
% 7.92/8.14 tff(11250,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 7.92/8.14 tff(11251,plain,
% 7.92/8.14 (~b(s(z), elem!1)),
% 7.92/8.14 inference(modus_ponens,[status(thm)],[11250, 11249])).
% 7.92/8.14 tff(11252,plain,
% 7.92/8.14 ($false),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[644, 11251])).
% 7.92/8.14 tff(11253,plain,((~(elem!1 = s(s(z)))) | (~b(s(z), elem!1)) | b(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.14 tff(11254,plain,
% 7.92/8.14 (~b(s(z), elem!1)),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[11253, 11238, 10667])).
% 7.92/8.14 tff(11255,plain,
% 7.92/8.14 (r(s(z), elem!1)),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[632, 11254, 11223])).
% 7.92/8.14 tff(11256,plain,
% 7.92/8.14 (~r(s(s(s(s(z)))), elem!1)),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[5396, 11255, 11227, 2913])).
% 7.92/8.14 tff(11257,plain,
% 7.92/8.14 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 7.92/8.14 inference(monotonicity,[status(thm)],[11238])).
% 7.92/8.14 tff(11258,plain,
% 7.92/8.14 (b(s(s(s(s(z)))), elem!1)),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[762, 11256, 11225])).
% 7.92/8.14 tff(11259,plain,
% 7.92/8.14 (b(s(s(s(s(z)))), s(s(z)))),
% 7.92/8.14 inference(modus_ponens,[status(thm)],[11258, 11257])).
% 7.92/8.14 tff(11260,plain,
% 7.92/8.14 (r(z, elem!1)),
% 7.92/8.14 inference(unit_resolution,[status(thm)],[10899, 11259, 1235, 3823, 11221, 11224, 11228, 11256, 2913, 11227, 10643, 10653, 115])).
% 7.92/8.14 tff(11261,plain,
% 7.92/8.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 7.92/8.14 inference(rewrite,[status(thm)],[])).
% 7.92/8.14 tff(11262,plain,
% 7.92/8.14 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~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(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 7.92/8.15 inference(rewrite,[status(thm)],[])).
% 7.92/8.15 tff(11263,plain,
% 7.92/8.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))))),
% 7.92/8.15 inference(monotonicity,[status(thm)],[11262])).
% 7.92/8.15 tff(11264,plain,
% 7.92/8.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 7.92/8.15 inference(transitivity,[status(thm)],[11263, 11261])).
% 7.92/8.15 tff(11265,plain,
% 7.92/8.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 7.92/8.15 inference(quant_inst,[status(thm)],[])).
% 7.92/8.15 tff(11266,plain,
% 7.92/8.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))),
% 7.92/8.15 inference(modus_ponens,[status(thm)],[11265, 11264])).
% 7.92/8.15 tff(11267,plain,
% 7.92/8.15 (~b(s(s(z)), elem!1)),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[11266, 391, 3823, 11229, 11172, 10653])).
% 7.92/8.15 tff(11268,plain,
% 7.92/8.15 (~r(s(s(z)), elem!1)),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[10999, 194, 11227, 2913, 10660])).
% 7.92/8.15 tff(11269,plain,
% 7.92/8.15 (s(s(z)) = elem!1),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[4730, 11268, 11267])).
% 7.92/8.15 tff(11270,plain,
% 7.92/8.15 (s(s(s(z))) = s(elem!1)),
% 7.92/8.15 inference(monotonicity,[status(thm)],[4579])).
% 7.92/8.15 tff(11271,plain,
% 7.92/8.15 (s(s(s(s(z)))) = s(s(elem!1))),
% 7.92/8.15 inference(monotonicity,[status(thm)],[11270])).
% 7.92/8.15 tff(11272,plain,
% 7.92/8.15 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(elem!1)))),
% 7.92/8.15 inference(monotonicity,[status(thm)],[11271])).
% 7.92/8.15 tff(11273,plain,
% 7.92/8.15 (r(s(z), s(s(elem!1)))),
% 7.92/8.15 inference(modus_ponens,[status(thm)],[1216, 11272])).
% 7.92/8.15 tff(11274,plain,
% 7.92/8.15 ($false),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[4845, 11273])).
% 7.92/8.15 tff(11275,plain,((~r(s(z), s(s(s(s(z)))))) | r(s(z), s(s(elem!1))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.15 tff(11276,plain,
% 7.92/8.15 (r(s(z), s(s(elem!1)))),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[11275, 11269, 2913])).
% 7.92/8.15 tff(11277,plain,
% 7.92/8.15 (r(s(s(elem!1)), z) <=> r(s(s(s(s(z)))), z)),
% 7.92/8.15 inference(monotonicity,[status(thm)],[11240])).
% 7.92/8.15 tff(11278,plain,
% 7.92/8.15 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 7.92/8.15 inference(symmetry,[status(thm)],[11277])).
% 7.92/8.15 tff(11279,plain,
% 7.92/8.15 (r(s(s(elem!1)), z)),
% 7.92/8.15 inference(modus_ponens,[status(thm)],[3447, 11278])).
% 7.92/8.15 tff(11280,plain,
% 7.92/8.15 (~r(s(z), s(s(s(elem!1))))),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[4840, 11279, 11243, 11276])).
% 7.92/8.15 tff(11281,plain,
% 7.92/8.15 (b(s(z), s(s(s(elem!1))))),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[247, 11280])).
% 7.92/8.15 tff(11282,plain,
% 7.92/8.15 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[11060, 194, 411, 174, 2053])).
% 7.92/8.15 tff(11283,plain,
% 7.92/8.15 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[4313, 42, 11282])).
% 7.92/8.15 tff(11284,plain,
% 7.92/8.15 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[11283, 6950])).
% 7.92/8.15 tff(11285,plain,
% 7.92/8.15 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[11066, 194, 411, 174, 2053])).
% 7.92/8.15 tff(11286,plain,
% 7.92/8.15 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 11285])).
% 7.92/8.15 tff(11287,plain,
% 7.92/8.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.92/8.15 inference(rewrite,[status(thm)],[])).
% 7.92/8.15 tff(11288,plain,
% 7.92/8.15 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.92/8.15 inference(rewrite,[status(thm)],[])).
% 7.92/8.15 tff(11289,plain,
% 7.92/8.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 7.92/8.15 inference(monotonicity,[status(thm)],[11288])).
% 7.92/8.15 tff(11290,plain,
% 7.92/8.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 7.92/8.15 inference(transitivity,[status(thm)],[11289, 11287])).
% 7.92/8.15 tff(11291,plain,
% 7.92/8.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 7.92/8.15 inference(quant_inst,[status(thm)],[])).
% 7.92/8.15 tff(11292,plain,
% 7.92/8.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 7.92/8.15 inference(modus_ponens,[status(thm)],[11291, 11290])).
% 7.92/8.15 tff(11293,plain,
% 7.92/8.15 ($false),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[11292, 391, 10682, 379, 590, 11286, 11284])).
% 7.92/8.15 tff(11294,plain,((~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.15 tff(11295,plain,
% 7.92/8.15 (~r(s(s(s(elem!1))), z)),
% 7.92/8.15 inference(unit_resolution,[status(thm)],[11294, 11281, 11260, 3447, 11246, 10653, 11224])).
% 7.92/8.15 tff(11296,plain,
% 7.92/8.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 7.92/8.16 inference(rewrite,[status(thm)],[])).
% 7.92/8.16 tff(11297,plain,
% 7.92/8.16 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 7.92/8.16 inference(rewrite,[status(thm)],[])).
% 7.92/8.16 tff(11298,plain,
% 7.92/8.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11297])).
% 7.92/8.16 tff(11299,plain,
% 7.92/8.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 7.92/8.16 inference(transitivity,[status(thm)],[11298, 11296])).
% 7.92/8.16 tff(11300,plain,
% 7.92/8.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 7.92/8.16 inference(quant_inst,[status(thm)],[])).
% 7.92/8.16 tff(11301,plain,
% 7.92/8.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 7.92/8.16 inference(modus_ponens,[status(thm)],[11300, 11299])).
% 7.92/8.16 tff(11302,plain,
% 7.92/8.16 ($false),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[11301, 391, 380, 10682, 379, 590])).
% 7.92/8.16 tff(11303,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.16 tff(11304,plain,
% 7.92/8.16 (~b(s(s(s(elem!1))), z)),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[11303, 11281, 11246, 10653])).
% 7.92/8.16 tff(11305,plain,
% 7.92/8.16 ($false),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[377, 11304, 11295])).
% 7.92/8.16 tff(11306,plain,((~b(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (z = elem!1) | b(s(s(s(elem!1))), s(s(elem!1))) | b(elem!1, s(z)) | b(s(z), s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 7.92/8.16 tff(11307,plain,
% 7.92/8.16 (~b(s(s(z)), z)),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[11306, 10645, 3823, 115, 8329, 31, 2881, 3446])).
% 7.92/8.16 tff(11308,plain,
% 7.92/8.16 (r(s(s(z)), z)),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[1211, 11307])).
% 7.92/8.16 tff(11309,plain,
% 7.92/8.16 (r(z, elem!1) <=> r(z, s(z))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[169])).
% 7.92/8.16 tff(11310,plain,
% 7.92/8.16 (r(z, s(z)) <=> r(z, elem!1)),
% 7.92/8.16 inference(symmetry,[status(thm)],[11309])).
% 7.92/8.16 tff(11311,plain,
% 7.92/8.16 ((~r(z, s(z))) <=> (~r(z, elem!1))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11310])).
% 7.92/8.16 tff(11312,plain,
% 7.92/8.16 (~r(z, elem!1)),
% 7.92/8.16 inference(modus_ponens,[status(thm)],[676, 11311])).
% 7.92/8.16 tff(11313,plain,
% 7.92/8.16 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[1552])).
% 7.92/8.16 tff(11314,plain,
% 7.92/8.16 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 7.92/8.16 inference(symmetry,[status(thm)],[11313])).
% 7.92/8.16 tff(11315,plain,
% 7.92/8.16 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(s(elem!1)))))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11314])).
% 7.92/8.16 tff(11316,plain,
% 7.92/8.16 (~b(z, s(s(s(elem!1))))),
% 7.92/8.16 inference(modus_ponens,[status(thm)],[10644, 11315])).
% 7.92/8.16 tff(11317,plain,
% 7.92/8.16 ($false),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[8231, 11316, 11312, 2])).
% 7.92/8.16 tff(11318,plain,((~(elem!1 = s(z))) | (elem!1 = z) | b(z, s(s(s(s(z))))) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.16 tff(11319,plain,
% 7.92/8.16 (~(elem!1 = s(z))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[11318, 10644, 10680, 10642])).
% 7.92/8.16 tff(11320,plain,
% 7.92/8.16 (~(s(z) = elem!1)),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[1495, 11319])).
% 7.92/8.16 tff(11321,plain,
% 7.92/8.16 (r(elem!1, s(z))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[837, 11319, 31])).
% 7.92/8.16 tff(11322,plain,
% 7.92/8.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.92/8.16 inference(rewrite,[status(thm)],[])).
% 7.92/8.16 tff(11323,plain,
% 7.92/8.16 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.92/8.16 inference(rewrite,[status(thm)],[])).
% 7.92/8.16 tff(11324,plain,
% 7.92/8.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11323])).
% 7.92/8.16 tff(11325,plain,
% 7.92/8.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.92/8.16 inference(transitivity,[status(thm)],[11324, 11322])).
% 7.92/8.16 tff(11326,plain,
% 7.92/8.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.92/8.16 inference(quant_inst,[status(thm)],[])).
% 7.92/8.16 tff(11327,plain,
% 7.92/8.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 7.92/8.16 inference(modus_ponens,[status(thm)],[11326, 11325])).
% 7.92/8.16 tff(11328,plain,
% 7.92/8.16 (~r(s(s(s(s(z)))), s(s(z)))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[11327, 194, 2053, 3557, 719])).
% 7.92/8.16 tff(11329,plain,
% 7.92/8.16 (b(s(s(s(s(z)))), s(s(z)))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[1714, 11328])).
% 7.92/8.16 tff(11330,plain,
% 7.92/8.16 (~b(s(s(s(s(z)))), s(z))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[11220, 2405, 31, 10680, 10677, 3823, 4028, 1216, 2053])).
% 7.92/8.16 tff(11331,plain,
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% 7.92/8.16 inference(unit_resolution,[status(thm)],[10815, 11330, 2405, 3823, 3563, 1216, 4028, 31, 719, 2053, 115])).
% 7.92/8.16 tff(11332,plain,((~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.92/8.16 tff(11333,plain,
% 7.92/8.16 (~r(s(s(z)), s(z))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[11332, 4028, 11329, 1216, 3823, 31, 719, 2053, 115])).
% 7.92/8.16 tff(11334,plain,
% 7.92/8.16 (b(s(s(z)), s(z))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[3778, 11333])).
% 7.92/8.16 tff(11335,plain,
% 7.92/8.16 (~(s(s(elem!1)) = s(s(z)))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[1962, 10968])).
% 7.92/8.16 tff(11336,plain,
% 7.92/8.16 (~b(s(s(s(elem!1))), s(z))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[10690, 10682, 10679, 10677])).
% 7.92/8.16 tff(11337,plain,
% 7.92/8.16 (r(s(s(s(elem!1))), s(z))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[223, 11336])).
% 7.92/8.16 tff(11338,plain,
% 7.92/8.16 (~r(elem!1, s(s(s(elem!1))))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[10776, 838, 1216, 11337])).
% 7.92/8.16 tff(11339,plain,
% 7.92/8.16 (elem!1 = s(s(s(elem!1)))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[424, 11338, 4028])).
% 7.92/8.16 tff(11340,plain,
% 7.92/8.16 (s(elem!1) = s(s(s(s(elem!1))))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11339])).
% 7.92/8.16 tff(11341,plain,
% 7.92/8.16 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11340])).
% 7.92/8.16 tff(11342,plain,
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% 7.92/8.16 inference(symmetry,[status(thm)],[11341])).
% 7.92/8.16 tff(11343,plain,
% 7.92/8.16 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11342])).
% 7.92/8.16 tff(11344,plain,
% 7.92/8.16 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 7.92/8.16 inference(symmetry,[status(thm)],[11343])).
% 7.92/8.16 tff(11345,plain,
% 7.92/8.16 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11339])).
% 7.92/8.16 tff(11346,plain,
% 7.92/8.16 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 7.92/8.16 inference(symmetry,[status(thm)],[11345])).
% 7.92/8.16 tff(11347,plain,
% 7.92/8.16 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(elem!1, s(s(elem!1))))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11346])).
% 7.92/8.16 tff(11348,plain,
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% 7.92/8.16 inference(modus_ponens,[status(thm)],[8329, 11347])).
% 7.92/8.16 tff(11349,plain,
% 7.92/8.16 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11339])).
% 7.92/8.16 tff(11350,plain,
% 7.92/8.16 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), elem!1)),
% 7.92/8.16 inference(symmetry,[status(thm)],[11349])).
% 7.92/8.16 tff(11351,plain,
% 7.92/8.16 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[11350])).
% 7.92/8.16 tff(11352,plain,
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% 7.92/8.16 inference(modus_ponens,[status(thm)],[463, 11351])).
% 7.92/8.16 tff(11353,plain,
% 7.92/8.16 (~r(elem!1, s(s(s(s(z)))))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[11195, 838, 2053, 1216])).
% 7.92/8.16 tff(11354,plain,
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% 7.92/8.16 inference(unit_resolution,[status(thm)],[1436, 11354])).
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% 7.92/8.16 tff(11358,plain,
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% 7.92/8.16 tff(11359,plain,
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% 7.92/8.16 tff(11360,plain,
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% 7.92/8.16 inference(monotonicity,[status(thm)],[11359])).
% 7.92/8.16 tff(11361,plain,
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% 7.92/8.16 tff(11362,plain,
% 7.92/8.16 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
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% 7.92/8.16 tff(11363,plain,
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% 7.92/8.16 tff(11374,assumption,(s(s(s(s(s(s(z)))))) = elem!1), introduced(assumption)).
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% 7.92/8.16 tff(11376,plain,
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% 7.92/8.16 tff(11380,plain,
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% 7.92/8.16 tff(11381,plain,
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% 7.92/8.16 tff(11384,plain,((~(s(s(s(s(s(s(z)))))) = elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
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% 7.92/8.16 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
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% 7.92/8.16 tff(11399,plain,
% 7.92/8.16 (~r(s(s(elem!1)), s(z))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[4206, 832, 445])).
% 7.92/8.16 tff(11400,plain,
% 7.92/8.16 (b(s(s(elem!1)), s(z))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[362, 11399])).
% 7.92/8.16 tff(11401,plain,
% 7.92/8.16 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 7.92/8.16 inference(monotonicity,[status(thm)],[445])).
% 7.92/8.16 tff(11402,plain,
% 7.92/8.16 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 7.92/8.16 inference(symmetry,[status(thm)],[11401])).
% 7.92/8.16 tff(11403,plain,
% 7.92/8.16 (b(z, s(s(elem!1)))),
% 7.92/8.16 inference(modus_ponens,[status(thm)],[133, 11402])).
% 7.92/8.16 tff(11404,plain,
% 7.92/8.16 (b(elem!1, s(z))),
% 7.92/8.16 inference(unit_resolution,[status(thm)],[837, 832, 173])).
% 7.92/8.16 tff(11405,plain,
% 7.92/8.16 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 7.92/8.16 inference(monotonicity,[status(thm)],[465])).
% 7.92/8.16 tff(11406,plain,
% 7.92/8.16 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 7.92/8.16 inference(symmetry,[status(thm)],[11405])).
% 7.92/8.16 tff(11407,plain,
% 7.92/8.16 (s(elem!1) = elem!1),
% 7.92/8.17 inference(transitivity,[status(thm)],[2268, 5])).
% 7.92/8.17 tff(11408,plain,
% 7.92/8.17 (b(s(elem!1), s(z)) <=> b(elem!1, s(z))),
% 7.92/8.17 inference(monotonicity,[status(thm)],[11407])).
% 7.92/8.17 tff(11409,plain,
% 7.92/8.17 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 7.92/8.17 inference(symmetry,[status(thm)],[11408])).
% 7.92/8.17 tff(11410,plain,
% 7.92/8.17 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 7.92/8.17 inference(transitivity,[status(thm)],[11409, 11406])).
% 7.92/8.17 tff(11411,plain,
% 7.92/8.17 (b(s(s(s(elem!1))), s(z))),
% 7.92/8.17 inference(modus_ponens,[status(thm)],[721, 11410])).
% 7.92/8.17 tff(11412,plain,
% 7.92/8.17 (~b(elem!1, s(s(s(s(z)))))),
% 7.92/8.17 inference(unit_resolution,[status(thm)],[6747, 391, 133, 665, 90])).
% 7.92/8.17 tff(11413,plain,
% 7.92/8.17 (r(elem!1, s(s(s(s(z)))))),
% 7.92/8.17 inference(unit_resolution,[status(thm)],[781, 11412, 8922])).
% 7.92/8.17 tff(11414,plain,
% 7.92/8.17 (~r(s(s(s(s(z)))), s(z))),
% 7.92/8.17 inference(unit_resolution,[status(thm)],[2026, 194, 1484, 11413, 2112])).
% 7.92/8.17 tff(11415,plain,
% 7.92/8.17 (b(s(s(s(s(z)))), s(z))),
% 7.92/8.17 inference(unit_resolution,[status(thm)],[749, 11414])).
% 7.92/8.17 tff(11416,plain,
% 7.92/8.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.92/8.17 inference(rewrite,[status(thm)],[])).
% 7.92/8.17 tff(11417,plain,
% 7.92/8.17 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.92/8.17 inference(rewrite,[status(thm)],[])).
% 7.92/8.17 tff(11418,plain,
% 7.92/8.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 7.92/8.17 inference(monotonicity,[status(thm)],[11417])).
% 7.92/8.17 tff(11419,plain,
% 7.92/8.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.92/8.17 inference(transitivity,[status(thm)],[11418, 11416])).
% 7.92/8.17 tff(11420,plain,
% 7.92/8.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 7.92/8.17 inference(quant_inst,[status(thm)],[])).
% 7.92/8.17 tff(11421,plain,
% 7.92/8.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 7.92/8.17 inference(modus_ponens,[status(thm)],[11420, 11419])).
% 7.92/8.17 tff(11422,plain,
% 7.92/8.17 (~r(s(z), s(s(s(s(z)))))),
% 7.92/8.17 inference(unit_resolution,[status(thm)],[11421, 194, 1484, 11413, 2112])).
% 7.92/8.17 tff(11423,plain,
% 7.92/8.17 (b(s(z), s(s(s(s(z)))))),
% 7.92/8.17 inference(unit_resolution,[status(thm)],[1230, 11422])).
% 7.92/8.17 tff(11424,plain,
% 7.92/8.17 (~b(z, s(s(s(s(z)))))),
% 7.92/8.17 inference(unit_resolution,[status(thm)],[6325, 90, 380, 1526, 590])).
% 7.92/8.17 tff(11425,plain,
% 7.92/8.17 (r(z, s(s(s(s(z)))))),
% 7.92/8.17 inference(unit_resolution,[status(thm)],[800, 11424])).
% 7.92/8.17 tff(11426,plain,
% 7.92/8.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.92/8.17 inference(rewrite,[status(thm)],[])).
% 7.92/8.17 tff(11427,plain,
% 7.92/8.17 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.92/8.17 inference(rewrite,[status(thm)],[])).
% 7.92/8.17 tff(11428,plain,
% 7.92/8.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))))),
% 7.92/8.17 inference(monotonicity,[status(thm)],[11427])).
% 7.92/8.17 tff(11429,plain,
% 7.92/8.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 7.92/8.17 inference(transitivity,[status(thm)],[11428, 11426])).
% 7.92/8.17 tff(11430,plain,
% 7.92/8.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 7.92/8.17 inference(quant_inst,[status(thm)],[])).
% 7.92/8.17 tff(11431,plain,
% 7.92/8.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))),
% 7.92/8.17 inference(modus_ponens,[status(thm)],[11430, 11429])).
% 7.92/8.17 tff(11432,plain,
% 7.92/8.17 (~r(elem!1, s(s(z)))),
% 7.92/8.17 inference(unit_resolution,[status(thm)],[11431, 194, 1749, 2032, 2112])).
% 7.92/8.17 tff(11433,plain,
% 7.92/8.17 (b(elem!1, s(s(z)))),
% 7.92/8.17 inference(unit_resolution,[status(thm)],[3394, 11432, 1405])).
% 7.92/8.17 tff(11434,plain,
% 7.92/8.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.92/8.17 inference(rewrite,[status(thm)],[])).
% 7.92/8.17 tff(11435,plain,
% 7.92/8.17 (((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.92/8.17 inference(rewrite,[status(thm)],[])).
% 7.92/8.17 tff(11436,plain,
% 7.92/8.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 7.92/8.17 inference(monotonicity,[status(thm)],[11435])).
% 7.92/8.17 tff(11437,plain,
% 7.92/8.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.92/8.17 inference(transitivity,[status(thm)],[11436, 11434])).
% 7.92/8.18 tff(11438,plain,
% 7.92/8.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 7.92/8.18 inference(quant_inst,[status(thm)],[])).
% 7.92/8.18 tff(11439,plain,
% 7.92/8.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 7.92/8.18 inference(modus_ponens,[status(thm)],[11438, 11437])).
% 7.92/8.18 tff(11440,plain,
% 7.92/8.18 (~r(s(s(z)), z)),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11439, 194, 1749, 2112, 719])).
% 7.92/8.18 tff(11441,plain,
% 7.92/8.18 (b(s(s(z)), z)),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[1211, 11440])).
% 7.92/8.18 tff(11442,plain,
% 7.92/8.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.92/8.18 inference(rewrite,[status(thm)],[])).
% 7.92/8.18 tff(11443,plain,
% 7.92/8.18 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.92/8.18 inference(rewrite,[status(thm)],[])).
% 7.92/8.18 tff(11444,plain,
% 7.92/8.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 7.92/8.18 inference(monotonicity,[status(thm)],[11443])).
% 7.92/8.18 tff(11445,plain,
% 7.92/8.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.92/8.18 inference(transitivity,[status(thm)],[11444, 11442])).
% 7.92/8.18 tff(11446,plain,
% 7.92/8.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 7.92/8.18 inference(quant_inst,[status(thm)],[])).
% 7.92/8.18 tff(11447,plain,
% 7.92/8.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 7.92/8.18 inference(modus_ponens,[status(thm)],[11446, 11445])).
% 7.92/8.18 tff(11448,plain,
% 7.92/8.18 ($false),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11447, 391, 380, 10682, 2641, 1235, 6192])).
% 7.92/8.18 tff(11449,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.18 tff(11450,plain,
% 7.92/8.18 (~b(s(s(elem!1)), s(s(z)))),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11449, 11441, 10682, 380, 2641])).
% 7.92/8.18 tff(11451,plain,
% 7.92/8.18 (inj_0(s(s(elem!1))) = inj_0(s(elem!1))),
% 7.92/8.18 inference(symmetry,[status(thm)],[8339])).
% 7.92/8.18 tff(11452,plain,
% 7.92/8.18 (s(s(elem!1)) = elem!1),
% 7.92/8.18 inference(transitivity,[status(thm)],[283, 282, 352, 11451, 108])).
% 7.92/8.18 tff(11453,plain,
% 7.92/8.18 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 7.92/8.18 inference(monotonicity,[status(thm)],[11452])).
% 7.92/8.18 tff(11454,plain,
% 7.92/8.18 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 7.92/8.18 inference(symmetry,[status(thm)],[11453])).
% 7.92/8.18 tff(11455,plain,
% 7.92/8.18 (b(s(s(elem!1)), s(s(z)))),
% 7.92/8.18 inference(modus_ponens,[status(thm)],[3369, 11454])).
% 7.92/8.18 tff(11456,assumption,(~b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 7.92/8.18 tff(11457,plain,
% 7.92/8.18 ($false),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11456, 11455])).
% 7.92/8.18 tff(11458,plain,(b(s(s(elem!1)), s(s(z))) | (~b(elem!1, s(s(z)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.18 tff(11459,plain,
% 7.92/8.18 ($false),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11458, 11450, 11433, 266])).
% 7.92/8.18 tff(11460,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.18 tff(11461,plain,
% 7.92/8.18 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11460, 11413, 10682, 380, 2641, 1405, 266, 2112, 11425])).
% 7.92/8.18 tff(11462,plain,
% 7.92/8.18 (b(s(s(z)), s(s(s(s(z)))))),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[3652, 11461])).
% 7.92/8.18 tff(11463,plain,
% 7.92/8.18 (~b(s(s(z)), s(z))),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[5108, 11462, 11423, 11415])).
% 7.92/8.18 tff(11464,plain,
% 7.92/8.18 (r(s(s(z)), s(z))),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[3778, 11463])).
% 7.92/8.18 tff(11465,plain,
% 7.92/8.18 (~b(s(s(z)), z)),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[5136, 11462, 133, 721, 90])).
% 7.92/8.18 tff(11466,plain,
% 7.92/8.18 (r(s(s(z)), z)),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[1211, 11465])).
% 7.92/8.18 tff(11467,plain,
% 7.92/8.18 ($false),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[4462, 11466, 11464, 1484, 722])).
% 7.92/8.18 tff(11468,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.18 tff(11469,plain,
% 7.92/8.18 (~b(s(s(s(s(z)))), z)),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11468, 2112, 722, 133, 721, 10682, 380, 2641, 1405, 266, 1484, 5511, 665, 11411, 590])).
% 7.92/8.18 tff(11470,plain,
% 7.92/8.18 (r(s(s(s(s(z)))), z)),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[87, 11469])).
% 7.92/8.18 tff(11471,plain,
% 7.92/8.18 (~r(s(s(s(s(z)))), s(z))),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[5500, 11470, 4832, 722])).
% 7.92/8.18 tff(11472,plain,
% 7.92/8.18 (b(s(s(s(s(z)))), s(z))),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[749, 11471])).
% 7.92/8.18 tff(11473,plain,
% 7.92/8.18 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 7.92/8.18 inference(monotonicity,[status(thm)],[465])).
% 7.92/8.18 tff(11474,plain,
% 7.92/8.18 (r(s(elem!1), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 7.92/8.18 inference(symmetry,[status(thm)],[11473])).
% 7.92/8.18 tff(11475,plain,
% 7.92/8.18 (r(s(elem!1), s(s(z))) <=> r(elem!1, s(s(z)))),
% 7.92/8.18 inference(monotonicity,[status(thm)],[11407])).
% 7.92/8.18 tff(11476,plain,
% 7.92/8.18 (r(elem!1, s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 7.92/8.18 inference(symmetry,[status(thm)],[11475])).
% 7.92/8.18 tff(11477,plain,
% 7.92/8.18 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 7.92/8.18 inference(transitivity,[status(thm)],[11476, 11474])).
% 7.92/8.18 tff(11478,plain,
% 7.92/8.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 7.92/8.18 inference(rewrite,[status(thm)],[])).
% 7.92/8.18 tff(11479,plain,
% 7.92/8.18 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 7.92/8.18 inference(rewrite,[status(thm)],[])).
% 7.92/8.18 tff(11480,plain,
% 7.92/8.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))))),
% 7.92/8.18 inference(monotonicity,[status(thm)],[11479])).
% 7.92/8.18 tff(11481,plain,
% 7.92/8.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 7.92/8.18 inference(transitivity,[status(thm)],[11480, 11478])).
% 7.92/8.18 tff(11482,plain,
% 7.92/8.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 7.92/8.18 inference(quant_inst,[status(thm)],[])).
% 7.92/8.18 tff(11483,plain,
% 7.92/8.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))),
% 7.92/8.18 inference(modus_ponens,[status(thm)],[11482, 11481])).
% 7.92/8.18 tff(11484,plain,
% 7.92/8.18 ($false),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11483, 194, 1484, 1748, 2112, 1216])).
% 7.92/8.18 tff(11485,plain,((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.18 tff(11486,plain,
% 7.92/8.18 (~r(elem!1, s(s(z)))),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11485, 1216, 2112, 1484])).
% 7.92/8.18 tff(11487,plain,
% 7.92/8.18 (b(elem!1, s(s(z)))),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[3394, 11486, 1405])).
% 7.92/8.18 tff(11488,plain,
% 7.92/8.18 (b(s(s(elem!1)), s(s(z)))),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11458, 11487, 266])).
% 7.92/8.18 tff(11489,plain,
% 7.92/8.18 (~b(s(s(z)), z)),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[11449, 11488, 10682, 380, 2641])).
% 7.92/8.18 tff(11490,plain,
% 7.92/8.18 (r(s(s(z)), z)),
% 7.92/8.18 inference(unit_resolution,[status(thm)],[1211, 11489])).
% 7.92/8.18 tff(11491,plain,
% 7.92/8.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.92/8.18 inference(rewrite,[status(thm)],[])).
% 7.92/8.18 tff(11492,plain,
% 7.92/8.18 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.92/8.18 inference(rewrite,[status(thm)],[])).
% 7.92/8.18 tff(11493,plain,
% 7.92/8.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 7.92/8.19 inference(monotonicity,[status(thm)],[11492])).
% 7.92/8.19 tff(11494,plain,
% 7.92/8.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.92/8.19 inference(transitivity,[status(thm)],[11493, 11491])).
% 7.92/8.19 tff(11495,plain,
% 7.92/8.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 7.92/8.19 inference(quant_inst,[status(thm)],[])).
% 7.92/8.19 tff(11496,plain,
% 7.92/8.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 7.92/8.19 inference(modus_ponens,[status(thm)],[11495, 11494])).
% 7.92/8.19 tff(11497,plain,
% 7.92/8.19 ($false),
% 7.92/8.19 inference(unit_resolution,[status(thm)],[11496, 391, 3823, 2064, 3369, 1759, 3563])).
% 7.92/8.19 tff(11498,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.19 tff(11499,plain,
% 7.92/8.19 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.92/8.19 inference(unit_resolution,[status(thm)],[11498, 11487, 2064, 3823, 1759])).
% 7.92/8.19 tff(11500,plain,
% 7.92/8.19 (r(s(s(s(s(z)))), s(s(z)))),
% 7.92/8.19 inference(unit_resolution,[status(thm)],[1714, 11499])).
% 7.92/8.19 tff(11501,plain,
% 7.92/8.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.92/8.19 inference(rewrite,[status(thm)],[])).
% 7.92/8.19 tff(11502,plain,
% 7.92/8.19 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.92/8.19 inference(rewrite,[status(thm)],[])).
% 7.92/8.19 tff(11503,plain,
% 7.92/8.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 7.92/8.19 inference(monotonicity,[status(thm)],[11502])).
% 7.92/8.19 tff(11504,plain,
% 7.92/8.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.92/8.19 inference(transitivity,[status(thm)],[11503, 11501])).
% 7.92/8.19 tff(11505,plain,
% 7.92/8.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 7.92/8.19 inference(quant_inst,[status(thm)],[])).
% 7.92/8.19 tff(11506,plain,
% 7.92/8.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 7.92/8.19 inference(modus_ponens,[status(thm)],[11505, 11504])).
% 7.92/8.19 tff(11507,plain,
% 7.92/8.19 ($false),
% 7.92/8.19 inference(unit_resolution,[status(thm)],[11506, 194, 3557, 1216, 1747, 1697])).
% 7.92/8.19 tff(11508,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.19 tff(11509,plain,
% 7.92/8.19 (~r(s(z), s(s(z)))),
% 7.92/8.19 inference(unit_resolution,[status(thm)],[11508, 11500, 1216, 11490])).
% 7.92/8.19 tff(11510,plain,
% 7.92/8.19 (b(s(z), s(s(z)))),
% 7.92/8.19 inference(unit_resolution,[status(thm)],[1788, 11509])).
% 7.92/8.19 tff(11511,plain,
% 7.92/8.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.92/8.19 inference(rewrite,[status(thm)],[])).
% 7.92/8.19 tff(11512,plain,
% 7.92/8.19 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.92/8.19 inference(rewrite,[status(thm)],[])).
% 7.92/8.19 tff(11513,plain,
% 7.92/8.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 7.92/8.19 inference(monotonicity,[status(thm)],[11512])).
% 7.92/8.19 tff(11514,plain,
% 7.92/8.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 7.92/8.19 inference(transitivity,[status(thm)],[11513, 11511])).
% 7.92/8.19 tff(11515,plain,
% 7.92/8.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))),
% 7.92/8.19 inference(quant_inst,[status(thm)],[])).
% 7.92/8.19 tff(11516,plain,
% 7.92/8.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 7.92/8.19 inference(modus_ponens,[status(thm)],[11515, 11514])).
% 7.92/8.19 tff(11517,plain,
% 7.92/8.19 ($false),
% 7.92/8.19 inference(unit_resolution,[status(thm)],[11516, 391, 3823, 11487, 1759, 11510, 721])).
% 7.92/8.19 tff(11518,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (elem!1 = s(s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.92/8.19 tff(11519,plain,
% 7.92/8.19 (~r(s(z), s(s(s(s(z)))))),
% 7.92/8.19 inference(unit_resolution,[status(thm)],[11518, 2064, 1759, 721, 3823, 10682, 380, 2641, 266, 1405, 2112, 1484])).
% 7.92/8.19 tff(11520,plain,
% 7.92/8.19 (b(s(z), s(s(s(s(z)))))),
% 7.92/8.19 inference(unit_resolution,[status(thm)],[1230, 11519])).
% 7.99/8.20 tff(11521,plain,
% 7.99/8.20 (~b(s(s(z)), s(z))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[5108, 11520, 3823, 1759])).
% 7.99/8.20 tff(11522,plain,
% 7.99/8.20 (r(s(s(z)), s(z))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[3778, 11521])).
% 7.99/8.20 tff(11523,plain,
% 7.99/8.20 (~r(s(s(z)), z)),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[4462, 11522, 1484, 722])).
% 7.99/8.20 tff(11524,plain,
% 7.99/8.20 (b(s(s(z)), z)),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[1211, 11523])).
% 7.99/8.20 tff(11525,plain,
% 7.99/8.20 (~b(s(s(elem!1)), s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11449, 11524, 10682, 380, 2641])).
% 7.99/8.20 tff(11526,plain,
% 7.99/8.20 (~b(elem!1, s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11458, 11525, 266])).
% 7.99/8.20 tff(11527,plain,
% 7.99/8.20 (r(elem!1, s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[3394, 11526, 1405])).
% 7.99/8.20 tff(11528,plain,
% 7.99/8.20 (r(s(s(s(elem!1))), s(s(z)))),
% 7.99/8.20 inference(modus_ponens,[status(thm)],[11527, 11477])).
% 7.99/8.20 tff(11529,plain,
% 7.99/8.20 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 7.99/8.20 inference(monotonicity,[status(thm)],[9211])).
% 7.99/8.20 tff(11530,plain,
% 7.99/8.20 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 7.99/8.20 inference(symmetry,[status(thm)],[11529])).
% 7.99/8.20 tff(11531,plain,
% 7.99/8.20 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 7.99/8.20 inference(modus_ponens,[status(thm)],[2064, 11530])).
% 7.99/8.20 tff(11532,plain,
% 7.99/8.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 7.99/8.20 inference(rewrite,[status(thm)],[])).
% 7.99/8.20 tff(11533,plain,
% 7.99/8.20 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 7.99/8.20 inference(rewrite,[status(thm)],[])).
% 7.99/8.20 tff(11534,plain,
% 7.99/8.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 7.99/8.20 inference(monotonicity,[status(thm)],[11533])).
% 7.99/8.20 tff(11535,plain,
% 7.99/8.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 7.99/8.20 inference(transitivity,[status(thm)],[11534, 11532])).
% 7.99/8.20 tff(11536,plain,
% 7.99/8.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 7.99/8.20 inference(quant_inst,[status(thm)],[])).
% 7.99/8.20 tff(11537,plain,
% 7.99/8.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 7.99/8.20 inference(modus_ponens,[status(thm)],[11536, 11535])).
% 7.99/8.20 tff(11538,plain,
% 7.99/8.20 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11537, 391, 3927, 1235, 2439, 590])).
% 7.99/8.20 tff(11539,plain,
% 7.99/8.20 ($false),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11538, 11531])).
% 7.99/8.20 tff(11540,plain,((~b(elem!1, s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.20 tff(11541,plain,
% 7.99/8.20 (~b(s(z), s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11540, 11524, 266, 2064, 3927, 590])).
% 7.99/8.20 tff(11542,plain,
% 7.99/8.20 (r(s(z), s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[1788, 11541])).
% 7.99/8.20 tff(11543,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 7.99/8.20 tff(11544,plain,
% 7.99/8.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.99/8.20 inference(rewrite,[status(thm)],[])).
% 7.99/8.20 tff(11545,plain,
% 7.99/8.20 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.99/8.20 inference(rewrite,[status(thm)],[])).
% 7.99/8.20 tff(11546,plain,
% 7.99/8.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 7.99/8.20 inference(monotonicity,[status(thm)],[11545])).
% 7.99/8.20 tff(11547,plain,
% 7.99/8.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 7.99/8.20 inference(transitivity,[status(thm)],[11546, 11544])).
% 7.99/8.20 tff(11548,plain,
% 7.99/8.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 7.99/8.20 inference(quant_inst,[status(thm)],[])).
% 7.99/8.20 tff(11549,plain,
% 7.99/8.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 7.99/8.20 inference(modus_ponens,[status(thm)],[11548, 11547])).
% 7.99/8.20 tff(11550,plain,
% 7.99/8.20 ($false),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11549, 194, 232, 1747, 2405, 11543])).
% 7.99/8.20 tff(11551,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.20 tff(11552,plain,
% 7.99/8.20 (~r(s(s(s(elem!1))), s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11551, 11542, 11372, 11522])).
% 7.99/8.20 tff(11553,plain,
% 7.99/8.20 ($false),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11552, 11528])).
% 7.99/8.20 tff(11554,plain,((~b(elem!1, s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.20 tff(11555,plain,
% 7.99/8.20 (~b(elem!1, s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11554, 3823, 5, 1405, 266, 3927, 590, 10682, 380, 2641, 1484, 722, 465, 1759, 721, 2112])).
% 7.99/8.20 tff(11556,plain,
% 7.99/8.20 (r(elem!1, s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[781, 11555, 5511])).
% 7.99/8.20 tff(11557,plain,
% 7.99/8.20 (~r(s(z), s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11421, 194, 1484, 11556, 2112])).
% 7.99/8.20 tff(11558,plain,
% 7.99/8.20 (b(s(z), s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[1230, 11557])).
% 7.99/8.20 tff(11559,plain,
% 7.99/8.20 (~b(s(s(z)), s(z))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[5108, 11558, 3823, 1759])).
% 7.99/8.20 tff(11560,plain,
% 7.99/8.20 (r(s(s(z)), s(z))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[3778, 11559])).
% 7.99/8.20 tff(11561,plain,
% 7.99/8.20 (~r(s(s(z)), z)),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[4462, 11560, 1484, 722])).
% 7.99/8.20 tff(11562,plain,
% 7.99/8.20 (b(s(s(z)), z)),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[1211, 11561])).
% 7.99/8.20 tff(11563,plain,
% 7.99/8.20 (~b(s(s(elem!1)), s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11449, 11562, 10682, 380, 2641])).
% 7.99/8.20 tff(11564,plain,
% 7.99/8.20 (~b(elem!1, s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11458, 11563, 266])).
% 7.99/8.20 tff(11565,plain,
% 7.99/8.20 (r(elem!1, s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[3394, 11564, 1405])).
% 7.99/8.20 tff(11566,plain,
% 7.99/8.20 (r(s(s(s(elem!1))), s(s(z)))),
% 7.99/8.20 inference(modus_ponens,[status(thm)],[11565, 11477])).
% 7.99/8.20 tff(11567,plain,
% 7.99/8.20 (~r(s(s(s(s(z)))), s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[9402, 11562, 266, 3927, 381, 2641, 9263])).
% 7.99/8.20 tff(11568,plain,
% 7.99/8.20 (b(s(s(s(s(z)))), s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[1714, 11567])).
% 7.99/8.20 tff(11569,plain,
% 7.99/8.20 (~b(s(z), s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[6275, 11568, 11558, 3823])).
% 7.99/8.20 tff(11570,plain,
% 7.99/8.20 (r(s(z), s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[1788, 11569])).
% 7.99/8.20 tff(11571,plain,
% 7.99/8.20 (~r(s(s(s(elem!1))), s(s(z)))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11551, 11570, 11372, 11560])).
% 7.99/8.20 tff(11572,plain,
% 7.99/8.20 ($false),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11571, 11566])).
% 7.99/8.20 tff(11573,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.20 tff(11574,plain,
% 7.99/8.20 (~b(s(s(z)), s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11573, 11472, 5, 1405, 266, 10682, 380, 2641, 3927, 381, 1484, 722, 465, 2112, 590, 721])).
% 7.99/8.20 tff(11575,plain,
% 7.99/8.20 (r(s(s(z)), s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[3652, 11574])).
% 7.99/8.20 tff(11576,plain,
% 7.99/8.20 (r(elem!1, s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[781, 2089, 8922])).
% 7.99/8.20 tff(11577,plain,
% 7.99/8.20 (~r(z, s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11460, 11576, 10682, 380, 2641, 1405, 266, 2112, 1749])).
% 7.99/8.20 tff(11578,plain,
% 7.99/8.20 (b(z, s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[800, 11577])).
% 7.99/8.20 tff(11579,plain,
% 7.99/8.20 ($false),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[10054, 391, 1234, 1759, 11578, 590])).
% 7.99/8.20 tff(11580,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.20 tff(11581,plain,
% 7.99/8.20 (~b(s(z), s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[11580, 11472, 590, 10682, 380, 2641, 1405, 266, 2112, 11575, 5511, 721])).
% 7.99/8.20 tff(11582,plain,
% 7.99/8.20 (r(s(z), s(s(s(s(z)))))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[1230, 11581])).
% 7.99/8.20 tff(11583,plain,
% 7.99/8.20 (~r(s(s(z)), s(z))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[5567, 11582, 11470, 11575])).
% 7.99/8.20 tff(11584,plain,
% 7.99/8.20 (b(s(s(z)), s(z))),
% 7.99/8.20 inference(unit_resolution,[status(thm)],[3778, 11583])).
% 7.99/8.20 tff(11585,plain,
% 7.99/8.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.99/8.21 inference(rewrite,[status(thm)],[])).
% 7.99/8.21 tff(11586,plain,
% 7.99/8.21 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.99/8.21 inference(rewrite,[status(thm)],[])).
% 7.99/8.21 tff(11587,plain,
% 7.99/8.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 7.99/8.21 inference(monotonicity,[status(thm)],[11586])).
% 7.99/8.21 tff(11588,plain,
% 7.99/8.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.99/8.21 inference(transitivity,[status(thm)],[11587, 11585])).
% 7.99/8.21 tff(11589,plain,
% 7.99/8.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 7.99/8.21 inference(quant_inst,[status(thm)],[])).
% 7.99/8.21 tff(11590,plain,
% 7.99/8.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 7.99/8.21 inference(modus_ponens,[status(thm)],[11589, 11588])).
% 7.99/8.21 tff(11591,plain,
% 7.99/8.21 (~r(s(z), s(s(z)))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[11590, 194, 11575, 11470, 11582])).
% 7.99/8.21 tff(11592,plain,
% 7.99/8.21 (b(s(z), s(s(z)))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[1788, 11591])).
% 7.99/8.21 tff(11593,plain,
% 7.99/8.21 (~r(elem!1, s(s(z)))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[11485, 11582, 2112, 1484])).
% 7.99/8.21 tff(11594,plain,
% 7.99/8.21 (b(elem!1, s(s(z)))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[3394, 11593, 1405])).
% 7.99/8.21 tff(11595,plain,
% 7.99/8.21 (((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 7.99/8.21 inference(rewrite,[status(thm)],[])).
% 7.99/8.21 tff(11596,plain,
% 7.99/8.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 7.99/8.21 inference(monotonicity,[status(thm)],[11595])).
% 7.99/8.21 tff(11597,plain,
% 7.99/8.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 7.99/8.21 inference(transitivity,[status(thm)],[11596, 10143])).
% 7.99/8.21 tff(11598,plain,
% 7.99/8.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))),
% 7.99/8.21 inference(quant_inst,[status(thm)],[])).
% 7.99/8.21 tff(11599,plain,
% 7.99/8.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 7.99/8.21 inference(modus_ponens,[status(thm)],[11598, 11597])).
% 7.99/8.21 tff(11600,plain,
% 7.99/8.21 ($false),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[11599, 391, 11594, 11592, 11584, 721])).
% 7.99/8.21 tff(11601,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(s(z))) | (~r(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~(s(s(s(elem!1))) = elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.21 tff(11602,plain,
% 7.99/8.21 (~r(s(s(s(s(z)))), elem!1)),
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% 7.99/8.21 tff(11603,plain,
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% 7.99/8.21 tff(11605,plain,
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% 7.99/8.21 inference(unit_resolution,[status(thm)],[800, 11604])).
% 7.99/8.21 tff(11606,plain,
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% 7.99/8.21 inference(unit_resolution,[status(thm)],[10872, 391, 133, 665, 11603])).
% 7.99/8.21 tff(11607,plain,
% 7.99/8.21 (r(s(s(s(s(z)))), z)),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[87, 11606])).
% 7.99/8.21 tff(11608,plain,
% 7.99/8.21 (~r(s(s(s(s(z)))), s(z))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[5500, 11607, 11398, 722])).
% 7.99/8.21 tff(11609,plain,
% 7.99/8.21 (b(s(s(s(s(z)))), s(z))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[749, 11608])).
% 7.99/8.21 tff(11610,plain,
% 7.99/8.21 (~b(s(s(elem!1)), s(s(z)))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[11449, 7115, 10682, 380, 2641])).
% 7.99/8.21 tff(11611,plain,
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% 7.99/8.21 inference(unit_resolution,[status(thm)],[11458, 11610, 266])).
% 7.99/8.21 tff(11612,plain,
% 7.99/8.21 (~b(s(z), s(s(z)))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[2447, 7115, 721, 1652, 1759])).
% 7.99/8.21 tff(11613,plain,
% 7.99/8.21 (r(s(z), s(s(z)))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[1788, 11612])).
% 7.99/8.21 tff(11614,plain,
% 7.99/8.21 (~r(elem!1, s(s(z)))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[1775, 11613, 150, 1749, 1759, 1652])).
% 7.99/8.21 tff(11615,plain,
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% 7.99/8.21 inference(unit_resolution,[status(thm)],[3394, 11614, 11611, 1405])).
% 7.99/8.21 tff(11616,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(z))) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.21 tff(11617,plain,
% 7.99/8.21 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[11616, 11609, 150, 1405, 11603, 11394, 10682, 380, 11397, 11404, 11607, 11605])).
% 7.99/8.21 tff(11618,plain,
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% 7.99/8.21 inference(unit_resolution,[status(thm)],[3652, 11617])).
% 7.99/8.21 tff(11619,plain,
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% 7.99/8.21 inference(unit_resolution,[status(thm)],[4462, 2405, 1484, 722])).
% 7.99/8.21 tff(11620,plain,
% 7.99/8.21 (b(s(s(z)), z)),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[1211, 11619])).
% 7.99/8.21 tff(11621,plain,
% 7.99/8.21 (~b(s(s(elem!1)), s(s(z)))),
% 7.99/8.21 inference(unit_resolution,[status(thm)],[11449, 11620, 10682, 380, 2641])).
% 7.99/8.21 tff(11622,plain,
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% 7.99/8.21 inference(unit_resolution,[status(thm)],[11458, 11621, 266])).
% 7.99/8.21 tff(11623,plain,
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% 7.99/8.21 inference(unit_resolution,[status(thm)],[3394, 11622, 1405])).
% 7.99/8.21 tff(11624,plain,
% 7.99/8.21 (r(s(s(s(elem!1))), s(s(z)))),
% 7.99/8.22 inference(modus_ponens,[status(thm)],[11623, 11477])).
% 7.99/8.22 tff(11625,plain,
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% 7.99/8.22 inference(unit_resolution,[status(thm)],[2447, 11620, 721, 1652, 1759])).
% 7.99/8.22 tff(11626,plain,
% 7.99/8.22 (r(s(z), s(s(z)))),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[1788, 11625])).
% 7.99/8.22 tff(11627,plain,
% 7.99/8.22 (~r(s(s(s(elem!1))), s(s(z)))),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[11551, 11626, 232, 2405])).
% 7.99/8.22 tff(11628,plain,
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% 7.99/8.22 inference(unit_resolution,[status(thm)],[11627, 11624])).
% 7.99/8.22 tff(11629,plain,((~r(s(s(z)), s(z))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.22 tff(11630,plain,
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% 7.99/8.22 inference(unit_resolution,[status(thm)],[11629, 11404, 5, 1405, 11372, 11394, 10682, 380, 11397, 452, 11603, 11609, 5237, 722])).
% 7.99/8.22 tff(11631,plain,
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% 7.99/8.22 inference(unit_resolution,[status(thm)],[3778, 11630])).
% 7.99/8.22 tff(11632,plain,
% 7.99/8.22 (~b(s(z), s(s(s(s(z)))))),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[5108, 11631, 11618, 11609])).
% 7.99/8.22 tff(11633,plain,
% 7.99/8.22 (r(s(z), s(s(s(s(z)))))),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[1230, 11632])).
% 7.99/8.22 tff(11634,plain,
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% 7.99/8.22 inference(unit_resolution,[status(thm)],[10566, 194, 722, 11607, 11633, 11605])).
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% 7.99/8.22 tff(11636,plain,
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% 7.99/8.22 inference(unit_resolution,[status(thm)],[11635, 722, 5, 1405, 10682, 380, 150, 133, 665, 590, 445])).
% 7.99/8.22 tff(11637,plain,
% 7.99/8.22 (~b(s(s(s(s(z)))), z)),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[5398, 11636, 665, 133, 718, 590, 5237])).
% 7.99/8.22 tff(11638,plain,
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% 7.99/8.22 inference(unit_resolution,[status(thm)],[87, 11637])).
% 7.99/8.22 tff(11639,plain,
% 7.99/8.22 (~r(s(s(s(s(z)))), s(z))),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[5500, 11638, 11398, 722])).
% 7.99/8.22 tff(11640,plain,
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% 7.99/8.22 inference(unit_resolution,[status(thm)],[749, 11639])).
% 7.99/8.22 tff(11641,plain,
% 7.99/8.22 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[11384, 5])).
% 7.99/8.22 tff(11642,plain,
% 7.99/8.22 ((z = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = z)),
% 7.99/8.22 inference(commutativity,[status(thm)],[])).
% 7.99/8.22 tff(11643,plain,
% 7.99/8.22 ((s(s(s(s(s(s(z)))))) = z) <=> (z = s(s(s(s(s(s(z)))))))),
% 7.99/8.22 inference(symmetry,[status(thm)],[11642])).
% 7.99/8.22 tff(11644,plain,
% 7.99/8.22 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(z = s(s(s(s(s(s(z))))))))),
% 7.99/8.22 inference(monotonicity,[status(thm)],[11643])).
% 7.99/8.22 tff(11645,plain,
% 7.99/8.22 (~(z = s(s(s(s(s(s(z)))))))),
% 7.99/8.22 inference(modus_ponens,[status(thm)],[6638, 11644])).
% 7.99/8.22 tff(11646,plain,
% 7.99/8.22 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 7.99/8.22 inference(symmetry,[status(thm)],[8179])).
% 7.99/8.22 tff(11647,plain,
% 7.99/8.22 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))))),
% 7.99/8.22 inference(monotonicity,[status(thm)],[11646])).
% 7.99/8.22 tff(11648,plain,
% 7.99/8.22 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 7.99/8.22 inference(modus_ponens,[status(thm)],[4995, 11647])).
% 7.99/8.22 tff(11649,plain,
% 7.99/8.22 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 7.99/8.22 inference(commutativity,[status(thm)],[])).
% 7.99/8.22 tff(11650,plain,
% 7.99/8.22 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(z)))))))),
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% 7.99/8.22 tff(11651,plain,
% 7.99/8.22 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(z))))))))),
% 7.99/8.22 inference(monotonicity,[status(thm)],[11650])).
% 7.99/8.22 tff(11652,plain,
% 7.99/8.22 (~(s(z) = s(s(s(s(s(s(z)))))))),
% 7.99/8.22 inference(modus_ponens,[status(thm)],[5065, 11651])).
% 7.99/8.22 tff(11653,assumption,(~(s(s(s(s(s(s(z)))))) = elem!1)), introduced(assumption)).
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% 7.99/8.22 inference(unit_resolution,[status(thm)],[8068, 1652, 133, 665, 2053])).
% 7.99/8.22 tff(11655,plain,
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% 7.99/8.22 inference(unit_resolution,[status(thm)],[8073, 11654, 11653])).
% 7.99/8.22 tff(11656,plain,
% 7.99/8.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 7.99/8.22 inference(rewrite,[status(thm)],[])).
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% 7.99/8.22 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 7.99/8.22 inference(rewrite,[status(thm)],[])).
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% 7.99/8.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 7.99/8.22 inference(monotonicity,[status(thm)],[11657])).
% 7.99/8.22 tff(11659,plain,
% 7.99/8.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 7.99/8.22 inference(transitivity,[status(thm)],[11658, 11656])).
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% 7.99/8.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 7.99/8.22 inference(quant_inst,[status(thm)],[])).
% 7.99/8.22 tff(11661,plain,
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% 7.99/8.22 inference(modus_ponens,[status(thm)],[11660, 11659])).
% 7.99/8.22 tff(11662,plain,
% 7.99/8.22 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[11661, 194, 1484, 847, 11655])).
% 7.99/8.22 tff(11663,plain,
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% 7.99/8.22 inference(rewrite,[status(thm)],[])).
% 7.99/8.22 tff(11664,plain,
% 7.99/8.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 7.99/8.22 inference(quant_inst,[status(thm)],[])).
% 7.99/8.22 tff(11665,plain,
% 7.99/8.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 7.99/8.22 inference(modus_ponens,[status(thm)],[11664, 11663])).
% 7.99/8.22 tff(11666,plain,
% 7.99/8.22 ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[11665, 42, 11662])).
% 7.99/8.22 tff(11667,plain,
% 7.99/8.22 (b(s(z), s(s(s(s(s(s(z)))))))),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[11666, 11652])).
% 7.99/8.22 tff(11668,plain,
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% 7.99/8.22 inference(rewrite,[status(thm)],[])).
% 7.99/8.22 tff(11669,plain,
% 7.99/8.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 7.99/8.22 inference(quant_inst,[status(thm)],[])).
% 7.99/8.22 tff(11670,plain,
% 7.99/8.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 7.99/8.22 inference(modus_ponens,[status(thm)],[11669, 11668])).
% 7.99/8.22 tff(11671,plain,
% 7.99/8.22 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[11670, 194, 1484, 847, 11655])).
% 7.99/8.22 tff(11672,plain,
% 7.99/8.22 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))),
% 7.99/8.22 inference(rewrite,[status(thm)],[])).
% 7.99/8.22 tff(11673,plain,
% 7.99/8.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))),
% 7.99/8.22 inference(quant_inst,[status(thm)],[])).
% 7.99/8.22 tff(11674,plain,
% 7.99/8.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 7.99/8.22 inference(modus_ponens,[status(thm)],[11673, 11672])).
% 7.99/8.22 tff(11675,plain,
% 7.99/8.22 (b(s(s(s(s(s(s(z)))))), s(z))),
% 7.99/8.22 inference(unit_resolution,[status(thm)],[11674, 42, 5065, 11671])).
% 7.99/8.22 tff(11676,plain,
% 7.99/8.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 7.99/8.22 inference(rewrite,[status(thm)],[])).
% 7.99/8.22 tff(11677,plain,
% 7.99/8.22 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 7.99/8.22 inference(rewrite,[status(thm)],[])).
% 7.99/8.22 tff(11678,plain,
% 7.99/8.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 7.99/8.22 inference(monotonicity,[status(thm)],[11677])).
% 7.99/8.22 tff(11679,plain,
% 7.99/8.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 7.99/8.23 inference(transitivity,[status(thm)],[11678, 11676])).
% 7.99/8.23 tff(11680,plain,
% 7.99/8.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 7.99/8.23 inference(quant_inst,[status(thm)],[])).
% 7.99/8.23 tff(11681,plain,
% 7.99/8.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 7.99/8.23 inference(modus_ponens,[status(thm)],[11680, 11679])).
% 7.99/8.23 tff(11682,plain,
% 7.99/8.23 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 7.99/8.23 inference(unit_resolution,[status(thm)],[11681, 391, 1759, 11675, 11667])).
% 7.99/8.23 tff(11683,plain,
% 7.99/8.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 7.99/8.23 inference(rewrite,[status(thm)],[])).
% 7.99/8.23 tff(11684,plain,
% 7.99/8.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 7.99/8.23 inference(quant_inst,[status(thm)],[])).
% 7.99/8.23 tff(11685,plain,
% 7.99/8.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 7.99/8.23 inference(modus_ponens,[status(thm)],[11684, 11683])).
% 7.99/8.23 tff(11686,plain,
% 7.99/8.23 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 7.99/8.23 inference(unit_resolution,[status(thm)],[11685, 42, 11682])).
% 7.99/8.23 tff(11687,plain,
% 7.99/8.23 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 7.99/8.23 inference(unit_resolution,[status(thm)],[11686, 11648])).
% 7.99/8.23 tff(11688,plain,
% 7.99/8.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 7.99/8.23 inference(rewrite,[status(thm)],[])).
% 7.99/8.23 tff(11689,plain,
% 7.99/8.23 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 7.99/8.23 inference(rewrite,[status(thm)],[])).
% 7.99/8.23 tff(11690,plain,
% 7.99/8.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 7.99/8.23 inference(monotonicity,[status(thm)],[11689])).
% 7.99/8.23 tff(11691,plain,
% 7.99/8.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 7.99/8.23 inference(transitivity,[status(thm)],[11690, 11688])).
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% 7.99/8.23 inference(quant_inst,[status(thm)],[])).
% 7.99/8.23 tff(11693,plain,
% 7.99/8.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 7.99/8.23 inference(modus_ponens,[status(thm)],[11692, 11691])).
% 7.99/8.23 tff(11694,plain,
% 7.99/8.23 (~r(z, s(s(s(s(s(s(z)))))))),
% 7.99/8.23 inference(unit_resolution,[status(thm)],[11693, 194, 2053, 8060, 11687])).
% 7.99/8.23 tff(11695,plain,
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% 7.99/8.23 inference(rewrite,[status(thm)],[])).
% 7.99/8.23 tff(11696,plain,
% 7.99/8.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))),
% 7.99/8.23 inference(quant_inst,[status(thm)],[])).
% 7.99/8.23 tff(11697,plain,
% 7.99/8.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 7.99/8.23 inference(modus_ponens,[status(thm)],[11696, 11695])).
% 7.99/8.23 tff(11698,plain,
% 7.99/8.23 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 7.99/8.23 inference(unit_resolution,[status(thm)],[11697, 42, 11694])).
% 7.99/8.23 tff(11699,plain,
% 7.99/8.23 (b(z, s(s(s(s(s(s(z)))))))),
% 7.99/8.23 inference(unit_resolution,[status(thm)],[11698, 11645])).
% 7.99/8.23 tff(11700,plain,
% 7.99/8.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 7.99/8.23 inference(rewrite,[status(thm)],[])).
% 7.99/8.23 tff(11701,plain,
% 7.99/8.23 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 7.99/8.23 inference(rewrite,[status(thm)],[])).
% 7.99/8.23 tff(11702,plain,
% 7.99/8.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 7.99/8.23 inference(monotonicity,[status(thm)],[11701])).
% 7.99/8.23 tff(11703,plain,
% 7.99/8.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 7.99/8.23 inference(transitivity,[status(thm)],[11702, 11700])).
% 7.99/8.23 tff(11704,plain,
% 7.99/8.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))),
% 7.99/8.24 inference(quant_inst,[status(thm)],[])).
% 7.99/8.24 tff(11705,plain,
% 7.99/8.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 7.99/8.24 inference(modus_ponens,[status(thm)],[11704, 11703])).
% 7.99/8.24 tff(11706,plain,
% 7.99/8.24 ($false),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[11705, 391, 590, 11675, 11667, 11699])).
% 7.99/8.24 tff(11707,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(s(s(z)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.99/8.24 tff(11708,plain,
% 7.99/8.24 (~b(s(s(s(s(z)))), elem!1)),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[11707, 11638, 590, 11640, 5237, 11636, 133, 665, 11641])).
% 7.99/8.24 tff(11709,plain,
% 7.99/8.24 (r(s(s(s(s(z)))), elem!1)),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[762, 11708, 718])).
% 7.99/8.24 tff(11710,plain,
% 7.99/8.24 (~r(s(z), s(s(s(s(z)))))),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[5396, 11709, 5237, 11636])).
% 7.99/8.24 tff(11711,plain,
% 7.99/8.24 (b(s(z), s(s(s(s(z)))))),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[1230, 11710])).
% 7.99/8.24 tff(11712,plain,
% 7.99/8.24 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[9262, 11709, 11394])).
% 7.99/8.24 tff(11713,plain,
% 7.99/8.24 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 7.99/8.24 inference(symmetry,[status(thm)],[4203])).
% 7.99/8.24 tff(11714,plain,
% 7.99/8.24 (r(s(s(elem!1)), s(z))),
% 7.99/8.24 inference(modus_ponens,[status(thm)],[11636, 11713])).
% 7.99/8.24 tff(11715,plain,
% 7.99/8.24 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 7.99/8.24 inference(commutativity,[status(thm)],[])).
% 7.99/8.24 tff(11716,plain,
% 7.99/8.24 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 7.99/8.24 inference(symmetry,[status(thm)],[11715])).
% 7.99/8.24 tff(11717,plain,
% 7.99/8.24 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 7.99/8.24 inference(monotonicity,[status(thm)],[11716])).
% 7.99/8.24 tff(11718,plain,
% 7.99/8.24 (~(z = s(s(z)))),
% 7.99/8.24 inference(modus_ponens,[status(thm)],[1207, 11717])).
% 7.99/8.24 tff(11719,plain,
% 7.99/8.24 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), elem!1)),
% 7.99/8.24 inference(monotonicity,[status(thm)],[11452])).
% 7.99/8.24 tff(11720,plain,
% 7.99/8.24 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(elem!1)))),
% 7.99/8.24 inference(symmetry,[status(thm)],[11719])).
% 7.99/8.24 tff(11721,plain,
% 7.99/8.24 (r(s(s(z)), s(s(elem!1)))),
% 7.99/8.24 inference(modus_ponens,[status(thm)],[6669, 11720])).
% 7.99/8.24 tff(11722,plain,
% 7.99/8.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 7.99/8.24 inference(rewrite,[status(thm)],[])).
% 7.99/8.24 tff(11723,plain,
% 7.99/8.24 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 7.99/8.24 inference(rewrite,[status(thm)],[])).
% 7.99/8.24 tff(11724,plain,
% 7.99/8.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1))))))),
% 7.99/8.24 inference(monotonicity,[status(thm)],[11723])).
% 7.99/8.24 tff(11725,plain,
% 7.99/8.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 7.99/8.24 inference(transitivity,[status(thm)],[11724, 11722])).
% 7.99/8.24 tff(11726,plain,
% 7.99/8.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 7.99/8.24 inference(quant_inst,[status(thm)],[])).
% 7.99/8.24 tff(11727,plain,
% 7.99/8.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1))))),
% 7.99/8.24 inference(modus_ponens,[status(thm)],[11726, 11725])).
% 7.99/8.24 tff(11728,plain,
% 7.99/8.24 (~r(s(s(z)), s(s(elem!1)))),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[11727, 194, 340, 1749, 6240])).
% 7.99/8.24 tff(11729,plain,
% 7.99/8.24 ($false),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[11728, 11721])).
% 7.99/8.24 tff(11730,plain,((~r(s(s(z)), elem!1)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.24 tff(11731,plain,
% 7.99/8.24 (~r(s(s(z)), elem!1)),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[11730, 1749, 266, 340, 6240])).
% 7.99/8.24 tff(11732,plain,
% 7.99/8.24 (b(s(s(z)), elem!1)),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[4730, 11731, 5547])).
% 7.99/8.24 tff(11733,plain,
% 7.99/8.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 7.99/8.24 inference(rewrite,[status(thm)],[])).
% 7.99/8.24 tff(11734,plain,
% 7.99/8.24 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 7.99/8.24 inference(rewrite,[status(thm)],[])).
% 7.99/8.24 tff(11735,plain,
% 7.99/8.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 7.99/8.24 inference(monotonicity,[status(thm)],[11734])).
% 7.99/8.24 tff(11736,plain,
% 7.99/8.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 7.99/8.24 inference(transitivity,[status(thm)],[11735, 11733])).
% 7.99/8.24 tff(11737,plain,
% 7.99/8.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))),
% 7.99/8.24 inference(quant_inst,[status(thm)],[])).
% 7.99/8.24 tff(11738,plain,
% 7.99/8.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 7.99/8.24 inference(modus_ponens,[status(thm)],[11737, 11736])).
% 7.99/8.24 tff(11739,plain,
% 7.99/8.24 (~b(z, s(s(z)))),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[11738, 391, 133, 665, 11732])).
% 7.99/8.24 tff(11740,plain,
% 7.99/8.24 ((z = s(s(z))) | r(z, s(s(z)))),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[10164, 42, 11739])).
% 7.99/8.24 tff(11741,plain,
% 7.99/8.24 (r(z, s(s(z)))),
% 7.99/8.24 inference(unit_resolution,[status(thm)],[11740, 11718])).
% 7.99/8.25 tff(11742,plain,
% 7.99/8.25 (~b(s(s(z)), z)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[7121, 391, 133, 665, 11732])).
% 7.99/8.25 tff(11743,plain,
% 7.99/8.25 (r(s(s(z)), z)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[1211, 11742])).
% 7.99/8.25 tff(11744,plain,
% 7.99/8.25 (~r(s(s(z)), s(z))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[4462, 11743, 1484, 722])).
% 7.99/8.25 tff(11745,plain,
% 7.99/8.25 (b(s(s(z)), s(z))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[3778, 11744])).
% 7.99/8.25 tff(11746,plain,
% 7.99/8.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.99/8.25 inference(rewrite,[status(thm)],[])).
% 7.99/8.25 tff(11747,plain,
% 7.99/8.25 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.99/8.25 inference(rewrite,[status(thm)],[])).
% 7.99/8.25 tff(11748,plain,
% 7.99/8.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 7.99/8.25 inference(monotonicity,[status(thm)],[11747])).
% 7.99/8.25 tff(11749,plain,
% 7.99/8.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 7.99/8.25 inference(transitivity,[status(thm)],[11748, 11746])).
% 7.99/8.25 tff(11750,plain,
% 7.99/8.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 7.99/8.25 inference(quant_inst,[status(thm)],[])).
% 7.99/8.25 tff(11751,plain,
% 7.99/8.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 7.99/8.25 inference(modus_ponens,[status(thm)],[11750, 11749])).
% 7.99/8.25 tff(11752,plain,
% 7.99/8.25 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11751, 391, 1234, 1759, 11745])).
% 7.99/8.25 tff(11753,plain,
% 7.99/8.25 (r(s(s(s(s(z)))), s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[1714, 11752])).
% 7.99/8.25 tff(11754,plain,
% 7.99/8.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.99/8.25 inference(rewrite,[status(thm)],[])).
% 7.99/8.25 tff(11755,plain,
% 7.99/8.25 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.99/8.25 inference(rewrite,[status(thm)],[])).
% 7.99/8.25 tff(11756,plain,
% 7.99/8.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 7.99/8.25 inference(monotonicity,[status(thm)],[11755])).
% 7.99/8.25 tff(11757,plain,
% 7.99/8.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 7.99/8.25 inference(transitivity,[status(thm)],[11756, 11754])).
% 7.99/8.25 tff(11758,plain,
% 7.99/8.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 7.99/8.25 inference(quant_inst,[status(thm)],[])).
% 7.99/8.25 tff(11759,plain,
% 7.99/8.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 7.99/8.25 inference(modus_ponens,[status(thm)],[11758, 11757])).
% 7.99/8.25 tff(11760,plain,
% 7.99/8.25 ($false),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11759, 194, 1749, 2053, 11753, 11741])).
% 7.99/8.25 tff(11761,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.25 tff(11762,plain,
% 7.99/8.25 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11761, 11638, 11711, 11640, 5237, 722, 133, 665, 5547, 11394, 11714, 11712])).
% 7.99/8.25 tff(11763,plain,
% 7.99/8.25 (b(s(s(z)), s(s(s(s(z)))))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[3652, 11762])).
% 7.99/8.25 tff(11764,plain,
% 7.99/8.25 (~b(s(s(z)), s(z))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[5108, 11763, 11711, 11640])).
% 7.99/8.25 tff(11765,plain,
% 7.99/8.25 (r(s(s(z)), s(z))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[3778, 11764])).
% 7.99/8.25 tff(11766,plain,
% 7.99/8.25 (~r(s(s(z)), z)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[4462, 11765, 5237, 722])).
% 7.99/8.25 tff(11767,plain,
% 7.99/8.25 (b(s(s(z)), z)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[1211, 11766])).
% 7.99/8.25 tff(11768,plain,
% 7.99/8.25 (~b(s(s(elem!1)), s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11449, 11767, 10682, 380, 11397])).
% 7.99/8.25 tff(11769,plain,
% 7.99/8.25 (~b(elem!1, s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11458, 11768, 11394])).
% 7.99/8.25 tff(11770,plain,
% 7.99/8.25 (r(elem!1, s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[3394, 11769, 1405])).
% 7.99/8.25 tff(11771,plain,
% 7.99/8.25 (r(s(s(s(elem!1))), s(s(z)))),
% 7.99/8.25 inference(modus_ponens,[status(thm)],[11770, 11391])).
% 7.99/8.25 tff(11772,plain,
% 7.99/8.25 (r(s(s(elem!1)), s(s(z))) <=> r(elem!1, s(s(z)))),
% 7.99/8.25 inference(monotonicity,[status(thm)],[11452])).
% 7.99/8.25 tff(11773,plain,
% 7.99/8.25 (r(elem!1, s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 7.99/8.25 inference(symmetry,[status(thm)],[11772])).
% 7.99/8.25 tff(11774,plain,
% 7.99/8.25 (r(s(s(elem!1)), s(s(z)))),
% 7.99/8.25 inference(modus_ponens,[status(thm)],[1748, 11773])).
% 7.99/8.25 tff(11775,assumption,(~r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 7.99/8.25 tff(11776,plain,
% 7.99/8.25 ($false),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11775, 11774])).
% 7.99/8.25 tff(11777,plain,(r(s(s(elem!1)), s(s(z))) | (~r(elem!1, s(s(z)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.25 tff(11778,plain,
% 7.99/8.25 (r(s(s(elem!1)), s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11777, 11770, 11394])).
% 7.99/8.25 tff(11779,plain,
% 7.99/8.25 (~r(s(s(s(s(z)))), s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[6285, 11778, 11712, 11765])).
% 7.99/8.25 tff(11780,plain,
% 7.99/8.25 (b(s(s(s(s(z)))), s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[1714, 11779])).
% 7.99/8.25 tff(11781,plain,
% 7.99/8.25 (~b(s(z), s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[6275, 11780, 11711, 11763])).
% 7.99/8.25 tff(11782,plain,
% 7.99/8.25 (r(s(z), s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[1788, 11781])).
% 7.99/8.25 tff(11783,plain,
% 7.99/8.25 (~r(s(s(s(elem!1))), s(s(z)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11551, 11782, 11372, 11765])).
% 7.99/8.25 tff(11784,plain,
% 7.99/8.25 ($false),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11783, 11771])).
% 7.99/8.25 tff(11785,plain,((~r(z, s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~(s(s(elem!1)) = elem!1)) | (~b(s(z), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 7.99/8.25 tff(11786,plain,
% 7.99/8.25 (~r(z, s(z))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11785, 11373, 1405, 10682, 380, 133, 665, 5547, 445, 590, 150])).
% 7.99/8.25 tff(11787,plain,
% 7.99/8.25 (b(z, s(z))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[678, 11786])).
% 7.99/8.25 tff(11788,plain,
% 7.99/8.25 (~b(elem!1, s(z))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[5970, 11787, 133, 590])).
% 7.99/8.25 tff(11789,plain,
% 7.99/8.25 (r(elem!1, s(z))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[837, 11788, 173])).
% 7.99/8.25 tff(11790,plain,
% 7.99/8.25 (~b(s(s(s(s(z)))), z)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[5398, 11789, 665, 133, 718, 590, 5237])).
% 7.99/8.25 tff(11791,plain,
% 7.99/8.25 (r(s(s(s(s(z)))), z)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[87, 11790])).
% 7.99/8.25 tff(11792,plain,
% 7.99/8.25 (~b(s(s(elem!1)), s(z))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[912, 11788, 445])).
% 7.99/8.25 tff(11793,plain,
% 7.99/8.25 (r(s(s(elem!1)), s(z))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[362, 11792])).
% 7.99/8.25 tff(11794,plain,
% 7.99/8.25 (s(s(s(elem!1))) = s(s(elem!1))),
% 7.99/8.25 inference(modus_ponens,[status(thm)],[11373, 11393])).
% 7.99/8.25 tff(11795,plain,
% 7.99/8.25 (~b(s(s(s(s(z)))), z)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[5398, 847, 665, 133, 5470, 590, 1484])).
% 7.99/8.25 tff(11796,plain,
% 7.99/8.25 (r(s(s(s(s(z)))), z)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[87, 11795])).
% 7.99/8.25 tff(11797,plain,
% 7.99/8.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.99/8.25 inference(rewrite,[status(thm)],[])).
% 7.99/8.25 tff(11798,plain,
% 7.99/8.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 7.99/8.25 inference(quant_inst,[status(thm)],[])).
% 7.99/8.25 tff(11799,plain,
% 7.99/8.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 7.99/8.25 inference(modus_ponens,[status(thm)],[11798, 11797])).
% 7.99/8.25 tff(11800,plain,
% 7.99/8.25 ($false),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11799, 194, 340, 723, 4832, 6240])).
% 7.99/8.25 tff(11801,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.25 tff(11802,plain,
% 7.99/8.25 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[11801, 723, 4832, 340])).
% 7.99/8.25 tff(11803,plain,
% 7.99/8.25 (~r(s(s(s(s(z)))), elem!1)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[9262, 11802, 266])).
% 7.99/8.25 tff(11804,plain,
% 7.99/8.25 (b(s(s(s(s(z)))), elem!1)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[762, 11803, 5470])).
% 7.99/8.25 tff(11805,plain,
% 7.99/8.25 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 7.99/8.25 inference(unit_resolution,[status(thm)],[8068, 11804, 133, 665, 11796])).
% 7.99/8.25 tff(11806,plain,
% 7.99/8.25 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[8073, 11805, 11641])).
% 7.99/8.26 tff(11807,plain,
% 7.99/8.26 (~r(elem!1, s(s(s(s(z)))))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[5517, 194, 1484, 847, 723])).
% 7.99/8.26 tff(11808,plain,
% 7.99/8.26 (b(elem!1, s(s(s(s(z)))))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[781, 11807, 5511])).
% 7.99/8.26 tff(11809,plain,
% 7.99/8.26 (~b(z, s(s(s(s(z)))))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[5600, 391, 133, 665, 11804])).
% 7.99/8.26 tff(11810,plain,
% 7.99/8.26 (r(z, s(s(s(s(z)))))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[800, 11809])).
% 7.99/8.26 tff(11811,plain,
% 7.99/8.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 7.99/8.26 inference(rewrite,[status(thm)],[])).
% 7.99/8.26 tff(11812,plain,
% 7.99/8.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 7.99/8.26 inference(quant_inst,[status(thm)],[])).
% 7.99/8.26 tff(11813,plain,
% 7.99/8.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 7.99/8.26 inference(modus_ponens,[status(thm)],[11812, 11811])).
% 7.99/8.26 tff(11814,plain,
% 7.99/8.26 (~b(s(s(z)), s(z))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11813, 391, 133, 665, 1235, 590])).
% 7.99/8.26 tff(11815,plain,
% 7.99/8.26 (~b(s(z), s(s(z)))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11540, 1235, 266, 2064, 3927, 590])).
% 7.99/8.26 tff(11816,plain,
% 7.99/8.26 (r(s(z), s(s(z)))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[1788, 11815])).
% 7.99/8.26 tff(11817,plain,
% 7.99/8.26 (~b(s(s(elem!1)), s(s(z)))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11449, 1235, 10682, 380, 2641])).
% 7.99/8.26 tff(11818,plain,
% 7.99/8.26 (~b(elem!1, s(s(z)))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11458, 11817, 266])).
% 7.99/8.26 tff(11819,plain,
% 7.99/8.26 (r(elem!1, s(s(z)))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[3394, 11818, 1405])).
% 7.99/8.26 tff(11820,plain,
% 7.99/8.26 (r(s(s(s(elem!1))), s(s(z)))),
% 7.99/8.26 inference(modus_ponens,[status(thm)],[11819, 11477])).
% 7.99/8.26 tff(11821,plain,
% 7.99/8.26 (~r(s(s(z)), s(z))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11551, 11820, 11372, 11816])).
% 7.99/8.26 tff(11822,plain,
% 7.99/8.26 ($false),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[3778, 11821, 11814])).
% 7.99/8.26 tff(11823,plain,((~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.26 tff(11824,plain,
% 7.99/8.26 (~b(s(s(z)), z)),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11823, 11808, 665, 590, 465, 5, 1405, 266, 133, 3927, 10682, 380, 2641])).
% 7.99/8.26 tff(11825,plain,
% 7.99/8.26 (r(s(s(z)), z)),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[1211, 11824])).
% 7.99/8.26 tff(11826,plain,
% 7.99/8.26 (~r(s(s(z)), s(s(s(s(z)))))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[10257, 194, 11796, 11825, 11810])).
% 7.99/8.26 tff(11827,plain,
% 7.99/8.26 (b(s(s(z)), s(s(s(s(z)))))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[3652, 11826])).
% 7.99/8.26 tff(11828,plain,
% 7.99/8.26 (~b(s(s(z)), elem!1)),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[5553, 391, 665, 11827, 11808, 11804])).
% 7.99/8.26 tff(11829,plain,
% 7.99/8.26 (r(s(s(z)), elem!1)),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[4730, 11828, 5547])).
% 7.99/8.26 tff(11830,plain,
% 7.99/8.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 7.99/8.26 inference(rewrite,[status(thm)],[])).
% 7.99/8.26 tff(11831,plain,
% 7.99/8.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 7.99/8.26 inference(quant_inst,[status(thm)],[])).
% 7.99/8.26 tff(11832,plain,
% 7.99/8.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 7.99/8.26 inference(modus_ponens,[status(thm)],[11831, 11830])).
% 7.99/8.26 tff(11833,plain,
% 7.99/8.26 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11832, 194, 847, 11829, 11806])).
% 7.99/8.26 tff(11834,plain,
% 7.99/8.26 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11670, 194, 1484, 847, 11806])).
% 7.99/8.26 tff(11835,plain,
% 7.99/8.26 (b(s(s(s(s(s(s(z)))))), s(z))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11674, 42, 5065, 11834])).
% 7.99/8.26 tff(11836,plain,
% 7.99/8.26 (~r(s(s(z)), s(z))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[6674, 11829, 1484, 847])).
% 7.99/8.26 tff(11837,plain,
% 7.99/8.26 (b(s(s(z)), s(z))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[3778, 11836])).
% 7.99/8.26 tff(11838,plain,
% 7.99/8.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 7.99/8.26 inference(rewrite,[status(thm)],[])).
% 7.99/8.26 tff(11839,plain,
% 7.99/8.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 7.99/8.26 inference(quant_inst,[status(thm)],[])).
% 7.99/8.26 tff(11840,plain,
% 7.99/8.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 7.99/8.26 inference(modus_ponens,[status(thm)],[11839, 11838])).
% 7.99/8.26 tff(11841,plain,
% 7.99/8.26 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11840, 391, 133, 11837, 590, 11835])).
% 7.99/8.26 tff(11842,plain,
% 7.99/8.26 ($false),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 11841, 11833])).
% 7.99/8.26 tff(11843,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~r(s(z), elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, z)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.26 tff(11844,plain,
% 7.99/8.26 (~r(s(s(s(s(z)))), s(z))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11843, 11789, 133, 590, 5237, 5547, 665, 452, 11373, 1405, 11794, 11403, 10682, 380, 11397, 11398, 11793])).
% 7.99/8.26 tff(11845,plain,
% 7.99/8.26 (b(s(s(s(s(z)))), s(z))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[749, 11844])).
% 7.99/8.26 tff(11846,plain,
% 7.99/8.26 (~b(s(s(s(s(z)))), elem!1)),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11707, 11845, 590, 11791, 5237, 11789, 133, 665, 11385])).
% 7.99/8.26 tff(11847,plain,
% 7.99/8.26 (r(s(s(s(s(z)))), elem!1)),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[762, 11846, 718])).
% 7.99/8.26 tff(11848,plain,
% 7.99/8.26 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11670, 194, 1484, 847, 2741])).
% 7.99/8.26 tff(11849,plain,
% 7.99/8.26 (b(s(s(s(s(s(s(z)))))), s(z))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11674, 42, 5065, 11848])).
% 7.99/8.26 tff(11850,plain,
% 7.99/8.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 7.99/8.26 inference(rewrite,[status(thm)],[])).
% 7.99/8.26 tff(11851,plain,
% 7.99/8.26 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 7.99/8.26 inference(rewrite,[status(thm)],[])).
% 7.99/8.26 tff(11852,plain,
% 7.99/8.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 7.99/8.26 inference(monotonicity,[status(thm)],[11851])).
% 7.99/8.26 tff(11853,plain,
% 7.99/8.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 7.99/8.26 inference(transitivity,[status(thm)],[11852, 11850])).
% 7.99/8.26 tff(11854,plain,
% 7.99/8.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 7.99/8.26 inference(quant_inst,[status(thm)],[])).
% 7.99/8.26 tff(11855,plain,
% 7.99/8.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 7.99/8.26 inference(modus_ponens,[status(thm)],[11854, 11853])).
% 7.99/8.26 tff(11856,plain,
% 7.99/8.26 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[11855, 194, 847, 2112, 2741])).
% 7.99/8.26 tff(11857,plain,
% 7.99/8.26 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 7.99/8.26 inference(unit_resolution,[status(thm)],[6652, 42, 4995, 11856])).
% 7.99/8.26 tff(11858,plain,
% 7.99/8.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 7.99/8.26 inference(rewrite,[status(thm)],[])).
% 7.99/8.26 tff(11859,plain,
% 7.99/8.26 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 7.99/8.26 inference(rewrite,[status(thm)],[])).
% 7.99/8.26 tff(11860,plain,
% 7.99/8.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 7.99/8.27 inference(monotonicity,[status(thm)],[11859])).
% 7.99/8.27 tff(11861,plain,
% 7.99/8.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 7.99/8.27 inference(transitivity,[status(thm)],[11860, 11858])).
% 7.99/8.27 tff(11862,plain,
% 7.99/8.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 7.99/8.27 inference(quant_inst,[status(thm)],[])).
% 7.99/8.27 tff(11863,plain,
% 7.99/8.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 7.99/8.27 inference(modus_ponens,[status(thm)],[11862, 11861])).
% 7.99/8.27 tff(11864,plain,
% 7.99/8.27 ($false),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11863, 391, 7016, 1759, 11857, 11849])).
% 7.99/8.27 tff(11865,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.27 tff(11866,plain,
% 7.99/8.27 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11865, 11845, 11789, 11847, 5237])).
% 7.99/8.27 tff(11867,plain,
% 7.99/8.27 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[8073, 11866, 11385])).
% 7.99/8.27 tff(11868,plain,
% 7.99/8.27 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[9262, 11847, 11794])).
% 7.99/8.27 tff(11869,plain,
% 7.99/8.27 (~r(s(z), s(s(s(s(z)))))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[5396, 11847, 5237, 11789])).
% 7.99/8.27 tff(11870,plain,
% 7.99/8.27 (b(s(z), s(s(s(s(z)))))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[1230, 11869])).
% 7.99/8.27 tff(11871,plain,
% 7.99/8.27 (~b(s(s(z)), s(s(s(s(z)))))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[5108, 1233, 1759, 1234])).
% 7.99/8.27 tff(11872,plain,
% 7.99/8.27 (r(s(s(z)), s(s(s(s(z)))))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[3652, 11871])).
% 7.99/8.27 tff(11873,plain,
% 7.99/8.27 (~r(s(s(z)), elem!1)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11730, 11872, 266, 340, 6240])).
% 7.99/8.27 tff(11874,plain,
% 7.99/8.27 (b(s(s(z)), elem!1)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[4730, 11873, 5547])).
% 7.99/8.27 tff(11875,plain,
% 7.99/8.27 (~b(z, s(s(z)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11738, 391, 133, 665, 11874])).
% 7.99/8.27 tff(11876,plain,
% 7.99/8.27 ((z = s(s(z))) | r(z, s(s(z)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[10164, 42, 11875])).
% 7.99/8.27 tff(11877,plain,
% 7.99/8.27 (r(z, s(s(z)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11876, 11718])).
% 7.99/8.27 tff(11878,plain,
% 7.99/8.27 (~b(s(s(s(s(z)))), s(s(z)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11751, 391, 1234, 1759, 1233])).
% 7.99/8.27 tff(11879,plain,
% 7.99/8.27 (r(s(s(s(s(z)))), s(s(z)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[1714, 11878])).
% 7.99/8.27 tff(11880,plain,
% 7.99/8.27 ($false),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11759, 194, 11872, 2053, 11879, 11877])).
% 7.99/8.27 tff(11881,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (s(s(z)) = elem!1) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.27 tff(11882,plain,
% 7.99/8.27 (~b(s(s(z)), s(z))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11881, 11791, 133, 665, 11870, 11845, 5547, 11794, 11793, 11868])).
% 7.99/8.27 tff(11883,plain,
% 7.99/8.27 (r(s(s(z)), s(z))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[3778, 11882])).
% 7.99/8.27 tff(11884,plain,
% 7.99/8.27 (~r(s(s(z)), elem!1)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[6674, 11883, 5237, 11789])).
% 7.99/8.27 tff(11885,plain,
% 7.99/8.27 (b(s(s(z)), elem!1)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[4730, 11884, 5547])).
% 7.99/8.27 tff(11886,plain,
% 7.99/8.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 7.99/8.27 inference(rewrite,[status(thm)],[])).
% 7.99/8.27 tff(11887,plain,
% 7.99/8.27 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 7.99/8.27 inference(rewrite,[status(thm)],[])).
% 7.99/8.27 tff(11888,plain,
% 7.99/8.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 7.99/8.27 inference(monotonicity,[status(thm)],[11887])).
% 7.99/8.27 tff(11889,plain,
% 7.99/8.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 7.99/8.27 inference(transitivity,[status(thm)],[11888, 11886])).
% 7.99/8.27 tff(11890,plain,
% 7.99/8.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 7.99/8.27 inference(quant_inst,[status(thm)],[])).
% 7.99/8.27 tff(11891,plain,
% 7.99/8.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 7.99/8.27 inference(modus_ponens,[status(thm)],[11890, 11889])).
% 7.99/8.27 tff(11892,plain,
% 7.99/8.27 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11891, 391, 133, 665, 11885, 11867])).
% 7.99/8.27 tff(11893,plain,
% 7.99/8.27 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 11892])).
% 7.99/8.27 tff(11894,plain,
% 7.99/8.27 (~b(s(s(s(s(s(s(z)))))), z)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[8048, 391, 133, 665, 11867])).
% 7.99/8.27 tff(11895,plain,
% 7.99/8.27 (r(s(s(s(s(s(s(z)))))), z)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[6641, 42, 6638, 11894])).
% 7.99/8.27 tff(11896,plain,
% 7.99/8.27 (~b(z, s(s(s(s(z)))))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[7102, 391, 11870, 11845, 11787])).
% 7.99/8.27 tff(11897,plain,
% 7.99/8.27 (r(z, s(s(s(s(z)))))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[800, 11896])).
% 7.99/8.27 tff(11898,plain,
% 7.99/8.27 (~b(s(s(z)), z)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[7121, 391, 133, 665, 11885])).
% 7.99/8.27 tff(11899,plain,
% 7.99/8.27 (r(s(s(z)), z)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[1211, 11898])).
% 7.99/8.27 tff(11900,plain,
% 7.99/8.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 7.99/8.27 inference(rewrite,[status(thm)],[])).
% 7.99/8.27 tff(11901,plain,
% 7.99/8.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 7.99/8.27 inference(quant_inst,[status(thm)],[])).
% 7.99/8.27 tff(11902,plain,
% 7.99/8.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 7.99/8.27 inference(modus_ponens,[status(thm)],[11901, 11900])).
% 7.99/8.27 tff(11903,plain,
% 7.99/8.27 ($false),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11902, 194, 11899, 11897, 11895, 11893])).
% 7.99/8.27 tff(11904,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (elem!1 = s(s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~(s(s(elem!1)) = elem!1)) | (s(z) = elem!1) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 7.99/8.27 tff(11905,plain,
% 7.99/8.27 (~(s(s(elem!1)) = elem!1)),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11904, 11370, 10677, 133, 10682, 11363, 11369, 11366, 150, 11352, 4028])).
% 7.99/8.27 tff(11906,plain,
% 7.99/8.27 (~(elem!1 = s(s(elem!1)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[1292, 11905])).
% 7.99/8.27 tff(11907,plain,
% 7.99/8.27 (r(elem!1, s(s(elem!1)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[1307, 11906, 11348])).
% 7.99/8.27 tff(11908,plain,
% 7.99/8.27 (~r(s(s(elem!1)), s(z))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[6408, 11907, 1216, 838])).
% 7.99/8.27 tff(11909,plain,
% 7.99/8.27 (b(s(s(elem!1)), s(z))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[362, 11908])).
% 7.99/8.27 tff(11910,plain,
% 7.99/8.27 (b(s(s(s(s(s(elem!1))))), s(z))),
% 7.99/8.27 inference(modus_ponens,[status(thm)],[11909, 11344])).
% 7.99/8.27 tff(11911,plain,
% 7.99/8.27 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.99/8.27 inference(monotonicity,[status(thm)],[11339])).
% 7.99/8.27 tff(11912,plain,
% 7.99/8.27 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 7.99/8.27 inference(modus_ponens,[status(thm)],[11357, 11911])).
% 7.99/8.27 tff(11913,plain,
% 7.99/8.27 (~b(s(s(z)), s(s(s(elem!1))))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[10977, 391, 3823, 11329, 11912])).
% 7.99/8.27 tff(11914,plain,
% 7.99/8.27 (r(s(s(z)), s(s(s(elem!1))))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11041, 11913])).
% 7.99/8.27 tff(11915,plain,
% 7.99/8.27 (r(s(s(s(elem!1))), s(s(z)))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[10022, 11364, 11339])).
% 7.99/8.27 tff(11916,plain,
% 7.99/8.27 (~b(s(z), s(s(s(elem!1))))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[11303, 11370, 10682, 10677])).
% 7.99/8.27 tff(11917,plain,
% 7.99/8.27 (r(s(z), s(s(s(elem!1))))),
% 7.99/8.27 inference(unit_resolution,[status(thm)],[247, 11916])).
% 7.99/8.27 tff(11918,plain,
% 7.99/8.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.99/8.27 inference(rewrite,[status(thm)],[])).
% 7.99/8.27 tff(11919,plain,
% 7.99/8.27 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.99/8.27 inference(rewrite,[status(thm)],[])).
% 7.99/8.27 tff(11920,plain,
% 7.99/8.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[11919])).
% 7.99/8.28 tff(11921,plain,
% 7.99/8.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 7.99/8.28 inference(transitivity,[status(thm)],[11920, 11918])).
% 7.99/8.28 tff(11922,plain,
% 7.99/8.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 7.99/8.28 inference(quant_inst,[status(thm)],[])).
% 7.99/8.28 tff(11923,plain,
% 7.99/8.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 7.99/8.28 inference(modus_ponens,[status(thm)],[11922, 11921])).
% 7.99/8.28 tff(11924,plain,
% 7.99/8.28 (~r(s(z), s(s(z)))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[11923, 194, 11917, 11915, 11914])).
% 7.99/8.28 tff(11925,plain,
% 7.99/8.28 (b(s(z), s(s(z)))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[1788, 11924])).
% 7.99/8.28 tff(11926,plain,
% 7.99/8.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(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))))))))),
% 7.99/8.28 inference(rewrite,[status(thm)],[])).
% 7.99/8.28 tff(11927,plain,
% 7.99/8.28 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~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)))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(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))))))))),
% 7.99/8.28 inference(rewrite,[status(thm)],[])).
% 7.99/8.28 tff(11928,plain,
% 7.99/8.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(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)))))))))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[11927])).
% 7.99/8.28 tff(11929,plain,
% 7.99/8.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(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))))))))),
% 7.99/8.28 inference(transitivity,[status(thm)],[11928, 11926])).
% 7.99/8.28 tff(11930,plain,
% 7.99/8.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~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))))))))),
% 7.99/8.28 inference(quant_inst,[status(thm)],[])).
% 7.99/8.28 tff(11931,plain,
% 7.99/8.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(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)))))))),
% 7.99/8.28 inference(modus_ponens,[status(thm)],[11930, 11929])).
% 7.99/8.28 tff(11932,plain,
% 7.99/8.28 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[11931, 391, 3823, 11925, 1233, 11910])).
% 7.99/8.28 tff(11933,plain,
% 7.99/8.28 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[11341])).
% 7.99/8.28 tff(11934,plain,
% 7.99/8.28 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[11339])).
% 7.99/8.28 tff(11935,plain,
% 7.99/8.28 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 7.99/8.28 inference(transitivity,[status(thm)],[11934, 11933])).
% 7.99/8.28 tff(11936,plain,
% 7.99/8.28 (b(elem!1, z)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[526, 2282, 2])).
% 7.99/8.28 tff(11937,plain,
% 7.99/8.28 (b(s(elem!1), z)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[549, 544])).
% 7.99/8.28 tff(11938,plain,
% 7.99/8.28 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[445])).
% 7.99/8.28 tff(11939,plain,
% 7.99/8.28 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[11938])).
% 7.99/8.28 tff(11940,plain,
% 7.99/8.28 (~(s(s(elem!1)) = s(s(z)))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[1962, 121])).
% 7.99/8.28 tff(11941,plain,
% 7.99/8.28 (~(elem!1 = s(s(z)))),
% 7.99/8.28 inference(modus_ponens,[status(thm)],[11940, 11939])).
% 7.99/8.28 tff(11942,plain,
% 7.99/8.28 (~(s(s(z)) = elem!1)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[4584, 452, 121])).
% 7.99/8.28 tff(11943,plain,
% 7.99/8.28 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[1845, 445, 168])).
% 7.99/8.28 tff(11944,plain,
% 7.99/8.28 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[452])).
% 7.99/8.28 tff(11945,plain,
% 7.99/8.28 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.99/8.28 inference(symmetry,[status(thm)],[11944])).
% 7.99/8.28 tff(11946,plain,
% 7.99/8.28 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[452])).
% 7.99/8.28 tff(11947,plain,
% 7.99/8.28 (s(s(s(s(elem!1)))) = elem!1),
% 7.99/8.28 inference(transitivity,[status(thm)],[11946, 445])).
% 7.99/8.28 tff(11948,plain,
% 7.99/8.28 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[11947])).
% 7.99/8.28 tff(11949,plain,
% 7.99/8.28 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 7.99/8.28 inference(symmetry,[status(thm)],[11948])).
% 7.99/8.28 tff(11950,plain,
% 7.99/8.28 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.99/8.28 inference(transitivity,[status(thm)],[11949, 11945])).
% 7.99/8.28 tff(11951,plain,
% 7.99/8.28 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[11950])).
% 7.99/8.28 tff(11952,plain,
% 7.99/8.28 (~b(elem!1, s(elem!1))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[4603, 452, 4028])).
% 7.99/8.28 tff(11953,plain,
% 7.99/8.28 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.99/8.28 inference(modus_ponens,[status(thm)],[11952, 11951])).
% 7.99/8.28 tff(11954,plain,
% 7.99/8.28 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[4794])).
% 7.99/8.28 tff(11955,plain,
% 7.99/8.28 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 7.99/8.28 inference(modus_ponens,[status(thm)],[4028, 11954])).
% 7.99/8.28 tff(11956,plain,
% 7.99/8.28 (~(s(elem!1) = s(z))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[123, 121])).
% 7.99/8.28 tff(11957,plain,
% 7.99/8.28 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[452])).
% 7.99/8.28 tff(11958,plain,
% 7.99/8.28 (b(z, s(elem!1))),
% 7.99/8.28 inference(modus_ponens,[status(thm)],[10682, 11957])).
% 7.99/8.28 tff(11959,plain,
% 7.99/8.28 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 7.99/8.28 inference(symmetry,[status(thm)],[682])).
% 7.99/8.28 tff(11960,plain,
% 7.99/8.28 (b(s(s(s(elem!1))), z)),
% 7.99/8.28 inference(modus_ponens,[status(thm)],[591, 11959])).
% 7.99/8.28 tff(11961,plain,
% 7.99/8.28 (~b(s(z), z)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[11904, 11942, 665, 133, 11941, 10682, 11960, 445, 150, 168, 4028])).
% 7.99/8.28 tff(11962,plain,
% 7.99/8.28 (r(s(z), z)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[180, 11961])).
% 7.99/8.28 tff(11963,plain,
% 7.99/8.28 (~(s(elem!1) = s(s(s(s(z)))))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[5377, 452, 3363])).
% 7.99/8.28 tff(11964,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 7.99/8.28 tff(11965,plain,
% 7.99/8.28 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[11947])).
% 7.99/8.28 tff(11966,plain,
% 7.99/8.28 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 7.99/8.28 inference(monotonicity,[status(thm)],[452])).
% 7.99/8.28 tff(11967,plain,
% 7.99/8.28 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 7.99/8.28 inference(transitivity,[status(thm)],[11966, 11965])).
% 7.99/8.28 tff(11968,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 7.99/8.28 tff(11969,plain,
% 7.99/8.28 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[1095, 310, 11968])).
% 7.99/8.28 tff(11970,plain,
% 7.99/8.28 (r(elem!1, s(elem!1))),
% 7.99/8.28 inference(modus_ponens,[status(thm)],[11969, 11967])).
% 7.99/8.28 tff(11971,plain,
% 7.99/8.28 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[1356, 315, 1351])).
% 7.99/8.28 tff(11972,plain,
% 7.99/8.28 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 7.99/8.28 inference(monotonicity,[status(thm)],[452])).
% 7.99/8.28 tff(11973,plain,
% 7.99/8.28 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), elem!1)),
% 7.99/8.28 inference(transitivity,[status(thm)],[4825, 11972])).
% 7.99/8.28 tff(11974,plain,
% 7.99/8.28 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[1370, 297, 8329])).
% 7.99/8.28 tff(11975,plain,
% 7.99/8.28 (r(s(elem!1), elem!1)),
% 7.99/8.28 inference(modus_ponens,[status(thm)],[11974, 11973])).
% 7.99/8.28 tff(11976,plain,
% 7.99/8.28 (~b(s(z), z)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[5231, 644, 665, 133])).
% 7.99/8.28 tff(11977,plain,
% 7.99/8.28 (r(s(z), z)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[180, 11976])).
% 7.99/8.28 tff(11978,plain,
% 7.99/8.28 (~b(s(s(s(s(z)))), z)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[5901, 2251, 665, 591, 718, 133, 2121, 485])).
% 7.99/8.28 tff(11979,plain,
% 7.99/8.28 (r(s(s(s(s(z)))), z)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[87, 11978])).
% 7.99/8.28 tff(11980,plain,
% 7.99/8.28 (~b(z, s(z))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[4651, 391, 133, 665, 644])).
% 7.99/8.28 tff(11981,plain,
% 7.99/8.28 (r(z, s(z))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[678, 11980])).
% 7.99/8.28 tff(11982,plain,
% 7.99/8.28 (~r(s(z), s(s(s(s(z)))))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[10558, 11981, 11979, 11977])).
% 7.99/8.28 tff(11983,plain,
% 7.99/8.28 (b(s(z), s(s(s(s(z)))))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[1230, 11982])).
% 7.99/8.28 tff(11984,plain,
% 7.99/8.28 (~b(s(s(s(s(z)))), elem!1)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[4062, 11983, 133, 665, 644])).
% 7.99/8.28 tff(11985,plain,
% 7.99/8.28 (r(s(s(s(s(z)))), elem!1)),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[762, 11984, 718])).
% 7.99/8.28 tff(11986,plain,
% 7.99/8.28 (~r(s(elem!1), s(s(s(s(z)))))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[4553, 194, 485, 2251, 11985])).
% 7.99/8.28 tff(11987,plain,
% 7.99/8.28 (b(s(elem!1), s(s(s(s(z)))))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[2142, 42, 11986, 2121])).
% 7.99/8.28 tff(11988,plain,
% 7.99/8.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 7.99/8.28 inference(quant_inst,[status(thm)],[])).
% 7.99/8.28 tff(11989,plain,
% 7.99/8.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 7.99/8.28 inference(modus_ponens,[status(thm)],[11988, 5111])).
% 7.99/8.28 tff(11990,plain,
% 7.99/8.28 (~r(s(s(s(s(z)))), s(z))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[11989, 194, 11981, 11977, 11979])).
% 7.99/8.28 tff(11991,plain,
% 7.99/8.28 (b(s(s(s(s(z)))), s(z))),
% 7.99/8.28 inference(unit_resolution,[status(thm)],[749, 11990])).
% 7.99/8.29 tff(11992,plain,
% 7.99/8.29 (~r(s(s(s(s(z)))), s(elem!1))),
% 7.99/8.29 inference(unit_resolution,[status(thm)],[4609, 194, 485, 2251, 11985])).
% 7.99/8.29 tff(11993,plain,
% 7.99/8.29 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 7.99/8.29 inference(unit_resolution,[status(thm)],[2136, 42, 11992])).
% 7.99/8.29 tff(11994,plain,
% 7.99/8.29 (b(s(s(s(s(z)))), s(elem!1))),
% 7.99/8.29 inference(unit_resolution,[status(thm)],[11993, 2126])).
% 7.99/8.29 tff(11995,plain,
% 7.99/8.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 7.99/8.29 inference(rewrite,[status(thm)],[])).
% 7.99/8.29 tff(11996,plain,
% 7.99/8.29 (((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 7.99/8.29 inference(rewrite,[status(thm)],[])).
% 7.99/8.29 tff(11997,plain,
% 7.99/8.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 7.99/8.29 inference(monotonicity,[status(thm)],[11996])).
% 7.99/8.29 tff(11998,plain,
% 7.99/8.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 7.99/8.29 inference(transitivity,[status(thm)],[11997, 11995])).
% 7.99/8.29 tff(11999,plain,
% 7.99/8.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 7.99/8.29 inference(quant_inst,[status(thm)],[])).
% 7.99/8.29 tff(12000,plain,
% 7.99/8.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 7.99/8.29 inference(modus_ponens,[status(thm)],[11999, 11998])).
% 7.99/8.29 tff(12001,plain,
% 7.99/8.29 (~b(z, s(s(s(s(z)))))),
% 7.99/8.29 inference(unit_resolution,[status(thm)],[12000, 391, 133, 592, 591, 11994])).
% 7.99/8.29 tff(12002,plain,
% 7.99/8.29 (r(z, s(s(s(s(z)))))),
% 7.99/8.29 inference(unit_resolution,[status(thm)],[800, 12001])).
% 7.99/8.29 tff(12003,plain,
% 7.99/8.29 (~(elem!1 = s(s(s(s(z)))))),
% 7.99/8.29 inference(unit_resolution,[status(thm)],[769, 718])).
% 7.99/8.29 tff(12004,plain,
% 7.99/8.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 7.99/8.29 inference(rewrite,[status(thm)],[])).
% 7.99/8.29 tff(12005,plain,
% 7.99/8.29 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 7.99/8.29 inference(rewrite,[status(thm)],[])).
% 7.99/8.29 tff(12006,plain,
% 7.99/8.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 7.99/8.29 inference(monotonicity,[status(thm)],[12005])).
% 7.99/8.29 tff(12007,plain,
% 7.99/8.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 7.99/8.29 inference(transitivity,[status(thm)],[12006, 12004])).
% 7.99/8.29 tff(12008,plain,
% 7.99/8.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))),
% 7.99/8.29 inference(quant_inst,[status(thm)],[])).
% 7.99/8.29 tff(12009,plain,
% 7.99/8.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 7.99/8.29 inference(modus_ponens,[status(thm)],[12008, 12007])).
% 7.99/8.29 tff(12010,plain,
% 7.99/8.29 (~b(s(elem!1), s(z))),
% 7.99/8.29 inference(unit_resolution,[status(thm)],[12009, 391, 644, 11983, 11991, 11987])).
% 7.99/8.29 tff(12011,plain,
% 7.99/8.29 (~b(s(s(s(elem!1))), s(z))),
% 7.99/8.29 inference(modus_ponens,[status(thm)],[12010, 4779])).
% 7.99/8.29 tff(12012,plain,
% 7.99/8.29 (r(s(s(s(elem!1))), s(z))),
% 7.99/8.29 inference(unit_resolution,[status(thm)],[223, 12011])).
% 7.99/8.29 tff(12013,plain,
% 7.99/8.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 7.99/8.29 inference(rewrite,[status(thm)],[])).
% 7.99/8.29 tff(12014,plain,
% 7.99/8.29 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 7.99/8.29 inference(rewrite,[status(thm)],[])).
% 7.99/8.29 tff(12015,plain,
% 7.99/8.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 7.99/8.29 inference(monotonicity,[status(thm)],[12014])).
% 7.99/8.29 tff(12016,plain,
% 7.99/8.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.09/8.30 inference(transitivity,[status(thm)],[12015, 12013])).
% 8.09/8.30 tff(12017,plain,
% 8.09/8.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))))),
% 8.09/8.30 inference(quant_inst,[status(thm)],[])).
% 8.09/8.30 tff(12018,plain,
% 8.09/8.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 8.09/8.30 inference(modus_ponens,[status(thm)],[12017, 12016])).
% 8.09/8.30 tff(12019,plain,
% 8.09/8.30 (~b(s(z), s(elem!1))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[12018, 391, 644, 11983, 11991, 11987])).
% 8.09/8.30 tff(12020,plain,
% 8.09/8.30 (~b(s(z), s(s(s(elem!1))))),
% 8.09/8.30 inference(modus_ponens,[status(thm)],[12019, 4829])).
% 8.09/8.30 tff(12021,plain,
% 8.09/8.30 (r(s(z), s(s(s(elem!1))))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[247, 12020])).
% 8.09/8.30 tff(12022,plain,
% 8.09/8.30 (~r(s(s(elem!1)), s(z))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[2201, 12021, 1378, 12012])).
% 8.09/8.30 tff(12023,plain,
% 8.09/8.30 (b(s(s(elem!1)), s(z))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[362, 12022])).
% 8.09/8.30 tff(12024,plain,
% 8.09/8.30 (b(elem!1, s(z))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[912, 12023, 445])).
% 8.09/8.30 tff(12025,plain,
% 8.09/8.30 (~b(elem!1, s(s(s(s(z)))))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[3150, 12024, 665, 644, 11991])).
% 8.09/8.30 tff(12026,plain,
% 8.09/8.30 (r(elem!1, s(s(s(s(z)))))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[781, 12025, 12003])).
% 8.09/8.30 tff(12027,plain,
% 8.09/8.30 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[7123, 12026, 665, 133, 5547, 12002, 11979])).
% 8.09/8.30 tff(12028,plain,
% 8.09/8.30 (b(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[3652, 12027])).
% 8.09/8.30 tff(12029,plain,
% 8.09/8.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 8.09/8.30 inference(rewrite,[status(thm)],[])).
% 8.09/8.30 tff(12030,plain,
% 8.09/8.30 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 8.09/8.30 inference(rewrite,[status(thm)],[])).
% 8.09/8.30 tff(12031,plain,
% 8.09/8.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))))),
% 8.09/8.30 inference(monotonicity,[status(thm)],[12030])).
% 8.09/8.30 tff(12032,plain,
% 8.09/8.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 8.09/8.30 inference(transitivity,[status(thm)],[12031, 12029])).
% 8.09/8.30 tff(12033,plain,
% 8.09/8.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))))),
% 8.09/8.30 inference(quant_inst,[status(thm)],[])).
% 8.09/8.30 tff(12034,plain,
% 8.09/8.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1)))),
% 8.09/8.30 inference(modus_ponens,[status(thm)],[12033, 12032])).
% 8.09/8.30 tff(12035,plain,
% 8.09/8.30 (~b(s(s(z)), s(elem!1))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[12034, 391, 644, 12028, 11991, 11987])).
% 8.09/8.30 tff(12036,plain,
% 8.09/8.30 (r(s(elem!1), s(z))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[1915, 42, 12010, 11964])).
% 8.09/8.30 tff(12037,plain,
% 8.09/8.30 (~b(s(s(z)), s(z))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[5126, 12028, 133, 11977, 11981, 11983])).
% 8.09/8.30 tff(12038,plain,
% 8.09/8.30 (r(s(s(z)), s(z))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[3778, 12037])).
% 8.09/8.30 tff(12039,plain,
% 8.09/8.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 8.09/8.30 inference(rewrite,[status(thm)],[])).
% 8.09/8.30 tff(12040,plain,
% 8.09/8.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 8.09/8.30 inference(quant_inst,[status(thm)],[])).
% 8.09/8.30 tff(12041,plain,
% 8.09/8.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1)))),
% 8.09/8.30 inference(modus_ponens,[status(thm)],[12040, 12039])).
% 8.09/8.30 tff(12042,plain,
% 8.09/8.30 (~r(s(s(z)), s(elem!1))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[12041, 194, 11977, 12038, 12036])).
% 8.09/8.30 tff(12043,plain,
% 8.09/8.30 (~(s(s(z)) = s(elem!1))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[2493, 452])).
% 8.09/8.30 tff(12044,plain,
% 8.09/8.30 ($false),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[4693, 42, 12043, 12042, 12035])).
% 8.09/8.30 tff(12045,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~(s(s(elem!1)) = elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.30 tff(12046,plain,
% 8.09/8.30 (~b(s(z), elem!1)),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[12045, 11975, 665, 5547, 445, 133, 592, 591, 11964, 11963, 11971, 11970])).
% 8.09/8.30 tff(12047,plain,
% 8.09/8.30 (r(s(z), elem!1)),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[632, 12046, 150])).
% 8.09/8.30 tff(12048,plain,
% 8.09/8.30 (~r(s(elem!1), s(z))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[5800, 194, 11975, 11970, 12047])).
% 8.09/8.30 tff(12049,plain,
% 8.09/8.30 (b(s(elem!1), s(z))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[1915, 42, 12048, 11964])).
% 8.09/8.30 tff(12050,plain,
% 8.09/8.30 (~b(s(s(s(s(z)))), z)),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[5901, 11970, 665, 591, 718, 133, 11963, 11975])).
% 8.09/8.30 tff(12051,plain,
% 8.09/8.30 (r(s(s(s(s(z)))), z)),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[87, 12050])).
% 8.09/8.30 tff(12052,plain,
% 8.09/8.30 (r(s(z), s(s(elem!1)))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[4847, 12047, 445])).
% 8.09/8.30 tff(12053,plain,
% 8.09/8.30 (~r(s(z), s(elem!1))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[5738, 194, 11975, 11970, 12047])).
% 8.09/8.30 tff(12054,plain,
% 8.09/8.30 (~r(s(z), s(s(s(elem!1))))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[2274, 12053, 452])).
% 8.09/8.30 tff(12055,plain,
% 8.09/8.30 (b(s(z), s(s(s(elem!1))))),
% 8.09/8.30 inference(unit_resolution,[status(thm)],[247, 12054])).
% 8.09/8.30 tff(12056,plain,
% 8.09/8.30 (b(s(z), s(elem!1))),
% 8.09/8.30 inference(modus_ponens,[status(thm)],[12055, 680])).
% 8.09/8.30 tff(12057,plain,
% 8.09/8.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 8.09/8.30 inference(rewrite,[status(thm)],[])).
% 8.09/8.30 tff(12058,plain,
% 8.09/8.30 (((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 8.09/8.31 inference(rewrite,[status(thm)],[])).
% 8.09/8.31 tff(12059,plain,
% 8.09/8.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1)))))),
% 8.09/8.31 inference(monotonicity,[status(thm)],[12058])).
% 8.09/8.31 tff(12060,plain,
% 8.09/8.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 8.09/8.31 inference(transitivity,[status(thm)],[12059, 12057])).
% 8.09/8.31 tff(12061,plain,
% 8.09/8.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 8.09/8.31 inference(quant_inst,[status(thm)],[])).
% 8.09/8.31 tff(12062,plain,
% 8.09/8.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1)))),
% 8.09/8.31 inference(modus_ponens,[status(thm)],[12061, 12060])).
% 8.09/8.31 tff(12063,plain,
% 8.09/8.31 (~b(z, s(z))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[12062, 391, 133, 592, 591, 12056])).
% 8.09/8.31 tff(12064,plain,
% 8.09/8.31 (r(z, s(z))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[678, 12063])).
% 8.09/8.31 tff(12065,plain,
% 8.09/8.31 (~r(s(s(s(s(z)))), s(z))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[5500, 12064, 12052, 12051])).
% 8.09/8.31 tff(12066,plain,
% 8.09/8.31 (b(s(s(s(s(z)))), s(z))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[749, 12065])).
% 8.09/8.31 tff(12067,plain,
% 8.09/8.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.09/8.31 inference(rewrite,[status(thm)],[])).
% 8.09/8.31 tff(12068,plain,
% 8.09/8.31 (((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.09/8.31 inference(rewrite,[status(thm)],[])).
% 8.09/8.31 tff(12069,plain,
% 8.09/8.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 8.09/8.31 inference(monotonicity,[status(thm)],[12068])).
% 8.09/8.31 tff(12070,plain,
% 8.09/8.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.09/8.31 inference(transitivity,[status(thm)],[12069, 12067])).
% 8.09/8.31 tff(12071,plain,
% 8.09/8.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.09/8.31 inference(quant_inst,[status(thm)],[])).
% 8.09/8.31 tff(12072,plain,
% 8.09/8.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 8.09/8.31 inference(modus_ponens,[status(thm)],[12071, 12070])).
% 8.09/8.31 tff(12073,plain,
% 8.09/8.31 (~b(s(elem!1), s(s(s(s(z)))))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[12072, 391, 591, 12056, 12066, 12049])).
% 8.09/8.31 tff(12074,plain,
% 8.09/8.31 (r(s(elem!1), s(s(s(s(z)))))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[2142, 42, 12073, 11963])).
% 8.09/8.31 tff(12075,plain,
% 8.09/8.31 (~r(s(z), s(s(s(s(z)))))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[10558, 12064, 182, 12051])).
% 8.09/8.31 tff(12076,plain,
% 8.09/8.31 (b(s(z), s(s(s(s(z)))))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[1230, 12075])).
% 8.09/8.31 tff(12077,plain,
% 8.09/8.31 (~(s(s(s(s(z)))) = s(elem!1))),
% 8.09/8.31 inference(modus_ponens,[status(thm)],[11963, 2125])).
% 8.09/8.31 tff(12078,plain,
% 8.09/8.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 8.09/8.31 inference(rewrite,[status(thm)],[])).
% 8.09/8.31 tff(12079,plain,
% 8.09/8.31 (((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 8.09/8.31 inference(rewrite,[status(thm)],[])).
% 8.09/8.31 tff(12080,plain,
% 8.09/8.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 8.09/8.31 inference(monotonicity,[status(thm)],[12079])).
% 8.09/8.31 tff(12081,plain,
% 8.09/8.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 8.09/8.31 inference(transitivity,[status(thm)],[12080, 12078])).
% 8.09/8.31 tff(12082,plain,
% 8.09/8.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 8.09/8.31 inference(quant_inst,[status(thm)],[])).
% 8.09/8.31 tff(12083,plain,
% 8.09/8.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 8.09/8.31 inference(modus_ponens,[status(thm)],[12082, 12081])).
% 8.09/8.31 tff(12084,plain,
% 8.09/8.31 (~b(s(s(s(s(z)))), s(elem!1))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[12083, 391, 591, 12056, 12066, 12049])).
% 8.09/8.31 tff(12085,plain,
% 8.09/8.31 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[2136, 42, 12084])).
% 8.09/8.31 tff(12086,plain,
% 8.09/8.31 (r(s(s(s(s(z)))), s(elem!1))),
% 8.09/8.31 inference(unit_resolution,[status(thm)],[12085, 12077])).
% 8.09/8.31 tff(12087,plain,
% 8.09/8.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 8.09/8.31 inference(rewrite,[status(thm)],[])).
% 8.09/8.31 tff(12088,plain,
% 8.09/8.31 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 8.09/8.31 inference(rewrite,[status(thm)],[])).
% 8.09/8.31 tff(12089,plain,
% 8.09/8.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 8.09/8.31 inference(monotonicity,[status(thm)],[12088])).
% 8.09/8.31 tff(12090,plain,
% 8.09/8.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 8.09/8.31 inference(transitivity,[status(thm)],[12089, 12087])).
% 8.09/8.31 tff(12091,plain,
% 8.09/8.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.09/8.31 inference(quant_inst,[status(thm)],[])).
% 8.09/8.31 tff(12092,plain,
% 8.09/8.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 8.09/8.31 inference(modus_ponens,[status(thm)],[12091, 12090])).
% 8.09/8.31 tff(12093,plain,
% 8.09/8.32 (~r(elem!1, s(s(s(s(z)))))),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[12092, 194, 11975, 11970, 12086])).
% 8.09/8.32 tff(12094,plain,
% 8.09/8.32 (b(elem!1, s(s(s(s(z)))))),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[781, 12093, 12003])).
% 8.09/8.32 tff(12095,plain,
% 8.09/8.32 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 8.09/8.32 inference(rewrite,[status(thm)],[])).
% 8.09/8.32 tff(12096,plain,
% 8.09/8.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 8.09/8.32 inference(monotonicity,[status(thm)],[12095])).
% 8.09/8.32 tff(12097,plain,
% 8.09/8.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 8.09/8.32 inference(transitivity,[status(thm)],[12096, 4607])).
% 8.09/8.32 tff(12098,plain,
% 8.09/8.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))),
% 8.09/8.32 inference(quant_inst,[status(thm)],[])).
% 8.09/8.32 tff(12099,plain,
% 8.09/8.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 8.09/8.32 inference(modus_ponens,[status(thm)],[12098, 12097])).
% 8.09/8.32 tff(12100,plain,
% 8.09/8.32 (~r(s(s(s(s(z)))), elem!1)),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[12099, 194, 11975, 11970, 12086])).
% 8.09/8.32 tff(12101,plain,
% 8.09/8.32 (b(s(s(s(s(z)))), elem!1)),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[762, 12100, 718])).
% 8.09/8.32 tff(12102,plain,
% 8.09/8.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 8.09/8.32 inference(rewrite,[status(thm)],[])).
% 8.09/8.32 tff(12103,plain,
% 8.09/8.32 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 8.09/8.32 inference(rewrite,[status(thm)],[])).
% 8.09/8.32 tff(12104,plain,
% 8.09/8.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 8.09/8.32 inference(monotonicity,[status(thm)],[12103])).
% 8.09/8.32 tff(12105,plain,
% 8.09/8.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 8.09/8.32 inference(transitivity,[status(thm)],[12104, 12102])).
% 8.09/8.32 tff(12106,plain,
% 8.09/8.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 8.09/8.32 inference(quant_inst,[status(thm)],[])).
% 8.09/8.32 tff(12107,plain,
% 8.09/8.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 8.09/8.32 inference(modus_ponens,[status(thm)],[12106, 12105])).
% 8.09/8.32 tff(12108,plain,
% 8.09/8.32 (~b(elem!1, s(z))),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[12107, 391, 665, 12094, 12101, 12076])).
% 8.09/8.32 tff(12109,plain,
% 8.09/8.32 (r(elem!1, s(z))),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[837, 12108, 173])).
% 8.09/8.32 tff(12110,plain,
% 8.09/8.32 (~b(s(s(z)), s(z))),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[5126, 3823, 133, 182, 722, 1234])).
% 8.09/8.32 tff(12111,plain,
% 8.09/8.32 (r(s(s(z)), s(z))),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[3778, 12110])).
% 8.09/8.32 tff(12112,plain,
% 8.09/8.32 (~r(s(s(z)), elem!1)),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[6674, 12111, 1484, 847])).
% 8.09/8.32 tff(12113,plain,
% 8.09/8.32 (b(s(s(z)), elem!1)),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[4730, 12112, 5547])).
% 8.09/8.32 tff(12114,plain,
% 8.09/8.32 ($false),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[5553, 391, 665, 3823, 2064, 1652, 12113])).
% 8.09/8.32 tff(12115,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(z)) = elem!1) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.32 tff(12116,plain,
% 8.09/8.32 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[12115, 12109, 665, 182, 5547, 12047, 12101, 133, 12094, 12064, 12076])).
% 8.09/8.32 tff(12117,plain,
% 8.09/8.32 (r(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.32 inference(unit_resolution,[status(thm)],[3652, 12116])).
% 8.09/8.32 tff(12118,plain,
% 8.09/8.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.09/8.32 inference(rewrite,[status(thm)],[])).
% 8.09/8.32 tff(12119,plain,
% 8.09/8.32 (((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.09/8.32 inference(rewrite,[status(thm)],[])).
% 8.09/8.32 tff(12120,plain,
% 8.09/8.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 8.09/8.32 inference(monotonicity,[status(thm)],[12119])).
% 8.09/8.32 tff(12121,plain,
% 8.09/8.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.09/8.33 inference(transitivity,[status(thm)],[12120, 12118])).
% 8.09/8.33 tff(12122,plain,
% 8.09/8.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))),
% 8.09/8.33 inference(quant_inst,[status(thm)],[])).
% 8.09/8.33 tff(12123,plain,
% 8.09/8.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 8.09/8.33 inference(modus_ponens,[status(thm)],[12122, 12121])).
% 8.09/8.33 tff(12124,plain,
% 8.09/8.33 (~r(s(s(z)), s(elem!1))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[12123, 194, 12117, 12051, 12074])).
% 8.09/8.33 tff(12125,plain,
% 8.09/8.33 (b(s(s(z)), s(elem!1))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[4693, 42, 12043, 12124])).
% 8.09/8.33 tff(12126,plain,
% 8.09/8.33 (~b(z, s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[5600, 391, 133, 665, 12101])).
% 8.09/8.33 tff(12127,plain,
% 8.09/8.33 (r(z, s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[800, 12126])).
% 8.09/8.33 tff(12128,plain,
% 8.09/8.33 (~r(s(s(z)), z)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[5608, 194, 12117, 12051, 12127])).
% 8.09/8.33 tff(12129,plain,
% 8.09/8.33 (b(s(s(z)), z)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[1211, 12128])).
% 8.09/8.33 tff(12130,plain,
% 8.09/8.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 8.09/8.33 inference(rewrite,[status(thm)],[])).
% 8.09/8.33 tff(12131,plain,
% 8.09/8.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 8.09/8.33 inference(quant_inst,[status(thm)],[])).
% 8.09/8.33 tff(12132,plain,
% 8.09/8.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))),
% 8.09/8.33 inference(modus_ponens,[status(thm)],[12131, 12130])).
% 8.09/8.33 tff(12133,plain,
% 8.09/8.33 ($false),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[12132, 391, 133, 665, 591, 12129, 12125])).
% 8.09/8.33 tff(12134,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~r(s(z), z)) | (s(s(z)) = elem!1) | (~b(z, s(elem!1))) | (s(elem!1) = s(z)) | (~(s(s(elem!1)) = elem!1)) | (s(z) = elem!1) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.33 tff(12135,plain,
% 8.09/8.33 (s(s(s(elem!1))) = s(s(elem!1))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[12134, 11962, 665, 591, 133, 11942, 11958, 11956, 445, 150, 11955, 11953, 11943])).
% 8.09/8.33 tff(12136,plain,
% 8.09/8.33 (s(s(s(elem!1))) = elem!1),
% 8.09/8.33 inference(modus_ponens,[status(thm)],[12135, 11392])).
% 8.09/8.33 tff(12137,plain,
% 8.09/8.33 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[11384, 12136])).
% 8.09/8.33 tff(12138,plain,
% 8.09/8.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 8.09/8.33 inference(rewrite,[status(thm)],[])).
% 8.09/8.33 tff(12139,plain,
% 8.09/8.33 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 8.09/8.33 inference(rewrite,[status(thm)],[])).
% 8.09/8.33 tff(12140,plain,
% 8.09/8.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 8.09/8.33 inference(monotonicity,[status(thm)],[12139])).
% 8.09/8.33 tff(12141,plain,
% 8.09/8.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 8.09/8.33 inference(transitivity,[status(thm)],[12140, 12138])).
% 8.09/8.33 tff(12142,plain,
% 8.09/8.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 8.09/8.33 inference(quant_inst,[status(thm)],[])).
% 8.09/8.33 tff(12143,plain,
% 8.09/8.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 8.09/8.33 inference(modus_ponens,[status(thm)],[12142, 12141])).
% 8.09/8.33 tff(12144,plain,
% 8.09/8.33 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[12143, 391, 133, 665, 644, 8042])).
% 8.09/8.33 tff(12145,plain,
% 8.09/8.33 (r(s(s(s(s(s(s(z)))))), s(z))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[11674, 42, 5065, 12144])).
% 8.09/8.33 tff(12146,plain,
% 8.09/8.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 8.09/8.33 inference(rewrite,[status(thm)],[])).
% 8.09/8.33 tff(12147,plain,
% 8.09/8.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 8.09/8.33 inference(quant_inst,[status(thm)],[])).
% 8.09/8.33 tff(12148,plain,
% 8.09/8.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 8.09/8.33 inference(modus_ponens,[status(thm)],[12147, 12146])).
% 8.09/8.33 tff(12149,plain,
% 8.09/8.33 ($false),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[12148, 194, 11981, 182, 8050, 12145])).
% 8.09/8.33 tff(12150,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.33 tff(12151,plain,
% 8.09/8.33 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[12150, 644, 133, 665, 182])).
% 8.09/8.33 tff(12152,plain,
% 8.09/8.33 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[8073, 12151, 11653])).
% 8.09/8.33 tff(12153,plain,
% 8.09/8.33 (~b(s(z), s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[4062, 1652, 133, 665, 644])).
% 8.09/8.33 tff(12154,plain,
% 8.09/8.33 (r(s(z), s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[1230, 12153])).
% 8.09/8.33 tff(12155,plain,
% 8.09/8.33 (~r(s(s(s(s(z)))), z)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[10558, 12154, 182, 11981])).
% 8.09/8.33 tff(12156,plain,
% 8.09/8.33 (b(s(s(s(s(z)))), z)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[87, 12155])).
% 8.09/8.33 tff(12157,plain,
% 8.09/8.33 ($false),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[10872, 391, 133, 665, 12156, 1652])).
% 8.09/8.33 tff(12158,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.33 tff(12159,plain,
% 8.09/8.33 (~b(s(s(s(s(z)))), elem!1)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[12158, 644, 665, 182, 133])).
% 8.09/8.33 tff(12160,plain,
% 8.09/8.33 (r(s(s(s(s(z)))), elem!1)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[762, 12159, 720])).
% 8.09/8.33 tff(12161,plain,
% 8.09/8.33 (~r(s(s(s(s(z)))), z)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[10558, 1216, 182, 11981])).
% 8.09/8.33 tff(12162,plain,
% 8.09/8.33 (b(s(s(s(s(z)))), z)),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[87, 12161])).
% 8.09/8.33 tff(12163,plain,
% 8.09/8.33 (~r(z, s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[2720, 1216, 182, 2112])).
% 8.09/8.33 tff(12164,plain,
% 8.09/8.33 (b(z, s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[800, 12163])).
% 8.09/8.33 tff(12165,plain,
% 8.09/8.33 (~b(elem!1, s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[3234, 12164, 665, 12162])).
% 8.09/8.33 tff(12166,plain,
% 8.09/8.33 (r(elem!1, s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[781, 12165, 8922])).
% 8.09/8.33 tff(12167,plain,
% 8.09/8.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 8.09/8.33 inference(rewrite,[status(thm)],[])).
% 8.09/8.33 tff(12168,plain,
% 8.09/8.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 8.09/8.33 inference(quant_inst,[status(thm)],[])).
% 8.09/8.33 tff(12169,plain,
% 8.09/8.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 8.09/8.33 inference(modus_ponens,[status(thm)],[12168, 12167])).
% 8.09/8.33 tff(12170,plain,
% 8.09/8.33 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[12169, 194, 12166, 2112, 2741])).
% 8.09/8.33 tff(12171,plain,
% 8.09/8.33 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[11685, 42, 12170])).
% 8.09/8.33 tff(12172,plain,
% 8.09/8.33 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 8.09/8.33 inference(unit_resolution,[status(thm)],[12171, 11648])).
% 8.09/8.33 tff(12173,plain,
% 8.09/8.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 8.09/8.33 inference(rewrite,[status(thm)],[])).
% 8.09/8.33 tff(12174,plain,
% 8.09/8.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 8.09/8.33 inference(quant_inst,[status(thm)],[])).
% 8.09/8.33 tff(12175,plain,
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% 8.09/8.34 inference(modus_ponens,[status(thm)],[12187, 12186])).
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% 8.09/8.34 inference(rewrite,[status(thm)],[])).
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% 8.09/8.34 inference(quant_inst,[status(thm)],[])).
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% 8.09/8.34 inference(modus_ponens,[status(thm)],[12192, 12191])).
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% 8.09/8.34 inference(unit_resolution,[status(thm)],[12193, 391, 665, 644, 12190, 12185, 12183])).
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% 8.09/8.34 inference(modus_ponens,[status(thm)],[12231, 12230])).
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% 8.09/8.34 inference(unit_resolution,[status(thm)],[11674, 42, 5065, 12236])).
% 8.09/8.34 tff(12238,plain,
% 8.09/8.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 8.09/8.35 inference(rewrite,[status(thm)],[])).
% 8.09/8.35 tff(12239,plain,
% 8.09/8.35 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 8.09/8.35 inference(rewrite,[status(thm)],[])).
% 8.09/8.35 tff(12240,plain,
% 8.09/8.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 8.09/8.35 inference(monotonicity,[status(thm)],[12239])).
% 8.09/8.35 tff(12241,plain,
% 8.09/8.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 8.09/8.35 inference(transitivity,[status(thm)],[12240, 12238])).
% 8.09/8.35 tff(12242,plain,
% 8.09/8.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 8.09/8.35 inference(quant_inst,[status(thm)],[])).
% 8.09/8.35 tff(12243,plain,
% 8.09/8.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 8.09/8.35 inference(modus_ponens,[status(thm)],[12242, 12241])).
% 8.09/8.35 tff(12244,plain,
% 8.09/8.35 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[12243, 194, 12216, 12214, 2741])).
% 8.09/8.35 tff(12245,plain,
% 8.09/8.35 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[6652, 42, 4995, 12244])).
% 8.09/8.35 tff(12246,plain,
% 8.09/8.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 8.09/8.35 inference(rewrite,[status(thm)],[])).
% 8.09/8.35 tff(12247,plain,
% 8.09/8.35 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 8.09/8.35 inference(rewrite,[status(thm)],[])).
% 8.09/8.35 tff(12248,plain,
% 8.09/8.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 8.09/8.35 inference(monotonicity,[status(thm)],[12247])).
% 8.09/8.35 tff(12249,plain,
% 8.09/8.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 8.09/8.35 inference(transitivity,[status(thm)],[12248, 12246])).
% 8.09/8.35 tff(12250,plain,
% 8.09/8.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.09/8.35 inference(quant_inst,[status(thm)],[])).
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% 8.09/8.35 inference(modus_ponens,[status(thm)],[12250, 12249])).
% 8.09/8.35 tff(12252,plain,
% 8.09/8.35 (~b(s(z), s(s(s(s(z)))))),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[12251, 391, 644, 12245, 12237, 12235])).
% 8.09/8.35 tff(12253,plain,
% 8.09/8.35 (r(s(z), s(s(s(s(z)))))),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[1230, 12252])).
% 8.09/8.35 tff(12254,plain,
% 8.09/8.35 (~r(elem!1, s(z))),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[6347, 12253, 12216, 723])).
% 8.09/8.35 tff(12255,plain,
% 8.09/8.35 (b(elem!1, s(z))),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[837, 12254, 831])).
% 8.09/8.35 tff(12256,plain,
% 8.09/8.35 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[5136, 12223, 133, 12212, 12255])).
% 8.09/8.35 tff(12257,plain,
% 8.09/8.35 (r(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[3652, 12256])).
% 8.09/8.35 tff(12258,plain,
% 8.09/8.35 ($false),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[11431, 194, 12257, 12216, 12226, 12214])).
% 8.09/8.35 tff(12259,plain,((~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~r(s(z), z)) | (elem!1 = s(z)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.09/8.35 tff(12260,plain,
% 8.09/8.35 (~r(s(s(s(s(z)))), s(z))),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[12259, 644, 266, 10682, 380, 2641, 133, 1405, 665, 182, 831, 12152, 720])).
% 8.09/8.35 tff(12261,plain,
% 8.09/8.35 (b(s(s(s(s(z)))), s(z))),
% 8.09/8.35 inference(unit_resolution,[status(thm)],[749, 12260])).
% 8.09/8.35 tff(12262,plain,
% 8.09/8.35 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 8.09/8.35 inference(rewrite,[status(thm)],[])).
% 8.09/8.35 tff(12263,plain,
% 8.09/8.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 8.09/8.35 inference(monotonicity,[status(thm)],[12262])).
% 8.09/8.35 tff(12264,plain,
% 8.09/8.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 8.09/8.35 inference(transitivity,[status(thm)],[12263, 7116])).
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% 8.09/8.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 8.09/8.36 inference(quant_inst,[status(thm)],[])).
% 8.09/8.36 tff(12266,plain,
% 8.09/8.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 8.09/8.36 inference(modus_ponens,[status(thm)],[12265, 12264])).
% 8.09/8.36 tff(12267,plain,
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% 8.09/8.36 inference(unit_resolution,[status(thm)],[12266, 391, 133, 665, 1235])).
% 8.09/8.36 tff(12268,plain,
% 8.09/8.36 (r(s(s(z)), elem!1)),
% 8.09/8.36 inference(unit_resolution,[status(thm)],[4730, 12267, 5547])).
% 8.09/8.36 tff(12269,plain,
% 8.09/8.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 8.09/8.36 inference(rewrite,[status(thm)],[])).
% 8.09/8.36 tff(12270,plain,
% 8.09/8.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 8.09/8.36 inference(quant_inst,[status(thm)],[])).
% 8.09/8.36 tff(12271,plain,
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% 8.09/8.36 inference(modus_ponens,[status(thm)],[12270, 12269])).
% 8.09/8.36 tff(12272,plain,
% 8.09/8.36 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 8.09/8.36 inference(unit_resolution,[status(thm)],[12271, 194, 11819, 12268, 2741])).
% 8.09/8.36 tff(12273,plain,
% 8.09/8.36 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 8.09/8.36 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 12272])).
% 8.09/8.36 tff(12274,plain,
% 8.09/8.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 8.09/8.36 inference(rewrite,[status(thm)],[])).
% 8.09/8.36 tff(12275,plain,
% 8.09/8.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 8.09/8.36 inference(quant_inst,[status(thm)],[])).
% 8.09/8.36 tff(12276,plain,
% 8.09/8.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 8.09/8.36 inference(modus_ponens,[status(thm)],[12275, 12274])).
% 8.09/8.36 tff(12277,plain,
% 8.09/8.36 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 8.09/8.36 inference(unit_resolution,[status(thm)],[12276, 194, 11819, 2112, 2741])).
% 8.09/8.36 tff(12278,plain,
% 8.09/8.36 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 8.09/8.36 inference(unit_resolution,[status(thm)],[11685, 42, 12277])).
% 8.09/8.36 tff(12279,plain,
% 8.09/8.36 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 8.09/8.36 inference(unit_resolution,[status(thm)],[12278, 11648])).
% 8.09/8.36 tff(12280,plain,
% 8.09/8.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.09/8.36 inference(rewrite,[status(thm)],[])).
% 8.09/8.36 tff(12281,plain,
% 8.09/8.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.09/8.36 inference(quant_inst,[status(thm)],[])).
% 8.09/8.36 tff(12282,plain,
% 8.09/8.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 8.09/8.36 inference(modus_ponens,[status(thm)],[12281, 12280])).
% 8.09/8.36 tff(12283,plain,
% 8.09/8.36 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.09/8.36 inference(unit_resolution,[status(thm)],[12282, 194, 11819, 2112, 12268])).
% 8.09/8.36 tff(12284,plain,
% 8.09/8.36 (b(s(s(s(s(z)))), s(s(z)))),
% 8.09/8.36 inference(unit_resolution,[status(thm)],[1714, 12283])).
% 8.09/8.36 tff(12285,plain,
% 8.09/8.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 8.09/8.36 inference(rewrite,[status(thm)],[])).
% 8.09/8.36 tff(12286,plain,
% 8.09/8.36 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 8.09/8.36 inference(rewrite,[status(thm)],[])).
% 8.09/8.36 tff(12287,plain,
% 8.09/8.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 8.09/8.36 inference(monotonicity,[status(thm)],[12286])).
% 8.09/8.36 tff(12288,plain,
% 8.09/8.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 8.09/8.36 inference(transitivity,[status(thm)],[12287, 12285])).
% 8.09/8.36 tff(12289,plain,
% 8.09/8.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 8.09/8.36 inference(quant_inst,[status(thm)],[])).
% 8.09/8.36 tff(12290,plain,
% 8.09/8.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1))),
% 8.09/8.36 inference(modus_ponens,[status(thm)],[12289, 12288])).
% 8.09/8.36 tff(12291,plain,
% 8.09/8.36 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.36 inference(unit_resolution,[status(thm)],[12290, 194, 11819, 2112, 12268])).
% 8.09/8.36 tff(12292,plain,
% 8.09/8.36 (b(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.36 inference(unit_resolution,[status(thm)],[3652, 12291])).
% 8.09/8.36 tff(12293,plain,
% 8.09/8.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 8.09/8.37 inference(rewrite,[status(thm)],[])).
% 8.09/8.37 tff(12294,plain,
% 8.09/8.37 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 8.09/8.37 inference(rewrite,[status(thm)],[])).
% 8.09/8.37 tff(12295,plain,
% 8.09/8.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 8.09/8.37 inference(monotonicity,[status(thm)],[12294])).
% 8.09/8.37 tff(12296,plain,
% 8.09/8.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 8.09/8.37 inference(transitivity,[status(thm)],[12295, 12293])).
% 8.09/8.37 tff(12297,plain,
% 8.09/8.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 8.09/8.37 inference(quant_inst,[status(thm)],[])).
% 8.09/8.37 tff(12298,plain,
% 8.09/8.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 8.09/8.37 inference(modus_ponens,[status(thm)],[12297, 12296])).
% 8.09/8.37 tff(12299,plain,
% 8.09/8.37 ($false),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[12298, 391, 12292, 1759, 12284, 12279, 12273])).
% 8.09/8.37 tff(12300,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (s(s(z)) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.37 tff(12301,plain,
% 8.09/8.37 (~b(s(s(z)), z)),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[12300, 12261, 12152, 12160, 5547, 133, 665, 1405, 266, 10682, 380, 2641])).
% 8.09/8.37 tff(12302,plain,
% 8.09/8.37 (r(s(s(z)), z)),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[1211, 12301])).
% 8.09/8.37 tff(12303,plain,
% 8.09/8.37 (~r(s(s(z)), s(z))),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[12188, 194, 11981, 182, 12302])).
% 8.09/8.37 tff(12304,plain,
% 8.09/8.37 (b(s(s(z)), s(z))),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[3778, 12303])).
% 8.09/8.37 tff(12305,plain,
% 8.09/8.37 (~b(elem!1, s(s(s(s(z)))))),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[6418, 90, 644, 133, 1234])).
% 8.09/8.37 tff(12306,plain,
% 8.09/8.37 (r(elem!1, s(s(s(s(z)))))),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[781, 12305, 8922])).
% 8.09/8.37 tff(12307,plain,
% 8.09/8.37 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[12169, 194, 12306, 2112, 2741])).
% 8.09/8.37 tff(12308,plain,
% 8.09/8.37 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[11685, 42, 12307])).
% 8.09/8.37 tff(12309,plain,
% 8.09/8.37 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[12308, 11648])).
% 8.09/8.37 tff(12310,plain,
% 8.09/8.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 8.09/8.37 inference(rewrite,[status(thm)],[])).
% 8.09/8.37 tff(12311,plain,
% 8.09/8.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 8.09/8.37 inference(quant_inst,[status(thm)],[])).
% 8.09/8.37 tff(12312,plain,
% 8.09/8.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 8.09/8.37 inference(modus_ponens,[status(thm)],[12311, 12310])).
% 8.09/8.37 tff(12313,plain,
% 8.09/8.37 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[12312, 391, 133, 90, 1234, 12309])).
% 8.09/8.37 tff(12314,plain,
% 8.09/8.37 (r(s(s(s(s(s(s(z)))))), s(z))),
% 8.09/8.37 inference(unit_resolution,[status(thm)],[11674, 42, 5065, 12313])).
% 8.09/8.37 tff(12315,plain,
% 8.09/8.37 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 8.09/8.37 inference(rewrite,[status(thm)],[])).
% 8.09/8.37 tff(12316,plain,
% 8.09/8.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 8.09/8.37 inference(monotonicity,[status(thm)],[12315])).
% 8.09/8.37 tff(12317,plain,
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% 8.09/8.37 inference(modus_ponens,[status(thm)],[12318, 12317])).
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% 8.09/8.37 inference(rewrite,[status(thm)],[])).
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% 8.09/8.37 inference(quant_inst,[status(thm)],[])).
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% 8.09/8.37 inference(modus_ponens,[status(thm)],[12323, 12322])).
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% 8.09/8.37 inference(unit_resolution,[status(thm)],[12324, 391, 133, 665, 90, 12309, 12321])).
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% 8.09/8.37 tff(12327,plain,
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% 8.09/8.37 tff(12328,plain,
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% 8.09/8.37 inference(unit_resolution,[status(thm)],[87, 12327])).
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% 8.09/8.37 inference(unit_resolution,[status(thm)],[9633, 194, 11981, 12328, 12302])).
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% 8.09/8.37 inference(unit_resolution,[status(thm)],[3652, 12329])).
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% 8.09/8.37 inference(unit_resolution,[status(thm)],[5108, 12330, 12304, 12261, 12208])).
% 8.09/8.37 tff(12332,plain,((~b(s(z), elem!1)) | (~r(s(z), z)) | (s(s(z)) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (elem!1 = s(z)) | (s(s(s(s(z)))) = elem!1) | (s(s(s(s(s(s(z)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.09/8.37 tff(12333,plain,
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% 8.09/8.37 inference(unit_resolution,[status(thm)],[11384, 12335])).
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% 8.09/8.38 inference(monotonicity,[status(thm)],[12351])).
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% 8.09/8.38 inference(unit_resolution,[status(thm)],[11449, 12341, 10682, 380, 11397])).
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% 8.09/8.38 inference(unit_resolution,[status(thm)],[1788, 12363])).
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% 8.09/8.38 tff(12368,plain,
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% 8.09/8.38 inference(rewrite,[status(thm)],[])).
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% 8.09/8.38 inference(monotonicity,[status(thm)],[12379])).
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% 8.09/8.38 inference(transitivity,[status(thm)],[12380, 12378])).
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% 8.09/8.38 inference(quant_inst,[status(thm)],[])).
% 8.09/8.38 tff(12383,plain,
% 8.09/8.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 8.09/8.38 inference(modus_ponens,[status(thm)],[12382, 12381])).
% 8.09/8.38 tff(12384,plain,
% 8.09/8.38 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.09/8.38 inference(unit_resolution,[status(thm)],[12383, 391, 380, 90, 12164])).
% 8.09/8.38 tff(12385,plain,
% 8.09/8.38 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.09/8.38 inference(unit_resolution,[status(thm)],[4313, 42, 12384])).
% 8.09/8.38 tff(12386,plain,
% 8.09/8.38 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.09/8.38 inference(unit_resolution,[status(thm)],[12385, 6950])).
% 8.09/8.38 tff(12387,plain,
% 8.09/8.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.09/8.38 inference(rewrite,[status(thm)],[])).
% 8.09/8.38 tff(12388,plain,
% 8.09/8.38 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.09/8.38 inference(rewrite,[status(thm)],[])).
% 8.09/8.38 tff(12389,plain,
% 8.09/8.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 8.09/8.38 inference(monotonicity,[status(thm)],[12388])).
% 8.09/8.38 tff(12390,plain,
% 8.09/8.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.09/8.38 inference(transitivity,[status(thm)],[12389, 12387])).
% 8.09/8.38 tff(12391,plain,
% 8.09/8.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 8.09/8.38 inference(quant_inst,[status(thm)],[])).
% 8.09/8.38 tff(12392,plain,
% 8.09/8.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 8.09/8.38 inference(modus_ponens,[status(thm)],[12391, 12390])).
% 8.09/8.38 tff(12393,plain,
% 8.09/8.38 ($false),
% 8.09/8.38 inference(unit_resolution,[status(thm)],[12392, 194, 232, 2112, 1216, 12386])).
% 8.09/8.38 tff(12394,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.38 tff(12395,plain,
% 8.09/8.38 (~b(s(s(s(s(z)))), z)),
% 8.09/8.38 inference(unit_resolution,[status(thm)],[12394, 1216, 3843, 380, 182, 232, 2112])).
% 8.09/8.38 tff(12396,plain,
% 8.09/8.38 (r(s(s(s(s(z)))), z)),
% 8.09/8.38 inference(unit_resolution,[status(thm)],[87, 12395])).
% 8.09/8.38 tff(12397,plain,
% 8.09/8.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.09/8.38 inference(rewrite,[status(thm)],[])).
% 8.09/8.38 tff(12398,plain,
% 8.09/8.38 (((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.09/8.38 inference(rewrite,[status(thm)],[])).
% 8.09/8.38 tff(12399,plain,
% 8.09/8.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.09/8.38 inference(monotonicity,[status(thm)],[12398])).
% 8.09/8.38 tff(12400,plain,
% 8.09/8.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.09/8.38 inference(transitivity,[status(thm)],[12399, 12397])).
% 8.09/8.38 tff(12401,plain,
% 8.09/8.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)))),
% 8.09/8.38 inference(quant_inst,[status(thm)],[])).
% 8.09/8.38 tff(12402,plain,
% 8.09/8.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.09/8.38 inference(modus_ponens,[status(thm)],[12401, 12400])).
% 8.09/8.39 tff(12403,plain,
% 8.09/8.39 ($false),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[12402, 194, 1484, 2053, 2032, 1216])).
% 8.09/8.39 tff(12404,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.39 tff(12405,plain,
% 8.09/8.39 (~r(elem!1, s(s(s(s(z)))))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[12404, 12396, 1484, 1216])).
% 8.09/8.39 tff(12406,plain,
% 8.09/8.39 (b(elem!1, s(s(s(s(z)))))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[781, 12405, 8922])).
% 8.09/8.39 tff(12407,plain,
% 8.09/8.39 (~r(elem!1, s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[11485, 1216, 1484, 2112])).
% 8.09/8.39 tff(12408,plain,
% 8.09/8.39 (b(elem!1, s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[3394, 12407, 1405])).
% 8.09/8.39 tff(12409,plain,
% 8.09/8.39 (b(s(s(elem!1)), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[11458, 12408, 266])).
% 8.09/8.39 tff(12410,plain,
% 8.09/8.39 (~b(s(s(z)), z)),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[11449, 12409, 10682, 380, 2641])).
% 8.09/8.39 tff(12411,plain,
% 8.09/8.39 (r(s(s(z)), z)),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[1211, 12410])).
% 8.09/8.39 tff(12412,plain,
% 8.09/8.39 (~b(s(s(s(s(z)))), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[9127, 3823, 2064, 3369])).
% 8.09/8.39 tff(12413,plain,
% 8.09/8.39 (r(s(s(s(s(z)))), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[1714, 12412])).
% 8.09/8.39 tff(12414,plain,
% 8.09/8.39 (~r(s(s(z)), s(z))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[2429, 12413, 1484, 723])).
% 8.09/8.39 tff(12415,plain,
% 8.09/8.39 (b(s(s(z)), s(z))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[3778, 12414])).
% 8.09/8.39 tff(12416,plain,
% 8.09/8.39 (~r(s(z), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[11508, 12413, 1216, 3557])).
% 8.09/8.39 tff(12417,plain,
% 8.09/8.39 (b(s(z), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[1788, 12416])).
% 8.09/8.39 tff(12418,plain,
% 8.09/8.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 8.09/8.39 inference(rewrite,[status(thm)],[])).
% 8.09/8.39 tff(12419,plain,
% 8.09/8.39 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 8.09/8.39 inference(rewrite,[status(thm)],[])).
% 8.09/8.39 tff(12420,plain,
% 8.09/8.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 8.09/8.39 inference(monotonicity,[status(thm)],[12419])).
% 8.09/8.39 tff(12421,plain,
% 8.09/8.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 8.09/8.39 inference(transitivity,[status(thm)],[12420, 12418])).
% 8.09/8.39 tff(12422,plain,
% 8.09/8.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 8.09/8.39 inference(quant_inst,[status(thm)],[])).
% 8.09/8.39 tff(12423,plain,
% 8.09/8.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 8.09/8.39 inference(modus_ponens,[status(thm)],[12422, 12421])).
% 8.09/8.39 tff(12424,plain,
% 8.09/8.39 ($false),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[12423, 391, 3823, 3369, 12417, 12415, 721])).
% 8.09/8.39 tff(12425,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.39 tff(12426,plain,
% 8.09/8.39 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[12425, 12408, 721, 1216, 12411, 1484, 723, 12406])).
% 8.09/8.39 tff(12427,plain,
% 8.09/8.39 (r(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[3652, 12426])).
% 8.09/8.39 tff(12428,plain,
% 8.09/8.39 (~r(s(s(z)), s(z))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[5567, 12427, 1216, 12396])).
% 8.09/8.39 tff(12429,plain,
% 8.09/8.39 (b(s(s(z)), s(z))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[3778, 12428])).
% 8.09/8.39 tff(12430,plain,
% 8.09/8.39 (~r(s(z), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[11590, 194, 12427, 12396, 1216])).
% 8.09/8.39 tff(12431,plain,
% 8.09/8.39 (b(s(z), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[1788, 12430])).
% 8.09/8.39 tff(12432,plain,
% 8.09/8.39 ($false),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[11599, 391, 12408, 12431, 12429, 721])).
% 8.09/8.39 tff(12433,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (elem!1 = s(s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.39 tff(12434,plain,
% 8.09/8.39 (~r(s(z), s(s(s(s(z)))))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[12433, 12377, 1484, 723, 8922, 10682, 380, 2641, 266, 1405, 2112, 3843, 182, 232])).
% 8.09/8.39 tff(12435,plain,
% 8.09/8.39 (b(s(z), s(s(s(s(z)))))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[1230, 12434])).
% 8.09/8.39 tff(12436,plain,
% 8.09/8.39 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[9171, 12374, 12372, 12435, 723, 12377, 1484])).
% 8.09/8.39 tff(12437,plain,
% 8.09/8.39 (b(s(s(z)), s(s(s(s(z)))))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[3652, 12436])).
% 8.09/8.39 tff(12438,plain,
% 8.09/8.39 (~b(s(s(s(s(z)))), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[9127, 12437, 12374, 12372])).
% 8.09/8.39 tff(12439,plain,
% 8.09/8.39 (r(s(s(s(s(z)))), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[1714, 12438])).
% 8.09/8.39 tff(12440,plain,
% 8.09/8.39 (~r(s(s(z)), s(z))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[2429, 12439, 1484, 723])).
% 8.09/8.39 tff(12441,plain,
% 8.09/8.39 (b(s(s(z)), s(z))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[3778, 12440])).
% 8.09/8.39 tff(12442,plain,
% 8.09/8.39 (~b(s(z), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[9159, 12441, 12435, 12372, 12377])).
% 8.09/8.39 tff(12443,plain,
% 8.09/8.39 (r(s(z), s(s(z)))),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[1788, 12442])).
% 8.09/8.39 tff(12444,plain,
% 8.09/8.39 ($false),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[6747, 391, 133, 665, 90, 2064])).
% 8.09/8.39 tff(12445,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.39 tff(12446,plain,
% 8.09/8.39 (~b(s(s(s(s(z)))), z)),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[12445, 12374, 665, 133])).
% 8.09/8.39 tff(12447,plain,
% 8.09/8.39 (r(s(s(s(s(z)))), z)),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[87, 12446])).
% 8.09/8.39 tff(12448,plain,
% 8.09/8.39 (~b(s(s(z)), z)),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[9349, 12447, 266, 664, 723, 2112, 12376, 12435])).
% 8.09/8.39 tff(12449,plain,
% 8.09/8.39 (r(s(s(z)), z)),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[1211, 12448])).
% 8.09/8.39 tff(12450,plain,
% 8.09/8.39 ($false),
% 8.09/8.39 inference(unit_resolution,[status(thm)],[9185, 194, 12449, 723, 12443, 12439])).
% 8.09/8.39 tff(12451,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (elem!1 = s(s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.09/8.40 tff(12452,plain,
% 8.09/8.40 (~r(s(s(s(s(z)))), s(z))),
% 8.09/8.40 inference(unit_resolution,[status(thm)],[12451, 12369, 1405, 1484, 266, 664, 665, 133, 12003, 10682, 380, 11397, 3843, 182, 12355, 12370])).
% 8.09/8.40 tff(12453,plain,
% 8.09/8.40 (b(s(s(s(s(z)))), s(z))),
% 8.09/8.40 inference(unit_resolution,[status(thm)],[749, 12452])).
% 8.09/8.40 tff(12454,plain,
% 8.09/8.40 (~r(s(z), s(s(s(s(z)))))),
% 8.09/8.40 inference(unit_resolution,[status(thm)],[12394, 90, 3843, 380, 182, 12355, 2112])).
% 8.09/8.40 tff(12455,plain,
% 8.09/8.40 (b(s(z), s(s(s(s(z)))))),
% 8.09/8.40 inference(unit_resolution,[status(thm)],[1230, 12454])).
% 8.09/8.40 tff(12456,plain,
% 8.09/8.40 (~b(s(s(z)), s(z))),
% 8.09/8.40 inference(unit_resolution,[status(thm)],[5108, 12455, 1759, 3823])).
% 8.09/8.40 tff(12457,plain,
% 8.09/8.40 (r(s(s(z)), s(z))),
% 8.09/8.40 inference(unit_resolution,[status(thm)],[3778, 12456])).
% 8.09/8.40 tff(12458,plain,
% 8.09/8.40 (~b(z, s(s(s(s(z)))))),
% 8.09/8.40 inference(unit_resolution,[status(thm)],[6922, 12455, 133, 182, 1484, 3823, 90])).
% 8.09/8.40 tff(12459,plain,
% 8.09/8.40 (r(z, s(s(s(s(z)))))),
% 8.09/8.40 inference(unit_resolution,[status(thm)],[800, 12458])).
% 8.09/8.40 tff(12460,plain,
% 8.09/8.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.09/8.40 inference(rewrite,[status(thm)],[])).
% 8.09/8.40 tff(12461,plain,
% 8.09/8.40 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.09/8.40 inference(rewrite,[status(thm)],[])).
% 8.09/8.40 tff(12462,plain,
% 8.09/8.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 8.09/8.40 inference(monotonicity,[status(thm)],[12461])).
% 8.09/8.40 tff(12463,plain,
% 8.09/8.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.09/8.40 inference(transitivity,[status(thm)],[12462, 12460])).
% 8.09/8.40 tff(12464,plain,
% 8.09/8.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 8.09/8.40 inference(quant_inst,[status(thm)],[])).
% 8.09/8.40 tff(12465,plain,
% 8.09/8.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 8.09/8.40 inference(modus_ponens,[status(thm)],[12464, 12463])).
% 8.09/8.40 tff(12466,plain,
% 8.19/8.40 (~b(s(z), s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[12465, 391, 133, 3823, 90, 12455])).
% 8.19/8.40 tff(12467,plain,
% 8.19/8.40 (r(s(z), s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[1788, 12466])).
% 8.19/8.40 tff(12468,plain,
% 8.19/8.40 (~r(s(s(s(elem!1))), s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[11551, 12467, 12355, 12457])).
% 8.19/8.40 tff(12469,plain,
% 8.19/8.40 (r(s(s(s(elem!1))), s(s(z)))),
% 8.19/8.40 inference(modus_ponens,[status(thm)],[1748, 12358])).
% 8.19/8.40 tff(12470,plain,
% 8.19/8.40 ($false),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[10020, 12469])).
% 8.19/8.40 tff(12471,plain,((~r(elem!1, s(s(z)))) | r(s(s(s(elem!1))), s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.40 tff(12472,plain,
% 8.19/8.40 (~r(elem!1, s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[12471, 12468, 266, 445])).
% 8.19/8.40 tff(12473,plain,
% 8.19/8.40 (b(elem!1, s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[3394, 12472, 1405])).
% 8.19/8.40 tff(12474,plain,
% 8.19/8.40 (b(s(s(elem!1)), s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[11458, 12473, 266])).
% 8.19/8.40 tff(12475,plain,
% 8.19/8.40 (~b(s(s(z)), z)),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[11449, 12474, 10682, 380, 2641])).
% 8.19/8.40 tff(12476,plain,
% 8.19/8.40 (r(s(s(z)), z)),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[1211, 12475])).
% 8.19/8.40 tff(12477,plain,
% 8.19/8.40 ($false),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[10250, 194, 182, 12476, 12459, 12457])).
% 8.19/8.40 tff(12478,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (elem!1 = s(s(z))) | (~(s(s(elem!1)) = elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.40 tff(12479,plain,
% 8.19/8.40 (~b(s(s(s(s(z)))), z)),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[12478, 3823, 10682, 380, 2641, 266, 1405, 445, 133, 182, 1759, 1484, 3843, 2112])).
% 8.19/8.40 tff(12480,plain,
% 8.19/8.40 (r(s(s(s(s(z)))), z)),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[87, 12479])).
% 8.19/8.40 tff(12481,plain,
% 8.19/8.40 (~r(elem!1, s(z))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[5396, 1216, 1484, 2112])).
% 8.19/8.40 tff(12482,plain,
% 8.19/8.40 (b(elem!1, s(z))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[837, 12481, 831])).
% 8.19/8.40 tff(12483,plain,
% 8.19/8.40 (~r(elem!1, s(s(s(s(z)))))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[12404, 1216, 1484, 2053])).
% 8.19/8.40 tff(12484,plain,
% 8.19/8.40 (b(elem!1, s(s(s(s(z)))))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[781, 12483, 8922])).
% 8.19/8.40 tff(12485,plain,
% 8.19/8.40 ($false),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[11518, 12484, 12482, 1759, 2112, 3823, 10682, 380, 2641, 266, 1405, 1216, 1484])).
% 8.19/8.40 tff(12486,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (elem!1 = s(s(z))) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(s(z))))) | (elem!1 = s(z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.40 tff(12487,plain,
% 8.19/8.40 (~r(s(z), s(s(s(s(z)))))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[12486, 3823, 2112, 1759, 10682, 380, 2641, 266, 1405, 1484, 12003, 831, 12480])).
% 8.19/8.40 tff(12488,plain,
% 8.19/8.40 (b(s(z), s(s(s(s(z)))))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[1230, 12487])).
% 8.19/8.40 tff(12489,plain,
% 8.19/8.40 (~b(s(s(z)), s(z))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[5108, 12488, 1759, 3823])).
% 8.19/8.40 tff(12490,plain,
% 8.19/8.40 (r(s(s(z)), s(z))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[3778, 12489])).
% 8.19/8.40 tff(12491,plain,
% 8.19/8.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.40 inference(rewrite,[status(thm)],[])).
% 8.19/8.40 tff(12492,plain,
% 8.19/8.40 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.40 inference(rewrite,[status(thm)],[])).
% 8.19/8.40 tff(12493,plain,
% 8.19/8.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 8.19/8.40 inference(monotonicity,[status(thm)],[12492])).
% 8.19/8.40 tff(12494,plain,
% 8.19/8.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.40 inference(transitivity,[status(thm)],[12493, 12491])).
% 8.19/8.40 tff(12495,plain,
% 8.19/8.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 8.19/8.40 inference(quant_inst,[status(thm)],[])).
% 8.19/8.40 tff(12496,plain,
% 8.19/8.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 8.19/8.40 inference(modus_ponens,[status(thm)],[12495, 12494])).
% 8.19/8.40 tff(12497,plain,
% 8.19/8.40 (~b(s(z), s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[12496, 391, 3823, 12488, 1759])).
% 8.19/8.40 tff(12498,plain,
% 8.19/8.40 (r(s(z), s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[1788, 12497])).
% 8.19/8.40 tff(12499,plain,
% 8.19/8.40 (~r(s(s(s(elem!1))), s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[11551, 12498, 12355, 12490])).
% 8.19/8.40 tff(12500,plain,
% 8.19/8.40 (~r(elem!1, s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[12471, 12499, 266, 445])).
% 8.19/8.40 tff(12501,plain,
% 8.19/8.40 (b(elem!1, s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[3394, 12500, 1405])).
% 8.19/8.40 tff(12502,plain,
% 8.19/8.40 (b(s(s(elem!1)), s(s(z)))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[11458, 12501, 266])).
% 8.19/8.40 tff(12503,plain,
% 8.19/8.40 (~b(s(s(z)), z)),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[11449, 12502, 10682, 380, 2641])).
% 8.19/8.40 tff(12504,plain,
% 8.19/8.40 (r(s(s(z)), z)),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[1211, 12503])).
% 8.19/8.40 tff(12505,plain,
% 8.19/8.40 (~r(z, s(s(s(s(z)))))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[10261, 12504, 12480, 182])).
% 8.19/8.40 tff(12506,plain,
% 8.19/8.40 (b(z, s(s(s(s(z)))))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[800, 12505])).
% 8.19/8.40 tff(12507,plain,
% 8.19/8.40 ($false),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[10476, 391, 12488, 1759, 12506, 664])).
% 8.19/8.40 tff(12508,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (elem!1 = s(s(z))) | (~(s(s(elem!1)) = elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (elem!1 = s(z)) | (~b(z, elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.40 tff(12509,plain,
% 8.19/8.40 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.19/8.40 inference(unit_resolution,[status(thm)],[12508, 12453, 664, 182, 10682, 380, 11397, 266, 1405, 445, 12369, 1484, 831, 133, 3843])).
% 8.19/8.40 tff(12510,plain,
% 8.19/8.40 (r(s(s(z)), s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[3652, 12509])).
% 8.19/8.41 tff(12511,plain,
% 8.19/8.41 (~r(s(z), s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[12394, 90, 3843, 380, 182, 232, 2112])).
% 8.19/8.41 tff(12512,plain,
% 8.19/8.41 (b(s(z), s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[1230, 12511])).
% 8.19/8.41 tff(12513,plain,
% 8.19/8.41 (~b(z, s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[6914, 12512, 664, 90, 133])).
% 8.19/8.41 tff(12514,plain,
% 8.19/8.41 (~b(elem!1, s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[12445, 90, 665, 133])).
% 8.19/8.41 tff(12515,plain,
% 8.19/8.41 (r(elem!1, s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[781, 12514, 8922])).
% 8.19/8.41 tff(12516,plain,
% 8.19/8.41 (~r(z, s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[11460, 12515, 10682, 380, 2641, 1405, 266, 2112, 1749])).
% 8.19/8.41 tff(12517,plain,
% 8.19/8.41 ($false),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[800, 12516, 12513])).
% 8.19/8.41 tff(12518,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, z)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.41 tff(12519,plain,
% 8.19/8.41 (~b(s(s(s(s(z)))), z)),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[12518, 12369, 380, 11397, 1405, 266, 10682, 12510, 664, 133, 12003, 665, 3843, 182, 12355])).
% 8.19/8.41 tff(12520,plain,
% 8.19/8.41 (r(s(s(s(s(z)))), z)),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[87, 12519])).
% 8.19/8.41 tff(12521,plain,
% 8.19/8.41 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[9262, 12369, 266])).
% 8.19/8.41 tff(12522,plain,
% 8.19/8.41 (~b(z, s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[10478, 1234, 1759, 664])).
% 8.19/8.41 tff(12523,plain,
% 8.19/8.41 (r(z, s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[800, 12522])).
% 8.19/8.41 tff(12524,plain,
% 8.19/8.41 (~r(s(s(z)), z)),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[10261, 12523, 2053, 182])).
% 8.19/8.41 tff(12525,plain,
% 8.19/8.41 (b(s(s(z)), z)),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[1211, 12524])).
% 8.19/8.41 tff(12526,plain,
% 8.19/8.41 (~b(s(s(elem!1)), s(s(z)))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[11449, 12525, 10682, 380, 11397])).
% 8.19/8.41 tff(12527,plain,
% 8.19/8.41 (~b(elem!1, s(s(z)))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[11458, 12526, 266])).
% 8.19/8.41 tff(12528,plain,
% 8.19/8.41 (r(elem!1, s(s(z)))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[3394, 12527, 1405])).
% 8.19/8.41 tff(12529,plain,
% 8.19/8.41 (r(s(s(s(elem!1))), s(s(z)))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[12471, 1748, 266, 445])).
% 8.19/8.41 tff(12530,plain,
% 8.19/8.41 (~r(s(z), s(s(z)))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[11551, 12529, 12355, 2405])).
% 8.19/8.41 tff(12531,plain,
% 8.19/8.41 (b(s(z), s(s(z)))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[1788, 12530])).
% 8.19/8.41 tff(12532,plain,
% 8.19/8.41 (r(s(s(elem!1)), s(s(z)))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[11777, 1748, 266])).
% 8.19/8.41 tff(12533,plain,
% 8.19/8.41 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[6265, 12532, 1749, 2053])).
% 8.19/8.41 tff(12534,plain,
% 8.19/8.41 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 8.19/8.41 inference(monotonicity,[status(thm)],[9211])).
% 8.19/8.41 tff(12535,plain,
% 8.19/8.41 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 8.19/8.41 inference(symmetry,[status(thm)],[12534])).
% 8.19/8.41 tff(12536,plain,
% 8.19/8.41 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 8.19/8.41 inference(modus_ponens,[status(thm)],[2032, 12535])).
% 8.19/8.41 tff(12537,plain,
% 8.19/8.41 ($false),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[4098, 12536])).
% 8.19/8.41 tff(12538,plain,(r(s(s(elem!1)), s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.41 tff(12539,plain,
% 8.19/8.41 (~r(elem!1, s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[12538, 12533, 266])).
% 8.19/8.41 tff(12540,plain,
% 8.19/8.41 (b(elem!1, s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[781, 12539, 12003])).
% 8.19/8.41 tff(12541,plain,
% 8.19/8.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.41 inference(rewrite,[status(thm)],[])).
% 8.19/8.41 tff(12542,plain,
% 8.19/8.41 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.41 inference(rewrite,[status(thm)],[])).
% 8.19/8.41 tff(12543,plain,
% 8.19/8.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 8.19/8.41 inference(monotonicity,[status(thm)],[12542])).
% 8.19/8.41 tff(12544,plain,
% 8.19/8.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.41 inference(transitivity,[status(thm)],[12543, 12541])).
% 8.19/8.41 tff(12545,plain,
% 8.19/8.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 8.19/8.41 inference(quant_inst,[status(thm)],[])).
% 8.19/8.41 tff(12546,plain,
% 8.19/8.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 8.19/8.41 inference(modus_ponens,[status(thm)],[12545, 12544])).
% 8.19/8.41 tff(12547,plain,
% 8.19/8.41 (~b(elem!1, s(z))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[12546, 391, 12540, 1234, 1759, 12531])).
% 8.19/8.41 tff(12548,plain,
% 8.19/8.41 (r(elem!1, s(z))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[837, 12547, 831])).
% 8.19/8.41 tff(12549,plain,
% 8.19/8.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 8.19/8.41 inference(rewrite,[status(thm)],[])).
% 8.19/8.41 tff(12550,plain,
% 8.19/8.41 (((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 8.19/8.41 inference(rewrite,[status(thm)],[])).
% 8.19/8.41 tff(12551,plain,
% 8.19/8.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))))),
% 8.19/8.41 inference(monotonicity,[status(thm)],[12550])).
% 8.19/8.41 tff(12552,plain,
% 8.19/8.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 8.19/8.41 inference(transitivity,[status(thm)],[12551, 12549])).
% 8.19/8.41 tff(12553,plain,
% 8.19/8.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 8.19/8.41 inference(quant_inst,[status(thm)],[])).
% 8.19/8.41 tff(12554,plain,
% 8.19/8.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))),
% 8.19/8.41 inference(modus_ponens,[status(thm)],[12553, 12552])).
% 8.19/8.41 tff(12555,plain,
% 8.19/8.41 ($false),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[12554, 194, 1484, 12548, 1748, 2405])).
% 8.19/8.41 tff(12556,plain,((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (elem!1 = s(z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.41 tff(12557,plain,
% 8.19/8.41 (~r(s(s(z)), s(z))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[12556, 12528, 1484, 831, 1234, 1759, 266, 1749, 2053, 445])).
% 8.19/8.41 tff(12558,plain,
% 8.19/8.41 (b(s(s(z)), s(z))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[3778, 12557])).
% 8.19/8.41 tff(12559,plain,
% 8.19/8.41 (~r(s(s(elem!1)), s(z))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[11881, 12558, 133, 665, 266, 12521, 5547, 1759, 2053, 1234])).
% 8.19/8.41 tff(12560,plain,
% 8.19/8.41 (b(s(s(elem!1)), s(z))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[362, 12559])).
% 8.19/8.41 tff(12561,plain,
% 8.19/8.41 (b(elem!1, s(z))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[8345, 12560, 266])).
% 8.19/8.41 tff(12562,plain,
% 8.19/8.41 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[9402, 12560, 266, 11403, 12521, 11397, 12525])).
% 8.19/8.41 tff(12563,plain,
% 8.19/8.41 (b(s(s(s(s(z)))), s(s(z)))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[1714, 12562])).
% 8.19/8.41 tff(12564,plain,
% 8.19/8.41 (~r(elem!1, s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[11460, 12523, 10682, 380, 11397, 1405, 266, 12369, 1749])).
% 8.19/8.41 tff(12565,plain,
% 8.19/8.41 (b(elem!1, s(s(s(s(z)))))),
% 8.19/8.41 inference(unit_resolution,[status(thm)],[781, 12564, 12003])).
% 8.19/8.41 tff(12566,plain,
% 8.19/8.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.41 inference(rewrite,[status(thm)],[])).
% 8.19/8.41 tff(12567,plain,
% 8.19/8.41 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.41 inference(rewrite,[status(thm)],[])).
% 8.19/8.41 tff(12568,plain,
% 8.19/8.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 8.19/8.41 inference(monotonicity,[status(thm)],[12567])).
% 8.19/8.41 tff(12569,plain,
% 8.19/8.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.42 inference(transitivity,[status(thm)],[12568, 12566])).
% 8.19/8.42 tff(12570,plain,
% 8.19/8.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 8.19/8.42 inference(quant_inst,[status(thm)],[])).
% 8.19/8.42 tff(12571,plain,
% 8.19/8.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 8.19/8.42 inference(modus_ponens,[status(thm)],[12570, 12569])).
% 8.19/8.42 tff(12572,plain,
% 8.19/8.42 ($false),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[12571, 391, 12525, 12565, 1234, 12563, 12561])).
% 8.19/8.42 tff(12573,plain,((~b(s(z), s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | (elem!1 = s(z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.42 tff(12574,plain,
% 8.19/8.42 (~b(s(z), s(s(s(s(z)))))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[12573, 12453, 133, 665, 5547, 266, 12520, 1484, 831, 12510, 445, 1405, 10682, 380, 182, 664])).
% 8.19/8.42 tff(12575,plain,
% 8.19/8.42 (r(s(z), s(s(s(s(z)))))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[1230, 12574])).
% 8.19/8.42 tff(12576,plain,
% 8.19/8.42 (~r(elem!1, s(z))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[5396, 12575, 1484, 12369])).
% 8.19/8.42 tff(12577,plain,
% 8.19/8.42 (b(elem!1, s(z))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[837, 12576, 831])).
% 8.19/8.42 tff(12578,plain,
% 8.19/8.42 (~r(s(s(z)), s(z))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[5567, 12575, 12510, 12520])).
% 8.19/8.42 tff(12579,plain,
% 8.19/8.42 (b(s(s(z)), s(z))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[3778, 12578])).
% 8.19/8.42 tff(12580,plain,
% 8.19/8.42 (~r(s(z), s(s(z)))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[11590, 194, 12510, 12520, 12575])).
% 8.19/8.42 tff(12581,plain,
% 8.19/8.42 (b(s(z), s(s(z)))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[1788, 12580])).
% 8.19/8.42 tff(12582,plain,
% 8.19/8.42 (~r(elem!1, s(s(z)))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[11485, 12575, 1484, 12369])).
% 8.19/8.42 tff(12583,plain,
% 8.19/8.42 (b(elem!1, s(s(z)))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[3394, 12582, 1405])).
% 8.19/8.42 tff(12584,plain,
% 8.19/8.42 ($false),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[11599, 391, 12583, 12581, 12579, 12577])).
% 8.19/8.42 tff(12585,plain,((~b(z, s(z))) | (elem!1 = s(s(z))) | (elem!1 = s(z)) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~(s(s(elem!1)) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.42 tff(12586,plain,
% 8.19/8.42 (~b(z, s(z))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[12585, 1405, 831, 1484, 133, 665, 5547, 266, 445, 10682, 380, 182, 3843])).
% 8.19/8.42 tff(12587,plain,
% 8.19/8.42 (r(z, s(z))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[678, 12586])).
% 8.19/8.42 tff(12588,plain,
% 8.19/8.42 (~r(s(s(s(s(z)))), z)),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[10558, 1216, 182, 722])).
% 8.19/8.42 tff(12589,plain,
% 8.19/8.42 (b(s(s(s(s(z)))), z)),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[87, 12588])).
% 8.19/8.42 tff(12590,plain,
% 8.19/8.42 (~r(s(s(s(s(z)))), elem!1)),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[12394, 12589, 3843, 380, 182, 232, 1216])).
% 8.19/8.42 tff(12591,plain,
% 8.19/8.42 (b(s(s(s(s(z)))), elem!1)),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[762, 12590, 720])).
% 8.19/8.42 tff(12592,plain,
% 8.19/8.42 ($false),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[4086, 391, 133, 665, 12589, 12591])).
% 8.19/8.42 tff(12593,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.42 tff(12594,plain,
% 8.19/8.42 (~r(s(z), s(s(s(s(z)))))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[12593, 718, 665, 133, 3843, 380, 182, 12355, 12587])).
% 8.19/8.42 tff(12595,plain,
% 8.19/8.42 (b(s(z), s(s(s(s(z)))))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[1230, 12594])).
% 8.19/8.42 tff(12596,plain,
% 8.19/8.42 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[8068, 10874, 133, 665, 1652])).
% 8.19/8.42 tff(12597,plain,
% 8.19/8.42 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[8073, 12596, 11653])).
% 8.19/8.42 tff(12598,plain,
% 8.19/8.42 (~b(s(s(elem!1)), s(s(z)))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[11449, 12341, 10682, 380, 2641])).
% 8.19/8.42 tff(12599,plain,
% 8.19/8.42 (~b(elem!1, s(s(z)))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[11458, 12598, 266])).
% 8.19/8.42 tff(12600,plain,
% 8.19/8.42 (r(elem!1, s(s(z)))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[3394, 12599, 1405])).
% 8.19/8.42 tff(12601,plain,
% 8.19/8.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 8.19/8.42 inference(rewrite,[status(thm)],[])).
% 8.19/8.42 tff(12602,plain,
% 8.19/8.42 (((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 8.19/8.42 inference(rewrite,[status(thm)],[])).
% 8.19/8.42 tff(12603,plain,
% 8.19/8.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 8.19/8.42 inference(monotonicity,[status(thm)],[12602])).
% 8.19/8.42 tff(12604,plain,
% 8.19/8.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 8.19/8.42 inference(transitivity,[status(thm)],[12603, 12601])).
% 8.19/8.42 tff(12605,plain,
% 8.19/8.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 8.19/8.42 inference(quant_inst,[status(thm)],[])).
% 8.19/8.42 tff(12606,plain,
% 8.19/8.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 8.19/8.42 inference(modus_ponens,[status(thm)],[12605, 12604])).
% 8.19/8.42 tff(12607,plain,
% 8.19/8.42 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[12606, 194, 1484, 12600, 12597])).
% 8.19/8.42 tff(12608,plain,
% 8.19/8.42 (b(s(s(s(s(s(s(z)))))), s(z))),
% 8.19/8.42 inference(unit_resolution,[status(thm)],[11674, 42, 5065, 12607])).
% 8.19/8.42 tff(12609,plain,
% 8.19/8.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 8.19/8.43 inference(rewrite,[status(thm)],[])).
% 8.19/8.43 tff(12610,plain,
% 8.19/8.43 (((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 8.19/8.43 inference(rewrite,[status(thm)],[])).
% 8.19/8.43 tff(12611,plain,
% 8.19/8.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 8.19/8.43 inference(monotonicity,[status(thm)],[12610])).
% 8.19/8.43 tff(12612,plain,
% 8.19/8.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 8.19/8.43 inference(transitivity,[status(thm)],[12611, 12609])).
% 8.19/8.43 tff(12613,plain,
% 8.19/8.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 8.19/8.43 inference(quant_inst,[status(thm)],[])).
% 8.19/8.43 tff(12614,plain,
% 8.19/8.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1))),
% 8.19/8.43 inference(modus_ponens,[status(thm)],[12613, 12612])).
% 8.19/8.43 tff(12615,plain,
% 8.19/8.43 (~r(s(s(z)), s(z))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[12614, 194, 1484, 12600, 12345])).
% 8.19/8.43 tff(12616,plain,
% 8.19/8.43 (b(s(s(z)), s(z))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[3778, 12615])).
% 8.19/8.43 tff(12617,plain,
% 8.19/8.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 8.19/8.43 inference(rewrite,[status(thm)],[])).
% 8.19/8.43 tff(12618,plain,
% 8.19/8.43 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 8.19/8.43 inference(rewrite,[status(thm)],[])).
% 8.19/8.43 tff(12619,plain,
% 8.19/8.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 8.19/8.43 inference(monotonicity,[status(thm)],[12618])).
% 8.19/8.43 tff(12620,plain,
% 8.19/8.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 8.19/8.43 inference(transitivity,[status(thm)],[12619, 12617])).
% 8.19/8.43 tff(12621,plain,
% 8.19/8.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 8.19/8.43 inference(quant_inst,[status(thm)],[])).
% 8.19/8.43 tff(12622,plain,
% 8.19/8.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 8.19/8.43 inference(modus_ponens,[status(thm)],[12621, 12620])).
% 8.19/8.43 tff(12623,plain,
% 8.19/8.43 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[12622, 391, 1652, 1234, 12616, 12608])).
% 8.19/8.43 tff(12624,plain,
% 8.19/8.43 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[12271, 194, 12600, 12345, 12597])).
% 8.19/8.43 tff(12625,plain,
% 8.19/8.43 ($false),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 12624, 12623])).
% 8.19/8.43 tff(12626,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (s(s(z)) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (s(s(s(s(s(s(z)))))) = elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.43 tff(12627,plain,
% 8.19/8.43 (~b(s(s(s(s(z)))), elem!1)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[12626, 12595, 1484, 5547, 133, 665, 1405, 266, 10682, 380, 11397, 12336, 182])).
% 8.19/8.43 tff(12628,plain,
% 8.19/8.43 (r(s(s(s(s(z)))), elem!1)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[762, 12627, 718])).
% 8.19/8.43 tff(12629,plain,
% 8.19/8.43 (r(elem!1, s(s(s(s(z)))))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[781, 12514, 12003])).
% 8.19/8.43 tff(12630,plain,
% 8.19/8.43 (~r(s(s(s(s(z)))), s(z))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[9103, 12629, 12628, 1484])).
% 8.19/8.43 tff(12631,plain,
% 8.19/8.43 (b(s(s(s(s(z)))), s(z))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[749, 12630])).
% 8.19/8.43 tff(12632,plain,
% 8.19/8.43 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[12478, 12631, 10682, 380, 11397, 266, 1405, 445, 133, 182, 12628, 1484, 3843, 90])).
% 8.19/8.43 tff(12633,plain,
% 8.19/8.43 (r(s(s(z)), s(s(s(s(z)))))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[3652, 12632])).
% 8.19/8.43 tff(12634,plain,
% 8.19/8.43 (~r(elem!1, s(s(z)))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[11431, 194, 12633, 12629, 12628])).
% 8.19/8.43 tff(12635,plain,
% 8.19/8.43 (b(elem!1, s(s(z)))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[3394, 12634, 1405])).
% 8.19/8.43 tff(12636,plain,
% 8.19/8.43 (b(s(s(elem!1)), s(s(z)))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[11458, 12635, 266])).
% 8.19/8.43 tff(12637,plain,
% 8.19/8.43 (~b(s(s(z)), z)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[11449, 12636, 10682, 380, 11397])).
% 8.19/8.43 tff(12638,plain,
% 8.19/8.43 (r(s(s(z)), z)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[1211, 12637])).
% 8.19/8.43 tff(12639,plain,
% 8.19/8.43 (~r(s(s(z)), s(z))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[4462, 12638, 1484, 12587])).
% 8.19/8.43 tff(12640,plain,
% 8.19/8.43 (b(s(s(z)), s(z))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[3778, 12639])).
% 8.19/8.43 tff(12641,plain,
% 8.19/8.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 8.19/8.43 inference(rewrite,[status(thm)],[])).
% 8.19/8.43 tff(12642,plain,
% 8.19/8.43 (((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 8.19/8.43 inference(rewrite,[status(thm)],[])).
% 8.19/8.43 tff(12643,plain,
% 8.19/8.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))))),
% 8.19/8.43 inference(monotonicity,[status(thm)],[12642])).
% 8.19/8.43 tff(12644,plain,
% 8.19/8.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 8.19/8.43 inference(transitivity,[status(thm)],[12643, 12641])).
% 8.19/8.43 tff(12645,plain,
% 8.19/8.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 8.19/8.43 inference(quant_inst,[status(thm)],[])).
% 8.19/8.43 tff(12646,plain,
% 8.19/8.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))),
% 8.19/8.43 inference(modus_ponens,[status(thm)],[12645, 12644])).
% 8.19/8.43 tff(12647,plain,
% 8.19/8.43 (~r(s(z), s(s(z)))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[12646, 194, 12587, 182, 12638])).
% 8.19/8.43 tff(12648,plain,
% 8.19/8.43 (b(s(z), s(s(z)))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[1788, 12647])).
% 8.19/8.43 tff(12649,plain,
% 8.19/8.43 (~b(elem!1, s(z))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[9159, 12648, 12595, 12635, 12640])).
% 8.19/8.43 tff(12650,plain,
% 8.19/8.43 (r(elem!1, s(z))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[837, 12649, 831])).
% 8.19/8.43 tff(12651,plain,
% 8.19/8.43 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[11865, 12650, 1484, 12628, 12631])).
% 8.19/8.43 tff(12652,plain,
% 8.19/8.43 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[8073, 12651, 12336])).
% 8.19/8.43 tff(12653,plain,
% 8.19/8.43 (~r(s(s(z)), elem!1)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[4725, 194, 12633, 12629, 12628])).
% 8.19/8.43 tff(12654,plain,
% 8.19/8.43 (b(s(s(z)), elem!1)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[4730, 12653, 5547])).
% 8.19/8.43 tff(12655,plain,
% 8.19/8.43 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[11891, 391, 133, 665, 12654, 12652])).
% 8.19/8.43 tff(12656,plain,
% 8.19/8.43 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 12655])).
% 8.19/8.43 tff(12657,plain,
% 8.19/8.43 (~b(s(s(s(s(s(s(z)))))), z)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[8048, 391, 133, 665, 12652])).
% 8.19/8.43 tff(12658,plain,
% 8.19/8.43 (r(s(s(s(s(s(s(z)))))), z)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[6641, 42, 6638, 12657])).
% 8.19/8.43 tff(12659,plain,
% 8.19/8.43 ($false),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[12181, 194, 12587, 12638, 12658, 12656])).
% 8.19/8.43 tff(12660,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), elem!1)) | (elem!1 = s(z)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(z)) = elem!1) | (elem!1 = s(s(z))) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.43 tff(12661,plain,
% 8.19/8.43 (~b(s(s(s(s(z)))), z)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[12660, 12334, 665, 133, 173, 11962, 10682, 11960, 12135, 11942, 11941, 445, 3363])).
% 8.19/8.43 tff(12662,plain,
% 8.19/8.43 (r(s(s(s(s(z)))), z)),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[87, 12661])).
% 8.19/8.43 tff(12663,plain,
% 8.19/8.43 (~b(z, s(z))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[12585, 11941, 173, 12334, 133, 665, 11942, 12135, 445, 10682, 11960, 11962, 3363])).
% 8.19/8.43 tff(12664,plain,
% 8.19/8.43 (r(z, s(z))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[678, 12663])).
% 8.19/8.43 tff(12665,plain,
% 8.19/8.43 (r(s(z), s(s(elem!1)))),
% 8.19/8.43 inference(unit_resolution,[status(thm)],[4847, 12334, 445])).
% 8.19/8.44 tff(12666,plain,
% 8.19/8.44 (~r(s(s(s(s(z)))), s(z))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[5500, 12662, 12665, 12664])).
% 8.19/8.44 tff(12667,plain,
% 8.19/8.44 (b(s(s(s(s(z)))), s(z))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[749, 12666])).
% 8.19/8.44 tff(12668,plain,
% 8.19/8.44 (s(elem!1) = elem!1),
% 8.19/8.44 inference(transitivity,[status(thm)],[479, 12135, 445])).
% 8.19/8.44 tff(12669,plain,
% 8.19/8.44 (r(s(z), s(elem!1)) <=> r(s(z), elem!1)),
% 8.19/8.44 inference(monotonicity,[status(thm)],[12668])).
% 8.19/8.44 tff(12670,plain,
% 8.19/8.44 (r(s(z), elem!1) <=> r(s(z), s(elem!1))),
% 8.19/8.44 inference(symmetry,[status(thm)],[12669])).
% 8.19/8.44 tff(12671,plain,
% 8.19/8.44 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 8.19/8.44 inference(transitivity,[status(thm)],[12670, 12350])).
% 8.19/8.44 tff(12672,plain,
% 8.19/8.44 (r(s(z), s(s(s(elem!1))))),
% 8.19/8.44 inference(modus_ponens,[status(thm)],[12334, 12671])).
% 8.19/8.44 tff(12673,plain,
% 8.19/8.44 (~r(s(z), s(s(s(s(z)))))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12593, 718, 665, 133, 3363, 11960, 11962, 12672, 12664])).
% 8.19/8.44 tff(12674,plain,
% 8.19/8.44 (b(s(z), s(s(s(s(z)))))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[1230, 12673])).
% 8.19/8.44 tff(12675,plain,
% 8.19/8.44 (~b(s(s(s(s(z)))), elem!1)),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12626, 12674, 12334, 11942, 133, 665, 11941, 12135, 10682, 11960, 11397, 12137, 11962])).
% 8.19/8.44 tff(12676,plain,
% 8.19/8.44 (r(s(s(s(s(z)))), elem!1)),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[762, 12675, 718])).
% 8.19/8.44 tff(12677,plain,
% 8.19/8.44 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[9262, 12676, 12135])).
% 8.19/8.44 tff(12678,plain,
% 8.19/8.44 (~r(s(s(elem!1)), s(z))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[11881, 1233, 133, 665, 266, 6240, 5547, 2053, 1759, 1234])).
% 8.19/8.44 tff(12679,plain,
% 8.19/8.44 (b(s(s(elem!1)), s(z))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[362, 12678])).
% 8.19/8.44 tff(12680,plain,
% 8.19/8.44 (b(elem!1, s(z))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[8345, 12679, 266])).
% 8.19/8.44 tff(12681,plain,
% 8.19/8.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.44 inference(rewrite,[status(thm)],[])).
% 8.19/8.44 tff(12682,plain,
% 8.19/8.44 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, 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))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.44 inference(rewrite,[status(thm)],[])).
% 8.19/8.44 tff(12683,plain,
% 8.19/8.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 8.19/8.44 inference(monotonicity,[status(thm)],[12682])).
% 8.19/8.44 tff(12684,plain,
% 8.19/8.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.19/8.44 inference(transitivity,[status(thm)],[12683, 12681])).
% 8.19/8.44 tff(12685,plain,
% 8.19/8.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 8.19/8.44 inference(quant_inst,[status(thm)],[])).
% 8.19/8.44 tff(12686,plain,
% 8.19/8.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 8.19/8.44 inference(modus_ponens,[status(thm)],[12685, 12684])).
% 8.19/8.44 tff(12687,plain,
% 8.19/8.44 (~b(elem!1, s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12686, 391, 1234, 1759, 1233, 12680])).
% 8.19/8.44 tff(12688,plain,
% 8.19/8.44 (r(elem!1, s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[3394, 12687, 1405])).
% 8.19/8.44 tff(12689,plain,
% 8.19/8.44 (r(s(s(elem!1)), s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[11777, 12688, 266])).
% 8.19/8.44 tff(12690,plain,
% 8.19/8.44 (~b(s(s(z)), z)),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[9402, 11879, 266, 3927, 6240, 2641, 12679])).
% 8.19/8.44 tff(12691,plain,
% 8.19/8.44 (r(s(s(z)), z)),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[1211, 12690])).
% 8.19/8.44 tff(12692,plain,
% 8.19/8.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.19/8.44 inference(rewrite,[status(thm)],[])).
% 8.19/8.44 tff(12693,plain,
% 8.19/8.44 (((~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.19/8.44 inference(rewrite,[status(thm)],[])).
% 8.19/8.44 tff(12694,plain,
% 8.19/8.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 8.19/8.44 inference(monotonicity,[status(thm)],[12693])).
% 8.19/8.44 tff(12695,plain,
% 8.19/8.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.19/8.44 inference(transitivity,[status(thm)],[12694, 12692])).
% 8.19/8.44 tff(12696,plain,
% 8.19/8.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.19/8.44 inference(quant_inst,[status(thm)],[])).
% 8.19/8.44 tff(12697,plain,
% 8.19/8.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 8.19/8.44 inference(modus_ponens,[status(thm)],[12696, 12695])).
% 8.19/8.44 tff(12698,plain,
% 8.19/8.44 ($false),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12697, 194, 3557, 1697, 6240, 6236])).
% 8.19/8.44 tff(12699,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.44 tff(12700,plain,
% 8.19/8.44 ($false),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12699, 12691, 12689, 6240, 11879])).
% 8.19/8.44 tff(12701,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.44 tff(12702,plain,
% 8.19/8.44 (~b(s(s(z)), s(z))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12701, 12677, 12135, 11403, 11397, 11941, 12674, 12667, 133, 665, 11942, 12662])).
% 8.19/8.44 tff(12703,plain,
% 8.19/8.44 (r(s(s(z)), s(z))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[3778, 12702])).
% 8.19/8.44 tff(12704,plain,
% 8.19/8.44 (~r(s(s(z)), z)),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[4462, 12703, 12334, 12664])).
% 8.19/8.44 tff(12705,plain,
% 8.19/8.44 (b(s(s(z)), z)),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[1211, 12704])).
% 8.19/8.44 tff(12706,plain,
% 8.19/8.44 (~b(s(s(elem!1)), s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[11449, 12705, 10682, 11960, 11397])).
% 8.19/8.44 tff(12707,plain,
% 8.19/8.44 (~b(elem!1, s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[11458, 12706, 12135])).
% 8.19/8.44 tff(12708,plain,
% 8.19/8.44 (r(elem!1, s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[3394, 12707, 11941])).
% 8.19/8.44 tff(12709,plain,
% 8.19/8.44 (r(s(s(elem!1)), s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[11777, 12708, 12135])).
% 8.19/8.44 tff(12710,plain,
% 8.19/8.44 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[6285, 12709, 12677, 12703])).
% 8.19/8.44 tff(12711,plain,
% 8.19/8.44 (b(s(s(s(s(z)))), s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[1714, 12710])).
% 8.19/8.44 tff(12712,plain,
% 8.19/8.44 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12556, 12708, 12334, 173, 12674, 12667, 12135, 12703, 12662, 445])).
% 8.19/8.44 tff(12713,plain,
% 8.19/8.44 (b(s(s(z)), s(s(s(s(z)))))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[3652, 12712])).
% 8.19/8.44 tff(12714,plain,
% 8.19/8.44 (r(s(s(s(elem!1))), s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12471, 12708, 12135, 445])).
% 8.19/8.44 tff(12715,plain,
% 8.19/8.44 (~r(s(z), s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[11551, 12714, 12672, 12703])).
% 8.19/8.44 tff(12716,plain,
% 8.19/8.44 (b(s(z), s(s(z)))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[1788, 12715])).
% 8.19/8.44 tff(12717,plain,
% 8.19/8.44 ($false),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[6275, 12716, 12713, 12674, 12711])).
% 8.19/8.44 tff(12718,plain,((~(s(s(elem!1)) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(z) = elem!1) | (~b(s(elem!1), z)) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1)))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.44 tff(12719,plain,
% 8.19/8.44 (b(elem!1, s(s(s(elem!1))))),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12718, 445, 133, 665, 150, 591, 168, 10682, 121])).
% 8.19/8.44 tff(12720,plain,
% 8.19/8.44 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 8.19/8.44 inference(monotonicity,[status(thm)],[445])).
% 8.19/8.44 tff(12721,plain,
% 8.19/8.44 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 8.19/8.44 inference(symmetry,[status(thm)],[12720])).
% 8.19/8.44 tff(12722,plain,
% 8.19/8.44 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 8.19/8.44 inference(transitivity,[status(thm)],[4804, 12721])).
% 8.19/8.44 tff(12723,plain,
% 8.19/8.44 (b(s(s(elem!1)), s(elem!1))),
% 8.19/8.44 inference(modus_ponens,[status(thm)],[448, 12722])).
% 8.19/8.44 tff(12724,plain,
% 8.19/8.44 ($false),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[7995, 12723, 11403, 591, 133, 11958])).
% 8.19/8.44 tff(12725,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.44 tff(12726,plain,
% 8.19/8.44 ($false),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12725, 12719, 445, 133, 591, 10682])).
% 8.19/8.44 tff(12727,plain,((~(s(s(elem!1)) = elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (s(z) = elem!1) | b(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.44 tff(12728,plain,
% 8.19/8.44 (~(s(s(elem!1)) = elem!1)),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12727, 11937, 133, 10682, 665, 150, 168, 121])).
% 8.19/8.44 tff(12729,plain,
% 8.19/8.44 (~(s(elem!1) = elem!1)),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[1943, 12728])).
% 8.19/8.44 tff(12730,plain,
% 8.19/8.44 (r(s(elem!1), elem!1)),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[2168, 12729, 2163])).
% 8.19/8.44 tff(12731,plain,
% 8.19/8.44 (~(s(s(elem!1)) = elem!1)),
% 8.19/8.44 inference(unit_resolution,[status(thm)],[12718, 4028, 133, 665, 150, 11937, 168, 10682, 121])).
% 8.19/8.45 tff(12732,plain,
% 8.19/8.45 (~(s(elem!1) = elem!1)),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[1943, 12731])).
% 8.19/8.45 tff(12733,plain,
% 8.19/8.45 (~(elem!1 = s(elem!1))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[166, 12732])).
% 8.19/8.45 tff(12734,plain,
% 8.19/8.45 (~b(elem!1, s(elem!1))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[7689, 391, 133, 665, 11937])).
% 8.19/8.45 tff(12735,plain,
% 8.19/8.45 (r(elem!1, s(elem!1))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[443, 12734, 12733])).
% 8.19/8.45 tff(12736,plain,
% 8.19/8.45 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[6159, 12731])).
% 8.19/8.45 tff(12737,plain,
% 8.19/8.45 (r(s(elem!1), elem!1)),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[2168, 12732, 2163])).
% 8.19/8.45 tff(12738,plain,
% 8.19/8.45 (~r(s(s(s(elem!1))), s(elem!1))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[7744, 8848, 2251, 485])).
% 8.19/8.45 tff(12739,plain,
% 8.19/8.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 8.19/8.45 inference(rewrite,[status(thm)],[])).
% 8.19/8.45 tff(12740,plain,
% 8.19/8.45 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 8.19/8.45 inference(rewrite,[status(thm)],[])).
% 8.19/8.45 tff(12741,plain,
% 8.19/8.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))))),
% 8.19/8.45 inference(monotonicity,[status(thm)],[12740])).
% 8.19/8.45 tff(12742,plain,
% 8.19/8.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 8.19/8.45 inference(transitivity,[status(thm)],[12741, 12739])).
% 8.19/8.45 tff(12743,plain,
% 8.19/8.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 8.19/8.45 inference(quant_inst,[status(thm)],[])).
% 8.19/8.45 tff(12744,plain,
% 8.19/8.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 8.19/8.45 inference(modus_ponens,[status(thm)],[12743, 12742])).
% 8.19/8.45 tff(12745,plain,
% 8.19/8.45 ($false),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[12744, 391, 6458, 10682, 591, 5624])).
% 8.19/8.45 tff(12746,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | r(s(elem!1), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.45 tff(12747,plain,
% 8.19/8.45 (r(s(elem!1), s(s(s(elem!1))))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[12746, 12738, 10682, 591, 279])).
% 8.19/8.45 tff(12748,plain,
% 8.19/8.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 8.19/8.45 inference(rewrite,[status(thm)],[])).
% 8.19/8.45 tff(12749,plain,
% 8.19/8.45 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), 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)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 8.19/8.45 inference(rewrite,[status(thm)],[])).
% 8.19/8.45 tff(12750,plain,
% 8.19/8.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 8.19/8.45 inference(monotonicity,[status(thm)],[12749])).
% 8.19/8.45 tff(12751,plain,
% 8.19/8.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 8.19/8.45 inference(transitivity,[status(thm)],[12750, 12748])).
% 8.19/8.45 tff(12752,plain,
% 8.19/8.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 8.19/8.45 inference(quant_inst,[status(thm)],[])).
% 8.19/8.45 tff(12753,plain,
% 8.19/8.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 8.19/8.45 inference(modus_ponens,[status(thm)],[12752, 12751])).
% 8.19/8.45 tff(12754,plain,
% 8.19/8.45 ($false),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[12753, 194, 485, 8848, 8849, 12747])).
% 8.19/8.45 tff(12755,plain,((elem!1 = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.45 tff(12756,plain,
% 8.19/8.45 (elem!1 = s(s(s(elem!1)))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[12755, 12737, 10682, 11937, 12736, 12735, 168, 4028])).
% 8.19/8.45 tff(12757,plain,
% 8.19/8.45 (s(elem!1) = s(s(s(s(elem!1))))),
% 8.19/8.45 inference(monotonicity,[status(thm)],[12756])).
% 8.19/8.45 tff(12758,plain,
% 8.19/8.45 (s(s(s(s(elem!1)))) = s(elem!1)),
% 8.19/8.45 inference(symmetry,[status(thm)],[12757])).
% 8.19/8.45 tff(12759,plain,
% 8.19/8.45 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(elem!1))),
% 8.19/8.45 inference(monotonicity,[status(thm)],[12758])).
% 8.19/8.45 tff(12760,plain,
% 8.19/8.45 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(elem!1)))))),
% 8.19/8.45 inference(symmetry,[status(thm)],[12759])).
% 8.19/8.45 tff(12761,plain,
% 8.19/8.45 (b(s(s(elem!1)), elem!1)),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[872, 12731, 888])).
% 8.19/8.45 tff(12762,plain,
% 8.19/8.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 8.19/8.45 inference(rewrite,[status(thm)],[])).
% 8.19/8.45 tff(12763,plain,
% 8.19/8.45 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 8.19/8.45 inference(rewrite,[status(thm)],[])).
% 8.19/8.45 tff(12764,plain,
% 8.19/8.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))))),
% 8.19/8.45 inference(monotonicity,[status(thm)],[12763])).
% 8.19/8.45 tff(12765,plain,
% 8.19/8.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 8.19/8.45 inference(transitivity,[status(thm)],[12764, 12762])).
% 8.19/8.45 tff(12766,plain,
% 8.19/8.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 8.19/8.45 inference(quant_inst,[status(thm)],[])).
% 8.19/8.45 tff(12767,plain,
% 8.19/8.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))),
% 8.19/8.45 inference(modus_ponens,[status(thm)],[12766, 12765])).
% 8.19/8.45 tff(12768,plain,
% 8.19/8.45 (~b(s(s(elem!1)), s(z))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[12767, 391, 133, 665, 973, 644])).
% 8.19/8.45 tff(12769,plain,
% 8.19/8.45 (r(s(s(elem!1)), s(z))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[362, 12768])).
% 8.19/8.45 tff(12770,plain,
% 8.19/8.45 ($false),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[4103, 12769, 11981, 7500, 11977])).
% 8.19/8.45 tff(12771,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.45 tff(12772,plain,
% 8.19/8.45 (~b(s(z), elem!1)),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[12771, 12761, 665, 133])).
% 8.19/8.45 tff(12773,plain,
% 8.19/8.45 (r(s(z), elem!1)),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[632, 12772, 150])).
% 8.19/8.45 tff(12774,plain,
% 8.19/8.45 (~r(s(z), s(elem!1))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[5738, 194, 12737, 12735, 12773])).
% 8.19/8.45 tff(12775,plain,
% 8.19/8.45 (b(s(z), s(elem!1))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[602, 42, 121, 12774])).
% 8.19/8.45 tff(12776,plain,
% 8.19/8.45 (b(s(z), s(s(s(s(elem!1)))))),
% 8.19/8.45 inference(modus_ponens,[status(thm)],[12775, 12760])).
% 8.19/8.45 tff(12777,plain,
% 8.19/8.45 (~(s(s(elem!1)) = elem!1)),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[12718, 4028, 133, 665, 150, 591, 168, 10682, 121])).
% 8.19/8.45 tff(12778,plain,
% 8.19/8.45 (r(s(s(s(elem!1))), z)),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[377, 9550])).
% 8.19/8.45 tff(12779,plain,
% 8.19/8.45 (~r(s(s(s(elem!1))), elem!1)),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[5368, 12778, 150, 249, 121, 133, 7464, 590, 665])).
% 8.19/8.45 tff(12780,plain,
% 8.19/8.45 (~(elem!1 = s(s(s(elem!1))))),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[9553, 9550, 665])).
% 8.19/8.45 tff(12781,plain,
% 8.19/8.45 (~(s(s(s(elem!1))) = elem!1)),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[8, 12780])).
% 8.19/8.45 tff(12782,plain,
% 8.19/8.45 ($false),
% 8.19/8.45 inference(unit_resolution,[status(thm)],[230, 12781, 12779, 168])).
% 8.19/8.45 tff(12783,plain,(b(s(s(s(elem!1))), z) | b(s(s(s(elem!1))), elem!1) | (s(z) = elem!1) | (s(s(elem!1)) = elem!1) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.46 tff(12784,plain,
% 8.19/8.46 (b(s(s(s(elem!1))), z)),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[12783, 590, 150, 12777, 121, 133, 168, 665])).
% 8.19/8.46 tff(12785,plain,
% 8.19/8.46 (~b(s(z), s(s(s(elem!1))))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[11303, 12784, 10682, 590])).
% 8.19/8.46 tff(12786,plain,
% 8.19/8.46 (r(s(z), s(s(s(elem!1))))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[247, 12785])).
% 8.19/8.46 tff(12787,plain,
% 8.19/8.46 (s(s(s(elem!1))) = elem!1),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[5715, 12786, 168, 1484, 4028])).
% 8.19/8.46 tff(12788,plain,
% 8.19/8.46 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), elem!1)),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12787])).
% 8.19/8.46 tff(12789,plain,
% 8.19/8.46 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(elem!1))))),
% 8.19/8.46 inference(symmetry,[status(thm)],[12788])).
% 8.19/8.46 tff(12790,plain,
% 8.19/8.46 (r(s(elem!1), s(s(s(elem!1))))),
% 8.19/8.46 inference(modus_ponens,[status(thm)],[485, 12789])).
% 8.19/8.46 tff(12791,plain,
% 8.19/8.46 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[6159, 12777])).
% 8.19/8.46 tff(12792,plain,
% 8.19/8.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 8.19/8.46 inference(rewrite,[status(thm)],[])).
% 8.19/8.46 tff(12793,plain,
% 8.19/8.46 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(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(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 8.19/8.46 inference(rewrite,[status(thm)],[])).
% 8.19/8.46 tff(12794,plain,
% 8.19/8.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))))),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12793])).
% 8.19/8.46 tff(12795,plain,
% 8.19/8.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 8.19/8.46 inference(transitivity,[status(thm)],[12794, 12792])).
% 8.19/8.46 tff(12796,plain,
% 8.19/8.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 8.19/8.46 inference(quant_inst,[status(thm)],[])).
% 8.19/8.46 tff(12797,plain,
% 8.19/8.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 8.19/8.46 inference(modus_ponens,[status(thm)],[12796, 12795])).
% 8.19/8.46 tff(12798,plain,
% 8.19/8.46 ($false),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[12797, 391, 1101, 380, 10682, 591])).
% 8.19/8.46 tff(12799,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.46 tff(12800,plain,
% 8.19/8.46 (~b(s(s(s(elem!1))), s(elem!1))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[12799, 12784, 10682, 591])).
% 8.19/8.46 tff(12801,plain,
% 8.19/8.46 (r(s(s(s(elem!1))), s(elem!1))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[588, 12800, 12791])).
% 8.19/8.46 tff(12802,plain,
% 8.19/8.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)))),
% 8.19/8.46 inference(rewrite,[status(thm)],[])).
% 8.19/8.46 tff(12803,plain,
% 8.19/8.46 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)))),
% 8.19/8.46 inference(rewrite,[status(thm)],[])).
% 8.19/8.46 tff(12804,plain,
% 8.19/8.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z))))),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12803])).
% 8.19/8.46 tff(12805,plain,
% 8.19/8.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)))),
% 8.19/8.46 inference(transitivity,[status(thm)],[12804, 12802])).
% 8.19/8.46 tff(12806,plain,
% 8.19/8.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 8.19/8.46 inference(quant_inst,[status(thm)],[])).
% 8.19/8.46 tff(12807,plain,
% 8.19/8.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z))),
% 8.19/8.46 inference(modus_ponens,[status(thm)],[12806, 12805])).
% 8.19/8.46 tff(12808,plain,
% 8.19/8.46 (~b(s(z), s(elem!1))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[12807, 391, 380, 10682, 591, 590])).
% 8.19/8.46 tff(12809,plain,
% 8.19/8.46 (r(s(z), s(elem!1))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[602, 42, 121, 12808])).
% 8.19/8.46 tff(12810,plain,
% 8.19/8.46 (~b(s(z), s(s(s(elem!1))))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[11301, 391, 380, 10682, 590])).
% 8.19/8.46 tff(12811,plain,
% 8.19/8.46 (r(s(z), s(s(s(elem!1))))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[247, 12810])).
% 8.19/8.46 tff(12812,plain,
% 8.19/8.46 ($false),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[619, 194, 613, 12811, 604, 12809])).
% 8.19/8.46 tff(12813,plain,((~b(s(z), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.46 tff(12814,plain,
% 8.19/8.46 (~r(s(elem!1), s(s(s(elem!1))))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[12813, 12801, 10682, 590, 12784, 121, 591])).
% 8.19/8.46 tff(12815,plain,
% 8.19/8.46 ($false),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[12814, 12790])).
% 8.19/8.46 tff(12816,plain,((~b(s(z), z)) | (~r(s(elem!1), elem!1)) | b(s(s(s(elem!1))), elem!1) | (~r(s(z), elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~b(s(elem!1), z)) | (s(z) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.46 tff(12817,plain,
% 8.19/8.46 (~b(s(z), z)),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[12816, 12737, 168, 12773, 4028, 10682, 121, 11937, 150, 133, 665])).
% 8.19/8.46 tff(12818,plain,
% 8.19/8.46 (r(s(z), z)),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[180, 12817])).
% 8.19/8.46 tff(12819,plain,
% 8.19/8.46 (~b(s(s(elem!1)), z)),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[5263, 391, 133, 665, 12761])).
% 8.19/8.46 tff(12820,plain,
% 8.19/8.46 (r(s(s(elem!1)), z)),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[2629, 12819])).
% 8.19/8.46 tff(12821,plain,
% 8.19/8.46 (s(s(s(elem!1))) = elem!1),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[129, 12756])).
% 8.19/8.46 tff(12822,plain,
% 8.19/8.46 (~(s(s(s(s(z)))) = elem!1)),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[1436, 12821])).
% 8.19/8.46 tff(12823,plain,
% 8.19/8.46 (~(s(elem!1) = s(s(s(s(z)))))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[1965, 12821])).
% 8.19/8.46 tff(12824,plain,
% 8.19/8.46 (~b(s(s(s(s(z)))), z)),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[5901, 12823, 665, 11937, 12735, 133, 12822, 12737])).
% 8.19/8.46 tff(12825,plain,
% 8.19/8.46 (r(s(s(s(s(z)))), z)),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[87, 12824])).
% 8.19/8.46 tff(12826,plain,
% 8.19/8.46 (~b(z, s(s(elem!1)))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[4944, 12761, 665, 133])).
% 8.19/8.46 tff(12827,plain,
% 8.19/8.46 (r(z, s(s(elem!1)))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[324, 12826])).
% 8.19/8.46 tff(12828,plain,
% 8.19/8.46 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12757])).
% 8.19/8.46 tff(12829,plain,
% 8.19/8.46 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 8.19/8.46 inference(symmetry,[status(thm)],[12828])).
% 8.19/8.46 tff(12830,plain,
% 8.19/8.46 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12829])).
% 8.19/8.46 tff(12831,plain,
% 8.19/8.46 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12829])).
% 8.19/8.46 tff(12832,plain,
% 8.19/8.46 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 8.19/8.46 inference(symmetry,[status(thm)],[12831])).
% 8.19/8.46 tff(12833,plain,
% 8.19/8.46 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))))),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12832])).
% 8.19/8.46 tff(12834,plain,
% 8.19/8.46 (s(s(s(elem!1))) = elem!1),
% 8.19/8.46 inference(symmetry,[status(thm)],[12756])).
% 8.19/8.46 tff(12835,plain,
% 8.19/8.46 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12834])).
% 8.19/8.46 tff(12836,plain,
% 8.19/8.46 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 8.19/8.46 inference(transitivity,[status(thm)],[12835, 698])).
% 8.19/8.46 tff(12837,plain,
% 8.19/8.46 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12836])).
% 8.19/8.46 tff(12838,plain,
% 8.19/8.46 (~(elem!1 = s(s(z)))),
% 8.19/8.46 inference(modus_ponens,[status(thm)],[1397, 12837])).
% 8.19/8.46 tff(12839,plain,
% 8.19/8.46 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[1407, 12838])).
% 8.19/8.46 tff(12840,plain,
% 8.19/8.46 (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 8.19/8.46 inference(modus_ponens,[status(thm)],[12839, 12833])).
% 8.19/8.46 tff(12841,plain,
% 8.19/8.46 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12829])).
% 8.19/8.46 tff(12842,plain,
% 8.19/8.46 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 8.19/8.46 inference(symmetry,[status(thm)],[12841])).
% 8.19/8.46 tff(12843,plain,
% 8.19/8.46 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 8.19/8.46 inference(monotonicity,[status(thm)],[12842])).
% 8.19/8.46 tff(12844,plain,
% 8.19/8.46 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[9284, 12825, 12820, 12827])).
% 8.19/8.46 tff(12845,plain,
% 8.19/8.46 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 8.19/8.46 inference(modus_ponens,[status(thm)],[12844, 12843])).
% 8.19/8.46 tff(12846,plain,
% 8.19/8.46 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[9442, 42, 12845])).
% 8.19/8.46 tff(12847,plain,
% 8.19/8.46 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 8.19/8.46 inference(unit_resolution,[status(thm)],[12846, 12840])).
% 8.19/8.46 tff(12848,plain,
% 8.19/8.46 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.19/8.46 inference(modus_ponens,[status(thm)],[12847, 12830])).
% 8.19/8.46 tff(12849,plain,
% 8.19/8.47 (~b(s(s(elem!1)), s(z))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[3471, 12848, 12827, 12818, 12825])).
% 8.19/8.47 tff(12850,plain,
% 8.19/8.47 (r(s(s(elem!1)), s(z))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[362, 12849])).
% 8.19/8.47 tff(12851,plain,
% 8.19/8.47 (~r(z, s(z))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[4103, 12850, 12820, 12818])).
% 8.19/8.47 tff(12852,plain,
% 8.19/8.47 (b(z, s(z))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[678, 12851])).
% 8.19/8.47 tff(12853,plain,
% 8.19/8.47 (r(s(s(s(s(elem!1)))), z) <=> r(s(elem!1), z)),
% 8.19/8.47 inference(monotonicity,[status(thm)],[3716])).
% 8.19/8.47 tff(12854,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 8.19/8.47 tff(12855,plain,
% 8.19/8.47 (r(s(elem!1), z)),
% 8.19/8.47 inference(modus_ponens,[status(thm)],[12854, 12853])).
% 8.19/8.47 tff(12856,plain,
% 8.19/8.47 ($false),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[544, 12855])).
% 8.19/8.47 tff(12857,plain,((~r(s(s(s(s(elem!1)))), z)) | r(s(elem!1), z) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.47 tff(12858,plain,
% 8.19/8.47 (~r(s(s(s(s(elem!1)))), z)),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[12857, 12821, 544])).
% 8.19/8.47 tff(12859,plain,
% 8.19/8.47 (b(s(s(s(s(elem!1)))), z)),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[1626, 12858])).
% 8.19/8.47 tff(12860,plain,
% 8.19/8.47 (b(z, s(elem!1)) <=> b(z, s(s(s(s(elem!1)))))),
% 8.19/8.47 inference(monotonicity,[status(thm)],[12757])).
% 8.19/8.47 tff(12861,plain,
% 8.19/8.47 (~r(z, s(elem!1))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[2621, 12850, 12820, 12818])).
% 8.19/8.47 tff(12862,plain,
% 8.19/8.47 (b(z, s(elem!1))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[566, 12861])).
% 8.19/8.47 tff(12863,plain,
% 8.19/8.47 (b(z, s(s(s(s(elem!1)))))),
% 8.19/8.47 inference(modus_ponens,[status(thm)],[12862, 12860])).
% 8.19/8.47 tff(12864,plain,
% 8.19/8.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 8.19/8.47 inference(rewrite,[status(thm)],[])).
% 8.19/8.47 tff(12865,plain,
% 8.19/8.47 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 8.19/8.47 inference(rewrite,[status(thm)],[])).
% 8.19/8.47 tff(12866,plain,
% 8.19/8.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 8.19/8.47 inference(monotonicity,[status(thm)],[12865])).
% 8.19/8.47 tff(12867,plain,
% 8.19/8.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 8.19/8.47 inference(transitivity,[status(thm)],[12866, 12864])).
% 8.19/8.47 tff(12868,plain,
% 8.19/8.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 8.19/8.47 inference(quant_inst,[status(thm)],[])).
% 8.19/8.47 tff(12869,plain,
% 8.19/8.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 8.19/8.47 inference(modus_ponens,[status(thm)],[12868, 12867])).
% 8.19/8.47 tff(12870,plain,
% 8.19/8.47 (~b(s(z), s(s(s(s(elem!1)))))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[12869, 391, 10682, 12863, 12859, 12852])).
% 8.19/8.47 tff(12871,plain,
% 8.19/8.47 ($false),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[12870, 12776])).
% 8.19/8.47 tff(12872,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | r(s(elem!1), z) | b(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1)) | (s(z) = elem!1) | b(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.19/8.47 tff(12873,plain,
% 8.19/8.47 (b(elem!1, s(s(s(elem!1))))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[12872, 888, 665, 133, 544, 168, 121, 150, 2163, 10682])).
% 8.19/8.47 tff(12874,plain,
% 8.19/8.47 (~(s(s(elem!1)) = elem!1)),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[12725, 12873, 133, 11937, 10682])).
% 8.19/8.47 tff(12875,plain,
% 8.19/8.47 (b(s(s(elem!1)), elem!1)),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[872, 12874, 888])).
% 8.19/8.47 tff(12876,plain,
% 8.19/8.47 (~b(s(s(elem!1)), z)),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[5263, 391, 133, 665, 12875])).
% 8.19/8.47 tff(12877,plain,
% 8.19/8.47 (r(s(s(elem!1)), z)),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[2629, 12876])).
% 8.19/8.47 tff(12878,plain,
% 8.19/8.47 (~b(z, s(s(elem!1)))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[4944, 12875, 665, 133])).
% 8.19/8.47 tff(12879,plain,
% 8.19/8.47 (r(z, s(s(elem!1)))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[324, 12878])).
% 8.19/8.47 tff(12880,plain,
% 8.19/8.47 (~(s(s(elem!1)) = s(elem!1))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[264, 12874])).
% 8.19/8.47 tff(12881,plain,
% 8.19/8.47 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[287, 12880])).
% 8.19/8.47 tff(12882,plain,
% 8.19/8.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.19/8.47 inference(rewrite,[status(thm)],[])).
% 8.19/8.47 tff(12883,plain,
% 8.19/8.47 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.19/8.47 inference(rewrite,[status(thm)],[])).
% 8.19/8.47 tff(12884,plain,
% 8.19/8.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 8.19/8.47 inference(monotonicity,[status(thm)],[12883])).
% 8.19/8.47 tff(12885,plain,
% 8.19/8.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.19/8.47 inference(transitivity,[status(thm)],[12884, 12882])).
% 8.19/8.47 tff(12886,plain,
% 8.19/8.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 8.19/8.47 inference(quant_inst,[status(thm)],[])).
% 8.19/8.47 tff(12887,plain,
% 8.19/8.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 8.19/8.47 inference(modus_ponens,[status(thm)],[12886, 12885])).
% 8.19/8.47 tff(12888,plain,
% 8.19/8.47 ($false),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[12887, 391, 665, 10682, 973, 448, 1374])).
% 8.19/8.47 tff(12889,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.47 tff(12890,plain,
% 8.19/8.47 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[12889, 12875, 10682, 665, 12873])).
% 8.19/8.47 tff(12891,plain,
% 8.19/8.47 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[1370, 12890, 12881])).
% 8.19/8.47 tff(12892,plain,
% 8.19/8.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 8.19/8.47 inference(rewrite,[status(thm)],[])).
% 8.19/8.47 tff(12893,plain,
% 8.19/8.47 (((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 8.19/8.47 inference(rewrite,[status(thm)],[])).
% 8.19/8.47 tff(12894,plain,
% 8.19/8.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 8.19/8.47 inference(monotonicity,[status(thm)],[12893])).
% 8.19/8.47 tff(12895,plain,
% 8.19/8.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 8.19/8.47 inference(transitivity,[status(thm)],[12894, 12892])).
% 8.19/8.47 tff(12896,plain,
% 8.19/8.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 8.19/8.47 inference(quant_inst,[status(thm)],[])).
% 8.19/8.47 tff(12897,plain,
% 8.19/8.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 8.19/8.47 inference(modus_ponens,[status(thm)],[12896, 12895])).
% 8.19/8.47 tff(12898,plain,
% 8.19/8.47 (~r(s(s(s(elem!1))), z)),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[12897, 194, 12891, 12879, 12877])).
% 8.19/8.47 tff(12899,plain,
% 8.19/8.47 (b(s(s(s(elem!1))), z)),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[377, 12898])).
% 8.19/8.47 tff(12900,plain,
% 8.19/8.47 ($false),
% 8.19/8.47 inference(unit_resolution,[status(thm)],[5856, 391, 133, 665, 12899, 12873])).
% 8.19/8.47 tff(12901,plain,(r(s(s(elem!1)), elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | r(s(elem!1), z) | b(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1)) | (s(z) = elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.19/8.48 tff(12902,plain,
% 8.19/8.48 (r(s(s(elem!1)), elem!1)),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12901, 544, 665, 10682, 133, 168, 121, 150, 2163])).
% 8.19/8.48 tff(12903,plain,
% 8.19/8.48 (~(elem!1 = s(elem!1))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[166, 12729])).
% 8.19/8.48 tff(12904,plain,
% 8.19/8.48 (~(s(s(elem!1)) = s(elem!1))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[264, 12728])).
% 8.19/8.48 tff(12905,plain,
% 8.19/8.48 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[287, 12904])).
% 8.19/8.48 tff(12906,plain,
% 8.19/8.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 8.19/8.48 inference(rewrite,[status(thm)],[])).
% 8.19/8.48 tff(12907,plain,
% 8.19/8.48 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 8.19/8.48 inference(rewrite,[status(thm)],[])).
% 8.19/8.48 tff(12908,plain,
% 8.19/8.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 8.19/8.48 inference(monotonicity,[status(thm)],[12907])).
% 8.19/8.48 tff(12909,plain,
% 8.19/8.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 8.19/8.48 inference(transitivity,[status(thm)],[12908, 12906])).
% 8.19/8.48 tff(12910,plain,
% 8.19/8.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 8.19/8.48 inference(quant_inst,[status(thm)],[])).
% 8.19/8.48 tff(12911,plain,
% 8.19/8.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 8.19/8.48 inference(modus_ponens,[status(thm)],[12910, 12909])).
% 8.19/8.48 tff(12912,plain,
% 8.19/8.48 (~r(s(z), s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12911, 194, 174, 11981, 11977])).
% 8.19/8.48 tff(12913,plain,
% 8.19/8.48 (b(s(z), s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[247, 12912])).
% 8.19/8.48 tff(12914,plain,
% 8.19/8.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 8.19/8.48 inference(rewrite,[status(thm)],[])).
% 8.19/8.48 tff(12915,plain,
% 8.19/8.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 8.19/8.48 inference(quant_inst,[status(thm)],[])).
% 8.19/8.48 tff(12916,plain,
% 8.19/8.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 8.19/8.48 inference(modus_ponens,[status(thm)],[12915, 12914])).
% 8.19/8.48 tff(12917,plain,
% 8.19/8.48 (~r(s(s(s(elem!1))), s(z))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12916, 194, 174, 11981, 11977])).
% 8.19/8.48 tff(12918,plain,
% 8.19/8.48 (b(s(s(s(elem!1))), s(z))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[223, 12917])).
% 8.19/8.48 tff(12919,plain,
% 8.19/8.48 (~b(elem!1, s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[4026, 12918, 12913, 644])).
% 8.19/8.48 tff(12920,plain,
% 8.19/8.48 (r(elem!1, s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[424, 12919, 1])).
% 8.19/8.48 tff(12921,plain,
% 8.19/8.48 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[5875, 12920, 364, 8848])).
% 8.19/8.48 tff(12922,plain,
% 8.19/8.48 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[1356, 12921, 315])).
% 8.19/8.48 tff(12923,plain,
% 8.19/8.48 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[4039, 12919, 168, 364, 9])).
% 8.19/8.48 tff(12924,plain,
% 8.19/8.48 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[1370, 12923, 297])).
% 8.19/8.48 tff(12925,plain,
% 8.19/8.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.19/8.48 inference(rewrite,[status(thm)],[])).
% 8.19/8.48 tff(12926,plain,
% 8.19/8.48 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.19/8.48 inference(rewrite,[status(thm)],[])).
% 8.19/8.48 tff(12927,plain,
% 8.19/8.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 8.19/8.48 inference(monotonicity,[status(thm)],[12926])).
% 8.19/8.48 tff(12928,plain,
% 8.19/8.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.19/8.48 inference(transitivity,[status(thm)],[12927, 12925])).
% 8.19/8.48 tff(12929,plain,
% 8.19/8.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 8.19/8.48 inference(quant_inst,[status(thm)],[])).
% 8.19/8.48 tff(12930,plain,
% 8.19/8.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 8.19/8.48 inference(modus_ponens,[status(thm)],[12929, 12928])).
% 8.19/8.48 tff(12931,plain,
% 8.19/8.48 ($false),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12930, 391, 10682, 1374, 3927, 328])).
% 8.19/8.48 tff(12932,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.48 tff(12933,plain,
% 8.19/8.48 (~b(z, s(s(elem!1)))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12932, 12924, 10682, 12922])).
% 8.19/8.48 tff(12934,plain,
% 8.19/8.48 (~r(z, s(s(elem!1)))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[3432, 12924, 12913, 11977, 12922])).
% 8.19/8.48 tff(12935,plain,
% 8.19/8.48 ($false),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[324, 12934, 12933])).
% 8.19/8.48 tff(12936,plain,((~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.48 tff(12937,plain,
% 8.19/8.48 (~b(s(z), elem!1)),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12936, 297, 10682, 364, 168, 12780, 12778, 133, 665])).
% 8.19/8.48 tff(12938,plain,
% 8.19/8.48 (r(s(z), elem!1)),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[632, 12937, 150])).
% 8.19/8.48 tff(12939,plain,
% 8.19/8.48 (s(s(elem!1)) = elem!1),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12783, 590, 150, 9550, 121, 133, 168, 665])).
% 8.19/8.48 tff(12940,plain,
% 8.19/8.48 (b(elem!1, s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12816, 590, 168, 485, 1484, 10682, 121, 591, 150, 133, 665])).
% 8.19/8.48 tff(12941,plain,
% 8.19/8.48 ($false),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12725, 12940, 12939, 133, 591, 10682])).
% 8.19/8.48 tff(12942,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (s(z) = s(elem!1)) | (s(z) = elem!1) | (~b(elem!1, z)) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 8.19/8.48 tff(12943,plain,
% 8.19/8.48 (~b(s(z), z)),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12942, 12938, 591, 10682, 168, 485, 133, 121, 150, 665, 9550])).
% 8.19/8.48 tff(12944,plain,
% 8.19/8.48 (r(s(z), z)),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[180, 12943])).
% 8.19/8.48 tff(12945,plain,
% 8.19/8.48 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[5875, 6124, 364, 8848])).
% 8.19/8.48 tff(12946,plain,
% 8.19/8.48 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[1356, 12945, 315])).
% 8.19/8.48 tff(12947,plain,
% 8.19/8.48 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[4039, 4028, 168, 364, 9])).
% 8.19/8.48 tff(12948,plain,
% 8.19/8.48 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[1370, 12947, 297])).
% 8.19/8.48 tff(12949,plain,
% 8.19/8.48 (~b(z, s(s(elem!1)))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12932, 12948, 10682, 12946])).
% 8.19/8.48 tff(12950,plain,
% 8.19/8.48 (~r(s(z), s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[5715, 4028, 168, 1484, 9])).
% 8.19/8.48 tff(12951,plain,
% 8.19/8.48 (b(s(z), s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[247, 12950])).
% 8.19/8.48 tff(12952,plain,
% 8.19/8.48 (~r(z, s(s(elem!1)))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[3432, 12948, 12951, 182, 12946])).
% 8.19/8.48 tff(12953,plain,
% 8.19/8.48 ($false),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[324, 12952, 12949])).
% 8.19/8.48 tff(12954,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(elem!1))), elem!1) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.48 tff(12955,plain,
% 8.19/8.48 (b(elem!1, s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12954, 12944, 10682, 297, 364, 168, 12938, 12780])).
% 8.19/8.48 tff(12956,plain,
% 8.19/8.48 (~(s(s(elem!1)) = elem!1)),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12725, 12955, 133, 591, 10682])).
% 8.19/8.48 tff(12957,plain,
% 8.19/8.48 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[6159, 12956])).
% 8.19/8.48 tff(12958,plain,
% 8.19/8.48 (r(s(s(s(elem!1))), elem!1)),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[230, 12781, 168])).
% 8.19/8.48 tff(12959,plain,
% 8.19/8.48 (~r(s(s(s(elem!1))), s(elem!1))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[7744, 2251, 233, 485])).
% 8.19/8.48 tff(12960,plain,
% 8.19/8.48 (r(s(elem!1), s(s(s(elem!1))))),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[12746, 12959, 10682, 591, 279])).
% 8.19/8.48 tff(12961,plain,
% 8.19/8.48 ($false),
% 8.19/8.48 inference(unit_resolution,[status(thm)],[7450, 194, 485, 233, 2251, 12960])).
% 8.19/8.49 tff(12962,plain,((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.49 tff(12963,plain,
% 8.19/8.49 (~r(elem!1, s(elem!1))),
% 8.19/8.49 inference(unit_resolution,[status(thm)],[12962, 12957, 12958, 10682, 591, 485])).
% 8.19/8.49 tff(12964,plain,
% 8.19/8.49 (b(elem!1, s(elem!1))),
% 8.19/8.49 inference(unit_resolution,[status(thm)],[443, 12963, 437])).
% 8.19/8.49 tff(12965,plain,
% 8.19/8.49 (~b(z, s(elem!1))),
% 8.19/8.49 inference(unit_resolution,[status(thm)],[1939, 12964, 665, 591])).
% 8.19/8.49 tff(12966,plain,
% 8.19/8.49 (r(z, s(elem!1))),
% 8.19/8.49 inference(unit_resolution,[status(thm)],[566, 12965])).
% 8.19/8.49 tff(12967,plain,
% 8.19/8.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.19/8.49 inference(rewrite,[status(thm)],[])).
% 8.19/8.49 tff(12968,plain,
% 8.19/8.49 (((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.19/8.49 inference(rewrite,[status(thm)],[])).
% 8.19/8.49 tff(12969,plain,
% 8.19/8.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 8.19/8.49 inference(monotonicity,[status(thm)],[12968])).
% 8.19/8.49 tff(12970,plain,
% 8.19/8.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.19/8.49 inference(transitivity,[status(thm)],[12969, 12967])).
% 8.19/8.49 tff(12971,plain,
% 8.19/8.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.19/8.49 inference(quant_inst,[status(thm)],[])).
% 8.19/8.49 tff(12972,plain,
% 8.19/8.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 8.19/8.49 inference(modus_ponens,[status(thm)],[12971, 12970])).
% 8.19/8.49 tff(12973,plain,
% 8.19/8.49 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.19/8.49 inference(unit_resolution,[status(thm)],[12972, 194, 174, 2144, 2053])).
% 8.19/8.49 tff(12974,plain,
% 8.19/8.49 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.19/8.49 inference(unit_resolution,[status(thm)],[4313, 42, 12973])).
% 8.19/8.49 tff(12975,plain,
% 8.19/8.49 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.19/8.49 inference(unit_resolution,[status(thm)],[12974, 6950])).
% 8.19/8.49 tff(12976,plain,
% 8.19/8.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.19/8.49 inference(rewrite,[status(thm)],[])).
% 8.19/8.49 tff(12977,plain,
% 8.19/8.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.19/8.49 inference(quant_inst,[status(thm)],[])).
% 8.19/8.49 tff(12978,plain,
% 8.19/8.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 8.19/8.49 inference(modus_ponens,[status(thm)],[12977, 12976])).
% 8.19/8.49 tff(12979,plain,
% 8.19/8.49 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.19/8.49 inference(unit_resolution,[status(thm)],[12978, 194, 174, 2144, 2053])).
% 8.19/8.49 tff(12980,plain,
% 8.19/8.49 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.19/8.49 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 12979])).
% 8.19/8.49 tff(12981,plain,
% 8.19/8.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.19/8.49 inference(rewrite,[status(thm)],[])).
% 8.19/8.49 tff(12982,plain,
% 8.19/8.49 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.19/8.49 inference(rewrite,[status(thm)],[])).
% 8.19/8.49 tff(12983,plain,
% 8.19/8.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 8.19/8.49 inference(monotonicity,[status(thm)],[12982])).
% 8.19/8.49 tff(12984,plain,
% 8.19/8.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.19/8.49 inference(transitivity,[status(thm)],[12983, 12981])).
% 8.19/8.49 tff(12985,plain,
% 8.19/8.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 8.19/8.49 inference(quant_inst,[status(thm)],[])).
% 8.19/8.49 tff(12986,plain,
% 8.19/8.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 8.19/8.49 inference(modus_ponens,[status(thm)],[12985, 12984])).
% 8.19/8.49 tff(12987,plain,
% 8.19/8.49 ($false),
% 8.19/8.49 inference(unit_resolution,[status(thm)],[12986, 391, 665, 10682, 448, 12980, 12975])).
% 8.19/8.49 tff(12988,plain,((~r(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 8.19/8.50 tff(12989,plain,
% 8.19/8.50 (~r(s(s(s(s(z)))), z)),
% 8.19/8.50 inference(unit_resolution,[status(thm)],[12988, 12955, 10682, 665, 3363, 12778, 12966])).
% 8.19/8.50 tff(12990,plain,
% 8.19/8.50 (b(s(s(s(s(z)))), z)),
% 8.19/8.50 inference(unit_resolution,[status(thm)],[87, 12989])).
% 8.19/8.50 tff(12991,plain,
% 8.19/8.50 (~b(elem!1, s(s(s(s(z)))))),
% 8.19/8.50 inference(unit_resolution,[status(thm)],[12445, 12990, 665, 133])).
% 8.19/8.50 tff(12992,plain,
% 8.19/8.50 (~b(z, s(s(s(s(z)))))),
% 8.19/8.50 inference(unit_resolution,[status(thm)],[2050, 90, 665, 591, 802])).
% 8.19/8.50 tff(12993,plain,
% 8.19/8.50 (r(z, s(s(s(s(z)))))),
% 8.19/8.50 inference(unit_resolution,[status(thm)],[800, 12992])).
% 8.19/8.50 tff(12994,plain,
% 8.19/8.50 (~r(s(s(s(s(z)))), elem!1)),
% 8.19/8.50 inference(unit_resolution,[status(thm)],[2720, 12993, 1216, 182])).
% 8.19/8.50 tff(12995,plain,
% 8.19/8.50 (s(s(s(s(z)))) = elem!1),
% 8.19/8.50 inference(unit_resolution,[status(thm)],[762, 4963, 12994])).
% 8.19/8.50 tff(12996,plain,
% 8.19/8.50 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 8.19/8.50 inference(monotonicity,[status(thm)],[12995])).
% 8.19/8.50 tff(12997,plain,
% 8.19/8.50 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 8.19/8.50 inference(symmetry,[status(thm)],[12996])).
% 8.29/8.50 tff(12998,plain,
% 8.29/8.50 (b(z, s(s(s(s(z)))))),
% 8.29/8.50 inference(modus_ponens,[status(thm)],[133, 12997])).
% 8.29/8.50 tff(12999,plain,
% 8.29/8.50 ($false),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[12992, 12998])).
% 8.29/8.50 tff(13000,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.50 tff(13001,plain,
% 8.29/8.50 (~b(s(s(s(s(z)))), z)),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[13000, 1216, 665, 133, 182, 591, 802])).
% 8.29/8.50 tff(13002,plain,
% 8.29/8.50 (r(s(s(s(s(z)))), z)),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[87, 13001])).
% 8.29/8.50 tff(13003,plain,
% 8.29/8.50 (~b(z, s(elem!1))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[1939, 802, 665, 591])).
% 8.29/8.50 tff(13004,plain,
% 8.29/8.50 (r(z, s(elem!1))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[566, 13003])).
% 8.29/8.50 tff(13005,plain,
% 8.29/8.50 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[12972, 194, 174, 13004, 13002])).
% 8.29/8.50 tff(13006,plain,
% 8.29/8.50 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[4313, 42, 13005])).
% 8.29/8.50 tff(13007,plain,
% 8.29/8.50 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[13006, 6950])).
% 8.29/8.50 tff(13008,plain,
% 8.29/8.50 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[12978, 194, 174, 13004, 13002])).
% 8.29/8.50 tff(13009,plain,
% 8.29/8.50 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 13008])).
% 8.29/8.50 tff(13010,plain,
% 8.29/8.50 (~r(elem!1, s(s(s(s(z)))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[12404, 13002, 1484, 1216])).
% 8.29/8.50 tff(13011,plain,
% 8.29/8.50 (~(s(s(s(s(z)))) = elem!1)),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[6966, 13001, 665])).
% 8.29/8.50 tff(13012,plain,
% 8.29/8.50 (~(elem!1 = s(s(s(s(z)))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[769, 13011])).
% 8.29/8.50 tff(13013,plain,
% 8.29/8.50 (b(elem!1, s(s(s(s(z)))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[781, 13012, 13010])).
% 8.29/8.50 tff(13014,plain,
% 8.29/8.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.29/8.50 inference(rewrite,[status(thm)],[])).
% 8.29/8.50 tff(13015,plain,
% 8.29/8.50 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.29/8.50 inference(rewrite,[status(thm)],[])).
% 8.29/8.50 tff(13016,plain,
% 8.29/8.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 8.29/8.50 inference(monotonicity,[status(thm)],[13015])).
% 8.29/8.50 tff(13017,plain,
% 8.29/8.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.29/8.50 inference(transitivity,[status(thm)],[13016, 13014])).
% 8.29/8.50 tff(13018,plain,
% 8.29/8.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 8.29/8.50 inference(quant_inst,[status(thm)],[])).
% 8.29/8.50 tff(13019,plain,
% 8.29/8.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 8.29/8.50 inference(modus_ponens,[status(thm)],[13018, 13017])).
% 8.29/8.50 tff(13020,plain,
% 8.29/8.50 ($false),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[13019, 391, 448, 13013, 13009, 13007])).
% 8.29/8.50 tff(13021,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.50 tff(13022,plain,
% 8.29/8.50 (~r(s(z), s(s(s(s(z)))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[13021, 12955, 3363, 12778, 12938, 665, 133, 12944, 591, 12964])).
% 8.29/8.50 tff(13023,plain,
% 8.29/8.50 (b(s(z), s(s(s(s(z)))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[1230, 13022])).
% 8.29/8.50 tff(13024,plain,
% 8.29/8.50 (~(s(s(s(s(z)))) = elem!1)),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[8916, 13023, 12937])).
% 8.29/8.50 tff(13025,plain,
% 8.29/8.50 (~(elem!1 = s(s(s(s(z)))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[769, 13024])).
% 8.29/8.50 tff(13026,plain,
% 8.29/8.50 (r(elem!1, s(s(s(s(z)))))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[781, 13025, 12991])).
% 8.29/8.50 tff(13027,plain,
% 8.29/8.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.50 inference(rewrite,[status(thm)],[])).
% 8.29/8.50 tff(13028,plain,
% 8.29/8.50 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.50 inference(rewrite,[status(thm)],[])).
% 8.29/8.50 tff(13029,plain,
% 8.29/8.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.29/8.50 inference(monotonicity,[status(thm)],[13028])).
% 8.29/8.50 tff(13030,plain,
% 8.29/8.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.50 inference(transitivity,[status(thm)],[13029, 13027])).
% 8.29/8.50 tff(13031,plain,
% 8.29/8.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 8.29/8.50 inference(quant_inst,[status(thm)],[])).
% 8.29/8.50 tff(13032,plain,
% 8.29/8.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 8.29/8.50 inference(modus_ponens,[status(thm)],[13031, 13030])).
% 8.29/8.50 tff(13033,plain,
% 8.29/8.50 (~r(s(s(s(elem!1))), s(elem!1))),
% 8.29/8.50 inference(unit_resolution,[status(thm)],[13032, 194, 485, 12958, 13026])).
% 8.29/8.50 tff(13034,plain,
% 8.29/8.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.50 inference(rewrite,[status(thm)],[])).
% 8.29/8.50 tff(13035,plain,
% 8.29/8.50 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), 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)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.50 inference(rewrite,[status(thm)],[])).
% 8.29/8.50 tff(13036,plain,
% 8.29/8.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.29/8.50 inference(monotonicity,[status(thm)],[13035])).
% 8.29/8.50 tff(13037,plain,
% 8.29/8.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.50 inference(transitivity,[status(thm)],[13036, 13034])).
% 8.29/8.50 tff(13038,plain,
% 8.29/8.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 8.29/8.50 inference(quant_inst,[status(thm)],[])).
% 8.29/8.50 tff(13039,plain,
% 8.29/8.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.29/8.50 inference(modus_ponens,[status(thm)],[13038, 13037])).
% 8.29/8.50 tff(13040,plain,
% 8.29/8.50 (~r(s(elem!1), s(s(s(elem!1))))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[13039, 194, 485, 12958, 13026])).
% 8.29/8.51 tff(13041,plain,
% 8.29/8.51 ($false),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[12746, 13040, 13033, 10682, 591, 12957])).
% 8.29/8.51 tff(13042,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (elem!1 = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(elem!1))), elem!1) | (s(z) = s(elem!1)) | (s(z) = elem!1) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 8.29/8.51 tff(13043,plain,
% 8.29/8.51 (b(s(s(s(elem!1))), z)),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[13042, 12905, 11937, 10682, 665, 133, 12903, 12902, 168, 121, 150, 12730])).
% 8.29/8.51 tff(13044,plain,
% 8.29/8.51 (~b(elem!1, s(s(s(elem!1))))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[5856, 391, 133, 665, 13043])).
% 8.29/8.51 tff(13045,plain,
% 8.29/8.51 (~r(s(z), elem!1)),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[12816, 590, 168, 485, 4028, 10682, 121, 591, 150, 133, 665])).
% 8.29/8.51 tff(13046,plain,
% 8.29/8.51 ($false),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[632, 13045, 5236, 150])).
% 8.29/8.51 tff(13047,plain,((~b(s(z), z)) | (s(z) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(s(elem!1), elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.51 tff(13048,plain,
% 8.29/8.51 (~b(s(z), z)),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[13047, 12730, 168, 150, 13044, 10682, 121, 11937, 133, 665])).
% 8.29/8.51 tff(13049,plain,
% 8.29/8.51 (r(s(z), z)),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[180, 13048])).
% 8.29/8.51 tff(13050,plain,
% 8.29/8.51 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[6159, 12728])).
% 8.29/8.51 tff(13051,plain,
% 8.29/8.51 (~b(s(s(s(elem!1))), s(elem!1))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[12799, 13043, 10682, 11937])).
% 8.29/8.51 tff(13052,plain,
% 8.29/8.51 (r(s(s(s(elem!1))), s(elem!1))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[588, 13051, 13050])).
% 8.29/8.51 tff(13053,plain,
% 8.29/8.51 ($false),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[7832, 4030, 4031, 485, 613])).
% 8.29/8.51 tff(13054,plain,((s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.29/8.51 tff(13055,plain,
% 8.29/8.51 (s(s(s(elem!1))) = elem!1),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[13054, 12730, 13052, 13044, 168])).
% 8.29/8.51 tff(13056,plain,
% 8.29/8.51 (~(s(s(s(s(z)))) = elem!1)),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[1436, 13055])).
% 8.29/8.51 tff(13057,plain,
% 8.29/8.51 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 8.29/8.51 inference(monotonicity,[status(thm)],[5])).
% 8.29/8.51 tff(13058,plain,
% 8.29/8.51 (r(elem!1, s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 8.29/8.51 inference(symmetry,[status(thm)],[13057])).
% 8.29/8.51 tff(13059,plain,
% 8.29/8.51 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 8.29/8.51 inference(monotonicity,[status(thm)],[13058])).
% 8.29/8.51 tff(13060,plain,
% 8.29/8.51 (~r(s(s(s(elem!1))), s(elem!1))),
% 8.29/8.51 inference(modus_ponens,[status(thm)],[438, 13059])).
% 8.29/8.51 tff(13061,plain,
% 8.29/8.51 ($false),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[613, 13060])).
% 8.29/8.51 tff(13062,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.51 tff(13063,plain,
% 8.29/8.51 (r(elem!1, s(elem!1))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[13062, 13055, 13052])).
% 8.29/8.51 tff(13064,plain,
% 8.29/8.51 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 8.29/8.51 inference(monotonicity,[status(thm)],[13055])).
% 8.29/8.51 tff(13065,plain,
% 8.29/8.51 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 8.29/8.51 inference(transitivity,[status(thm)],[13064, 698])).
% 8.29/8.51 tff(13066,plain,
% 8.29/8.51 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 8.29/8.51 inference(monotonicity,[status(thm)],[13065])).
% 8.29/8.51 tff(13067,plain,
% 8.29/8.51 (~(elem!1 = s(s(z)))),
% 8.29/8.51 inference(modus_ponens,[status(thm)],[1397, 13066])).
% 8.29/8.51 tff(13068,plain,
% 8.29/8.51 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[1407, 13067])).
% 8.29/8.51 tff(13069,plain,
% 8.29/8.51 (~(s(elem!1) = s(s(s(s(z)))))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[1965, 13055])).
% 8.29/8.51 tff(13070,plain,
% 8.29/8.51 (s(s(s(s(elem!1)))) = s(elem!1)),
% 8.29/8.51 inference(monotonicity,[status(thm)],[13055])).
% 8.29/8.51 tff(13071,plain,
% 8.29/8.51 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 8.29/8.51 inference(monotonicity,[status(thm)],[13070])).
% 8.29/8.51 tff(13072,plain,
% 8.29/8.51 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[2686, 13050])).
% 8.29/8.51 tff(13073,plain,
% 8.29/8.51 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[2711, 13072])).
% 8.29/8.51 tff(13074,plain,
% 8.29/8.51 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 8.29/8.51 inference(monotonicity,[status(thm)],[13070])).
% 8.29/8.51 tff(13075,plain,
% 8.29/8.51 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.29/8.51 inference(symmetry,[status(thm)],[13074])).
% 8.29/8.51 tff(13076,plain,
% 8.29/8.51 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 8.29/8.51 inference(monotonicity,[status(thm)],[13075])).
% 8.29/8.51 tff(13077,plain,
% 8.29/8.51 (~r(s(elem!1), s(s(elem!1)))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[7596, 194, 12730, 13063, 12902])).
% 8.29/8.51 tff(13078,plain,
% 8.29/8.51 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.29/8.51 inference(modus_ponens,[status(thm)],[13077, 13076])).
% 8.29/8.51 tff(13079,plain,
% 8.29/8.51 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[1061, 13078, 13073])).
% 8.29/8.51 tff(13080,plain,
% 8.29/8.51 (b(s(elem!1), s(s(elem!1)))),
% 8.29/8.51 inference(modus_ponens,[status(thm)],[13079, 13071])).
% 8.29/8.51 tff(13081,plain,
% 8.29/8.51 (~r(s(s(elem!1)), s(elem!1))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[5806, 194, 12730, 13063, 12902])).
% 8.29/8.51 tff(13082,plain,
% 8.29/8.51 (b(s(s(elem!1)), s(elem!1))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[1135, 13081, 12904])).
% 8.29/8.51 tff(13083,plain,
% 8.29/8.51 (~r(s(elem!1), s(s(s(s(z)))))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[4553, 194, 485, 2251, 2112])).
% 8.29/8.51 tff(13084,plain,
% 8.29/8.51 (b(s(elem!1), s(s(s(s(z)))))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[2142, 42, 13083, 2121])).
% 8.29/8.51 tff(13085,plain,
% 8.29/8.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.29/8.51 inference(rewrite,[status(thm)],[])).
% 8.29/8.51 tff(13086,plain,
% 8.29/8.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.29/8.51 inference(quant_inst,[status(thm)],[])).
% 8.29/8.51 tff(13087,plain,
% 8.29/8.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 8.29/8.51 inference(modus_ponens,[status(thm)],[13086, 13085])).
% 8.29/8.51 tff(13088,plain,
% 8.29/8.51 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[13087, 194, 2251, 364, 2112])).
% 8.29/8.51 tff(13089,plain,
% 8.29/8.51 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[2003, 42, 13088, 1983])).
% 8.29/8.51 tff(13090,plain,
% 8.29/8.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.51 inference(rewrite,[status(thm)],[])).
% 8.29/8.51 tff(13091,plain,
% 8.29/8.51 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(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(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.51 inference(rewrite,[status(thm)],[])).
% 8.29/8.51 tff(13092,plain,
% 8.29/8.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 8.29/8.51 inference(monotonicity,[status(thm)],[13091])).
% 8.29/8.51 tff(13093,plain,
% 8.29/8.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.51 inference(transitivity,[status(thm)],[13092, 13090])).
% 8.29/8.51 tff(13094,plain,
% 8.29/8.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.51 inference(quant_inst,[status(thm)],[])).
% 8.29/8.51 tff(13095,plain,
% 8.29/8.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 8.29/8.51 inference(modus_ponens,[status(thm)],[13094, 13093])).
% 8.29/8.51 tff(13096,plain,
% 8.29/8.51 ($false),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[13095, 391, 591, 1037, 7625, 13089, 13084])).
% 8.29/8.51 tff(13097,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(s(s(z))))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.51 tff(13098,plain,
% 8.29/8.51 (~r(s(s(s(s(z)))), elem!1)),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[13097, 11937, 13082, 13080, 13069, 13068, 12730, 13063, 12902])).
% 8.29/8.51 tff(13099,plain,
% 8.29/8.51 (b(s(s(s(s(z)))), elem!1)),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[762, 13098, 13056])).
% 8.29/8.51 tff(13100,plain,
% 8.29/8.51 (~b(s(z), elem!1)),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[12158, 13099, 665, 13049, 133])).
% 8.29/8.51 tff(13101,plain,
% 8.29/8.51 (r(s(z), elem!1)),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[632, 13100, 150])).
% 8.29/8.51 tff(13102,plain,
% 8.29/8.51 (~r(s(z), s(elem!1))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[5738, 194, 12730, 13063, 13101])).
% 8.29/8.51 tff(13103,plain,
% 8.29/8.51 (b(s(z), s(elem!1))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[602, 42, 121, 13102])).
% 8.29/8.51 tff(13104,plain,
% 8.29/8.51 (~r(s(s(elem!1)), s(z))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[5811, 194, 13063, 12902, 13101])).
% 8.29/8.51 tff(13105,plain,
% 8.29/8.51 (b(s(s(elem!1)), s(z))),
% 8.29/8.51 inference(unit_resolution,[status(thm)],[362, 13104])).
% 8.29/8.51 tff(13106,plain,
% 8.29/8.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 8.29/8.52 inference(rewrite,[status(thm)],[])).
% 8.29/8.52 tff(13107,plain,
% 8.29/8.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 8.29/8.52 inference(quant_inst,[status(thm)],[])).
% 8.29/8.52 tff(13108,plain,
% 8.29/8.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))),
% 8.29/8.52 inference(modus_ponens,[status(thm)],[13107, 13106])).
% 8.29/8.52 tff(13109,plain,
% 8.29/8.52 ($false),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[13108, 391, 133, 13105, 11937, 13082, 13103])).
% 8.29/8.52 tff(13110,plain,(r(s(elem!1), z) | (~b(z, elem!1)) | (s(z) = s(elem!1)) | (s(z) = elem!1) | (~b(elem!1, z)) | b(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.29/8.52 tff(13111,plain,
% 8.29/8.52 (r(s(elem!1), z)),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[13110, 11936, 118, 150, 133, 168, 10682, 2163])).
% 8.29/8.52 tff(13112,plain,
% 8.29/8.52 (r(s(elem!1), z) <=> r(elem!1, z)),
% 8.29/8.52 inference(monotonicity,[status(thm)],[152])).
% 8.29/8.52 tff(13113,plain,
% 8.29/8.52 (r(elem!1, z) <=> r(s(elem!1), z)),
% 8.29/8.52 inference(symmetry,[status(thm)],[13112])).
% 8.29/8.52 tff(13114,plain,
% 8.29/8.52 ((~r(elem!1, z)) <=> (~r(s(elem!1), z))),
% 8.29/8.52 inference(monotonicity,[status(thm)],[13113])).
% 8.29/8.52 tff(13115,plain,
% 8.29/8.52 (~r(s(elem!1), z)),
% 8.29/8.52 inference(modus_ponens,[status(thm)],[2282, 13114])).
% 8.29/8.52 tff(13116,plain,
% 8.29/8.52 ($false),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[1628, 13115])).
% 8.29/8.52 tff(13117,plain,((~(s(elem!1) = elem!1)) | (~r(s(elem!1), z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 8.29/8.52 tff(13118,plain,
% 8.29/8.52 (~(s(elem!1) = elem!1)),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[13117, 13111, 2282])).
% 8.29/8.52 tff(13119,plain,
% 8.29/8.52 (~(elem!1 = s(elem!1))),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[166, 13118])).
% 8.29/8.52 tff(13120,plain,
% 8.29/8.52 (r(s(elem!1), elem!1)),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[2168, 13118, 2163])).
% 8.29/8.52 tff(13121,plain,
% 8.29/8.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 8.29/8.52 inference(rewrite,[status(thm)],[])).
% 8.29/8.52 tff(13122,plain,
% 8.29/8.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 8.29/8.52 inference(quant_inst,[status(thm)],[])).
% 8.29/8.52 tff(13123,plain,
% 8.29/8.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 8.29/8.52 inference(modus_ponens,[status(thm)],[13122, 13121])).
% 8.29/8.52 tff(13124,plain,
% 8.29/8.52 (~r(s(z), s(elem!1))),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[13123, 194, 1628, 11981, 11977])).
% 8.29/8.52 tff(13125,plain,
% 8.29/8.52 (b(s(z), s(elem!1))),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[602, 42, 121, 13124])).
% 8.29/8.52 tff(13126,plain,
% 8.29/8.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 8.29/8.52 inference(rewrite,[status(thm)],[])).
% 8.29/8.52 tff(13127,plain,
% 8.29/8.52 (((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 8.29/8.52 inference(rewrite,[status(thm)],[])).
% 8.29/8.52 tff(13128,plain,
% 8.29/8.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 8.29/8.52 inference(monotonicity,[status(thm)],[13127])).
% 8.29/8.52 tff(13129,plain,
% 8.29/8.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 8.29/8.52 inference(transitivity,[status(thm)],[13128, 13126])).
% 8.29/8.52 tff(13130,plain,
% 8.29/8.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 8.29/8.52 inference(quant_inst,[status(thm)],[])).
% 8.29/8.52 tff(13131,plain,
% 8.29/8.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 8.29/8.52 inference(modus_ponens,[status(thm)],[13130, 13129])).
% 8.29/8.52 tff(13132,plain,
% 8.29/8.52 (~r(s(elem!1), s(z))),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[13131, 194, 1628, 11981, 11977])).
% 8.29/8.52 tff(13133,plain,
% 8.29/8.52 (b(s(elem!1), s(z))),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[1915, 42, 13132, 11956])).
% 8.29/8.52 tff(13134,plain,
% 8.29/8.52 (~b(s(s(s(s(z)))), elem!1)),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[12158, 11977, 665, 644, 133])).
% 8.29/8.52 tff(13135,plain,
% 8.29/8.52 (~(s(elem!1) = s(s(s(s(z)))))),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[5377, 465, 3843])).
% 8.29/8.52 tff(13136,plain,
% 8.29/8.52 (~(s(s(s(s(z)))) = s(elem!1))),
% 8.29/8.52 inference(modus_ponens,[status(thm)],[13135, 2125])).
% 8.29/8.52 tff(13137,plain,
% 8.29/8.52 (r(s(s(s(s(z)))), elem!1)),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[762, 5470, 1549])).
% 8.29/8.52 tff(13138,plain,
% 8.29/8.52 (~r(s(s(s(s(z)))), s(elem!1))),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[4609, 194, 485, 5538, 13137])).
% 8.29/8.52 tff(13139,plain,
% 8.29/8.52 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[2136, 42, 13138])).
% 8.29/8.52 tff(13140,plain,
% 8.29/8.52 (b(s(s(s(s(z)))), s(elem!1))),
% 8.29/8.52 inference(unit_resolution,[status(thm)],[13139, 13136])).
% 8.29/8.52 tff(13141,plain,
% 8.29/8.52 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 8.29/8.52 inference(monotonicity,[status(thm)],[465])).
% 8.29/8.52 tff(13142,plain,
% 8.29/8.52 (b(z, s(elem!1))),
% 8.29/8.52 inference(modus_ponens,[status(thm)],[10682, 13141])).
% 8.29/8.52 tff(13143,plain,
% 8.29/8.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 8.29/8.52 inference(rewrite,[status(thm)],[])).
% 8.29/8.52 tff(13144,plain,
% 8.29/8.52 (((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 8.29/8.52 inference(rewrite,[status(thm)],[])).
% 8.29/8.52 tff(13145,plain,
% 8.29/8.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 8.29/8.52 inference(monotonicity,[status(thm)],[13144])).
% 8.29/8.52 tff(13146,plain,
% 8.29/8.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 8.29/8.53 inference(transitivity,[status(thm)],[13145, 13143])).
% 8.29/8.53 tff(13147,plain,
% 8.29/8.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 8.29/8.53 inference(quant_inst,[status(thm)],[])).
% 8.29/8.53 tff(13148,plain,
% 8.29/8.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 8.29/8.53 inference(modus_ponens,[status(thm)],[13147, 13146])).
% 8.29/8.53 tff(13149,plain,
% 8.29/8.53 (~b(s(s(s(s(z)))), z)),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[13148, 391, 13142, 644, 5469, 13140])).
% 8.29/8.53 tff(13150,plain,
% 8.29/8.53 (r(s(s(s(s(z)))), z)),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[87, 13149])).
% 8.29/8.53 tff(13151,plain,
% 8.29/8.53 (~b(s(z), s(s(s(s(z)))))),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[4622, 391, 644, 751, 5469, 13140])).
% 8.29/8.53 tff(13152,plain,
% 8.29/8.53 (r(s(z), s(s(s(s(z)))))),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[1230, 13151])).
% 8.29/8.53 tff(13153,plain,
% 8.29/8.53 ($false),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[10558, 13152, 13150, 182, 722])).
% 8.29/8.53 tff(13154,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.53 tff(13155,plain,
% 8.29/8.53 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[13154, 4028, 11981, 644, 751, 5469, 485, 10682, 437, 13134, 11977, 3843])).
% 8.29/8.53 tff(13156,plain,
% 8.29/8.53 (~(s(s(elem!1)) = elem!1)),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[451, 13155])).
% 8.29/8.53 tff(13157,plain,
% 8.29/8.53 (~b(s(s(elem!1)), elem!1)),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[12771, 644, 665, 133])).
% 8.29/8.53 tff(13158,plain,
% 8.29/8.53 (r(s(s(elem!1)), elem!1)),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[872, 249, 13157])).
% 8.29/8.53 tff(13159,plain,
% 8.29/8.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 8.29/8.53 inference(rewrite,[status(thm)],[])).
% 8.29/8.53 tff(13160,plain,
% 8.29/8.53 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 8.29/8.53 inference(rewrite,[status(thm)],[])).
% 8.29/8.53 tff(13161,plain,
% 8.29/8.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))))),
% 8.29/8.53 inference(monotonicity,[status(thm)],[13160])).
% 8.29/8.53 tff(13162,plain,
% 8.29/8.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 8.29/8.53 inference(transitivity,[status(thm)],[13161, 13159])).
% 8.29/8.53 tff(13163,plain,
% 8.29/8.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 8.29/8.53 inference(quant_inst,[status(thm)],[])).
% 8.29/8.53 tff(13164,plain,
% 8.29/8.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 8.29/8.53 inference(modus_ponens,[status(thm)],[13163, 13162])).
% 8.29/8.53 tff(13165,plain,
% 8.29/8.53 (~r(s(s(elem!1)), s(elem!1))),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[13164, 194, 485, 13158, 4030])).
% 8.29/8.53 tff(13166,plain,
% 8.29/8.53 (~r(s(s(s(elem!1))), z)),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[12936, 288, 10682, 4029, 168, 13158, 644, 133, 665])).
% 8.29/8.53 tff(13167,plain,
% 8.29/8.53 (b(s(s(s(elem!1))), z)),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[377, 13166])).
% 8.29/8.53 tff(13168,plain,
% 8.29/8.53 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[4039, 13158, 168, 127, 4028])).
% 8.29/8.53 tff(13169,plain,
% 8.29/8.53 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[1370, 13168, 288])).
% 8.29/8.53 tff(13170,plain,
% 8.29/8.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.29/8.53 inference(rewrite,[status(thm)],[])).
% 8.29/8.53 tff(13171,plain,
% 8.29/8.53 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(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))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.29/8.53 inference(rewrite,[status(thm)],[])).
% 8.29/8.53 tff(13172,plain,
% 8.29/8.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 8.29/8.53 inference(monotonicity,[status(thm)],[13171])).
% 8.29/8.53 tff(13173,plain,
% 8.29/8.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.29/8.53 inference(transitivity,[status(thm)],[13172, 13170])).
% 8.29/8.53 tff(13174,plain,
% 8.29/8.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(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)))))),
% 8.29/8.53 inference(quant_inst,[status(thm)],[])).
% 8.29/8.53 tff(13175,plain,
% 8.29/8.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 8.29/8.53 inference(modus_ponens,[status(thm)],[13174, 13173])).
% 8.29/8.53 tff(13176,plain,
% 8.29/8.53 ($false),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[13175, 391, 380, 10682, 1374, 2641])).
% 8.29/8.53 tff(13177,plain,((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.53 tff(13178,plain,
% 8.29/8.53 (~b(s(s(elem!1)), z)),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[13177, 13169, 10682, 13167])).
% 8.29/8.53 tff(13179,plain,
% 8.29/8.53 (r(s(s(elem!1)), z)),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[2629, 13178])).
% 8.29/8.53 tff(13180,plain,
% 8.29/8.53 (~r(s(s(elem!1)), s(z))),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[4103, 13179, 11981, 11977])).
% 8.29/8.53 tff(13181,plain,
% 8.29/8.53 (b(s(s(elem!1)), s(z))),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[362, 13180])).
% 8.29/8.53 tff(13182,plain,
% 8.29/8.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 8.29/8.53 inference(rewrite,[status(thm)],[])).
% 8.29/8.53 tff(13183,plain,
% 8.29/8.53 (((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 8.29/8.53 inference(rewrite,[status(thm)],[])).
% 8.29/8.53 tff(13184,plain,
% 8.29/8.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))))),
% 8.29/8.53 inference(monotonicity,[status(thm)],[13183])).
% 8.29/8.53 tff(13185,plain,
% 8.29/8.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 8.29/8.53 inference(transitivity,[status(thm)],[13184, 13182])).
% 8.29/8.53 tff(13186,plain,
% 8.29/8.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 8.29/8.53 inference(quant_inst,[status(thm)],[])).
% 8.29/8.53 tff(13187,plain,
% 8.29/8.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 8.29/8.53 inference(modus_ponens,[status(thm)],[13186, 13185])).
% 8.29/8.53 tff(13188,plain,
% 8.29/8.53 (~b(s(s(elem!1)), s(elem!1))),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[13187, 391, 665, 13181, 644, 5469])).
% 8.29/8.53 tff(13189,plain,
% 8.29/8.53 ($false),
% 8.29/8.53 inference(unit_resolution,[status(thm)],[1135, 13188, 13165, 265])).
% 8.29/8.53 tff(13190,plain,((s(s(elem!1)) = elem!1) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (~b(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.54 tff(13191,plain,
% 8.29/8.54 (s(s(s(elem!1))) = elem!1),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[13190, 13156, 644, 5469, 485, 10682, 168, 133, 665, 4028])).
% 8.29/8.54 tff(13192,plain,
% 8.29/8.54 (~(s(elem!1) = s(s(s(s(z)))))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[1965, 13191])).
% 8.29/8.54 tff(13193,plain,
% 8.29/8.54 (~(s(s(s(s(z)))) = elem!1)),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[1436, 13191])).
% 8.29/8.54 tff(13194,plain,
% 8.29/8.54 (~(elem!1 = s(s(s(s(z)))))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[769, 13193])).
% 8.29/8.54 tff(13195,plain,
% 8.29/8.54 (r(s(s(elem!1)), elem!1)),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[872, 13156, 13157])).
% 8.29/8.54 tff(13196,plain,
% 8.29/8.54 (r(s(s(s(s(z)))), elem!1)),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[762, 13193, 13134])).
% 8.29/8.54 tff(13197,plain,
% 8.29/8.54 (~(s(s(elem!1)) = s(elem!1))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[2279, 13155])).
% 8.29/8.54 tff(13198,plain,
% 8.29/8.54 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[2686, 13155])).
% 8.29/8.54 tff(13199,plain,
% 8.29/8.54 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[2711, 13198])).
% 8.29/8.54 tff(13200,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.54 inference(rewrite,[status(thm)],[])).
% 8.29/8.54 tff(13201,plain,
% 8.29/8.54 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), 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(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.54 inference(rewrite,[status(thm)],[])).
% 8.29/8.54 tff(13202,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 8.29/8.54 inference(monotonicity,[status(thm)],[13201])).
% 8.29/8.54 tff(13203,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.54 inference(transitivity,[status(thm)],[13202, 13200])).
% 8.29/8.54 tff(13204,plain,
% 8.29/8.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.54 inference(quant_inst,[status(thm)],[])).
% 8.29/8.54 tff(13205,plain,
% 8.29/8.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 8.29/8.54 inference(modus_ponens,[status(thm)],[13204, 13203])).
% 8.29/8.54 tff(13206,plain,
% 8.29/8.54 (~r(s(elem!1), s(s(s(s(z)))))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[13205, 194, 485, 2032, 2112])).
% 8.29/8.54 tff(13207,plain,
% 8.29/8.54 (b(s(elem!1), s(s(s(s(z)))))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[2142, 42, 13206, 3122])).
% 8.29/8.54 tff(13208,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.54 inference(rewrite,[status(thm)],[])).
% 8.29/8.54 tff(13209,plain,
% 8.29/8.54 (((~r(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(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.54 inference(rewrite,[status(thm)],[])).
% 8.29/8.54 tff(13210,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.29/8.54 inference(monotonicity,[status(thm)],[13209])).
% 8.29/8.54 tff(13211,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.54 inference(transitivity,[status(thm)],[13210, 13208])).
% 8.29/8.54 tff(13212,plain,
% 8.29/8.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(s(z)))), s(s(elem!1)))))),
% 8.29/8.54 inference(quant_inst,[status(thm)],[])).
% 8.29/8.54 tff(13213,plain,
% 8.29/8.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.29/8.54 inference(modus_ponens,[status(thm)],[13212, 13211])).
% 8.29/8.54 tff(13214,plain,
% 8.29/8.54 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[13213, 194, 364, 2032, 2112])).
% 8.29/8.54 tff(13215,plain,
% 8.29/8.54 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[2003, 42, 13214, 3695])).
% 8.29/8.54 tff(13216,plain,
% 8.29/8.54 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 8.29/8.54 inference(monotonicity,[status(thm)],[3716])).
% 8.29/8.54 tff(13217,plain,
% 8.29/8.54 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 8.29/8.54 inference(monotonicity,[status(thm)],[3716])).
% 8.29/8.54 tff(13218,plain,
% 8.29/8.54 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.29/8.54 inference(symmetry,[status(thm)],[13217])).
% 8.29/8.54 tff(13219,plain,
% 8.29/8.54 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 8.29/8.54 inference(monotonicity,[status(thm)],[13218])).
% 8.29/8.54 tff(13220,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.54 inference(rewrite,[status(thm)],[])).
% 8.29/8.54 tff(13221,plain,
% 8.29/8.54 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(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)) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.54 inference(rewrite,[status(thm)],[])).
% 8.29/8.54 tff(13222,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.29/8.54 inference(monotonicity,[status(thm)],[13221])).
% 8.29/8.54 tff(13223,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.54 inference(transitivity,[status(thm)],[13222, 13220])).
% 8.29/8.54 tff(13224,plain,
% 8.29/8.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 8.29/8.54 inference(quant_inst,[status(thm)],[])).
% 8.29/8.54 tff(13225,plain,
% 8.29/8.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(s(s(z))))))),
% 8.29/8.54 inference(modus_ponens,[status(thm)],[13224, 13223])).
% 8.29/8.54 tff(13226,plain,
% 8.29/8.54 (~r(s(elem!1), s(s(elem!1)))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[13225, 194, 485, 364, 2032])).
% 8.29/8.54 tff(13227,plain,
% 8.29/8.54 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.29/8.54 inference(modus_ponens,[status(thm)],[13226, 13219])).
% 8.29/8.54 tff(13228,plain,
% 8.29/8.54 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.29/8.54 inference(unit_resolution,[status(thm)],[1061, 13227, 1050])).
% 8.29/8.54 tff(13229,plain,
% 8.29/8.54 (b(s(elem!1), s(s(elem!1)))),
% 8.29/8.54 inference(modus_ponens,[status(thm)],[13228, 13216])).
% 8.29/8.54 tff(13230,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.54 inference(rewrite,[status(thm)],[])).
% 8.29/8.54 tff(13231,plain,
% 8.29/8.54 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(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)) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.54 inference(rewrite,[status(thm)],[])).
% 8.29/8.54 tff(13232,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.29/8.54 inference(monotonicity,[status(thm)],[13231])).
% 8.29/8.54 tff(13233,plain,
% 8.29/8.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.29/8.54 inference(transitivity,[status(thm)],[13232, 13230])).
% 8.29/8.54 tff(13234,plain,
% 8.29/8.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 8.29/8.55 inference(quant_inst,[status(thm)],[])).
% 8.29/8.55 tff(13235,plain,
% 8.29/8.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(s(s(z))))))),
% 8.29/8.55 inference(modus_ponens,[status(thm)],[13234, 13233])).
% 8.29/8.55 tff(13236,plain,
% 8.29/8.55 (~r(s(s(elem!1)), s(elem!1))),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[13235, 194, 485, 364, 2032])).
% 8.29/8.55 tff(13237,plain,
% 8.29/8.55 (b(s(s(elem!1)), s(elem!1))),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[1135, 13236, 285])).
% 8.29/8.55 tff(13238,plain,
% 8.29/8.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.55 inference(rewrite,[status(thm)],[])).
% 8.29/8.55 tff(13239,plain,
% 8.29/8.55 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(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(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.55 inference(rewrite,[status(thm)],[])).
% 8.29/8.55 tff(13240,plain,
% 8.29/8.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 8.29/8.55 inference(monotonicity,[status(thm)],[13239])).
% 8.29/8.55 tff(13241,plain,
% 8.29/8.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.55 inference(transitivity,[status(thm)],[13240, 13238])).
% 8.29/8.55 tff(13242,plain,
% 8.29/8.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.55 inference(quant_inst,[status(thm)],[])).
% 8.29/8.55 tff(13243,plain,
% 8.29/8.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 8.29/8.55 inference(modus_ponens,[status(thm)],[13242, 13241])).
% 8.29/8.55 tff(13244,plain,
% 8.29/8.55 ($false),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[13243, 391, 13237, 13229, 13215, 13207])).
% 8.29/8.55 tff(13245,plain,((~r(elem!1, s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.55 tff(13246,plain,
% 8.29/8.55 (~r(elem!1, s(s(s(s(z)))))),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[13245, 13191, 13199, 13197, 485, 13196, 13195])).
% 8.29/8.55 tff(13247,plain,
% 8.29/8.55 (b(elem!1, s(s(s(s(z)))))),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[781, 13246, 13194])).
% 8.29/8.55 tff(13248,plain,
% 8.29/8.55 (~b(s(s(s(s(z)))), z)),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[12445, 13247, 665, 133])).
% 8.29/8.55 tff(13249,plain,
% 8.29/8.55 (r(s(s(s(s(z)))), z)),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[87, 13248])).
% 8.29/8.55 tff(13250,plain,
% 8.29/8.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.55 inference(rewrite,[status(thm)],[])).
% 8.29/8.55 tff(13251,plain,
% 8.29/8.55 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.55 inference(rewrite,[status(thm)],[])).
% 8.29/8.55 tff(13252,plain,
% 8.29/8.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 8.29/8.55 inference(monotonicity,[status(thm)],[13251])).
% 8.29/8.55 tff(13253,plain,
% 8.29/8.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.55 inference(transitivity,[status(thm)],[13252, 13250])).
% 8.29/8.55 tff(13254,plain,
% 8.29/8.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.55 inference(quant_inst,[status(thm)],[])).
% 8.29/8.55 tff(13255,plain,
% 8.29/8.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 8.29/8.55 inference(modus_ponens,[status(thm)],[13254, 13253])).
% 8.29/8.55 tff(13256,plain,
% 8.29/8.55 (~r(s(elem!1), s(s(s(s(z)))))),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[13255, 194, 1628, 11981, 13249])).
% 8.29/8.55 tff(13257,plain,
% 8.29/8.55 (b(s(elem!1), s(s(s(s(z)))))),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[2142, 42, 13256, 13192])).
% 8.29/8.55 tff(13258,plain,
% 8.29/8.55 (~r(s(s(s(s(z)))), s(z))),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[11989, 194, 11981, 11977, 13249])).
% 8.29/8.55 tff(13259,plain,
% 8.29/8.55 (b(s(s(s(s(z)))), s(z))),
% 8.29/8.55 inference(unit_resolution,[status(thm)],[749, 13258])).
% 8.29/8.55 tff(13260,plain,
% 8.29/8.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.55 inference(rewrite,[status(thm)],[])).
% 8.29/8.55 tff(13261,plain,
% 8.29/8.55 (((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.55 inference(rewrite,[status(thm)],[])).
% 8.29/8.55 tff(13262,plain,
% 8.29/8.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 8.29/8.56 inference(monotonicity,[status(thm)],[13261])).
% 8.29/8.56 tff(13263,plain,
% 8.29/8.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.56 inference(transitivity,[status(thm)],[13262, 13260])).
% 8.29/8.56 tff(13264,plain,
% 8.29/8.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.29/8.56 inference(quant_inst,[status(thm)],[])).
% 8.29/8.56 tff(13265,plain,
% 8.29/8.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 8.29/8.56 inference(modus_ponens,[status(thm)],[13264, 13263])).
% 8.29/8.56 tff(13266,plain,
% 8.29/8.56 ($false),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13265, 391, 665, 644, 13259, 5469, 13257])).
% 8.29/8.56 tff(13267,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (~b(s(z), s(elem!1))) | (elem!1 = s(elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.56 tff(13268,plain,
% 8.29/8.56 (b(elem!1, s(s(s(elem!1))))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13267, 644, 665, 13133, 1628, 133, 485, 10682, 168, 13125, 437, 3843])).
% 8.29/8.56 tff(13269,plain,
% 8.29/8.56 (~b(s(s(s(elem!1))), z)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[10876, 13268, 665, 133])).
% 8.29/8.56 tff(13270,plain,
% 8.29/8.56 (r(s(s(s(elem!1))), z)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[377, 13269])).
% 8.29/8.56 tff(13271,plain,
% 8.29/8.56 (~r(s(s(s(elem!1))), s(z))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[12916, 194, 13270, 11981, 11977])).
% 8.29/8.56 tff(13272,plain,
% 8.29/8.56 (b(s(s(s(elem!1))), s(z))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[223, 13271])).
% 8.29/8.56 tff(13273,plain,
% 8.29/8.56 (~r(s(z), s(s(s(elem!1))))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[12911, 194, 13270, 11981, 11977])).
% 8.29/8.56 tff(13274,plain,
% 8.29/8.56 (b(s(z), s(s(s(elem!1))))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[247, 13273])).
% 8.29/8.56 tff(13275,plain,
% 8.29/8.56 ($false),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[4026, 13274, 13272, 644, 13268])).
% 8.29/8.56 tff(13276,plain,((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.56 tff(13277,plain,
% 8.29/8.56 (~b(s(z), elem!1)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13276, 11936, 133, 13111, 13120, 10682, 168, 13119, 3363, 118])).
% 8.29/8.56 tff(13278,plain,
% 8.29/8.56 (r(s(elem!1), z)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13110, 665, 121, 150, 133, 168, 10682, 2163])).
% 8.29/8.56 tff(13279,plain,
% 8.29/8.56 (~(s(elem!1) = elem!1)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13117, 13278, 2282])).
% 8.29/8.56 tff(13280,plain,
% 8.29/8.56 (r(s(elem!1), elem!1)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[2168, 13279, 2163])).
% 8.29/8.56 tff(13281,plain,
% 8.29/8.56 (~(elem!1 = s(elem!1))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[166, 13279])).
% 8.29/8.56 tff(13282,plain,
% 8.29/8.56 (~b(s(z), elem!1)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13276, 665, 133, 13278, 13280, 10682, 168, 13281, 3363, 121])).
% 8.29/8.56 tff(13283,plain,
% 8.29/8.56 (r(s(z), elem!1)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[632, 13282, 150])).
% 8.29/8.56 tff(13284,plain,
% 8.29/8.56 ($false),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[5221, 391, 133, 665, 590, 721])).
% 8.29/8.56 tff(13285,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.56 tff(13286,plain,
% 8.29/8.56 (~b(elem!1, s(z))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13285, 590, 665, 133])).
% 8.29/8.56 tff(13287,plain,
% 8.29/8.56 (r(elem!1, s(z))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[837, 13286, 173])).
% 8.29/8.56 tff(13288,plain,
% 8.29/8.56 (s(s(s(elem!1))) = s(elem!1)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[451, 9221])).
% 8.29/8.56 tff(13289,plain,
% 8.29/8.56 (s(s(s(elem!1))) = elem!1),
% 8.29/8.56 inference(transitivity,[status(thm)],[13288, 152])).
% 8.29/8.56 tff(13290,plain,
% 8.29/8.56 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 8.29/8.56 inference(monotonicity,[status(thm)],[13289])).
% 8.29/8.56 tff(13291,plain,
% 8.29/8.56 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 8.29/8.56 inference(symmetry,[status(thm)],[13290])).
% 8.29/8.56 tff(13292,plain,
% 8.29/8.56 ((~r(elem!1, z)) <=> (~r(s(s(s(elem!1))), z))),
% 8.29/8.56 inference(monotonicity,[status(thm)],[13291])).
% 8.29/8.56 tff(13293,plain,
% 8.29/8.56 (~r(s(s(s(elem!1))), z)),
% 8.29/8.56 inference(modus_ponens,[status(thm)],[2282, 13292])).
% 8.29/8.56 tff(13294,plain,
% 8.29/8.56 ($false),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[174, 13293])).
% 8.29/8.56 tff(13295,plain,((~(s(elem!1) = elem!1)) | (~r(s(s(s(elem!1))), z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 8.29/8.56 tff(13296,plain,
% 8.29/8.56 (~r(s(s(s(elem!1))), z)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13295, 152, 2282])).
% 8.29/8.56 tff(13297,plain,
% 8.29/8.56 (b(s(s(s(elem!1))), z)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[377, 13296])).
% 8.29/8.56 tff(13298,plain,
% 8.29/8.56 (~(s(s(z)) = elem!1)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[4584, 13288, 121])).
% 8.29/8.56 tff(13299,plain,
% 8.29/8.56 (elem!1 = s(s(z))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[11904, 13298, 665, 133, 590, 10682, 13297, 9221, 150, 168, 4028])).
% 8.29/8.56 tff(13300,plain,
% 8.29/8.56 (s(s(z)) = elem!1),
% 8.29/8.56 inference(modus_ponens,[status(thm)],[13299, 8492])).
% 8.29/8.56 tff(13301,plain,
% 8.29/8.56 ($false),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13298, 13300])).
% 8.29/8.56 tff(13302,plain,((~(s(elem!1) = elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1)))) | (s(z) = s(elem!1)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 8.29/8.56 tff(13303,plain,
% 8.29/8.56 (~(s(elem!1) = elem!1)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13302, 590, 133, 665, 10682, 150, 168, 4028, 121, 2282])).
% 8.29/8.56 tff(13304,plain,
% 8.29/8.56 (r(s(elem!1), elem!1)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[2168, 13303, 2163])).
% 8.29/8.56 tff(13305,plain,
% 8.29/8.56 (~r(s(elem!1), s(z))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[5339, 194, 13304, 5237, 13287])).
% 8.29/8.56 tff(13306,plain,
% 8.29/8.56 (b(s(elem!1), s(z))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[1915, 42, 13305, 11956])).
% 8.29/8.56 tff(13307,plain,
% 8.29/8.56 (~r(s(z), s(elem!1))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[6849, 194, 13304, 5237, 13287])).
% 8.29/8.56 tff(13308,plain,
% 8.29/8.56 (b(s(z), s(elem!1))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[602, 42, 121, 13307])).
% 8.29/8.56 tff(13309,plain,
% 8.29/8.56 (~b(s(s(s(s(z)))), z)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[5398, 2691, 665, 133, 590, 847, 1484])).
% 8.29/8.56 tff(13310,plain,
% 8.29/8.56 (r(s(s(s(s(z)))), z)),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[87, 13309])).
% 8.29/8.56 tff(13311,assumption,(s(s(s(s(s(s(z)))))) = s(elem!1)), introduced(assumption)).
% 8.29/8.56 tff(13312,plain,
% 8.29/8.56 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 8.29/8.56 inference(monotonicity,[status(thm)],[13311])).
% 8.29/8.56 tff(13313,plain,
% 8.29/8.56 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 8.29/8.56 inference(transitivity,[status(thm)],[5003, 13312, 108, 1422])).
% 8.29/8.56 tff(13314,plain,
% 8.29/8.56 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 8.29/8.56 inference(monotonicity,[status(thm)],[13313])).
% 8.29/8.56 tff(13315,plain,
% 8.29/8.56 (s(s(s(s(z)))) = s(s(elem!1))),
% 8.29/8.56 inference(transitivity,[status(thm)],[5006, 13314, 211])).
% 8.29/8.56 tff(13316,plain,
% 8.29/8.56 ($false),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[3695, 13315])).
% 8.29/8.56 tff(13317,plain,((~(s(s(s(s(s(s(z)))))) = s(elem!1))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.56 tff(13318,plain,
% 8.29/8.56 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13317, 5])).
% 8.29/8.56 tff(13319,plain,
% 8.29/8.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 8.29/8.56 inference(rewrite,[status(thm)],[])).
% 8.29/8.56 tff(13320,plain,
% 8.29/8.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 8.29/8.56 inference(quant_inst,[status(thm)],[])).
% 8.29/8.56 tff(13321,plain,
% 8.29/8.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 8.29/8.56 inference(modus_ponens,[status(thm)],[13320, 13319])).
% 8.29/8.56 tff(13322,plain,
% 8.29/8.56 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13321, 194, 485, 847, 2741])).
% 8.29/8.56 tff(13323,assumption,(~(s(s(s(s(s(s(z)))))) = s(elem!1))), introduced(assumption)).
% 8.29/8.56 tff(13324,plain,
% 8.29/8.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 8.29/8.56 inference(rewrite,[status(thm)],[])).
% 8.29/8.56 tff(13325,plain,
% 8.29/8.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 8.29/8.56 inference(quant_inst,[status(thm)],[])).
% 8.29/8.56 tff(13326,plain,
% 8.29/8.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 8.29/8.56 inference(modus_ponens,[status(thm)],[13325, 13324])).
% 8.29/8.56 tff(13327,plain,
% 8.29/8.56 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 8.29/8.56 inference(unit_resolution,[status(thm)],[13326, 42, 13323, 13322])).
% 8.29/8.56 tff(13328,plain,
% 8.29/8.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 8.29/8.56 inference(rewrite,[status(thm)],[])).
% 8.29/8.56 tff(13329,plain,
% 8.29/8.56 (((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 8.29/8.56 inference(rewrite,[status(thm)],[])).
% 8.29/8.56 tff(13330,plain,
% 8.29/8.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 8.29/8.56 inference(monotonicity,[status(thm)],[13329])).
% 8.29/8.56 tff(13331,plain,
% 8.29/8.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 8.29/8.57 inference(transitivity,[status(thm)],[13330, 13328])).
% 8.29/8.57 tff(13332,plain,
% 8.29/8.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 8.29/8.57 inference(quant_inst,[status(thm)],[])).
% 8.29/8.57 tff(13333,plain,
% 8.29/8.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 8.29/8.57 inference(modus_ponens,[status(thm)],[13332, 13331])).
% 8.29/8.57 tff(13334,plain,
% 8.29/8.57 ($false),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[13333, 391, 751, 5469, 11849, 13327])).
% 8.29/8.57 tff(13335,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.57 tff(13336,plain,
% 8.29/8.57 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[13335, 13318, 5469, 751, 1484, 847, 485])).
% 8.29/8.57 tff(13337,plain,
% 8.29/8.57 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[8073, 13336, 11641])).
% 8.29/8.57 tff(13338,plain,
% 8.29/8.57 (~b(s(s(s(s(z)))), elem!1)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[8068, 13337, 133, 665, 13310])).
% 8.29/8.57 tff(13339,plain,
% 8.29/8.57 (r(s(s(s(s(z)))), elem!1)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[762, 13338, 2691])).
% 8.29/8.57 tff(13340,plain,
% 8.29/8.57 (~r(s(elem!1), s(s(s(s(z)))))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[4341, 194, 485, 847, 13339])).
% 8.29/8.57 tff(13341,plain,
% 8.29/8.57 (b(s(elem!1), s(s(s(s(z)))))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[2142, 42, 13340, 3122])).
% 8.29/8.57 tff(13342,plain,
% 8.29/8.57 (~r(s(s(s(s(z)))), s(z))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[7012, 194, 1484, 847, 13339])).
% 8.29/8.57 tff(13343,plain,
% 8.29/8.57 (b(s(s(s(s(z)))), s(z))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[749, 13342])).
% 8.29/8.57 tff(13344,plain,
% 8.29/8.57 ($false),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[4570, 391, 751, 13343, 5469, 13341])).
% 8.29/8.57 tff(13345,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.57 tff(13346,plain,
% 8.29/8.57 (~(s(s(s(elem!1))) = elem!1)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[13345, 13308, 13306, 13304, 13287, 5237, 133, 665, 590])).
% 8.29/8.57 tff(13347,plain,
% 8.29/8.57 (~r(s(z), s(s(s(elem!1))))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[5715, 13346, 168, 4028, 5237])).
% 8.29/8.57 tff(13348,plain,
% 8.29/8.57 (b(s(z), s(s(s(elem!1))))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[247, 13347])).
% 8.29/8.57 tff(13349,plain,
% 8.29/8.57 (~b(s(s(s(elem!1))), z)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[11303, 13348, 10682, 590])).
% 8.29/8.57 tff(13350,plain,
% 8.29/8.57 (s(s(elem!1)) = elem!1),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[12783, 13349, 150, 590, 121, 133, 168, 665])).
% 8.29/8.57 tff(13351,plain,
% 8.29/8.57 (s(s(s(elem!1))) = s(elem!1)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[451, 13350])).
% 8.29/8.57 tff(13352,plain,
% 8.29/8.57 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 8.29/8.57 inference(monotonicity,[status(thm)],[13351])).
% 8.29/8.57 tff(13353,plain,
% 8.29/8.57 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 8.29/8.57 inference(symmetry,[status(thm)],[13352])).
% 8.29/8.57 tff(13354,plain,
% 8.29/8.57 (~b(z, s(elem!1))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[7240, 13348, 590, 13306, 13308])).
% 8.29/8.57 tff(13355,plain,
% 8.29/8.57 (r(z, s(elem!1))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[566, 13354])).
% 8.29/8.57 tff(13356,plain,
% 8.29/8.57 (r(z, s(s(s(elem!1))))),
% 8.29/8.57 inference(modus_ponens,[status(thm)],[13355, 13353])).
% 8.29/8.57 tff(13357,plain,
% 8.29/8.57 (~(elem!1 = s(elem!1))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[166, 13303])).
% 8.29/8.57 tff(13358,plain,
% 8.29/8.57 (~r(z, s(s(s(elem!1))))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[5611, 13351, 13278, 4028, 590, 665, 121, 5237, 13304, 133, 3363, 13287, 13308, 13357, 13306])).
% 8.29/8.57 tff(13359,plain,
% 8.29/8.57 ($false),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[13358, 13356])).
% 8.29/8.57 tff(13360,plain,((~b(s(z), z)) | b(elem!1, s(s(s(elem!1)))) | (~b(elem!1, z)) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (s(z) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | b(s(elem!1), elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 8.29/8.57 tff(13361,plain,
% 8.29/8.57 (~b(s(z), z)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[13360, 4028, 665, 121, 133, 150, 168, 10682, 2163, 2282])).
% 8.29/8.57 tff(13362,plain,
% 8.29/8.57 (r(s(z), z)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[180, 13361])).
% 8.29/8.57 tff(13363,plain,
% 8.29/8.57 (~r(s(s(s(elem!1))), s(elem!1))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[13054, 127, 485, 4028, 168])).
% 8.29/8.57 tff(13364,plain,
% 8.29/8.57 (~r(s(elem!1), s(z))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[5465, 194, 485, 4030, 1484])).
% 8.29/8.57 tff(13365,plain,
% 8.29/8.57 (b(s(elem!1), s(z))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[1915, 42, 13364, 11956])).
% 8.29/8.57 tff(13366,plain,
% 8.29/8.57 (~r(s(z), s(elem!1))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[5446, 194, 485, 4030, 1484])).
% 8.29/8.57 tff(13367,plain,
% 8.29/8.57 (b(s(z), s(elem!1))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[602, 42, 121, 13366])).
% 8.29/8.57 tff(13368,plain,
% 8.29/8.57 (~r(s(s(s(elem!1))), s(z))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[5677, 194, 4031, 4030, 1484])).
% 8.29/8.57 tff(13369,plain,
% 8.29/8.57 (b(s(s(s(elem!1))), s(z))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[223, 13368])).
% 8.29/8.57 tff(13370,plain,
% 8.29/8.57 (~b(s(s(s(elem!1))), s(elem!1))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[2592, 391, 13369, 13367, 13365])).
% 8.29/8.57 tff(13371,plain,
% 8.29/8.57 (s(s(s(elem!1))) = s(elem!1)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[588, 13370, 13363])).
% 8.29/8.57 tff(13372,plain,
% 8.29/8.57 (~(s(s(s(s(z)))) = elem!1)),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[717, 13371])).
% 8.29/8.57 tff(13373,plain,
% 8.29/8.57 (s(s(elem!1)) = elem!1),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[6159, 13371])).
% 8.29/8.57 tff(13374,plain,
% 8.29/8.57 (r(s(z), s(s(elem!1)))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[4847, 13373, 1484])).
% 8.29/8.57 tff(13375,plain,
% 8.29/8.57 (~r(s(z), s(s(s(elem!1))))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[5715, 127, 168, 1484, 4028])).
% 8.29/8.57 tff(13376,plain,
% 8.29/8.57 (b(s(z), s(s(s(elem!1))))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[247, 13375])).
% 8.29/8.57 tff(13377,plain,
% 8.29/8.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 8.29/8.57 inference(rewrite,[status(thm)],[])).
% 8.29/8.57 tff(13378,plain,
% 8.29/8.57 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 8.29/8.57 inference(rewrite,[status(thm)],[])).
% 8.29/8.57 tff(13379,plain,
% 8.29/8.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 8.29/8.57 inference(monotonicity,[status(thm)],[13378])).
% 8.29/8.57 tff(13380,plain,
% 8.29/8.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 8.29/8.57 inference(transitivity,[status(thm)],[13379, 13377])).
% 8.29/8.57 tff(13381,plain,
% 8.29/8.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 8.29/8.57 inference(quant_inst,[status(thm)],[])).
% 8.29/8.57 tff(13382,plain,
% 8.29/8.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 8.29/8.57 inference(modus_ponens,[status(thm)],[13381, 13380])).
% 8.29/8.57 tff(13383,plain,
% 8.29/8.57 (~b(z, s(z))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[13382, 391, 10682, 13376, 13369])).
% 8.29/8.57 tff(13384,plain,
% 8.29/8.57 (r(z, s(z))),
% 8.29/8.57 inference(unit_resolution,[status(thm)],[678, 13383])).
% 8.29/8.57 tff(13385,plain,
% 8.29/8.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 8.29/8.57 inference(rewrite,[status(thm)],[])).
% 8.29/8.57 tff(13386,plain,
% 8.29/8.57 (((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 8.29/8.57 inference(rewrite,[status(thm)],[])).
% 8.29/8.57 tff(13387,plain,
% 8.29/8.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 8.29/8.57 inference(monotonicity,[status(thm)],[13386])).
% 8.29/8.57 tff(13388,plain,
% 8.29/8.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 8.29/8.57 inference(transitivity,[status(thm)],[13387, 13385])).
% 8.29/8.57 tff(13389,plain,
% 8.29/8.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 8.29/8.57 inference(quant_inst,[status(thm)],[])).
% 8.29/8.57 tff(13390,plain,
% 8.29/8.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 8.29/8.57 inference(modus_ponens,[status(thm)],[13389, 13388])).
% 8.29/8.58 tff(13391,plain,
% 8.29/8.58 (~b(s(elem!1), s(s(s(elem!1))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[13390, 391, 13369, 13367, 13365])).
% 8.29/8.58 tff(13392,plain,
% 8.29/8.58 (~r(s(elem!1), s(s(s(elem!1))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[12753, 194, 485, 4031, 4030])).
% 8.29/8.58 tff(13393,plain,
% 8.29/8.58 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[579, 42, 13392])).
% 8.29/8.58 tff(13394,plain,
% 8.29/8.58 (s(elem!1) = s(s(s(elem!1)))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[13393, 13391])).
% 8.29/8.58 tff(13395,plain,
% 8.29/8.58 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 8.29/8.58 inference(monotonicity,[status(thm)],[13394])).
% 8.29/8.58 tff(13396,plain,
% 8.29/8.58 (r(s(s(s(elem!1))), z)),
% 8.29/8.58 inference(modus_ponens,[status(thm)],[1628, 13395])).
% 8.29/8.58 tff(13397,plain,
% 8.29/8.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.29/8.58 inference(rewrite,[status(thm)],[])).
% 8.29/8.58 tff(13398,plain,
% 8.29/8.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.29/8.58 inference(quant_inst,[status(thm)],[])).
% 8.29/8.58 tff(13399,plain,
% 8.29/8.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 8.29/8.58 inference(modus_ponens,[status(thm)],[13398, 13397])).
% 8.29/8.58 tff(13400,plain,
% 8.29/8.58 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[13399, 194, 174, 722, 10874])).
% 8.29/8.58 tff(13401,plain,
% 8.29/8.58 (~r(s(s(s(s(z)))), s(z))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[5500, 10874, 722, 4832])).
% 8.29/8.58 tff(13402,plain,
% 8.29/8.58 (b(s(s(s(s(z)))), s(z))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[749, 13401])).
% 8.29/8.58 tff(13403,plain,
% 8.29/8.58 (~r(s(z), s(s(s(s(z)))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[10558, 10874, 182, 722])).
% 8.29/8.58 tff(13404,plain,
% 8.29/8.58 (b(s(z), s(s(s(s(z)))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[1230, 13403])).
% 8.29/8.58 tff(13405,plain,
% 8.29/8.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.29/8.58 inference(rewrite,[status(thm)],[])).
% 8.29/8.58 tff(13406,plain,
% 8.29/8.58 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.29/8.58 inference(rewrite,[status(thm)],[])).
% 8.29/8.58 tff(13407,plain,
% 8.29/8.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 8.29/8.58 inference(monotonicity,[status(thm)],[13406])).
% 8.29/8.58 tff(13408,plain,
% 8.29/8.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.29/8.58 inference(transitivity,[status(thm)],[13407, 13405])).
% 8.29/8.58 tff(13409,plain,
% 8.29/8.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.29/8.58 inference(quant_inst,[status(thm)],[])).
% 8.29/8.58 tff(13410,plain,
% 8.29/8.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 8.29/8.58 inference(modus_ponens,[status(thm)],[13409, 13408])).
% 8.29/8.58 tff(13411,plain,
% 8.29/8.58 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[13410, 391, 1526, 1652, 13404, 13402])).
% 8.29/8.58 tff(13412,plain,
% 8.29/8.58 ($false),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 13411, 13400])).
% 8.29/8.58 tff(13413,plain,((~b(s(s(s(s(z)))), elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.58 tff(13414,plain,
% 8.29/8.58 (~b(s(s(s(s(z)))), elem!1)),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[13413, 13396, 3843, 13384, 13369, 13374, 182, 133, 665])).
% 8.29/8.58 tff(13415,plain,
% 8.29/8.58 (r(s(s(s(s(z)))), elem!1)),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[762, 13414, 13372])).
% 8.29/8.58 tff(13416,plain,
% 8.29/8.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.29/8.58 inference(rewrite,[status(thm)],[])).
% 8.29/8.58 tff(13417,plain,
% 8.29/8.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.29/8.58 inference(quant_inst,[status(thm)],[])).
% 8.29/8.58 tff(13418,plain,
% 8.29/8.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 8.29/8.58 inference(modus_ponens,[status(thm)],[13417, 13416])).
% 8.29/8.58 tff(13419,plain,
% 8.29/8.58 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[13418, 194, 4031, 4030, 13415])).
% 8.29/8.58 tff(13420,plain,
% 8.29/8.58 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 13419])).
% 8.29/8.58 tff(13421,plain,
% 8.29/8.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 8.29/8.58 inference(rewrite,[status(thm)],[])).
% 8.29/8.58 tff(13422,plain,
% 8.29/8.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 8.29/8.58 inference(quant_inst,[status(thm)],[])).
% 8.29/8.58 tff(13423,plain,
% 8.29/8.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 8.29/8.58 inference(modus_ponens,[status(thm)],[13422, 13421])).
% 8.29/8.58 tff(13424,plain,
% 8.29/8.58 (~r(s(s(s(s(z)))), s(z))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[13423, 194, 4030, 1484, 13415])).
% 8.29/8.58 tff(13425,plain,
% 8.29/8.58 (b(s(s(s(s(z)))), s(z))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[749, 13424])).
% 8.29/8.58 tff(13426,plain,
% 8.29/8.58 ($false),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[3967, 391, 13376, 13369, 13425, 13420])).
% 8.29/8.58 tff(13427,plain,((s(s(s(elem!1))) = elem!1) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~r(s(elem!1), elem!1)) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.29/8.58 tff(13428,plain,
% 8.29/8.58 (s(s(s(elem!1))) = elem!1),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[13427, 13362, 13283, 3363, 133, 665, 13278, 10682, 121, 13280, 4028, 168])).
% 8.29/8.58 tff(13429,plain,
% 8.29/8.58 ((s(s(s(elem!1))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 8.29/8.58 inference(monotonicity,[status(thm)],[13428])).
% 8.29/8.58 tff(13430,plain,
% 8.29/8.58 ((elem!1 = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 8.29/8.58 inference(symmetry,[status(thm)],[13429])).
% 8.29/8.58 tff(13431,plain,
% 8.29/8.58 ((~(elem!1 = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 8.29/8.58 inference(monotonicity,[status(thm)],[13430])).
% 8.29/8.58 tff(13432,plain,
% 8.29/8.58 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.29/8.58 inference(modus_ponens,[status(thm)],[13281, 13431])).
% 8.29/8.58 tff(13433,plain,
% 8.29/8.58 (~(s(s(elem!1)) = elem!1)),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[451, 13432])).
% 8.29/8.58 tff(13434,plain,
% 8.29/8.58 (~(s(s(s(s(z)))) = elem!1)),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[1436, 13428])).
% 8.29/8.58 tff(13435,plain,
% 8.29/8.58 (~r(s(z), s(s(s(s(z)))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[10234, 194, 182, 10874, 10867])).
% 8.29/8.58 tff(13436,plain,
% 8.29/8.58 (b(s(z), s(s(s(s(z)))))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[1230, 13435])).
% 8.29/8.58 tff(13437,plain,
% 8.29/8.58 (~r(s(s(s(s(z)))), s(z))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[10242, 194, 182, 10874, 10867])).
% 8.29/8.58 tff(13438,plain,
% 8.29/8.58 (b(s(s(s(s(z)))), s(z))),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[749, 13437])).
% 8.29/8.58 tff(13439,plain,
% 8.29/8.58 (~r(s(s(z)), z)),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[10261, 10874, 182, 10867])).
% 8.29/8.58 tff(13440,plain,
% 8.29/8.58 (b(s(s(z)), z)),
% 8.29/8.58 inference(unit_resolution,[status(thm)],[1211, 13439])).
% 8.29/8.58 tff(13441,plain,
% 8.29/8.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 8.29/8.58 inference(rewrite,[status(thm)],[])).
% 8.29/8.58 tff(13442,plain,
% 8.29/8.58 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 8.29/8.58 inference(rewrite,[status(thm)],[])).
% 8.29/8.58 tff(13443,plain,
% 8.29/8.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 8.29/8.58 inference(monotonicity,[status(thm)],[13442])).
% 8.29/8.58 tff(13444,plain,
% 8.29/8.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 8.29/8.59 inference(transitivity,[status(thm)],[13443, 13441])).
% 8.29/8.59 tff(13445,plain,
% 8.29/8.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))),
% 8.29/8.59 inference(quant_inst,[status(thm)],[])).
% 8.29/8.59 tff(13446,plain,
% 8.29/8.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 8.29/8.59 inference(modus_ponens,[status(thm)],[13445, 13444])).
% 8.29/8.59 tff(13447,plain,
% 8.29/8.59 ($false),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[13446, 391, 133, 665, 1235, 3369])).
% 8.29/8.59 tff(13448,plain,((~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.59 tff(13449,plain,
% 8.29/8.59 (~b(elem!1, s(s(z)))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[13448, 13440, 665, 133])).
% 8.29/8.59 tff(13450,plain,
% 8.29/8.59 (r(elem!1, s(s(z)))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[3394, 13449, 3694])).
% 8.29/8.59 tff(13451,plain,
% 8.29/8.59 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[8073, 12596, 11641])).
% 8.29/8.59 tff(13452,plain,
% 8.29/8.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 8.29/8.59 inference(rewrite,[status(thm)],[])).
% 8.29/8.59 tff(13453,plain,
% 8.29/8.59 (((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 8.29/8.59 inference(rewrite,[status(thm)],[])).
% 8.29/8.59 tff(13454,plain,
% 8.29/8.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(z))))))))),
% 8.29/8.59 inference(monotonicity,[status(thm)],[13453])).
% 8.29/8.59 tff(13455,plain,
% 8.29/8.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 8.29/8.59 inference(transitivity,[status(thm)],[13454, 13452])).
% 8.29/8.59 tff(13456,plain,
% 8.29/8.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 8.29/8.59 inference(quant_inst,[status(thm)],[])).
% 8.29/8.59 tff(13457,plain,
% 8.29/8.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(s(s(s(z))))))),
% 8.29/8.59 inference(modus_ponens,[status(thm)],[13456, 13455])).
% 8.29/8.59 tff(13458,plain,
% 8.29/8.59 (~r(s(z), s(elem!1))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[13457, 194, 1628, 182, 10867])).
% 8.29/8.59 tff(13459,plain,
% 8.29/8.59 (b(s(z), s(elem!1))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[602, 42, 121, 13458])).
% 8.29/8.59 tff(13460,plain,
% 8.29/8.59 (~r(elem!1, s(z))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[13335, 13459, 485, 1484, 13318, 5469, 13451])).
% 8.29/8.59 tff(13461,plain,
% 8.29/8.59 (b(elem!1, s(z))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[837, 13460, 173])).
% 8.29/8.59 tff(13462,plain,
% 8.29/8.59 (~b(s(z), s(s(z)))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[2447, 13461, 1652, 13440, 13438])).
% 8.29/8.59 tff(13463,plain,
% 8.29/8.59 (r(s(z), s(s(z)))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[1788, 13462])).
% 8.29/8.59 tff(13464,plain,
% 8.29/8.59 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[1775, 13463, 150, 1652, 13438, 13450])).
% 8.29/8.59 tff(13465,plain,
% 8.29/8.59 (b(s(s(z)), s(s(s(s(z)))))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[3652, 13464])).
% 8.29/8.59 tff(13466,plain,
% 8.29/8.59 (r(s(s(s(elem!1))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 8.29/8.59 inference(monotonicity,[status(thm)],[5])).
% 8.29/8.59 tff(13467,plain,
% 8.29/8.59 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 8.29/8.59 inference(symmetry,[status(thm)],[13466])).
% 8.29/8.59 tff(13468,plain,
% 8.29/8.59 (r(s(s(s(elem!1))), s(s(z)))),
% 8.29/8.59 inference(modus_ponens,[status(thm)],[13450, 13467])).
% 8.29/8.59 tff(13469,plain,
% 8.29/8.59 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 8.29/8.59 inference(symmetry,[status(thm)],[3697])).
% 8.29/8.59 tff(13470,plain,
% 8.29/8.59 (r(s(z), s(s(s(elem!1))))),
% 8.29/8.59 inference(modus_ponens,[status(thm)],[1484, 13469])).
% 8.29/8.59 tff(13471,plain,
% 8.29/8.59 (~r(s(s(z)), s(z))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[11551, 13463, 13470, 13468])).
% 8.29/8.59 tff(13472,plain,
% 8.29/8.59 (b(s(s(z)), s(z))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[3778, 13471])).
% 8.29/8.59 tff(13473,plain,
% 8.29/8.59 ($false),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[5108, 13472, 13465, 13438, 13436])).
% 8.29/8.59 tff(13474,plain,((~b(s(s(s(s(z)))), elem!1)) | (s(z) = elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~r(s(z), z)) | (s(z) = s(elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.59 tff(13475,plain,
% 8.29/8.59 (~b(s(elem!1), s(z))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[13474, 1652, 485, 1484, 150, 182, 121, 5, 665, 133, 1628])).
% 8.29/8.59 tff(13476,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 8.29/8.59 tff(13477,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 8.29/8.59 tff(13478,plain,
% 8.29/8.59 ($false),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[1915, 42, 13477, 13476, 11964])).
% 8.29/8.59 tff(13479,plain,(r(s(elem!1), s(z)) | b(s(elem!1), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.59 tff(13480,plain,
% 8.29/8.59 (r(s(elem!1), s(z))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[13479, 13475, 11956])).
% 8.29/8.59 tff(13481,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 8.29/8.59 tff(13482,plain,
% 8.29/8.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 8.29/8.59 inference(rewrite,[status(thm)],[])).
% 8.29/8.59 tff(13483,plain,
% 8.29/8.59 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 8.29/8.59 inference(rewrite,[status(thm)],[])).
% 8.29/8.59 tff(13484,plain,
% 8.29/8.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 8.29/8.59 inference(monotonicity,[status(thm)],[13483])).
% 8.29/8.59 tff(13485,plain,
% 8.29/8.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 8.29/8.59 inference(transitivity,[status(thm)],[13484, 13482])).
% 8.29/8.59 tff(13486,plain,
% 8.29/8.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 8.29/8.59 inference(quant_inst,[status(thm)],[])).
% 8.29/8.59 tff(13487,plain,
% 8.29/8.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(s(s(z))))))),
% 8.29/8.59 inference(modus_ponens,[status(thm)],[13486, 13485])).
% 8.29/8.59 tff(13488,plain,
% 8.29/8.59 ($false),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[13487, 194, 1628, 182, 719, 13481])).
% 8.29/8.59 tff(13489,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.59 tff(13490,plain,
% 8.29/8.59 ($false),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[13489, 13480, 10867, 182, 1628])).
% 8.29/8.59 tff(13491,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (s(z) = elem!1) | (s(z) = s(elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.29/8.59 tff(13492,plain,
% 8.29/8.59 (~b(s(s(s(s(z)))), elem!1)),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[13491, 13362, 13278, 13280, 13283, 150, 121, 13428, 665, 133])).
% 8.29/8.59 tff(13493,plain,
% 8.29/8.59 (r(s(s(s(s(z)))), elem!1)),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[762, 13492, 13434])).
% 8.29/8.59 tff(13494,plain,
% 8.29/8.59 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[2686, 13432])).
% 8.29/8.59 tff(13495,plain,
% 8.29/8.59 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[2711, 13494])).
% 8.29/8.59 tff(13496,plain,
% 8.29/8.59 (~(s(s(elem!1)) = s(elem!1))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[2279, 13432])).
% 8.29/8.59 tff(13497,plain,
% 8.29/8.59 (~(elem!1 = s(s(s(s(z)))))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[769, 13434])).
% 8.29/8.59 tff(13498,plain,
% 8.29/8.59 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 8.29/8.59 inference(monotonicity,[status(thm)],[13428])).
% 8.29/8.59 tff(13499,plain,
% 8.29/8.59 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 8.29/8.59 inference(transitivity,[status(thm)],[13498, 698])).
% 8.29/8.59 tff(13500,plain,
% 8.29/8.59 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 8.29/8.59 inference(monotonicity,[status(thm)],[13499])).
% 8.29/8.59 tff(13501,plain,
% 8.29/8.59 (~(elem!1 = s(s(z)))),
% 8.29/8.59 inference(modus_ponens,[status(thm)],[1397, 13500])).
% 8.29/8.59 tff(13502,plain,
% 8.29/8.59 (elem!1 = s(s(s(elem!1)))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[8, 13428])).
% 8.29/8.59 tff(13503,plain,
% 8.29/8.59 (b(s(s(s(elem!1))), z)),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[9553, 13502, 665])).
% 8.29/8.59 tff(13504,plain,
% 8.29/8.59 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 8.29/8.59 inference(monotonicity,[status(thm)],[13428])).
% 8.29/8.59 tff(13505,plain,
% 8.29/8.59 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 8.29/8.59 inference(symmetry,[status(thm)],[13504])).
% 8.29/8.59 tff(13506,plain,
% 8.29/8.59 (r(s(z), s(s(s(elem!1))))),
% 8.29/8.59 inference(modus_ponens,[status(thm)],[13283, 13505])).
% 8.29/8.59 tff(13507,plain,
% 8.29/8.59 (b(s(s(s(elem!1))), z)),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[9553, 3807, 665])).
% 8.29/8.59 tff(13508,plain,
% 8.29/8.59 (~r(z, s(s(s(s(z)))))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[13489, 13481, 182, 1628])).
% 8.29/8.59 tff(13509,plain,
% 8.29/8.59 (b(z, s(s(s(s(z)))))),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[800, 13508])).
% 8.29/8.59 tff(13510,plain,
% 8.29/8.59 (~b(s(s(s(s(z)))), elem!1)),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[10865, 13509, 665, 133])).
% 8.29/8.59 tff(13511,plain,
% 8.29/8.59 (r(s(s(s(s(z)))), elem!1)),
% 8.29/8.59 inference(unit_resolution,[status(thm)],[762, 13510, 720])).
% 8.29/8.59 tff(13512,plain,
% 8.29/8.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 8.29/8.59 inference(rewrite,[status(thm)],[])).
% 8.29/8.59 tff(13513,plain,
% 8.39/8.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 8.39/8.60 inference(quant_inst,[status(thm)],[])).
% 8.39/8.60 tff(13514,plain,
% 8.39/8.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 8.39/8.60 inference(modus_ponens,[status(thm)],[13513, 13512])).
% 8.39/8.60 tff(13515,plain,
% 8.39/8.60 (~r(s(s(s(s(z)))), s(elem!1))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[13514, 194, 1484, 723, 13481])).
% 8.39/8.60 tff(13516,plain,
% 8.39/8.60 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[2136, 42, 13515])).
% 8.39/8.60 tff(13517,plain,
% 8.39/8.60 (b(s(s(s(s(z)))), s(elem!1))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[13516, 2126])).
% 8.39/8.60 tff(13518,plain,
% 8.39/8.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.60 inference(rewrite,[status(thm)],[])).
% 8.39/8.60 tff(13519,plain,
% 8.39/8.60 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.60 inference(rewrite,[status(thm)],[])).
% 8.39/8.60 tff(13520,plain,
% 8.39/8.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 8.39/8.60 inference(monotonicity,[status(thm)],[13519])).
% 8.39/8.60 tff(13521,plain,
% 8.39/8.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.60 inference(transitivity,[status(thm)],[13520, 13518])).
% 8.39/8.60 tff(13522,plain,
% 8.39/8.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.60 inference(quant_inst,[status(thm)],[])).
% 8.39/8.60 tff(13523,plain,
% 8.39/8.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 8.39/8.60 inference(modus_ponens,[status(thm)],[13522, 13521])).
% 8.39/8.60 tff(13524,plain,
% 8.39/8.60 (~r(s(elem!1), s(s(s(s(z)))))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[13523, 194, 1484, 723, 13481])).
% 8.39/8.60 tff(13525,plain,
% 8.39/8.60 (b(s(elem!1), s(s(s(s(z)))))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[2142, 42, 13524, 2121])).
% 8.39/8.60 tff(13526,plain,
% 8.39/8.60 (~r(elem!1, s(s(s(s(z)))))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[9103, 723, 1484, 2112])).
% 8.39/8.60 tff(13527,plain,
% 8.39/8.60 (b(elem!1, s(s(s(s(z)))))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[781, 13526, 8922])).
% 8.39/8.60 tff(13528,plain,
% 8.39/8.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.60 inference(rewrite,[status(thm)],[])).
% 8.39/8.60 tff(13529,plain,
% 8.39/8.60 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.60 inference(rewrite,[status(thm)],[])).
% 8.39/8.60 tff(13530,plain,
% 8.39/8.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 8.39/8.60 inference(monotonicity,[status(thm)],[13529])).
% 8.39/8.60 tff(13531,plain,
% 8.39/8.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.60 inference(transitivity,[status(thm)],[13530, 13528])).
% 8.39/8.60 tff(13532,plain,
% 8.39/8.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 8.39/8.60 inference(quant_inst,[status(thm)],[])).
% 8.39/8.60 tff(13533,plain,
% 8.39/8.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 8.39/8.60 inference(modus_ponens,[status(thm)],[13532, 13531])).
% 8.39/8.60 tff(13534,plain,
% 8.39/8.60 ($false),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[13533, 391, 133, 13527, 1686, 13525, 13517])).
% 8.39/8.60 tff(13535,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.60 tff(13536,plain,
% 8.39/8.60 (~r(s(s(s(s(z)))), s(z))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[13535, 13509, 133, 2121, 1484, 13481, 770, 13511])).
% 8.39/8.60 tff(13537,plain,
% 8.39/8.60 (b(s(s(s(s(z)))), s(z))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[749, 13536])).
% 8.39/8.60 tff(13538,plain,
% 8.39/8.60 (~b(s(z), s(s(s(s(z)))))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[10478, 13537, 664, 13509])).
% 8.39/8.60 tff(13539,plain,
% 8.39/8.60 (r(s(z), s(s(s(s(z)))))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[1230, 13538])).
% 8.39/8.60 tff(13540,plain,
% 8.39/8.60 (~r(elem!1, s(z))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[5396, 13539, 1484, 13511])).
% 8.39/8.60 tff(13541,plain,
% 8.39/8.60 (b(elem!1, s(z))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[837, 13540, 831])).
% 8.39/8.60 tff(13542,plain,
% 8.39/8.60 (~r(s(z), s(s(s(s(z)))))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[12394, 90, 3843, 182, 380, 232, 2112])).
% 8.39/8.60 tff(13543,plain,
% 8.39/8.60 (~b(s(z), s(s(s(s(z)))))),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[6914, 90, 664, 1686, 133])).
% 8.39/8.60 tff(13544,plain,
% 8.39/8.60 ($false),
% 8.39/8.60 inference(unit_resolution,[status(thm)],[1230, 13543, 13542])).
% 8.39/8.60 tff(13545,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.61 tff(13546,plain,
% 8.39/8.61 (~b(s(s(s(s(z)))), z)),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[13545, 13509, 664, 133, 3843, 182, 380, 232, 13511])).
% 8.39/8.61 tff(13547,plain,
% 8.39/8.61 (r(s(s(s(s(z)))), z)),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[87, 13546])).
% 8.39/8.61 tff(13548,plain,
% 8.39/8.61 (~r(elem!1, s(s(z)))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[11485, 13539, 1484, 13511])).
% 8.39/8.61 tff(13549,plain,
% 8.39/8.61 (b(elem!1, s(s(z)))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[3394, 13548, 1405])).
% 8.39/8.61 tff(13550,plain,
% 8.39/8.61 (~b(s(s(z)), z)),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[13448, 13549, 665, 133])).
% 8.39/8.61 tff(13551,plain,
% 8.39/8.61 (r(s(s(z)), z)),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[1211, 13550])).
% 8.39/8.61 tff(13552,plain,
% 8.39/8.61 (~r(elem!1, s(s(s(s(z)))))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[12404, 13539, 1484, 13547])).
% 8.39/8.61 tff(13553,plain,
% 8.39/8.61 (b(elem!1, s(s(s(s(z)))))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[781, 13552, 770])).
% 8.39/8.61 tff(13554,plain,
% 8.39/8.61 (~b(s(s(s(s(z)))), s(s(z)))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[11498, 3823, 2064, 1759, 3369])).
% 8.39/8.61 tff(13555,plain,
% 8.39/8.61 (r(s(s(s(s(z)))), s(s(z)))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[1714, 13554])).
% 8.39/8.61 tff(13556,plain,
% 8.39/8.61 (~r(s(z), s(s(z)))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[11508, 13555, 1216, 3557])).
% 8.39/8.61 tff(13557,plain,
% 8.39/8.61 (b(s(z), s(s(z)))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[1788, 13556])).
% 8.39/8.61 tff(13558,plain,
% 8.39/8.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 8.39/8.61 inference(rewrite,[status(thm)],[])).
% 8.39/8.61 tff(13559,plain,
% 8.39/8.61 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 8.39/8.61 inference(rewrite,[status(thm)],[])).
% 8.39/8.61 tff(13560,plain,
% 8.39/8.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 8.39/8.61 inference(monotonicity,[status(thm)],[13559])).
% 8.39/8.61 tff(13561,plain,
% 8.39/8.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 8.39/8.61 inference(transitivity,[status(thm)],[13560, 13558])).
% 8.39/8.61 tff(13562,plain,
% 8.39/8.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 8.39/8.61 inference(quant_inst,[status(thm)],[])).
% 8.39/8.61 tff(13563,plain,
% 8.39/8.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 8.39/8.61 inference(modus_ponens,[status(thm)],[13562, 13561])).
% 8.39/8.61 tff(13564,plain,
% 8.39/8.61 ($false),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[13563, 391, 3823, 2064, 3369, 1759, 13557])).
% 8.39/8.61 tff(13565,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.61 tff(13566,plain,
% 8.39/8.61 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[13565, 13553, 13549, 13537, 13539, 13551])).
% 8.39/8.61 tff(13567,plain,
% 8.39/8.61 (r(s(s(z)), s(s(s(s(z)))))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[3652, 13566])).
% 8.39/8.61 tff(13568,plain,
% 8.39/8.61 (~r(s(s(z)), s(z))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[5567, 13567, 13539, 13547])).
% 8.39/8.61 tff(13569,plain,
% 8.39/8.61 (b(s(s(z)), s(z))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[3778, 13568])).
% 8.39/8.61 tff(13570,plain,
% 8.39/8.61 (~r(s(z), s(s(z)))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[11590, 194, 13567, 13547, 13539])).
% 8.39/8.61 tff(13571,plain,
% 8.39/8.61 (b(s(z), s(s(z)))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[1788, 13570])).
% 8.39/8.61 tff(13572,plain,
% 8.39/8.61 ($false),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[11599, 391, 13549, 13571, 13569, 13541])).
% 8.39/8.61 tff(13573,plain,((~r(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (elem!1 = s(s(z))) | (elem!1 = s(z)) | (~r(s(z), elem!1)) | (~b(z, s(z))) | (s(elem!1) = s(s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.61 tff(13574,plain,
% 8.39/8.61 (~r(s(elem!1), s(z))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[13573, 664, 133, 3694, 173, 1484, 665, 3122, 3363, 182, 13507, 13470, 2691, 1628])).
% 8.39/8.61 tff(13575,plain,
% 8.39/8.61 (b(s(elem!1), s(z))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[13479, 13574, 11956])).
% 8.39/8.61 tff(13576,plain,
% 8.39/8.61 (~b(s(s(s(s(z)))), elem!1)),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[13474, 13575, 485, 1484, 150, 182, 121, 5, 665, 133, 1628])).
% 8.39/8.61 tff(13577,plain,
% 8.39/8.61 (r(s(s(s(s(z)))), elem!1)),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[762, 13576, 2691])).
% 8.39/8.61 tff(13578,plain,
% 8.39/8.61 (~b(s(s(z)), z)),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[13448, 12372, 665, 133])).
% 8.39/8.61 tff(13579,plain,
% 8.39/8.61 (r(s(s(z)), z)),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[1211, 13578])).
% 8.39/8.61 tff(13580,plain,
% 8.39/8.61 (~b(elem!1, s(z))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[9187, 13579, 723, 12372, 1234, 1484, 13527])).
% 8.39/8.61 tff(13581,plain,
% 8.39/8.61 (r(elem!1, s(z))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[837, 13580, 831])).
% 8.39/8.61 tff(13582,plain,
% 8.39/8.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 8.39/8.61 inference(rewrite,[status(thm)],[])).
% 8.39/8.61 tff(13583,plain,
% 8.39/8.61 (((~r(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))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 8.39/8.61 inference(rewrite,[status(thm)],[])).
% 8.39/8.61 tff(13584,plain,
% 8.39/8.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 8.39/8.61 inference(monotonicity,[status(thm)],[13583])).
% 8.39/8.61 tff(13585,plain,
% 8.39/8.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 8.39/8.61 inference(transitivity,[status(thm)],[13584, 13582])).
% 8.39/8.61 tff(13586,plain,
% 8.39/8.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))),
% 8.39/8.61 inference(quant_inst,[status(thm)],[])).
% 8.39/8.61 tff(13587,plain,
% 8.39/8.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 8.39/8.61 inference(modus_ponens,[status(thm)],[13586, 13585])).
% 8.39/8.61 tff(13588,plain,
% 8.39/8.61 ($false),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[13587, 194, 1484, 13581, 2112, 723])).
% 8.39/8.61 tff(13589,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (elem!1 = s(z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (elem!1 = s(s(z))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.61 tff(13590,plain,
% 8.39/8.61 (~r(s(s(s(s(z)))), s(z))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[13589, 1234, 2112, 831, 1484, 665, 133, 1405, 8922])).
% 8.39/8.61 tff(13591,plain,
% 8.39/8.61 (b(s(s(s(s(z)))), s(z))),
% 8.39/8.61 inference(unit_resolution,[status(thm)],[749, 13590])).
% 8.39/8.61 tff(13592,plain,
% 8.39/8.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.61 inference(rewrite,[status(thm)],[])).
% 8.39/8.61 tff(13593,plain,
% 8.39/8.61 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), 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(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.61 inference(rewrite,[status(thm)],[])).
% 8.39/8.61 tff(13594,plain,
% 8.39/8.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 8.39/8.61 inference(monotonicity,[status(thm)],[13593])).
% 8.39/8.61 tff(13595,plain,
% 8.39/8.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.61 inference(transitivity,[status(thm)],[13594, 13592])).
% 8.39/8.61 tff(13596,plain,
% 8.39/8.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.61 inference(quant_inst,[status(thm)],[])).
% 8.39/8.61 tff(13597,plain,
% 8.39/8.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 8.39/8.62 inference(modus_ponens,[status(thm)],[13596, 13595])).
% 8.39/8.62 tff(13598,plain,
% 8.39/8.62 (~b(s(elem!1), s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13597, 391, 1234, 13591, 5469])).
% 8.39/8.62 tff(13599,plain,
% 8.39/8.62 (r(s(elem!1), s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[2142, 42, 13598, 2121])).
% 8.39/8.62 tff(13600,plain,
% 8.39/8.62 (~b(z, s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[10478, 13591, 664, 1234])).
% 8.39/8.62 tff(13601,plain,
% 8.39/8.62 (r(z, s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[800, 13600])).
% 8.39/8.62 tff(13602,plain,
% 8.39/8.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.62 inference(rewrite,[status(thm)],[])).
% 8.39/8.62 tff(13603,plain,
% 8.39/8.62 (((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.62 inference(rewrite,[status(thm)],[])).
% 8.39/8.62 tff(13604,plain,
% 8.39/8.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 8.39/8.62 inference(monotonicity,[status(thm)],[13603])).
% 8.39/8.62 tff(13605,plain,
% 8.39/8.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.62 inference(transitivity,[status(thm)],[13604, 13602])).
% 8.39/8.62 tff(13606,plain,
% 8.39/8.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))),
% 8.39/8.62 inference(quant_inst,[status(thm)],[])).
% 8.39/8.62 tff(13607,plain,
% 8.39/8.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 8.39/8.62 inference(modus_ponens,[status(thm)],[13606, 13605])).
% 8.39/8.62 tff(13608,plain,
% 8.39/8.62 ($false),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13607, 194, 1628, 2112, 13601, 13599])).
% 8.39/8.62 tff(13609,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (elem!1 = s(z)) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (elem!1 = s(s(z))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.62 tff(13610,plain,
% 8.39/8.62 (~b(s(z), s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13609, 13577, 1628, 3122, 13575, 664, 173, 1484, 665, 133, 3694, 3696])).
% 8.39/8.62 tff(13611,plain,
% 8.39/8.62 (r(s(z), s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[1230, 13610])).
% 8.39/8.62 tff(13612,plain,
% 8.39/8.62 (~r(elem!1, s(s(z)))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[11485, 13611, 1484, 13577])).
% 8.39/8.62 tff(13613,plain,
% 8.39/8.62 (b(elem!1, s(s(z)))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[3394, 13612, 3694])).
% 8.39/8.62 tff(13614,plain,
% 8.39/8.62 (~b(s(s(z)), z)),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13448, 13613, 665, 133])).
% 8.39/8.62 tff(13615,plain,
% 8.39/8.62 (r(s(s(z)), z)),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[1211, 13614])).
% 8.39/8.62 tff(13616,plain,
% 8.39/8.62 (~b(s(s(s(s(z)))), z)),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[12394, 13611, 3363, 182, 13507, 13470, 13577])).
% 8.39/8.62 tff(13617,plain,
% 8.39/8.62 (r(s(s(s(s(z)))), z)),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[87, 13616])).
% 8.39/8.62 tff(13618,plain,
% 8.39/8.62 (~r(elem!1, s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[12404, 13617, 1484, 13611])).
% 8.39/8.62 tff(13619,plain,
% 8.39/8.62 (b(elem!1, s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[781, 13618, 3696])).
% 8.39/8.62 tff(13620,plain,
% 8.39/8.62 (~r(elem!1, s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[5396, 13611, 1484, 13577])).
% 8.39/8.62 tff(13621,plain,
% 8.39/8.62 (b(elem!1, s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[837, 13620, 173])).
% 8.39/8.62 tff(13622,plain,
% 8.39/8.62 (~r(s(s(z)), s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[5567, 1749, 1216, 2053])).
% 8.39/8.62 tff(13623,plain,
% 8.39/8.62 (b(s(s(z)), s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[3778, 13622])).
% 8.39/8.62 tff(13624,plain,
% 8.39/8.62 (~r(s(z), s(s(z)))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[11590, 194, 1749, 2053, 1216])).
% 8.39/8.62 tff(13625,plain,
% 8.39/8.62 (b(s(z), s(s(z)))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[1788, 13624])).
% 8.39/8.62 tff(13626,plain,
% 8.39/8.62 ($false),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[11599, 391, 3369, 13625, 13623, 721])).
% 8.39/8.62 tff(13627,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.62 tff(13628,plain,
% 8.39/8.62 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13627, 13613, 13621, 13617, 13611])).
% 8.39/8.62 tff(13629,plain,
% 8.39/8.62 (b(s(s(z)), s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[3652, 13628])).
% 8.39/8.62 tff(13630,plain,
% 8.39/8.62 (~b(s(s(s(s(z)))), s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13565, 13629, 13613, 13619, 13611, 13615])).
% 8.39/8.62 tff(13631,plain,
% 8.39/8.62 (~r(s(s(s(s(z)))), s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[12425, 13629, 13611, 13613, 13621, 1484, 13615, 13619])).
% 8.39/8.62 tff(13632,plain,
% 8.39/8.62 ($false),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[749, 13631, 13630])).
% 8.39/8.62 tff(13633,plain,((~b(z, s(z))) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (s(z) = elem!1) | (s(z) = s(elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.62 tff(13634,plain,
% 8.39/8.62 (~b(z, s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13633, 13362, 665, 133, 13283, 13278, 13280, 150, 121, 13428])).
% 8.39/8.62 tff(13635,plain,
% 8.39/8.62 (r(z, s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[678, 13634])).
% 8.39/8.62 tff(13636,plain,
% 8.39/8.62 (~r(s(z), s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[12593, 13635, 665, 133, 3363, 13362, 13506, 13434, 13503])).
% 8.39/8.62 tff(13637,plain,
% 8.39/8.62 (b(s(z), s(s(s(s(z)))))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[1230, 13636])).
% 8.39/8.62 tff(13638,plain,
% 8.39/8.62 (~r(s(s(s(s(z)))), s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13589, 13493, 13637, 173, 13283, 665, 133, 13501, 13497])).
% 8.39/8.62 tff(13639,plain,
% 8.39/8.62 (b(s(s(s(s(z)))), s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[749, 13638])).
% 8.39/8.62 tff(13640,plain,
% 8.39/8.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(z)))))),
% 8.39/8.62 inference(rewrite,[status(thm)],[])).
% 8.39/8.62 tff(13641,plain,
% 8.39/8.62 (((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(z)))))),
% 8.39/8.62 inference(rewrite,[status(thm)],[])).
% 8.39/8.62 tff(13642,plain,
% 8.39/8.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(z))))))),
% 8.39/8.62 inference(monotonicity,[status(thm)],[13641])).
% 8.39/8.62 tff(13643,plain,
% 8.39/8.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(z)))))),
% 8.39/8.62 inference(transitivity,[status(thm)],[13642, 13640])).
% 8.39/8.62 tff(13644,plain,
% 8.39/8.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 8.39/8.62 inference(quant_inst,[status(thm)],[])).
% 8.39/8.62 tff(13645,plain,
% 8.39/8.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(s(z))))),
% 8.39/8.62 inference(modus_ponens,[status(thm)],[13644, 13643])).
% 8.39/8.62 tff(13646,plain,
% 8.39/8.62 (~r(s(elem!1), s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13645, 194, 485, 1484, 1748])).
% 8.39/8.62 tff(13647,plain,
% 8.39/8.62 (b(s(elem!1), s(z))),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13479, 13646, 11956])).
% 8.39/8.62 tff(13648,plain,
% 8.39/8.62 (~b(s(s(s(s(z)))), elem!1)),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[13474, 13647, 485, 1484, 150, 182, 121, 5, 665, 133, 1628])).
% 8.39/8.62 tff(13649,plain,
% 8.39/8.62 (r(s(s(s(s(z)))), elem!1)),
% 8.39/8.62 inference(unit_resolution,[status(thm)],[762, 13648, 2691])).
% 8.39/8.62 tff(13650,plain,
% 8.39/8.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.62 inference(rewrite,[status(thm)],[])).
% 8.39/8.62 tff(13651,plain,
% 8.39/8.62 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), 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(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.62 inference(rewrite,[status(thm)],[])).
% 8.39/8.62 tff(13652,plain,
% 8.39/8.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 8.39/8.62 inference(monotonicity,[status(thm)],[13651])).
% 8.39/8.62 tff(13653,plain,
% 8.39/8.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.62 inference(transitivity,[status(thm)],[13652, 13650])).
% 8.39/8.62 tff(13654,plain,
% 8.39/8.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.39/8.62 inference(quant_inst,[status(thm)],[])).
% 8.39/8.62 tff(13655,plain,
% 8.39/8.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 8.39/8.63 inference(modus_ponens,[status(thm)],[13654, 13653])).
% 8.39/8.63 tff(13656,plain,
% 8.39/8.63 (~r(s(elem!1), s(s(s(s(z)))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[13655, 194, 485, 1748, 13649])).
% 8.39/8.63 tff(13657,plain,
% 8.39/8.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 8.39/8.63 inference(rewrite,[status(thm)],[])).
% 8.39/8.63 tff(13658,plain,
% 8.39/8.63 (((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 8.39/8.63 inference(rewrite,[status(thm)],[])).
% 8.39/8.63 tff(13659,plain,
% 8.39/8.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(z))))))),
% 8.39/8.63 inference(monotonicity,[status(thm)],[13658])).
% 8.39/8.63 tff(13660,plain,
% 8.39/8.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 8.39/8.63 inference(transitivity,[status(thm)],[13659, 13657])).
% 8.39/8.63 tff(13661,plain,
% 8.39/8.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 8.39/8.63 inference(quant_inst,[status(thm)],[])).
% 8.39/8.63 tff(13662,plain,
% 8.39/8.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(z))))),
% 8.39/8.63 inference(modus_ponens,[status(thm)],[13661, 13660])).
% 8.39/8.63 tff(13663,plain,
% 8.39/8.63 (~r(s(z), s(elem!1))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[13662, 194, 485, 1484, 1748])).
% 8.39/8.63 tff(13664,plain,
% 8.39/8.63 (b(s(z), s(elem!1))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[602, 42, 121, 13663])).
% 8.39/8.63 tff(13665,plain,
% 8.39/8.63 (~b(s(elem!1), s(s(s(s(z)))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[4570, 391, 13664, 1759, 13647])).
% 8.39/8.63 tff(13666,plain,
% 8.39/8.63 ($false),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[2142, 42, 13665, 13656, 3122])).
% 8.39/8.63 tff(13667,plain,((~r(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), elem!1)) | (s(z) = s(elem!1)) | (~r(s(z), elem!1)) | (s(z) = elem!1) | (~r(s(z), z)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.63 tff(13668,plain,
% 8.39/8.63 (~r(elem!1, s(s(z)))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[13667, 13639, 13280, 121, 13283, 150, 13362, 13428, 665, 133, 13278])).
% 8.39/8.63 tff(13669,plain,
% 8.39/8.63 (b(elem!1, s(s(z)))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[3394, 13668, 13501])).
% 8.39/8.63 tff(13670,plain,
% 8.39/8.63 (~b(s(s(z)), z)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[13448, 13669, 665, 133])).
% 8.39/8.63 tff(13671,plain,
% 8.39/8.63 (r(s(s(z)), z)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[1211, 13670])).
% 8.39/8.63 tff(13672,plain,
% 8.39/8.63 (~r(s(s(z)), s(z))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[4462, 13671, 13283, 13635])).
% 8.39/8.63 tff(13673,plain,
% 8.39/8.63 (b(s(s(z)), s(z))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[3778, 13672])).
% 8.39/8.63 tff(13674,plain,
% 8.39/8.63 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[5108, 13673, 13639, 13637])).
% 8.39/8.63 tff(13675,plain,
% 8.39/8.63 (r(s(s(z)), s(s(s(s(z)))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[3652, 13674])).
% 8.39/8.63 tff(13676,plain,
% 8.39/8.63 (~r(s(s(s(s(z)))), z)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[9635, 13675, 13635, 13671])).
% 8.39/8.63 tff(13677,plain,
% 8.39/8.63 (b(s(s(s(s(z)))), z)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[87, 13676])).
% 8.39/8.63 tff(13678,plain,
% 8.39/8.63 (~b(elem!1, s(s(s(s(z)))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[12445, 13677, 665, 133])).
% 8.39/8.63 tff(13679,plain,
% 8.39/8.63 (r(elem!1, s(s(s(s(z)))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[781, 13678, 13497])).
% 8.39/8.63 tff(13680,plain,
% 8.39/8.63 (~r(s(s(elem!1)), elem!1)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[13245, 13679, 13428, 13496, 13280, 13495, 13493])).
% 8.39/8.63 tff(13681,plain,
% 8.39/8.63 (b(s(s(elem!1)), elem!1)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[872, 13680, 13433])).
% 8.39/8.63 tff(13682,plain,
% 8.39/8.63 (~b(z, s(s(elem!1)))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[4944, 13681, 665, 133])).
% 8.39/8.63 tff(13683,plain,
% 8.39/8.63 (~(s(elem!1) = s(s(s(s(z)))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[1965, 13428])).
% 8.39/8.63 tff(13684,plain,
% 8.39/8.63 (~r(elem!1, s(z))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[6859, 13677, 133, 121, 13280, 13283, 13683, 13493])).
% 8.39/8.63 tff(13685,plain,
% 8.39/8.63 (b(elem!1, s(z))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[837, 13684, 173])).
% 8.39/8.63 tff(13686,plain,
% 8.39/8.63 (~b(s(z), s(s(z)))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[9159, 13685, 13637, 13669, 13673])).
% 8.39/8.63 tff(13687,plain,
% 8.39/8.63 (r(s(z), s(s(z)))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[1788, 13686])).
% 8.39/8.63 tff(13688,plain,
% 8.39/8.63 (~r(z, s(s(elem!1)))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[3787, 13687, 13671, 13362])).
% 8.39/8.63 tff(13689,plain,
% 8.39/8.63 ($false),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[324, 13688, 13682])).
% 8.39/8.63 tff(13690,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(z) = s(elem!1)) | (s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | b(s(elem!1), elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 8.39/8.63 tff(13691,plain,
% 8.39/8.63 (b(elem!1, s(s(s(elem!1))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[13690, 11936, 133, 118, 150, 10682, 168, 2163, 2282])).
% 8.39/8.63 tff(13692,plain,
% 8.39/8.63 (~b(s(s(s(elem!1))), z)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[10876, 13691, 11936, 133])).
% 8.39/8.63 tff(13693,plain,
% 8.39/8.63 (~(elem!1 = s(s(s(elem!1))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[9553, 13692, 11936])).
% 8.39/8.63 tff(13694,plain,
% 8.39/8.63 (~(s(s(s(elem!1))) = elem!1)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[8, 13693])).
% 8.39/8.63 tff(13695,plain,
% 8.39/8.63 (r(s(s(s(elem!1))), elem!1)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[230, 13694, 168])).
% 8.39/8.63 tff(13696,plain,
% 8.39/8.63 (r(elem!1, s(z))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[837, 31, 173])).
% 8.39/8.63 tff(13697,plain,
% 8.39/8.63 (~r(s(s(s(elem!1))), s(z))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[5345, 194, 233, 5429, 13696])).
% 8.39/8.63 tff(13698,plain,
% 8.39/8.63 (b(s(s(s(elem!1))), s(z))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[223, 13697])).
% 8.39/8.63 tff(13699,plain,
% 8.39/8.63 (~r(s(z), s(s(s(elem!1))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[5246, 31, 150, 2829, 233])).
% 8.39/8.63 tff(13700,plain,
% 8.39/8.63 (b(s(z), s(s(s(elem!1))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[247, 13699])).
% 8.39/8.63 tff(13701,plain,
% 8.39/8.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 8.39/8.63 inference(rewrite,[status(thm)],[])).
% 8.39/8.63 tff(13702,plain,
% 8.39/8.63 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 8.39/8.63 inference(rewrite,[status(thm)],[])).
% 8.39/8.63 tff(13703,plain,
% 8.39/8.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 8.39/8.63 inference(monotonicity,[status(thm)],[13702])).
% 8.39/8.63 tff(13704,plain,
% 8.39/8.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 8.39/8.63 inference(transitivity,[status(thm)],[13703, 13701])).
% 8.39/8.63 tff(13705,plain,
% 8.39/8.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 8.39/8.63 inference(quant_inst,[status(thm)],[])).
% 8.39/8.63 tff(13706,plain,
% 8.39/8.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 8.39/8.63 inference(modus_ponens,[status(thm)],[13705, 13704])).
% 8.39/8.63 tff(13707,plain,
% 8.39/8.63 ($false),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[13706, 391, 665, 10682, 448, 13700, 13698])).
% 8.39/8.63 tff(13708,plain,(b(elem!1, s(z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(z) = elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.39/8.63 tff(13709,plain,
% 8.39/8.63 (b(elem!1, s(z))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[13708, 11936, 10682, 13691, 13695, 150, 13277])).
% 8.39/8.63 tff(13710,plain,
% 8.39/8.63 (~b(s(s(s(s(z)))), elem!1)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[10895, 11936, 10682, 13691, 3363, 133])).
% 8.39/8.63 tff(13711,plain,
% 8.39/8.63 (~r(s(elem!1), s(z))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[5339, 194, 485, 5429, 13287])).
% 8.39/8.63 tff(13712,plain,
% 8.39/8.63 (s(s(elem!1)) = elem!1),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[12783, 590, 150, 10877, 121, 133, 168, 665])).
% 8.39/8.63 tff(13713,plain,
% 8.39/8.63 (s(s(s(elem!1))) = s(elem!1)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[451, 13712])).
% 8.39/8.63 tff(13714,plain,
% 8.39/8.63 (~(s(s(s(s(z)))) = elem!1)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[717, 13713])).
% 8.39/8.63 tff(13715,plain,
% 8.39/8.63 (~b(s(s(s(s(z)))), z)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[5398, 13714, 665, 133, 590, 13287, 5429])).
% 8.39/8.63 tff(13716,plain,
% 8.39/8.63 (r(s(s(s(s(z)))), z)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[87, 13715])).
% 8.39/8.63 tff(13717,plain,
% 8.39/8.63 (~r(z, s(elem!1))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[12988, 13716, 10682, 665, 3363, 448, 10878])).
% 8.39/8.63 tff(13718,plain,
% 8.39/8.63 (b(z, s(elem!1))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[566, 13717])).
% 8.39/8.63 tff(13719,plain,
% 8.39/8.63 (~(elem!1 = s(s(s(elem!1))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[9553, 10877, 665])).
% 8.39/8.63 tff(13720,plain,
% 8.39/8.63 (~(s(s(s(elem!1))) = elem!1)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[8, 13719])).
% 8.39/8.63 tff(13721,plain,
% 8.39/8.63 (r(s(s(s(elem!1))), elem!1)),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[230, 13720, 168])).
% 8.39/8.63 tff(13722,plain,
% 8.39/8.63 (~r(s(z), s(s(s(elem!1))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[5246, 13286, 150, 2829, 13721])).
% 8.39/8.63 tff(13723,plain,
% 8.39/8.63 (b(s(z), s(s(s(elem!1))))),
% 8.39/8.63 inference(unit_resolution,[status(thm)],[247, 13722])).
% 8.39/8.63 tff(13724,plain,
% 8.39/8.63 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[13713])).
% 8.39/8.64 tff(13725,plain,
% 8.39/8.64 (b(s(z), s(elem!1))),
% 8.39/8.64 inference(modus_ponens,[status(thm)],[13723, 13724])).
% 8.39/8.64 tff(13726,plain,
% 8.39/8.64 (~b(s(elem!1), s(z))),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[7240, 13725, 590, 13723, 13718])).
% 8.39/8.64 tff(13727,plain,
% 8.39/8.64 ($false),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[13479, 13726, 13711, 11956])).
% 8.39/8.64 tff(13728,plain,((~b(s(z), z)) | (~r(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(z) = elem!1) | b(s(z), elem!1) | (s(z) = s(elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.39/8.64 tff(13729,plain,
% 8.39/8.64 (~b(s(z), z)),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[13728, 13120, 10682, 11936, 13691, 133, 150, 13277, 118, 168])).
% 8.39/8.64 tff(13730,plain,
% 8.39/8.64 (r(s(z), z)),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[180, 13729])).
% 8.39/8.64 tff(13731,plain,
% 8.39/8.64 (r(s(z), elem!1)),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[632, 13277, 150])).
% 8.39/8.64 tff(13732,plain,
% 8.39/8.64 (~b(s(s(s(s(z)))), elem!1)),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[10895, 665, 10682, 448, 3363, 133])).
% 8.39/8.64 tff(13733,plain,
% 8.39/8.64 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[766])).
% 8.39/8.64 tff(13734,plain,
% 8.39/8.64 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 8.39/8.64 inference(symmetry,[status(thm)],[13733])).
% 8.39/8.64 tff(13735,plain,
% 8.39/8.64 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(elem!1, s(z)))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[13734])).
% 8.39/8.64 tff(13736,plain,
% 8.39/8.64 (~b(elem!1, s(z))),
% 8.39/8.64 inference(modus_ponens,[status(thm)],[9024, 13735])).
% 8.39/8.64 tff(13737,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[721, 13736])).
% 8.39/8.64 tff(13738,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(elem!1, s(z))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.64 tff(13739,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[13738, 9024, 721])).
% 8.39/8.64 tff(13740,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[9108, 10646, 1484, 13732, 13739])).
% 8.39/8.64 tff(13741,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[12445, 13740, 665, 133])).
% 8.39/8.64 tff(13742,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[6966, 13741, 665])).
% 8.39/8.64 tff(13743,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[762, 13742, 13732])).
% 8.39/8.64 tff(13744,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[9117, 13743, 10646, 1484])).
% 8.39/8.64 tff(13745,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[9108, 723, 1484, 13732, 8922])).
% 8.39/8.64 tff(13746,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[12445, 13745, 665, 133])).
% 8.39/8.64 tff(13747,plain,
% 8.39/8.64 (~(s(s(s(s(z)))) = elem!1)),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[6966, 13746, 665])).
% 8.39/8.64 tff(13748,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[762, 13747, 13732])).
% 8.39/8.64 tff(13749,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[12445, 2064, 665, 133])).
% 8.39/8.64 tff(13750,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[6966, 13749, 665])).
% 8.39/8.64 tff(13751,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[762, 13750, 13732])).
% 8.39/8.64 tff(13752,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[9117, 13751, 723, 1484])).
% 8.39/8.64 tff(13753,plain,
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% 8.39/8.64 inference(monotonicity,[status(thm)],[9026])).
% 8.39/8.64 tff(13754,plain,
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% 8.39/8.64 tff(13755,plain,
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% 8.39/8.64 inference(modus_ponens,[status(thm)],[1686, 13754])).
% 8.39/8.64 tff(13756,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[9253, 3584])).
% 8.39/8.64 tff(13757,plain,
% 8.39/8.64 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[9026])).
% 8.39/8.64 tff(13758,plain,
% 8.39/8.64 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.64 inference(symmetry,[status(thm)],[13757])).
% 8.39/8.64 tff(13759,plain,
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% 8.39/8.64 inference(monotonicity,[status(thm)],[9026])).
% 8.39/8.64 tff(13760,plain,
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% 8.39/8.64 inference(symmetry,[status(thm)],[13759])).
% 8.39/8.64 tff(13761,plain,
% 8.39/8.64 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[13760])).
% 8.39/8.64 tff(13762,plain,
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% 8.39/8.64 inference(transitivity,[status(thm)],[13761, 13758])).
% 8.39/8.64 tff(13763,plain,
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% 8.39/8.64 inference(monotonicity,[status(thm)],[13762])).
% 8.39/8.64 tff(13764,plain,
% 8.39/8.64 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[13760])).
% 8.39/8.64 tff(13765,plain,
% 8.39/8.64 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 8.39/8.64 inference(symmetry,[status(thm)],[13764])).
% 8.39/8.64 tff(13766,plain,
% 8.39/8.64 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[9026])).
% 8.39/8.64 tff(13767,plain,
% 8.39/8.64 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 8.39/8.64 inference(symmetry,[status(thm)],[13766])).
% 8.39/8.64 tff(13768,plain,
% 8.39/8.64 (r(s(s(elem!1)), s(z))),
% 8.39/8.64 inference(modus_ponens,[status(thm)],[723, 13767])).
% 8.39/8.64 tff(13769,plain,
% 8.39/8.64 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[3584])).
% 8.39/8.64 tff(13770,plain,
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% 8.39/8.64 inference(modus_ponens,[status(thm)],[2112, 13769])).
% 8.39/8.64 tff(13771,plain,
% 8.39/8.64 (r(s(s(elem!1)), elem!1)),
% 8.39/8.64 inference(modus_ponens,[status(thm)],[13770, 9052])).
% 8.39/8.64 tff(13772,plain,
% 8.39/8.64 (~b(s(s(s(elem!1))), s(z))),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[4958, 13771, 150, 448, 379, 13768])).
% 8.39/8.64 tff(13773,plain,
% 8.39/8.64 (r(s(s(s(elem!1))), s(z))),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[223, 13772])).
% 8.39/8.64 tff(13774,plain,
% 8.39/8.64 (r(s(s(s(s(s(z))))), s(z))),
% 8.39/8.64 inference(modus_ponens,[status(thm)],[13773, 13765])).
% 8.39/8.64 tff(13775,plain,
% 8.39/8.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 8.39/8.64 inference(rewrite,[status(thm)],[])).
% 8.39/8.64 tff(13776,plain,
% 8.39/8.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 8.39/8.64 inference(quant_inst,[status(thm)],[])).
% 8.39/8.64 tff(13777,plain,
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% 8.39/8.64 inference(modus_ponens,[status(thm)],[13776, 13775])).
% 8.39/8.64 tff(13778,plain,
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% 8.39/8.64 inference(unit_resolution,[status(thm)],[13777, 194, 1216, 723])).
% 8.39/8.64 tff(13779,plain,
% 8.39/8.64 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[13778, 13774])).
% 8.39/8.64 tff(13780,plain,
% 8.39/8.64 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.64 inference(modus_ponens,[status(thm)],[13779, 13763])).
% 8.39/8.64 tff(13781,plain,
% 8.39/8.64 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[1370, 13780, 13756])).
% 8.39/8.64 tff(13782,plain,
% 8.39/8.64 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[314, 13756])).
% 8.39/8.64 tff(13783,plain,
% 8.39/8.64 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[9026])).
% 8.39/8.64 tff(13784,plain,
% 8.39/8.64 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.64 inference(symmetry,[status(thm)],[13783])).
% 8.39/8.64 tff(13785,plain,
% 8.39/8.64 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[13760])).
% 8.39/8.64 tff(13786,plain,
% 8.39/8.64 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.64 inference(transitivity,[status(thm)],[13785, 13784])).
% 8.39/8.64 tff(13787,plain,
% 8.39/8.64 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[13786])).
% 8.39/8.64 tff(13788,plain,
% 8.39/8.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.64 inference(rewrite,[status(thm)],[])).
% 8.39/8.64 tff(13789,plain,
% 8.39/8.64 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.64 inference(rewrite,[status(thm)],[])).
% 8.39/8.64 tff(13790,plain,
% 8.39/8.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 8.39/8.64 inference(monotonicity,[status(thm)],[13789])).
% 8.39/8.64 tff(13791,plain,
% 8.39/8.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.64 inference(transitivity,[status(thm)],[13790, 13788])).
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% 8.39/8.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.64 inference(quant_inst,[status(thm)],[])).
% 8.39/8.64 tff(13793,plain,
% 8.39/8.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 8.39/8.64 inference(modus_ponens,[status(thm)],[13792, 13791])).
% 8.39/8.64 tff(13794,plain,
% 8.39/8.64 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[13793, 194, 1216, 723])).
% 8.39/8.64 tff(13795,plain,
% 8.39/8.64 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[13794, 13774])).
% 8.39/8.64 tff(13796,plain,
% 8.39/8.64 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.64 inference(modus_ponens,[status(thm)],[13795, 13787])).
% 8.39/8.64 tff(13797,plain,
% 8.39/8.64 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[1356, 13796, 13782])).
% 8.39/8.64 tff(13798,plain,
% 8.39/8.64 ($false),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[12932, 13797, 13781, 10682, 13755])).
% 8.39/8.64 tff(13799,plain,((~(elem!1 = s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (s(z) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.64 tff(13800,plain,
% 8.39/8.64 (~(elem!1 = s(s(z)))),
% 8.39/8.64 inference(unit_resolution,[status(thm)],[13799, 1216, 10682, 723, 150, 448, 379, 3226, 13751])).
% 8.39/8.65 tff(13801,plain,
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% 8.39/8.65 inference(unit_resolution,[status(thm)],[3394, 13800, 13752])).
% 8.39/8.65 tff(13802,plain,
% 8.39/8.65 (~b(s(s(z)), z)),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[13448, 13801, 665, 133])).
% 8.39/8.65 tff(13803,plain,
% 8.39/8.65 (r(s(s(z)), z)),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[1211, 13802])).
% 8.39/8.65 tff(13804,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), z)),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[87, 13749])).
% 8.39/8.65 tff(13805,plain,
% 8.39/8.65 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[13627, 13801, 721, 13804, 1216])).
% 8.39/8.65 tff(13806,plain,
% 8.39/8.65 (b(s(s(z)), s(s(s(s(z)))))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[3652, 13805])).
% 8.39/8.65 tff(13807,plain,
% 8.39/8.65 ($false),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[12425, 13806, 13803, 1216, 723, 721, 1484, 13801, 2064])).
% 8.39/8.65 tff(13808,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.65 tff(13809,plain,
% 8.39/8.65 (~r(s(z), s(s(s(s(z)))))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[13808, 379, 721, 1484, 13745, 665, 133, 10682, 150, 448, 723, 182])).
% 8.39/8.65 tff(13810,plain,
% 8.39/8.65 (b(s(z), s(s(s(s(z)))))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[1230, 13809])).
% 8.39/8.65 tff(13811,plain,
% 8.39/8.65 (elem!1 = s(s(z))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[13589, 13810, 723, 173, 1484, 665, 133, 13748, 8922])).
% 8.39/8.65 tff(13812,plain,
% 8.39/8.65 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13811])).
% 8.39/8.65 tff(13813,plain,
% 8.39/8.65 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 8.39/8.65 inference(symmetry,[status(thm)],[13812])).
% 8.39/8.65 tff(13814,plain,
% 8.39/8.65 (s(elem!1) = s(s(s(z)))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13811])).
% 8.39/8.65 tff(13815,plain,
% 8.39/8.65 (s(s(elem!1)) = s(s(s(s(z))))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13814])).
% 8.39/8.65 tff(13816,plain,
% 8.39/8.65 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13815])).
% 8.39/8.65 tff(13817,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 8.39/8.65 inference(symmetry,[status(thm)],[13816])).
% 8.39/8.65 tff(13818,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 8.39/8.65 inference(transitivity,[status(thm)],[13817, 13813])).
% 8.39/8.65 tff(13819,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13811])).
% 8.39/8.65 tff(13820,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), s(s(z)))),
% 8.39/8.65 inference(modus_ponens,[status(thm)],[13748, 13819])).
% 8.39/8.65 tff(13821,plain,
% 8.39/8.65 (r(s(s(elem!1)), elem!1)),
% 8.39/8.65 inference(modus_ponens,[status(thm)],[13820, 13818])).
% 8.39/8.65 tff(13822,plain,
% 8.39/8.65 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[9253, 13811])).
% 8.39/8.65 tff(13823,plain,
% 8.39/8.65 (r(s(s(elem!1)), z) <=> r(s(s(s(s(z)))), z)),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13815])).
% 8.39/8.65 tff(13824,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 8.39/8.65 inference(symmetry,[status(thm)],[13823])).
% 8.39/8.65 tff(13825,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), z)),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[87, 13746])).
% 8.39/8.65 tff(13826,plain,
% 8.39/8.65 (r(s(s(elem!1)), z)),
% 8.39/8.65 inference(modus_ponens,[status(thm)],[13825, 13824])).
% 8.39/8.65 tff(13827,plain,
% 8.39/8.65 ($false),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[5329, 194, 174, 364, 327, 326])).
% 8.39/8.65 tff(13828,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.65 tff(13829,plain,
% 8.39/8.65 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[13828, 326, 364, 174])).
% 8.39/8.65 tff(13830,plain,
% 8.39/8.65 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[1370, 13829, 297])).
% 8.39/8.65 tff(13831,plain,
% 8.39/8.65 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[3432, 13830, 379, 182, 326])).
% 8.39/8.65 tff(13832,plain,
% 8.39/8.65 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[1356, 13831, 315])).
% 8.39/8.65 tff(13833,plain,
% 8.39/8.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.39/8.65 inference(rewrite,[status(thm)],[])).
% 8.39/8.65 tff(13834,plain,
% 8.39/8.65 (((~r(z, 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)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.39/8.65 inference(rewrite,[status(thm)],[])).
% 8.39/8.65 tff(13835,plain,
% 8.39/8.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13834])).
% 8.39/8.65 tff(13836,plain,
% 8.39/8.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.39/8.65 inference(transitivity,[status(thm)],[13835, 13833])).
% 8.39/8.65 tff(13837,plain,
% 8.39/8.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))),
% 8.39/8.65 inference(quant_inst,[status(thm)],[])).
% 8.39/8.65 tff(13838,plain,
% 8.39/8.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 8.39/8.65 inference(modus_ponens,[status(thm)],[13837, 13836])).
% 8.39/8.65 tff(13839,plain,
% 8.39/8.65 ($false),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[13838, 194, 174, 326, 13832, 2616])).
% 8.39/8.65 tff(13840,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.65 tff(13841,plain,
% 8.39/8.65 (~r(z, s(s(elem!1)))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[13840, 13826, 379, 10878, 182, 13822, 13821])).
% 8.39/8.65 tff(13842,plain,
% 8.39/8.65 (b(z, s(s(elem!1)))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[324, 13841])).
% 8.39/8.65 tff(13843,plain,
% 8.39/8.65 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13815])).
% 8.39/8.65 tff(13844,plain,
% 8.39/8.65 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.65 inference(symmetry,[status(thm)],[13843])).
% 8.39/8.65 tff(13845,plain,
% 8.39/8.65 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13815])).
% 8.39/8.65 tff(13846,plain,
% 8.39/8.65 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 8.39/8.65 inference(symmetry,[status(thm)],[13845])).
% 8.39/8.65 tff(13847,plain,
% 8.39/8.65 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13846])).
% 8.39/8.65 tff(13848,plain,
% 8.39/8.65 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.65 inference(transitivity,[status(thm)],[13847, 13844])).
% 8.39/8.65 tff(13849,plain,
% 8.39/8.65 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13848])).
% 8.39/8.65 tff(13850,plain,
% 8.39/8.65 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13846])).
% 8.39/8.65 tff(13851,plain,
% 8.39/8.65 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 8.39/8.65 inference(symmetry,[status(thm)],[13850])).
% 8.39/8.65 tff(13852,plain,
% 8.39/8.65 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13815])).
% 8.39/8.65 tff(13853,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 8.39/8.65 inference(symmetry,[status(thm)],[13852])).
% 8.39/8.65 tff(13854,plain,
% 8.39/8.65 (r(s(s(elem!1)), s(z))),
% 8.39/8.65 inference(modus_ponens,[status(thm)],[723, 13853])).
% 8.39/8.65 tff(13855,plain,
% 8.39/8.65 (~b(s(s(s(elem!1))), s(z))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[4958, 13821, 150, 448, 379, 13854])).
% 8.39/8.65 tff(13856,plain,
% 8.39/8.65 (r(s(s(s(elem!1))), s(z))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[223, 13855])).
% 8.39/8.65 tff(13857,plain,
% 8.39/8.65 (r(s(s(s(s(s(z))))), s(z))),
% 8.39/8.65 inference(modus_ponens,[status(thm)],[13856, 13851])).
% 8.39/8.65 tff(13858,plain,
% 8.39/8.65 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13811])).
% 8.39/8.65 tff(13859,plain,
% 8.39/8.65 (r(s(z), s(s(z)))),
% 8.39/8.65 inference(modus_ponens,[status(thm)],[1484, 13858])).
% 8.39/8.65 tff(13860,plain,
% 8.39/8.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 8.39/8.65 inference(rewrite,[status(thm)],[])).
% 8.39/8.65 tff(13861,plain,
% 8.39/8.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 8.39/8.65 inference(quant_inst,[status(thm)],[])).
% 8.39/8.65 tff(13862,plain,
% 8.39/8.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 8.39/8.65 inference(modus_ponens,[status(thm)],[13861, 13860])).
% 8.39/8.65 tff(13863,plain,
% 8.39/8.65 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[13862, 194, 723, 13859])).
% 8.39/8.65 tff(13864,plain,
% 8.39/8.65 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[13863, 13857])).
% 8.39/8.65 tff(13865,plain,
% 8.39/8.65 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.65 inference(modus_ponens,[status(thm)],[13864, 13849])).
% 8.39/8.65 tff(13866,plain,
% 8.39/8.65 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[1370, 13865, 13822])).
% 8.39/8.65 tff(13867,plain,
% 8.39/8.65 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 8.39/8.65 inference(unit_resolution,[status(thm)],[314, 13822])).
% 8.39/8.65 tff(13868,plain,
% 8.39/8.65 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13815])).
% 8.39/8.65 tff(13869,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.65 inference(symmetry,[status(thm)],[13868])).
% 8.39/8.65 tff(13870,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13846])).
% 8.39/8.65 tff(13871,plain,
% 8.39/8.65 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.65 inference(transitivity,[status(thm)],[13870, 13869])).
% 8.39/8.65 tff(13872,plain,
% 8.39/8.65 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 8.39/8.65 inference(monotonicity,[status(thm)],[13871])).
% 8.39/8.65 tff(13873,plain,
% 8.39/8.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.66 inference(rewrite,[status(thm)],[])).
% 8.39/8.66 tff(13874,plain,
% 8.39/8.66 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.66 inference(rewrite,[status(thm)],[])).
% 8.39/8.66 tff(13875,plain,
% 8.39/8.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13874])).
% 8.39/8.66 tff(13876,plain,
% 8.39/8.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.66 inference(transitivity,[status(thm)],[13875, 13873])).
% 8.39/8.66 tff(13877,plain,
% 8.39/8.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.66 inference(quant_inst,[status(thm)],[])).
% 8.39/8.66 tff(13878,plain,
% 8.39/8.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 8.39/8.66 inference(modus_ponens,[status(thm)],[13877, 13876])).
% 8.39/8.66 tff(13879,plain,
% 8.39/8.66 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[13878, 194, 723, 13859])).
% 8.39/8.66 tff(13880,plain,
% 8.39/8.66 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[13879, 13857])).
% 8.39/8.66 tff(13881,plain,
% 8.39/8.66 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.66 inference(modus_ponens,[status(thm)],[13880, 13872])).
% 8.39/8.66 tff(13882,plain,
% 8.39/8.66 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[1356, 13881, 13867])).
% 8.39/8.66 tff(13883,plain,
% 8.39/8.66 ($false),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[12932, 13882, 13866, 10682, 13842])).
% 8.39/8.66 tff(13884,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (s(z) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.66 tff(13885,plain,
% 8.39/8.66 (~b(s(z), s(s(s(elem!1))))),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[13884, 10646, 10682, 150, 448, 182, 1484, 665, 133, 13739, 721])).
% 8.39/8.66 tff(13886,plain,
% 8.39/8.66 (r(s(z), s(s(s(elem!1))))),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[247, 13885])).
% 8.39/8.66 tff(13887,plain,
% 8.39/8.66 (~b(s(s(s(s(z)))), elem!1)),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[10895, 665, 10682, 448, 3843, 133])).
% 8.39/8.66 tff(13888,plain,
% 8.39/8.66 (b(elem!1, s(s(s(s(z)))))),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[9108, 723, 1484, 13887, 8922])).
% 8.39/8.66 tff(13889,plain,
% 8.39/8.66 (~b(s(s(s(s(z)))), z)),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[12445, 13888, 665, 133])).
% 8.39/8.66 tff(13890,plain,
% 8.39/8.66 (~(s(s(s(s(z)))) = elem!1)),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[6966, 13889, 665])).
% 8.39/8.66 tff(13891,plain,
% 8.39/8.66 (r(s(s(s(s(z)))), elem!1)),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[762, 13890, 13887])).
% 8.39/8.66 tff(13892,plain,
% 8.39/8.66 (elem!1 = s(s(z))),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[13589, 1234, 723, 831, 1484, 665, 133, 13891, 8922])).
% 8.39/8.66 tff(13893,plain,
% 8.39/8.66 (s(elem!1) = s(s(s(z)))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13892])).
% 8.39/8.66 tff(13894,plain,
% 8.39/8.66 (s(s(elem!1)) = s(s(s(s(z))))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13893])).
% 8.39/8.66 tff(13895,plain,
% 8.39/8.66 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13894])).
% 8.39/8.66 tff(13896,plain,
% 8.39/8.66 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 8.39/8.66 inference(symmetry,[status(thm)],[13895])).
% 8.39/8.66 tff(13897,plain,
% 8.39/8.66 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(elem!1))))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13896])).
% 8.39/8.66 tff(13898,plain,
% 8.39/8.66 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(s(z))))))),
% 8.39/8.66 inference(symmetry,[status(thm)],[13897])).
% 8.39/8.66 tff(13899,plain,
% 8.39/8.66 (r(s(z), s(s(s(s(s(z))))))),
% 8.39/8.66 inference(modus_ponens,[status(thm)],[232, 13898])).
% 8.39/8.66 tff(13900,plain,
% 8.39/8.66 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13896])).
% 8.39/8.66 tff(13901,plain,
% 8.39/8.66 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 8.39/8.66 inference(symmetry,[status(thm)],[13900])).
% 8.39/8.66 tff(13902,plain,
% 8.39/8.66 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13894])).
% 8.39/8.66 tff(13903,plain,
% 8.39/8.66 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[9253, 13892])).
% 8.39/8.66 tff(13904,plain,
% 8.39/8.66 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(z)))))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13894])).
% 8.39/8.66 tff(13905,plain,
% 8.39/8.66 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 8.39/8.66 inference(symmetry,[status(thm)],[13904])).
% 8.39/8.66 tff(13906,plain,
% 8.39/8.66 (r(s(s(s(s(z)))), z)),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[87, 13889])).
% 8.39/8.66 tff(13907,plain,
% 8.39/8.66 (r(s(elem!1), z) <=> r(s(s(s(z))), z)),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13893])).
% 8.39/8.66 tff(13908,plain,
% 8.39/8.66 (r(s(s(s(z))), z)),
% 8.39/8.66 inference(modus_ponens,[status(thm)],[1628, 13907])).
% 8.39/8.66 tff(13909,plain,
% 8.39/8.66 (s(s(z)) = elem!1),
% 8.39/8.66 inference(modus_ponens,[status(thm)],[13892, 8492])).
% 8.39/8.66 tff(13910,plain,
% 8.39/8.66 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.39/8.66 inference(unit_resolution,[status(thm)],[4584, 13909, 121])).
% 8.39/8.66 tff(13911,plain,
% 8.39/8.66 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13892])).
% 8.39/8.66 tff(13912,plain,
% 8.39/8.66 (b(s(s(z)), s(z))),
% 8.39/8.66 inference(modus_ponens,[status(thm)],[721, 13911])).
% 8.39/8.66 tff(13913,plain,
% 8.39/8.66 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13892])).
% 8.39/8.66 tff(13914,plain,
% 8.39/8.66 (b(s(s(z)), s(s(s(s(z)))))),
% 8.39/8.66 inference(modus_ponens,[status(thm)],[13888, 13913])).
% 8.39/8.66 tff(13915,plain,
% 8.39/8.66 (s(s(s(z))) = s(elem!1)),
% 8.39/8.66 inference(symmetry,[status(thm)],[9025])).
% 8.39/8.66 tff(13916,plain,
% 8.39/8.66 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13760, 13915])).
% 8.39/8.66 tff(13917,plain,
% 8.39/8.66 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 8.39/8.66 inference(symmetry,[status(thm)],[13916])).
% 8.39/8.66 tff(13918,plain,
% 8.39/8.66 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13760, 13915])).
% 8.39/8.66 tff(13919,plain,
% 8.39/8.66 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13918])).
% 8.39/8.66 tff(13920,plain,
% 8.39/8.66 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(elem!1))), z)),
% 8.39/8.66 inference(monotonicity,[status(thm)],[13760])).
% 8.39/8.66 tff(13921,plain,
% 8.39/8.66 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(z))))), z)),
% 8.39/8.66 inference(symmetry,[status(thm)],[13920])).
% 8.39/8.66 tff(13922,plain,
% 8.39/8.66 (r(s(s(s(s(s(z))))), z)),
% 8.39/8.66 inference(modus_ponens,[status(thm)],[174, 13921])).
% 8.39/8.66 tff(13923,plain,
% 8.39/8.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 8.39/8.66 inference(rewrite,[status(thm)],[])).
% 8.39/8.66 tff(13924,plain,
% 8.39/8.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 8.39/8.67 inference(quant_inst,[status(thm)],[])).
% 8.39/8.67 tff(13925,plain,
% 8.39/8.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[13924, 13923])).
% 8.39/8.67 tff(13926,plain,
% 8.39/8.67 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[13925, 194, 719, 4428])).
% 8.39/8.67 tff(13927,plain,
% 8.39/8.67 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[13926, 13922])).
% 8.39/8.67 tff(13928,plain,
% 8.39/8.67 (~r(s(s(s(elem!1))), s(elem!1))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[13927, 13919])).
% 8.39/8.67 tff(13929,plain,
% 8.39/8.67 (b(s(s(s(elem!1))), s(elem!1))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[588, 13928, 279])).
% 8.39/8.67 tff(13930,plain,
% 8.39/8.67 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[13929, 13917])).
% 8.39/8.67 tff(13931,plain,
% 8.39/8.67 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 8.39/8.67 inference(monotonicity,[status(thm)],[13760])).
% 8.39/8.67 tff(13932,plain,
% 8.39/8.67 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 8.39/8.67 inference(symmetry,[status(thm)],[13931])).
% 8.39/8.67 tff(13933,plain,
% 8.39/8.67 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 8.39/8.67 inference(monotonicity,[status(thm)],[13932])).
% 8.39/8.67 tff(13934,plain,
% 8.39/8.67 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[3843, 13933])).
% 8.39/8.67 tff(13935,plain,
% 8.39/8.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.67 inference(rewrite,[status(thm)],[])).
% 8.39/8.67 tff(13936,plain,
% 8.39/8.67 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.67 inference(rewrite,[status(thm)],[])).
% 8.39/8.67 tff(13937,plain,
% 8.39/8.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 8.39/8.67 inference(monotonicity,[status(thm)],[13936])).
% 8.39/8.67 tff(13938,plain,
% 8.39/8.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.67 inference(transitivity,[status(thm)],[13937, 13935])).
% 8.39/8.67 tff(13939,plain,
% 8.39/8.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.39/8.67 inference(quant_inst,[status(thm)],[])).
% 8.39/8.67 tff(13940,plain,
% 8.39/8.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[13939, 13938])).
% 8.39/8.67 tff(13941,plain,
% 8.39/8.67 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[13940, 194, 2053, 719])).
% 8.39/8.67 tff(13942,plain,
% 8.39/8.67 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[13941, 13922])).
% 8.39/8.67 tff(13943,plain,
% 8.39/8.67 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[8759, 42, 13942])).
% 8.39/8.67 tff(13944,plain,
% 8.39/8.67 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[13943, 13934])).
% 8.39/8.67 tff(13945,plain,
% 8.39/8.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 8.39/8.67 inference(rewrite,[status(thm)],[])).
% 8.39/8.67 tff(13946,plain,
% 8.39/8.67 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 8.39/8.67 inference(rewrite,[status(thm)],[])).
% 8.39/8.67 tff(13947,plain,
% 8.39/8.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 8.39/8.67 inference(monotonicity,[status(thm)],[13946])).
% 8.39/8.67 tff(13948,plain,
% 8.39/8.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 8.39/8.67 inference(transitivity,[status(thm)],[13947, 13945])).
% 8.39/8.67 tff(13949,plain,
% 8.39/8.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 8.39/8.67 inference(quant_inst,[status(thm)],[])).
% 8.39/8.67 tff(13950,plain,
% 8.39/8.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[13949, 13948])).
% 8.39/8.67 tff(13951,plain,
% 8.39/8.67 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[13950, 391, 3823, 1234, 1233, 13944])).
% 8.39/8.67 tff(13952,plain,
% 8.39/8.67 ($false),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[13951, 13930])).
% 8.39/8.67 tff(13953,plain,((~r(z, s(s(s(s(z)))))) | (~(elem!1 = s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.67 tff(13954,plain,
% 8.39/8.67 (~r(z, s(s(s(s(z)))))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[13953, 13892, 13914, 1234, 13912, 3843, 13910, 13908, 13906, 10878])).
% 8.39/8.67 tff(13955,plain,
% 8.39/8.67 (b(z, s(s(s(s(z)))))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[800, 13954])).
% 8.39/8.67 tff(13956,plain,
% 8.39/8.67 (b(z, s(s(elem!1)))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[13955, 13905])).
% 8.39/8.67 tff(13957,plain,
% 8.39/8.67 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 8.39/8.67 inference(unit_resolution,[status(thm)],[314, 13903])).
% 8.39/8.67 tff(13958,plain,
% 8.39/8.67 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 8.39/8.67 inference(monotonicity,[status(thm)],[13894])).
% 8.39/8.67 tff(13959,plain,
% 8.39/8.67 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 8.39/8.67 inference(symmetry,[status(thm)],[13958])).
% 8.39/8.67 tff(13960,plain,
% 8.39/8.67 (r(s(s(elem!1)), s(z))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[723, 13959])).
% 8.39/8.67 tff(13961,plain,
% 8.39/8.67 (b(elem!1, z) <=> b(s(s(z)), z)),
% 8.39/8.67 inference(monotonicity,[status(thm)],[13892])).
% 8.39/8.67 tff(13962,plain,
% 8.39/8.67 (b(s(s(z)), z)),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[665, 13961])).
% 8.39/8.67 tff(13963,plain,
% 8.39/8.67 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(elem!1))))),
% 8.39/8.67 inference(monotonicity,[status(thm)],[9247, 13760])).
% 8.39/8.67 tff(13964,plain,
% 8.39/8.67 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 8.39/8.67 inference(symmetry,[status(thm)],[13963])).
% 8.39/8.67 tff(13965,plain,
% 8.39/8.67 (b(s(s(z)), s(s(s(s(s(z))))))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[448, 13964])).
% 8.39/8.67 tff(13966,plain,
% 8.39/8.67 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(elem!1))))),
% 8.39/8.67 inference(monotonicity,[status(thm)],[13760])).
% 8.39/8.67 tff(13967,plain,
% 8.39/8.67 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(z))))))),
% 8.39/8.67 inference(symmetry,[status(thm)],[13966])).
% 8.39/8.67 tff(13968,plain,
% 8.39/8.67 (b(z, s(s(s(s(s(z))))))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[10682, 13967])).
% 8.39/8.67 tff(13969,plain,
% 8.39/8.67 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 8.39/8.67 inference(monotonicity,[status(thm)],[13760])).
% 8.39/8.67 tff(13970,plain,
% 8.39/8.67 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 8.39/8.67 inference(symmetry,[status(thm)],[13969])).
% 8.39/8.67 tff(13971,plain,
% 8.39/8.67 (b(s(s(s(s(s(z))))), s(z))),
% 8.39/8.67 inference(modus_ponens,[status(thm)],[1526, 13970])).
% 8.39/8.67 tff(13972,plain,
% 8.39/8.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 8.39/8.67 inference(rewrite,[status(thm)],[])).
% 8.39/8.67 tff(13973,plain,
% 8.39/8.67 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 8.39/8.67 inference(rewrite,[status(thm)],[])).
% 8.39/8.67 tff(13974,plain,
% 8.39/8.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 8.39/8.67 inference(monotonicity,[status(thm)],[13973])).
% 8.39/8.67 tff(13975,plain,
% 8.39/8.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 8.39/8.68 inference(transitivity,[status(thm)],[13974, 13972])).
% 8.39/8.68 tff(13976,plain,
% 8.39/8.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))),
% 8.39/8.68 inference(quant_inst,[status(thm)],[])).
% 8.39/8.68 tff(13977,plain,
% 8.39/8.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 8.39/8.68 inference(modus_ponens,[status(thm)],[13976, 13975])).
% 8.39/8.68 tff(13978,plain,
% 8.39/8.68 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 8.39/8.68 inference(unit_resolution,[status(thm)],[13977, 391, 1235, 1234])).
% 8.39/8.68 tff(13979,plain,
% 8.39/8.68 ($false),
% 8.39/8.68 inference(unit_resolution,[status(thm)],[13978, 13971, 13968, 13965])).
% 8.39/8.68 tff(13980,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~(elem!1 = s(s(z)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.68 tff(13981,plain,
% 8.39/8.68 (~b(s(s(s(elem!1))), s(z))),
% 8.39/8.68 inference(unit_resolution,[status(thm)],[13980, 13962, 1234, 448, 13892, 10682])).
% 8.39/8.68 tff(13982,plain,
% 8.39/8.68 (r(s(s(s(elem!1))), s(z))),
% 8.39/8.68 inference(unit_resolution,[status(thm)],[223, 13981])).
% 8.39/8.68 tff(13983,plain,
% 8.39/8.68 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.68 inference(unit_resolution,[status(thm)],[2201, 13982, 232, 13960])).
% 8.39/8.68 tff(13984,plain,
% 8.39/8.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.39/8.68 inference(unit_resolution,[status(thm)],[1356, 13983, 13957])).
% 8.39/8.68 tff(13985,plain,
% 8.39/8.68 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.68 inference(unit_resolution,[status(thm)],[12932, 13984, 10682, 13956])).
% 8.39/8.68 tff(13986,plain,
% 8.39/8.68 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.39/8.68 inference(unit_resolution,[status(thm)],[1370, 13985, 13903])).
% 8.39/8.68 tff(13987,plain,
% 8.39/8.68 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.39/8.68 inference(modus_ponens,[status(thm)],[13986, 13902])).
% 8.39/8.68 tff(13988,plain,
% 8.39/8.68 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 8.39/8.68 inference(modus_ponens,[status(thm)],[13987, 13901])).
% 8.39/8.68 tff(13989,plain,
% 8.39/8.68 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 8.39/8.68 inference(monotonicity,[status(thm)],[13896])).
% 8.39/8.68 tff(13990,plain,
% 8.39/8.68 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 8.39/8.68 inference(symmetry,[status(thm)],[13989])).
% 8.39/8.68 tff(13991,plain,
% 8.39/8.68 (r(s(s(s(s(s(z))))), s(z))),
% 8.39/8.68 inference(modus_ponens,[status(thm)],[13982, 13990])).
% 8.39/8.68 tff(13992,plain,
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% 8.39/8.69 inference(rewrite,[status(thm)],[])).
% 8.39/8.69 tff(14064,plain,
% 8.39/8.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 8.39/8.69 inference(monotonicity,[status(thm)],[14063])).
% 8.39/8.69 tff(14065,plain,
% 8.39/8.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 8.39/8.69 inference(transitivity,[status(thm)],[14064, 14062])).
% 8.39/8.69 tff(14066,plain,
% 8.39/8.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 8.39/8.69 inference(quant_inst,[status(thm)],[])).
% 8.39/8.69 tff(14067,plain,
% 8.39/8.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 8.39/8.69 inference(modus_ponens,[status(thm)],[14066, 14065])).
% 8.39/8.69 tff(14068,plain,
% 8.39/8.69 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 8.39/8.69 inference(unit_resolution,[status(thm)],[14067, 194, 723, 1747, 1697])).
% 8.39/8.69 tff(14069,plain,
% 8.39/8.69 ($false),
% 8.39/8.69 inference(unit_resolution,[status(thm)],[14068, 14061])).
% 8.39/8.69 tff(14070,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.69 tff(14071,plain,
% 8.39/8.69 (~r(elem!1, s(s(s(s(elem!1)))))),
% 8.39/8.69 inference(unit_resolution,[status(thm)],[14070, 14010, 10646, 14056, 14054])).
% 8.39/8.69 tff(14072,plain,
% 8.39/8.69 (b(elem!1, s(s(s(s(elem!1)))))),
% 8.39/8.69 inference(unit_resolution,[status(thm)],[1018, 14071, 14052])).
% 8.39/8.69 tff(14073,plain,
% 8.39/8.69 (b(s(s(z)), s(s(s(s(s(s(z))))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 8.39/8.69 inference(monotonicity,[status(thm)],[9247, 14058])).
% 8.39/8.69 tff(14074,plain,
% 8.39/8.69 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 8.39/8.69 inference(symmetry,[status(thm)],[14073])).
% 8.39/8.69 tff(14075,plain,
% 8.39/8.69 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 8.39/8.69 inference(modus_ponens,[status(thm)],[974, 14074])).
% 8.39/8.69 tff(14076,assumption,(~b(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 8.39/8.69 tff(14077,plain,
% 8.39/8.69 ($false),
% 8.39/8.69 inference(unit_resolution,[status(thm)],[14076, 14075])).
% 8.39/8.69 tff(14078,plain,(b(s(s(z)), s(s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.69 tff(14079,plain,
% 8.39/8.69 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 8.39/8.69 inference(unit_resolution,[status(thm)],[14078, 14072, 14010])).
% 8.39/8.69 tff(14080,plain,
% 8.39/8.69 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 8.39/8.69 inference(monotonicity,[status(thm)],[14018])).
% 8.39/8.69 tff(14081,plain,
% 8.39/8.69 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(s(s(z)))))))),
% 8.39/8.69 inference(monotonicity,[status(thm)],[14018])).
% 8.39/8.69 tff(14082,plain,
% 8.39/8.69 (r(z, s(s(s(s(s(s(z))))))) <=> r(z, s(s(s(s(elem!1)))))),
% 8.39/8.69 inference(symmetry,[status(thm)],[14081])).
% 8.39/8.69 tff(14083,plain,
% 8.39/8.69 ((~r(z, s(s(s(s(s(s(z)))))))) <=> (~r(z, s(s(s(s(elem!1))))))),
% 8.39/8.69 inference(monotonicity,[status(thm)],[14082])).
% 8.39/8.69 tff(14084,assumption,(r(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 8.39/8.69 tff(14085,plain,
% 8.39/8.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 8.39/8.69 inference(rewrite,[status(thm)],[])).
% 8.39/8.69 tff(14086,plain,
% 8.39/8.69 (((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 8.39/8.69 inference(rewrite,[status(thm)],[])).
% 8.39/8.69 tff(14087,plain,
% 8.39/8.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 8.39/8.69 inference(monotonicity,[status(thm)],[14086])).
% 8.39/8.69 tff(14088,plain,
% 8.39/8.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 8.39/8.69 inference(transitivity,[status(thm)],[14087, 14085])).
% 8.39/8.69 tff(14089,plain,
% 8.39/8.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 8.39/8.69 inference(quant_inst,[status(thm)],[])).
% 8.39/8.69 tff(14090,plain,
% 8.39/8.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 8.39/8.70 inference(modus_ponens,[status(thm)],[14089, 14088])).
% 8.39/8.70 tff(14091,plain,
% 8.39/8.70 ($false),
% 8.39/8.70 inference(unit_resolution,[status(thm)],[14090, 194, 182, 2053, 723, 14084])).
% 8.39/8.70 tff(14092,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.39/8.70 tff(14093,plain,
% 8.39/8.70 (~r(z, s(s(s(s(s(s(z)))))))),
% 8.39/8.70 inference(unit_resolution,[status(thm)],[14092, 14037, 182, 10646])).
% 8.39/8.70 tff(14094,plain,
% 8.39/8.70 (~r(z, s(s(s(s(elem!1)))))),
% 8.39/8.70 inference(modus_ponens,[status(thm)],[14093, 14083])).
% 8.39/8.70 tff(14095,plain,
% 8.39/8.70 (b(z, s(s(s(s(elem!1)))))),
% 8.39/8.70 inference(unit_resolution,[status(thm)],[2767, 14094])).
% 8.39/8.70 tff(14096,plain,
% 8.39/8.70 (b(z, s(s(s(s(s(s(z)))))))),
% 8.39/8.70 inference(modus_ponens,[status(thm)],[14095, 14080])).
% 8.39/8.70 tff(14097,plain,
% 8.39/8.70 (b(elem!1, z) <=> b(s(s(z)), z)),
% 8.39/8.70 inference(monotonicity,[status(thm)],[14010])).
% 8.39/8.70 tff(14098,plain,
% 8.39/8.70 (b(s(s(z)), z)),
% 8.39/8.70 inference(modus_ponens,[status(thm)],[665, 14097])).
% 8.49/8.70 tff(14099,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 8.49/8.70 tff(14100,assumption,(b(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 8.49/8.70 tff(14101,assumption,(b(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 8.49/8.70 tff(14102,plain,
% 8.49/8.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 8.49/8.70 inference(rewrite,[status(thm)],[])).
% 8.49/8.70 tff(14103,plain,
% 8.49/8.70 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 8.49/8.70 inference(rewrite,[status(thm)],[])).
% 8.49/8.70 tff(14104,plain,
% 8.49/8.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 8.49/8.70 inference(monotonicity,[status(thm)],[14103])).
% 8.49/8.70 tff(14105,plain,
% 8.49/8.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 8.49/8.70 inference(transitivity,[status(thm)],[14104, 14102])).
% 8.49/8.70 tff(14106,plain,
% 8.49/8.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))),
% 8.49/8.70 inference(quant_inst,[status(thm)],[])).
% 8.49/8.70 tff(14107,plain,
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% 8.49/8.70 inference(modus_ponens,[status(thm)],[14106, 14105])).
% 8.49/8.70 tff(14108,plain,
% 8.49/8.70 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 8.49/8.70 inference(unit_resolution,[status(thm)],[14107, 391, 1235, 14101, 14100])).
% 8.49/8.70 tff(14109,plain,
% 8.49/8.70 ($false),
% 8.49/8.70 inference(unit_resolution,[status(thm)],[14108, 13971, 14099])).
% 8.49/8.70 tff(14110,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.70 tff(14111,plain,
% 8.49/8.70 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 8.49/8.70 inference(unit_resolution,[status(thm)],[14110, 14098, 14096, 14079, 14047, 14010])).
% 8.49/8.70 tff(14112,plain,
% 8.49/8.70 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 8.49/8.70 inference(modus_ponens,[status(thm)],[14111, 14025])).
% 8.49/8.70 tff(14113,plain,
% 8.49/8.70 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 8.49/8.70 inference(unit_resolution,[status(thm)],[1095, 14112, 14023])).
% 8.49/8.70 tff(14114,plain,
% 8.49/8.70 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 8.49/8.70 inference(modus_ponens,[status(thm)],[14113, 14021])).
% 8.49/8.70 tff(14115,plain,
% 8.49/8.70 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(elem!1))))),
% 8.49/8.70 inference(monotonicity,[status(thm)],[14014])).
% 8.49/8.70 tff(14116,plain,
% 8.49/8.70 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(s(z))))))),
% 8.49/8.70 inference(symmetry,[status(thm)],[14115])).
% 8.49/8.70 tff(14117,plain,
% 8.49/8.70 (r(s(z), s(s(s(s(s(z))))))),
% 8.49/8.70 inference(modus_ponens,[status(thm)],[13886, 14116])).
% 8.49/8.70 tff(14118,plain,
% 8.49/8.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 8.49/8.70 inference(rewrite,[status(thm)],[])).
% 8.49/8.70 tff(14119,plain,
% 8.49/8.70 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 8.49/8.70 inference(rewrite,[status(thm)],[])).
% 8.49/8.70 tff(14120,plain,
% 8.49/8.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 8.49/8.70 inference(monotonicity,[status(thm)],[14119])).
% 8.49/8.70 tff(14121,plain,
% 8.49/8.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 8.49/8.70 inference(transitivity,[status(thm)],[14120, 14118])).
% 8.49/8.70 tff(14122,plain,
% 8.49/8.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 8.49/8.70 inference(quant_inst,[status(thm)],[])).
% 8.49/8.70 tff(14123,plain,
% 8.49/8.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 8.49/8.70 inference(modus_ponens,[status(thm)],[14122, 14121])).
% 8.49/8.70 tff(14124,plain,
% 8.49/8.70 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 8.49/8.70 inference(unit_resolution,[status(thm)],[14123, 194])).
% 8.49/8.70 tff(14125,plain,
% 8.49/8.70 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 8.49/8.70 inference(unit_resolution,[status(thm)],[14124, 14117, 14114, 14017])).
% 8.49/8.70 tff(14126,plain,
% 8.49/8.70 ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))),
% 8.49/8.70 inference(unit_resolution,[status(thm)],[11665, 42, 14125])).
% 8.49/8.70 tff(14127,plain,
% 8.49/8.70 (b(s(z), s(s(s(s(s(s(z)))))))),
% 8.49/8.70 inference(unit_resolution,[status(thm)],[14126, 11652])).
% 8.49/8.70 tff(14128,plain,
% 8.49/8.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 8.49/8.70 inference(rewrite,[status(thm)],[])).
% 8.49/8.70 tff(14129,plain,
% 8.49/8.70 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 8.49/8.70 inference(rewrite,[status(thm)],[])).
% 8.49/8.70 tff(14130,plain,
% 8.49/8.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 8.49/8.70 inference(monotonicity,[status(thm)],[14129])).
% 8.49/8.70 tff(14131,plain,
% 8.49/8.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 8.49/8.70 inference(transitivity,[status(thm)],[14130, 14128])).
% 8.49/8.70 tff(14132,plain,
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% 8.49/8.70 inference(quant_inst,[status(thm)],[])).
% 8.49/8.70 tff(14133,plain,
% 8.49/8.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 8.49/8.70 inference(modus_ponens,[status(thm)],[14132, 14131])).
% 8.49/8.70 tff(14134,plain,
% 8.49/8.70 ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 8.49/8.70 inference(unit_resolution,[status(thm)],[14133, 194])).
% 8.49/8.70 tff(14135,plain,
% 8.49/8.70 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 8.49/8.70 inference(unit_resolution,[status(thm)],[14134, 14017, 14117, 14114])).
% 8.49/8.70 tff(14136,assumption,(~r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 8.49/8.70 tff(14137,assumption,(~b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 8.49/8.70 tff(14138,plain,
% 8.49/8.71 ($false),
% 8.49/8.71 inference(unit_resolution,[status(thm)],[11674, 42, 5065, 14137, 14136])).
% 8.49/8.71 tff(14139,plain,(r(s(s(s(s(s(s(z)))))), s(z)) | b(s(s(s(s(s(s(z)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.71 tff(14140,plain,
% 8.49/8.71 (b(s(s(s(s(s(s(z)))))), s(z))),
% 8.49/8.71 inference(unit_resolution,[status(thm)],[14139, 14135])).
% 8.49/8.71 tff(14141,plain,
% 8.49/8.71 (~r(z, s(z))),
% 8.49/8.71 inference(unit_resolution,[status(thm)],[10558, 14002, 182, 14037])).
% 8.49/8.71 tff(14142,plain,
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% 8.49/8.71 inference(unit_resolution,[status(thm)],[678, 14141])).
% 8.49/8.71 tff(14143,plain,
% 8.49/8.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 8.49/8.71 inference(rewrite,[status(thm)],[])).
% 8.49/8.71 tff(14144,plain,
% 8.49/8.71 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 8.49/8.71 inference(rewrite,[status(thm)],[])).
% 8.49/8.71 tff(14145,plain,
% 8.49/8.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 8.49/8.71 inference(monotonicity,[status(thm)],[14144])).
% 8.49/8.71 tff(14146,plain,
% 8.49/8.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 8.49/8.71 inference(transitivity,[status(thm)],[14145, 14143])).
% 8.49/8.71 tff(14147,plain,
% 8.49/8.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))),
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% 8.49/8.71 tff(14148,plain,
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% 8.49/8.71 inference(modus_ponens,[status(thm)],[14147, 14146])).
% 8.49/8.71 tff(14149,plain,
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% 8.49/8.71 tff(14151,plain,
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% 8.49/8.71 tff(14152,plain,
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% 8.49/8.71 tff(14154,plain,
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% 8.49/8.71 tff(14155,plain,
% 8.49/8.71 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 8.49/8.71 inference(transitivity,[status(thm)],[14154, 14153])).
% 8.49/8.71 tff(14156,plain,
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% 8.49/8.71 inference(monotonicity,[status(thm)],[3584])).
% 8.49/8.71 tff(14157,plain,
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% 8.49/8.71 tff(14158,plain,
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% 8.49/8.71 tff(14159,plain,
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% 8.49/8.71 inference(monotonicity,[status(thm)],[14158])).
% 8.49/8.71 tff(14160,plain,
% 8.49/8.71 (~(elem!1 = s(s(elem!1)))),
% 8.49/8.71 inference(modus_ponens,[status(thm)],[11940, 14159])).
% 8.49/8.71 tff(14161,plain,
% 8.49/8.71 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = elem!1))),
% 8.49/8.71 inference(monotonicity,[status(thm)],[14157])).
% 8.49/8.71 tff(14162,plain,
% 8.49/8.71 (~(s(s(elem!1)) = elem!1)),
% 8.49/8.71 inference(modus_ponens,[status(thm)],[11940, 14161])).
% 8.49/8.71 tff(14163,plain,
% 8.49/8.71 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(z)))),
% 8.49/8.71 inference(monotonicity,[status(thm)],[3584])).
% 8.49/8.71 tff(14164,plain,
% 8.49/8.71 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 8.49/8.71 inference(symmetry,[status(thm)],[14163])).
% 8.49/8.71 tff(14165,plain,
% 8.49/8.71 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 8.49/8.71 inference(monotonicity,[status(thm)],[9026])).
% 8.49/8.71 tff(14166,plain,
% 8.49/8.71 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 8.49/8.71 inference(symmetry,[status(thm)],[14165])).
% 8.49/8.71 tff(14167,plain,
% 8.49/8.71 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 8.49/8.71 inference(transitivity,[status(thm)],[14166, 14164])).
% 8.49/8.71 tff(14168,plain,
% 8.49/8.71 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(elem!1)), elem!1))),
% 8.49/8.71 inference(monotonicity,[status(thm)],[14167])).
% 8.49/8.71 tff(14169,plain,
% 8.49/8.71 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 8.49/8.71 inference(monotonicity,[status(thm)],[3584])).
% 8.49/8.71 tff(14170,plain,
% 8.49/8.71 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 8.49/8.71 inference(monotonicity,[status(thm)],[14169])).
% 8.49/8.71 tff(14171,plain,
% 8.49/8.71 (~b(s(s(s(s(z)))), s(s(z)))),
% 8.49/8.71 inference(modus_ponens,[status(thm)],[1549, 14170])).
% 8.49/8.71 tff(14172,plain,
% 8.49/8.71 (~b(s(s(elem!1)), elem!1)),
% 8.49/8.71 inference(modus_ponens,[status(thm)],[14171, 14168])).
% 8.49/8.71 tff(14173,plain,
% 8.49/8.71 (r(s(s(elem!1)), elem!1)),
% 8.49/8.71 inference(unit_resolution,[status(thm)],[872, 14172, 14162])).
% 8.49/8.71 tff(14174,plain,
% 8.49/8.71 (~(s(s(elem!1)) = s(elem!1))),
% 8.49/8.71 inference(unit_resolution,[status(thm)],[264, 14162])).
% 8.49/8.71 tff(14175,plain,
% 8.49/8.71 (~(s(elem!1) = s(s(elem!1)))),
% 8.49/8.71 inference(unit_resolution,[status(thm)],[9802, 14174])).
% 8.49/8.71 tff(14176,plain,
% 8.49/8.71 (s(s(z)) = elem!1),
% 8.49/8.71 inference(modus_ponens,[status(thm)],[3584, 8492])).
% 8.49/8.71 tff(14177,plain,
% 8.49/8.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.49/8.71 inference(unit_resolution,[status(thm)],[4584, 14176, 121])).
% 8.49/8.71 tff(14178,plain,
% 8.49/8.71 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 8.49/8.71 inference(monotonicity,[status(thm)],[3584, 14057])).
% 8.49/8.71 tff(14179,plain,
% 8.49/8.71 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 8.49/8.71 inference(transitivity,[status(thm)],[14178, 8194])).
% 8.49/8.71 tff(14180,plain,
% 8.49/8.71 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 8.49/8.71 inference(symmetry,[status(thm)],[14179])).
% 8.49/8.71 tff(14181,plain,
% 8.49/8.71 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 8.49/8.71 inference(monotonicity,[status(thm)],[14180])).
% 8.49/8.71 tff(14182,plain,
% 8.49/8.71 (~(elem!1 = s(s(s(s(elem!1)))))),
% 8.49/8.71 inference(modus_ponens,[status(thm)],[5009, 14181])).
% 8.49/8.71 tff(14183,plain,
% 8.49/8.71 (s(s(s(s(z)))) = s(s(elem!1))),
% 8.49/8.71 inference(symmetry,[status(thm)],[9026])).
% 8.49/8.71 tff(14184,plain,
% 8.49/8.71 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 8.49/8.71 inference(monotonicity,[status(thm)],[14183, 14058])).
% 8.49/8.71 tff(14185,plain,
% 8.49/8.71 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 8.49/8.71 inference(transitivity,[status(thm)],[14184, 1020])).
% 8.49/8.72 tff(14186,plain,
% 8.49/8.72 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 8.49/8.72 inference(transitivity,[status(thm)],[14185, 1021])).
% 8.49/8.72 tff(14187,plain,
% 8.49/8.72 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 8.49/8.72 inference(monotonicity,[status(thm)],[14186])).
% 8.49/8.72 tff(14188,plain,
% 8.49/8.72 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 8.49/8.72 inference(modus_ponens,[status(thm)],[4995, 14187])).
% 8.49/8.72 tff(14189,plain,
% 8.49/8.72 (b(s(s(elem!1)), s(z))),
% 8.49/8.72 inference(modus_ponens,[status(thm)],[1759, 9028])).
% 8.49/8.72 tff(14190,plain,
% 8.49/8.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.49/8.72 inference(rewrite,[status(thm)],[])).
% 8.49/8.72 tff(14191,plain,
% 8.49/8.72 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.49/8.72 inference(rewrite,[status(thm)],[])).
% 8.49/8.72 tff(14192,plain,
% 8.49/8.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 8.49/8.72 inference(monotonicity,[status(thm)],[14191])).
% 8.49/8.72 tff(14193,plain,
% 8.49/8.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.49/8.72 inference(transitivity,[status(thm)],[14192, 14190])).
% 8.49/8.72 tff(14194,plain,
% 8.49/8.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 8.49/8.72 inference(quant_inst,[status(thm)],[])).
% 8.49/8.72 tff(14195,plain,
% 8.49/8.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 8.49/8.72 inference(modus_ponens,[status(thm)],[14194, 14193])).
% 8.49/8.72 tff(14196,plain,
% 8.49/8.72 ($false),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[14195, 391, 665, 381, 10682, 448, 1374])).
% 8.49/8.72 tff(14197,plain,((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.72 tff(14198,plain,
% 8.49/8.72 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[14197, 14189, 10682, 448, 665])).
% 8.49/8.72 tff(14199,plain,
% 8.49/8.72 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[1370, 14198, 13756])).
% 8.49/8.72 tff(14200,plain,
% 8.49/8.72 (~r(z, s(s(elem!1)))),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[13828, 14199, 14173, 10878])).
% 8.49/8.72 tff(14201,plain,
% 8.49/8.72 (b(z, s(s(elem!1)))),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[324, 14200])).
% 8.49/8.72 tff(14202,plain,
% 8.49/8.72 (r(s(s(elem!1)), elem!1)),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[872, 6564, 249])).
% 8.49/8.72 tff(14203,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 8.49/8.72 tff(14204,plain,
% 8.49/8.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 8.49/8.72 inference(rewrite,[status(thm)],[])).
% 8.49/8.72 tff(14205,plain,
% 8.49/8.72 (((~r(elem!1, s(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)))))) <=> ((~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))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 8.49/8.72 inference(rewrite,[status(thm)],[])).
% 8.49/8.72 tff(14206,plain,
% 8.49/8.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 8.49/8.72 inference(monotonicity,[status(thm)],[14205])).
% 8.49/8.72 tff(14207,plain,
% 8.49/8.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 8.49/8.72 inference(transitivity,[status(thm)],[14206, 14204])).
% 8.49/8.72 tff(14208,plain,
% 8.49/8.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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))))))),
% 8.49/8.72 inference(quant_inst,[status(thm)],[])).
% 8.49/8.72 tff(14209,plain,
% 8.49/8.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 8.49/8.72 inference(modus_ponens,[status(thm)],[14208, 14207])).
% 8.49/8.72 tff(14210,plain,
% 8.49/8.72 ($false),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[14209, 194, 233, 364, 1063, 1378])).
% 8.49/8.72 tff(14211,plain,((~r(elem!1, s(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)))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.72 tff(14212,plain,
% 8.49/8.72 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[14211, 1063, 364, 233])).
% 8.49/8.72 tff(14213,plain,
% 8.49/8.72 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[1356, 14212, 270])).
% 8.49/8.72 tff(14214,plain,
% 8.49/8.72 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[12932, 14213, 10682, 3927])).
% 8.49/8.72 tff(14215,plain,
% 8.49/8.72 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[1370, 14214, 297])).
% 8.49/8.72 tff(14216,plain,
% 8.49/8.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 8.49/8.72 inference(rewrite,[status(thm)],[])).
% 8.49/8.72 tff(14217,plain,
% 8.49/8.72 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 8.49/8.72 inference(rewrite,[status(thm)],[])).
% 8.49/8.72 tff(14218,plain,
% 8.49/8.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 8.49/8.72 inference(monotonicity,[status(thm)],[14217])).
% 8.49/8.72 tff(14219,plain,
% 8.49/8.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 8.49/8.72 inference(transitivity,[status(thm)],[14218, 14216])).
% 8.49/8.72 tff(14220,plain,
% 8.49/8.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.49/8.72 inference(quant_inst,[status(thm)],[])).
% 8.49/8.72 tff(14221,plain,
% 8.49/8.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 8.49/8.72 inference(modus_ponens,[status(thm)],[14220, 14219])).
% 8.49/8.72 tff(14222,plain,
% 8.49/8.72 ($false),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[14221, 194, 233, 364, 14215, 1063])).
% 8.49/8.72 tff(14223,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.72 tff(14224,plain,
% 8.49/8.72 (~r(elem!1, s(s(s(s(elem!1)))))),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[14223, 14202, 233, 297, 10682, 3927, 270])).
% 8.49/8.72 tff(14225,plain,
% 8.49/8.72 (b(elem!1, s(s(s(s(elem!1)))))),
% 8.49/8.72 inference(unit_resolution,[status(thm)],[1018, 14224, 14203])).
% 8.49/8.72 tff(14226,plain,
% 8.49/8.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 8.49/8.72 inference(rewrite,[status(thm)],[])).
% 8.49/8.72 tff(14227,plain,
% 8.49/8.72 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 8.49/8.72 inference(rewrite,[status(thm)],[])).
% 8.49/8.72 tff(14228,plain,
% 8.49/8.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 8.49/8.73 inference(monotonicity,[status(thm)],[14227])).
% 8.49/8.73 tff(14229,plain,
% 8.49/8.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 8.49/8.73 inference(transitivity,[status(thm)],[14228, 14226])).
% 8.49/8.73 tff(14230,plain,
% 8.49/8.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 8.49/8.73 inference(quant_inst,[status(thm)],[])).
% 8.49/8.73 tff(14231,plain,
% 8.49/8.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 8.49/8.73 inference(modus_ponens,[status(thm)],[14230, 14229])).
% 8.49/8.73 tff(14232,plain,
% 8.49/8.73 ($false),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[14231, 391, 665, 10682, 448, 1733, 1573])).
% 8.49/8.73 tff(14233,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.73 tff(14234,plain,
% 8.49/8.73 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[14233, 1573, 10682, 448, 665])).
% 8.49/8.73 tff(14235,plain,
% 8.49/8.73 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[1061, 14234, 1050])).
% 8.49/8.73 tff(14236,plain,
% 8.49/8.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 8.49/8.73 inference(rewrite,[status(thm)],[])).
% 8.49/8.73 tff(14237,plain,
% 8.49/8.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 8.49/8.73 inference(quant_inst,[status(thm)],[])).
% 8.49/8.73 tff(14238,plain,
% 8.49/8.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 8.49/8.73 inference(modus_ponens,[status(thm)],[14237, 14236])).
% 8.49/8.73 tff(14239,plain,
% 8.49/8.73 ($false),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[14238, 194, 364, 327, 1177, 1082])).
% 8.49/8.73 tff(14240,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.73 tff(14241,plain,
% 8.49/8.73 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[14240, 14235, 327, 364])).
% 8.49/8.73 tff(14242,plain,
% 8.49/8.73 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[1095, 14241, 305])).
% 8.49/8.73 tff(14243,plain,
% 8.49/8.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 8.49/8.73 inference(rewrite,[status(thm)],[])).
% 8.49/8.73 tff(14244,plain,
% 8.49/8.73 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 8.49/8.73 inference(rewrite,[status(thm)],[])).
% 8.49/8.73 tff(14245,plain,
% 8.49/8.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 8.49/8.73 inference(monotonicity,[status(thm)],[14244])).
% 8.49/8.73 tff(14246,plain,
% 8.49/8.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 8.49/8.73 inference(transitivity,[status(thm)],[14245, 14243])).
% 8.49/8.73 tff(14247,plain,
% 8.49/8.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 8.49/8.73 inference(quant_inst,[status(thm)],[])).
% 8.49/8.73 tff(14248,plain,
% 8.49/8.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 8.49/8.73 inference(modus_ponens,[status(thm)],[14247, 14246])).
% 8.49/8.73 tff(14249,plain,
% 8.49/8.73 ($false),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[14248, 391, 448, 974, 1573, 14242])).
% 8.49/8.73 tff(14250,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.73 tff(14251,plain,
% 8.49/8.73 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[14250, 14225, 448, 310, 327, 14202, 2712, 10682, 665])).
% 8.49/8.73 tff(14252,plain,
% 8.49/8.73 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[1164, 14251, 311])).
% 8.49/8.73 tff(14253,plain,
% 8.49/8.73 (elem!1 = s(s(s(s(elem!1))))),
% 8.49/8.73 inference(modus_ponens,[status(thm)],[7465, 950])).
% 8.49/8.73 tff(14254,plain,
% 8.49/8.73 ($false),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[14203, 14253])).
% 8.49/8.73 tff(14255,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.73 tff(14256,plain,
% 8.49/8.73 (~(s(s(s(s(elem!1)))) = elem!1)),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[14255, 14203])).
% 8.49/8.73 tff(14257,plain,
% 8.49/8.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 8.49/8.73 inference(rewrite,[status(thm)],[])).
% 8.49/8.73 tff(14258,plain,
% 8.49/8.73 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 8.49/8.73 inference(rewrite,[status(thm)],[])).
% 8.49/8.73 tff(14259,plain,
% 8.49/8.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 8.49/8.73 inference(monotonicity,[status(thm)],[14258])).
% 8.49/8.73 tff(14260,plain,
% 8.49/8.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 8.49/8.73 inference(transitivity,[status(thm)],[14259, 14257])).
% 8.49/8.73 tff(14261,plain,
% 8.49/8.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 8.49/8.73 inference(quant_inst,[status(thm)],[])).
% 8.49/8.73 tff(14262,plain,
% 8.49/8.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 8.49/8.73 inference(modus_ponens,[status(thm)],[14261, 14260])).
% 8.49/8.73 tff(14263,plain,
% 8.49/8.73 ($false),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[14262, 391, 133, 665, 2698, 2781])).
% 8.49/8.73 tff(14264,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.73 tff(14265,plain,
% 8.49/8.73 (~b(s(s(s(s(elem!1)))), elem!1)),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[14264, 2781, 665, 133])).
% 8.49/8.73 tff(14266,plain,
% 8.49/8.73 (r(s(s(s(s(elem!1)))), elem!1)),
% 8.49/8.73 inference(unit_resolution,[status(thm)],[1004, 14265, 14256])).
% 8.49/8.73 tff(14267,plain,
% 8.49/8.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 8.49/8.74 inference(rewrite,[status(thm)],[])).
% 8.49/8.74 tff(14268,plain,
% 8.49/8.74 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 8.49/8.74 inference(rewrite,[status(thm)],[])).
% 8.49/8.74 tff(14269,plain,
% 8.49/8.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 8.49/8.74 inference(monotonicity,[status(thm)],[14268])).
% 8.49/8.74 tff(14270,plain,
% 8.49/8.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 8.49/8.74 inference(transitivity,[status(thm)],[14269, 14267])).
% 8.49/8.74 tff(14271,plain,
% 8.49/8.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 8.49/8.74 inference(quant_inst,[status(thm)],[])).
% 8.49/8.74 tff(14272,plain,
% 8.49/8.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 8.49/8.74 inference(modus_ponens,[status(thm)],[14271, 14270])).
% 8.49/8.74 tff(14273,plain,
% 8.49/8.74 ($false),
% 8.49/8.74 inference(unit_resolution,[status(thm)],[14272, 194, 327, 991, 1538, 1176])).
% 8.49/8.74 tff(14274,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.74 tff(14275,plain,
% 8.49/8.74 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 8.49/8.74 inference(unit_resolution,[status(thm)],[14274, 14252, 327, 14266])).
% 8.49/8.74 tff(14276,plain,
% 8.49/8.74 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 8.49/8.74 inference(unit_resolution,[status(thm)],[1048, 14275, 1035])).
% 8.49/8.74 tff(14277,plain,
% 8.49/8.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 8.49/8.74 inference(rewrite,[status(thm)],[])).
% 8.49/8.74 tff(14278,plain,
% 8.49/8.74 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 8.49/8.74 inference(rewrite,[status(thm)],[])).
% 8.49/8.74 tff(14279,plain,
% 8.49/8.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 8.49/8.74 inference(monotonicity,[status(thm)],[14278])).
% 8.49/8.74 tff(14280,plain,
% 8.49/8.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 8.49/8.74 inference(transitivity,[status(thm)],[14279, 14277])).
% 8.49/8.74 tff(14281,plain,
% 8.49/8.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 8.49/8.74 inference(quant_inst,[status(thm)],[])).
% 8.49/8.74 tff(14282,plain,
% 8.49/8.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 8.49/8.74 inference(modus_ponens,[status(thm)],[14281, 14280])).
% 8.49/8.74 tff(14283,plain,
% 8.49/8.74 ($false),
% 8.49/8.74 inference(unit_resolution,[status(thm)],[14282, 391, 3927, 1733, 2781, 1152])).
% 8.49/8.74 tff(14284,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.74 tff(14285,plain,
% 8.49/8.74 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.49/8.74 inference(unit_resolution,[status(thm)],[14284, 3927, 2781, 14276])).
% 8.49/8.74 tff(14286,plain,
% 8.49/8.74 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.49/8.74 inference(unit_resolution,[status(thm)],[1061, 14285, 2712])).
% 8.49/8.74 tff(14287,plain,
% 8.49/8.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.49/8.74 inference(rewrite,[status(thm)],[])).
% 8.49/8.74 tff(14288,plain,
% 8.49/8.74 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.49/8.74 inference(rewrite,[status(thm)],[])).
% 8.49/8.74 tff(14289,plain,
% 8.49/8.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 8.49/8.74 inference(monotonicity,[status(thm)],[14288])).
% 8.49/8.74 tff(14290,plain,
% 8.49/8.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.49/8.75 inference(transitivity,[status(thm)],[14289, 14287])).
% 8.49/8.75 tff(14291,plain,
% 8.49/8.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 8.49/8.75 inference(quant_inst,[status(thm)],[])).
% 8.49/8.75 tff(14292,plain,
% 8.49/8.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 8.49/8.75 inference(modus_ponens,[status(thm)],[14291, 14290])).
% 8.49/8.75 tff(14293,plain,
% 8.49/8.75 ($false),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[14292, 194, 14202, 327, 14286, 14252])).
% 8.49/8.75 tff(14294,plain,((~b(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.75 tff(14295,plain,
% 8.49/8.75 (~b(z, s(s(s(s(elem!1)))))),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[14294, 14201, 14199, 14188, 448, 10682, 665, 14182, 233, 13756, 13782, 14162, 133])).
% 8.49/8.75 tff(14296,plain,
% 8.49/8.75 (r(z, s(s(s(s(elem!1)))))),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[2767, 14295])).
% 8.49/8.75 tff(14297,plain,
% 8.49/8.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))),
% 8.49/8.75 inference(rewrite,[status(thm)],[])).
% 8.49/8.75 tff(14298,plain,
% 8.49/8.75 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))),
% 8.49/8.75 inference(rewrite,[status(thm)],[])).
% 8.49/8.75 tff(14299,plain,
% 8.49/8.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(elem!1))))))))),
% 8.49/8.75 inference(monotonicity,[status(thm)],[14298])).
% 8.49/8.75 tff(14300,plain,
% 8.49/8.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))),
% 8.49/8.75 inference(transitivity,[status(thm)],[14299, 14297])).
% 8.49/8.75 tff(14301,plain,
% 8.49/8.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 8.49/8.75 inference(quant_inst,[status(thm)],[])).
% 8.49/8.75 tff(14302,plain,
% 8.49/8.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(elem!1))))))),
% 8.49/8.75 inference(modus_ponens,[status(thm)],[14301, 14300])).
% 8.49/8.75 tff(14303,plain,
% 8.49/8.75 ($false),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[14302, 194, 613, 1628, 174, 2792])).
% 8.49/8.75 tff(14304,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.75 tff(14305,plain,
% 8.49/8.75 (~r(s(s(s(elem!1))), s(elem!1))),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[14304, 14296, 1628, 10878])).
% 8.49/8.75 tff(14306,plain,
% 8.49/8.75 (b(s(s(s(elem!1))), s(elem!1))),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[588, 14305, 14177])).
% 8.49/8.75 tff(14307,plain,
% 8.49/8.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 8.49/8.75 inference(rewrite,[status(thm)],[])).
% 8.49/8.75 tff(14308,plain,
% 8.49/8.75 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 8.49/8.75 inference(rewrite,[status(thm)],[])).
% 8.49/8.75 tff(14309,plain,
% 8.49/8.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))))),
% 8.49/8.75 inference(monotonicity,[status(thm)],[14308])).
% 8.49/8.75 tff(14310,plain,
% 8.49/8.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 8.49/8.75 inference(transitivity,[status(thm)],[14309, 14307])).
% 8.49/8.75 tff(14311,plain,
% 8.49/8.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 8.49/8.75 inference(quant_inst,[status(thm)],[])).
% 8.49/8.75 tff(14312,plain,
% 8.49/8.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))),
% 8.49/8.75 inference(modus_ponens,[status(thm)],[14311, 14310])).
% 8.49/8.75 tff(14313,plain,
% 8.49/8.75 ($false),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[14312, 391, 665, 1101, 10682, 448, 7625])).
% 8.49/8.75 tff(14314,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.75 tff(14315,plain,
% 8.49/8.75 (~b(s(elem!1), s(s(elem!1)))),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[14314, 14306, 665, 10682, 448])).
% 8.49/8.75 tff(14316,plain,
% 8.49/8.75 (r(s(elem!1), s(s(elem!1)))),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[8644, 14315, 14175])).
% 8.49/8.75 tff(14317,plain,
% 8.49/8.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(elem!1)))))),
% 8.49/8.75 inference(rewrite,[status(thm)],[])).
% 8.49/8.75 tff(14318,plain,
% 8.49/8.75 (((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 8.49/8.75 inference(rewrite,[status(thm)],[])).
% 8.49/8.75 tff(14319,plain,
% 8.49/8.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(elem!1))))))),
% 8.49/8.75 inference(monotonicity,[status(thm)],[14318])).
% 8.49/8.75 tff(14320,plain,
% 8.49/8.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(elem!1, s(s(elem!1)))))),
% 8.49/8.75 inference(transitivity,[status(thm)],[14319, 14317])).
% 8.49/8.75 tff(14321,plain,
% 8.49/8.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 8.49/8.75 inference(quant_inst,[status(thm)],[])).
% 8.49/8.75 tff(14322,plain,
% 8.49/8.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 8.49/8.75 inference(modus_ponens,[status(thm)],[14321, 14320])).
% 8.49/8.75 tff(14323,plain,
% 8.49/8.75 ($false),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[14322, 194, 485, 364, 1064, 7538])).
% 8.49/8.75 tff(14324,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.75 tff(14325,plain,
% 8.49/8.75 (~r(elem!1, s(s(elem!1)))),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[14324, 14316, 14173, 485])).
% 8.49/8.75 tff(14326,plain,
% 8.49/8.75 (b(elem!1, s(s(elem!1)))),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[1307, 14325, 14160])).
% 8.49/8.75 tff(14327,plain,
% 8.49/8.75 (b(elem!1, s(s(s(s(z)))))),
% 8.49/8.75 inference(modus_ponens,[status(thm)],[14326, 14155])).
% 8.49/8.75 tff(14328,plain,
% 8.49/8.75 (~b(s(s(s(s(z)))), z)),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[12445, 14327, 665, 133])).
% 8.49/8.75 tff(14329,plain,
% 8.49/8.75 (r(s(s(s(s(z)))), z)),
% 8.49/8.75 inference(unit_resolution,[status(thm)],[87, 14328])).
% 8.49/8.75 tff(14330,plain,
% 8.49/8.75 (r(s(s(elem!1)), z)),
% 8.49/8.75 inference(modus_ponens,[status(thm)],[14329, 9036])).
% 8.49/8.75 tff(14331,plain,
% 8.49/8.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 8.49/8.75 inference(rewrite,[status(thm)],[])).
% 8.49/8.76 tff(14332,plain,
% 8.49/8.76 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 8.49/8.76 inference(rewrite,[status(thm)],[])).
% 8.49/8.76 tff(14333,plain,
% 8.49/8.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 8.49/8.76 inference(monotonicity,[status(thm)],[14332])).
% 8.49/8.76 tff(14334,plain,
% 8.49/8.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 8.49/8.76 inference(transitivity,[status(thm)],[14333, 14331])).
% 8.49/8.76 tff(14335,plain,
% 8.49/8.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 8.49/8.76 inference(quant_inst,[status(thm)],[])).
% 8.49/8.76 tff(14336,plain,
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% 8.49/8.76 inference(modus_ponens,[status(thm)],[14335, 14334])).
% 8.49/8.76 tff(14337,plain,
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% 8.49/8.76 inference(unit_resolution,[status(thm)],[14336, 391, 665, 381, 3927, 1294, 379])).
% 8.49/8.76 tff(14338,plain,((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.76 tff(14339,plain,
% 8.49/8.76 (~b(s(z), s(s(s(elem!1))))),
% 8.49/8.76 inference(unit_resolution,[status(thm)],[14338, 14326, 665, 14189, 14201])).
% 8.49/8.76 tff(14340,plain,
% 8.49/8.76 (r(s(z), s(s(s(elem!1))))),
% 8.49/8.76 inference(unit_resolution,[status(thm)],[247, 14339])).
% 8.49/8.76 tff(14341,plain,
% 8.49/8.76 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 8.49/8.76 inference(monotonicity,[status(thm)],[3584])).
% 8.49/8.76 tff(14342,plain,
% 8.49/8.76 (b(s(s(z)), s(z))),
% 8.49/8.76 inference(modus_ponens,[status(thm)],[721, 14341])).
% 8.49/8.76 tff(14343,plain,
% 8.49/8.76 (b(s(s(z)), s(s(s(s(z)))))),
% 8.49/8.76 inference(modus_ponens,[status(thm)],[14326, 14154])).
% 8.49/8.76 tff(14344,plain,
% 8.49/8.76 (~b(s(z), s(s(s(s(z)))))),
% 8.49/8.76 inference(unit_resolution,[status(thm)],[5108, 14343, 1759, 14342])).
% 8.49/8.76 tff(14345,plain,
% 8.49/8.76 (r(s(z), s(s(s(s(z)))))),
% 8.49/8.76 inference(unit_resolution,[status(thm)],[1230, 14344])).
% 8.49/8.76 tff(14346,plain,
% 8.49/8.76 (r(s(z), s(s(elem!1)))),
% 8.49/8.76 inference(unit_resolution,[status(thm)],[11275, 14345, 14176])).
% 8.49/8.76 tff(14347,plain,
% 8.49/8.76 (~r(s(s(elem!1)), z)),
% 8.49/8.76 inference(unit_resolution,[status(thm)],[4840, 14346, 14340, 14199])).
% 8.49/8.76 tff(14348,plain,
% 8.49/8.76 ($false),
% 8.49/8.76 inference(unit_resolution,[status(thm)],[14347, 14330])).
% 8.49/8.76 tff(14349,plain,((~(elem!1 = s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (s(z) = s(elem!1)) | (~b(elem!1, s(z))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.49/8.76 tff(14350,plain,
% 8.49/8.76 (~(elem!1 = s(s(z)))),
% 8.49/8.76 inference(unit_resolution,[status(thm)],[14349, 14151, 11936, 133, 13120, 10682, 13691, 13111, 13695, 118, 13709, 13710])).
% 8.49/8.76 tff(14351,plain,
% 8.49/8.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z)))))),
% 8.49/8.76 inference(rewrite,[status(thm)],[])).
% 8.49/8.76 tff(14352,plain,
% 8.49/8.76 (((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z)))))),
% 8.49/8.76 inference(rewrite,[status(thm)],[])).
% 8.49/8.76 tff(14353,plain,
% 8.49/8.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z))))))),
% 8.49/8.76 inference(monotonicity,[status(thm)],[14352])).
% 8.49/8.76 tff(14354,plain,
% 8.49/8.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z)))))),
% 8.49/8.76 inference(transitivity,[status(thm)],[14353, 14351])).
% 8.49/8.76 tff(14355,plain,
% 8.49/8.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 8.49/8.76 inference(quant_inst,[status(thm)],[])).
% 8.49/8.76 tff(14356,plain,
% 8.49/8.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z))))),
% 8.49/8.76 inference(modus_ponens,[status(thm)],[14355, 14354])).
% 8.49/8.76 tff(14357,plain,
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% 8.49/8.76 inference(unit_resolution,[status(thm)],[14356, 194, 233, 1484, 183, 1748])).
% 8.49/8.76 tff(14358,plain,((~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.76 tff(14359,plain,
% 8.49/8.76 (~r(s(s(s(elem!1))), s(z))),
% 8.49/8.76 inference(unit_resolution,[status(thm)],[14358, 1748, 1484, 233])).
% 8.49/8.76 tff(14360,plain,
% 8.49/8.76 (b(s(s(s(elem!1))), s(z))),
% 8.49/8.76 inference(unit_resolution,[status(thm)],[223, 14359])).
% 8.49/8.76 tff(14361,plain,
% 8.49/8.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))),
% 8.49/8.76 inference(rewrite,[status(thm)],[])).
% 8.49/8.76 tff(14362,plain,
% 8.49/8.76 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))),
% 8.49/8.76 inference(rewrite,[status(thm)],[])).
% 8.49/8.76 tff(14363,plain,
% 8.49/8.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(z))))))),
% 8.49/8.76 inference(monotonicity,[status(thm)],[14362])).
% 8.49/8.77 tff(14364,plain,
% 8.49/8.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))),
% 8.49/8.77 inference(transitivity,[status(thm)],[14363, 14361])).
% 8.49/8.77 tff(14365,plain,
% 8.49/8.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 8.49/8.77 inference(quant_inst,[status(thm)],[])).
% 8.49/8.77 tff(14366,plain,
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% 8.49/8.77 inference(modus_ponens,[status(thm)],[14365, 14364])).
% 8.49/8.77 tff(14367,plain,
% 8.49/8.77 (~r(s(z), s(s(s(elem!1))))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[14366, 194, 233, 1484, 1748])).
% 8.49/8.77 tff(14368,plain,
% 8.49/8.77 (b(s(z), s(s(s(elem!1))))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[247, 14367])).
% 8.49/8.77 tff(14369,plain,
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% 8.49/8.77 tff(14370,plain,((~r(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.77 tff(14371,plain,
% 8.49/8.77 (~r(elem!1, s(s(z)))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[14370, 13691, 13709, 13695, 13731])).
% 8.49/8.77 tff(14372,plain,
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% 8.49/8.77 inference(unit_resolution,[status(thm)],[3394, 14350, 14371])).
% 8.49/8.77 tff(14373,plain,
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% 8.49/8.77 inference(unit_resolution,[status(thm)],[13448, 14372, 11936, 133])).
% 8.49/8.77 tff(14374,plain,
% 8.49/8.77 (r(s(s(z)), z)),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[1211, 14373])).
% 8.49/8.77 tff(14375,plain,
% 8.49/8.77 (~b(s(z), s(s(s(s(z)))))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[8916, 688, 2829])).
% 8.49/8.77 tff(14376,plain,
% 8.49/8.77 (r(s(z), s(s(s(s(z)))))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[1230, 14375])).
% 8.49/8.77 tff(14377,plain,
% 8.49/8.77 (b(elem!1, s(z))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[13708, 665, 10682, 448, 233, 150, 2829])).
% 8.49/8.77 tff(14378,plain,
% 8.49/8.77 (~b(s(s(s(s(z)))), s(s(z)))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[11029, 3583, 688])).
% 8.49/8.77 tff(14379,plain,
% 8.49/8.77 (r(s(s(s(s(z)))), s(s(z)))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[1714, 14378])).
% 8.49/8.77 tff(14380,plain,
% 8.49/8.77 (r(elem!1, s(s(z)))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[3394, 3583, 1405])).
% 8.49/8.77 tff(14381,plain,
% 8.49/8.77 (~r(s(s(s(elem!1))), s(z))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[14358, 14380, 1484, 233])).
% 8.49/8.77 tff(14382,plain,
% 8.49/8.77 (b(s(s(s(elem!1))), s(z))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[223, 14381])).
% 8.49/8.77 tff(14383,plain,
% 8.49/8.77 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 8.49/8.77 inference(monotonicity,[status(thm)],[688])).
% 8.49/8.77 tff(14384,plain,
% 8.49/8.77 (~r(s(z), s(s(z)))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[11508, 1697, 3557, 1216])).
% 8.49/8.77 tff(14385,plain,
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% 8.49/8.77 inference(unit_resolution,[status(thm)],[1788, 14384])).
% 8.49/8.77 tff(14386,plain,
% 8.49/8.77 (~b(s(s(z)), s(z))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[9961, 14385, 448, 721, 1526])).
% 8.49/8.77 tff(14387,plain,
% 8.49/8.77 (r(s(s(z)), s(z))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[3778, 14386])).
% 8.49/8.77 tff(14388,plain,
% 8.49/8.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.49/8.77 inference(rewrite,[status(thm)],[])).
% 8.49/8.77 tff(14389,plain,
% 8.49/8.77 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(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)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.49/8.77 inference(rewrite,[status(thm)],[])).
% 8.49/8.77 tff(14390,plain,
% 8.49/8.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 8.49/8.77 inference(monotonicity,[status(thm)],[14389])).
% 8.49/8.77 tff(14391,plain,
% 8.49/8.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.49/8.77 inference(transitivity,[status(thm)],[14390, 14388])).
% 8.49/8.77 tff(14392,plain,
% 8.49/8.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 8.49/8.77 inference(quant_inst,[status(thm)],[])).
% 8.49/8.77 tff(14393,plain,
% 8.49/8.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 8.49/8.77 inference(modus_ponens,[status(thm)],[14392, 14391])).
% 8.49/8.77 tff(14394,plain,
% 8.49/8.77 ($false),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[14393, 194, 1749, 1216, 1697, 2405])).
% 8.49/8.77 tff(14395,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.77 tff(14396,plain,
% 8.49/8.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[14395, 14387, 1697, 1216])).
% 8.49/8.77 tff(14397,plain,
% 8.49/8.77 (b(s(s(z)), s(s(s(s(z)))))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[3652, 14396])).
% 8.49/8.77 tff(14398,plain,
% 8.49/8.77 (b(s(s(z)), elem!1)),
% 8.49/8.77 inference(modus_ponens,[status(thm)],[14397, 14383])).
% 8.49/8.77 tff(14399,plain,
% 8.49/8.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 8.49/8.77 inference(rewrite,[status(thm)],[])).
% 8.49/8.77 tff(14400,plain,
% 8.49/8.77 (((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 8.49/8.77 inference(rewrite,[status(thm)],[])).
% 8.49/8.77 tff(14401,plain,
% 8.49/8.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 8.49/8.77 inference(monotonicity,[status(thm)],[14400])).
% 8.49/8.77 tff(14402,plain,
% 8.49/8.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 8.49/8.77 inference(transitivity,[status(thm)],[14401, 14399])).
% 8.49/8.77 tff(14403,plain,
% 8.49/8.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 8.49/8.77 inference(quant_inst,[status(thm)],[])).
% 8.49/8.77 tff(14404,plain,
% 8.49/8.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 8.49/8.77 inference(modus_ponens,[status(thm)],[14403, 14402])).
% 8.49/8.77 tff(14405,plain,
% 8.49/8.77 ($false),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[14404, 391, 448, 1526, 14385, 14398, 721])).
% 8.49/8.77 tff(14406,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.77 tff(14407,plain,
% 8.49/8.77 ($false),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[14406, 14382, 14379, 448, 721, 688, 1216, 3557])).
% 8.49/8.77 tff(14408,plain,(b(elem!1, s(s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.77 tff(14409,plain,
% 8.49/8.77 (b(elem!1, s(s(z)))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[14408, 688, 14377, 448, 14376, 3557, 5429, 233, 1405])).
% 8.49/8.77 tff(14410,plain,
% 8.49/8.77 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[717, 688])).
% 8.49/8.77 tff(14411,plain,
% 8.49/8.77 (~(s(s(elem!1)) = elem!1)),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[451, 14410])).
% 8.49/8.77 tff(14412,plain,
% 8.49/8.77 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[281, 14410])).
% 8.49/8.77 tff(14413,plain,
% 8.49/8.77 (~(s(s(elem!1)) = s(elem!1))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[2279, 14410])).
% 8.49/8.77 tff(14414,plain,
% 8.49/8.77 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[287, 14413])).
% 8.49/8.77 tff(14415,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 8.49/8.77 tff(14416,plain,
% 8.49/8.77 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 8.49/8.77 inference(transitivity,[status(thm)],[688, 14415])).
% 8.49/8.77 tff(14417,plain,
% 8.49/8.77 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 8.49/8.77 inference(monotonicity,[status(thm)],[14416])).
% 8.49/8.77 tff(14418,plain,
% 8.49/8.77 (s(s(s(z))) = s(s(s(elem!1)))),
% 8.49/8.77 inference(transitivity,[status(thm)],[693, 14417, 294])).
% 8.49/8.77 tff(14419,plain,
% 8.49/8.77 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 8.49/8.77 inference(monotonicity,[status(thm)],[14418])).
% 8.49/8.77 tff(14420,plain,
% 8.49/8.77 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 8.49/8.77 inference(symmetry,[status(thm)],[14419])).
% 8.49/8.77 tff(14421,plain,
% 8.49/8.77 (s(s(elem!1)) = s(s(z))),
% 8.49/8.77 inference(transitivity,[status(thm)],[212, 14420, 685])).
% 8.49/8.77 tff(14422,plain,
% 8.49/8.77 ($false),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[2689, 14421])).
% 8.49/8.77 tff(14423,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(z))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.77 tff(14424,plain,
% 8.49/8.77 (~(elem!1 = s(s(s(s(elem!1)))))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[14423, 688, 2689])).
% 8.49/8.77 tff(14425,plain,
% 8.49/8.77 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[2686, 14410])).
% 8.49/8.77 tff(14426,plain,
% 8.49/8.77 (~r(s(s(s(elem!1))), s(elem!1))),
% 8.49/8.77 inference(unit_resolution,[status(thm)],[14304, 2792, 1628, 174])).
% 8.49/8.77 tff(14427,plain,
% 8.49/8.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 8.49/8.78 inference(rewrite,[status(thm)],[])).
% 8.49/8.78 tff(14428,plain,
% 8.49/8.78 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 8.49/8.78 inference(rewrite,[status(thm)],[])).
% 8.49/8.78 tff(14429,plain,
% 8.49/8.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 8.49/8.78 inference(monotonicity,[status(thm)],[14428])).
% 8.49/8.78 tff(14430,plain,
% 8.49/8.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 8.49/8.78 inference(transitivity,[status(thm)],[14429, 14427])).
% 8.49/8.78 tff(14431,plain,
% 8.49/8.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 8.49/8.78 inference(quant_inst,[status(thm)],[])).
% 8.49/8.78 tff(14432,plain,
% 8.49/8.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 8.49/8.78 inference(modus_ponens,[status(thm)],[14431, 14430])).
% 8.49/8.78 tff(14433,plain,
% 8.49/8.78 (~r(s(s(z)), s(s(s(elem!1))))),
% 8.49/8.78 inference(unit_resolution,[status(thm)],[14432, 194, 174, 2792, 3557])).
% 8.49/8.78 tff(14434,plain,
% 8.49/8.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 8.49/8.78 inference(rewrite,[status(thm)],[])).
% 8.49/8.78 tff(14435,plain,
% 8.49/8.78 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 8.49/8.78 inference(rewrite,[status(thm)],[])).
% 8.49/8.78 tff(14436,plain,
% 8.49/8.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 8.49/8.78 inference(monotonicity,[status(thm)],[14435])).
% 8.49/8.78 tff(14437,plain,
% 8.49/8.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 8.49/8.78 inference(transitivity,[status(thm)],[14436, 14434])).
% 8.49/8.78 tff(14438,plain,
% 8.49/8.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 8.49/8.78 inference(quant_inst,[status(thm)],[])).
% 8.49/8.78 tff(14439,plain,
% 8.49/8.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 8.49/8.78 inference(modus_ponens,[status(thm)],[14438, 14437])).
% 8.49/8.78 tff(14440,plain,
% 8.49/8.78 (~r(s(s(s(elem!1))), s(s(z)))),
% 8.49/8.78 inference(unit_resolution,[status(thm)],[14439, 194, 174, 2792, 3557])).
% 8.49/8.78 tff(14441,plain,
% 8.49/8.78 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 8.49/8.78 inference(unit_resolution,[status(thm)],[10713, 42, 10020])).
% 8.49/8.78 tff(14442,plain,
% 8.49/8.78 (b(s(s(s(elem!1))), s(s(z)))),
% 8.49/8.78 inference(unit_resolution,[status(thm)],[14441, 10703])).
% 8.49/8.78 tff(14443,plain,
% 8.49/8.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 8.49/8.78 inference(rewrite,[status(thm)],[])).
% 8.49/8.78 tff(14444,plain,
% 8.49/8.78 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 8.49/8.78 inference(rewrite,[status(thm)],[])).
% 8.49/8.78 tff(14445,plain,
% 8.49/8.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 8.49/8.78 inference(monotonicity,[status(thm)],[14444])).
% 8.49/8.78 tff(14446,plain,
% 8.49/8.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 8.49/8.78 inference(transitivity,[status(thm)],[14445, 14443])).
% 8.49/8.78 tff(14447,plain,
% 8.49/8.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 8.49/8.78 inference(quant_inst,[status(thm)],[])).
% 8.49/8.78 tff(14448,plain,
% 8.49/8.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 8.49/8.78 inference(modus_ponens,[status(thm)],[14447, 14446])).
% 8.49/8.79 tff(14449,plain,
% 8.49/8.79 ($false),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14448, 391, 1101, 448, 3369, 8553, 14442])).
% 8.49/8.79 tff(14450,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.79 tff(14451,plain,
% 8.49/8.79 (~b(s(s(z)), s(s(s(elem!1))))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14450, 14440, 448, 3369, 1101])).
% 8.49/8.79 tff(14452,plain,
% 8.49/8.79 ($false),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 14451, 14433])).
% 8.49/8.79 tff(14453,plain,((~r(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.79 tff(14454,plain,
% 8.49/8.79 (~b(s(s(s(elem!1))), s(elem!1))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14453, 2792, 3369, 448, 174, 3557])).
% 8.49/8.79 tff(14455,plain,
% 8.49/8.79 ($false),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[588, 14454, 14426, 279])).
% 8.49/8.79 tff(14456,plain,((~r(z, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.79 tff(14457,plain,
% 8.49/8.79 (~r(z, s(s(s(s(elem!1)))))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14456, 14409, 14410, 448, 10878, 3557, 1628])).
% 8.49/8.79 tff(14458,plain,
% 8.49/8.79 (b(z, s(s(s(s(elem!1)))))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[2767, 14457])).
% 8.49/8.79 tff(14459,plain,
% 8.49/8.79 (~(s(elem!1) = s(s(elem!1)))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[9802, 14413])).
% 8.49/8.79 tff(14460,plain,
% 8.49/8.79 (elem!1 = s(s(s(s(z))))),
% 8.49/8.79 inference(modus_ponens,[status(thm)],[688, 764])).
% 8.49/8.79 tff(14461,plain,
% 8.49/8.79 (~b(s(s(elem!1)), s(z))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14197, 1374, 10682, 448, 665])).
% 8.49/8.79 tff(14462,plain,
% 8.49/8.79 (r(s(s(elem!1)), s(z))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[362, 14461])).
% 8.49/8.79 tff(14463,plain,
% 8.49/8.79 (~r(elem!1, s(s(z)))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14358, 183, 1484, 233])).
% 8.49/8.79 tff(14464,plain,
% 8.49/8.79 (b(elem!1, s(s(z)))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[3394, 14463, 1405])).
% 8.49/8.79 tff(14465,plain,
% 8.49/8.79 (~r(s(s(z)), s(z))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[10933, 14464, 448, 1484, 183])).
% 8.49/8.79 tff(14466,plain,
% 8.49/8.79 (b(s(s(z)), s(z))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[3778, 14465])).
% 8.49/8.79 tff(14467,plain,
% 8.49/8.79 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 8.49/8.79 inference(monotonicity,[status(thm)],[2731])).
% 8.49/8.79 tff(14468,plain,
% 8.49/8.79 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 8.49/8.79 inference(symmetry,[status(thm)],[14467])).
% 8.49/8.79 tff(14469,plain,
% 8.49/8.79 (r(s(s(s(s(s(s(z)))))), s(z))),
% 8.49/8.79 inference(modus_ponens,[status(thm)],[340, 14468])).
% 8.49/8.79 tff(14470,plain,
% 8.49/8.79 (r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 8.49/8.79 inference(modus_ponens,[status(thm)],[327, 6606])).
% 8.49/8.79 tff(14471,plain,
% 8.49/8.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 8.49/8.79 inference(rewrite,[status(thm)],[])).
% 8.49/8.79 tff(14472,plain,
% 8.49/8.79 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 8.49/8.79 inference(rewrite,[status(thm)],[])).
% 8.49/8.79 tff(14473,plain,
% 8.49/8.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 8.49/8.79 inference(monotonicity,[status(thm)],[14472])).
% 8.49/8.79 tff(14474,plain,
% 8.49/8.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 8.49/8.79 inference(transitivity,[status(thm)],[14473, 14471])).
% 8.49/8.79 tff(14475,plain,
% 8.49/8.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 8.49/8.79 inference(quant_inst,[status(thm)],[])).
% 8.49/8.79 tff(14476,plain,
% 8.49/8.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 8.49/8.79 inference(modus_ponens,[status(thm)],[14475, 14474])).
% 8.49/8.79 tff(14477,plain,
% 8.49/8.79 ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14476, 194, 183, 1216])).
% 8.49/8.79 tff(14478,plain,
% 8.49/8.79 ($false),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14477, 14470, 14469])).
% 8.49/8.79 tff(14479,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.79 tff(14480,plain,
% 8.49/8.79 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14479, 340, 766, 1216, 183])).
% 8.49/8.79 tff(14481,plain,
% 8.49/8.79 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[1370, 14480, 297])).
% 8.49/8.79 tff(14482,plain,
% 8.49/8.79 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[12932, 14481, 10682, 3927])).
% 8.49/8.79 tff(14483,plain,
% 8.49/8.79 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[1356, 14482, 270])).
% 8.49/8.79 tff(14484,plain,
% 8.49/8.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.49/8.79 inference(rewrite,[status(thm)],[])).
% 8.49/8.79 tff(14485,plain,
% 8.49/8.79 (((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.49/8.79 inference(rewrite,[status(thm)],[])).
% 8.49/8.79 tff(14486,plain,
% 8.49/8.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 8.49/8.79 inference(monotonicity,[status(thm)],[14485])).
% 8.49/8.79 tff(14487,plain,
% 8.49/8.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.49/8.79 inference(transitivity,[status(thm)],[14486, 14484])).
% 8.49/8.79 tff(14488,plain,
% 8.49/8.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.49/8.79 inference(quant_inst,[status(thm)],[])).
% 8.49/8.79 tff(14489,plain,
% 8.49/8.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 8.49/8.79 inference(modus_ponens,[status(thm)],[14488, 14487])).
% 8.49/8.79 tff(14490,plain,
% 8.49/8.79 ($false),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14489, 194, 340, 1484, 183, 14483])).
% 8.49/8.79 tff(14491,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.79 tff(14492,plain,
% 8.49/8.79 (~b(z, s(s(elem!1)))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14491, 183, 1484, 270, 10682, 340, 297, 766, 1216])).
% 8.49/8.79 tff(14493,plain,
% 8.49/8.79 (r(z, s(s(elem!1)))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[324, 14492])).
% 8.49/8.79 tff(14494,plain,
% 8.49/8.79 (~r(s(z), s(s(z)))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[3787, 14493, 3557, 182])).
% 8.49/8.79 tff(14495,plain,
% 8.49/8.79 (b(s(z), s(s(z)))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[1788, 14494])).
% 8.49/8.79 tff(14496,plain,
% 8.49/8.79 ($false),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[10150, 14495, 14466, 14464, 721])).
% 8.49/8.79 tff(14497,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (elem!1 = s(s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.49/8.79 tff(14498,plain,
% 8.49/8.79 (~r(s(s(s(elem!1))), s(z))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[14497, 14462, 3557, 182, 448, 1484, 1405, 14412, 10682, 721, 14414, 14460, 1216, 233])).
% 8.49/8.79 tff(14499,plain,
% 8.49/8.79 (b(s(s(s(elem!1))), s(z))),
% 8.49/8.79 inference(unit_resolution,[status(thm)],[223, 14498])).
% 8.49/8.79 tff(14500,plain,
% 8.49/8.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))))),
% 8.49/8.79 inference(rewrite,[status(thm)],[])).
% 8.49/8.79 tff(14501,plain,
% 8.49/8.79 (((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))))),
% 8.49/8.79 inference(rewrite,[status(thm)],[])).
% 8.49/8.79 tff(14502,plain,
% 8.49/8.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z))))))),
% 8.49/8.79 inference(monotonicity,[status(thm)],[14501])).
% 8.49/8.79 tff(14503,plain,
% 8.49/8.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))))),
% 8.59/8.80 inference(transitivity,[status(thm)],[14502, 14500])).
% 8.59/8.80 tff(14504,plain,
% 8.59/8.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 8.59/8.80 inference(quant_inst,[status(thm)],[])).
% 8.59/8.80 tff(14505,plain,
% 8.59/8.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z))))),
% 8.59/8.80 inference(modus_ponens,[status(thm)],[14504, 14503])).
% 8.59/8.80 tff(14506,plain,
% 8.59/8.80 ($false),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[14505, 391, 665, 10682, 448, 1526, 2439])).
% 8.59/8.80 tff(14507,plain,((~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.80 tff(14508,plain,
% 8.59/8.80 (~b(s(z), s(s(z)))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[14507, 14499, 10682, 448, 665])).
% 8.59/8.80 tff(14509,plain,
% 8.59/8.80 (r(s(z), s(s(z)))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[1788, 14508])).
% 8.59/8.80 tff(14510,plain,
% 8.59/8.80 (~r(z, s(s(elem!1)))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[3787, 14509, 3557, 182])).
% 8.59/8.80 tff(14511,plain,
% 8.59/8.80 (b(z, s(s(elem!1)))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[324, 14510])).
% 8.59/8.80 tff(14512,plain,
% 8.59/8.80 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[12932, 14511, 10682, 1374])).
% 8.59/8.80 tff(14513,plain,
% 8.59/8.80 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[1356, 14512, 14412])).
% 8.59/8.80 tff(14514,plain,
% 8.59/8.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 8.59/8.80 inference(rewrite,[status(thm)],[])).
% 8.59/8.80 tff(14515,plain,
% 8.59/8.80 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 8.59/8.80 inference(rewrite,[status(thm)],[])).
% 8.59/8.80 tff(14516,plain,
% 8.59/8.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 8.59/8.80 inference(monotonicity,[status(thm)],[14515])).
% 8.59/8.80 tff(14517,plain,
% 8.59/8.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 8.59/8.80 inference(transitivity,[status(thm)],[14516, 14514])).
% 8.59/8.80 tff(14518,plain,
% 8.59/8.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 8.59/8.80 inference(quant_inst,[status(thm)],[])).
% 8.59/8.80 tff(14519,plain,
% 8.59/8.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 8.59/8.80 inference(modus_ponens,[status(thm)],[14518, 14517])).
% 8.59/8.80 tff(14520,plain,
% 8.59/8.80 ($false),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[14519, 391, 665, 10682, 448, 1374, 1152])).
% 8.59/8.80 tff(14521,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.80 tff(14522,plain,
% 8.59/8.80 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[14521, 1374, 10682, 448, 665])).
% 8.59/8.80 tff(14523,plain,
% 8.59/8.80 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[1048, 14522, 14425])).
% 8.59/8.80 tff(14524,plain,
% 8.59/8.80 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[299, 14414])).
% 8.59/8.80 tff(14525,plain,
% 8.59/8.80 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[307, 14524])).
% 8.59/8.80 tff(14526,plain,
% 8.59/8.80 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[929, 13720])).
% 8.59/8.80 tff(14527,plain,
% 8.59/8.80 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[2711, 14425])).
% 8.59/8.80 tff(14528,plain,
% 8.59/8.80 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[14406, 14499, 448, 721, 688, 1216, 3557])).
% 8.59/8.80 tff(14529,plain,
% 8.59/8.80 (b(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[1714, 14528])).
% 8.59/8.80 tff(14530,plain,
% 8.59/8.80 (b(elem!1, s(s(z)))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[11029, 14529, 688])).
% 8.59/8.80 tff(14531,plain,
% 8.59/8.80 (~r(z, s(s(s(s(elem!1)))))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[14456, 14530, 14410, 448, 10878, 3557, 1628])).
% 8.59/8.80 tff(14532,plain,
% 8.59/8.80 (b(z, s(s(s(s(elem!1)))))),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[2767, 14531])).
% 8.59/8.80 tff(14533,plain,
% 8.59/8.80 (~b(s(s(s(s(elem!1)))), elem!1)),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[14264, 14532, 665, 133])).
% 8.59/8.80 tff(14534,plain,
% 8.59/8.80 (r(s(s(s(s(elem!1)))), elem!1)),
% 8.59/8.80 inference(unit_resolution,[status(thm)],[1004, 14533, 14256])).
% 8.59/8.80 tff(14535,plain,
% 8.59/8.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 8.59/8.80 inference(rewrite,[status(thm)],[])).
% 8.59/8.80 tff(14536,plain,
% 8.59/8.80 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 8.59/8.80 inference(rewrite,[status(thm)],[])).
% 8.59/8.80 tff(14537,plain,
% 8.59/8.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 8.59/8.81 inference(monotonicity,[status(thm)],[14536])).
% 8.59/8.81 tff(14538,plain,
% 8.59/8.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 8.59/8.81 inference(transitivity,[status(thm)],[14537, 14535])).
% 8.59/8.81 tff(14539,plain,
% 8.59/8.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.59/8.81 inference(quant_inst,[status(thm)],[])).
% 8.59/8.81 tff(14540,plain,
% 8.59/8.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 8.59/8.81 inference(modus_ponens,[status(thm)],[14539, 14538])).
% 8.59/8.81 tff(14541,plain,
% 8.59/8.81 ($false),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[14540, 194, 991, 1538, 1176, 1378])).
% 8.59/8.81 tff(14542,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.81 tff(14543,plain,
% 8.59/8.81 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[14542, 14534, 14523, 14513])).
% 8.59/8.81 tff(14544,plain,
% 8.59/8.81 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[1164, 14543, 14525])).
% 8.59/8.81 tff(14545,plain,
% 8.59/8.81 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[14233, 14544, 10682, 448, 665])).
% 8.59/8.81 tff(14546,plain,
% 8.59/8.81 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[1061, 14545, 14527])).
% 8.59/8.81 tff(14547,plain,
% 8.59/8.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.59/8.81 inference(rewrite,[status(thm)],[])).
% 8.59/8.81 tff(14548,plain,
% 8.59/8.81 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.59/8.81 inference(rewrite,[status(thm)],[])).
% 8.59/8.81 tff(14549,plain,
% 8.59/8.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 8.59/8.81 inference(monotonicity,[status(thm)],[14548])).
% 8.59/8.81 tff(14550,plain,
% 8.59/8.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.59/8.81 inference(transitivity,[status(thm)],[14549, 14547])).
% 8.59/8.81 tff(14551,plain,
% 8.59/8.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.59/8.81 inference(quant_inst,[status(thm)],[])).
% 8.59/8.81 tff(14552,plain,
% 8.59/8.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 8.59/8.81 inference(modus_ponens,[status(thm)],[14551, 14550])).
% 8.59/8.81 tff(14553,plain,
% 8.59/8.81 ($false),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[14552, 194, 1177, 1538, 1176, 1378])).
% 8.59/8.81 tff(14554,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.81 tff(14555,plain,
% 8.59/8.81 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[14554, 1177, 1176, 1378])).
% 8.59/8.81 tff(14556,plain,
% 8.59/8.81 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[1164, 14555, 1373])).
% 8.59/8.81 tff(14557,plain,
% 8.59/8.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 8.59/8.81 inference(rewrite,[status(thm)],[])).
% 8.59/8.81 tff(14558,plain,
% 8.59/8.81 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 8.59/8.81 inference(rewrite,[status(thm)],[])).
% 8.59/8.81 tff(14559,plain,
% 8.59/8.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 8.59/8.81 inference(monotonicity,[status(thm)],[14558])).
% 8.59/8.81 tff(14560,plain,
% 8.59/8.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 8.59/8.81 inference(transitivity,[status(thm)],[14559, 14557])).
% 8.59/8.81 tff(14561,plain,
% 8.59/8.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 8.59/8.81 inference(quant_inst,[status(thm)],[])).
% 8.59/8.81 tff(14562,plain,
% 8.59/8.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 8.59/8.81 inference(modus_ponens,[status(thm)],[14561, 14560])).
% 8.59/8.81 tff(14563,plain,
% 8.59/8.81 ($false),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[14562, 391, 665, 10682, 448, 1573, 975])).
% 8.59/8.81 tff(14564,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.81 tff(14565,plain,
% 8.59/8.81 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[14564, 14556, 10682, 448, 665])).
% 8.59/8.81 tff(14566,plain,
% 8.59/8.81 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[988, 14565, 957])).
% 8.59/8.81 tff(14567,plain,
% 8.59/8.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 8.59/8.81 inference(rewrite,[status(thm)],[])).
% 8.59/8.81 tff(14568,plain,
% 8.59/8.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 8.59/8.81 inference(quant_inst,[status(thm)],[])).
% 8.59/8.81 tff(14569,plain,
% 8.59/8.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 8.59/8.81 inference(modus_ponens,[status(thm)],[14568, 14567])).
% 8.59/8.81 tff(14570,plain,
% 8.59/8.81 ($false),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[14569, 194, 340, 1177, 14566, 7538])).
% 8.59/8.81 tff(14571,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.81 tff(14572,plain,
% 8.59/8.81 (~r(s(elem!1), s(s(elem!1)))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[14571, 14546, 14462, 14526, 10682, 448, 665, 14525, 14523, 14513])).
% 8.59/8.81 tff(14573,plain,
% 8.59/8.81 (b(s(elem!1), s(s(elem!1)))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[8644, 14572, 14459])).
% 8.59/8.81 tff(14574,plain,
% 8.59/8.81 (~b(s(s(elem!1)), elem!1)),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[12889, 1374, 10682, 665, 448])).
% 8.59/8.81 tff(14575,plain,
% 8.59/8.81 (r(s(s(elem!1)), elem!1)),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[872, 14574, 14411])).
% 8.59/8.81 tff(14576,plain,
% 8.59/8.81 (~b(s(z), s(s(s(elem!1))))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[4958, 14499, 150, 448, 14462, 14575])).
% 8.59/8.81 tff(14577,plain,
% 8.59/8.81 (r(s(z), s(s(s(elem!1))))),
% 8.59/8.81 inference(unit_resolution,[status(thm)],[247, 14576])).
% 8.59/8.82 tff(14578,plain,
% 8.59/8.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 8.59/8.82 inference(rewrite,[status(thm)],[])).
% 8.59/8.82 tff(14579,plain,
% 8.59/8.82 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 8.59/8.82 inference(rewrite,[status(thm)],[])).
% 8.59/8.82 tff(14580,plain,
% 8.59/8.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 8.59/8.82 inference(monotonicity,[status(thm)],[14579])).
% 8.59/8.82 tff(14581,plain,
% 8.59/8.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 8.59/8.82 inference(transitivity,[status(thm)],[14580, 14578])).
% 8.59/8.82 tff(14582,plain,
% 8.59/8.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 8.59/8.82 inference(quant_inst,[status(thm)],[])).
% 8.59/8.82 tff(14583,plain,
% 8.59/8.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 8.59/8.82 inference(modus_ponens,[status(thm)],[14582, 14581])).
% 8.59/8.82 tff(14584,plain,
% 8.59/8.82 ($false),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14583, 194, 233, 1484, 232, 1063])).
% 8.59/8.82 tff(14585,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.82 tff(14586,plain,
% 8.59/8.82 (~r(elem!1, s(s(s(s(elem!1)))))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14585, 14577, 1484, 233])).
% 8.59/8.82 tff(14587,plain,
% 8.59/8.82 (b(elem!1, s(s(s(s(elem!1)))))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[1018, 14586, 14203])).
% 8.59/8.82 tff(14588,plain,
% 8.59/8.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 8.59/8.82 inference(rewrite,[status(thm)],[])).
% 8.59/8.82 tff(14589,plain,
% 8.59/8.82 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 8.59/8.82 inference(rewrite,[status(thm)],[])).
% 8.59/8.82 tff(14590,plain,
% 8.59/8.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 8.59/8.82 inference(monotonicity,[status(thm)],[14589])).
% 8.59/8.82 tff(14591,plain,
% 8.59/8.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 8.59/8.82 inference(transitivity,[status(thm)],[14590, 14588])).
% 8.59/8.82 tff(14592,plain,
% 8.59/8.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))),
% 8.59/8.82 inference(quant_inst,[status(thm)],[])).
% 8.59/8.82 tff(14593,plain,
% 8.59/8.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 8.59/8.82 inference(modus_ponens,[status(thm)],[14592, 14591])).
% 8.59/8.82 tff(14594,plain,
% 8.59/8.82 ($false),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14593, 391, 133, 1526, 974, 2781, 1114])).
% 8.59/8.82 tff(14595,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.82 tff(14596,plain,
% 8.59/8.82 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14595, 14587, 14499, 133, 14532])).
% 8.59/8.82 tff(14597,plain,
% 8.59/8.82 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[1095, 14596, 14524])).
% 8.59/8.82 tff(14598,plain,
% 8.59/8.82 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14564, 14544, 10682, 448, 665])).
% 8.59/8.82 tff(14599,plain,
% 8.59/8.82 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[988, 14598, 14526])).
% 8.59/8.82 tff(14600,plain,
% 8.59/8.82 ($false),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[1149, 194, 613, 485, 1082, 990])).
% 8.59/8.82 tff(14601,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.82 tff(14602,plain,
% 8.59/8.82 (~r(s(s(s(elem!1))), s(elem!1))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14601, 14599, 14597, 485])).
% 8.59/8.82 tff(14603,plain,
% 8.59/8.82 (b(s(s(s(elem!1))), s(elem!1))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[588, 14602, 14410])).
% 8.59/8.82 tff(14604,plain,
% 8.59/8.82 ($false),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14314, 14603, 14573, 665, 10682, 448])).
% 8.59/8.82 tff(14605,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~(s(s(s(s(z)))) = elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.82 tff(14606,plain,
% 8.59/8.82 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14605, 14424, 10682, 448, 485, 133, 665, 3557, 1628, 5429, 233, 182, 688, 150, 14377, 14376, 1405])).
% 8.59/8.82 tff(14607,plain,
% 8.59/8.82 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[1370, 14606, 14414])).
% 8.59/8.82 tff(14608,plain,
% 8.59/8.82 (~b(z, s(s(elem!1)))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14294, 14607, 14458, 14425, 448, 10682, 665, 14424, 233, 14414, 14412, 14411, 133])).
% 8.59/8.82 tff(14609,plain,
% 8.59/8.82 (r(z, s(s(elem!1)))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[324, 14608])).
% 8.59/8.82 tff(14610,plain,
% 8.59/8.82 (~r(s(z), s(s(z)))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[3787, 14609, 3557, 182])).
% 8.59/8.82 tff(14611,plain,
% 8.59/8.82 (b(s(z), s(s(z)))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[1788, 14610])).
% 8.59/8.82 tff(14612,plain,
% 8.59/8.82 (~b(s(s(z)), s(z))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[10150, 14611, 14409, 14377])).
% 8.59/8.82 tff(14613,plain,
% 8.59/8.82 (r(s(s(z)), s(z))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[3778, 14612])).
% 8.59/8.82 tff(14614,plain,
% 8.59/8.82 (~b(s(s(s(elem!1))), s(z))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14507, 14611, 10682, 448, 665])).
% 8.59/8.82 tff(14615,plain,
% 8.59/8.82 (r(s(s(s(elem!1))), s(z))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[223, 14614])).
% 8.59/8.82 tff(14616,plain,
% 8.59/8.82 ($false),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[10933, 14615, 14613, 448, 5429, 14409])).
% 8.59/8.82 tff(14617,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (elem!1 = s(s(z))) | (~r(s(elem!1), elem!1)) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(z))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.59/8.82 tff(14618,plain,
% 8.59/8.82 (~(s(s(s(s(z)))) = elem!1)),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14617, 14374, 10682, 11936, 13691, 13730, 13695, 133, 13111, 14350, 13120, 150, 2680, 13277])).
% 8.59/8.82 tff(14619,plain,
% 8.59/8.82 (~(elem!1 = s(s(s(s(z)))))),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[769, 14618])).
% 8.59/8.82 tff(14620,plain,
% 8.59/8.82 (r(s(s(s(s(z)))), elem!1)),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[762, 14618, 13710])).
% 8.59/8.82 tff(14621,plain,
% 8.59/8.82 (((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.82 inference(rewrite,[status(thm)],[])).
% 8.59/8.82 tff(14622,plain,
% 8.59/8.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.59/8.82 inference(monotonicity,[status(thm)],[14621])).
% 8.59/8.82 tff(14623,plain,
% 8.59/8.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.82 inference(transitivity,[status(thm)],[14622, 11416])).
% 8.59/8.82 tff(14624,plain,
% 8.59/8.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)))),
% 8.59/8.82 inference(quant_inst,[status(thm)],[])).
% 8.59/8.82 tff(14625,plain,
% 8.59/8.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.59/8.82 inference(modus_ponens,[status(thm)],[14624, 14623])).
% 8.59/8.82 tff(14626,plain,
% 8.59/8.82 ($false),
% 8.59/8.82 inference(unit_resolution,[status(thm)],[14625, 194, 1484, 2032, 2112, 1216])).
% 8.59/8.82 tff(14627,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.83 tff(14628,plain,
% 8.59/8.83 (~r(elem!1, s(s(s(s(z)))))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[14627, 1216, 2112, 1484])).
% 8.59/8.83 tff(14629,plain,
% 8.59/8.83 (b(elem!1, s(s(s(s(z)))))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[781, 14628, 8922])).
% 8.59/8.83 tff(14630,plain,
% 8.59/8.83 (~b(s(s(s(s(z)))), z)),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[12445, 14629, 665, 133])).
% 8.59/8.83 tff(14631,plain,
% 8.59/8.83 (r(s(s(s(s(z)))), z)),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[87, 14630])).
% 8.59/8.83 tff(14632,plain,
% 8.59/8.83 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[13565, 14629, 1759, 3369, 1216, 14004])).
% 8.59/8.83 tff(14633,plain,
% 8.59/8.83 (r(s(s(z)), s(s(s(s(z)))))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[3652, 14632])).
% 8.59/8.83 tff(14634,plain,
% 8.59/8.83 ($false),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[13627, 14633, 14631, 721, 3369, 1216])).
% 8.59/8.83 tff(14635,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.83 tff(14636,plain,
% 8.59/8.83 (~r(s(z), s(s(s(s(z)))))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[14635, 13709, 14372, 14151, 11936, 133, 14619, 14620, 13731])).
% 8.59/8.83 tff(14637,plain,
% 8.59/8.83 (b(s(z), s(s(s(s(z)))))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[1230, 14636])).
% 8.59/8.83 tff(14638,plain,
% 8.59/8.83 (~b(elem!1, s(s(s(s(z)))))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[2088, 391, 14637, 14151, 13709])).
% 8.59/8.83 tff(14639,plain,
% 8.59/8.83 (r(elem!1, s(s(s(s(z)))))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[781, 14638, 14619])).
% 8.59/8.83 tff(14640,plain,
% 8.59/8.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.83 inference(rewrite,[status(thm)],[])).
% 8.59/8.83 tff(14641,plain,
% 8.59/8.83 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.83 inference(rewrite,[status(thm)],[])).
% 8.59/8.83 tff(14642,plain,
% 8.59/8.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.59/8.83 inference(monotonicity,[status(thm)],[14641])).
% 8.59/8.83 tff(14643,plain,
% 8.59/8.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.83 inference(transitivity,[status(thm)],[14642, 14640])).
% 8.59/8.83 tff(14644,plain,
% 8.59/8.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 8.59/8.83 inference(quant_inst,[status(thm)],[])).
% 8.59/8.83 tff(14645,plain,
% 8.59/8.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.59/8.83 inference(modus_ponens,[status(thm)],[14644, 14643])).
% 8.59/8.83 tff(14646,plain,
% 8.59/8.83 (~r(s(s(s(elem!1))), s(z))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[14645, 194, 13695, 13731, 14639])).
% 8.59/8.83 tff(14647,plain,
% 8.59/8.83 (b(s(s(s(elem!1))), s(z))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[223, 14646])).
% 8.59/8.83 tff(14648,plain,
% 8.59/8.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.83 inference(rewrite,[status(thm)],[])).
% 8.59/8.83 tff(14649,plain,
% 8.59/8.83 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.83 inference(rewrite,[status(thm)],[])).
% 8.59/8.83 tff(14650,plain,
% 8.59/8.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.59/8.83 inference(monotonicity,[status(thm)],[14649])).
% 8.59/8.83 tff(14651,plain,
% 8.59/8.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.83 inference(transitivity,[status(thm)],[14650, 14648])).
% 8.59/8.83 tff(14652,plain,
% 8.59/8.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 8.59/8.83 inference(quant_inst,[status(thm)],[])).
% 8.59/8.83 tff(14653,plain,
% 8.59/8.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.59/8.83 inference(modus_ponens,[status(thm)],[14652, 14651])).
% 8.59/8.83 tff(14654,plain,
% 8.59/8.83 (~r(s(z), s(s(s(elem!1))))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[14653, 194, 13695, 13731, 14639])).
% 8.59/8.83 tff(14655,plain,
% 8.59/8.83 (b(s(z), s(s(s(elem!1))))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[247, 14654])).
% 8.59/8.83 tff(14656,plain,
% 8.59/8.83 ($false),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[4956, 391, 13691, 14655, 14647, 13709])).
% 8.59/8.83 tff(14657,plain,(r(elem!1, z) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1) | b(s(s(s(elem!1))), elem!1) | b(s(elem!1), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 8.59/8.83 tff(14658,plain,
% 8.59/8.83 (b(s(elem!1), elem!1)),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[14657, 11365, 133, 150, 10682, 11352, 2])).
% 8.59/8.83 tff(14659,plain,
% 8.59/8.83 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 8.59/8.83 inference(symmetry,[status(thm)],[2464])).
% 8.59/8.83 tff(14660,plain,
% 8.59/8.83 (b(s(s(s(elem!1))), elem!1)),
% 8.59/8.83 inference(modus_ponens,[status(thm)],[2122, 14659])).
% 8.59/8.83 tff(14661,plain,
% 8.59/8.83 ($false),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[168, 14660])).
% 8.59/8.83 tff(14662,plain,((~(s(s(s(elem!1))) = s(elem!1))) | b(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.83 tff(14663,plain,
% 8.59/8.83 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[14662, 14658, 11352])).
% 8.59/8.83 tff(14664,plain,
% 8.59/8.83 (~(s(s(elem!1)) = s(elem!1))),
% 8.59/8.83 inference(unit_resolution,[status(thm)],[2279, 14663])).
% 8.59/8.83 tff(14665,plain,
% 8.59/8.83 (~b(s(s(elem!1)), elem!1)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[5286, 14664, 133, 11366, 14658])).
% 8.59/8.84 tff(14666,plain,
% 8.59/8.84 (r(s(s(elem!1)), elem!1)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[872, 14665, 11905])).
% 8.59/8.84 tff(14667,plain,
% 8.59/8.84 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 8.59/8.84 inference(modus_ponens,[status(thm)],[14666, 11935])).
% 8.59/8.84 tff(14668,plain,
% 8.59/8.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 8.59/8.84 inference(rewrite,[status(thm)],[])).
% 8.59/8.84 tff(14669,plain,
% 8.59/8.84 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 8.59/8.84 inference(rewrite,[status(thm)],[])).
% 8.59/8.84 tff(14670,plain,
% 8.59/8.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 8.59/8.84 inference(monotonicity,[status(thm)],[14669])).
% 8.59/8.84 tff(14671,plain,
% 8.59/8.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 8.59/8.84 inference(transitivity,[status(thm)],[14670, 14668])).
% 8.59/8.84 tff(14672,plain,
% 8.59/8.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 8.59/8.84 inference(quant_inst,[status(thm)],[])).
% 8.59/8.84 tff(14673,plain,
% 8.59/8.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 8.59/8.84 inference(modus_ponens,[status(thm)],[14672, 14671])).
% 8.59/8.84 tff(14674,plain,
% 8.59/8.84 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[14673, 194, 11915, 11914, 14667])).
% 8.59/8.84 tff(14675,plain,
% 8.59/8.84 ((s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[9497, 42, 14674])).
% 8.59/8.84 tff(14676,plain,
% 8.59/8.84 (s(s(z)) = s(s(s(s(s(elem!1)))))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[14675, 11932])).
% 8.59/8.84 tff(14677,plain,
% 8.59/8.84 (s(s(s(s(s(elem!1))))) = s(s(z))),
% 8.59/8.84 inference(symmetry,[status(thm)],[14676])).
% 8.59/8.84 tff(14678,plain,
% 8.59/8.84 (s(s(elem!1)) = s(s(z))),
% 8.59/8.84 inference(transitivity,[status(thm)],[11341, 14677])).
% 8.59/8.84 tff(14679,plain,
% 8.59/8.84 ($false),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[2689, 14678])).
% 8.59/8.84 tff(14680,plain,((s(z) = elem!1) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = z) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~r(s(s(s(s(z)))), z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.84 tff(14681,plain,
% 8.59/8.84 ($false),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[14680, 10681, 10729, 3823, 11335, 1216, 150, 11334, 4028, 10680, 3557, 719, 8329, 2053, 31])).
% 8.59/8.84 tff(14682,plain,(r(z, elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (s(z) = elem!1) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~r(s(s(s(s(z)))), z)) | b(elem!1, s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.59/8.84 tff(14683,plain,
% 8.59/8.84 (r(z, elem!1)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[14682, 4028, 1216, 150, 3823, 3557, 719, 8329, 2053, 31, 115])).
% 8.59/8.84 tff(14684,plain,
% 8.59/8.84 (r(z, s(s(s(elem!1))))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[10797, 14683, 1216, 31, 10679, 10677, 4028, 719])).
% 8.59/8.84 tff(14685,plain,
% 8.59/8.84 (~b(s(s(s(elem!1))), s(z))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[10635, 14684, 10677, 10679, 4028, 14683, 31])).
% 8.59/8.84 tff(14686,plain,
% 8.59/8.84 (r(s(s(s(elem!1))), s(z))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[223, 14685])).
% 8.59/8.84 tff(14687,plain,
% 8.59/8.84 (~r(elem!1, s(s(s(elem!1))))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[10776, 14686, 1216, 847])).
% 8.59/8.84 tff(14688,plain,
% 8.59/8.84 (elem!1 = s(s(s(elem!1)))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[424, 14687, 4028])).
% 8.59/8.84 tff(14689,plain,
% 8.59/8.84 (s(s(s(elem!1))) = elem!1),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[129, 14688])).
% 8.59/8.84 tff(14690,plain,
% 8.59/8.84 (~r(elem!1, s(s(s(s(z)))))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[11195, 847, 2053, 1216])).
% 8.59/8.84 tff(14691,plain,
% 8.59/8.84 (~(s(s(s(s(z)))) = elem!1)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[1436, 14689])).
% 8.59/8.84 tff(14692,plain,
% 8.59/8.84 (~(elem!1 = s(s(s(s(z)))))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[769, 14691])).
% 8.59/8.84 tff(14693,plain,
% 8.59/8.84 (b(elem!1, s(s(s(s(z)))))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[781, 14692, 14690])).
% 8.59/8.84 tff(14694,plain,
% 8.59/8.84 (~b(elem!1, s(s(z)))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[9127, 14693, 11329, 3823])).
% 8.59/8.84 tff(14695,plain,
% 8.59/8.84 (s(s(s(elem!1))) = elem!1),
% 8.59/8.84 inference(symmetry,[status(thm)],[14688])).
% 8.59/8.84 tff(14696,plain,
% 8.59/8.84 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 8.59/8.84 inference(monotonicity,[status(thm)],[14695])).
% 8.59/8.84 tff(14697,plain,
% 8.59/8.84 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 8.59/8.84 inference(transitivity,[status(thm)],[14696, 698])).
% 8.59/8.84 tff(14698,plain,
% 8.59/8.84 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 8.59/8.84 inference(monotonicity,[status(thm)],[14697])).
% 8.59/8.84 tff(14699,plain,
% 8.59/8.84 (~(elem!1 = s(s(z)))),
% 8.59/8.84 inference(modus_ponens,[status(thm)],[1397, 14698])).
% 8.59/8.84 tff(14700,plain,
% 8.59/8.84 (r(elem!1, s(s(z)))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[3394, 14699, 14694])).
% 8.59/8.84 tff(14701,plain,
% 8.59/8.84 (~r(elem!1, z)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[8570, 14700, 3557, 719])).
% 8.59/8.84 tff(14702,plain,
% 8.59/8.84 (b(elem!1, z)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[526, 14701, 10680])).
% 8.59/8.84 tff(14703,plain,
% 8.59/8.84 (r(elem!1, s(z))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[8406, 5, 183])).
% 8.59/8.84 tff(14704,plain,
% 8.59/8.84 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 8.59/8.84 inference(monotonicity,[status(thm)],[5])).
% 8.59/8.84 tff(14705,plain,
% 8.59/8.84 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 8.59/8.84 inference(transitivity,[status(thm)],[14704, 250])).
% 8.59/8.84 tff(14706,plain,
% 8.59/8.84 ((s(s(elem!1)) = elem!1) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 8.59/8.84 inference(symmetry,[status(thm)],[14705])).
% 8.59/8.84 tff(14707,plain,
% 8.59/8.84 (s(s(s(elem!1))) = s(s(elem!1))),
% 8.59/8.84 inference(modus_ponens,[status(thm)],[445, 14706])).
% 8.59/8.84 tff(14708,plain,
% 8.59/8.84 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 8.59/8.84 inference(transitivity,[status(thm)],[3692, 8492])).
% 8.59/8.84 tff(14709,plain,
% 8.59/8.84 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 8.59/8.84 inference(monotonicity,[status(thm)],[14708])).
% 8.59/8.84 tff(14710,plain,
% 8.59/8.84 (~(s(s(z)) = elem!1)),
% 8.59/8.84 inference(modus_ponens,[status(thm)],[1397, 14709])).
% 8.59/8.84 tff(14711,plain,
% 8.59/8.84 (~r(s(s(s(s(z)))), elem!1)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[10408, 2053, 847, 411])).
% 8.59/8.84 tff(14712,plain,
% 8.59/8.84 (b(s(s(s(s(z)))), elem!1)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[762, 14711, 2691])).
% 8.59/8.84 tff(14713,plain,
% 8.59/8.84 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[9242, 14712, 266])).
% 8.59/8.84 tff(14714,plain,
% 8.59/8.84 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 8.59/8.84 inference(monotonicity,[status(thm)],[5])).
% 8.59/8.84 tff(14715,plain,
% 8.59/8.84 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 8.59/8.84 inference(monotonicity,[status(thm)],[14714])).
% 8.59/8.84 tff(14716,plain,
% 8.59/8.84 (~(s(z) = elem!1)),
% 8.59/8.84 inference(modus_ponens,[status(thm)],[217, 14715])).
% 8.59/8.84 tff(14717,plain,
% 8.59/8.84 (~b(s(z), elem!1)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[10491, 2064, 665, 14712, 1234])).
% 8.59/8.84 tff(14718,plain,
% 8.59/8.84 (r(s(z), elem!1)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[632, 14717, 14716])).
% 8.59/8.84 tff(14719,plain,
% 8.59/8.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))),
% 8.59/8.84 inference(rewrite,[status(thm)],[])).
% 8.59/8.84 tff(14720,plain,
% 8.59/8.84 (((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))),
% 8.59/8.84 inference(rewrite,[status(thm)],[])).
% 8.59/8.84 tff(14721,plain,
% 8.59/8.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))))),
% 8.59/8.84 inference(monotonicity,[status(thm)],[14720])).
% 8.59/8.84 tff(14722,plain,
% 8.59/8.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))),
% 8.59/8.84 inference(transitivity,[status(thm)],[14721, 14719])).
% 8.59/8.84 tff(14723,plain,
% 8.59/8.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 8.59/8.84 inference(quant_inst,[status(thm)],[])).
% 8.59/8.84 tff(14724,plain,
% 8.59/8.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))),
% 8.59/8.84 inference(modus_ponens,[status(thm)],[14723, 14722])).
% 8.59/8.84 tff(14725,plain,
% 8.59/8.84 ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[14724, 194])).
% 8.59/8.84 tff(14726,plain,
% 8.59/8.84 (~r(z, s(z))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[14725, 14718, 847, 411])).
% 8.59/8.84 tff(14727,plain,
% 8.59/8.84 (b(z, s(z))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[678, 14726])).
% 8.59/8.84 tff(14728,plain,
% 8.59/8.84 (~b(s(s(z)), s(z))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[1243, 1235, 1232, 1234, 664])).
% 8.59/8.84 tff(14729,plain,
% 8.59/8.84 (r(s(s(z)), s(z))),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[3778, 14728])).
% 8.59/8.84 tff(14730,plain,
% 8.59/8.84 (~r(s(s(z)), elem!1)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[6674, 14729, 847, 1484])).
% 8.59/8.84 tff(14731,plain,
% 8.59/8.84 (b(s(s(z)), elem!1)),
% 8.59/8.84 inference(unit_resolution,[status(thm)],[4730, 14730, 5547])).
% 8.59/8.84 tff(14732,plain,
% 8.59/8.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 8.59/8.85 inference(rewrite,[status(thm)],[])).
% 8.59/8.85 tff(14733,plain,
% 8.59/8.85 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 8.59/8.85 inference(rewrite,[status(thm)],[])).
% 8.59/8.85 tff(14734,plain,
% 8.59/8.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 8.59/8.85 inference(monotonicity,[status(thm)],[14733])).
% 8.59/8.85 tff(14735,plain,
% 8.59/8.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 8.59/8.85 inference(transitivity,[status(thm)],[14734, 14732])).
% 8.59/8.85 tff(14736,plain,
% 8.59/8.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 8.59/8.85 inference(quant_inst,[status(thm)],[])).
% 8.59/8.85 tff(14737,plain,
% 8.59/8.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 8.59/8.85 inference(modus_ponens,[status(thm)],[14736, 14735])).
% 8.59/8.85 tff(14738,plain,
% 8.59/8.85 ($false),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14737, 391, 665, 1235, 1234, 14731, 664])).
% 8.59/8.85 tff(14739,plain,((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (s(s(z)) = elem!1) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.85 tff(14740,plain,
% 8.59/8.85 (~b(s(s(z)), z)),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14739, 14727, 1234, 665, 14710, 847, 14718, 1232])).
% 8.59/8.85 tff(14741,plain,
% 8.59/8.85 (r(s(s(z)), z)),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[1211, 14740])).
% 8.59/8.85 tff(14742,plain,
% 8.59/8.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 8.59/8.85 inference(rewrite,[status(thm)],[])).
% 8.59/8.85 tff(14743,plain,
% 8.59/8.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 8.59/8.85 inference(quant_inst,[status(thm)],[])).
% 8.59/8.85 tff(14744,plain,
% 8.59/8.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 8.59/8.85 inference(modus_ponens,[status(thm)],[14743, 14742])).
% 8.59/8.85 tff(14745,plain,
% 8.59/8.85 ($false),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14744, 194, 184, 1749, 2053, 3557])).
% 8.59/8.85 tff(14746,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.85 tff(14747,plain,
% 8.59/8.85 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14746, 14741, 184, 2053])).
% 8.59/8.85 tff(14748,plain,
% 8.59/8.85 (b(s(s(z)), s(s(s(s(z)))))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[3652, 14747])).
% 8.59/8.85 tff(14749,plain,
% 8.59/8.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.59/8.85 inference(rewrite,[status(thm)],[])).
% 8.59/8.85 tff(14750,plain,
% 8.59/8.85 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.59/8.85 inference(rewrite,[status(thm)],[])).
% 8.59/8.85 tff(14751,plain,
% 8.59/8.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 8.59/8.85 inference(monotonicity,[status(thm)],[14750])).
% 8.59/8.85 tff(14752,plain,
% 8.59/8.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.59/8.85 inference(transitivity,[status(thm)],[14751, 14749])).
% 8.59/8.85 tff(14753,plain,
% 8.59/8.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 8.59/8.85 inference(quant_inst,[status(thm)],[])).
% 8.59/8.85 tff(14754,plain,
% 8.59/8.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 8.59/8.85 inference(modus_ponens,[status(thm)],[14753, 14752])).
% 8.59/8.85 tff(14755,plain,
% 8.59/8.85 ($false),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14754, 391, 2641, 3823, 1234, 1233, 1232])).
% 8.59/8.85 tff(14756,plain,((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.85 tff(14757,plain,
% 8.59/8.85 (~b(s(s(z)), s(z))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14756, 14748, 1232, 1234, 2641])).
% 8.59/8.85 tff(14758,plain,
% 8.59/8.85 (r(s(s(z)), s(z))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[3778, 14757])).
% 8.59/8.85 tff(14759,plain,
% 8.59/8.85 (r(s(z), s(s(s(elem!1))))),
% 8.59/8.85 inference(modus_ponens,[status(thm)],[14718, 13469])).
% 8.59/8.85 tff(14760,plain,
% 8.59/8.85 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14746, 3557, 184, 2053])).
% 8.59/8.85 tff(14761,plain,
% 8.59/8.85 (b(s(s(z)), s(s(s(s(z)))))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[3652, 14760])).
% 8.59/8.85 tff(14762,plain,
% 8.59/8.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.59/8.85 inference(rewrite,[status(thm)],[])).
% 8.59/8.85 tff(14763,plain,
% 8.59/8.85 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.59/8.85 inference(rewrite,[status(thm)],[])).
% 8.59/8.85 tff(14764,plain,
% 8.59/8.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 8.59/8.85 inference(monotonicity,[status(thm)],[14763])).
% 8.59/8.85 tff(14765,plain,
% 8.59/8.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.59/8.85 inference(transitivity,[status(thm)],[14764, 14762])).
% 8.59/8.85 tff(14766,plain,
% 8.59/8.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 8.59/8.85 inference(quant_inst,[status(thm)],[])).
% 8.59/8.85 tff(14767,plain,
% 8.59/8.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 8.59/8.85 inference(modus_ponens,[status(thm)],[14766, 14765])).
% 8.59/8.85 tff(14768,plain,
% 8.59/8.85 ($false),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14767, 194, 184, 2053, 3557, 1697])).
% 8.59/8.85 tff(14769,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.85 tff(14770,plain,
% 8.59/8.85 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14769, 3557, 2053, 184])).
% 8.59/8.85 tff(14771,plain,
% 8.59/8.85 (b(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[1714, 14770])).
% 8.59/8.85 tff(14772,plain,
% 8.59/8.85 ($false),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[9127, 14771, 14761, 2064, 3369])).
% 8.59/8.85 tff(14773,plain,((~r(s(s(z)), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.85 tff(14774,plain,
% 8.59/8.85 (~b(elem!1, s(s(z)))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14773, 14741, 2053, 2064, 184])).
% 8.59/8.85 tff(14775,plain,
% 8.59/8.85 (r(elem!1, s(s(z)))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[3394, 14774, 3694])).
% 8.59/8.85 tff(14776,plain,
% 8.59/8.85 (r(s(s(s(elem!1))), s(s(z)))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[10022, 14775, 3807])).
% 8.59/8.85 tff(14777,plain,
% 8.59/8.85 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[14769, 14741, 2053, 184])).
% 8.59/8.85 tff(14778,plain,
% 8.59/8.85 (b(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[1714, 14777])).
% 8.59/8.85 tff(14779,plain,
% 8.59/8.85 (~b(s(z), s(s(z)))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[6275, 14778, 1234, 14748])).
% 8.59/8.85 tff(14780,plain,
% 8.59/8.85 (r(s(z), s(s(z)))),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[1788, 14779])).
% 8.59/8.85 tff(14781,plain,
% 8.59/8.85 ($false),
% 8.59/8.85 inference(unit_resolution,[status(thm)],[11551, 14780, 14776, 14759, 14758])).
% 8.59/8.85 tff(14782,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~r(elem!1, s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.85 tff(14783,plain,
% 8.59/8.86 (~b(elem!1, s(s(s(s(z)))))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[14782, 1234, 1232, 2641, 2053, 184, 665, 847, 5, 411])).
% 8.59/8.86 tff(14784,plain,
% 8.59/8.86 (r(elem!1, s(s(s(s(z)))))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[781, 14783, 3696])).
% 8.59/8.86 tff(14785,plain,
% 8.59/8.86 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.59/8.86 inference(monotonicity,[status(thm)],[125])).
% 8.59/8.86 tff(14786,plain,
% 8.59/8.86 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.59/8.86 inference(modus_ponens,[status(thm)],[2032, 14785])).
% 8.59/8.86 tff(14787,plain,
% 8.59/8.86 ($false),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[10970, 14786])).
% 8.59/8.86 tff(14788,plain,((~r(elem!1, s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.86 tff(14789,plain,
% 8.59/8.86 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[14788, 14784, 3807])).
% 8.59/8.86 tff(14790,plain,
% 8.59/8.86 (~r(z, s(s(s(s(z)))))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[10090, 14789, 2053, 184])).
% 8.59/8.86 tff(14791,plain,
% 8.59/8.86 (b(z, s(s(s(s(z)))))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[800, 14790])).
% 8.59/8.86 tff(14792,plain,
% 8.59/8.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.59/8.86 inference(rewrite,[status(thm)],[])).
% 8.59/8.86 tff(14793,plain,
% 8.59/8.86 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.59/8.86 inference(rewrite,[status(thm)],[])).
% 8.59/8.86 tff(14794,plain,
% 8.59/8.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 8.59/8.86 inference(monotonicity,[status(thm)],[14793])).
% 8.59/8.86 tff(14795,plain,
% 8.59/8.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.59/8.86 inference(transitivity,[status(thm)],[14794, 14792])).
% 8.59/8.86 tff(14796,plain,
% 8.59/8.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 8.59/8.86 inference(quant_inst,[status(thm)],[])).
% 8.59/8.86 tff(14797,plain,
% 8.59/8.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 8.59/8.86 inference(modus_ponens,[status(thm)],[14796, 14795])).
% 8.59/8.86 tff(14798,plain,
% 8.59/8.86 ($false),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[14797, 391, 665, 1652, 1234, 1686, 590])).
% 8.59/8.86 tff(14799,plain,((~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.86 tff(14800,plain,
% 8.59/8.86 (~b(s(z), z)),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[14799, 14791, 14712, 1234, 665])).
% 8.59/8.86 tff(14801,plain,
% 8.59/8.86 (r(s(z), z)),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[180, 14800])).
% 8.59/8.86 tff(14802,plain,
% 8.59/8.86 (~r(s(s(s(s(z)))), s(z))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[3243, 14801, 2053, 411])).
% 8.59/8.86 tff(14803,plain,
% 8.59/8.86 (b(s(s(s(s(z)))), s(z))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[749, 14802])).
% 8.59/8.86 tff(14804,plain,
% 8.59/8.86 (~r(z, s(z))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[845, 14801, 847, 411])).
% 8.59/8.86 tff(14805,plain,
% 8.59/8.86 (b(z, s(z))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[678, 14804])).
% 8.59/8.86 tff(14806,plain,
% 8.59/8.86 ($false),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[10478, 14805, 14803, 1234, 14791])).
% 8.59/8.86 tff(14807,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.86 tff(14808,plain,
% 8.59/8.86 (~b(s(z), s(s(s(s(z)))))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[14807, 2053, 411, 847, 665, 184, 14713, 2641, 5])).
% 8.59/8.86 tff(14809,plain,
% 8.59/8.86 (r(s(z), s(s(s(s(z)))))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[1230, 14808])).
% 8.59/8.86 tff(14810,plain,
% 8.59/8.86 (~r(elem!1, s(s(s(s(z)))))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[11195, 14809, 2053, 847])).
% 8.59/8.86 tff(14811,plain,
% 8.59/8.86 (b(elem!1, s(s(s(s(z)))))),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[781, 14810, 3696])).
% 8.59/8.86 tff(14812,plain,
% 8.59/8.86 (~r(s(z), z)),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[2061, 14809, 2053, 411])).
% 8.59/8.86 tff(14813,plain,
% 8.59/8.86 (b(s(z), z)),
% 8.59/8.86 inference(unit_resolution,[status(thm)],[180, 14812])).
% 8.59/8.86 tff(14814,plain,
% 8.59/8.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 8.59/8.86 inference(rewrite,[status(thm)],[])).
% 8.59/8.86 tff(14815,plain,
% 8.59/8.86 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 8.59/8.86 inference(rewrite,[status(thm)],[])).
% 8.59/8.86 tff(14816,plain,
% 8.59/8.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 8.59/8.86 inference(monotonicity,[status(thm)],[14815])).
% 8.59/8.86 tff(14817,plain,
% 8.59/8.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 8.59/8.86 inference(transitivity,[status(thm)],[14816, 14814])).
% 8.59/8.86 tff(14818,plain,
% 8.59/8.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))),
% 8.59/8.86 inference(quant_inst,[status(thm)],[])).
% 8.59/8.86 tff(14819,plain,
% 8.59/8.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 8.59/8.87 inference(modus_ponens,[status(thm)],[14818, 14817])).
% 8.59/8.87 tff(14820,plain,
% 8.59/8.87 ($false),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[14819, 391, 665, 2064, 1652, 1686])).
% 8.59/8.87 tff(14821,plain,((~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.87 tff(14822,plain,
% 8.59/8.87 (~b(z, s(s(s(s(z)))))),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[14821, 14811, 665, 14712])).
% 8.59/8.87 tff(14823,plain,
% 8.59/8.87 (r(z, s(s(s(s(z)))))),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[800, 14822])).
% 8.59/8.87 tff(14824,plain,
% 8.59/8.87 (~r(z, s(z))),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[10568, 14823, 2053, 14809])).
% 8.59/8.87 tff(14825,plain,
% 8.59/8.87 (b(z, s(z))),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[678, 14824])).
% 8.59/8.87 tff(14826,plain,
% 8.59/8.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 8.59/8.87 inference(rewrite,[status(thm)],[])).
% 8.59/8.87 tff(14827,plain,
% 8.59/8.87 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 8.59/8.87 inference(rewrite,[status(thm)],[])).
% 8.59/8.87 tff(14828,plain,
% 8.59/8.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 8.59/8.87 inference(monotonicity,[status(thm)],[14827])).
% 8.59/8.87 tff(14829,plain,
% 8.59/8.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 8.59/8.87 inference(transitivity,[status(thm)],[14828, 14826])).
% 8.59/8.87 tff(14830,plain,
% 8.59/8.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 8.59/8.87 inference(quant_inst,[status(thm)],[])).
% 8.59/8.87 tff(14831,plain,
% 8.59/8.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 8.59/8.87 inference(modus_ponens,[status(thm)],[14830, 14829])).
% 8.59/8.87 tff(14832,plain,
% 8.59/8.87 (~b(s(z), elem!1)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[14831, 391, 665, 14825, 14813])).
% 8.59/8.87 tff(14833,plain,
% 8.59/8.87 (r(s(z), elem!1)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[632, 14832, 14716])).
% 8.59/8.87 tff(14834,plain,
% 8.59/8.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 8.59/8.87 inference(rewrite,[status(thm)],[])).
% 8.59/8.87 tff(14835,plain,
% 8.59/8.87 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 8.59/8.87 inference(rewrite,[status(thm)],[])).
% 8.59/8.87 tff(14836,plain,
% 8.59/8.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 8.59/8.87 inference(monotonicity,[status(thm)],[14835])).
% 8.59/8.87 tff(14837,plain,
% 8.59/8.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 8.59/8.87 inference(transitivity,[status(thm)],[14836, 14834])).
% 8.59/8.87 tff(14838,plain,
% 8.59/8.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 8.59/8.87 inference(quant_inst,[status(thm)],[])).
% 8.59/8.87 tff(14839,plain,
% 8.59/8.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 8.59/8.87 inference(modus_ponens,[status(thm)],[14838, 14837])).
% 8.59/8.87 tff(14840,plain,
% 8.59/8.87 (~b(s(s(z)), elem!1)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[14839, 391, 665, 1235, 664, 590])).
% 8.59/8.87 tff(14841,plain,
% 8.59/8.87 (r(s(s(z)), elem!1)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[4730, 14840, 5547])).
% 8.59/8.87 tff(14842,plain,
% 8.59/8.87 ($false),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[6674, 10830, 14841, 847, 1484])).
% 8.59/8.87 tff(14843,plain,((~b(s(s(z)), z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (s(s(z)) = elem!1) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.87 tff(14844,plain,
% 8.59/8.87 (~b(s(s(z)), z)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[14843, 14833, 847, 14710, 14825, 14813, 665])).
% 8.59/8.87 tff(14845,plain,
% 8.59/8.87 (r(s(s(z)), z)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[1211, 14844])).
% 8.59/8.87 tff(14846,plain,
% 8.59/8.87 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[14746, 14845, 184, 2053])).
% 8.59/8.87 tff(14847,plain,
% 8.59/8.87 (b(s(s(z)), s(s(s(s(z)))))),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[3652, 14846])).
% 8.59/8.87 tff(14848,plain,
% 8.59/8.87 (~b(s(s(z)), elem!1)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[5553, 391, 665, 14847, 14811, 14712])).
% 8.59/8.87 tff(14849,plain,
% 8.59/8.87 (r(s(s(z)), elem!1)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[4730, 14848, 14710])).
% 8.59/8.87 tff(14850,plain,
% 8.59/8.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 8.59/8.87 inference(rewrite,[status(thm)],[])).
% 8.59/8.87 tff(14851,plain,
% 8.59/8.87 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 8.59/8.87 inference(rewrite,[status(thm)],[])).
% 8.59/8.87 tff(14852,plain,
% 8.59/8.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))))),
% 8.59/8.87 inference(monotonicity,[status(thm)],[14851])).
% 8.59/8.87 tff(14853,plain,
% 8.59/8.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 8.59/8.87 inference(transitivity,[status(thm)],[14852, 14850])).
% 8.59/8.87 tff(14854,plain,
% 8.59/8.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 8.59/8.87 inference(quant_inst,[status(thm)],[])).
% 8.59/8.87 tff(14855,plain,
% 8.59/8.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 8.59/8.87 inference(modus_ponens,[status(thm)],[14854, 14853])).
% 8.59/8.87 tff(14856,plain,
% 8.59/8.87 ($false),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[14855, 194, 411, 847, 14845, 14849])).
% 8.59/8.87 tff(14857,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~(s(s(s(elem!1))) = elem!1)) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.87 tff(14858,plain,
% 8.59/8.87 (~r(s(s(s(s(z)))), z)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[14857, 11397, 14703, 665, 184, 411, 5, 14707])).
% 8.59/8.87 tff(14859,plain,
% 8.59/8.87 (b(s(s(s(s(z)))), z)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[87, 14858])).
% 8.59/8.87 tff(14860,plain,
% 8.59/8.87 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 8.59/8.87 inference(monotonicity,[status(thm)],[445])).
% 8.59/8.87 tff(14861,plain,
% 8.59/8.87 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 8.59/8.87 inference(symmetry,[status(thm)],[14860])).
% 8.59/8.87 tff(14862,plain,
% 8.59/8.87 (r(z, s(s(elem!1)))),
% 8.59/8.87 inference(modus_ponens,[status(thm)],[411, 14861])).
% 8.59/8.87 tff(14863,plain,
% 8.59/8.87 (~r(z, s(s(s(s(z)))))),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[10416, 194, 411, 847, 2112])).
% 8.59/8.87 tff(14864,plain,
% 8.59/8.87 (b(z, s(s(s(s(z)))))),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[800, 14863])).
% 8.59/8.87 tff(14865,plain,
% 8.59/8.87 (~r(s(z), elem!1)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[5396, 2112, 847, 1216])).
% 8.59/8.87 tff(14866,plain,
% 8.59/8.87 (b(s(z), elem!1)),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[632, 14865, 14716])).
% 8.59/8.87 tff(14867,plain,
% 8.59/8.87 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 8.59/8.87 inference(monotonicity,[status(thm)],[5])).
% 8.59/8.87 tff(14868,plain,
% 8.59/8.87 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 8.59/8.87 inference(symmetry,[status(thm)],[14867])).
% 8.59/8.87 tff(14869,plain,
% 8.59/8.87 (b(s(z), s(s(s(elem!1))))),
% 8.59/8.87 inference(modus_ponens,[status(thm)],[644, 14868])).
% 8.59/8.87 tff(14870,assumption,(~b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 8.59/8.87 tff(14871,plain,
% 8.59/8.87 ($false),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[14870, 14869])).
% 8.59/8.87 tff(14872,plain,((~(s(s(s(elem!1))) = elem!1)) | b(s(z), s(s(s(elem!1)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.87 tff(14873,plain,
% 8.59/8.87 (b(s(z), s(s(s(elem!1))))),
% 8.59/8.87 inference(unit_resolution,[status(thm)],[14872, 14866, 5])).
% 8.59/8.87 tff(14874,plain,
% 8.59/8.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 8.59/8.87 inference(rewrite,[status(thm)],[])).
% 8.59/8.87 tff(14875,plain,
% 8.59/8.87 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 8.59/8.87 inference(rewrite,[status(thm)],[])).
% 8.59/8.87 tff(14876,plain,
% 8.59/8.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 8.59/8.88 inference(monotonicity,[status(thm)],[14875])).
% 8.59/8.88 tff(14877,plain,
% 8.59/8.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 8.59/8.88 inference(transitivity,[status(thm)],[14876, 14874])).
% 8.59/8.88 tff(14878,plain,
% 8.59/8.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 8.59/8.88 inference(quant_inst,[status(thm)],[])).
% 8.59/8.88 tff(14879,plain,
% 8.59/8.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 8.59/8.88 inference(modus_ponens,[status(thm)],[14878, 14877])).
% 8.59/8.88 tff(14880,plain,
% 8.59/8.88 ($false),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[14879, 391, 665, 644, 90, 1686, 590])).
% 8.59/8.88 tff(14881,plain,((~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.88 tff(14882,plain,
% 8.59/8.88 (~b(s(z), z)),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[14881, 14864, 90, 665, 14866])).
% 8.59/8.88 tff(14883,plain,
% 8.59/8.88 (r(s(z), z)),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[180, 14882])).
% 8.59/8.88 tff(14884,plain,
% 8.59/8.88 (~r(z, s(z))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[845, 14883, 847, 411])).
% 8.59/8.88 tff(14885,plain,
% 8.59/8.88 (b(z, s(z))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[678, 14884])).
% 8.59/8.88 tff(14886,plain,
% 8.59/8.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.59/8.88 inference(rewrite,[status(thm)],[])).
% 8.59/8.88 tff(14887,plain,
% 8.59/8.88 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.59/8.88 inference(rewrite,[status(thm)],[])).
% 8.59/8.88 tff(14888,plain,
% 8.59/8.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 8.59/8.88 inference(monotonicity,[status(thm)],[14887])).
% 8.59/8.88 tff(14889,plain,
% 8.59/8.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.59/8.88 inference(transitivity,[status(thm)],[14888, 14886])).
% 8.59/8.88 tff(14890,plain,
% 8.59/8.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.59/8.88 inference(quant_inst,[status(thm)],[])).
% 8.59/8.88 tff(14891,plain,
% 8.59/8.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 8.59/8.88 inference(modus_ponens,[status(thm)],[14890, 14889])).
% 8.59/8.88 tff(14892,plain,
% 8.59/8.88 (~b(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[14891, 391, 90, 1235, 1686])).
% 8.59/8.88 tff(14893,plain,
% 8.59/8.88 (r(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[1714, 14892])).
% 8.59/8.88 tff(14894,plain,
% 8.59/8.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.88 inference(rewrite,[status(thm)],[])).
% 8.59/8.88 tff(14895,plain,
% 8.59/8.88 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.88 inference(rewrite,[status(thm)],[])).
% 8.59/8.88 tff(14896,plain,
% 8.59/8.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.59/8.88 inference(monotonicity,[status(thm)],[14895])).
% 8.59/8.88 tff(14897,plain,
% 8.59/8.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.59/8.88 inference(transitivity,[status(thm)],[14896, 14894])).
% 8.59/8.88 tff(14898,plain,
% 8.59/8.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))))),
% 8.59/8.88 inference(quant_inst,[status(thm)],[])).
% 8.59/8.88 tff(14899,plain,
% 8.59/8.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.59/8.88 inference(modus_ponens,[status(thm)],[14898, 14897])).
% 8.59/8.88 tff(14900,plain,
% 8.59/8.88 ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[14899, 194])).
% 8.59/8.88 tff(14901,plain,
% 8.59/8.88 (~r(elem!1, s(s(s(s(z)))))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[14900, 14893, 1216, 847])).
% 8.59/8.88 tff(14902,plain,
% 8.59/8.88 (b(elem!1, s(s(s(s(z)))))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[781, 14901, 8922])).
% 8.59/8.88 tff(14903,plain,
% 8.59/8.88 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.59/8.88 inference(modus_ponens,[status(thm)],[14902, 3811])).
% 8.59/8.88 tff(14904,plain,
% 8.59/8.88 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[4472, 1235, 1686, 90])).
% 8.59/8.88 tff(14905,plain,
% 8.59/8.88 (r(s(s(z)), s(s(s(s(z)))))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[3652, 14904])).
% 8.59/8.88 tff(14906,plain,
% 8.59/8.88 (~r(s(s(z)), s(z))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[14395, 14893, 14905, 1216])).
% 8.59/8.88 tff(14907,plain,
% 8.59/8.88 (b(s(s(z)), s(z))),
% 8.59/8.88 inference(unit_resolution,[status(thm)],[3778, 14906])).
% 8.59/8.89 tff(14908,plain,
% 8.59/8.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.59/8.89 inference(rewrite,[status(thm)],[])).
% 8.59/8.89 tff(14909,plain,
% 8.59/8.89 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.59/8.89 inference(rewrite,[status(thm)],[])).
% 8.59/8.89 tff(14910,plain,
% 8.59/8.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 8.59/8.89 inference(monotonicity,[status(thm)],[14909])).
% 8.59/8.89 tff(14911,plain,
% 8.59/8.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.59/8.89 inference(transitivity,[status(thm)],[14910, 14908])).
% 8.59/8.89 tff(14912,plain,
% 8.59/8.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 8.59/8.89 inference(quant_inst,[status(thm)],[])).
% 8.59/8.89 tff(14913,plain,
% 8.59/8.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 8.59/8.89 inference(modus_ponens,[status(thm)],[14912, 14911])).
% 8.59/8.89 tff(14914,plain,
% 8.59/8.89 ($false),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[14913, 391, 379, 1235, 14907, 664, 14903])).
% 8.59/8.89 tff(14915,plain,((~b(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~(elem!1 = s(s(s(elem!1))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.89 tff(14916,plain,
% 8.59/8.89 (~b(s(s(z)), z)),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[14915, 14885, 3807, 1216, 3696, 14873, 847, 90, 14864])).
% 8.59/8.89 tff(14917,plain,
% 8.59/8.89 (~b(elem!1, s(s(s(s(z)))))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[3234, 14864, 665, 90])).
% 8.59/8.89 tff(14918,plain,
% 8.59/8.89 (r(elem!1, s(s(s(s(z)))))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[781, 14917, 3696])).
% 8.59/8.89 tff(14919,plain,
% 8.59/8.89 (~r(s(s(s(s(z)))), s(z))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[6347, 14918, 1216, 847])).
% 8.59/8.89 tff(14920,plain,
% 8.59/8.89 (b(s(s(s(s(z)))), s(z))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[749, 14919])).
% 8.59/8.89 tff(14921,plain,
% 8.59/8.89 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[14900, 14918, 847, 1216])).
% 8.59/8.89 tff(14922,plain,
% 8.59/8.89 (b(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[1714, 14921])).
% 8.59/8.89 tff(14923,plain,
% 8.59/8.89 (~r(s(s(z)), z)),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[3796, 14922, 411, 14883, 14920, 326])).
% 8.59/8.89 tff(14924,plain,
% 8.59/8.89 ($false),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[1211, 14923, 14916])).
% 8.59/8.89 tff(14925,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.89 tff(14926,plain,
% 8.59/8.89 (~r(s(s(s(s(z)))), elem!1)),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[14925, 1216, 326, 411, 14703, 90, 665, 5])).
% 8.59/8.89 tff(14927,plain,
% 8.59/8.89 (b(s(s(s(s(z)))), elem!1)),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[762, 14926, 2691])).
% 8.59/8.89 tff(14928,plain,
% 8.59/8.89 (~b(z, s(s(s(s(z)))))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[4246, 14927, 665, 90])).
% 8.59/8.89 tff(14929,plain,
% 8.59/8.89 (r(z, s(s(s(s(z)))))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[800, 14928])).
% 8.59/8.89 tff(14930,plain,
% 8.59/8.89 (~b(z, s(s(s(s(z)))))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[4246, 1652, 665, 90])).
% 8.59/8.89 tff(14931,plain,
% 8.59/8.89 (r(z, s(s(s(s(z)))))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[800, 14930])).
% 8.59/8.89 tff(14932,plain,
% 8.59/8.89 (~r(s(z), elem!1)),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[14725, 722, 847, 411])).
% 8.59/8.89 tff(14933,plain,
% 8.59/8.89 (b(s(z), elem!1)),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[632, 14932, 150])).
% 8.59/8.89 tff(14934,plain,
% 8.59/8.89 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[14900, 2032, 847, 1216])).
% 8.59/8.89 tff(14935,plain,
% 8.59/8.89 (b(s(s(s(s(z)))), s(s(z)))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[1714, 14934])).
% 8.59/8.89 tff(14936,plain,
% 8.59/8.89 (~r(s(s(s(s(z)))), s(z))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[6347, 2032, 1216, 847])).
% 8.59/8.89 tff(14937,plain,
% 8.59/8.89 (b(s(s(s(s(z)))), s(z))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[749, 14936])).
% 8.59/8.89 tff(14938,plain,
% 8.59/8.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.59/8.89 inference(rewrite,[status(thm)],[])).
% 8.59/8.89 tff(14939,plain,
% 8.59/8.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.59/8.89 inference(quant_inst,[status(thm)],[])).
% 8.59/8.89 tff(14940,plain,
% 8.59/8.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 8.59/8.89 inference(modus_ponens,[status(thm)],[14939, 14938])).
% 8.59/8.89 tff(14941,plain,
% 8.59/8.89 ($false),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[14940, 391, 665, 644, 1759, 3563, 1233])).
% 8.59/8.89 tff(14942,plain,((~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.89 tff(14943,plain,
% 8.59/8.89 (~b(s(s(z)), s(z))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[14942, 14937, 644, 665, 14935])).
% 8.59/8.89 tff(14944,plain,
% 8.59/8.89 (r(s(s(z)), s(z))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[3778, 14943])).
% 8.59/8.89 tff(14945,plain,
% 8.59/8.89 (~r(s(s(z)), elem!1)),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[10999, 194, 847, 1216, 14944])).
% 8.59/8.89 tff(14946,plain,
% 8.59/8.89 (b(s(s(z)), elem!1)),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[4730, 14945, 5547])).
% 8.59/8.89 tff(14947,plain,
% 8.59/8.89 (~r(elem!1, s(s(z)))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[10836, 194, 847, 1216, 14944])).
% 8.59/8.89 tff(14948,plain,
% 8.59/8.89 (b(elem!1, s(s(z)))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[3394, 14947, 1405])).
% 8.59/8.89 tff(14949,plain,
% 8.59/8.89 ($false),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[11012, 14948, 14946, 14935, 1652])).
% 8.59/8.89 tff(14950,plain,((~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(z))) | (s(s(z)) = elem!1) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 8.59/8.89 tff(14951,plain,
% 8.59/8.89 (~r(elem!1, s(s(s(s(z)))))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[14950, 14933, 1405, 5547, 847, 1216, 1652, 665])).
% 8.59/8.89 tff(14952,plain,
% 8.59/8.89 (b(elem!1, s(s(s(s(z)))))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[781, 14951, 8922])).
% 8.59/8.89 tff(14953,plain,
% 8.59/8.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 8.59/8.89 inference(rewrite,[status(thm)],[])).
% 8.59/8.89 tff(14954,plain,
% 8.59/8.89 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 8.59/8.89 inference(rewrite,[status(thm)],[])).
% 8.59/8.89 tff(14955,plain,
% 8.59/8.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 8.59/8.89 inference(monotonicity,[status(thm)],[14954])).
% 8.59/8.89 tff(14956,plain,
% 8.59/8.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 8.59/8.89 inference(transitivity,[status(thm)],[14955, 14953])).
% 8.59/8.89 tff(14957,plain,
% 8.59/8.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 8.59/8.89 inference(quant_inst,[status(thm)],[])).
% 8.59/8.89 tff(14958,plain,
% 8.59/8.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 8.59/8.89 inference(modus_ponens,[status(thm)],[14957, 14956])).
% 8.59/8.89 tff(14959,plain,
% 8.59/8.89 (~b(s(s(s(s(z)))), s(z))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[14958, 391, 14933, 90, 14952, 1652])).
% 8.59/8.89 tff(14960,plain,
% 8.59/8.89 (r(s(s(s(s(z)))), s(z))),
% 8.59/8.89 inference(unit_resolution,[status(thm)],[749, 14959])).
% 8.59/8.89 tff(14961,plain,
% 8.59/8.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 8.59/8.89 inference(rewrite,[status(thm)],[])).
% 8.59/8.89 tff(14962,plain,
% 8.59/8.89 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 8.69/8.90 inference(rewrite,[status(thm)],[])).
% 8.69/8.90 tff(14963,plain,
% 8.69/8.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 8.69/8.90 inference(monotonicity,[status(thm)],[14962])).
% 8.69/8.90 tff(14964,plain,
% 8.69/8.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 8.69/8.90 inference(transitivity,[status(thm)],[14963, 14961])).
% 8.69/8.90 tff(14965,plain,
% 8.69/8.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 8.69/8.90 inference(quant_inst,[status(thm)],[])).
% 8.69/8.90 tff(14966,plain,
% 8.69/8.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 8.69/8.90 inference(modus_ponens,[status(thm)],[14965, 14964])).
% 8.69/8.90 tff(14967,plain,
% 8.69/8.90 ($false),
% 8.69/8.90 inference(unit_resolution,[status(thm)],[14966, 194, 722, 1216, 14960, 14931])).
% 8.69/8.90 tff(14968,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(s(s(z))))) | (elem!1 = s(s(z))) | (s(s(z)) = elem!1) | (~r(elem!1, s(z))) | (~b(elem!1, z)) | (s(z) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.90 tff(14969,plain,
% 8.69/8.90 (~r(z, s(z))),
% 8.69/8.90 inference(unit_resolution,[status(thm)],[14968, 1216, 90, 14927, 3696, 3694, 14710, 14703, 665, 14716, 411])).
% 8.69/8.90 tff(14970,plain,
% 8.69/8.90 (b(z, s(z))),
% 8.69/8.90 inference(unit_resolution,[status(thm)],[678, 14969])).
% 8.69/8.90 tff(14971,plain,
% 8.69/8.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 8.69/8.90 inference(rewrite,[status(thm)],[])).
% 8.69/8.90 tff(14972,plain,
% 8.69/8.90 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 8.69/8.90 inference(rewrite,[status(thm)],[])).
% 8.69/8.90 tff(14973,plain,
% 8.69/8.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 8.69/8.90 inference(monotonicity,[status(thm)],[14972])).
% 8.69/8.90 tff(14974,plain,
% 8.69/8.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 8.69/8.90 inference(transitivity,[status(thm)],[14973, 14971])).
% 8.69/8.90 tff(14975,plain,
% 8.69/8.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 8.69/8.90 inference(quant_inst,[status(thm)],[])).
% 8.69/8.90 tff(14976,plain,
% 8.69/8.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 8.69/8.90 inference(modus_ponens,[status(thm)],[14975, 14974])).
% 8.69/8.90 tff(14977,plain,
% 8.69/8.90 ($false),
% 8.69/8.90 inference(unit_resolution,[status(thm)],[14976, 391, 665, 90, 1652, 664, 590])).
% 8.69/8.90 tff(14978,plain,((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.90 tff(14979,plain,
% 8.69/8.90 (~b(s(z), z)),
% 8.69/8.90 inference(unit_resolution,[status(thm)],[14978, 14927, 90, 665, 14970])).
% 8.69/8.90 tff(14980,plain,
% 8.69/8.90 (r(s(z), z)),
% 8.69/8.90 inference(unit_resolution,[status(thm)],[180, 14979])).
% 8.69/8.90 tff(14981,plain,
% 8.69/8.90 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.69/8.90 inference(unit_resolution,[status(thm)],[1705, 14980, 1216, 14929])).
% 8.69/8.90 tff(14982,plain,
% 8.69/8.90 (b(s(s(s(s(z)))), s(s(z)))),
% 8.69/8.90 inference(unit_resolution,[status(thm)],[1714, 14981])).
% 8.69/8.90 tff(14983,plain,
% 8.69/8.90 (~r(s(z), s(s(s(elem!1))))),
% 8.69/8.90 inference(unit_resolution,[status(thm)],[3499, 14980, 184, 183])).
% 8.69/8.90 tff(14984,plain,
% 8.69/8.90 (b(s(z), s(s(s(elem!1))))),
% 8.69/8.90 inference(unit_resolution,[status(thm)],[247, 14983])).
% 8.69/8.90 tff(14985,plain,
% 8.69/8.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.69/8.90 inference(rewrite,[status(thm)],[])).
% 8.69/8.90 tff(14986,plain,
% 8.69/8.90 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.69/8.90 inference(rewrite,[status(thm)],[])).
% 8.69/8.90 tff(14987,plain,
% 8.69/8.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 8.69/8.90 inference(monotonicity,[status(thm)],[14986])).
% 8.69/8.90 tff(14988,plain,
% 8.69/8.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.69/8.90 inference(transitivity,[status(thm)],[14987, 14985])).
% 8.69/8.90 tff(14989,plain,
% 8.69/8.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.69/8.90 inference(quant_inst,[status(thm)],[])).
% 8.69/8.90 tff(14990,plain,
% 8.69/8.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 8.69/8.91 inference(modus_ponens,[status(thm)],[14989, 14988])).
% 8.69/8.91 tff(14991,plain,
% 8.69/8.91 ($false),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[14990, 391, 379, 90, 1235, 3563, 664])).
% 8.69/8.91 tff(14992,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.91 tff(14993,plain,
% 8.69/8.91 (~b(s(s(z)), z)),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[14992, 14984, 90, 14970, 14982])).
% 8.69/8.91 tff(14994,plain,
% 8.69/8.91 (~r(s(s(s(s(z)))), s(z))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[1224, 14980, 1216, 14929])).
% 8.69/8.91 tff(14995,plain,
% 8.69/8.91 (b(s(s(s(s(z)))), s(z))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[749, 14994])).
% 8.69/8.91 tff(14996,plain,
% 8.69/8.91 (~r(s(s(z)), z)),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[3796, 14982, 411, 14980, 14995, 326])).
% 8.69/8.91 tff(14997,plain,
% 8.69/8.91 ($false),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[1211, 14996, 14993])).
% 8.69/8.91 tff(14998,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.91 tff(14999,plain,
% 8.69/8.91 (~r(s(z), s(s(s(s(z)))))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[14998, 14862, 411, 14859, 184, 183, 665, 5])).
% 8.69/8.91 tff(15000,plain,
% 8.69/8.91 (b(s(z), s(s(s(s(z)))))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[1230, 14999])).
% 8.69/8.91 tff(15001,plain,
% 8.69/8.91 (~b(z, s(s(s(s(z)))))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[10438, 14859, 411, 14703, 15000])).
% 8.69/8.91 tff(15002,plain,
% 8.69/8.91 (r(z, s(s(s(s(z)))))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[800, 15001])).
% 8.69/8.91 tff(15003,plain,
% 8.69/8.91 (~r(s(s(s(s(z)))), elem!1)),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[10418, 15002, 14703, 411])).
% 8.69/8.91 tff(15004,plain,
% 8.69/8.91 (b(s(s(s(s(z)))), elem!1)),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[762, 15003, 2691])).
% 8.69/8.91 tff(15005,plain,
% 8.69/8.91 (~b(z, s(s(s(s(z)))))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[10438, 90, 411, 847, 1234])).
% 8.69/8.91 tff(15006,plain,
% 8.69/8.91 (r(z, s(s(s(s(z)))))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[800, 15005])).
% 8.69/8.91 tff(15007,plain,
% 8.69/8.91 (~b(elem!1, s(s(s(s(z)))))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[10491, 14933, 665, 1234, 1652])).
% 8.69/8.91 tff(15008,plain,
% 8.69/8.91 (r(elem!1, s(s(s(s(z)))))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[781, 15007, 8922])).
% 8.69/8.91 tff(15009,plain,
% 8.69/8.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.69/8.91 inference(rewrite,[status(thm)],[])).
% 8.69/8.91 tff(15010,plain,
% 8.69/8.91 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.69/8.91 inference(rewrite,[status(thm)],[])).
% 8.69/8.91 tff(15011,plain,
% 8.69/8.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.69/8.91 inference(monotonicity,[status(thm)],[15010])).
% 8.69/8.91 tff(15012,plain,
% 8.69/8.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.69/8.91 inference(transitivity,[status(thm)],[15011, 15009])).
% 8.69/8.91 tff(15013,plain,
% 8.69/8.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))),
% 8.69/8.91 inference(quant_inst,[status(thm)],[])).
% 8.69/8.91 tff(15014,plain,
% 8.69/8.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.69/8.91 inference(modus_ponens,[status(thm)],[15013, 15012])).
% 8.69/8.91 tff(15015,plain,
% 8.69/8.91 ($false),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[15014, 194, 411, 2032, 1697, 719])).
% 8.69/8.91 tff(15016,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.91 tff(15017,plain,
% 8.69/8.91 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[15016, 15008, 411, 15006])).
% 8.69/8.91 tff(15018,plain,
% 8.69/8.91 (b(s(s(s(s(z)))), s(s(z)))),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[1714, 15017])).
% 8.69/8.91 tff(15019,plain,
% 8.69/8.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 8.69/8.91 inference(rewrite,[status(thm)],[])).
% 8.69/8.91 tff(15020,plain,
% 8.69/8.91 (((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 8.69/8.91 inference(rewrite,[status(thm)],[])).
% 8.69/8.91 tff(15021,plain,
% 8.69/8.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 8.69/8.91 inference(monotonicity,[status(thm)],[15020])).
% 8.69/8.91 tff(15022,plain,
% 8.69/8.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 8.69/8.91 inference(transitivity,[status(thm)],[15021, 15019])).
% 8.69/8.91 tff(15023,plain,
% 8.69/8.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 8.69/8.91 inference(quant_inst,[status(thm)],[])).
% 8.69/8.91 tff(15024,plain,
% 8.69/8.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 8.69/8.91 inference(modus_ponens,[status(thm)],[15023, 15022])).
% 8.69/8.91 tff(15025,plain,
% 8.69/8.91 ($false),
% 8.69/8.91 inference(unit_resolution,[status(thm)],[15024, 391, 665, 1234, 2439, 3563, 8498])).
% 8.69/8.91 tff(15026,plain,((~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.92 tff(15027,plain,
% 8.69/8.92 (~b(s(z), s(s(z)))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[15026, 8498, 1234, 3563, 665])).
% 8.69/8.92 tff(15028,plain,
% 8.69/8.92 (r(s(z), s(s(z)))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[1788, 15027])).
% 8.69/8.92 tff(15029,plain,
% 8.69/8.92 (~b(elem!1, s(s(z)))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[11012, 8498, 3563, 1652])).
% 8.69/8.92 tff(15030,plain,
% 8.69/8.92 (r(elem!1, s(s(z)))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[3394, 15029, 1405])).
% 8.69/8.92 tff(15031,plain,
% 8.69/8.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 8.69/8.92 inference(rewrite,[status(thm)],[])).
% 8.69/8.92 tff(15032,plain,
% 8.69/8.92 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 8.69/8.92 inference(rewrite,[status(thm)],[])).
% 8.69/8.92 tff(15033,plain,
% 8.69/8.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z))))))),
% 8.69/8.92 inference(monotonicity,[status(thm)],[15032])).
% 8.69/8.92 tff(15034,plain,
% 8.69/8.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 8.69/8.92 inference(transitivity,[status(thm)],[15033, 15031])).
% 8.69/8.92 tff(15035,plain,
% 8.69/8.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))),
% 8.69/8.92 inference(quant_inst,[status(thm)],[])).
% 8.69/8.92 tff(15036,plain,
% 8.69/8.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z))))),
% 8.69/8.92 inference(modus_ponens,[status(thm)],[15035, 15034])).
% 8.69/8.92 tff(15037,plain,
% 8.69/8.92 ($false),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[15036, 194, 847, 3557, 15030, 15028])).
% 8.69/8.92 tff(15038,plain,((~b(s(s(z)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, z)) | (elem!1 = s(s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.92 tff(15039,plain,
% 8.69/8.92 (~b(s(s(z)), elem!1)),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[15038, 3557, 847, 1234, 3563, 665, 1405, 1652])).
% 8.69/8.92 tff(15040,plain,
% 8.69/8.92 (r(s(s(z)), elem!1)),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[4730, 15039, 5547])).
% 8.69/8.92 tff(15041,plain,
% 8.69/8.92 ($false),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[14855, 194, 411, 847, 3557, 15040])).
% 8.69/8.92 tff(15042,plain,((~r(s(s(z)), z)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (s(s(z)) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, z)) | (elem!1 = s(s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.92 tff(15043,plain,
% 8.69/8.92 (~r(s(s(z)), z)),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[15042, 15018, 847, 5547, 1234, 411, 665, 1405, 1652])).
% 8.69/8.92 tff(15044,plain,
% 8.69/8.92 (b(s(s(z)), z)),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[1211, 15043])).
% 8.69/8.92 tff(15045,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 8.69/8.92 tff(15046,plain,
% 8.69/8.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))))),
% 8.69/8.92 inference(rewrite,[status(thm)],[])).
% 8.69/8.92 tff(15047,plain,
% 8.69/8.92 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(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(z, s(s(z)))))),
% 8.69/8.92 inference(rewrite,[status(thm)],[])).
% 8.69/8.92 tff(15048,plain,
% 8.69/8.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z))))))),
% 8.69/8.92 inference(monotonicity,[status(thm)],[15047])).
% 8.69/8.92 tff(15049,plain,
% 8.69/8.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))))),
% 8.69/8.92 inference(transitivity,[status(thm)],[15048, 15046])).
% 8.69/8.92 tff(15050,plain,
% 8.69/8.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 8.69/8.92 inference(quant_inst,[status(thm)],[])).
% 8.69/8.92 tff(15051,plain,
% 8.69/8.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z))))),
% 8.69/8.92 inference(modus_ponens,[status(thm)],[15050, 15049])).
% 8.69/8.92 tff(15052,plain,
% 8.69/8.92 ($false),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[15051, 391, 90, 1235, 3563, 15045])).
% 8.69/8.92 tff(15053,plain,((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.92 tff(15054,plain,
% 8.69/8.92 (~b(z, s(s(z)))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[15053, 15044, 90, 15018])).
% 8.69/8.92 tff(15055,plain,
% 8.69/8.92 (r(z, s(s(z)))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[10164, 42, 15054, 8912])).
% 8.69/8.92 tff(15056,plain,
% 8.69/8.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.69/8.92 inference(rewrite,[status(thm)],[])).
% 8.69/8.92 tff(15057,plain,
% 8.69/8.92 (((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.69/8.92 inference(rewrite,[status(thm)],[])).
% 8.69/8.92 tff(15058,plain,
% 8.69/8.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 8.69/8.92 inference(monotonicity,[status(thm)],[15057])).
% 8.69/8.92 tff(15059,plain,
% 8.69/8.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.69/8.92 inference(transitivity,[status(thm)],[15058, 15056])).
% 8.69/8.92 tff(15060,plain,
% 8.69/8.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))),
% 8.69/8.92 inference(quant_inst,[status(thm)],[])).
% 8.69/8.92 tff(15061,plain,
% 8.69/8.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.69/8.92 inference(modus_ponens,[status(thm)],[15060, 15059])).
% 8.69/8.92 tff(15062,plain,
% 8.69/8.92 ($false),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[15061, 194, 411, 2032, 723, 719])).
% 8.69/8.92 tff(15063,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.92 tff(15064,plain,
% 8.69/8.92 (~r(s(s(s(s(z)))), s(z))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[15063, 15008, 411, 15006])).
% 8.69/8.92 tff(15065,plain,
% 8.69/8.92 (b(s(s(s(s(z)))), s(z))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[749, 15064])).
% 8.69/8.92 tff(15066,plain,
% 8.69/8.92 (~b(s(s(z)), s(z))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[14942, 15018, 14933, 665, 15065])).
% 8.69/8.92 tff(15067,plain,
% 8.69/8.92 (r(s(s(z)), s(z))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[3778, 15066])).
% 8.69/8.92 tff(15068,plain,
% 8.69/8.92 (~r(s(z), s(s(z)))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[9720, 15055, 722, 15067])).
% 8.69/8.92 tff(15069,plain,
% 8.69/8.92 (b(s(z), s(s(z)))),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[1788, 15068])).
% 8.69/8.92 tff(15070,plain,
% 8.69/8.92 (~b(s(s(z)), elem!1)),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[15026, 15069, 1234, 15018, 665])).
% 8.69/8.92 tff(15071,plain,
% 8.69/8.92 (r(s(s(z)), elem!1)),
% 8.69/8.92 inference(unit_resolution,[status(thm)],[4730, 15070, 5547])).
% 8.69/8.92 tff(15072,plain,
% 8.69/8.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 8.69/8.92 inference(rewrite,[status(thm)],[])).
% 8.69/8.92 tff(15073,plain,
% 8.69/8.92 (((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 8.69/8.92 inference(rewrite,[status(thm)],[])).
% 8.69/8.92 tff(15074,plain,
% 8.69/8.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))))),
% 8.69/8.92 inference(monotonicity,[status(thm)],[15073])).
% 8.69/8.92 tff(15075,plain,
% 8.69/8.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 8.69/8.92 inference(transitivity,[status(thm)],[15074, 15072])).
% 8.69/8.92 tff(15076,plain,
% 8.69/8.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))),
% 8.69/8.92 inference(quant_inst,[status(thm)],[])).
% 8.69/8.92 tff(15077,plain,
% 8.69/8.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))),
% 8.69/8.93 inference(modus_ponens,[status(thm)],[15076, 15075])).
% 8.69/8.93 tff(15078,plain,
% 8.69/8.93 ($false),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[15077, 194, 411, 847, 15071, 15055])).
% 8.69/8.93 tff(15079,plain,((~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (s(s(z)) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (elem!1 = s(s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(s(s(z))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.69/8.93 tff(15080,plain,
% 8.69/8.93 (~r(z, s(z))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[15079, 15000, 14703, 14710, 411, 665, 14859, 3694, 15004, 3696, 14716])).
% 8.69/8.93 tff(15081,plain,
% 8.69/8.93 (b(z, s(z))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[678, 15080])).
% 8.69/8.93 tff(15082,plain,
% 8.69/8.93 (~b(s(z), z)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[14978, 15081, 14859, 665, 15004])).
% 8.69/8.93 tff(15083,plain,
% 8.69/8.93 (r(s(z), z)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[180, 15082])).
% 8.69/8.93 tff(15084,plain,
% 8.69/8.93 (~r(s(z), elem!1)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[2475, 15083, 14703, 411])).
% 8.69/8.93 tff(15085,plain,
% 8.69/8.93 (b(s(z), elem!1)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[632, 15084, 14716])).
% 8.69/8.93 tff(15086,plain,
% 8.69/8.93 (~b(elem!1, s(s(s(s(z)))))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[10491, 15085, 665, 15000, 15004])).
% 8.69/8.93 tff(15087,plain,
% 8.69/8.93 (r(elem!1, s(s(s(s(z)))))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[781, 15086, 3696])).
% 8.69/8.93 tff(15088,plain,
% 8.69/8.93 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[15016, 15087, 411, 15002])).
% 8.69/8.93 tff(15089,plain,
% 8.69/8.93 (b(s(s(s(s(z)))), s(s(z)))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[1714, 15088])).
% 8.69/8.93 tff(15090,plain,
% 8.69/8.93 (~r(s(s(z)), z)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[15042, 15089, 14703, 14710, 15000, 411, 665, 3694, 15004])).
% 8.69/8.93 tff(15091,plain,
% 8.69/8.93 (~r(s(z), s(s(s(elem!1))))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[3499, 15083, 184, 183])).
% 8.69/8.93 tff(15092,plain,
% 8.69/8.93 (b(s(z), s(s(s(elem!1))))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[247, 15091])).
% 8.69/8.93 tff(15093,plain,
% 8.69/8.93 (~b(s(s(z)), z)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[14992, 15089, 14859, 15081, 15092])).
% 8.69/8.93 tff(15094,plain,
% 8.69/8.93 ($false),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[1211, 15093, 15090])).
% 8.69/8.93 tff(15095,plain,((~(s(s(elem!1)) = elem!1)) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.93 tff(15096,plain,
% 8.69/8.93 (~(s(s(elem!1)) = elem!1)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[15095, 14702, 14683, 14684, 14689, 14686])).
% 8.69/8.93 tff(15097,plain,
% 8.69/8.93 (~r(s(s(s(s(z)))), elem!1)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[10450, 847, 3696, 411, 665])).
% 8.69/8.93 tff(15098,plain,
% 8.69/8.93 (b(s(s(s(s(z)))), elem!1)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[762, 15097, 2691])).
% 8.69/8.93 tff(15099,plain,
% 8.69/8.93 (~r(s(z), z)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[2061, 2053, 1216, 411])).
% 8.69/8.93 tff(15100,plain,
% 8.69/8.93 (b(s(z), z)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[180, 15099])).
% 8.69/8.93 tff(15101,plain,
% 8.69/8.93 (~r(elem!1, s(s(s(s(z)))))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[11195, 2053, 1216, 847])).
% 8.69/8.93 tff(15102,plain,
% 8.69/8.93 (b(elem!1, s(s(s(s(z)))))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[781, 15101, 8922])).
% 8.69/8.93 tff(15103,plain,
% 8.69/8.93 (~b(z, s(s(s(s(z)))))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[14821, 15102, 665, 1652])).
% 8.69/8.93 tff(15104,plain,
% 8.69/8.93 (r(z, s(s(s(s(z)))))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[800, 15103])).
% 8.69/8.93 tff(15105,plain,
% 8.69/8.93 (~r(z, s(z))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[10568, 15104, 2053, 1216])).
% 8.69/8.93 tff(15106,plain,
% 8.69/8.93 (b(z, s(z))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[678, 15105])).
% 8.69/8.93 tff(15107,plain,
% 8.69/8.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.93 inference(rewrite,[status(thm)],[])).
% 8.69/8.93 tff(15108,plain,
% 8.69/8.93 (((~b(s(s(s(s(z)))), elem!1)) | (~b(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(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.93 inference(rewrite,[status(thm)],[])).
% 8.69/8.93 tff(15109,plain,
% 8.69/8.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(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(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 8.69/8.93 inference(monotonicity,[status(thm)],[15108])).
% 8.69/8.93 tff(15110,plain,
% 8.69/8.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(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(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.93 inference(transitivity,[status(thm)],[15109, 15107])).
% 8.69/8.93 tff(15111,plain,
% 8.69/8.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(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(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.93 inference(quant_inst,[status(thm)],[])).
% 8.69/8.93 tff(15112,plain,
% 8.69/8.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 8.69/8.93 inference(modus_ponens,[status(thm)],[15111, 15110])).
% 8.69/8.93 tff(15113,plain,
% 8.69/8.93 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[15112, 391, 973, 15102, 1652])).
% 8.69/8.93 tff(15114,plain,
% 8.69/8.93 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[2003, 42, 15113, 1983])).
% 8.69/8.93 tff(15115,plain,
% 8.69/8.93 (~r(s(s(elem!1)), z)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[7615, 15114, 2053, 15104])).
% 8.69/8.93 tff(15116,plain,
% 8.69/8.93 (b(s(s(elem!1)), z)),
% 8.69/8.93 inference(unit_resolution,[status(thm)],[2629, 15115])).
% 8.69/8.93 tff(15117,plain,
% 8.69/8.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.69/8.93 inference(rewrite,[status(thm)],[])).
% 8.69/8.93 tff(15118,plain,
% 8.69/8.93 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.69/8.93 inference(rewrite,[status(thm)],[])).
% 8.69/8.93 tff(15119,plain,
% 8.69/8.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 8.69/8.94 inference(monotonicity,[status(thm)],[15118])).
% 8.69/8.94 tff(15120,plain,
% 8.69/8.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.69/8.94 inference(transitivity,[status(thm)],[15119, 15117])).
% 8.69/8.94 tff(15121,plain,
% 8.69/8.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.69/8.94 inference(quant_inst,[status(thm)],[])).
% 8.69/8.94 tff(15122,plain,
% 8.69/8.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 8.69/8.94 inference(modus_ponens,[status(thm)],[15121, 15120])).
% 8.69/8.94 tff(15123,plain,
% 8.69/8.94 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[15122, 391, 973, 15102, 1652])).
% 8.69/8.94 tff(15124,plain,
% 8.69/8.94 ((s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[1994, 42, 15123])).
% 8.69/8.94 tff(15125,plain,
% 8.69/8.94 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[15124, 1984])).
% 8.69/8.94 tff(15126,plain,
% 8.69/8.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.69/8.94 inference(rewrite,[status(thm)],[])).
% 8.69/8.94 tff(15127,plain,
% 8.69/8.94 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.69/8.94 inference(rewrite,[status(thm)],[])).
% 8.69/8.94 tff(15128,plain,
% 8.69/8.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 8.69/8.94 inference(monotonicity,[status(thm)],[15127])).
% 8.69/8.94 tff(15129,plain,
% 8.69/8.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.69/8.94 inference(transitivity,[status(thm)],[15128, 15126])).
% 8.69/8.94 tff(15130,plain,
% 8.69/8.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))))),
% 8.69/8.94 inference(quant_inst,[status(thm)],[])).
% 8.69/8.94 tff(15131,plain,
% 8.69/8.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 8.69/8.94 inference(modus_ponens,[status(thm)],[15130, 15129])).
% 8.69/8.94 tff(15132,plain,
% 8.69/8.94 (~r(z, s(s(elem!1)))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[15131, 194, 2053, 15104, 15125])).
% 8.69/8.94 tff(15133,plain,
% 8.69/8.94 (b(z, s(s(elem!1)))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[324, 15132])).
% 8.69/8.94 tff(15134,plain,
% 8.69/8.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.69/8.94 inference(rewrite,[status(thm)],[])).
% 8.69/8.94 tff(15135,plain,
% 8.69/8.94 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.69/8.94 inference(rewrite,[status(thm)],[])).
% 8.69/8.94 tff(15136,plain,
% 8.69/8.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 8.69/8.94 inference(monotonicity,[status(thm)],[15135])).
% 8.69/8.94 tff(15137,plain,
% 8.69/8.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.69/8.94 inference(transitivity,[status(thm)],[15136, 15134])).
% 8.69/8.94 tff(15138,plain,
% 8.69/8.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))))),
% 8.69/8.94 inference(quant_inst,[status(thm)],[])).
% 8.69/8.94 tff(15139,plain,
% 8.69/8.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 8.69/8.94 inference(modus_ponens,[status(thm)],[15138, 15137])).
% 8.69/8.94 tff(15140,plain,
% 8.69/8.94 (~r(s(s(elem!1)), s(z))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[15139, 194, 2053, 1216, 15125])).
% 8.69/8.94 tff(15141,plain,
% 8.69/8.94 (b(s(s(elem!1)), s(z))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[362, 15140])).
% 8.69/8.94 tff(15142,plain,
% 8.69/8.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 8.69/8.94 inference(rewrite,[status(thm)],[])).
% 8.69/8.94 tff(15143,plain,
% 8.69/8.94 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 8.69/8.94 inference(rewrite,[status(thm)],[])).
% 8.69/8.94 tff(15144,plain,
% 8.69/8.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))))),
% 8.69/8.94 inference(monotonicity,[status(thm)],[15143])).
% 8.69/8.94 tff(15145,plain,
% 8.69/8.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 8.69/8.94 inference(transitivity,[status(thm)],[15144, 15142])).
% 8.69/8.94 tff(15146,plain,
% 8.69/8.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 8.69/8.94 inference(quant_inst,[status(thm)],[])).
% 8.69/8.94 tff(15147,plain,
% 8.69/8.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))),
% 8.69/8.94 inference(modus_ponens,[status(thm)],[15146, 15145])).
% 8.69/8.94 tff(15148,plain,
% 8.69/8.94 ($false),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[15147, 391, 15141, 15133, 15116, 15106, 15100])).
% 8.69/8.94 tff(15149,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (elem!1 = s(s(s(s(z))))) | (~r(z, elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.94 tff(15150,plain,
% 8.69/8.94 (~r(s(s(s(s(z)))), z)),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[15149, 1216, 3695, 973, 15098, 665, 3696, 411, 847])).
% 8.69/8.94 tff(15151,plain,
% 8.69/8.94 (b(s(s(s(s(z)))), z)),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[87, 15150])).
% 8.69/8.94 tff(15152,plain,
% 8.69/8.94 (~r(z, s(z))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[14968, 15151, 15098, 1216, 3696, 3694, 14710, 847, 665, 14716, 411])).
% 8.69/8.94 tff(15153,plain,
% 8.69/8.94 (b(z, s(z))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[678, 15152])).
% 8.69/8.94 tff(15154,plain,
% 8.69/8.94 (~b(s(z), z)),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[14978, 15153, 15151, 665, 15098])).
% 8.69/8.94 tff(15155,plain,
% 8.69/8.94 (r(s(z), z)),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[180, 15154])).
% 8.69/8.94 tff(15156,plain,
% 8.69/8.94 (~r(s(z), elem!1)),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[2475, 15155, 847, 411])).
% 8.69/8.94 tff(15157,plain,
% 8.69/8.94 (b(s(z), elem!1)),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[632, 15156, 14716])).
% 8.69/8.94 tff(15158,plain,
% 8.69/8.94 (~r(elem!1, s(s(s(s(z)))))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[14950, 15157, 3694, 14710, 847, 15098, 1216, 665])).
% 8.69/8.94 tff(15159,plain,
% 8.69/8.94 (~b(z, s(s(s(s(z)))))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[3234, 3118, 665, 2064])).
% 8.69/8.94 tff(15160,plain,
% 8.69/8.94 (r(z, s(s(s(s(z)))))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[800, 15159])).
% 8.69/8.94 tff(15161,plain,
% 8.69/8.94 (~r(s(s(s(s(z)))), s(z))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[1224, 15160, 182, 1216])).
% 8.69/8.94 tff(15162,plain,
% 8.69/8.94 (b(s(s(s(s(z)))), s(z))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[749, 15161])).
% 8.69/8.94 tff(15163,plain,
% 8.69/8.94 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[2108, 15160, 182, 1216])).
% 8.69/8.94 tff(15164,plain,
% 8.69/8.94 (b(s(s(s(s(z)))), elem!1)),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[2694, 15163, 5])).
% 8.69/8.94 tff(15165,plain,
% 8.69/8.94 ($false),
% 8.69/8.94 inference(unit_resolution,[status(thm)],[14958, 391, 644, 3118, 2064, 15164, 15162])).
% 8.69/8.95 tff(15166,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = elem!1)) | (~r(s(z), z)) | (~b(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.95 tff(15167,plain,
% 8.69/8.95 (~b(elem!1, s(s(s(s(z)))))),
% 8.69/8.95 inference(unit_resolution,[status(thm)],[15166, 15157, 5, 411, 15155, 665, 1216])).
% 8.69/8.95 tff(15168,plain,
% 8.69/8.95 ($false),
% 8.69/8.95 inference(unit_resolution,[status(thm)],[781, 15167, 15158, 3696])).
% 8.69/8.95 tff(15169,plain,((~r(s(z), s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = elem!1)) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~r(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.95 tff(15170,plain,
% 8.69/8.95 (~b(s(s(elem!1)), elem!1)),
% 8.69/8.95 inference(unit_resolution,[status(thm)],[15169, 14702, 1216, 847, 14683, 14689])).
% 8.69/8.95 tff(15171,plain,
% 8.69/8.95 (b(s(s(s(s(elem!1)))), z) <=> b(s(elem!1), z)),
% 8.69/8.95 inference(monotonicity,[status(thm)],[3716])).
% 8.69/8.95 tff(15172,plain,
% 8.69/8.95 (b(s(elem!1), z) <=> b(s(s(s(s(elem!1)))), z)),
% 8.69/8.95 inference(symmetry,[status(thm)],[15171])).
% 8.69/8.95 tff(15173,plain,
% 8.69/8.95 ((~b(s(elem!1), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 8.69/8.95 inference(monotonicity,[status(thm)],[15172])).
% 8.69/8.95 tff(15174,plain,
% 8.69/8.95 (r(s(s(elem!1)), elem!1)),
% 8.69/8.95 inference(unit_resolution,[status(thm)],[872, 5625, 4017])).
% 8.69/8.95 tff(15175,plain,
% 8.69/8.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 8.69/8.95 inference(rewrite,[status(thm)],[])).
% 8.69/8.95 tff(15176,plain,
% 8.69/8.95 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 8.69/8.95 inference(rewrite,[status(thm)],[])).
% 8.69/8.95 tff(15177,plain,
% 8.69/8.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 8.69/8.95 inference(monotonicity,[status(thm)],[15176])).
% 8.69/8.95 tff(15178,plain,
% 8.69/8.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 8.69/8.95 inference(transitivity,[status(thm)],[15177, 15175])).
% 8.69/8.95 tff(15179,plain,
% 8.69/8.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 8.69/8.95 inference(quant_inst,[status(thm)],[])).
% 8.69/8.95 tff(15180,plain,
% 8.69/8.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 8.69/8.95 inference(modus_ponens,[status(thm)],[15179, 15178])).
% 8.69/8.95 tff(15181,plain,
% 8.69/8.95 (~r(s(s(elem!1)), z)),
% 8.69/8.95 inference(unit_resolution,[status(thm)],[15180, 194, 411, 15174, 847])).
% 8.69/8.95 tff(15182,plain,
% 8.69/8.95 (b(s(s(elem!1)), z)),
% 8.69/8.95 inference(unit_resolution,[status(thm)],[2629, 15181])).
% 8.69/8.95 tff(15183,plain,
% 8.69/8.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 8.69/8.95 inference(rewrite,[status(thm)],[])).
% 8.69/8.95 tff(15184,plain,
% 8.69/8.95 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 8.69/8.95 inference(rewrite,[status(thm)],[])).
% 8.69/8.95 tff(15185,plain,
% 8.69/8.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 8.69/8.95 inference(monotonicity,[status(thm)],[15184])).
% 8.69/8.95 tff(15186,plain,
% 8.69/8.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 8.69/8.95 inference(transitivity,[status(thm)],[15185, 15183])).
% 8.69/8.95 tff(15187,plain,
% 8.69/8.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 8.69/8.95 inference(quant_inst,[status(thm)],[])).
% 8.69/8.95 tff(15188,plain,
% 8.69/8.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))),
% 8.69/8.95 inference(modus_ponens,[status(thm)],[15187, 15186])).
% 8.69/8.95 tff(15189,plain,
% 8.69/8.95 (~r(z, s(s(elem!1)))),
% 8.69/8.95 inference(unit_resolution,[status(thm)],[15188, 194, 411, 15174, 847])).
% 8.69/8.95 tff(15190,plain,
% 8.69/8.95 (b(z, s(s(elem!1)))),
% 8.69/8.95 inference(unit_resolution,[status(thm)],[324, 15189])).
% 8.69/8.95 tff(15191,plain,
% 8.69/8.95 (~(s(elem!1) = s(s(elem!1)))),
% 8.69/8.95 inference(unit_resolution,[status(thm)],[9802, 5682])).
% 8.69/8.95 tff(15192,plain,
% 8.69/8.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 8.69/8.95 inference(rewrite,[status(thm)],[])).
% 8.69/8.95 tff(15193,plain,
% 8.69/8.95 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 8.69/8.95 inference(rewrite,[status(thm)],[])).
% 8.69/8.95 tff(15194,plain,
% 8.69/8.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))))),
% 8.69/8.95 inference(monotonicity,[status(thm)],[15193])).
% 8.69/8.95 tff(15195,plain,
% 8.69/8.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 8.69/8.95 inference(transitivity,[status(thm)],[15194, 15192])).
% 8.69/8.95 tff(15196,plain,
% 8.69/8.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 8.69/8.96 inference(quant_inst,[status(thm)],[])).
% 8.69/8.96 tff(15197,plain,
% 8.69/8.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))),
% 8.69/8.96 inference(modus_ponens,[status(thm)],[15196, 15195])).
% 8.69/8.96 tff(15198,plain,
% 8.69/8.96 (~b(elem!1, s(s(elem!1)))),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[15197, 391, 665, 15190, 15182])).
% 8.69/8.96 tff(15199,plain,
% 8.69/8.96 (r(elem!1, s(s(elem!1)))),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[1307, 15198, 6460])).
% 8.69/8.96 tff(15200,plain,
% 8.69/8.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 8.69/8.96 inference(rewrite,[status(thm)],[])).
% 8.69/8.96 tff(15201,plain,
% 8.69/8.96 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 8.69/8.96 inference(rewrite,[status(thm)],[])).
% 8.69/8.96 tff(15202,plain,
% 8.69/8.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))))),
% 8.69/8.96 inference(monotonicity,[status(thm)],[15201])).
% 8.69/8.96 tff(15203,plain,
% 8.69/8.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 8.69/8.96 inference(transitivity,[status(thm)],[15202, 15200])).
% 8.69/8.96 tff(15204,plain,
% 8.69/8.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 8.69/8.96 inference(quant_inst,[status(thm)],[])).
% 8.69/8.96 tff(15205,plain,
% 8.69/8.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))),
% 8.69/8.96 inference(modus_ponens,[status(thm)],[15204, 15203])).
% 8.69/8.96 tff(15206,plain,
% 8.69/8.96 (~b(s(elem!1), elem!1)),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[15205, 391, 665, 3927, 591, 2641])).
% 8.69/8.96 tff(15207,plain,
% 8.69/8.96 (r(s(elem!1), elem!1)),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[2168, 15206, 164])).
% 8.69/8.96 tff(15208,plain,
% 8.69/8.96 (~b(s(elem!1), s(s(elem!1)))),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[10308, 391, 3927, 591, 2641])).
% 8.69/8.96 tff(15209,plain,
% 8.69/8.96 (r(s(elem!1), s(s(elem!1)))),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[8644, 15208, 8611])).
% 8.69/8.96 tff(15210,plain,
% 8.69/8.96 ($false),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[14324, 15209, 15207, 364, 1064])).
% 8.69/8.96 tff(15211,plain,((~b(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = elem!1) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.96 tff(15212,plain,
% 8.69/8.96 (~b(s(elem!1), z)),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[15211, 15174, 15199, 15191, 5626, 15190, 15182, 665])).
% 8.69/8.96 tff(15213,plain,
% 8.69/8.96 (~b(s(s(s(s(elem!1)))), z)),
% 8.69/8.96 inference(modus_ponens,[status(thm)],[15212, 15173])).
% 8.69/8.96 tff(15214,plain,
% 8.69/8.96 (r(s(s(s(s(elem!1)))), z)),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[1626, 15213])).
% 8.69/8.96 tff(15215,plain,
% 8.69/8.96 (r(s(elem!1), z)),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[549, 15212])).
% 8.69/8.96 tff(15216,plain,
% 8.69/8.96 (~(s(s(s(s(z)))) = s(elem!1))),
% 8.69/8.96 inference(modus_ponens,[status(thm)],[3122, 2125])).
% 8.69/8.96 tff(15217,plain,
% 8.69/8.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 8.69/8.96 inference(rewrite,[status(thm)],[])).
% 8.69/8.96 tff(15218,plain,
% 8.69/8.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 8.69/8.96 inference(quant_inst,[status(thm)],[])).
% 8.69/8.96 tff(15219,plain,
% 8.69/8.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 8.69/8.96 inference(modus_ponens,[status(thm)],[15218, 15217])).
% 8.69/8.96 tff(15220,plain,
% 8.69/8.96 (~r(s(s(s(s(z)))), s(elem!1))),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[15219, 194, 411, 1628, 2053])).
% 8.69/8.96 tff(15221,plain,
% 8.69/8.96 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[2136, 42, 15220])).
% 8.69/8.96 tff(15222,plain,
% 8.69/8.96 (b(s(s(s(s(z)))), s(elem!1))),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[15221, 15216])).
% 8.69/8.96 tff(15223,plain,
% 8.69/8.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.69/8.96 inference(rewrite,[status(thm)],[])).
% 8.69/8.96 tff(15224,plain,
% 8.69/8.96 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.69/8.96 inference(rewrite,[status(thm)],[])).
% 8.69/8.96 tff(15225,plain,
% 8.69/8.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 8.69/8.96 inference(monotonicity,[status(thm)],[15224])).
% 8.69/8.96 tff(15226,plain,
% 8.69/8.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.69/8.96 inference(transitivity,[status(thm)],[15225, 15223])).
% 8.69/8.96 tff(15227,plain,
% 8.69/8.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 8.69/8.96 inference(quant_inst,[status(thm)],[])).
% 8.69/8.96 tff(15228,plain,
% 8.69/8.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 8.69/8.96 inference(modus_ponens,[status(thm)],[15227, 15226])).
% 8.69/8.96 tff(15229,plain,
% 8.69/8.96 (~r(s(elem!1), s(s(s(s(z)))))),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[15228, 194, 411, 1628, 2053])).
% 8.69/8.96 tff(15230,plain,
% 8.69/8.96 (b(s(elem!1), s(s(s(s(z)))))),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[2142, 42, 15229, 3122])).
% 8.69/8.96 tff(15231,plain,
% 8.69/8.96 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 8.69/8.96 inference(monotonicity,[status(thm)],[5])).
% 8.69/8.96 tff(15232,plain,
% 8.69/8.96 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.69/8.96 inference(symmetry,[status(thm)],[15231])).
% 8.69/8.96 tff(15233,plain,
% 8.69/8.96 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.69/8.96 inference(modus_ponens,[status(thm)],[1064, 15232])).
% 8.69/8.96 tff(15234,plain,
% 8.69/8.96 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[9541, 2053, 184, 15233, 3807])).
% 8.69/8.96 tff(15235,plain,
% 8.69/8.96 (b(s(s(s(s(z)))), elem!1)),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[2694, 15234, 5])).
% 8.69/8.96 tff(15236,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 8.69/8.96 tff(15237,plain,
% 8.69/8.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.69/8.96 inference(rewrite,[status(thm)],[])).
% 8.69/8.96 tff(15238,plain,
% 8.69/8.96 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.69/8.96 inference(rewrite,[status(thm)],[])).
% 8.69/8.96 tff(15239,plain,
% 8.69/8.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 8.69/8.96 inference(monotonicity,[status(thm)],[15238])).
% 8.69/8.96 tff(15240,plain,
% 8.69/8.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.69/8.96 inference(transitivity,[status(thm)],[15239, 15237])).
% 8.69/8.96 tff(15241,plain,
% 8.69/8.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 8.69/8.96 inference(quant_inst,[status(thm)],[])).
% 8.69/8.96 tff(15242,plain,
% 8.69/8.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 8.69/8.96 inference(modus_ponens,[status(thm)],[15241, 15240])).
% 8.69/8.96 tff(15243,plain,
% 8.69/8.96 ($false),
% 8.69/8.96 inference(unit_resolution,[status(thm)],[15242, 391, 802, 1652, 4682, 15236])).
% 8.69/8.97 tff(15244,plain,((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.97 tff(15245,plain,
% 8.69/8.97 (~b(elem!1, s(elem!1))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[15244, 15235, 15230, 15222])).
% 8.69/8.97 tff(15246,plain,
% 8.69/8.97 (r(elem!1, s(elem!1))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[443, 15245, 7437])).
% 8.69/8.97 tff(15247,plain,
% 8.69/8.97 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(elem!1))),
% 8.69/8.97 inference(monotonicity,[status(thm)],[3716])).
% 8.69/8.97 tff(15248,plain,
% 8.69/8.97 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(elem!1))),
% 8.69/8.97 inference(monotonicity,[status(thm)],[3716])).
% 8.69/8.97 tff(15249,plain,
% 8.69/8.97 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 8.69/8.97 inference(symmetry,[status(thm)],[15248])).
% 8.69/8.97 tff(15250,plain,
% 8.69/8.97 (r(elem!1, s(s(s(s(elem!1)))))),
% 8.69/8.97 inference(modus_ponens,[status(thm)],[15246, 15249])).
% 8.69/8.97 tff(15251,plain,
% 8.69/8.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))),
% 8.69/8.97 inference(rewrite,[status(thm)],[])).
% 8.69/8.97 tff(15252,plain,
% 8.69/8.97 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))),
% 8.69/8.97 inference(rewrite,[status(thm)],[])).
% 8.69/8.97 tff(15253,plain,
% 8.69/8.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1))))))),
% 8.69/8.97 inference(monotonicity,[status(thm)],[15252])).
% 8.69/8.97 tff(15254,plain,
% 8.69/8.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))),
% 8.69/8.97 inference(transitivity,[status(thm)],[15253, 15251])).
% 8.69/8.97 tff(15255,plain,
% 8.69/8.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))),
% 8.69/8.97 inference(quant_inst,[status(thm)],[])).
% 8.69/8.97 tff(15256,plain,
% 8.69/8.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1))))),
% 8.69/8.97 inference(modus_ponens,[status(thm)],[15255, 15254])).
% 8.69/8.97 tff(15257,plain,
% 8.69/8.97 ($false),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[15256, 194, 1064, 1063, 1176, 12854])).
% 8.69/8.97 tff(15258,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.97 tff(15259,plain,
% 8.69/8.97 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[15258, 15250, 1064, 12854])).
% 8.69/8.97 tff(15260,plain,
% 8.69/8.97 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[1048, 15259, 1035])).
% 8.69/8.97 tff(15261,plain,
% 8.69/8.97 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(elem!1))),
% 8.69/8.97 inference(monotonicity,[status(thm)],[3716])).
% 8.69/8.97 tff(15262,plain,
% 8.69/8.97 (b(s(s(elem!1)), s(elem!1))),
% 8.69/8.97 inference(modus_ponens,[status(thm)],[15260, 15261])).
% 8.69/8.97 tff(15263,plain,
% 8.69/8.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.69/8.97 inference(rewrite,[status(thm)],[])).
% 8.69/8.97 tff(15264,plain,
% 8.69/8.97 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.69/8.97 inference(rewrite,[status(thm)],[])).
% 8.69/8.97 tff(15265,plain,
% 8.69/8.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 8.69/8.97 inference(monotonicity,[status(thm)],[15264])).
% 8.69/8.97 tff(15266,plain,
% 8.69/8.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 8.69/8.97 inference(transitivity,[status(thm)],[15265, 15263])).
% 8.69/8.97 tff(15267,plain,
% 8.69/8.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.97 inference(quant_inst,[status(thm)],[])).
% 8.69/8.97 tff(15268,plain,
% 8.69/8.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 8.69/8.97 inference(modus_ponens,[status(thm)],[15267, 15266])).
% 8.69/8.97 tff(15269,plain,
% 8.69/8.97 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[15268, 391, 15262, 15235, 15230, 15222])).
% 8.69/8.97 tff(15270,plain,
% 8.69/8.97 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[2003, 42, 15269, 3695])).
% 8.69/8.97 tff(15271,plain,
% 8.69/8.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.69/8.97 inference(rewrite,[status(thm)],[])).
% 8.69/8.97 tff(15272,plain,
% 8.69/8.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 8.69/8.97 inference(quant_inst,[status(thm)],[])).
% 8.69/8.97 tff(15273,plain,
% 8.69/8.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z))))))),
% 8.69/8.97 inference(modus_ponens,[status(thm)],[15272, 15271])).
% 8.69/8.97 tff(15274,plain,
% 8.69/8.97 (~r(elem!1, s(s(s(s(z)))))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[15273, 194, 364, 1064, 15270])).
% 8.69/8.97 tff(15275,plain,
% 8.69/8.97 (b(elem!1, s(s(s(s(z)))))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[781, 15274, 3696])).
% 8.69/8.97 tff(15276,plain,
% 8.69/8.97 (~b(s(elem!1), elem!1)),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[2159, 391, 665, 15275, 15235, 15230])).
% 8.69/8.97 tff(15277,plain,
% 8.69/8.97 (r(s(elem!1), elem!1)),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[2168, 15276, 164])).
% 8.69/8.97 tff(15278,plain,
% 8.69/8.97 (~r(s(elem!1), s(s(elem!1)))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[14324, 15277, 364, 1064])).
% 8.69/8.97 tff(15279,plain,
% 8.69/8.97 (r(s(elem!1), s(s(elem!1)))),
% 8.69/8.97 inference(modus_ponens,[status(thm)],[1177, 13217])).
% 8.69/8.97 tff(15280,plain,
% 8.69/8.97 ($false),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[8641, 15279])).
% 8.69/8.97 tff(15281,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | r(s(elem!1), s(s(elem!1))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.97 tff(15282,plain,
% 8.69/8.97 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[15281, 15278, 5])).
% 8.69/8.97 tff(15283,plain,
% 8.69/8.97 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[1061, 15282, 2712])).
% 8.69/8.97 tff(15284,plain,
% 8.69/8.97 (~b(z, s(s(s(s(elem!1)))))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[14284, 15283, 3927, 15260])).
% 8.69/8.97 tff(15285,plain,
% 8.69/8.97 (r(z, s(s(s(s(elem!1)))))),
% 8.69/8.97 inference(unit_resolution,[status(thm)],[2767, 15284])).
% 8.69/8.97 tff(15286,plain,
% 8.69/8.97 (r(z, s(elem!1))),
% 8.69/8.97 inference(modus_ponens,[status(thm)],[15285, 15247])).
% 8.69/8.97 tff(15287,plain,
% 8.69/8.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 8.69/8.97 inference(rewrite,[status(thm)],[])).
% 8.69/8.97 tff(15288,plain,
% 8.69/8.97 (((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 8.69/8.97 inference(rewrite,[status(thm)],[])).
% 8.69/8.97 tff(15289,plain,
% 8.69/8.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))))),
% 8.69/8.98 inference(monotonicity,[status(thm)],[15288])).
% 8.69/8.98 tff(15290,plain,
% 8.69/8.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 8.69/8.98 inference(transitivity,[status(thm)],[15289, 15287])).
% 8.69/8.98 tff(15291,plain,
% 8.69/8.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 8.69/8.98 inference(quant_inst,[status(thm)],[])).
% 8.69/8.98 tff(15292,plain,
% 8.69/8.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 8.69/8.98 inference(modus_ponens,[status(thm)],[15291, 15290])).
% 8.69/8.98 tff(15293,plain,
% 8.69/8.98 ($false),
% 8.69/8.98 inference(unit_resolution,[status(thm)],[15292, 194, 411, 1628, 15286, 15246])).
% 8.69/8.98 tff(15294,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(elem!1) = elem!1) | (~b(elem!1, z)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.98 tff(15295,plain,
% 8.69/8.98 (~r(s(s(s(s(z)))), z)),
% 8.69/8.98 inference(unit_resolution,[status(thm)],[15294, 15215, 411, 5, 15190, 15174, 15199, 5626, 665, 9895, 15214, 184])).
% 8.69/8.98 tff(15296,plain,
% 8.69/8.98 (b(s(s(s(s(z)))), z)),
% 8.69/8.98 inference(unit_resolution,[status(thm)],[87, 15295])).
% 8.69/8.98 tff(15297,plain,
% 8.69/8.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.98 inference(rewrite,[status(thm)],[])).
% 8.69/8.98 tff(15298,plain,
% 8.69/8.98 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.98 inference(rewrite,[status(thm)],[])).
% 8.69/8.98 tff(15299,plain,
% 8.69/8.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 8.69/8.98 inference(monotonicity,[status(thm)],[15298])).
% 8.69/8.98 tff(15300,plain,
% 8.69/8.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.98 inference(transitivity,[status(thm)],[15299, 15297])).
% 8.69/8.98 tff(15301,plain,
% 8.69/8.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.98 inference(quant_inst,[status(thm)],[])).
% 8.69/8.98 tff(15302,plain,
% 8.69/8.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 8.69/8.98 inference(modus_ponens,[status(thm)],[15301, 15300])).
% 8.69/8.98 tff(15303,plain,
% 8.69/8.98 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.69/8.98 inference(unit_resolution,[status(thm)],[15302, 391, 15190, 15182, 15296])).
% 8.69/8.98 tff(15304,plain,
% 8.69/8.98 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.69/8.98 inference(unit_resolution,[status(thm)],[2003, 42, 15303, 3695])).
% 8.69/8.98 tff(15305,plain,
% 8.69/8.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 8.69/8.98 inference(rewrite,[status(thm)],[])).
% 8.69/8.98 tff(15306,plain,
% 8.69/8.98 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 8.69/8.98 inference(rewrite,[status(thm)],[])).
% 8.69/8.98 tff(15307,plain,
% 8.69/8.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 8.69/8.98 inference(monotonicity,[status(thm)],[15306])).
% 8.69/8.98 tff(15308,plain,
% 8.69/8.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 8.69/8.98 inference(transitivity,[status(thm)],[15307, 15305])).
% 8.69/8.98 tff(15309,plain,
% 8.69/8.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 8.69/8.98 inference(quant_inst,[status(thm)],[])).
% 8.69/8.98 tff(15310,plain,
% 8.69/8.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 8.69/8.98 inference(modus_ponens,[status(thm)],[15309, 15308])).
% 8.69/8.98 tff(15311,plain,
% 8.69/8.98 (~b(s(s(s(s(z)))), elem!1)),
% 8.69/8.98 inference(unit_resolution,[status(thm)],[15310, 391, 665, 15190, 15182, 15296])).
% 8.69/8.98 tff(15312,plain,
% 8.69/8.98 (r(s(s(s(s(z)))), elem!1)),
% 8.69/8.98 inference(unit_resolution,[status(thm)],[762, 15311, 2691])).
% 8.69/8.98 tff(15313,plain,
% 8.69/8.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.98 inference(rewrite,[status(thm)],[])).
% 8.69/8.98 tff(15314,plain,
% 8.69/8.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.69/8.98 inference(quant_inst,[status(thm)],[])).
% 8.69/8.98 tff(15315,plain,
% 8.69/8.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 8.69/8.98 inference(modus_ponens,[status(thm)],[15314, 15313])).
% 8.69/8.98 tff(15316,plain,
% 8.69/8.98 ($false),
% 8.69/8.98 inference(unit_resolution,[status(thm)],[15315, 194, 15174, 15199, 15312, 15304])).
% 8.69/8.98 tff(15317,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.69/8.99 tff(15318,plain,
% 8.69/8.99 (s(s(s(elem!1))) = s(elem!1)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15317, 15170, 14683, 14689, 14684, 847, 14702])).
% 8.69/8.99 tff(15319,plain,
% 8.69/8.99 ($false),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[6159, 15318, 15096])).
% 8.69/8.99 tff(15320,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(z)) | (s(z) = elem!1) | b(s(s(s(elem!1))), s(s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.69/8.99 tff(15321,plain,
% 8.69/8.99 (b(elem!1, s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15320, 11321, 2913, 11308, 10645, 3823, 31, 11320, 8329, 3447, 115])).
% 8.69/8.99 tff(15322,plain,
% 8.69/8.99 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[2849, 11320])).
% 8.69/8.99 tff(15323,plain,
% 8.69/8.99 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[10940, 15322])).
% 8.69/8.99 tff(15324,plain,
% 8.69/8.99 (~r(s(z), z)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[10651, 194, 3447, 2913, 10645])).
% 8.69/8.99 tff(15325,plain,
% 8.69/8.99 (b(s(z), z)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[180, 15324])).
% 8.69/8.99 tff(15326,plain,
% 8.69/8.99 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[11327, 194, 3447, 11308, 10645])).
% 8.69/8.99 tff(15327,plain,
% 8.69/8.99 (b(s(s(s(s(z)))), s(s(z)))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[1714, 15326])).
% 8.69/8.99 tff(15328,plain,
% 8.69/8.99 (~b(z, s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[10690, 1526, 664, 590])).
% 8.69/8.99 tff(15329,plain,
% 8.69/8.99 (r(z, s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[58, 15328])).
% 8.69/8.99 tff(15330,plain,
% 8.69/8.99 (~b(s(s(s(elem!1))), z)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[10633, 391, 1526, 664, 590])).
% 8.69/8.99 tff(15331,plain,
% 8.69/8.99 (r(s(s(s(elem!1))), z)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[377, 15330])).
% 8.69/8.99 tff(15332,plain,
% 8.69/8.99 (~r(s(s(z)), s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[7211, 194, 15331, 15329, 3557])).
% 8.69/8.99 tff(15333,plain,
% 8.69/8.99 (b(s(s(z)), s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[11041, 15332])).
% 8.69/8.99 tff(15334,plain,
% 8.69/8.99 ($false),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[3954, 194, 174, 184, 2053, 2100])).
% 8.69/8.99 tff(15335,plain,((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.99 tff(15336,plain,
% 8.69/8.99 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15335, 15331, 2053, 15329])).
% 8.69/8.99 tff(15337,plain,
% 8.69/8.99 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 15336])).
% 8.69/8.99 tff(15338,plain,
% 8.69/8.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.69/8.99 inference(rewrite,[status(thm)],[])).
% 8.69/8.99 tff(15339,plain,
% 8.69/8.99 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.69/8.99 inference(rewrite,[status(thm)],[])).
% 8.69/8.99 tff(15340,plain,
% 8.69/8.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 8.69/8.99 inference(monotonicity,[status(thm)],[15339])).
% 8.69/8.99 tff(15341,plain,
% 8.69/8.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.69/8.99 inference(transitivity,[status(thm)],[15340, 15338])).
% 8.69/8.99 tff(15342,plain,
% 8.69/8.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 8.69/8.99 inference(quant_inst,[status(thm)],[])).
% 8.69/8.99 tff(15343,plain,
% 8.69/8.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 8.69/8.99 inference(modus_ponens,[status(thm)],[15342, 15341])).
% 8.69/8.99 tff(15344,plain,
% 8.69/8.99 ($false),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15343, 391, 1526, 3563, 590, 15337, 15333])).
% 8.69/8.99 tff(15345,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), z)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.99 tff(15346,plain,
% 8.69/8.99 (~b(s(s(s(elem!1))), s(z))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15345, 15327, 15325, 15322, 11308, 3447, 10643])).
% 8.69/8.99 tff(15347,plain,
% 8.69/8.99 (r(s(s(s(elem!1))), s(z))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[223, 15346])).
% 8.69/8.99 tff(15348,assumption,(~(s(s(s(elem!1))) = s(s(s(s(z)))))), introduced(assumption)).
% 8.69/8.99 tff(15349,plain,
% 8.69/8.99 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[10090, 184, 2053, 719])).
% 8.69/8.99 tff(15350,plain,
% 8.69/8.99 ($false),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[4313, 42, 9606, 10970, 15348])).
% 8.69/8.99 tff(15351,plain,(b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.99 tff(15352,plain,
% 8.69/8.99 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15351, 15349, 15348])).
% 8.69/8.99 tff(15353,plain,
% 8.69/8.99 (~b(s(s(z)), s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[10977, 391, 3823, 11329, 15352])).
% 8.69/8.99 tff(15354,plain,
% 8.69/8.99 (r(s(s(z)), s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[11041, 15353])).
% 8.69/8.99 tff(15355,plain,
% 8.69/8.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 8.69/8.99 inference(rewrite,[status(thm)],[])).
% 8.69/8.99 tff(15356,plain,
% 8.69/8.99 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 8.69/8.99 inference(rewrite,[status(thm)],[])).
% 8.69/8.99 tff(15357,plain,
% 8.69/8.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 8.69/8.99 inference(monotonicity,[status(thm)],[15356])).
% 8.69/8.99 tff(15358,plain,
% 8.69/8.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 8.69/8.99 inference(transitivity,[status(thm)],[15357, 15355])).
% 8.69/8.99 tff(15359,plain,
% 8.69/8.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 8.69/8.99 inference(quant_inst,[status(thm)],[])).
% 8.69/8.99 tff(15360,plain,
% 8.69/8.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 8.69/8.99 inference(modus_ponens,[status(thm)],[15359, 15358])).
% 8.69/8.99 tff(15361,plain,
% 8.69/8.99 ($false),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15360, 194, 184, 183, 3557, 15354])).
% 8.69/8.99 tff(15362,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.99 tff(15363,plain,
% 8.69/8.99 (~r(z, s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15362, 15347, 11308, 3823, 15323, 3447, 10645])).
% 8.69/8.99 tff(15364,plain,
% 8.69/8.99 (b(z, s(s(s(elem!1))))),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[58, 15363])).
% 8.69/8.99 tff(15365,plain,
% 8.69/8.99 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, elem!1)),
% 8.69/8.99 inference(monotonicity,[status(thm)],[5])).
% 8.69/8.99 tff(15366,plain,
% 8.69/8.99 (b(elem!1, elem!1) <=> b(elem!1, s(s(s(elem!1))))),
% 8.69/8.99 inference(symmetry,[status(thm)],[15365])).
% 8.69/8.99 tff(15367,plain,
% 8.69/8.99 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 8.69/8.99 inference(monotonicity,[status(thm)],[15366])).
% 8.69/8.99 tff(15368,plain,
% 8.69/8.99 (~b(elem!1, s(s(s(elem!1))))),
% 8.69/8.99 inference(modus_ponens,[status(thm)],[4741, 15367])).
% 8.69/8.99 tff(15369,plain,
% 8.69/8.99 ($false),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[448, 15368])).
% 8.69/8.99 tff(15370,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.69/8.99 tff(15371,plain,
% 8.69/8.99 (~(s(s(s(elem!1))) = elem!1)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15370, 15321])).
% 8.69/8.99 tff(15372,plain,
% 8.69/8.99 (~r(s(s(s(elem!1))), elem!1)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[10856, 15347, 2913, 11321])).
% 8.69/8.99 tff(15373,plain,
% 8.69/8.99 (b(s(s(s(elem!1))), elem!1)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[230, 15372, 15371])).
% 8.69/8.99 tff(15374,plain,
% 8.69/8.99 (~b(elem!1, z)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[10911, 391, 15373, 15364, 15321])).
% 8.69/8.99 tff(15375,plain,
% 8.69/8.99 (r(elem!1, z)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[526, 15374, 10680])).
% 8.69/8.99 tff(15376,plain,
% 8.69/8.99 (~(s(s(s(elem!1))) = elem!1)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15370, 448])).
% 8.69/8.99 tff(15377,plain,
% 8.69/8.99 (r(s(s(s(elem!1))), elem!1)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[230, 10846, 15376])).
% 8.69/8.99 tff(15378,plain,
% 8.69/8.99 ($false),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[10856, 15377, 10848, 1216, 847])).
% 8.69/8.99 tff(15379,plain,(r(z, elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.69/8.99 tff(15380,plain,
% 8.69/8.99 (r(z, elem!1)),
% 8.69/8.99 inference(unit_resolution,[status(thm)],[15379, 11321, 2913, 15321, 10643, 15325, 115])).
% 8.69/8.99 tff(15381,plain,
% 8.69/8.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 8.69/9.00 inference(rewrite,[status(thm)],[])).
% 8.69/9.00 tff(15382,plain,
% 8.69/9.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 8.69/9.00 inference(quant_inst,[status(thm)],[])).
% 8.69/9.00 tff(15383,plain,
% 8.69/9.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 8.69/9.00 inference(modus_ponens,[status(thm)],[15382, 15381])).
% 8.69/9.00 tff(15384,plain,
% 8.69/9.00 (~r(s(s(z)), elem!1)),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[15383, 194, 15380, 15375, 11308])).
% 8.69/9.00 tff(15385,plain,
% 8.69/9.00 (~r(elem!1, s(s(z)))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[8570, 15375, 11308, 10645])).
% 8.69/9.00 tff(15386,plain,
% 8.69/9.00 (~r(elem!1, s(s(s(s(z)))))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[11195, 11321, 3447, 2913])).
% 8.69/9.00 tff(15387,plain,
% 8.69/9.00 (~r(s(s(s(s(z)))), elem!1)),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[10418, 15380, 10645, 11321])).
% 8.69/9.00 tff(15388,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 8.69/9.00 tff(15389,plain,
% 8.69/9.00 (r(elem!1, s(z)) <=> r(s(s(z)), s(z))),
% 8.69/9.00 inference(monotonicity,[status(thm)],[3584])).
% 8.69/9.00 tff(15390,plain,
% 8.69/9.00 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 8.69/9.00 inference(symmetry,[status(thm)],[15389])).
% 8.69/9.00 tff(15391,plain,
% 8.69/9.00 ((~r(s(s(z)), s(z))) <=> (~r(elem!1, s(z)))),
% 8.69/9.00 inference(monotonicity,[status(thm)],[15390])).
% 8.69/9.00 tff(15392,plain,
% 8.69/9.00 (~r(elem!1, s(z))),
% 8.69/9.00 inference(modus_ponens,[status(thm)],[15388, 15391])).
% 8.69/9.00 tff(15393,plain,
% 8.69/9.00 ($false),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[847, 15392])).
% 8.69/9.00 tff(15394,plain,((~(elem!1 = s(s(z)))) | (~r(elem!1, s(z))) | r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 8.69/9.00 tff(15395,plain,
% 8.69/9.00 (~(elem!1 = s(s(z)))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[15394, 15388, 847])).
% 8.69/9.00 tff(15396,plain,
% 8.69/9.00 (b(elem!1, s(s(z)))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[3394, 15395, 3816])).
% 8.69/9.00 tff(15397,plain,
% 8.69/9.00 (~b(elem!1, s(s(s(s(z)))))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[9127, 15396, 3563, 3823])).
% 8.69/9.00 tff(15398,plain,
% 8.69/9.00 (elem!1 = s(s(s(s(z))))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[781, 15397, 3222])).
% 8.69/9.00 tff(15399,plain,
% 8.69/9.00 (s(elem!1) = s(s(s(s(s(z)))))),
% 8.69/9.00 inference(monotonicity,[status(thm)],[15398])).
% 8.69/9.00 tff(15400,plain,
% 8.69/9.00 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 8.69/9.00 inference(monotonicity,[status(thm)],[15399])).
% 8.69/9.00 tff(15401,plain,
% 8.69/9.00 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 8.69/9.00 inference(monotonicity,[status(thm)],[15400])).
% 8.69/9.00 tff(15402,plain,
% 8.69/9.00 (~(s(s(z)) = elem!1)),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[11003, 15395])).
% 8.69/9.00 tff(15403,plain,
% 8.69/9.00 (b(s(s(z)), elem!1)),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[4730, 15402, 5149])).
% 8.69/9.00 tff(15404,plain,
% 8.69/9.00 (~b(s(s(s(s(z)))), elem!1)),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[11012, 15403, 3563, 15396])).
% 8.69/9.00 tff(15405,plain,
% 8.69/9.00 (s(s(s(s(z)))) = elem!1),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[762, 15404, 6221])).
% 8.69/9.00 tff(15406,plain,
% 8.69/9.00 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[717, 15405])).
% 8.69/9.00 tff(15407,plain,
% 8.69/9.00 (~(s(s(elem!1)) = s(elem!1))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[2279, 15406])).
% 8.69/9.00 tff(15408,plain,
% 8.69/9.00 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[287, 15407])).
% 8.69/9.00 tff(15409,plain,
% 8.69/9.00 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[1370, 15408, 8329])).
% 8.69/9.00 tff(15410,plain,
% 8.69/9.00 (~r(s(s(elem!1)), s(z))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[11169, 15409, 1216, 183])).
% 8.69/9.00 tff(15411,plain,
% 8.69/9.00 (b(s(s(elem!1)), s(z))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[362, 15410])).
% 8.69/9.00 tff(15412,plain,
% 8.69/9.00 (b(s(s(s(s(s(s(z)))))), s(z))),
% 8.69/9.00 inference(modus_ponens,[status(thm)],[15411, 15401])).
% 8.69/9.00 tff(15413,plain,
% 8.69/9.00 (b(s(s(z)), s(z))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[3778, 15388])).
% 8.69/9.00 tff(15414,plain,
% 8.69/9.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 8.69/9.00 inference(rewrite,[status(thm)],[])).
% 8.69/9.00 tff(15415,plain,
% 8.69/9.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 8.69/9.00 inference(quant_inst,[status(thm)],[])).
% 8.69/9.00 tff(15416,plain,
% 8.69/9.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 8.69/9.00 inference(modus_ponens,[status(thm)],[15415, 15414])).
% 8.69/9.00 tff(15417,plain,
% 8.69/9.00 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[15416, 391, 15413, 664, 590, 15412])).
% 8.69/9.00 tff(15418,plain,
% 8.69/9.00 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 15417])).
% 8.69/9.00 tff(15419,plain,
% 8.69/9.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 8.69/9.00 inference(rewrite,[status(thm)],[])).
% 8.69/9.00 tff(15420,plain,
% 8.69/9.00 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 8.69/9.00 inference(rewrite,[status(thm)],[])).
% 8.69/9.00 tff(15421,plain,
% 8.69/9.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 8.69/9.00 inference(monotonicity,[status(thm)],[15420])).
% 8.69/9.00 tff(15422,plain,
% 8.69/9.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 8.69/9.00 inference(transitivity,[status(thm)],[15421, 15419])).
% 8.69/9.00 tff(15423,plain,
% 8.69/9.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 8.69/9.00 inference(quant_inst,[status(thm)],[])).
% 8.69/9.00 tff(15424,plain,
% 8.69/9.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 8.69/9.00 inference(modus_ponens,[status(thm)],[15423, 15422])).
% 8.69/9.00 tff(15425,plain,
% 8.69/9.00 (~b(s(s(s(s(s(s(z)))))), z)),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[15424, 391, 664, 590, 15412])).
% 8.69/9.00 tff(15426,plain,
% 8.69/9.00 (r(s(s(s(s(s(s(z)))))), z)),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[6641, 42, 6638, 15425])).
% 8.69/9.00 tff(15427,plain,
% 8.69/9.00 ($false),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[11902, 194, 3557, 719, 15426, 15418])).
% 8.69/9.00 tff(15428,plain,(r(s(s(z)), s(z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | r(s(s(z)), elem!1) | r(elem!1, s(s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.69/9.00 tff(15429,plain,
% 8.69/9.00 (r(s(s(z)), s(z))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[15428, 11308, 10645, 10643, 15325, 2913, 15347, 8329, 15387, 15386, 15327, 3823, 15384, 15385, 11321])).
% 8.69/9.00 tff(15430,plain,
% 8.69/9.00 (~r(s(s(z)), s(s(s(elem!1))))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[11211, 194, 15347, 2913, 15429])).
% 8.69/9.00 tff(15431,plain,
% 8.69/9.00 (b(s(s(z)), s(s(s(elem!1))))),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[11041, 15430])).
% 8.69/9.00 tff(15432,plain,
% 8.69/9.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 8.69/9.00 inference(rewrite,[status(thm)],[])).
% 8.69/9.00 tff(15433,plain,
% 8.69/9.00 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 8.69/9.00 inference(rewrite,[status(thm)],[])).
% 8.69/9.00 tff(15434,plain,
% 8.69/9.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))))),
% 8.69/9.00 inference(monotonicity,[status(thm)],[15433])).
% 8.69/9.00 tff(15435,plain,
% 8.69/9.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 8.69/9.00 inference(transitivity,[status(thm)],[15434, 15432])).
% 8.69/9.00 tff(15436,plain,
% 8.69/9.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 8.69/9.00 inference(quant_inst,[status(thm)],[])).
% 8.69/9.00 tff(15437,plain,
% 8.69/9.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))),
% 8.69/9.00 inference(modus_ponens,[status(thm)],[15436, 15435])).
% 8.69/9.00 tff(15438,plain,
% 8.69/9.00 (~b(s(s(z)), elem!1)),
% 8.69/9.00 inference(unit_resolution,[status(thm)],[15437, 391, 15373, 15321, 15431])).
% 8.69/9.00 tff(15439,plain,
% 8.69/9.01 (s(s(z)) = elem!1),
% 8.69/9.01 inference(unit_resolution,[status(thm)],[4730, 15438, 15384])).
% 8.69/9.01 tff(15440,plain,
% 8.69/9.01 (s(s(s(z))) = s(elem!1)),
% 8.69/9.01 inference(monotonicity,[status(thm)],[15439])).
% 8.69/9.01 tff(15441,plain,
% 8.69/9.01 (s(s(s(s(z)))) = s(s(elem!1))),
% 8.69/9.01 inference(monotonicity,[status(thm)],[15440])).
% 8.69/9.01 tff(15442,plain,
% 8.69/9.01 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 8.69/9.01 inference(monotonicity,[status(thm)],[15441])).
% 8.69/9.01 tff(15443,plain,
% 8.69/9.01 (r(s(s(elem!1)), z)),
% 8.69/9.01 inference(modus_ponens,[status(thm)],[3447, 15442])).
% 8.69/9.01 tff(15444,plain,
% 8.69/9.01 (r(s(z), s(s(elem!1)))),
% 8.69/9.01 inference(unit_resolution,[status(thm)],[11275, 15439, 2913])).
% 8.69/9.01 tff(15445,plain,
% 8.69/9.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 8.69/9.01 inference(rewrite,[status(thm)],[])).
% 8.69/9.01 tff(15446,plain,
% 8.69/9.01 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 8.69/9.01 inference(rewrite,[status(thm)],[])).
% 8.69/9.01 tff(15447,plain,
% 8.69/9.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 8.69/9.01 inference(monotonicity,[status(thm)],[15446])).
% 8.69/9.01 tff(15448,plain,
% 8.69/9.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 8.69/9.01 inference(transitivity,[status(thm)],[15447, 15445])).
% 8.69/9.01 tff(15449,plain,
% 8.69/9.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))))),
% 8.69/9.01 inference(quant_inst,[status(thm)],[])).
% 8.69/9.01 tff(15450,plain,
% 8.69/9.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 8.69/9.01 inference(modus_ponens,[status(thm)],[15449, 15448])).
% 8.69/9.01 tff(15451,plain,
% 8.69/9.01 (~b(elem!1, s(s(z)))),
% 8.69/9.01 inference(unit_resolution,[status(thm)],[15450, 391, 15373, 15321, 15431])).
% 8.69/9.01 tff(15452,plain,
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% 8.69/9.01 inference(unit_resolution,[status(thm)],[3394, 15451, 15385])).
% 8.69/9.01 tff(15453,plain,
% 8.69/9.01 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.69/9.01 inference(unit_resolution,[status(thm)],[9253, 15452])).
% 8.69/9.01 tff(15454,plain,
% 8.69/9.01 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.69/9.01 inference(unit_resolution,[status(thm)],[1370, 15453, 8329])).
% 8.69/9.01 tff(15455,plain,
% 8.69/9.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))),
% 8.69/9.01 inference(rewrite,[status(thm)],[])).
% 8.69/9.01 tff(15456,plain,
% 8.69/9.01 (((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))),
% 8.69/9.01 inference(rewrite,[status(thm)],[])).
% 8.69/9.01 tff(15457,plain,
% 8.69/9.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z))))),
% 8.69/9.01 inference(monotonicity,[status(thm)],[15456])).
% 8.69/9.01 tff(15458,plain,
% 8.69/9.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))),
% 8.69/9.01 inference(transitivity,[status(thm)],[15457, 15455])).
% 8.69/9.01 tff(15459,plain,
% 8.69/9.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 8.69/9.01 inference(quant_inst,[status(thm)],[])).
% 8.69/9.01 tff(15460,plain,
% 8.69/9.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z))),
% 8.69/9.01 inference(modus_ponens,[status(thm)],[15459, 15458])).
% 8.69/9.01 tff(15461,plain,
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% 8.69/9.01 inference(unit_resolution,[status(thm)],[15460, 194, 15454, 15347, 15444, 15443])).
% 8.69/9.01 tff(15462,plain,(b(z, s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (z = elem!1) | b(elem!1, s(z)) | b(s(z), s(s(s(s(z))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 8.69/9.01 tff(15463,plain,
% 8.69/9.01 (b(z, s(s(s(s(z)))))),
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% 8.69/9.01 tff(15464,plain,
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% 8.69/9.01 inference(unit_resolution,[status(thm)],[10620, 2913, 2053])).
% 8.69/9.01 tff(15465,plain,
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% 8.69/9.01 inference(unit_resolution,[status(thm)],[678, 15464])).
% 8.69/9.01 tff(15466,plain,
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% 8.69/9.01 tff(15467,plain,
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% 8.69/9.01 tff(15468,plain,
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% 8.69/9.01 inference(unit_resolution,[status(thm)],[141, 15466, 115])).
% 8.69/9.01 tff(15469,plain,
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% 8.69/9.01 inference(symmetry,[status(thm)],[1552])).
% 8.69/9.01 tff(15470,plain,
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% 8.69/9.01 inference(monotonicity,[status(thm)],[8668, 15469])).
% 8.69/9.01 tff(15471,plain,
% 8.69/9.01 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 8.69/9.01 inference(symmetry,[status(thm)],[15470])).
% 8.69/9.01 tff(15472,plain,
% 8.69/9.01 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 8.69/9.01 inference(monotonicity,[status(thm)],[15469, 8668])).
% 8.69/9.01 tff(15473,plain,
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% 8.69/9.01 inference(transitivity,[status(thm)],[15472, 302])).
% 8.69/9.01 tff(15474,plain,
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% 8.69/9.02 inference(monotonicity,[status(thm)],[15473])).
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% 8.69/9.02 inference(modus_ponens,[status(thm)],[8755, 15474])).
% 8.69/9.02 tff(15476,plain,
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% 8.69/9.02 tff(15480,plain,
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% 8.69/9.02 tff(15503,plain,
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% 8.69/9.02 tff(15506,plain,
% 8.69/9.02 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 8.69/9.02 inference(commutativity,[status(thm)],[])).
% 8.69/9.02 tff(15507,plain,
% 8.69/9.02 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 8.69/9.02 inference(symmetry,[status(thm)],[15506])).
% 8.69/9.02 tff(15508,plain,
% 8.69/9.02 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 8.69/9.02 inference(monotonicity,[status(thm)],[15507])).
% 8.69/9.02 tff(15509,plain,
% 8.69/9.02 (~(z = s(s(s(z))))),
% 8.69/9.02 inference(modus_ponens,[status(thm)],[741, 15508])).
% 8.69/9.02 tff(15510,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 8.69/9.02 tff(15511,plain,
% 8.69/9.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 8.69/9.02 inference(rewrite,[status(thm)],[])).
% 8.69/9.02 tff(15512,plain,
% 8.69/9.02 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 8.69/9.02 inference(rewrite,[status(thm)],[])).
% 8.69/9.02 tff(15513,plain,
% 8.69/9.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))))),
% 8.69/9.02 inference(monotonicity,[status(thm)],[15512])).
% 8.69/9.02 tff(15514,plain,
% 8.69/9.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 8.69/9.02 inference(transitivity,[status(thm)],[15513, 15511])).
% 8.69/9.02 tff(15515,plain,
% 8.69/9.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 8.69/9.02 inference(quant_inst,[status(thm)],[])).
% 8.69/9.02 tff(15516,plain,
% 8.69/9.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))),
% 8.69/9.02 inference(modus_ponens,[status(thm)],[15515, 15514])).
% 8.69/9.02 tff(15517,plain,
% 8.69/9.02 ($false),
% 8.69/9.02 inference(unit_resolution,[status(thm)],[15516, 194, 182, 2053, 1216, 15510])).
% 8.69/9.02 tff(15518,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.69/9.02 tff(15519,plain,
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% 8.69/9.02 inference(unit_resolution,[status(thm)],[15518, 182, 2053, 2913])).
% 8.69/9.02 tff(15520,plain,
% 8.69/9.02 (((~![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)))))),
% 8.69/9.02 inference(rewrite,[status(thm)],[])).
% 8.69/9.02 tff(15521,plain,
% 8.69/9.02 ((~![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)))))),
% 8.69/9.02 inference(quant_inst,[status(thm)],[])).
% 8.69/9.02 tff(15522,plain,
% 8.69/9.02 ((~![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))))),
% 8.69/9.02 inference(modus_ponens,[status(thm)],[15521, 15520])).
% 8.69/9.02 tff(15523,plain,
% 8.69/9.02 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 8.69/9.02 inference(unit_resolution,[status(thm)],[15522, 42, 15519])).
% 8.69/9.02 tff(15524,plain,
% 8.69/9.02 (b(z, s(s(s(z))))),
% 8.69/9.02 inference(unit_resolution,[status(thm)],[15523, 15509])).
% 8.69/9.02 tff(15525,plain,
% 8.69/9.02 (b(z, s(s(elem!1)))),
% 8.69/9.02 inference(modus_ponens,[status(thm)],[15524, 15505])).
% 8.69/9.02 tff(15526,plain,
% 8.69/9.02 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 8.69/9.02 inference(monotonicity,[status(thm)],[8615])).
% 8.69/9.02 tff(15527,plain,
% 8.69/9.02 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 8.69/9.02 inference(symmetry,[status(thm)],[15526])).
% 8.69/9.02 tff(15528,plain,
% 8.69/9.02 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 8.69/9.02 inference(transitivity,[status(thm)],[8595, 2206])).
% 8.69/9.02 tff(15529,plain,
% 8.69/9.02 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 8.69/9.02 inference(monotonicity,[status(thm)],[15528])).
% 8.69/9.02 tff(15530,plain,
% 8.69/9.02 (~(elem!1 = s(s(elem!1)))),
% 8.69/9.02 inference(modus_ponens,[status(thm)],[357, 15529])).
% 8.69/9.02 tff(15531,plain,
% 8.69/9.02 (r(elem!1, s(s(s(elem!1))))),
% 8.69/9.02 inference(unit_resolution,[status(thm)],[2570, 232, 8598])).
% 8.69/9.02 tff(15532,plain,
% 8.69/9.02 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 8.69/9.02 inference(monotonicity,[status(thm)],[1550])).
% 8.69/9.02 tff(15533,plain,
% 8.69/9.02 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(elem!1))))),
% 8.69/9.02 inference(transitivity,[status(thm)],[15532, 10700])).
% 8.69/9.02 tff(15534,plain,
% 8.69/9.02 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 8.69/9.02 inference(symmetry,[status(thm)],[15533])).
% 8.69/9.02 tff(15535,plain,
% 8.69/9.02 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 8.69/9.02 inference(monotonicity,[status(thm)],[15534])).
% 8.69/9.02 tff(15536,plain,
% 8.69/9.02 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.69/9.02 inference(modus_ponens,[status(thm)],[1397, 15535])).
% 8.69/9.02 tff(15537,plain,
% 8.69/9.02 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 8.69/9.02 inference(unit_resolution,[status(thm)],[281, 15536])).
% 8.69/9.02 tff(15538,plain,
% 8.69/9.02 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 8.69/9.02 inference(monotonicity,[status(thm)],[1550])).
% 8.69/9.02 tff(15539,plain,
% 8.69/9.02 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 8.69/9.02 inference(symmetry,[status(thm)],[15538])).
% 8.69/9.02 tff(15540,plain,
% 8.69/9.02 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 8.69/9.02 inference(monotonicity,[status(thm)],[1552])).
% 8.69/9.02 tff(15541,plain,
% 8.69/9.02 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 8.69/9.02 inference(symmetry,[status(thm)],[15540])).
% 8.69/9.02 tff(15542,plain,
% 8.69/9.02 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 8.69/9.02 inference(transitivity,[status(thm)],[15541, 15539])).
% 8.69/9.02 tff(15543,plain,
% 8.69/9.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))))),
% 8.69/9.02 inference(rewrite,[status(thm)],[])).
% 8.69/9.02 tff(15544,plain,
% 8.69/9.02 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))))),
% 8.81/9.03 inference(rewrite,[status(thm)],[])).
% 8.81/9.03 tff(15545,plain,
% 8.81/9.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z))))))),
% 8.81/9.03 inference(monotonicity,[status(thm)],[15544])).
% 8.81/9.03 tff(15546,plain,
% 8.81/9.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))))),
% 8.81/9.03 inference(transitivity,[status(thm)],[15545, 15543])).
% 8.81/9.03 tff(15547,plain,
% 8.81/9.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 8.81/9.03 inference(quant_inst,[status(thm)],[])).
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% 8.81/9.03 inference(modus_ponens,[status(thm)],[15547, 15546])).
% 8.81/9.03 tff(15549,plain,
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% 8.81/9.03 tff(15550,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.03 tff(15551,plain,
% 8.81/9.03 (~b(s(s(s(s(z)))), s(s(z)))),
% 8.81/9.03 inference(unit_resolution,[status(thm)],[15550, 15045, 3823, 1686])).
% 8.81/9.03 tff(15552,plain,
% 8.81/9.03 (r(s(s(s(s(z)))), s(s(z)))),
% 8.81/9.03 inference(unit_resolution,[status(thm)],[1714, 15551])).
% 8.81/9.03 tff(15553,plain,
% 8.81/9.03 (r(s(s(s(elem!1))), s(elem!1))),
% 8.81/9.03 inference(modus_ponens,[status(thm)],[15552, 15542])).
% 8.81/9.03 tff(15554,plain,
% 8.81/9.03 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 8.81/9.03 inference(monotonicity,[status(thm)],[169])).
% 8.81/9.03 tff(15555,plain,
% 8.81/9.03 ((s(s(s(elem!1))) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 8.81/9.03 inference(transitivity,[status(thm)],[15554, 204])).
% 8.81/9.03 tff(15556,plain,
% 8.81/9.03 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 8.81/9.03 inference(symmetry,[status(thm)],[15555])).
% 8.81/9.03 tff(15557,plain,
% 8.81/9.03 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 8.81/9.03 inference(monotonicity,[status(thm)],[15556])).
% 8.81/9.03 tff(15558,plain,
% 8.81/9.03 (~(s(s(s(elem!1))) = elem!1)),
% 8.81/9.03 inference(modus_ponens,[status(thm)],[217, 15557])).
% 8.81/9.03 tff(15559,plain,
% 8.81/9.03 (~(elem!1 = s(z))),
% 8.81/9.03 inference(unit_resolution,[status(thm)],[172, 4018])).
% 8.81/9.03 tff(15560,plain,
% 8.81/9.03 ($false),
% 8.81/9.03 inference(unit_resolution,[status(thm)],[13382, 391, 10682, 379, 1526, 664])).
% 8.81/9.03 tff(15561,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.03 tff(15562,plain,
% 8.81/9.03 (~b(s(z), s(s(s(elem!1))))),
% 8.81/9.03 inference(unit_resolution,[status(thm)],[15561, 664, 1526, 10682])).
% 8.81/9.03 tff(15563,plain,
% 8.81/9.03 (r(s(z), s(s(s(elem!1))))),
% 8.81/9.03 inference(unit_resolution,[status(thm)],[247, 15562])).
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% 8.81/9.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.81/9.03 inference(rewrite,[status(thm)],[])).
% 8.81/9.03 tff(15565,plain,
% 8.81/9.03 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z)))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.81/9.03 inference(rewrite,[status(thm)],[])).
% 8.81/9.03 tff(15566,plain,
% 8.81/9.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))))),
% 8.81/9.03 inference(monotonicity,[status(thm)],[15565])).
% 8.81/9.03 tff(15567,plain,
% 8.81/9.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.81/9.03 inference(transitivity,[status(thm)],[15566, 15564])).
% 8.81/9.03 tff(15568,plain,
% 8.81/9.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.81/9.03 inference(quant_inst,[status(thm)],[])).
% 8.81/9.03 tff(15569,plain,
% 8.81/9.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))),
% 8.81/9.03 inference(modus_ponens,[status(thm)],[15568, 15567])).
% 8.81/9.03 tff(15570,plain,
% 8.81/9.03 (~r(elem!1, s(z))),
% 8.81/9.03 inference(unit_resolution,[status(thm)],[15569, 194, 4486, 410, 15563])).
% 8.81/9.03 tff(15571,plain,
% 8.81/9.03 (b(elem!1, s(z))),
% 8.81/9.03 inference(unit_resolution,[status(thm)],[837, 15570, 15559])).
% 8.81/9.03 tff(15572,plain,
% 8.81/9.03 (~r(s(z), elem!1)),
% 8.81/9.03 inference(unit_resolution,[status(thm)],[5715, 15563, 4028, 168, 127])).
% 8.81/9.03 tff(15573,plain,
% 8.81/9.03 (b(s(z), elem!1)),
% 8.81/9.03 inference(unit_resolution,[status(thm)],[632, 15572, 4018])).
% 8.81/9.03 tff(15574,plain,
% 8.81/9.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 8.81/9.03 inference(rewrite,[status(thm)],[])).
% 8.81/9.03 tff(15575,plain,
% 8.81/9.03 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 8.81/9.03 inference(rewrite,[status(thm)],[])).
% 8.81/9.03 tff(15576,plain,
% 8.81/9.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 8.81/9.03 inference(monotonicity,[status(thm)],[15575])).
% 8.81/9.03 tff(15577,plain,
% 8.81/9.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 8.81/9.04 inference(transitivity,[status(thm)],[15576, 15574])).
% 8.81/9.04 tff(15578,plain,
% 8.81/9.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 8.81/9.04 inference(quant_inst,[status(thm)],[])).
% 8.81/9.04 tff(15579,plain,
% 8.81/9.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 8.81/9.04 inference(modus_ponens,[status(thm)],[15578, 15577])).
% 8.81/9.04 tff(15580,plain,
% 8.81/9.04 ($false),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[15579, 391, 10682, 15573, 1526, 664, 15571])).
% 8.81/9.04 tff(15581,plain,((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.81/9.04 tff(15582,plain,
% 8.81/9.04 (b(s(s(s(elem!1))), elem!1)),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[15581, 1526, 664, 4028, 10682, 15531, 15558])).
% 8.81/9.04 tff(15583,plain,
% 8.81/9.04 (~b(s(s(elem!1)), elem!1)),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[3979, 1294, 133, 3927])).
% 8.81/9.04 tff(15584,plain,
% 8.81/9.04 (r(s(s(elem!1)), elem!1)),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[872, 15583, 249])).
% 8.81/9.04 tff(15585,plain,
% 8.81/9.04 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[4168, 1294, 133, 3927, 900])).
% 8.81/9.04 tff(15586,plain,
% 8.81/9.04 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[1356, 15585, 270])).
% 8.81/9.04 tff(15587,plain,
% 8.81/9.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.81/9.04 inference(rewrite,[status(thm)],[])).
% 8.81/9.04 tff(15588,plain,
% 8.81/9.04 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.81/9.04 inference(rewrite,[status(thm)],[])).
% 8.81/9.04 tff(15589,plain,
% 8.81/9.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 8.81/9.04 inference(monotonicity,[status(thm)],[15588])).
% 8.81/9.04 tff(15590,plain,
% 8.81/9.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.81/9.04 inference(transitivity,[status(thm)],[15589, 15587])).
% 8.81/9.04 tff(15591,plain,
% 8.81/9.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 8.81/9.04 inference(quant_inst,[status(thm)],[])).
% 8.81/9.04 tff(15592,plain,
% 8.81/9.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 8.81/9.04 inference(modus_ponens,[status(thm)],[15591, 15590])).
% 8.81/9.04 tff(15593,plain,
% 8.81/9.04 ($false),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[15592, 194, 613, 364, 410, 1378])).
% 8.81/9.04 tff(15594,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.04 tff(15595,plain,
% 8.81/9.04 ($false),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[15594, 15586, 15584, 410, 613])).
% 8.81/9.04 tff(15596,plain,((~b(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.04 tff(15597,plain,
% 8.81/9.04 (~b(elem!1, s(s(elem!1)))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[15596, 15582, 15553, 15537, 8597, 133, 3927, 15531])).
% 8.81/9.04 tff(15598,plain,
% 8.81/9.04 (r(elem!1, s(s(elem!1)))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[1307, 15597, 15530])).
% 8.81/9.04 tff(15599,plain,
% 8.81/9.04 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 8.81/9.04 inference(monotonicity,[status(thm)],[169])).
% 8.81/9.04 tff(15600,plain,
% 8.81/9.04 (r(s(z), s(s(elem!1)))),
% 8.81/9.04 inference(modus_ponens,[status(thm)],[1064, 15599])).
% 8.81/9.04 tff(15601,plain,
% 8.81/9.04 ($false),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[4845, 15600])).
% 8.81/9.04 tff(15602,plain,((~r(elem!1, s(s(elem!1)))) | r(s(z), s(s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.04 tff(15603,plain,
% 8.81/9.04 (r(s(z), s(s(elem!1)))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[15602, 15598, 169])).
% 8.81/9.04 tff(15604,plain,
% 8.81/9.04 (r(s(z), s(s(s(z))))),
% 8.81/9.04 inference(modus_ponens,[status(thm)],[15603, 15527])).
% 8.81/9.04 tff(15605,plain,
% 8.81/9.04 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[2686, 15536])).
% 8.81/9.04 tff(15606,plain,
% 8.81/9.04 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[2711, 15605])).
% 8.81/9.04 tff(15607,plain,
% 8.81/9.04 (b(s(s(s(s(z)))), s(z))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[9618, 1526, 8598])).
% 8.81/9.04 tff(15608,plain,
% 8.81/9.04 (s(s(s(s(elem!1)))) = elem!1),
% 8.81/9.04 inference(modus_ponens,[status(thm)],[14415, 964])).
% 8.81/9.04 tff(15609,plain,
% 8.81/9.04 ($false),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[972, 15608])).
% 8.81/9.04 tff(15610,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.81/9.04 tff(15611,plain,
% 8.81/9.04 (~(elem!1 = s(s(s(s(elem!1)))))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[15610, 8664])).
% 8.81/9.04 tff(15612,plain,
% 8.81/9.04 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 8.81/9.04 inference(monotonicity,[status(thm)],[8584])).
% 8.81/9.04 tff(15613,plain,
% 8.81/9.04 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 8.81/9.04 inference(symmetry,[status(thm)],[15612])).
% 8.81/9.04 tff(15614,plain,
% 8.81/9.04 ((~b(elem!1, s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 8.81/9.04 inference(monotonicity,[status(thm)],[15613])).
% 8.81/9.04 tff(15615,plain,
% 8.81/9.04 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 8.81/9.04 inference(monotonicity,[status(thm)],[170])).
% 8.81/9.04 tff(15616,plain,
% 8.81/9.04 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 8.81/9.04 inference(symmetry,[status(thm)],[15615])).
% 8.81/9.04 tff(15617,assumption,(b(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 8.81/9.04 tff(15618,plain,
% 8.81/9.04 (b(s(z), s(s(s(s(s(z))))))),
% 8.81/9.04 inference(modus_ponens,[status(thm)],[15617, 15616])).
% 8.81/9.04 tff(15619,plain,
% 8.81/9.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 8.81/9.04 inference(rewrite,[status(thm)],[])).
% 8.81/9.04 tff(15620,plain,
% 8.81/9.04 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 8.81/9.04 inference(rewrite,[status(thm)],[])).
% 8.81/9.04 tff(15621,plain,
% 8.81/9.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 8.81/9.04 inference(monotonicity,[status(thm)],[15620])).
% 8.81/9.04 tff(15622,plain,
% 8.81/9.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 8.81/9.04 inference(transitivity,[status(thm)],[15621, 15619])).
% 8.81/9.04 tff(15623,plain,
% 8.81/9.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 8.81/9.04 inference(quant_inst,[status(thm)],[])).
% 8.81/9.04 tff(15624,plain,
% 8.81/9.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 8.81/9.04 inference(modus_ponens,[status(thm)],[15623, 15622])).
% 8.81/9.04 tff(15625,plain,
% 8.81/9.04 (~b(s(z), s(s(s(s(s(z))))))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[15624, 391, 3823, 1759, 1686, 15045])).
% 8.81/9.04 tff(15626,plain,
% 8.81/9.04 ($false),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[15625, 15618])).
% 8.81/9.04 tff(15627,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~(elem!1 = s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.04 tff(15628,plain,
% 8.81/9.04 (~b(elem!1, s(s(s(s(s(z))))))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[15627, 15607, 3823, 169, 1686, 15045])).
% 8.81/9.04 tff(15629,plain,
% 8.81/9.04 (~b(elem!1, s(s(s(s(elem!1)))))),
% 8.81/9.04 inference(modus_ponens,[status(thm)],[15628, 15614])).
% 8.81/9.04 tff(15630,plain,
% 8.81/9.04 (r(elem!1, s(s(s(s(elem!1)))))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[1018, 15629, 15611])).
% 8.81/9.04 tff(15631,plain,
% 8.81/9.04 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[1090, 15630, 327, 15531])).
% 8.81/9.04 tff(15632,plain,
% 8.81/9.04 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 8.81/9.04 inference(unit_resolution,[status(thm)],[1095, 15631, 15475])).
% 8.81/9.04 tff(15633,plain,
% 8.81/9.04 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 8.81/9.04 inference(monotonicity,[status(thm)],[8668, 15469])).
% 8.81/9.04 tff(15634,plain,
% 8.81/9.04 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 8.81/9.04 inference(symmetry,[status(thm)],[15633])).
% 8.81/9.04 tff(15635,plain,
% 8.81/9.04 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 8.81/9.04 inference(modus_ponens,[status(thm)],[1114, 15634])).
% 8.81/9.04 tff(15636,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 8.81/9.05 tff(15637,plain,
% 8.81/9.05 ($false),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[15636, 15635])).
% 8.81/9.05 tff(15638,plain,(b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.05 tff(15639,plain,
% 8.81/9.05 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[15638, 15632, 169])).
% 8.81/9.05 tff(15640,plain,
% 8.81/9.05 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 8.81/9.05 inference(monotonicity,[status(thm)],[15472])).
% 8.81/9.05 tff(15641,plain,
% 8.81/9.05 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 8.81/9.05 inference(modus_ponens,[status(thm)],[8755, 15640])).
% 8.81/9.05 tff(15642,plain,
% 8.81/9.05 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 8.81/9.05 inference(monotonicity,[status(thm)],[1552, 8584])).
% 8.81/9.05 tff(15643,plain,
% 8.81/9.05 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 8.81/9.05 inference(symmetry,[status(thm)],[15642])).
% 8.81/9.05 tff(15644,plain,
% 8.81/9.05 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 8.81/9.05 inference(monotonicity,[status(thm)],[15643])).
% 8.81/9.05 tff(15645,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 8.81/9.05 tff(15646,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 8.81/9.05 tff(15647,plain,
% 8.81/9.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 8.81/9.05 inference(rewrite,[status(thm)],[])).
% 8.81/9.05 tff(15648,plain,
% 8.81/9.05 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 8.81/9.05 inference(rewrite,[status(thm)],[])).
% 8.81/9.05 tff(15649,plain,
% 8.81/9.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 8.81/9.05 inference(monotonicity,[status(thm)],[15648])).
% 8.81/9.05 tff(15650,plain,
% 8.81/9.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 8.81/9.05 inference(transitivity,[status(thm)],[15649, 15647])).
% 8.81/9.05 tff(15651,plain,
% 8.81/9.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 8.81/9.05 inference(quant_inst,[status(thm)],[])).
% 8.81/9.05 tff(15652,plain,
% 8.81/9.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 8.81/9.05 inference(modus_ponens,[status(thm)],[15651, 15650])).
% 8.81/9.05 tff(15653,plain,
% 8.81/9.05 ($false),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[15652, 391, 3823, 1686, 15045, 15646, 15645])).
% 8.81/9.05 tff(15654,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.05 tff(15655,plain,
% 8.81/9.05 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[15654, 15639, 1686, 15045, 3823])).
% 8.81/9.05 tff(15656,plain,
% 8.81/9.05 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 8.81/9.05 inference(modus_ponens,[status(thm)],[15655, 15644])).
% 8.81/9.05 tff(15657,plain,
% 8.81/9.05 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[1164, 15656, 15641])).
% 8.81/9.05 tff(15658,plain,
% 8.81/9.05 (~r(s(s(elem!1)), z)),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[4840, 15603, 232, 327])).
% 8.81/9.05 tff(15659,plain,
% 8.81/9.05 (b(s(s(elem!1)), z)),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[2629, 15658])).
% 8.81/9.05 tff(15660,plain,
% 8.81/9.05 (b(s(s(s(z))), z)),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[7886, 15659, 8598])).
% 8.81/9.05 tff(15661,plain,
% 8.81/9.05 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 8.81/9.05 inference(monotonicity,[status(thm)],[8584])).
% 8.81/9.05 tff(15662,plain,
% 8.81/9.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.81/9.05 inference(rewrite,[status(thm)],[])).
% 8.81/9.05 tff(15663,plain,
% 8.81/9.05 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.81/9.05 inference(rewrite,[status(thm)],[])).
% 8.81/9.05 tff(15664,plain,
% 8.81/9.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 8.81/9.05 inference(monotonicity,[status(thm)],[15663])).
% 8.81/9.05 tff(15665,plain,
% 8.81/9.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.81/9.05 inference(transitivity,[status(thm)],[15664, 15662])).
% 8.81/9.05 tff(15666,plain,
% 8.81/9.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, z)))),
% 8.81/9.05 inference(quant_inst,[status(thm)],[])).
% 8.81/9.05 tff(15667,plain,
% 8.81/9.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 8.81/9.05 inference(modus_ponens,[status(thm)],[15666, 15665])).
% 8.81/9.05 tff(15668,plain,
% 8.81/9.05 ($false),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[15667, 194, 530, 1063, 1177, 2792])).
% 8.81/9.05 tff(15669,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.05 tff(15670,plain,
% 8.81/9.05 (~r(z, s(s(s(s(elem!1)))))),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[15669, 1177, 530, 1063])).
% 8.81/9.05 tff(15671,plain,
% 8.81/9.05 (b(z, s(s(s(s(elem!1)))))),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[2767, 15670])).
% 8.81/9.05 tff(15672,plain,
% 8.81/9.05 (b(z, s(s(s(s(s(z))))))),
% 8.81/9.05 inference(modus_ponens,[status(thm)],[15671, 15661])).
% 8.81/9.05 tff(15673,plain,
% 8.81/9.05 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 8.81/9.05 inference(monotonicity,[status(thm)],[1551, 8584])).
% 8.81/9.05 tff(15674,plain,
% 8.81/9.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.81/9.05 inference(rewrite,[status(thm)],[])).
% 8.81/9.05 tff(15675,plain,
% 8.81/9.05 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.81/9.05 inference(rewrite,[status(thm)],[])).
% 8.81/9.05 tff(15676,plain,
% 8.81/9.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 8.81/9.05 inference(monotonicity,[status(thm)],[15675])).
% 8.81/9.05 tff(15677,plain,
% 8.81/9.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 8.81/9.05 inference(transitivity,[status(thm)],[15676, 15674])).
% 8.81/9.05 tff(15678,plain,
% 8.81/9.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 8.81/9.05 inference(quant_inst,[status(thm)],[])).
% 8.81/9.05 tff(15679,plain,
% 8.81/9.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 8.81/9.05 inference(modus_ponens,[status(thm)],[15678, 15677])).
% 8.81/9.05 tff(15680,plain,
% 8.81/9.05 ($false),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[15679, 194, 327, 1177, 1538, 1176])).
% 8.81/9.05 tff(15681,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.05 tff(15682,plain,
% 8.81/9.05 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[15681, 1177, 327, 1538])).
% 8.81/9.05 tff(15683,plain,
% 8.81/9.05 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 8.81/9.05 inference(unit_resolution,[status(thm)],[1048, 15682, 15605])).
% 8.81/9.06 tff(15684,plain,
% 8.81/9.06 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 8.81/9.06 inference(modus_ponens,[status(thm)],[15683, 15673])).
% 8.81/9.06 tff(15685,plain,
% 8.81/9.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 8.81/9.06 inference(rewrite,[status(thm)],[])).
% 8.81/9.06 tff(15686,plain,
% 8.81/9.06 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 8.81/9.06 inference(rewrite,[status(thm)],[])).
% 8.81/9.06 tff(15687,plain,
% 8.81/9.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 8.81/9.06 inference(monotonicity,[status(thm)],[15686])).
% 8.81/9.06 tff(15688,plain,
% 8.81/9.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 8.81/9.06 inference(transitivity,[status(thm)],[15687, 15685])).
% 8.81/9.06 tff(15689,plain,
% 8.81/9.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 8.81/9.06 inference(quant_inst,[status(thm)],[])).
% 8.81/9.06 tff(15690,plain,
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% 8.81/9.06 inference(modus_ponens,[status(thm)],[15689, 15688])).
% 8.81/9.06 tff(15691,plain,
% 8.81/9.06 ($false),
% 8.81/9.06 inference(unit_resolution,[status(thm)],[15690, 391, 1759, 1685, 15684, 15672, 15645])).
% 8.81/9.06 tff(15692,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.06 tff(15693,plain,
% 8.81/9.06 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.81/9.06 inference(unit_resolution,[status(thm)],[15692, 15660, 15657, 15639, 169, 530, 15630, 327, 15607])).
% 8.81/9.06 tff(15694,plain,
% 8.81/9.06 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 8.81/9.06 inference(unit_resolution,[status(thm)],[1061, 15693, 15606])).
% 8.81/9.06 tff(15695,plain,
% 8.81/9.06 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 8.81/9.06 inference(unit_resolution,[status(thm)],[14284, 15694, 3927, 2781])).
% 8.81/9.06 tff(15696,plain,
% 8.81/9.06 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 8.81/9.06 inference(unit_resolution,[status(thm)],[1048, 15695, 15605])).
% 8.81/9.06 tff(15697,plain,
% 8.81/9.06 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 8.81/9.06 inference(monotonicity,[status(thm)],[1551, 8584])).
% 8.81/9.06 tff(15698,plain,
% 8.81/9.06 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 8.81/9.06 inference(modus_ponens,[status(thm)],[1176, 15697])).
% 8.81/9.06 tff(15699,assumption,(~r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 8.81/9.06 tff(15700,plain,
% 8.81/9.06 ($false),
% 8.81/9.06 inference(unit_resolution,[status(thm)],[15699, 15698])).
% 8.81/9.06 tff(15701,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.06 tff(15702,plain,
% 8.81/9.06 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 8.81/9.06 inference(unit_resolution,[status(thm)],[15701, 15696, 169])).
% 8.81/9.06 tff(15703,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 8.81/9.06 tff(15704,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 8.81/9.06 tff(15705,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 8.81/9.06 tff(15706,plain,
% 8.81/9.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(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(z))), s(s(s(s(s(z))))))))),
% 8.81/9.06 inference(rewrite,[status(thm)],[])).
% 8.81/9.06 tff(15707,plain,
% 8.81/9.06 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(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(z))), s(s(s(s(s(z))))))))),
% 8.81/9.06 inference(rewrite,[status(thm)],[])).
% 8.81/9.06 tff(15708,plain,
% 8.81/9.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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(z))), s(s(s(s(s(z)))))))))),
% 8.81/9.06 inference(monotonicity,[status(thm)],[15707])).
% 8.81/9.06 tff(15709,plain,
% 8.81/9.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(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(z))), s(s(s(s(s(z))))))))),
% 8.81/9.06 inference(transitivity,[status(thm)],[15708, 15706])).
% 8.81/9.06 tff(15710,plain,
% 8.81/9.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 8.81/9.06 inference(quant_inst,[status(thm)],[])).
% 8.81/9.06 tff(15711,plain,
% 8.81/9.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 8.81/9.06 inference(modus_ponens,[status(thm)],[15710, 15709])).
% 8.81/9.06 tff(15712,plain,
% 8.81/9.06 ($false),
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% 8.81/9.06 tff(15714,plain,
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% 8.81/9.06 tff(15716,plain,((~b(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.06 tff(15717,plain,
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% 8.81/9.06 tff(15718,plain,
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% 8.81/9.06 tff(15719,plain,
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% 8.81/9.06 tff(15731,plain,
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% 8.81/9.06 tff(15732,plain,
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% 8.81/9.06 tff(15739,plain,
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% 8.81/9.06 tff(15742,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
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% 8.81/9.07 tff(15746,plain,
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% 8.81/9.07 tff(15747,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 8.81/9.07 tff(15748,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 8.81/9.07 tff(15749,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
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% 8.81/9.07 tff(15751,plain,
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% 8.81/9.07 tff(15758,plain,
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% 8.81/9.07 tff(15763,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.07 tff(15764,plain,
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% 8.81/9.07 tff(15768,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 8.81/9.07 tff(15769,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
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% 8.81/9.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
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% 8.81/9.07 tff(15771,plain,
% 8.81/9.07 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
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% 8.81/9.07 tff(15772,plain,
% 8.81/9.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 8.81/9.07 inference(monotonicity,[status(thm)],[15771])).
% 8.81/9.07 tff(15773,plain,
% 8.81/9.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 8.81/9.07 inference(transitivity,[status(thm)],[15772, 15770])).
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% 8.81/9.07 inference(quant_inst,[status(thm)],[])).
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% 8.81/9.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 8.81/9.07 inference(modus_ponens,[status(thm)],[15774, 15773])).
% 8.81/9.07 tff(15776,plain,
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% 8.81/9.07 tff(15778,plain,
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% 8.81/9.07 tff(15782,plain,
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% 8.81/9.08 tff(15783,plain,
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% 8.81/9.08 tff(15794,plain,
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% 8.81/9.08 tff(15795,plain,
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% 8.81/9.08 tff(15797,plain,
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% 8.81/9.08 tff(15799,plain,
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% 8.81/9.08 tff(15805,plain,
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% 8.81/9.08 tff(15806,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 8.81/9.08 tff(15807,plain,
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% 8.81/9.08 tff(15816,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~(elem!1 = s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.08 tff(15817,plain,
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% 8.81/9.08 tff(15818,plain,
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% 8.81/9.08 tff(15822,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | b(s(s(s(s(s(z))))), elem!1) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.08 tff(15823,plain,
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% 8.81/9.08 tff(15824,plain,
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% 8.81/9.08 tff(15825,plain,
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% 8.81/9.08 tff(15826,plain,
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% 8.81/9.08 inference(modus_ponens,[status(thm)],[15827, 15826])).
% 8.81/9.08 tff(15829,plain,
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% 8.81/9.08 tff(15830,plain,
% 8.81/9.08 ($false),
% 8.81/9.08 inference(unit_resolution,[status(thm)],[15829, 15799])).
% 8.81/9.08 tff(15831,plain,((~(elem!1 = s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | b(s(s(s(elem!1))), s(s(elem!1))) | (s(s(elem!1)) = s(s(z))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.08 tff(15832,plain,
% 8.81/9.08 (~(elem!1 = s(z))),
% 8.81/9.08 inference(unit_resolution,[status(thm)],[15831, 182, 1686, 3823, 15468, 4028, 15467, 2053, 8329, 11335, 2881])).
% 8.81/9.08 tff(15833,plain,
% 8.81/9.08 (r(elem!1, s(z))),
% 8.81/9.08 inference(unit_resolution,[status(thm)],[837, 15832, 31])).
% 8.81/9.08 tff(15834,plain,
% 8.81/9.08 (~r(s(s(s(elem!1))), s(z))),
% 8.81/9.08 inference(unit_resolution,[status(thm)],[10776, 4030, 1216, 847])).
% 8.81/9.08 tff(15835,plain,
% 8.81/9.08 (b(s(s(s(elem!1))), s(z))),
% 8.81/9.08 inference(unit_resolution,[status(thm)],[223, 15834])).
% 8.81/9.08 tff(15836,plain,
% 8.81/9.08 (~b(s(z), s(s(s(elem!1))))),
% 8.81/9.08 inference(unit_resolution,[status(thm)],[15561, 15835, 664, 10682])).
% 8.81/9.08 tff(15837,plain,
% 8.81/9.08 (r(s(z), s(s(s(elem!1))))),
% 8.81/9.08 inference(unit_resolution,[status(thm)],[247, 15836])).
% 8.81/9.08 tff(15838,plain,
% 8.81/9.08 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.81/9.08 inference(unit_resolution,[status(thm)],[8251, 127])).
% 8.81/9.08 tff(15839,plain,
% 8.81/9.08 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.81/9.08 inference(unit_resolution,[status(thm)],[1370, 15838, 8329])).
% 8.81/9.08 tff(15840,plain,
% 8.81/9.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.81/9.09 inference(rewrite,[status(thm)],[])).
% 8.81/9.09 tff(15841,plain,
% 8.81/9.09 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.81/9.09 inference(rewrite,[status(thm)],[])).
% 8.81/9.09 tff(15842,plain,
% 8.81/9.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))))),
% 8.81/9.09 inference(monotonicity,[status(thm)],[15841])).
% 8.81/9.09 tff(15843,plain,
% 8.81/9.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.81/9.09 inference(transitivity,[status(thm)],[15842, 15840])).
% 8.81/9.09 tff(15844,plain,
% 8.81/9.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.81/9.09 inference(quant_inst,[status(thm)],[])).
% 8.81/9.09 tff(15845,plain,
% 8.81/9.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))),
% 8.81/9.09 inference(modus_ponens,[status(thm)],[15844, 15843])).
% 8.81/9.09 tff(15846,plain,
% 8.81/9.09 ($false),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[15845, 194, 4030, 15839, 15837, 847])).
% 8.81/9.09 tff(15847,plain,((s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.09 tff(15848,plain,
% 8.81/9.09 (s(s(s(elem!1))) = elem!1),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[15847, 15833, 8329, 15465, 15467, 2913, 4028])).
% 8.81/9.09 tff(15849,plain,
% 8.81/9.09 (~(s(s(s(s(z)))) = elem!1)),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[1436, 15848])).
% 8.81/9.09 tff(15850,plain,
% 8.81/9.09 (~r(elem!1, s(s(s(s(z)))))),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[11195, 15833, 2053, 2913])).
% 8.81/9.09 tff(15851,plain,
% 8.81/9.09 (~(elem!1 = s(s(s(s(z)))))),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[769, 15849])).
% 8.81/9.09 tff(15852,plain,
% 8.81/9.09 (b(elem!1, s(s(s(s(z)))))),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[781, 15851, 15850])).
% 8.81/9.09 tff(15853,plain,
% 8.81/9.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.09 inference(rewrite,[status(thm)],[])).
% 8.81/9.09 tff(15854,plain,
% 8.81/9.09 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.09 inference(rewrite,[status(thm)],[])).
% 8.81/9.09 tff(15855,plain,
% 8.81/9.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 8.81/9.09 inference(monotonicity,[status(thm)],[15854])).
% 8.81/9.09 tff(15856,plain,
% 8.81/9.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.09 inference(transitivity,[status(thm)],[15855, 15853])).
% 8.81/9.09 tff(15857,plain,
% 8.81/9.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.09 inference(quant_inst,[status(thm)],[])).
% 8.81/9.09 tff(15858,plain,
% 8.81/9.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 8.81/9.09 inference(modus_ponens,[status(thm)],[15857, 15856])).
% 8.81/9.09 tff(15859,plain,
% 8.81/9.09 ($false),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[15858, 391, 133, 2064, 1652, 1686])).
% 8.81/9.09 tff(15860,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.09 tff(15861,plain,
% 8.81/9.09 (~b(s(s(s(s(z)))), elem!1)),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[15860, 15468, 15852, 1686])).
% 8.81/9.09 tff(15862,plain,
% 8.81/9.09 (r(s(s(s(s(z)))), elem!1)),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[762, 15861, 15849])).
% 8.81/9.09 tff(15863,plain,
% 8.81/9.09 ($false),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[4235, 194, 847, 182, 2112, 723])).
% 8.81/9.09 tff(15864,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.09 tff(15865,plain,
% 8.81/9.09 (~r(s(s(s(s(z)))), s(z))),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[15864, 15833, 182, 15862])).
% 8.81/9.09 tff(15866,plain,
% 8.81/9.09 (b(s(s(s(s(z)))), s(z))),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[749, 15865])).
% 8.81/9.09 tff(15867,plain,
% 8.81/9.09 (~(s(z) = elem!1)),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[1495, 15832])).
% 8.81/9.09 tff(15868,plain,
% 8.81/9.09 (~r(s(z), elem!1)),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[5396, 15862, 15833, 2913])).
% 8.81/9.09 tff(15869,plain,
% 8.81/9.09 (b(s(z), elem!1)),
% 8.81/9.09 inference(unit_resolution,[status(thm)],[632, 15868, 15867])).
% 8.81/9.09 tff(15870,plain,
% 8.81/9.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 8.81/9.09 inference(rewrite,[status(thm)],[])).
% 8.81/9.09 tff(15871,plain,
% 8.81/9.09 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 8.81/9.09 inference(rewrite,[status(thm)],[])).
% 8.81/9.10 tff(15872,plain,
% 8.81/9.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 8.81/9.10 inference(monotonicity,[status(thm)],[15871])).
% 8.81/9.10 tff(15873,plain,
% 8.81/9.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 8.81/9.10 inference(transitivity,[status(thm)],[15872, 15870])).
% 8.81/9.10 tff(15874,plain,
% 8.81/9.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.10 inference(quant_inst,[status(thm)],[])).
% 8.81/9.10 tff(15875,plain,
% 8.81/9.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 8.81/9.10 inference(modus_ponens,[status(thm)],[15874, 15873])).
% 8.81/9.10 tff(15876,plain,
% 8.81/9.10 ($false),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[15875, 391, 15869, 15852, 15866, 1686, 15465])).
% 8.81/9.10 tff(15877,plain,((~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | b(elem!1, s(z)) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(z), s(s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.81/9.10 tff(15878,plain,
% 8.81/9.10 (~r(s(z), z)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[15877, 4028, 8329, 1686, 2053, 31, 3823, 2881, 115])).
% 8.81/9.10 tff(15879,plain,
% 8.81/9.10 (b(s(z), z)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[180, 15878])).
% 8.81/9.10 tff(15880,plain,
% 8.81/9.10 (~b(z, s(s(s(elem!1))))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[15847, 127, 8329, 664, 847, 1216, 4028])).
% 8.81/9.10 tff(15881,plain,
% 8.81/9.10 (r(z, elem!1)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[8231, 15880, 2])).
% 8.81/9.10 tff(15882,plain,
% 8.81/9.10 (r(z, s(s(s(elem!1))))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[58, 15880])).
% 8.81/9.10 tff(15883,plain,
% 8.81/9.10 (~b(s(s(s(elem!1))), s(z))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[10635, 15882, 4028, 664, 590, 15881, 31])).
% 8.81/9.10 tff(15884,plain,
% 8.81/9.10 ($false),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[223, 15883, 15834])).
% 8.81/9.10 tff(15885,plain,((s(s(s(elem!1))) = elem!1) | b(elem!1, s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | b(elem!1, s(z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (elem!1 = z) | b(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.10 tff(15886,plain,
% 8.81/9.10 (s(s(s(elem!1))) = elem!1),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[15885, 1810, 10679, 590, 31, 1216, 4028, 2, 8329])).
% 8.81/9.10 tff(15887,plain,
% 8.81/9.10 (~r(elem!1, s(s(s(s(z)))))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[11195, 1810, 2053, 1216])).
% 8.81/9.10 tff(15888,plain,
% 8.81/9.10 (~(s(s(s(s(z)))) = elem!1)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[1436, 15886])).
% 8.81/9.10 tff(15889,plain,
% 8.81/9.10 (~(elem!1 = s(s(s(s(z)))))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[769, 15888])).
% 8.81/9.10 tff(15890,plain,
% 8.81/9.10 (b(elem!1, s(s(s(s(z)))))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[781, 15889, 15887])).
% 8.81/9.10 tff(15891,plain,
% 8.81/9.10 (elem!1 = s(s(s(elem!1)))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[8, 15886])).
% 8.81/9.10 tff(15892,plain,
% 8.81/9.10 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 8.81/9.10 inference(monotonicity,[status(thm)],[15891])).
% 8.81/9.10 tff(15893,plain,
% 8.81/9.10 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 8.81/9.10 inference(symmetry,[status(thm)],[15892])).
% 8.81/9.10 tff(15894,plain,
% 8.81/9.10 (~b(s(s(s(elem!1))), s(z))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[8400, 15886, 31])).
% 8.81/9.10 tff(15895,plain,
% 8.81/9.10 (r(s(s(s(elem!1))), s(z))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[223, 15894])).
% 8.81/9.10 tff(15896,plain,
% 8.81/9.10 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.81/9.10 inference(monotonicity,[status(thm)],[15891])).
% 8.81/9.10 tff(15897,plain,
% 8.81/9.10 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.81/9.10 inference(modus_ponens,[status(thm)],[15890, 15896])).
% 8.81/9.10 tff(15898,plain,
% 8.81/9.10 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.81/9.10 inference(monotonicity,[status(thm)],[3807])).
% 8.81/9.10 tff(15899,plain,
% 8.81/9.10 (r(z, elem!1)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[8231, 10, 2])).
% 8.81/9.10 tff(15900,plain,
% 8.81/9.10 (~r(s(s(s(s(z)))), elem!1)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[10408, 15899, 2053, 847])).
% 8.81/9.10 tff(15901,plain,
% 8.81/9.10 (b(s(s(s(s(z)))), elem!1)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[762, 15900, 2691])).
% 8.81/9.10 tff(15902,plain,
% 8.81/9.10 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.81/9.10 inference(modus_ponens,[status(thm)],[15901, 15898])).
% 8.81/9.10 tff(15903,plain,
% 8.81/9.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.81/9.10 inference(rewrite,[status(thm)],[])).
% 8.81/9.10 tff(15904,plain,
% 8.81/9.10 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.81/9.10 inference(rewrite,[status(thm)],[])).
% 8.81/9.10 tff(15905,plain,
% 8.81/9.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 8.81/9.10 inference(monotonicity,[status(thm)],[15904])).
% 8.81/9.10 tff(15906,plain,
% 8.81/9.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.81/9.10 inference(transitivity,[status(thm)],[15905, 15903])).
% 8.81/9.10 tff(15907,plain,
% 8.81/9.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 8.81/9.10 inference(quant_inst,[status(thm)],[])).
% 8.81/9.10 tff(15908,plain,
% 8.81/9.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 8.81/9.10 inference(modus_ponens,[status(thm)],[15907, 15906])).
% 8.81/9.10 tff(15909,plain,
% 8.81/9.10 (~b(s(s(z)), s(s(s(elem!1))))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[15908, 391, 3823, 15902, 1669])).
% 8.81/9.10 tff(15910,plain,
% 8.81/9.10 (r(s(s(z)), s(s(s(elem!1))))),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[11041, 15909])).
% 8.81/9.10 tff(15911,plain,
% 8.81/9.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.81/9.10 inference(rewrite,[status(thm)],[])).
% 8.81/9.10 tff(15912,plain,
% 8.81/9.10 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.81/9.10 inference(rewrite,[status(thm)],[])).
% 8.81/9.10 tff(15913,plain,
% 8.81/9.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 8.81/9.10 inference(monotonicity,[status(thm)],[15912])).
% 8.81/9.10 tff(15914,plain,
% 8.81/9.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.81/9.10 inference(transitivity,[status(thm)],[15913, 15911])).
% 8.81/9.10 tff(15915,plain,
% 8.81/9.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 8.81/9.10 inference(quant_inst,[status(thm)],[])).
% 8.81/9.10 tff(15916,plain,
% 8.81/9.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 8.81/9.10 inference(modus_ponens,[status(thm)],[15915, 15914])).
% 8.81/9.10 tff(15917,plain,
% 8.81/9.10 (~b(s(s(z)), z)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[15916, 391, 3823, 1686, 15902, 1669])).
% 8.81/9.10 tff(15918,plain,
% 8.81/9.10 (r(s(s(z)), z)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[1211, 15917])).
% 8.81/9.10 tff(15919,plain,
% 8.81/9.10 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 8.81/9.10 inference(transitivity,[status(thm)],[1953, 93])).
% 8.81/9.10 tff(15920,plain,
% 8.81/9.10 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = z))),
% 8.81/9.10 inference(monotonicity,[status(thm)],[15919])).
% 8.81/9.10 tff(15921,plain,
% 8.81/9.10 (~(elem!1 = z)),
% 8.81/9.10 inference(modus_ponens,[status(thm)],[50, 15920])).
% 8.81/9.10 tff(15922,plain,
% 8.81/9.10 (b(elem!1, z)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[526, 15921, 2282])).
% 8.81/9.10 tff(15923,plain,
% 8.81/9.10 (r(z, elem!1)),
% 8.81/9.10 inference(unit_resolution,[status(thm)],[147, 3807, 10])).
% 8.81/9.11 tff(15924,plain,
% 8.81/9.11 (~r(s(s(s(s(z)))), elem!1)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[10450, 14703, 3696, 15923, 15922])).
% 8.81/9.11 tff(15925,plain,
% 8.81/9.11 (b(s(s(s(s(z)))), elem!1)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[762, 15924, 2691])).
% 8.81/9.11 tff(15926,plain,
% 8.81/9.11 (~(s(s(elem!1)) = elem!1)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[15095, 15923, 15922, 59, 183, 5])).
% 8.81/9.11 tff(15927,plain,
% 8.81/9.11 (~(s(s(s(elem!1))) = s(elem!1))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[6159, 15926])).
% 8.81/9.11 tff(15928,plain,
% 8.81/9.11 (b(s(s(elem!1)), elem!1)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[15317, 15927, 15923, 5, 59, 14703, 15922])).
% 8.81/9.11 tff(15929,plain,
% 8.81/9.11 (~r(s(z), s(s(s(s(z)))))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[15169, 5, 15923, 15922, 14703, 15928])).
% 8.81/9.11 tff(15930,plain,
% 8.81/9.11 (b(s(z), s(s(s(s(z)))))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[1230, 15929])).
% 8.81/9.11 tff(15931,plain,
% 8.81/9.11 (~r(z, s(z))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[14725, 1484, 847, 411])).
% 8.81/9.11 tff(15932,plain,
% 8.81/9.11 (b(z, s(z))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[678, 15931])).
% 8.81/9.11 tff(15933,plain,
% 8.81/9.11 (~r(s(z), z)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[2475, 1484, 847, 411])).
% 8.81/9.11 tff(15934,plain,
% 8.81/9.11 (b(s(z), z)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[180, 15933])).
% 8.81/9.11 tff(15935,plain,
% 8.81/9.11 (~b(s(s(z)), z)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[14843, 15934, 847, 5547, 1484, 15932, 665])).
% 8.81/9.11 tff(15936,plain,
% 8.81/9.11 (r(s(s(z)), z)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[1211, 15935])).
% 8.81/9.11 tff(15937,plain,
% 8.81/9.11 (~b(s(s(s(s(z)))), s(s(z)))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[15042, 15936, 847, 5547, 1234, 411, 665, 1405, 1652])).
% 8.81/9.11 tff(15938,plain,
% 8.81/9.11 (~b(s(s(s(s(z)))), z)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[14978, 15934, 15932, 665, 1652])).
% 8.81/9.11 tff(15939,plain,
% 8.81/9.11 (r(s(s(s(s(z)))), z)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[87, 15938])).
% 8.81/9.11 tff(15940,plain,
% 8.81/9.11 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[14769, 15936, 15939, 184])).
% 8.81/9.11 tff(15941,plain,
% 8.81/9.11 ($false),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[1714, 15940, 15937])).
% 8.81/9.11 tff(15942,plain,((~r(s(z), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (s(s(z)) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.11 tff(15943,plain,
% 8.81/9.11 (~r(s(z), elem!1)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[15942, 14703, 59, 14710, 15930, 15923, 15922, 3694, 15925])).
% 8.81/9.11 tff(15944,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[632, 15943, 14716])).
% 8.81/9.11 tff(15945,plain,
% 8.81/9.11 (~b(elem!1, s(s(s(s(z)))))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[10491, 15944, 15922, 15930, 15925])).
% 8.81/9.11 tff(15946,plain,
% 8.81/9.11 (r(elem!1, s(s(s(s(z)))))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[781, 15945, 3696])).
% 8.81/9.11 tff(15947,plain,
% 8.81/9.11 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[14788, 15946, 3807])).
% 8.81/9.11 tff(15948,plain,
% 8.81/9.11 (~r(z, s(s(s(s(z)))))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[10090, 2053, 4317, 184])).
% 8.81/9.11 tff(15949,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[800, 15948])).
% 8.81/9.11 tff(15950,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[14799, 15949, 1652, 1234, 665])).
% 8.81/9.11 tff(15951,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[180, 15950])).
% 8.81/9.11 tff(15952,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[845, 15951, 847, 411])).
% 8.81/9.11 tff(15953,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[678, 15952])).
% 8.81/9.11 tff(15954,plain,
% 8.81/9.11 (~r(s(s(s(s(z)))), s(z))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[3243, 15951, 2053, 411])).
% 8.81/9.11 tff(15955,plain,
% 8.81/9.11 (b(s(s(s(s(z)))), s(z))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[749, 15954])).
% 8.81/9.11 tff(15956,plain,
% 8.81/9.11 ($false),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[10478, 15955, 15953, 1234, 15949])).
% 8.81/9.11 tff(15957,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.11 tff(15958,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[15957, 15930, 15923, 14703, 15925, 15922, 15947, 59])).
% 8.81/9.11 tff(15959,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[87, 15958])).
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[4246, 15959, 15922, 15925])).
% 8.81/9.11 tff(15961,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[800, 15960])).
% 8.81/9.11 tff(15962,plain,
% 8.81/9.11 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[15016, 15961, 15923, 15946])).
% 8.81/9.11 tff(15963,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[1714, 15962])).
% 8.81/9.11 tff(15964,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[15042, 15963, 14703, 14710, 15930, 15923, 15922, 3694, 15925])).
% 8.81/9.11 tff(15965,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[15079, 15959, 14703, 14710, 15923, 15922, 15930, 3694, 15925, 3696, 14716])).
% 8.81/9.11 tff(15966,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[678, 15965])).
% 8.81/9.11 tff(15967,plain,
% 8.81/9.11 (b(s(z), s(s(s(elem!1))))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[14872, 15944, 5])).
% 8.81/9.11 tff(15968,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[14992, 15963, 15967, 15959, 15966])).
% 8.81/9.11 tff(15969,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[1211, 15968, 15964])).
% 8.81/9.11 tff(15970,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(elem!1))), s(z))) | r(elem!1, z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.11 tff(15971,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[15970, 10, 5, 183])).
% 8.81/9.11 tff(15972,plain,
% 8.81/9.11 (r(s(s(s(elem!1))), z)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[533, 15971, 5])).
% 8.81/9.11 tff(15973,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[7211, 194, 15972, 59, 15918, 15910])).
% 8.81/9.11 tff(15974,plain,(b(z, s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 8.81/9.11 tff(15975,plain,
% 8.81/9.11 (b(z, s(s(s(elem!1))))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[15974, 15897, 3823, 1686, 15886, 2053, 1810, 15895, 2])).
% 8.81/9.11 tff(15976,plain,
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% 8.81/9.11 inference(modus_ponens,[status(thm)],[15975, 15893])).
% 8.81/9.11 tff(15977,plain,
% 8.81/9.11 (~b(s(s(s(s(z)))), elem!1)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[15860, 15976, 15890, 1686])).
% 8.81/9.11 tff(15978,plain,
% 8.81/9.11 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[2694, 15977, 15886])).
% 8.81/9.11 tff(15979,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[762, 15977, 15888])).
% 8.81/9.11 tff(15980,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[5396, 15979, 1810, 1216])).
% 8.81/9.11 tff(15981,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[632, 15980, 1496])).
% 8.81/9.11 tff(15982,plain,
% 8.81/9.11 (b(s(z), s(s(s(elem!1))))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[14872, 15981, 15886])).
% 8.81/9.11 tff(15983,plain,
% 8.81/9.11 (~r(s(s(z)), s(z))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[11220, 1759, 31, 2, 4028, 3823, 590, 1216, 2053])).
% 8.81/9.11 tff(15984,plain,
% 8.81/9.11 (b(s(s(z)), s(z))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[3778, 15983])).
% 8.81/9.11 tff(15985,plain,
% 8.81/9.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.81/9.11 inference(rewrite,[status(thm)],[])).
% 8.81/9.11 tff(15986,plain,
% 8.81/9.11 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.81/9.11 inference(rewrite,[status(thm)],[])).
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% 8.81/9.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 8.81/9.11 inference(monotonicity,[status(thm)],[15986])).
% 8.81/9.11 tff(15988,plain,
% 8.81/9.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.81/9.11 inference(transitivity,[status(thm)],[15987, 15985])).
% 8.81/9.11 tff(15989,plain,
% 8.81/9.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 8.81/9.11 inference(quant_inst,[status(thm)],[])).
% 8.81/9.11 tff(15990,plain,
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% 8.81/9.11 inference(modus_ponens,[status(thm)],[15989, 15988])).
% 8.81/9.11 tff(15991,plain,
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% 8.81/9.11 inference(unit_resolution,[status(thm)],[15990, 391, 379, 3823, 1759, 15984, 1669])).
% 8.81/9.11 tff(15992,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(elem!1, s(z)) | (elem!1 = z) | b(elem!1, s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.11 tff(15993,plain,
% 8.81/9.11 (~b(s(s(s(s(z)))), s(z))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[15992, 15982, 3823, 15897, 31, 2, 4028, 590, 1216, 2053])).
% 8.81/9.11 tff(15994,plain,
% 8.81/9.11 (r(s(s(s(s(z)))), s(z))),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[749, 15993])).
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% 8.81/9.11 tff(15996,plain,((elem!1 = s(z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(z)) | (elem!1 = z) | b(elem!1, s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.11 tff(15997,plain,
% 8.81/9.11 (elem!1 = s(z)),
% 8.81/9.11 inference(unit_resolution,[status(thm)],[15996, 4028, 3823, 31, 10680, 2913, 15879, 2053, 1686, 8329])).
% 8.81/9.11 tff(15998,plain,
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% 8.81/9.11 tff(15999,plain,
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% 8.81/9.11 tff(16000,plain,
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% 8.81/9.11 tff(16002,plain,
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% 8.81/9.12 tff(16003,plain,
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% 8.81/9.12 tff(16004,plain,
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% 8.81/9.12 tff(16005,plain,
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% 8.81/9.12 tff(16006,plain,
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% 8.81/9.12 tff(16007,plain,
% 8.81/9.12 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
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% 8.81/9.12 tff(16008,plain,
% 8.81/9.12 ((s(s(s(elem!1))) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
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% 8.81/9.12 tff(16009,plain,
% 8.81/9.12 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
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% 8.81/9.12 tff(16010,plain,
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% 8.81/9.12 tff(16011,plain,
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% 8.81/9.12 tff(16012,plain,
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% 8.81/9.12 tff(16014,plain,
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% 8.81/9.12 tff(16015,plain,
% 8.81/9.12 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
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% 8.81/9.12 tff(16016,plain,
% 8.81/9.12 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
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% 8.81/9.12 tff(16017,plain,
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% 8.81/9.12 tff(16018,plain,
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% 8.81/9.12 inference(unit_resolution,[status(thm)],[10743, 16000, 16002, 16017])).
% 8.81/9.12 tff(16019,plain,
% 8.81/9.12 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[8251, 16011])).
% 8.81/9.12 tff(16020,plain,
% 8.81/9.12 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[1370, 16019, 8329])).
% 8.81/9.12 tff(16021,plain,
% 8.81/9.12 (~r(s(s(elem!1)), elem!1)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[4039, 16020, 4028, 16018, 16011])).
% 8.81/9.12 tff(16022,plain,
% 8.81/9.12 (b(s(s(elem!1)), elem!1)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[872, 16021, 16006])).
% 8.81/9.12 tff(16023,plain,
% 8.81/9.12 (~b(z, s(s(elem!1)))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[4944, 16022, 16002, 16000])).
% 8.81/9.12 tff(16024,plain,
% 8.81/9.12 (r(z, s(s(elem!1)))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[324, 16023])).
% 8.81/9.12 tff(16025,plain,
% 8.81/9.12 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 8.81/9.12 inference(monotonicity,[status(thm)],[16013])).
% 8.81/9.12 tff(16026,plain,
% 8.81/9.12 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.81/9.12 inference(symmetry,[status(thm)],[16025])).
% 8.81/9.12 tff(16027,plain,
% 8.81/9.12 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 8.81/9.12 inference(monotonicity,[status(thm)],[16014, 16013])).
% 8.81/9.12 tff(16028,plain,
% 8.81/9.12 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.81/9.12 inference(transitivity,[status(thm)],[16027, 16026])).
% 8.81/9.12 tff(16029,plain,
% 8.81/9.12 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.81/9.12 inference(modus_ponens,[status(thm)],[16020, 16028])).
% 8.81/9.12 tff(16030,plain,
% 8.81/9.12 (~r(s(s(elem!1)), z)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[9284, 16029, 2053, 16024])).
% 8.81/9.12 tff(16031,plain,
% 8.81/9.12 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 8.81/9.12 inference(monotonicity,[status(thm)],[819, 812])).
% 8.81/9.12 tff(16032,plain,
% 8.81/9.12 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), s(z))),
% 8.81/9.12 inference(symmetry,[status(thm)],[16031])).
% 8.81/9.12 tff(16033,plain,
% 8.81/9.12 (b(s(s(s(z))), s(z))),
% 8.81/9.12 inference(modus_ponens,[status(thm)],[973, 16032])).
% 8.81/9.12 tff(16034,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 8.81/9.12 tff(16035,plain,
% 8.81/9.12 ($false),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[16034, 16033])).
% 8.81/9.12 tff(16036,plain,((~(s(z) = elem!1)) | b(s(s(s(z))), s(z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.81/9.12 tff(16037,plain,
% 8.81/9.12 (b(s(s(s(z))), s(z))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[16036, 16022, 16001])).
% 8.81/9.12 tff(16038,plain,
% 8.81/9.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.12 inference(rewrite,[status(thm)],[])).
% 8.81/9.12 tff(16039,plain,
% 8.81/9.12 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.12 inference(rewrite,[status(thm)],[])).
% 8.81/9.12 tff(16040,plain,
% 8.81/9.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z))))))))),
% 8.81/9.12 inference(monotonicity,[status(thm)],[16039])).
% 8.81/9.12 tff(16041,plain,
% 8.81/9.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.12 inference(transitivity,[status(thm)],[16040, 16038])).
% 8.81/9.12 tff(16042,plain,
% 8.81/9.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 8.81/9.12 inference(quant_inst,[status(thm)],[])).
% 8.81/9.12 tff(16043,plain,
% 8.81/9.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z))))))),
% 8.81/9.12 inference(modus_ponens,[status(thm)],[16042, 16041])).
% 8.81/9.12 tff(16044,plain,
% 8.81/9.12 (~b(s(s(s(z))), z)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[16043, 391, 1686, 15465, 15879, 16037])).
% 8.81/9.12 tff(16045,plain,
% 8.81/9.12 (~b(s(s(elem!1)), z)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[7886, 16044, 16001])).
% 8.81/9.12 tff(16046,plain,
% 8.81/9.12 ($false),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[2629, 16045, 16030])).
% 8.81/9.12 tff(16047,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(z)) | b(s(z), s(s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.81/9.12 tff(16048,plain,
% 8.81/9.12 (b(elem!1, s(s(s(elem!1))))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[16047, 15463, 3447, 8329, 3823, 31, 2881, 115])).
% 8.81/9.12 tff(16049,plain,
% 8.81/9.12 (~(elem!1 = s(z))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[8314, 16048, 2881])).
% 8.81/9.12 tff(16050,plain,
% 8.81/9.12 (r(elem!1, s(z))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[837, 16049, 31])).
% 8.81/9.12 tff(16051,plain,
% 8.81/9.12 (~(s(z) = elem!1)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[1495, 16049])).
% 8.81/9.12 tff(16052,plain,
% 8.81/9.12 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[2849, 16051])).
% 8.81/9.12 tff(16053,plain,
% 8.81/9.12 (~(s(s(s(elem!1))) = elem!1)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[15370, 16048])).
% 8.81/9.12 tff(16054,plain,
% 8.81/9.12 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[8251, 16053])).
% 8.81/9.12 tff(16055,plain,
% 8.81/9.12 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[1370, 16054, 8329])).
% 8.81/9.12 tff(16056,plain,
% 8.81/9.12 (~r(s(z), z)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[2061, 15899, 2053, 1216])).
% 8.81/9.12 tff(16057,plain,
% 8.81/9.12 (b(s(z), z)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[180, 16056])).
% 8.81/9.12 tff(16058,plain,
% 8.81/9.12 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[10940, 3843])).
% 8.81/9.12 tff(16059,plain,
% 8.81/9.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.12 inference(rewrite,[status(thm)],[])).
% 8.81/9.12 tff(16060,plain,
% 8.81/9.12 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.12 inference(rewrite,[status(thm)],[])).
% 8.81/9.12 tff(16061,plain,
% 8.81/9.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 8.81/9.12 inference(monotonicity,[status(thm)],[16060])).
% 8.81/9.12 tff(16062,plain,
% 8.81/9.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 8.81/9.12 inference(transitivity,[status(thm)],[16061, 16059])).
% 8.81/9.12 tff(16063,plain,
% 8.81/9.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 8.81/9.12 inference(quant_inst,[status(thm)],[])).
% 8.81/9.12 tff(16064,plain,
% 8.81/9.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 8.81/9.12 inference(modus_ponens,[status(thm)],[16063, 16062])).
% 8.81/9.12 tff(16065,plain,
% 8.81/9.12 (~b(s(s(s(elem!1))), z)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[16064, 391, 1526, 1686, 664, 590])).
% 8.81/9.12 tff(16066,plain,
% 8.81/9.12 (r(s(s(s(elem!1))), z)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[377, 16065])).
% 8.81/9.12 tff(16067,plain,
% 8.81/9.12 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[11060, 194, 411, 16066, 2053])).
% 8.81/9.12 tff(16068,plain,
% 8.81/9.12 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[15351, 16067, 16058])).
% 8.81/9.12 tff(16069,plain,
% 8.81/9.12 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[15335, 16066, 2053, 184])).
% 8.81/9.12 tff(16070,plain,
% 8.81/9.12 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 16069])).
% 8.81/9.12 tff(16071,plain,
% 8.81/9.12 (~b(s(s(z)), z)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[15916, 391, 3823, 1686, 16070, 16068])).
% 8.81/9.12 tff(16072,plain,
% 8.81/9.12 (r(s(s(z)), z)),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[1211, 16071])).
% 8.81/9.12 tff(16073,plain,
% 8.81/9.12 (~r(s(s(s(s(z)))), s(s(z)))),
% 8.81/9.12 inference(unit_resolution,[status(thm)],[14769, 16072, 2053, 184])).
% 8.91/9.13 tff(16074,plain,
% 8.91/9.13 (~b(s(s(s(s(z)))), s(s(z)))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[15345, 16072, 590, 3843, 1526, 2053, 664])).
% 8.91/9.13 tff(16075,plain,
% 8.91/9.13 ($false),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[1714, 16074, 16073])).
% 8.91/9.13 tff(16076,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.91/9.13 tff(16077,plain,
% 8.91/9.13 (~b(s(s(s(elem!1))), s(z))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[16076, 16057, 3843, 2053, 10679, 59, 3823, 1686, 15899])).
% 8.91/9.13 tff(16078,plain,
% 8.91/9.13 (r(s(s(s(elem!1))), s(z))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[223, 16077])).
% 8.91/9.13 tff(16079,plain,
% 8.91/9.13 (~r(s(s(s(elem!1))), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[10856, 16078, 1216, 847])).
% 8.91/9.13 tff(16080,plain,
% 8.91/9.13 (b(s(s(s(elem!1))), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[230, 16079, 15376])).
% 8.91/9.13 tff(16081,plain,
% 8.91/9.13 (~r(s(s(elem!1)), s(z))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[11169, 16078, 1216, 327])).
% 8.91/9.13 tff(16082,plain,
% 8.91/9.13 (b(s(s(elem!1)), s(z))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[362, 16081])).
% 8.91/9.13 tff(16083,plain,
% 8.91/9.13 (~(s(s(elem!1)) = elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[912, 16082, 31])).
% 8.91/9.13 tff(16084,plain,
% 8.91/9.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 8.91/9.13 inference(rewrite,[status(thm)],[])).
% 8.91/9.13 tff(16085,plain,
% 8.91/9.13 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 8.91/9.13 inference(rewrite,[status(thm)],[])).
% 8.91/9.13 tff(16086,plain,
% 8.91/9.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))))),
% 8.91/9.13 inference(monotonicity,[status(thm)],[16085])).
% 8.91/9.13 tff(16087,plain,
% 8.91/9.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 8.91/9.13 inference(transitivity,[status(thm)],[16086, 16084])).
% 8.91/9.13 tff(16088,plain,
% 8.91/9.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 8.91/9.13 inference(quant_inst,[status(thm)],[])).
% 8.91/9.13 tff(16089,plain,
% 8.91/9.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))),
% 8.91/9.13 inference(modus_ponens,[status(thm)],[16088, 16087])).
% 8.91/9.13 tff(16090,plain,
% 8.91/9.13 (~b(z, s(s(elem!1)))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[16089, 391, 16082, 1686, 10679, 16057])).
% 8.91/9.13 tff(16091,plain,
% 8.91/9.13 (r(z, s(s(elem!1)))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[324, 16090])).
% 8.91/9.13 tff(16092,plain,
% 8.91/9.13 (~r(s(s(elem!1)), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[372, 16091, 59, 327])).
% 8.91/9.13 tff(16093,plain,
% 8.91/9.13 (b(s(s(elem!1)), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[872, 16092, 16083])).
% 8.91/9.13 tff(16094,plain,
% 8.91/9.13 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[8251, 15376])).
% 8.91/9.13 tff(16095,plain,
% 8.91/9.13 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[314, 16094])).
% 8.91/9.13 tff(16096,plain,
% 8.91/9.13 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[1418, 16091, 59, 16078])).
% 8.91/9.13 tff(16097,plain,
% 8.91/9.13 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[1356, 16096, 16095])).
% 8.91/9.13 tff(16098,plain,
% 8.91/9.13 ($false),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[6001, 16097, 16093, 448, 16080])).
% 8.91/9.13 tff(16099,plain,(b(z, s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | b(elem!1, s(z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 8.91/9.13 tff(16100,plain,
% 8.91/9.13 (b(z, s(s(s(elem!1))))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[16099, 16048, 16055, 15463, 31, 2913, 16050, 16052, 3447, 3823, 10680])).
% 8.91/9.13 tff(16101,plain,
% 8.91/9.13 (~b(s(s(s(elem!1))), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[10845, 133, 448, 10682])).
% 8.91/9.13 tff(16102,plain,
% 8.91/9.13 (r(s(s(s(elem!1))), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[230, 16101, 15376])).
% 8.91/9.13 tff(16103,plain,
% 8.91/9.13 (~r(s(s(s(elem!1))), s(z))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[10856, 16102, 1216, 847])).
% 8.91/9.13 tff(16104,plain,
% 8.91/9.13 (b(s(s(s(elem!1))), s(z))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[223, 16103])).
% 8.91/9.13 tff(16105,plain,
% 8.91/9.13 (~b(s(z), s(s(s(elem!1))))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[15561, 16104, 664, 10682])).
% 8.91/9.13 tff(16106,plain,
% 8.91/9.13 (r(s(z), s(s(s(elem!1))))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[247, 16105])).
% 8.91/9.13 tff(16107,plain,
% 8.91/9.13 (b(s(z), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[5246, 16106, 31, 150, 16102])).
% 8.91/9.13 tff(16108,plain,
% 8.91/9.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 8.91/9.13 inference(rewrite,[status(thm)],[])).
% 8.91/9.13 tff(16109,plain,
% 8.91/9.13 (((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 8.91/9.13 inference(rewrite,[status(thm)],[])).
% 8.91/9.13 tff(16110,plain,
% 8.91/9.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 8.91/9.13 inference(monotonicity,[status(thm)],[16109])).
% 8.91/9.13 tff(16111,plain,
% 8.91/9.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 8.91/9.13 inference(transitivity,[status(thm)],[16110, 16108])).
% 8.91/9.13 tff(16112,plain,
% 8.91/9.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 8.91/9.13 inference(quant_inst,[status(thm)],[])).
% 8.91/9.13 tff(16113,plain,
% 8.91/9.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 8.91/9.13 inference(modus_ponens,[status(thm)],[16112, 16111])).
% 8.91/9.13 tff(16114,plain,
% 8.91/9.13 ($false),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[16113, 391, 133, 448, 16107, 16104, 664])).
% 8.91/9.13 tff(16115,plain,((~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | b(elem!1, s(z)) | (s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.91/9.13 tff(16116,plain,
% 8.91/9.13 (~b(z, elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[16115, 16048, 10643, 31, 16051, 16100, 2913, 16050])).
% 8.91/9.13 tff(16117,plain,
% 8.91/9.13 (r(z, elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[141, 16116, 115])).
% 8.91/9.13 tff(16118,plain,
% 8.91/9.13 (~r(s(s(s(s(z)))), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[10408, 16117, 3447, 16050])).
% 8.91/9.13 tff(16119,plain,
% 8.91/9.13 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 8.91/9.13 inference(monotonicity,[status(thm)],[688])).
% 8.91/9.13 tff(16120,plain,
% 8.91/9.13 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 8.91/9.13 inference(symmetry,[status(thm)],[16119])).
% 8.91/9.13 tff(16121,plain,
% 8.91/9.13 ((~b(z, elem!1)) <=> (~b(z, s(s(s(s(z))))))),
% 8.91/9.13 inference(monotonicity,[status(thm)],[16120])).
% 8.91/9.13 tff(16122,plain,
% 8.91/9.13 (~b(z, s(s(s(s(z)))))),
% 8.91/9.13 inference(modus_ponens,[status(thm)],[89, 16121])).
% 8.91/9.13 tff(16123,plain,
% 8.91/9.13 ($false),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[1686, 16122])).
% 8.91/9.13 tff(16124,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(z, s(s(s(s(z)))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 8.91/9.13 tff(16125,plain,
% 8.91/9.13 (~(s(s(s(s(z)))) = elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[16124, 15463, 16116])).
% 8.91/9.13 tff(16126,plain,
% 8.91/9.13 (b(s(s(s(s(z)))), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[762, 16125, 16118])).
% 8.91/9.13 tff(16127,plain,
% 8.91/9.13 (~r(s(z), z)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[2061, 16117, 3447, 2913])).
% 8.91/9.13 tff(16128,plain,
% 8.91/9.13 (b(s(z), z)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[180, 16127])).
% 8.91/9.13 tff(16129,plain,
% 8.91/9.13 (~b(s(s(s(elem!1))), s(z))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[10690, 16128, 10643, 16100])).
% 8.91/9.13 tff(16130,plain,
% 8.91/9.13 (r(s(s(s(elem!1))), s(z))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[223, 16129])).
% 8.91/9.13 tff(16131,plain,
% 8.91/9.13 (~r(s(s(elem!1)), s(z))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[11169, 16130, 2913, 16055])).
% 8.91/9.13 tff(16132,plain,
% 8.91/9.13 (b(s(s(elem!1)), s(z))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[362, 16131])).
% 8.91/9.13 tff(16133,plain,
% 8.91/9.13 (~(s(s(elem!1)) = elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[912, 16132, 31])).
% 8.91/9.13 tff(16134,plain,
% 8.91/9.13 (~r(s(s(s(elem!1))), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[10856, 16130, 2913, 16050])).
% 8.91/9.13 tff(16135,plain,
% 8.91/9.13 (b(s(s(s(elem!1))), elem!1)),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[230, 16134, 16053])).
% 8.91/9.13 tff(16136,plain,
% 8.91/9.13 (~(elem!1 = s(s(s(elem!1))))),
% 8.91/9.13 inference(unit_resolution,[status(thm)],[129, 16053])).
% 8.91/9.13 tff(16137,plain,
% 8.91/9.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 8.91/9.13 inference(rewrite,[status(thm)],[])).
% 8.91/9.13 tff(16138,plain,
% 8.91/9.13 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 8.91/9.14 inference(rewrite,[status(thm)],[])).
% 8.91/9.14 tff(16139,plain,
% 8.91/9.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 8.91/9.14 inference(monotonicity,[status(thm)],[16138])).
% 8.91/9.14 tff(16140,plain,
% 8.91/9.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 8.91/9.14 inference(transitivity,[status(thm)],[16139, 16137])).
% 8.91/9.14 tff(16141,plain,
% 8.91/9.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 8.91/9.14 inference(quant_inst,[status(thm)],[])).
% 8.91/9.14 tff(16142,plain,
% 8.91/9.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z))),
% 8.91/9.14 inference(modus_ponens,[status(thm)],[16141, 16140])).
% 8.91/9.14 tff(16143,plain,
% 8.91/9.14 (~b(z, s(s(elem!1)))),
% 8.91/9.14 inference(unit_resolution,[status(thm)],[16142, 391, 16132, 16100, 10643, 16128])).
% 8.91/9.14 tff(16144,plain,
% 8.91/9.14 (r(z, s(s(elem!1)))),
% 8.91/9.14 inference(unit_resolution,[status(thm)],[324, 16143])).
% 8.91/9.14 tff(16145,plain,
% 8.91/9.14 (~r(elem!1, s(s(s(elem!1))))),
% 8.91/9.14 inference(unit_resolution,[status(thm)],[2562, 326, 411, 364])).
% 8.91/9.14 tff(16146,plain,
% 8.91/9.14 (b(elem!1, s(s(s(elem!1))))),
% 8.91/9.14 inference(unit_resolution,[status(thm)],[424, 16145, 1])).
% 8.91/9.14 tff(16147,plain,
% 8.91/9.14 (~r(elem!1, z)),
% 8.91/9.14 inference(unit_resolution,[status(thm)],[867, 326, 364, 411])).
% 8.91/9.14 tff(16148,plain,
% 8.91/9.14 (b(elem!1, z)),
% 8.91/9.14 inference(unit_resolution,[status(thm)],[526, 16147, 2])).
% 8.91/9.14 tff(16149,plain,
% 8.91/9.14 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 8.91/9.14 inference(rewrite,[status(thm)],[])).
% 8.91/9.14 tff(16150,plain,
% 8.91/9.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 8.91/9.14 inference(monotonicity,[status(thm)],[16149])).
% 8.91/9.14 tff(16151,plain,
% 8.91/9.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 8.91/9.14 inference(transitivity,[status(thm)],[16150, 10906])).
% 8.91/9.14 tff(16152,plain,
% 8.91/9.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 8.91/9.14 inference(quant_inst,[status(thm)],[])).
% 8.91/9.14 tff(16153,plain,
% 8.91/9.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 8.91/9.14 inference(modus_ponens,[status(thm)],[16152, 16151])).
% 8.91/9.14 tff(16154,plain,
% 8.91/9.14 ($false),
% 8.91/9.14 inference(unit_resolution,[status(thm)],[16153, 391, 16148, 900, 10682, 16146])).
% 8.91/9.14 tff(16155,plain,((~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 8.91/9.14 tff(16156,plain,
% 8.91/9.14 (~r(s(s(elem!1)), elem!1)),
% 8.91/9.14 inference(unit_resolution,[status(thm)],[16155, 16144, 16117, 16100, 16136, 16135, 10680])).
% 8.91/9.14 tff(16157,plain,
% 8.91/9.14 (b(s(s(elem!1)), elem!1)),
% 8.91/9.14 inference(unit_resolution,[status(thm)],[872, 16156, 16133])).
% 8.91/9.14 tff(16158,plain,
% 8.91/9.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.91/9.14 inference(rewrite,[status(thm)],[])).
% 8.91/9.14 tff(16159,plain,
% 8.91/9.14 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.91/9.14 inference(rewrite,[status(thm)],[])).
% 8.91/9.14 tff(16160,plain,
% 8.91/9.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 8.91/9.14 inference(monotonicity,[status(thm)],[16159])).
% 8.91/9.14 tff(16161,plain,
% 8.91/9.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.91/9.14 inference(transitivity,[status(thm)],[16160, 16158])).
% 8.91/9.14 tff(16162,plain,
% 8.91/9.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 8.91/9.14 inference(quant_inst,[status(thm)],[])).
% 8.91/9.14 tff(16163,plain,
% 8.91/9.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 8.91/9.15 inference(modus_ponens,[status(thm)],[16162, 16161])).
% 8.91/9.15 tff(16164,plain,
% 8.91/9.15 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[16163, 391, 16135, 16157, 16048, 16126])).
% 8.91/9.15 tff(16165,plain,
% 8.91/9.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 8.91/9.15 inference(rewrite,[status(thm)],[])).
% 8.91/9.15 tff(16166,plain,
% 8.91/9.15 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 8.91/9.15 inference(rewrite,[status(thm)],[])).
% 8.91/9.15 tff(16167,plain,
% 8.91/9.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))))),
% 8.91/9.15 inference(monotonicity,[status(thm)],[16166])).
% 8.91/9.15 tff(16168,plain,
% 8.91/9.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 8.91/9.15 inference(transitivity,[status(thm)],[16167, 16165])).
% 8.91/9.15 tff(16169,plain,
% 8.91/9.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 8.91/9.15 inference(quant_inst,[status(thm)],[])).
% 8.91/9.15 tff(16170,plain,
% 8.91/9.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))),
% 8.91/9.15 inference(modus_ponens,[status(thm)],[16169, 16168])).
% 8.91/9.15 tff(16171,plain,
% 8.91/9.15 (~b(s(s(elem!1)), z)),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[16170, 391, 16132, 16100, 10643, 16128])).
% 8.91/9.15 tff(16172,plain,
% 8.91/9.15 (r(s(s(elem!1)), z)),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[2629, 16171])).
% 8.91/9.15 tff(16173,plain,
% 8.91/9.15 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[9284, 16172, 3447, 16144])).
% 8.91/9.15 tff(16174,plain,
% 8.91/9.15 ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[2003, 42, 16173])).
% 8.91/9.15 tff(16175,plain,
% 8.91/9.15 (s(s(s(s(z)))) = s(s(elem!1))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[16174, 16164])).
% 8.91/9.15 tff(16176,plain,
% 8.91/9.15 (elem!1 = s(s(z))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[1407, 16175])).
% 8.91/9.15 tff(16177,plain,
% 8.91/9.15 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[314, 16054])).
% 8.91/9.15 tff(16178,plain,
% 8.91/9.15 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[6001, 16157, 16048, 16135])).
% 8.91/9.15 tff(16179,plain,
% 8.91/9.15 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[1356, 16178, 16177])).
% 8.91/9.15 tff(16180,plain,
% 8.91/9.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.91/9.15 inference(rewrite,[status(thm)],[])).
% 8.91/9.15 tff(16181,plain,
% 8.91/9.15 (((~r(z, 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)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.91/9.15 inference(rewrite,[status(thm)],[])).
% 8.91/9.15 tff(16182,plain,
% 8.91/9.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 8.91/9.15 inference(monotonicity,[status(thm)],[16181])).
% 8.91/9.15 tff(16183,plain,
% 8.91/9.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 8.91/9.15 inference(transitivity,[status(thm)],[16182, 16180])).
% 8.91/9.15 tff(16184,plain,
% 8.91/9.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))),
% 8.91/9.15 inference(quant_inst,[status(thm)],[])).
% 8.91/9.15 tff(16185,plain,
% 8.91/9.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 8.91/9.15 inference(modus_ponens,[status(thm)],[16184, 16183])).
% 8.91/9.15 tff(16186,plain,
% 8.91/9.15 ($false),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[16185, 194, 411, 174, 1378, 2616])).
% 8.91/9.15 tff(16187,plain,((~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.91/9.15 tff(16188,plain,
% 8.91/9.15 (~r(s(s(s(elem!1))), z)),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[16187, 16179, 16117, 16172])).
% 8.91/9.15 tff(16189,plain,
% 8.91/9.15 (b(s(s(s(elem!1))), z)),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[377, 16188])).
% 8.91/9.15 tff(16190,plain,
% 8.91/9.15 (~b(s(z), s(s(s(elem!1))))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[11303, 16189, 16128, 16100])).
% 8.91/9.15 tff(16191,plain,
% 8.91/9.15 (r(s(z), s(s(s(elem!1))))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[247, 16190])).
% 8.91/9.15 tff(16192,plain,
% 8.91/9.15 (~r(s(z), s(s(elem!1)))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[4840, 16191, 16172, 16055])).
% 8.91/9.15 tff(16193,plain,
% 8.91/9.15 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[3414, 42, 16192])).
% 8.91/9.15 tff(16194,plain,
% 8.91/9.15 (b(s(z), s(s(elem!1)))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[16193, 3404])).
% 8.91/9.15 tff(16195,plain,
% 8.91/9.15 (~(elem!1 = s(s(elem!1)))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[1292, 16133])).
% 8.91/9.15 tff(16196,plain,
% 8.91/9.15 (~b(elem!1, z)),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[10911, 391, 16135, 16100, 16048])).
% 8.91/9.15 tff(16197,plain,
% 8.91/9.15 (r(elem!1, z)),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[526, 16196, 10680])).
% 8.91/9.15 tff(16198,plain,
% 8.91/9.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 8.91/9.15 inference(rewrite,[status(thm)],[])).
% 8.91/9.15 tff(16199,plain,
% 8.91/9.15 (((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 8.91/9.15 inference(rewrite,[status(thm)],[])).
% 8.91/9.15 tff(16200,plain,
% 8.91/9.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))))),
% 8.91/9.15 inference(monotonicity,[status(thm)],[16199])).
% 8.91/9.15 tff(16201,plain,
% 8.91/9.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 8.91/9.15 inference(transitivity,[status(thm)],[16200, 16198])).
% 8.91/9.15 tff(16202,plain,
% 8.91/9.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 8.91/9.15 inference(quant_inst,[status(thm)],[])).
% 8.91/9.15 tff(16203,plain,
% 8.91/9.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))),
% 8.91/9.15 inference(modus_ponens,[status(thm)],[16202, 16201])).
% 8.91/9.15 tff(16204,plain,
% 8.91/9.15 (~r(elem!1, s(s(elem!1)))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[16203, 194, 16117, 16197, 16172])).
% 8.91/9.15 tff(16205,plain,
% 8.91/9.15 (b(elem!1, s(s(elem!1)))),
% 8.91/9.15 inference(unit_resolution,[status(thm)],[1307, 16204, 16195])).
% 8.91/9.15 tff(16206,plain,
% 8.91/9.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 8.91/9.15 inference(rewrite,[status(thm)],[])).
% 8.91/9.15 tff(16207,plain,
% 8.91/9.15 (((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 8.91/9.15 inference(rewrite,[status(thm)],[])).
% 8.91/9.15 tff(16208,plain,
% 8.91/9.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 8.91/9.15 inference(monotonicity,[status(thm)],[16207])).
% 8.91/9.15 tff(16209,plain,
% 8.91/9.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 8.91/9.15 inference(transitivity,[status(thm)],[16208, 16206])).
% 8.91/9.15 tff(16210,plain,
% 8.91/9.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 8.91/9.16 inference(quant_inst,[status(thm)],[])).
% 8.91/9.16 tff(16211,plain,
% 8.91/9.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))),
% 8.91/9.16 inference(modus_ponens,[status(thm)],[16210, 16209])).
% 8.91/9.16 tff(16212,plain,
% 8.91/9.16 (~b(s(z), elem!1)),
% 8.91/9.16 inference(unit_resolution,[status(thm)],[16211, 391, 16132, 16205, 16128, 16194])).
% 8.91/9.16 tff(16213,plain,
% 8.91/9.16 (r(s(z), elem!1)),
% 8.91/9.16 inference(unit_resolution,[status(thm)],[632, 16212, 16051])).
% 8.91/9.16 tff(16214,plain,
% 8.91/9.16 (~(s(s(z)) = elem!1)),
% 8.91/9.16 inference(unit_resolution,[status(thm)],[11275, 16192, 2913])).
% 8.91/9.16 tff(16215,plain,
% 8.91/9.16 (~r(elem!1, s(s(s(s(z)))))),
% 8.91/9.16 inference(unit_resolution,[status(thm)],[11195, 16050, 3447, 2913])).
% 8.91/9.16 tff(16216,plain,
% 8.91/9.16 (~(elem!1 = s(s(s(s(z)))))),
% 8.91/9.16 inference(unit_resolution,[status(thm)],[769, 16125])).
% 8.91/9.16 tff(16217,plain,
% 8.91/9.16 (b(elem!1, s(s(s(s(z)))))),
% 8.91/9.16 inference(unit_resolution,[status(thm)],[781, 16216, 16215])).
% 8.91/9.16 tff(16218,plain,
% 8.91/9.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 8.91/9.16 inference(rewrite,[status(thm)],[])).
% 8.91/9.16 tff(16219,plain,
% 8.91/9.16 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 8.91/9.16 inference(rewrite,[status(thm)],[])).
% 8.91/9.16 tff(16220,plain,
% 8.91/9.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 8.91/9.16 inference(monotonicity,[status(thm)],[16219])).
% 8.91/9.16 tff(16221,plain,
% 8.91/9.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 8.91/9.16 inference(transitivity,[status(thm)],[16220, 16218])).
% 8.91/9.16 tff(16222,plain,
% 8.91/9.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 8.91/9.16 inference(quant_inst,[status(thm)],[])).
% 8.91/9.16 tff(16223,plain,
% 8.91/9.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))),
% 8.91/9.16 inference(modus_ponens,[status(thm)],[16222, 16221])).
% 8.91/9.16 tff(16224,plain,
% 8.91/9.16 (~b(s(s(z)), elem!1)),
% 8.91/9.16 inference(unit_resolution,[status(thm)],[16223, 391, 16048, 3823, 16217, 16126])).
% 8.91/9.16 tff(16225,plain,
% 8.91/9.16 (r(s(s(z)), elem!1)),
% 8.91/9.16 inference(unit_resolution,[status(thm)],[4730, 16224, 16214])).
% 8.91/9.16 tff(16226,plain,
% 8.91/9.16 (~r(s(s(z)), s(z))),
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% 8.91/9.17 tff(16289,plain,
% 8.91/9.17 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 8.91/9.17 inference(modus_ponens,[status(thm)],[328, 16288])).
% 8.91/9.17 tff(16290,plain,
% 8.91/9.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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)))))))),
% 8.91/9.17 inference(rewrite,[status(thm)],[])).
% 8.91/9.17 tff(16291,plain,
% 8.91/9.17 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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)))))))),
% 8.91/9.17 inference(rewrite,[status(thm)],[])).
% 8.91/9.17 tff(16292,plain,
% 8.91/9.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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))))))))),
% 8.91/9.17 inference(monotonicity,[status(thm)],[16291])).
% 8.91/9.17 tff(16293,plain,
% 8.91/9.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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)))))))),
% 8.91/9.17 inference(transitivity,[status(thm)],[16292, 16290])).
% 8.91/9.17 tff(16294,plain,
% 8.91/9.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z)))))))),
% 8.91/9.17 inference(quant_inst,[status(thm)],[])).
% 8.91/9.17 tff(16295,plain,
% 8.91/9.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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))))))),
% 8.91/9.17 inference(modus_ponens,[status(thm)],[16294, 16293])).
% 8.91/9.17 tff(16296,plain,
% 8.91/9.17 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 8.91/9.17 inference(unit_resolution,[status(thm)],[16295, 391, 3325, 1669, 16289])).
% 8.91/9.17 tff(16297,plain,
% 8.91/9.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 8.91/9.17 inference(rewrite,[status(thm)],[])).
% 8.91/9.17 tff(16298,plain,
% 8.91/9.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 8.91/9.17 inference(quant_inst,[status(thm)],[])).
% 8.91/9.18 tff(16299,plain,
% 8.91/9.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 8.91/9.18 inference(modus_ponens,[status(thm)],[16298, 16297])).
% 8.91/9.18 tff(16300,plain,
% 8.91/9.18 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 8.91/9.18 inference(unit_resolution,[status(thm)],[16299, 42, 16296])).
% 8.91/9.18 tff(16301,plain,
% 8.91/9.18 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 8.91/9.18 inference(unit_resolution,[status(thm)],[16300, 16286])).
% 8.91/9.18 tff(16302,plain,
% 8.91/9.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 8.91/9.18 inference(rewrite,[status(thm)],[])).
% 8.91/9.18 tff(16303,plain,
% 8.91/9.18 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 8.91/9.18 inference(rewrite,[status(thm)],[])).
% 8.91/9.18 tff(16304,plain,
% 8.91/9.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 8.91/9.18 inference(monotonicity,[status(thm)],[16303])).
% 8.91/9.18 tff(16305,plain,
% 8.91/9.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 8.91/9.18 inference(transitivity,[status(thm)],[16304, 16302])).
% 8.91/9.18 tff(16306,plain,
% 8.91/9.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 8.91/9.18 inference(quant_inst,[status(thm)],[])).
% 8.91/9.18 tff(16307,plain,
% 8.91/9.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 8.91/9.18 inference(modus_ponens,[status(thm)],[16306, 16305])).
% 8.91/9.18 tff(16308,plain,
% 8.91/9.18 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 8.91/9.18 inference(unit_resolution,[status(thm)],[16307, 194, 2053, 1216, 16301])).
% 8.91/9.18 tff(16309,assumption,(r(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 8.91/9.18 tff(16310,plain,
% 8.91/9.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 8.91/9.18 inference(rewrite,[status(thm)],[])).
% 8.91/9.18 tff(16311,plain,
% 8.91/9.18 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 8.91/9.18 inference(rewrite,[status(thm)],[])).
% 8.91/9.18 tff(16312,plain,
% 8.91/9.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 8.91/9.18 inference(monotonicity,[status(thm)],[16311])).
% 8.91/9.18 tff(16313,plain,
% 8.91/9.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 8.91/9.18 inference(transitivity,[status(thm)],[16312, 16310])).
% 8.91/9.18 tff(16314,plain,
% 8.91/9.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 8.91/9.18 inference(quant_inst,[status(thm)],[])).
% 8.91/9.18 tff(16315,plain,
% 8.91/9.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 8.91/9.18 inference(modus_ponens,[status(thm)],[16314, 16313])).
% 8.91/9.18 tff(16316,plain,
% 8.91/9.18 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 8.91/9.18 inference(unit_resolution,[status(thm)],[16315, 194, 184, 2053, 16309])).
% 8.91/9.18 tff(16317,plain,
% 8.91/9.18 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.91/9.18 inference(unit_resolution,[status(thm)],[9445, 16316, 125, 16285])).
% 8.91/9.18 tff(16318,plain,
% 8.91/9.18 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 8.91/9.18 inference(modus_ponens,[status(thm)],[16317, 9436])).
% 8.91/9.18 tff(16319,plain,
% 8.91/9.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 8.91/9.18 inference(rewrite,[status(thm)],[])).
% 8.91/9.18 tff(16320,plain,
% 8.91/9.18 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 8.91/9.18 inference(rewrite,[status(thm)],[])).
% 8.91/9.18 tff(16321,plain,
% 8.91/9.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 8.91/9.18 inference(monotonicity,[status(thm)],[16320])).
% 8.91/9.19 tff(16322,plain,
% 8.91/9.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 8.91/9.19 inference(transitivity,[status(thm)],[16321, 16319])).
% 8.91/9.19 tff(16323,plain,
% 8.91/9.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 8.91/9.19 inference(quant_inst,[status(thm)],[])).
% 8.91/9.19 tff(16324,plain,
% 8.91/9.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 8.91/9.19 inference(modus_ponens,[status(thm)],[16323, 16322])).
% 8.91/9.19 tff(16325,plain,
% 8.91/9.19 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[16324, 391, 3325, 1669, 16289])).
% 8.91/9.19 tff(16326,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[16325, 16318])).
% 8.91/9.19 tff(16327,plain,((~r(s(s(s(s(s(elem!1))))), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.91/9.19 tff(16328,plain,
% 8.91/9.19 (~r(s(s(s(s(s(elem!1))))), z)),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[16327, 328, 3325, 1669, 184, 2053, 125])).
% 8.91/9.19 tff(16329,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[8165, 42, 8162, 16328])).
% 8.91/9.19 tff(16330,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[10620, 2053, 1216])).
% 8.91/9.19 tff(16331,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[678, 16330])).
% 8.91/9.19 tff(16332,plain,
% 8.91/9.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 8.91/9.19 inference(rewrite,[status(thm)],[])).
% 8.91/9.19 tff(16333,plain,
% 8.91/9.19 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 8.91/9.19 inference(rewrite,[status(thm)],[])).
% 8.91/9.19 tff(16334,plain,
% 8.91/9.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 8.91/9.19 inference(monotonicity,[status(thm)],[16333])).
% 8.91/9.19 tff(16335,plain,
% 8.91/9.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 8.91/9.19 inference(transitivity,[status(thm)],[16334, 16332])).
% 8.91/9.19 tff(16336,plain,
% 8.91/9.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 8.91/9.19 inference(quant_inst,[status(thm)],[])).
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% 8.91/9.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 8.91/9.19 inference(modus_ponens,[status(thm)],[16336, 16335])).
% 8.91/9.19 tff(16338,plain,
% 8.91/9.19 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[16337, 391, 16331, 590, 16329])).
% 8.91/9.19 tff(16339,plain,
% 8.91/9.19 ((s(z) = s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[8448, 42, 16338])).
% 8.91/9.19 tff(16340,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[16339, 16308, 16280])).
% 8.91/9.19 tff(16341,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.91/9.19 tff(16342,plain,
% 8.91/9.19 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[16341, 3447, 2913, 10639, 10550, 16275, 16271, 59])).
% 8.91/9.19 tff(16343,plain,
% 8.91/9.19 (r(s(s(elem!1)), s(s(s(elem!1))))),
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% 8.91/9.19 tff(16344,plain,
% 8.91/9.19 (~r(s(z), s(s(s(elem!1))))),
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% 8.91/9.19 tff(16345,plain,
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% 8.91/9.19 tff(16346,plain,
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% 8.91/9.19 tff(16348,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[264, 16263])).
% 8.91/9.19 tff(16349,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[287, 16348])).
% 8.91/9.19 tff(16350,plain,
% 8.91/9.19 (~b(s(z), s(s(s(elem!1))))),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[6047, 16346, 59, 10550, 16349, 16347, 3618, 847])).
% 8.91/9.19 tff(16351,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[247, 16350, 16344])).
% 8.91/9.19 tff(16352,plain,(b(s(s(s(s(z)))), z) | (~r(elem!1, s(z))) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, z) | b(elem!1, s(z)) | b(elem!1, s(s(s(elem!1)))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 8.91/9.19 tff(16353,plain,
% 8.91/9.19 (b(s(s(s(s(z)))), z)),
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% 8.91/9.19 tff(16354,plain,
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% 8.91/9.19 tff(16355,plain,
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% 8.91/9.19 tff(16357,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[484, 16356])).
% 8.91/9.19 tff(16358,plain,((~(elem!1 = s(s(s(s(z)))))) | b(elem!1, z) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 8.91/9.19 tff(16359,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[16358, 16353, 484])).
% 8.91/9.19 tff(16360,plain,
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% 8.91/9.19 tff(16361,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[424, 16360, 4028])).
% 8.91/9.19 tff(16362,plain,
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% 8.91/9.19 tff(16363,plain,
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% 8.91/9.19 tff(16364,plain,
% 8.91/9.19 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 8.91/9.19 inference(transitivity,[status(thm)],[16363, 698])).
% 8.91/9.19 tff(16365,plain,
% 8.91/9.19 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
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% 8.91/9.19 tff(16366,plain,
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% 8.91/9.19 inference(modus_ponens,[status(thm)],[1397, 16365])).
% 8.91/9.19 tff(16367,plain,
% 8.91/9.19 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.91/9.19 inference(monotonicity,[status(thm)],[16361])).
% 8.91/9.19 tff(16368,plain,
% 8.91/9.19 (s(s(s(elem!1))) = elem!1),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[129, 16361])).
% 8.91/9.19 tff(16369,plain,
% 8.91/9.19 (r(s(s(s(elem!1))), z)),
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% 8.91/9.19 tff(16370,plain,
% 8.91/9.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 8.91/9.19 inference(rewrite,[status(thm)],[])).
% 8.91/9.19 tff(16371,plain,
% 8.91/9.19 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 8.91/9.19 inference(rewrite,[status(thm)],[])).
% 8.91/9.19 tff(16372,plain,
% 8.91/9.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 8.91/9.19 inference(monotonicity,[status(thm)],[16371])).
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% 8.91/9.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 8.91/9.19 inference(transitivity,[status(thm)],[16372, 16370])).
% 8.91/9.19 tff(16374,plain,
% 8.91/9.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 8.91/9.19 inference(quant_inst,[status(thm)],[])).
% 8.91/9.19 tff(16375,plain,
% 8.91/9.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 8.91/9.19 inference(modus_ponens,[status(thm)],[16374, 16373])).
% 8.91/9.19 tff(16376,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[16375, 194, 174, 183, 722, 1216])).
% 8.91/9.19 tff(16377,plain,((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.91/9.19 tff(16378,plain,
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% 8.91/9.19 inference(unit_resolution,[status(thm)],[16377, 16369, 1216, 183])).
% 8.91/9.19 tff(16379,plain,
% 8.91/9.19 (b(z, s(z))),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[678, 16378])).
% 8.91/9.19 tff(16380,plain,
% 8.91/9.19 (~b(s(s(s(s(z)))), s(z))),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[5575, 391, 90, 16379, 590])).
% 8.91/9.19 tff(16381,plain,
% 8.91/9.19 (r(s(s(s(s(z)))), s(z))),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[749, 16380])).
% 8.91/9.19 tff(16382,plain,
% 8.91/9.19 (~r(elem!1, s(s(s(s(z)))))),
% 8.91/9.19 inference(unit_resolution,[status(thm)],[6347, 16381, 1216, 838])).
% 8.91/9.19 tff(16383,plain,
% 8.91/9.19 (b(elem!1, s(s(s(s(z)))))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[781, 16382, 8922])).
% 8.99/9.20 tff(16384,plain,
% 8.99/9.20 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.99/9.20 inference(modus_ponens,[status(thm)],[16383, 16367])).
% 8.99/9.20 tff(16385,plain,
% 8.99/9.20 (~b(s(s(s(s(z)))), s(z))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[5575, 391, 90, 664, 590])).
% 8.99/9.20 tff(16386,plain,
% 8.99/9.20 (r(s(s(s(s(z)))), s(z))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[749, 16385])).
% 8.99/9.20 tff(16387,plain,
% 8.99/9.20 (~r(s(s(z)), s(z))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[5585, 1749, 590, 664, 1216])).
% 8.99/9.20 tff(16388,plain,
% 8.99/9.20 (b(s(s(z)), s(z))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[3778, 16387])).
% 8.99/9.20 tff(16389,plain,
% 8.99/9.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 8.99/9.20 inference(rewrite,[status(thm)],[])).
% 8.99/9.20 tff(16390,plain,
% 8.99/9.20 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(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)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 8.99/9.20 inference(rewrite,[status(thm)],[])).
% 8.99/9.20 tff(16391,plain,
% 8.99/9.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 8.99/9.20 inference(monotonicity,[status(thm)],[16390])).
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% 8.99/9.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 8.99/9.20 inference(transitivity,[status(thm)],[16391, 16389])).
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% 8.99/9.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 8.99/9.20 inference(quant_inst,[status(thm)],[])).
% 8.99/9.20 tff(16394,plain,
% 8.99/9.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 8.99/9.20 inference(modus_ponens,[status(thm)],[16393, 16392])).
% 8.99/9.20 tff(16395,plain,
% 8.99/9.20 ($false),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[16394, 194, 1749, 1216, 723, 1747])).
% 8.99/9.20 tff(16396,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.20 tff(16397,plain,
% 8.99/9.20 (~r(s(z), s(s(z)))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[16396, 1749, 1216, 723])).
% 8.99/9.20 tff(16398,plain,
% 8.99/9.20 (b(s(z), s(s(z)))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[1788, 16397])).
% 8.99/9.20 tff(16399,plain,
% 8.99/9.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 8.99/9.20 inference(rewrite,[status(thm)],[])).
% 8.99/9.20 tff(16400,plain,
% 8.99/9.20 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 8.99/9.20 inference(rewrite,[status(thm)],[])).
% 8.99/9.20 tff(16401,plain,
% 8.99/9.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 8.99/9.20 inference(monotonicity,[status(thm)],[16400])).
% 8.99/9.20 tff(16402,plain,
% 8.99/9.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 8.99/9.20 inference(transitivity,[status(thm)],[16401, 16399])).
% 8.99/9.20 tff(16403,plain,
% 8.99/9.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 8.99/9.20 inference(quant_inst,[status(thm)],[])).
% 8.99/9.20 tff(16404,plain,
% 8.99/9.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 8.99/9.20 inference(modus_ponens,[status(thm)],[16403, 16402])).
% 8.99/9.20 tff(16405,plain,
% 8.99/9.20 ($false),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[16404, 194, 1749, 3557, 723, 719])).
% 8.99/9.20 tff(16406,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.20 tff(16407,plain,
% 8.99/9.20 (~r(s(s(z)), z)),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[16406, 1749, 719, 723])).
% 8.99/9.20 tff(16408,plain,
% 8.99/9.20 (b(s(s(z)), z)),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[1211, 16407])).
% 8.99/9.20 tff(16409,plain,
% 8.99/9.20 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 8.99/9.20 inference(rewrite,[status(thm)],[])).
% 8.99/9.20 tff(16410,plain,
% 8.99/9.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 8.99/9.20 inference(monotonicity,[status(thm)],[16409])).
% 8.99/9.20 tff(16411,plain,
% 8.99/9.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 8.99/9.20 inference(transitivity,[status(thm)],[16410, 16245])).
% 8.99/9.20 tff(16412,plain,
% 8.99/9.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 8.99/9.20 inference(quant_inst,[status(thm)],[])).
% 8.99/9.20 tff(16413,plain,
% 8.99/9.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 8.99/9.20 inference(modus_ponens,[status(thm)],[16412, 16411])).
% 8.99/9.20 tff(16414,plain,
% 8.99/9.20 ($false),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[16413, 391, 16408, 16398, 16388, 664])).
% 8.99/9.20 tff(16415,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.20 tff(16416,plain,
% 8.99/9.20 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[16415, 719, 664, 16386, 590, 1216])).
% 8.99/9.20 tff(16417,plain,
% 8.99/9.20 (b(s(s(z)), s(s(s(s(z)))))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[3652, 16416])).
% 8.99/9.20 tff(16418,plain,
% 8.99/9.20 (~b(s(s(z)), z)),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[7203, 16417, 664, 90, 590])).
% 8.99/9.20 tff(16419,plain,
% 8.99/9.20 (r(s(s(z)), z)),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[1211, 16418])).
% 8.99/9.20 tff(16420,plain,
% 8.99/9.20 (~r(elem!1, s(s(z)))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[8570, 16419, 530, 719])).
% 8.99/9.20 tff(16421,plain,
% 8.99/9.20 (b(elem!1, s(s(z)))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[3394, 16420, 3820])).
% 8.99/9.20 tff(16422,plain,
% 8.99/9.20 (b(s(s(s(elem!1))), s(s(z)))),
% 8.99/9.20 inference(modus_ponens,[status(thm)],[3369, 3815])).
% 8.99/9.20 tff(16423,assumption,(~b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 8.99/9.20 tff(16424,plain,
% 8.99/9.20 ($false),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[16423, 16422])).
% 8.99/9.20 tff(16425,plain,(b(s(s(s(elem!1))), s(s(z))) | (~b(elem!1, s(s(z)))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.20 tff(16426,plain,
% 8.99/9.20 (b(s(s(s(elem!1))), s(s(z)))),
% 8.99/9.20 inference(unit_resolution,[status(thm)],[16425, 16421, 125])).
% 8.99/9.20 tff(16427,plain,
% 8.99/9.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.20 inference(rewrite,[status(thm)],[])).
% 8.99/9.20 tff(16428,plain,
% 8.99/9.20 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.20 inference(rewrite,[status(thm)],[])).
% 8.99/9.20 tff(16429,plain,
% 8.99/9.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 8.99/9.20 inference(monotonicity,[status(thm)],[16428])).
% 8.99/9.20 tff(16430,plain,
% 8.99/9.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.20 inference(transitivity,[status(thm)],[16429, 16427])).
% 8.99/9.20 tff(16431,plain,
% 8.99/9.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.20 inference(quant_inst,[status(thm)],[])).
% 8.99/9.20 tff(16432,plain,
% 8.99/9.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 8.99/9.21 inference(modus_ponens,[status(thm)],[16431, 16430])).
% 8.99/9.21 tff(16433,plain,
% 8.99/9.21 ($false),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[16432, 391, 16417, 90, 664, 1669, 16426])).
% 8.99/9.21 tff(16434,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(elem!1, z)) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.21 tff(16435,plain,
% 8.99/9.21 (~r(z, s(s(s(s(z)))))),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[16434, 16379, 90, 16384, 16361, 530, 590, 1216])).
% 8.99/9.21 tff(16436,plain,
% 8.99/9.21 (b(z, s(s(s(s(z)))))),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[800, 16435])).
% 8.99/9.21 tff(16437,plain,
% 8.99/9.21 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 8.99/9.21 inference(monotonicity,[status(thm)],[283])).
% 8.99/9.21 tff(16438,plain,
% 8.99/9.21 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 8.99/9.21 inference(symmetry,[status(thm)],[16437])).
% 8.99/9.21 tff(16439,plain,
% 8.99/9.21 (r(elem!1, s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 8.99/9.21 inference(transitivity,[status(thm)],[10018, 16438])).
% 8.99/9.21 tff(16440,plain,
% 8.99/9.21 ((~r(elem!1, s(s(z)))) <=> (~r(s(s(elem!1)), s(s(z))))),
% 8.99/9.21 inference(monotonicity,[status(thm)],[16439])).
% 8.99/9.21 tff(16441,plain,
% 8.99/9.21 (r(s(s(s(elem!1))), z)),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[533, 130, 530])).
% 8.99/9.21 tff(16442,plain,
% 8.99/9.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.99/9.21 inference(rewrite,[status(thm)],[])).
% 8.99/9.21 tff(16443,plain,
% 8.99/9.21 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.99/9.21 inference(rewrite,[status(thm)],[])).
% 8.99/9.21 tff(16444,plain,
% 8.99/9.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 8.99/9.21 inference(monotonicity,[status(thm)],[16443])).
% 8.99/9.21 tff(16445,plain,
% 8.99/9.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 8.99/9.21 inference(transitivity,[status(thm)],[16444, 16442])).
% 8.99/9.21 tff(16446,plain,
% 8.99/9.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 8.99/9.21 inference(quant_inst,[status(thm)],[])).
% 8.99/9.21 tff(16447,plain,
% 8.99/9.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 8.99/9.21 inference(modus_ponens,[status(thm)],[16446, 16445])).
% 8.99/9.21 tff(16448,plain,
% 8.99/9.21 (~b(s(s(z)), s(s(s(elem!1))))),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[16447, 391, 3823, 90, 1686, 1669])).
% 8.99/9.21 tff(16449,plain,
% 8.99/9.21 (~b(s(s(z)), z)),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[7203, 3823, 664, 90, 590])).
% 8.99/9.21 tff(16450,plain,
% 8.99/9.21 (r(s(s(z)), z)),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[1211, 16449])).
% 8.99/9.21 tff(16451,plain,
% 8.99/9.21 (~r(s(s(z)), s(s(s(elem!1))))),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[7211, 194, 174, 184, 16450])).
% 8.99/9.21 tff(16452,plain,
% 8.99/9.21 ($false),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[11041, 16451, 16448])).
% 8.99/9.21 tff(16453,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.21 tff(16454,plain,
% 8.99/9.21 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[16453, 1686, 184, 90, 174, 1669, 664, 590])).
% 8.99/9.21 tff(16455,plain,
% 8.99/9.21 (r(s(s(z)), s(s(s(s(z)))))),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[3652, 16454])).
% 8.99/9.21 tff(16456,plain,
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% 8.99/9.21 inference(unit_resolution,[status(thm)],[16396, 16455, 1216, 16386])).
% 8.99/9.21 tff(16457,plain,
% 8.99/9.21 (b(s(z), s(s(z)))),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[1788, 16456])).
% 8.99/9.21 tff(16458,plain,
% 8.99/9.21 (s(s(s(s(elem!1)))) = s(elem!1)),
% 8.99/9.21 inference(monotonicity,[status(thm)],[144])).
% 8.99/9.21 tff(16459,plain,
% 8.99/9.21 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 8.99/9.21 inference(monotonicity,[status(thm)],[16458])).
% 8.99/9.21 tff(16460,plain,
% 8.99/9.21 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 8.99/9.21 inference(symmetry,[status(thm)],[16459])).
% 8.99/9.21 tff(16461,plain,
% 8.99/9.21 (r(s(s(elem!1)), z) <=> r(s(s(s(s(s(elem!1))))), z)),
% 8.99/9.21 inference(monotonicity,[status(thm)],[16460])).
% 8.99/9.21 tff(16462,plain,
% 8.99/9.21 (r(s(s(s(s(s(elem!1))))), z) <=> r(s(s(elem!1)), z)),
% 8.99/9.21 inference(symmetry,[status(thm)],[16461])).
% 8.99/9.21 tff(16463,plain,
% 8.99/9.21 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 8.99/9.21 inference(transitivity,[status(thm)],[16459, 283])).
% 8.99/9.21 tff(16464,plain,
% 8.99/9.21 (r(s(s(s(s(s(elem!1))))), z) <=> r(s(s(s(elem!1))), z)),
% 8.99/9.21 inference(monotonicity,[status(thm)],[16463])).
% 8.99/9.21 tff(16465,plain,
% 8.99/9.21 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(elem!1))))), z)),
% 8.99/9.21 inference(symmetry,[status(thm)],[16464])).
% 8.99/9.21 tff(16466,plain,
% 8.99/9.21 (r(s(s(s(elem!1))), z) <=> r(s(s(elem!1)), z)),
% 8.99/9.21 inference(transitivity,[status(thm)],[16465, 16462])).
% 8.99/9.21 tff(16467,plain,
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% 8.99/9.21 inference(modus_ponens,[status(thm)],[174, 16466])).
% 8.99/9.21 tff(16468,plain,
% 8.99/9.21 (r(z, s(s(elem!1))) <=> r(z, s(s(s(elem!1))))),
% 8.99/9.21 inference(monotonicity,[status(thm)],[283])).
% 8.99/9.21 tff(16469,plain,
% 8.99/9.21 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(elem!1)))),
% 8.99/9.21 inference(symmetry,[status(thm)],[16468])).
% 8.99/9.21 tff(16470,plain,
% 8.99/9.21 (r(z, s(s(elem!1)))),
% 8.99/9.21 inference(modus_ponens,[status(thm)],[184, 16469])).
% 8.99/9.21 tff(16471,assumption,(s(s(s(s(s(z))))) = s(s(elem!1))), introduced(assumption)).
% 8.99/9.21 tff(16472,plain,
% 8.99/9.21 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 8.99/9.21 inference(monotonicity,[status(thm)],[16471])).
% 8.99/9.21 tff(16473,plain,
% 8.99/9.21 (s(s(s(s(z)))) = s(s(elem!1))),
% 8.99/9.21 inference(transitivity,[status(thm)],[5006, 16472, 259, 8337, 266])).
% 8.99/9.21 tff(16474,plain,
% 8.99/9.21 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[1407, 9254])).
% 8.99/9.21 tff(16475,plain,
% 8.99/9.21 ($false),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[16474, 16473])).
% 8.99/9.21 tff(16476,plain,((~(s(s(s(s(s(z))))) = s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.21 tff(16477,plain,
% 8.99/9.21 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[16476, 266])).
% 8.99/9.21 tff(16478,plain,
% 8.99/9.21 (~r(s(s(z)), s(z))),
% 8.99/9.21 inference(unit_resolution,[status(thm)],[5585, 16455, 590, 664, 1216])).
% 8.99/9.22 tff(16479,plain,
% 8.99/9.22 (b(s(s(z)), s(z))),
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% 8.99/9.22 tff(16480,plain,
% 8.99/9.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 8.99/9.22 inference(rewrite,[status(thm)],[])).
% 8.99/9.22 tff(16481,plain,
% 8.99/9.22 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 8.99/9.22 inference(rewrite,[status(thm)],[])).
% 8.99/9.22 tff(16482,plain,
% 8.99/9.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z))))))),
% 8.99/9.22 inference(monotonicity,[status(thm)],[16481])).
% 8.99/9.22 tff(16483,plain,
% 8.99/9.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 8.99/9.22 inference(transitivity,[status(thm)],[16482, 16480])).
% 8.99/9.22 tff(16484,plain,
% 8.99/9.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 8.99/9.22 inference(quant_inst,[status(thm)],[])).
% 8.99/9.22 tff(16485,plain,
% 8.99/9.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z))))),
% 8.99/9.22 inference(modus_ponens,[status(thm)],[16484, 16483])).
% 8.99/9.22 tff(16486,plain,
% 8.99/9.22 ($false),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[16485, 391, 90, 1235, 2439, 1686, 590])).
% 8.99/9.22 tff(16487,plain,((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.22 tff(16488,plain,
% 8.99/9.22 (~b(s(s(z)), z)),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[16487, 16457, 590, 90, 1686])).
% 8.99/9.22 tff(16489,plain,
% 8.99/9.22 (r(s(s(z)), z)),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[1211, 16488])).
% 8.99/9.22 tff(16490,plain,
% 8.99/9.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.22 inference(rewrite,[status(thm)],[])).
% 8.99/9.22 tff(16491,plain,
% 8.99/9.22 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.22 inference(rewrite,[status(thm)],[])).
% 8.99/9.22 tff(16492,plain,
% 8.99/9.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 8.99/9.22 inference(monotonicity,[status(thm)],[16491])).
% 8.99/9.22 tff(16493,plain,
% 8.99/9.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.22 inference(transitivity,[status(thm)],[16492, 16490])).
% 8.99/9.22 tff(16494,plain,
% 8.99/9.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.22 inference(quant_inst,[status(thm)],[])).
% 8.99/9.22 tff(16495,plain,
% 8.99/9.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 8.99/9.22 inference(modus_ponens,[status(thm)],[16494, 16493])).
% 8.99/9.22 tff(16496,plain,
% 8.99/9.22 (~r(s(s(s(elem!1))), s(s(z)))),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[16495, 194, 174, 184, 16489])).
% 8.99/9.22 tff(16497,plain,
% 8.99/9.22 (~r(elem!1, s(s(z)))),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[10022, 16496, 125])).
% 8.99/9.22 tff(16498,plain,
% 8.99/9.22 (b(elem!1, s(s(z)))),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[3394, 16497, 3820])).
% 8.99/9.22 tff(16499,plain,
% 8.99/9.22 (b(s(s(elem!1)), s(s(z)))),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[11458, 16498, 266])).
% 8.99/9.22 tff(16500,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 8.99/9.22 tff(16501,plain,
% 8.99/9.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 8.99/9.22 inference(rewrite,[status(thm)],[])).
% 8.99/9.22 tff(16502,plain,
% 8.99/9.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 8.99/9.22 inference(quant_inst,[status(thm)],[])).
% 8.99/9.22 tff(16503,plain,
% 8.99/9.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 8.99/9.22 inference(modus_ponens,[status(thm)],[16502, 16501])).
% 8.99/9.22 tff(16504,plain,
% 8.99/9.22 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[16503, 194, 326, 2616, 16500])).
% 8.99/9.22 tff(16505,assumption,(~(s(s(s(s(s(z))))) = s(s(elem!1)))), introduced(assumption)).
% 8.99/9.22 tff(16506,plain,
% 8.99/9.22 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(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(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 8.99/9.22 inference(rewrite,[status(thm)],[])).
% 8.99/9.22 tff(16507,plain,
% 8.99/9.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 8.99/9.22 inference(quant_inst,[status(thm)],[])).
% 8.99/9.22 tff(16508,plain,
% 8.99/9.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 8.99/9.22 inference(modus_ponens,[status(thm)],[16507, 16506])).
% 8.99/9.22 tff(16509,plain,
% 8.99/9.22 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[16508, 42, 16505, 16504])).
% 8.99/9.22 tff(16510,plain,
% 8.99/9.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 8.99/9.22 inference(rewrite,[status(thm)],[])).
% 8.99/9.22 tff(16511,plain,
% 8.99/9.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 8.99/9.22 inference(quant_inst,[status(thm)],[])).
% 8.99/9.22 tff(16512,plain,
% 8.99/9.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 8.99/9.22 inference(modus_ponens,[status(thm)],[16511, 16510])).
% 8.99/9.22 tff(16513,plain,
% 8.99/9.22 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[16512, 194, 326, 3557, 16500])).
% 8.99/9.22 tff(16514,plain,
% 8.99/9.22 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 8.99/9.22 inference(rewrite,[status(thm)],[])).
% 8.99/9.22 tff(16515,plain,
% 8.99/9.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 8.99/9.22 inference(quant_inst,[status(thm)],[])).
% 8.99/9.22 tff(16516,plain,
% 8.99/9.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))),
% 8.99/9.22 inference(modus_ponens,[status(thm)],[16515, 16514])).
% 8.99/9.22 tff(16517,plain,
% 8.99/9.22 (b(s(s(s(s(s(z))))), s(s(z)))),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[16516, 42, 8678, 16513])).
% 8.99/9.22 tff(16518,plain,
% 8.99/9.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 8.99/9.22 inference(rewrite,[status(thm)],[])).
% 8.99/9.22 tff(16519,plain,
% 8.99/9.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 8.99/9.22 inference(quant_inst,[status(thm)],[])).
% 8.99/9.22 tff(16520,plain,
% 8.99/9.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 8.99/9.22 inference(modus_ponens,[status(thm)],[16519, 16518])).
% 8.99/9.22 tff(16521,plain,
% 8.99/9.22 ($false),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[16520, 391, 2439, 1233, 6192, 16517, 16509])).
% 8.99/9.22 tff(16522,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.22 tff(16523,plain,
% 8.99/9.22 (~r(s(s(s(s(s(z))))), z)),
% 8.99/9.22 inference(unit_resolution,[status(thm)],[16522, 16499, 16489, 16479, 16477, 16470, 16467, 16457])).
% 8.99/9.23 tff(16524,assumption,(~r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 8.99/9.23 tff(16525,assumption,(~b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 8.99/9.23 tff(16526,plain,
% 8.99/9.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 8.99/9.23 inference(rewrite,[status(thm)],[])).
% 8.99/9.23 tff(16527,plain,
% 8.99/9.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 8.99/9.23 inference(quant_inst,[status(thm)],[])).
% 8.99/9.23 tff(16528,plain,
% 8.99/9.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 8.99/9.23 inference(modus_ponens,[status(thm)],[16527, 16526])).
% 8.99/9.23 tff(16529,plain,
% 8.99/9.23 ($false),
% 8.99/9.23 inference(unit_resolution,[status(thm)],[16528, 42, 5063, 16525, 16524])).
% 8.99/9.23 tff(16530,plain,(b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)), inference(lemma,lemma(discharge,[]))).
% 8.99/9.23 tff(16531,plain,
% 8.99/9.23 (b(s(s(s(s(s(z))))), z)),
% 8.99/9.23 inference(unit_resolution,[status(thm)],[16530, 16523])).
% 8.99/9.23 tff(16532,plain,
% 8.99/9.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 8.99/9.23 inference(rewrite,[status(thm)],[])).
% 8.99/9.23 tff(16533,plain,
% 8.99/9.23 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 8.99/9.23 inference(rewrite,[status(thm)],[])).
% 8.99/9.23 tff(16534,plain,
% 8.99/9.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 8.99/9.23 inference(monotonicity,[status(thm)],[16533])).
% 8.99/9.23 tff(16535,plain,
% 8.99/9.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 8.99/9.23 inference(transitivity,[status(thm)],[16534, 16532])).
% 8.99/9.23 tff(16536,plain,
% 8.99/9.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.99/9.23 inference(quant_inst,[status(thm)],[])).
% 8.99/9.23 tff(16537,plain,
% 8.99/9.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 8.99/9.23 inference(modus_ponens,[status(thm)],[16536, 16535])).
% 8.99/9.23 tff(16538,plain,
% 8.99/9.23 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 8.99/9.23 inference(unit_resolution,[status(thm)],[16537, 391, 90, 1686, 16531])).
% 8.99/9.23 tff(16539,plain,
% 8.99/9.23 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 8.99/9.23 inference(unit_resolution,[status(thm)],[8761, 16538])).
% 8.99/9.23 tff(16540,plain,
% 8.99/9.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 8.99/9.23 inference(rewrite,[status(thm)],[])).
% 8.99/9.23 tff(16541,plain,
% 8.99/9.23 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 8.99/9.23 inference(rewrite,[status(thm)],[])).
% 8.99/9.23 tff(16542,plain,
% 8.99/9.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 8.99/9.23 inference(monotonicity,[status(thm)],[16541])).
% 8.99/9.23 tff(16543,plain,
% 8.99/9.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 8.99/9.23 inference(transitivity,[status(thm)],[16542, 16540])).
% 8.99/9.23 tff(16544,plain,
% 8.99/9.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 8.99/9.23 inference(quant_inst,[status(thm)],[])).
% 8.99/9.23 tff(16545,plain,
% 8.99/9.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 8.99/9.23 inference(modus_ponens,[status(thm)],[16544, 16543])).
% 8.99/9.23 tff(16546,plain,
% 8.99/9.23 (~b(s(s(s(s(s(z))))), s(z))),
% 8.99/9.23 inference(unit_resolution,[status(thm)],[16545, 391, 90, 1686, 590, 16531])).
% 8.99/9.23 tff(16547,plain,
% 8.99/9.23 (r(s(s(s(s(s(z))))), s(z))),
% 8.99/9.23 inference(unit_resolution,[status(thm)],[15766, 42, 15763, 16546])).
% 8.99/9.23 tff(16548,assumption,(s(z) = s(s(s(s(s(z)))))), introduced(assumption)).
% 8.99/9.23 tff(16549,plain,
% 8.99/9.23 (s(s(s(s(s(z))))) = s(z)),
% 8.99/9.23 inference(symmetry,[status(thm)],[16548])).
% 8.99/9.23 tff(16550,plain,
% 8.99/9.23 ($false),
% 8.99/9.23 inference(unit_resolution,[status(thm)],[15763, 16549])).
% 8.99/9.23 tff(16551,plain,(~(s(z) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.23 tff(16552,plain,
% 8.99/9.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 8.99/9.23 inference(rewrite,[status(thm)],[])).
% 8.99/9.23 tff(16553,plain,
% 8.99/9.23 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 8.99/9.24 inference(rewrite,[status(thm)],[])).
% 8.99/9.24 tff(16554,plain,
% 8.99/9.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 8.99/9.24 inference(monotonicity,[status(thm)],[16553])).
% 8.99/9.24 tff(16555,plain,
% 8.99/9.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 8.99/9.24 inference(transitivity,[status(thm)],[16554, 16552])).
% 8.99/9.24 tff(16556,plain,
% 8.99/9.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 8.99/9.24 inference(quant_inst,[status(thm)],[])).
% 8.99/9.24 tff(16557,plain,
% 8.99/9.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 8.99/9.24 inference(modus_ponens,[status(thm)],[16556, 16555])).
% 8.99/9.24 tff(16558,plain,
% 8.99/9.24 (~b(s(z), s(s(s(s(s(z))))))),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[16557, 391, 90, 1686, 590, 16531])).
% 8.99/9.24 tff(16559,plain,
% 8.99/9.24 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 8.99/9.24 inference(rewrite,[status(thm)],[])).
% 8.99/9.24 tff(16560,plain,
% 8.99/9.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 8.99/9.24 inference(quant_inst,[status(thm)],[])).
% 8.99/9.24 tff(16561,plain,
% 8.99/9.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 8.99/9.24 inference(modus_ponens,[status(thm)],[16560, 16559])).
% 8.99/9.24 tff(16562,plain,
% 8.99/9.24 (r(s(z), s(s(s(s(s(z))))))),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[16561, 42, 16558, 16551])).
% 8.99/9.24 tff(16563,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 8.99/9.24 tff(16564,plain,
% 8.99/9.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.99/9.24 inference(rewrite,[status(thm)],[])).
% 8.99/9.24 tff(16565,plain,
% 8.99/9.24 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.99/9.24 inference(rewrite,[status(thm)],[])).
% 8.99/9.24 tff(16566,plain,
% 8.99/9.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 8.99/9.24 inference(monotonicity,[status(thm)],[16565])).
% 8.99/9.24 tff(16567,plain,
% 8.99/9.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 8.99/9.24 inference(transitivity,[status(thm)],[16566, 16564])).
% 8.99/9.24 tff(16568,plain,
% 8.99/9.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 8.99/9.24 inference(quant_inst,[status(thm)],[])).
% 8.99/9.24 tff(16569,plain,
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% 8.99/9.24 inference(modus_ponens,[status(thm)],[16568, 16567])).
% 8.99/9.24 tff(16570,plain,
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% 8.99/9.24 inference(unit_resolution,[status(thm)],[16569, 194, 1216, 16563, 15749, 15748])).
% 8.99/9.24 tff(16571,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.24 tff(16572,plain,
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% 8.99/9.24 tff(16573,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.24 tff(16574,plain,
% 8.99/9.24 (~b(z, s(s(s(s(z)))))),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[16573, 266, 90, 590, 1216, 125, 16441, 184, 664, 1669])).
% 8.99/9.24 tff(16575,plain,
% 8.99/9.24 (r(z, s(s(s(s(z)))))),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[800, 16574])).
% 8.99/9.24 tff(16576,plain,
% 8.99/9.24 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[16415, 16575, 664, 16386, 590, 1216])).
% 8.99/9.24 tff(16577,plain,
% 8.99/9.24 (b(s(s(z)), s(s(s(s(z)))))),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[3652, 16576])).
% 8.99/9.24 tff(16578,plain,
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% 8.99/9.24 inference(unit_resolution,[status(thm)],[7203, 16577, 664, 90, 590])).
% 8.99/9.24 tff(16579,plain,
% 8.99/9.24 (r(s(s(z)), z)),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[1211, 16578])).
% 8.99/9.24 tff(16580,plain,
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% 8.99/9.24 inference(unit_resolution,[status(thm)],[8570, 16579, 530, 16575])).
% 8.99/9.24 tff(16581,plain,
% 8.99/9.24 (~r(s(s(elem!1)), s(s(z)))),
% 8.99/9.24 inference(modus_ponens,[status(thm)],[16580, 16440])).
% 8.99/9.24 tff(16582,plain,
% 8.99/9.24 (~r(elem!1, s(s(z)))),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[11777, 266, 11775])).
% 8.99/9.24 tff(16583,plain,
% 8.99/9.24 (b(elem!1, s(s(z)))),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[3394, 16582, 9254])).
% 8.99/9.24 tff(16584,plain,
% 8.99/9.24 (b(s(s(elem!1)), s(s(z)))),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[11458, 16583, 266])).
% 8.99/9.24 tff(16585,plain,
% 8.99/9.24 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 8.99/9.24 inference(monotonicity,[status(thm)],[266])).
% 8.99/9.24 tff(16586,plain,
% 8.99/9.24 (~(s(s(s(s(z)))) = elem!1)),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[717, 282])).
% 8.99/9.24 tff(16587,plain,
% 8.99/9.24 (~(elem!1 = s(s(s(s(z)))))),
% 8.99/9.24 inference(unit_resolution,[status(thm)],[769, 16586])).
% 8.99/9.24 tff(16588,plain,
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% 8.99/9.24 inference(unit_resolution,[status(thm)],[781, 16587, 3222])).
% 8.99/9.25 tff(16589,plain,
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% 8.99/9.25 inference(unit_resolution,[status(thm)],[9608, 16588, 266])).
% 8.99/9.25 tff(16590,plain,
% 8.99/9.25 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 8.99/9.25 inference(modus_ponens,[status(thm)],[16589, 16585])).
% 8.99/9.25 tff(16591,plain,
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% 8.99/9.25 inference(rewrite,[status(thm)],[])).
% 8.99/9.25 tff(16592,plain,
% 8.99/9.25 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.99/9.25 inference(rewrite,[status(thm)],[])).
% 8.99/9.25 tff(16593,plain,
% 8.99/9.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 8.99/9.25 inference(monotonicity,[status(thm)],[16592])).
% 8.99/9.25 tff(16594,plain,
% 8.99/9.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 8.99/9.25 inference(transitivity,[status(thm)],[16593, 16591])).
% 8.99/9.25 tff(16595,plain,
% 8.99/9.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 8.99/9.25 inference(quant_inst,[status(thm)],[])).
% 8.99/9.25 tff(16596,plain,
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% 8.99/9.25 inference(modus_ponens,[status(thm)],[16595, 16594])).
% 8.99/9.25 tff(16597,plain,
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% 8.99/9.25 inference(unit_resolution,[status(thm)],[16596, 391, 3823, 90, 664, 16590, 16584])).
% 8.99/9.25 tff(16598,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | r(elem!1, s(s(s(s(z))))) | r(s(s(elem!1)), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.25 tff(16599,plain,
% 8.99/9.25 (r(s(s(elem!1)), s(s(z)))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[16598, 16577, 90, 664, 3222, 266])).
% 8.99/9.25 tff(16600,plain,
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% 8.99/9.25 inference(unit_resolution,[status(thm)],[16599, 16581])).
% 8.99/9.25 tff(16601,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | r(elem!1, s(s(s(s(z))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.25 tff(16602,plain,
% 8.99/9.25 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[16601, 16361, 530, 90, 16379, 16382, 590, 1216, 184, 16384])).
% 8.99/9.25 tff(16603,plain,
% 8.99/9.25 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.99/9.25 inference(monotonicity,[status(thm)],[16361])).
% 8.99/9.25 tff(16604,plain,
% 8.99/9.25 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[10698, 194, 183, 1216, 16381])).
% 8.99/9.25 tff(16605,plain,
% 8.99/9.25 (b(s(s(s(s(z)))), elem!1)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[2694, 16604, 16368])).
% 8.99/9.25 tff(16606,plain,
% 8.99/9.25 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.99/9.25 inference(modus_ponens,[status(thm)],[16605, 16603])).
% 8.99/9.25 tff(16607,assumption,(s(s(z)) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 8.99/9.25 tff(16608,plain,
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% 8.99/9.25 tff(16609,plain,
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% 8.99/9.25 tff(16610,plain,
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% 8.99/9.25 inference(unit_resolution,[status(thm)],[2689, 16609])).
% 8.99/9.25 tff(16611,plain,((~(s(s(z)) = s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = s(s(z))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.25 tff(16612,plain,
% 8.99/9.25 (~(s(s(z)) = s(s(s(s(s(elem!1))))))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[16611, 16361, 2680])).
% 8.99/9.25 tff(16613,plain,
% 8.99/9.25 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 8.99/9.25 inference(monotonicity,[status(thm)],[3067])).
% 8.99/9.25 tff(16614,plain,
% 8.99/9.25 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
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% 8.99/9.25 tff(16615,plain,
% 8.99/9.25 (~r(s(s(s(elem!1))), s(z))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[11169, 327, 1216, 340])).
% 8.99/9.25 tff(16616,plain,
% 8.99/9.25 (b(s(s(s(elem!1))), s(z))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[223, 16615])).
% 8.99/9.25 tff(16617,plain,
% 8.99/9.25 (~(s(z) = elem!1)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[9618, 16616, 9024])).
% 8.99/9.25 tff(16618,plain,
% 8.99/9.25 (~(elem!1 = s(z))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[172, 16617])).
% 8.99/9.25 tff(16619,plain,
% 8.99/9.25 (r(elem!1, s(z))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[837, 16618, 31])).
% 8.99/9.25 tff(16620,plain,
% 8.99/9.25 (~(s(s(s(elem!1))) = elem!1)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[8400, 16616, 31])).
% 8.99/9.25 tff(16621,plain,
% 8.99/9.25 (~(elem!1 = s(s(s(elem!1))))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[129, 16620])).
% 8.99/9.25 tff(16622,plain,
% 8.99/9.25 (r(elem!1, s(s(s(elem!1))))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[424, 16621, 4028])).
% 8.99/9.25 tff(16623,plain,
% 8.99/9.25 (~r(s(s(s(elem!1))), z)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[8380, 16622, 184, 411])).
% 8.99/9.25 tff(16624,plain,
% 8.99/9.25 (b(s(s(s(elem!1))), z)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[377, 16623])).
% 8.99/9.25 tff(16625,plain,
% 8.99/9.25 (~b(s(z), z)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[6325, 16624, 1686, 90, 16616])).
% 8.99/9.25 tff(16626,plain,
% 8.99/9.25 (r(s(z), z)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[180, 16625])).
% 8.99/9.25 tff(16627,plain,
% 8.99/9.25 (~r(s(z), elem!1)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[2475, 16626, 16619, 411])).
% 8.99/9.25 tff(16628,plain,
% 8.99/9.25 (~r(elem!1, z)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[6153, 16622, 184, 327])).
% 8.99/9.25 tff(16629,plain,
% 8.99/9.25 (b(elem!1, z)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[526, 16628, 2])).
% 8.99/9.25 tff(16630,plain,
% 8.99/9.25 (b(s(s(s(elem!1))), elem!1)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[10519, 16621, 4028, 184, 411])).
% 8.99/9.25 tff(16631,plain,
% 8.99/9.25 (~b(s(z), elem!1)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[2522, 16626, 16616, 16624, 16630, 16629, 411, 16618])).
% 8.99/9.25 tff(16632,plain,
% 8.99/9.25 ($false),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[632, 16631, 16627, 16617])).
% 8.99/9.25 tff(16633,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(z)) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.25 tff(16634,plain,
% 8.99/9.25 (~r(s(s(elem!1)), s(z))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[16633, 327, 2, 90, 16385, 184, 31, 4028, 411, 1216, 1686])).
% 8.99/9.25 tff(16635,plain,
% 8.99/9.25 (b(s(s(elem!1)), s(z))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[362, 16634])).
% 8.99/9.25 tff(16636,plain,
% 8.99/9.25 (b(s(s(s(s(s(elem!1))))), s(z))),
% 8.99/9.25 inference(modus_ponens,[status(thm)],[16635, 16614])).
% 8.99/9.25 tff(16637,plain,
% 8.99/9.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 8.99/9.25 inference(rewrite,[status(thm)],[])).
% 8.99/9.25 tff(16638,plain,
% 8.99/9.25 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 8.99/9.25 inference(rewrite,[status(thm)],[])).
% 8.99/9.25 tff(16639,plain,
% 8.99/9.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 8.99/9.25 inference(monotonicity,[status(thm)],[16638])).
% 8.99/9.25 tff(16640,plain,
% 8.99/9.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 8.99/9.25 inference(transitivity,[status(thm)],[16639, 16637])).
% 8.99/9.25 tff(16641,plain,
% 8.99/9.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 8.99/9.25 inference(quant_inst,[status(thm)],[])).
% 8.99/9.25 tff(16642,plain,
% 8.99/9.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 8.99/9.25 inference(modus_ponens,[status(thm)],[16641, 16640])).
% 8.99/9.25 tff(16643,plain,
% 8.99/9.25 ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[16642, 391, 1686, 664, 590])).
% 8.99/9.25 tff(16644,plain,
% 8.99/9.25 (~b(s(s(s(s(s(elem!1))))), z)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[16643, 16636])).
% 8.99/9.25 tff(16645,plain,
% 8.99/9.25 (r(s(s(s(s(s(elem!1))))), z)),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[8165, 42, 8162, 16644])).
% 8.99/9.25 tff(16646,plain,
% 8.99/9.25 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[8172, 194, 174, 184, 16645])).
% 8.99/9.25 tff(16647,plain,
% 8.99/9.25 ($false),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[16646, 9532])).
% 8.99/9.25 tff(16648,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (elem!1 = z) | (~b(s(s(s(s(z)))), z)) | b(elem!1, s(z)) | b(elem!1, s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.25 tff(16649,plain,
% 8.99/9.25 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[16648, 16436, 16369, 184, 16361, 16379, 590, 2, 90, 31, 4028, 411, 1216])).
% 8.99/9.25 tff(16650,plain,
% 8.99/9.25 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 8.99/9.25 inference(unit_resolution,[status(thm)],[5792, 9968, 174, 184])).
% 8.99/9.26 tff(16651,plain,
% 8.99/9.26 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 8.99/9.26 inference(unit_resolution,[status(thm)],[1356, 315, 16650])).
% 8.99/9.26 tff(16652,plain,
% 8.99/9.26 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 8.99/9.26 inference(modus_ponens,[status(thm)],[16651, 16288])).
% 8.99/9.26 tff(16653,plain,
% 8.99/9.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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)))))))),
% 8.99/9.26 inference(rewrite,[status(thm)],[])).
% 8.99/9.26 tff(16654,plain,
% 8.99/9.26 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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)))))))),
% 8.99/9.26 inference(rewrite,[status(thm)],[])).
% 8.99/9.26 tff(16655,plain,
% 8.99/9.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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))))))))),
% 8.99/9.26 inference(monotonicity,[status(thm)],[16654])).
% 8.99/9.26 tff(16656,plain,
% 8.99/9.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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)))))))),
% 8.99/9.26 inference(transitivity,[status(thm)],[16655, 16653])).
% 8.99/9.26 tff(16657,plain,
% 8.99/9.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z)))))))),
% 8.99/9.26 inference(quant_inst,[status(thm)],[])).
% 8.99/9.26 tff(16658,plain,
% 8.99/9.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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))))))),
% 8.99/9.26 inference(modus_ponens,[status(thm)],[16657, 16656])).
% 8.99/9.26 tff(16659,plain,
% 8.99/9.26 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 8.99/9.26 inference(unit_resolution,[status(thm)],[16658, 391, 90, 3325, 1669, 16652])).
% 8.99/9.26 tff(16660,plain,
% 8.99/9.26 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 8.99/9.26 inference(unit_resolution,[status(thm)],[16299, 42, 16659])).
% 8.99/9.26 tff(16661,plain,
% 8.99/9.26 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 8.99/9.26 inference(unit_resolution,[status(thm)],[16660, 16286])).
% 8.99/9.26 tff(16662,assumption,(~(s(s(z)) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 8.99/9.26 tff(16663,plain,
% 8.99/9.26 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.99/9.26 inference(monotonicity,[status(thm)],[125])).
% 8.99/9.26 tff(16664,plain,
% 8.99/9.26 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 8.99/9.26 inference(symmetry,[status(thm)],[16663])).
% 8.99/9.26 tff(16665,plain,
% 8.99/9.26 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 8.99/9.26 inference(unit_resolution,[status(thm)],[1370, 297, 6155])).
% 8.99/9.26 tff(16666,plain,
% 8.99/9.26 (b(elem!1, s(s(elem!1)))),
% 8.99/9.26 inference(modus_ponens,[status(thm)],[16665, 16664])).
% 8.99/9.26 tff(16667,plain,
% 8.99/9.26 (~r(s(s(elem!1)), s(z))),
% 8.99/9.26 inference(unit_resolution,[status(thm)],[2648, 16666, 125, 16386, 1484])).
% 8.99/9.26 tff(16668,plain,
% 8.99/9.26 (b(s(s(elem!1)), s(z))),
% 8.99/9.26 inference(unit_resolution,[status(thm)],[362, 16667])).
% 8.99/9.26 tff(16669,plain,
% 8.99/9.26 (b(s(s(s(s(s(elem!1))))), s(z))),
% 8.99/9.26 inference(modus_ponens,[status(thm)],[16668, 16614])).
% 8.99/9.26 tff(16670,assumption,(b(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 8.99/9.26 tff(16671,plain,
% 8.99/9.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(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))))))))),
% 8.99/9.26 inference(rewrite,[status(thm)],[])).
% 8.99/9.26 tff(16672,plain,
% 8.99/9.26 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~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)))))))) <=> ((~b(s(z), s(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))))))))),
% 8.99/9.26 inference(rewrite,[status(thm)],[])).
% 8.99/9.26 tff(16673,plain,
% 8.99/9.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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)))))))))),
% 8.99/9.26 inference(monotonicity,[status(thm)],[16672])).
% 8.99/9.26 tff(16674,plain,
% 8.99/9.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(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))))))))),
% 8.99/9.26 inference(transitivity,[status(thm)],[16673, 16671])).
% 8.99/9.26 tff(16675,plain,
% 8.99/9.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~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))))))))),
% 8.99/9.26 inference(quant_inst,[status(thm)],[])).
% 8.99/9.26 tff(16676,plain,
% 8.99/9.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(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)))))))),
% 8.99/9.26 inference(modus_ponens,[status(thm)],[16675, 16674])).
% 8.99/9.26 tff(16677,plain,
% 8.99/9.26 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 8.99/9.26 inference(unit_resolution,[status(thm)],[16676, 391, 16398, 16388, 16670])).
% 8.99/9.26 tff(16678,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))), introduced(assumption)).
% 8.99/9.26 tff(16679,plain,
% 8.99/9.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 8.99/9.27 inference(rewrite,[status(thm)],[])).
% 8.99/9.27 tff(16680,plain,
% 8.99/9.27 (((~r(s(s(s(s(z)))), s(z))) | (~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(z)), 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(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 8.99/9.27 inference(rewrite,[status(thm)],[])).
% 8.99/9.27 tff(16681,plain,
% 8.99/9.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~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(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 8.99/9.27 inference(monotonicity,[status(thm)],[16680])).
% 8.99/9.27 tff(16682,plain,
% 8.99/9.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~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(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 8.99/9.27 inference(transitivity,[status(thm)],[16681, 16679])).
% 8.99/9.27 tff(16683,plain,
% 8.99/9.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~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(z)), s(s(s(s(s(elem!1))))))))),
% 8.99/9.27 inference(quant_inst,[status(thm)],[])).
% 8.99/9.27 tff(16684,plain,
% 8.99/9.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 8.99/9.27 inference(modus_ponens,[status(thm)],[16683, 16682])).
% 8.99/9.27 tff(16685,plain,
% 8.99/9.27 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[16684, 194, 1749, 723, 16678])).
% 8.99/9.27 tff(16686,plain,
% 8.99/9.27 ($false),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[9497, 42, 16662, 16685, 16677])).
% 8.99/9.27 tff(16687,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.27 tff(16688,plain,
% 8.99/9.27 (~r(s(s(z)), s(s(s(s(z)))))),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[16687, 16669, 16662, 16386, 16661, 590, 664, 1216])).
% 8.99/9.27 tff(16689,plain,
% 8.99/9.27 (b(s(s(z)), s(s(s(s(z)))))),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[3652, 16688])).
% 8.99/9.27 tff(16690,plain,
% 8.99/9.27 (~b(s(s(z)), z)),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[7203, 16689, 664, 90, 590])).
% 8.99/9.27 tff(16691,plain,
% 8.99/9.27 (r(s(s(z)), z)),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[1211, 16690])).
% 8.99/9.27 tff(16692,plain,
% 8.99/9.27 (~r(s(s(z)), s(s(s(elem!1))))),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[7211, 194, 174, 184, 16691])).
% 8.99/9.27 tff(16693,plain,
% 8.99/9.27 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(elem!1)))),
% 8.99/9.27 inference(monotonicity,[status(thm)],[3067])).
% 8.99/9.27 tff(16694,plain,
% 8.99/9.27 ((~b(z, s(s(s(s(s(elem!1))))))) <=> (~b(z, s(s(elem!1))))),
% 8.99/9.27 inference(monotonicity,[status(thm)],[16693])).
% 8.99/9.27 tff(16695,plain,
% 8.99/9.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 8.99/9.27 inference(rewrite,[status(thm)],[])).
% 8.99/9.27 tff(16696,plain,
% 8.99/9.27 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 8.99/9.27 inference(rewrite,[status(thm)],[])).
% 8.99/9.27 tff(16697,plain,
% 8.99/9.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 8.99/9.27 inference(monotonicity,[status(thm)],[16696])).
% 8.99/9.27 tff(16698,plain,
% 8.99/9.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 8.99/9.27 inference(transitivity,[status(thm)],[16697, 16695])).
% 8.99/9.27 tff(16699,plain,
% 8.99/9.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 8.99/9.27 inference(quant_inst,[status(thm)],[])).
% 8.99/9.27 tff(16700,plain,
% 8.99/9.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 8.99/9.27 inference(modus_ponens,[status(thm)],[16699, 16698])).
% 8.99/9.27 tff(16701,plain,
% 8.99/9.27 ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[16700, 391, 664, 590])).
% 8.99/9.27 tff(16702,plain,
% 8.99/9.27 (~b(z, s(s(s(s(s(elem!1))))))),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[16701, 16669])).
% 8.99/9.27 tff(16703,plain,
% 8.99/9.27 (~b(z, s(s(elem!1)))),
% 8.99/9.27 inference(modus_ponens,[status(thm)],[16702, 16694])).
% 8.99/9.27 tff(16704,plain,
% 8.99/9.27 (r(z, s(s(elem!1)))),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[324, 16703])).
% 8.99/9.27 tff(16705,plain,
% 8.99/9.27 (r(z, s(s(s(s(s(elem!1))))))),
% 8.99/9.27 inference(modus_ponens,[status(thm)],[16704, 3072])).
% 8.99/9.27 tff(16706,plain,
% 8.99/9.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 8.99/9.27 inference(rewrite,[status(thm)],[])).
% 8.99/9.27 tff(16707,plain,
% 8.99/9.27 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 8.99/9.27 inference(rewrite,[status(thm)],[])).
% 8.99/9.27 tff(16708,plain,
% 8.99/9.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 8.99/9.27 inference(monotonicity,[status(thm)],[16707])).
% 8.99/9.27 tff(16709,plain,
% 8.99/9.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 8.99/9.27 inference(transitivity,[status(thm)],[16708, 16706])).
% 8.99/9.27 tff(16710,plain,
% 8.99/9.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 8.99/9.27 inference(quant_inst,[status(thm)],[])).
% 8.99/9.27 tff(16711,plain,
% 8.99/9.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 8.99/9.27 inference(modus_ponens,[status(thm)],[16710, 16709])).
% 8.99/9.27 tff(16712,plain,
% 8.99/9.27 ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[16711, 391, 664, 590])).
% 8.99/9.27 tff(16713,plain,
% 8.99/9.27 (~b(s(s(s(s(s(elem!1))))), z)),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[16712, 16669])).
% 8.99/9.27 tff(16714,plain,
% 8.99/9.27 (r(s(s(s(s(s(elem!1))))), z)),
% 8.99/9.27 inference(unit_resolution,[status(thm)],[8165, 42, 8162, 16713])).
% 8.99/9.27 tff(16715,plain,
% 8.99/9.27 ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 8.99/9.27 inference(monotonicity,[status(thm)],[9435])).
% 8.99/9.27 tff(16716,plain,
% 8.99/9.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 8.99/9.27 inference(rewrite,[status(thm)],[])).
% 8.99/9.27 tff(16717,plain,
% 8.99/9.27 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 8.99/9.27 inference(rewrite,[status(thm)],[])).
% 8.99/9.27 tff(16718,plain,
% 8.99/9.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 8.99/9.27 inference(monotonicity,[status(thm)],[16717])).
% 8.99/9.27 tff(16719,plain,
% 8.99/9.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 8.99/9.28 inference(transitivity,[status(thm)],[16718, 16716])).
% 8.99/9.28 tff(16720,plain,
% 8.99/9.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 8.99/9.28 inference(quant_inst,[status(thm)],[])).
% 8.99/9.28 tff(16721,plain,
% 8.99/9.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 8.99/9.28 inference(modus_ponens,[status(thm)],[16720, 16719])).
% 8.99/9.28 tff(16722,plain,
% 8.99/9.28 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[16721, 391, 90, 3325, 1669, 16652])).
% 8.99/9.28 tff(16723,plain,
% 8.99/9.28 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 8.99/9.28 inference(modus_ponens,[status(thm)],[16722, 16715])).
% 8.99/9.28 tff(16724,plain,
% 8.99/9.28 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[9445, 16723, 125, 16285])).
% 8.99/9.28 tff(16725,plain,
% 8.99/9.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 8.99/9.28 inference(rewrite,[status(thm)],[])).
% 8.99/9.28 tff(16726,plain,
% 8.99/9.28 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 8.99/9.28 inference(rewrite,[status(thm)],[])).
% 8.99/9.28 tff(16727,plain,
% 8.99/9.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 8.99/9.28 inference(monotonicity,[status(thm)],[16726])).
% 8.99/9.28 tff(16728,plain,
% 8.99/9.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 8.99/9.28 inference(transitivity,[status(thm)],[16727, 16725])).
% 8.99/9.28 tff(16729,plain,
% 8.99/9.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(z)))))))),
% 8.99/9.28 inference(quant_inst,[status(thm)],[])).
% 8.99/9.28 tff(16730,plain,
% 8.99/9.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 8.99/9.28 inference(modus_ponens,[status(thm)],[16729, 16728])).
% 8.99/9.28 tff(16731,plain,
% 8.99/9.28 (~r(z, s(s(s(s(z)))))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[16730, 194, 16724, 16714, 16705])).
% 8.99/9.28 tff(16732,plain,
% 8.99/9.28 (b(z, s(s(s(s(z)))))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[800, 16731])).
% 8.99/9.28 tff(16733,plain,
% 8.99/9.28 (~b(s(s(z)), s(s(s(elem!1))))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[16447, 391, 16689, 90, 16732, 1669])).
% 8.99/9.28 tff(16734,plain,
% 8.99/9.28 ($false),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[11041, 16733, 16692])).
% 8.99/9.28 tff(16735,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (s(s(z)) = s(s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), elem!1)) | r(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.28 tff(16736,plain,
% 8.99/9.28 (~r(s(z), elem!1)),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[16735, 16649, 16384, 16369, 184, 16379, 590, 16612, 1216, 16361, 16606, 16602, 90])).
% 8.99/9.28 tff(16737,plain,
% 8.99/9.28 (b(s(z), elem!1)),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[632, 16736, 150])).
% 8.99/9.28 tff(16738,plain,
% 8.99/9.28 (b(s(z), s(s(s(elem!1))))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[14872, 16737, 16368])).
% 8.99/9.28 tff(16739,plain,
% 8.99/9.28 (~b(s(s(z)), z)),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[14915, 16738, 90, 838, 1216, 16379, 8922, 16361, 16436])).
% 8.99/9.28 tff(16740,plain,
% 8.99/9.28 (r(s(s(z)), z)),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[1211, 16739])).
% 8.99/9.28 tff(16741,plain,
% 8.99/9.28 (~r(s(s(s(elem!1))), s(s(z)))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[16495, 194, 16369, 184, 16740])).
% 8.99/9.28 tff(16742,plain,
% 8.99/9.28 (~r(elem!1, s(s(z)))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[10022, 16741, 16361])).
% 8.99/9.28 tff(16743,plain,
% 8.99/9.28 (b(elem!1, s(s(z)))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[3394, 16742, 16366])).
% 8.99/9.28 tff(16744,plain,
% 8.99/9.28 (b(s(s(s(elem!1))), s(s(z)))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[16425, 16743, 16361])).
% 8.99/9.28 tff(16745,plain,
% 8.99/9.28 (~b(s(s(z)), s(s(s(s(z)))))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[16453, 16436, 184, 90, 16369, 16384, 16379, 590])).
% 8.99/9.28 tff(16746,plain,
% 8.99/9.28 (r(s(s(z)), s(s(s(s(z)))))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[3652, 16745])).
% 8.99/9.28 tff(16747,plain,
% 8.99/9.28 (~r(s(s(z)), s(z))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[5585, 16746, 590, 16379, 1216])).
% 8.99/9.28 tff(16748,plain,
% 8.99/9.28 (b(s(s(z)), s(z))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[3778, 16747])).
% 8.99/9.28 tff(16749,plain,
% 8.99/9.28 (~r(s(z), s(s(z)))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[16396, 16746, 1216, 16381])).
% 8.99/9.28 tff(16750,plain,
% 8.99/9.28 (b(s(z), s(s(z)))),
% 8.99/9.28 inference(unit_resolution,[status(thm)],[1788, 16749])).
% 8.99/9.28 tff(16751,plain,
% 8.99/9.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.28 inference(rewrite,[status(thm)],[])).
% 8.99/9.28 tff(16752,plain,
% 8.99/9.28 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.28 inference(rewrite,[status(thm)],[])).
% 8.99/9.28 tff(16753,plain,
% 8.99/9.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 8.99/9.29 inference(monotonicity,[status(thm)],[16752])).
% 8.99/9.29 tff(16754,plain,
% 8.99/9.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 8.99/9.29 inference(transitivity,[status(thm)],[16753, 16751])).
% 8.99/9.29 tff(16755,plain,
% 8.99/9.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 8.99/9.29 inference(quant_inst,[status(thm)],[])).
% 8.99/9.29 tff(16756,plain,
% 8.99/9.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 8.99/9.29 inference(modus_ponens,[status(thm)],[16755, 16754])).
% 8.99/9.29 tff(16757,plain,
% 8.99/9.29 ($false),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[16756, 391, 16738, 16750, 16748, 16744])).
% 8.99/9.29 tff(16758,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(s(z), z)) | (s(z) = elem!1) | (elem!1 = z) | b(elem!1, s(z)) | b(elem!1, s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.29 tff(16759,plain,
% 8.99/9.29 (~r(s(s(s(elem!1))), s(z))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[16758, 16353, 59, 2913, 16359, 10550, 150, 2, 31, 4028, 8232, 3618])).
% 8.99/9.29 tff(16760,plain,
% 8.99/9.29 (b(s(s(s(elem!1))), s(z))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[223, 16759])).
% 8.99/9.29 tff(16761,plain,
% 8.99/9.29 (~b(z, s(z))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[10635, 16760, 8232, 59, 10550, 4028, 31])).
% 8.99/9.29 tff(16762,plain,
% 8.99/9.29 (r(z, s(z))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[678, 16761])).
% 8.99/9.29 tff(16763,plain,
% 8.99/9.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.99/9.29 inference(rewrite,[status(thm)],[])).
% 8.99/9.29 tff(16764,plain,
% 8.99/9.29 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.99/9.29 inference(rewrite,[status(thm)],[])).
% 8.99/9.29 tff(16765,plain,
% 8.99/9.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))))),
% 8.99/9.29 inference(monotonicity,[status(thm)],[16764])).
% 8.99/9.29 tff(16766,plain,
% 8.99/9.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 8.99/9.29 inference(transitivity,[status(thm)],[16765, 16763])).
% 8.99/9.29 tff(16767,plain,
% 8.99/9.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 8.99/9.29 inference(quant_inst,[status(thm)],[])).
% 8.99/9.29 tff(16768,plain,
% 8.99/9.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))),
% 8.99/9.29 inference(modus_ponens,[status(thm)],[16767, 16766])).
% 8.99/9.29 tff(16769,plain,
% 8.99/9.29 ($false),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[16768, 194, 530, 232, 722, 847])).
% 8.99/9.29 tff(16770,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.29 tff(16771,plain,
% 8.99/9.29 (~r(s(z), s(s(s(elem!1))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[16770, 16762, 3618, 838])).
% 8.99/9.29 tff(16772,plain,
% 8.99/9.29 (b(s(z), s(s(s(elem!1))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[247, 16771])).
% 8.99/9.29 tff(16773,plain,
% 8.99/9.29 (~(s(s(s(elem!1))) = elem!1)),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[8400, 16760, 31])).
% 8.99/9.29 tff(16774,plain,
% 8.99/9.29 (b(s(s(s(elem!1))), elem!1)),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[230, 16773, 8290])).
% 8.99/9.29 tff(16775,plain,
% 8.99/9.29 (~(elem!1 = s(s(s(elem!1))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[129, 16773])).
% 8.99/9.29 tff(16776,plain,
% 8.99/9.29 (r(elem!1, s(s(s(elem!1))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[424, 16775, 4028])).
% 8.99/9.29 tff(16777,plain,
% 8.99/9.29 (~r(s(s(s(elem!1))), z)),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[8380, 16776, 59, 8232])).
% 8.99/9.29 tff(16778,plain,
% 8.99/9.29 (b(s(s(s(elem!1))), z)),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[377, 16777])).
% 8.99/9.29 tff(16779,plain,
% 8.99/9.29 (~b(z, s(s(s(s(z)))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[6325, 16778, 10550, 16353, 16760])).
% 8.99/9.29 tff(16780,plain,
% 8.99/9.29 (r(z, s(s(s(s(z)))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[800, 16779])).
% 8.99/9.29 tff(16781,plain,
% 8.99/9.29 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[6767, 391, 900, 379, 1526, 1759])).
% 8.99/9.29 tff(16782,plain,
% 8.99/9.29 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[15351, 16781, 16058])).
% 8.99/9.29 tff(16783,plain,
% 8.99/9.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.99/9.29 inference(rewrite,[status(thm)],[])).
% 8.99/9.29 tff(16784,plain,
% 8.99/9.29 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.99/9.29 inference(rewrite,[status(thm)],[])).
% 8.99/9.29 tff(16785,plain,
% 8.99/9.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 8.99/9.29 inference(monotonicity,[status(thm)],[16784])).
% 8.99/9.29 tff(16786,plain,
% 8.99/9.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.99/9.29 inference(transitivity,[status(thm)],[16785, 16783])).
% 8.99/9.29 tff(16787,plain,
% 8.99/9.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 8.99/9.29 inference(quant_inst,[status(thm)],[])).
% 8.99/9.29 tff(16788,plain,
% 8.99/9.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 8.99/9.29 inference(modus_ponens,[status(thm)],[16787, 16786])).
% 8.99/9.29 tff(16789,plain,
% 8.99/9.29 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[16788, 391, 900, 379, 1526, 1759])).
% 8.99/9.29 tff(16790,plain,
% 8.99/9.29 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 16789])).
% 8.99/9.29 tff(16791,plain,
% 8.99/9.29 ($false),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[3850, 194, 184, 719, 16790, 16782])).
% 8.99/9.29 tff(16792,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 8.99/9.29 tff(16793,plain,
% 8.99/9.29 (~b(s(s(s(s(z)))), s(z))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[16792, 16780, 59, 3363, 16774, 16772, 16760])).
% 8.99/9.29 tff(16794,plain,
% 8.99/9.29 (r(s(s(s(s(z)))), s(z))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[749, 16793])).
% 8.99/9.29 tff(16795,plain,
% 8.99/9.29 (~r(elem!1, s(s(s(s(z)))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[6347, 16794, 2913, 838])).
% 8.99/9.29 tff(16796,plain,
% 8.99/9.29 (b(elem!1, s(s(s(s(z)))))),
% 8.99/9.29 inference(unit_resolution,[status(thm)],[781, 16795, 16359])).
% 8.99/9.29 tff(16797,plain,
% 8.99/9.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 8.99/9.29 inference(rewrite,[status(thm)],[])).
% 8.99/9.29 tff(16798,plain,
% 8.99/9.29 (((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 8.99/9.29 inference(rewrite,[status(thm)],[])).
% 8.99/9.29 tff(16799,plain,
% 8.99/9.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), elem!1))))),
% 8.99/9.29 inference(monotonicity,[status(thm)],[16798])).
% 8.99/9.29 tff(16800,plain,
% 8.99/9.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 8.99/9.29 inference(transitivity,[status(thm)],[16799, 16797])).
% 8.99/9.29 tff(16801,plain,
% 8.99/9.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 8.99/9.29 inference(quant_inst,[status(thm)],[])).
% 8.99/9.29 tff(16802,plain,
% 8.99/9.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), elem!1))),
% 9.09/9.30 inference(modus_ponens,[status(thm)],[16801, 16800])).
% 9.09/9.30 tff(16803,plain,
% 9.09/9.30 ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), elem!1))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[16802, 194])).
% 9.09/9.30 tff(16804,plain,
% 9.09/9.30 (~r(s(z), elem!1)),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[16803, 16762, 3618, 8232])).
% 9.09/9.30 tff(16805,plain,
% 9.09/9.30 (b(s(z), elem!1)),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[632, 16804, 150])).
% 9.09/9.30 tff(16806,plain,
% 9.09/9.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 9.09/9.30 inference(rewrite,[status(thm)],[])).
% 9.09/9.30 tff(16807,plain,
% 9.09/9.30 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 9.09/9.30 inference(rewrite,[status(thm)],[])).
% 9.09/9.30 tff(16808,plain,
% 9.09/9.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 9.09/9.30 inference(monotonicity,[status(thm)],[16807])).
% 9.09/9.30 tff(16809,plain,
% 9.09/9.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 9.09/9.30 inference(transitivity,[status(thm)],[16808, 16806])).
% 9.09/9.30 tff(16810,plain,
% 9.09/9.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 9.09/9.30 inference(quant_inst,[status(thm)],[])).
% 9.09/9.30 tff(16811,plain,
% 9.09/9.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 9.09/9.30 inference(modus_ponens,[status(thm)],[16810, 16809])).
% 9.09/9.30 tff(16812,plain,
% 9.09/9.30 ($false),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[16811, 391, 16774, 16805, 16772, 16353, 16796])).
% 9.09/9.30 tff(16813,plain,(b(elem!1, s(s(s(elem!1)))) | (s(z) = elem!1) | b(elem!1, s(z)) | (elem!1 = z) | b(elem!1, z) | b(z, s(s(s(elem!1)))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.30 tff(16814,plain,
% 9.09/9.30 (b(elem!1, s(s(s(elem!1))))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[16813, 2881, 31, 2, 484, 10, 150])).
% 9.09/9.30 tff(16815,plain,
% 9.09/9.30 (~(s(s(s(elem!1))) = elem!1)),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[15370, 16814])).
% 9.09/9.30 tff(16816,plain,
% 9.09/9.30 (b(s(s(s(elem!1))), elem!1)),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[230, 16815, 8290])).
% 9.09/9.30 tff(16817,plain,
% 9.09/9.30 (~r(s(z), s(s(s(elem!1))))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[16770, 722, 530, 847])).
% 9.09/9.30 tff(16818,plain,
% 9.09/9.30 (b(s(z), s(s(s(elem!1))))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[247, 16817])).
% 9.09/9.30 tff(16819,plain,
% 9.09/9.30 (~r(s(z), elem!1)),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[16803, 722, 530, 411])).
% 9.09/9.30 tff(16820,plain,
% 9.09/9.30 (b(s(z), elem!1)),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[632, 16819, 150])).
% 9.09/9.30 tff(16821,plain,
% 9.09/9.30 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 9.09/9.30 inference(rewrite,[status(thm)],[])).
% 9.09/9.30 tff(16822,plain,
% 9.09/9.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 9.09/9.30 inference(monotonicity,[status(thm)],[16821])).
% 9.09/9.30 tff(16823,plain,
% 9.09/9.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 9.09/9.30 inference(transitivity,[status(thm)],[16822, 9841])).
% 9.09/9.30 tff(16824,plain,
% 9.09/9.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 9.09/9.30 inference(quant_inst,[status(thm)],[])).
% 9.09/9.30 tff(16825,plain,
% 9.09/9.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 9.09/9.30 inference(modus_ponens,[status(thm)],[16824, 16823])).
% 9.09/9.30 tff(16826,plain,
% 9.09/9.30 ($false),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[16825, 391, 900, 448, 16820, 16818])).
% 9.09/9.30 tff(16827,plain,((~r(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(z) = elem!1) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.30 tff(16828,plain,
% 9.09/9.30 (~r(z, s(z))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[16827, 16816, 16814, 150, 3618, 838, 8232])).
% 9.09/9.30 tff(16829,plain,
% 9.09/9.30 (b(z, s(z))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[678, 16828])).
% 9.09/9.30 tff(16830,plain,
% 9.09/9.30 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[10940, 3363])).
% 9.09/9.30 tff(16831,plain,
% 9.09/9.30 (~(elem!1 = s(s(s(elem!1))))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[129, 16815])).
% 9.09/9.30 tff(16832,plain,
% 9.09/9.30 (~(s(elem!1) = elem!1)),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[158, 16815])).
% 9.09/9.30 tff(16833,plain,
% 9.09/9.30 (~(elem!1 = s(elem!1))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[166, 16832])).
% 9.09/9.30 tff(16834,plain,
% 9.09/9.30 (~b(z, elem!1)),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[6505, 16816, 59, 150, 484, 16833, 16831, 2])).
% 9.09/9.30 tff(16835,plain,
% 9.09/9.30 (~r(s(s(s(s(z)))), elem!1)),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[10408, 3447, 838, 411])).
% 9.09/9.30 tff(16836,plain,
% 9.09/9.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.30 inference(rewrite,[status(thm)],[])).
% 9.09/9.30 tff(16837,plain,
% 9.09/9.30 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.30 inference(rewrite,[status(thm)],[])).
% 9.09/9.30 tff(16838,plain,
% 9.09/9.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.09/9.30 inference(monotonicity,[status(thm)],[16837])).
% 9.09/9.30 tff(16839,plain,
% 9.09/9.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.30 inference(transitivity,[status(thm)],[16838, 16836])).
% 9.09/9.30 tff(16840,plain,
% 9.09/9.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.30 inference(quant_inst,[status(thm)],[])).
% 9.09/9.30 tff(16841,plain,
% 9.09/9.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.09/9.30 inference(modus_ponens,[status(thm)],[16840, 16839])).
% 9.09/9.30 tff(16842,plain,
% 9.09/9.30 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[16841, 391, 900, 448, 1652])).
% 9.09/9.30 tff(16843,plain,
% 9.09/9.30 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.09/9.30 inference(unit_resolution,[status(thm)],[15351, 16842, 16058])).
% 9.09/9.30 tff(16844,plain,
% 9.09/9.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.30 inference(rewrite,[status(thm)],[])).
% 9.09/9.30 tff(16845,plain,
% 9.09/9.30 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.30 inference(rewrite,[status(thm)],[])).
% 9.09/9.30 tff(16846,plain,
% 9.09/9.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.09/9.31 inference(monotonicity,[status(thm)],[16845])).
% 9.09/9.31 tff(16847,plain,
% 9.09/9.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.31 inference(transitivity,[status(thm)],[16846, 16844])).
% 9.09/9.31 tff(16848,plain,
% 9.09/9.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 9.09/9.31 inference(quant_inst,[status(thm)],[])).
% 9.09/9.31 tff(16849,plain,
% 9.09/9.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.09/9.31 inference(modus_ponens,[status(thm)],[16848, 16847])).
% 9.09/9.31 tff(16850,plain,
% 9.09/9.31 ($false),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[16849, 194, 184, 2053, 2100, 4317])).
% 9.09/9.31 tff(16851,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.31 tff(16852,plain,
% 9.09/9.31 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[16851, 16843, 2053, 184])).
% 9.09/9.31 tff(16853,plain,
% 9.09/9.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.09/9.31 inference(rewrite,[status(thm)],[])).
% 9.09/9.31 tff(16854,plain,
% 9.09/9.31 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.09/9.31 inference(rewrite,[status(thm)],[])).
% 9.09/9.31 tff(16855,plain,
% 9.09/9.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 9.09/9.31 inference(monotonicity,[status(thm)],[16854])).
% 9.09/9.31 tff(16856,plain,
% 9.09/9.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.09/9.31 inference(transitivity,[status(thm)],[16855, 16853])).
% 9.09/9.31 tff(16857,plain,
% 9.09/9.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.09/9.31 inference(quant_inst,[status(thm)],[])).
% 9.09/9.31 tff(16858,plain,
% 9.09/9.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 9.09/9.31 inference(modus_ponens,[status(thm)],[16857, 16856])).
% 9.09/9.31 tff(16859,plain,
% 9.09/9.31 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[16858, 391, 900, 448, 1652])).
% 9.09/9.31 tff(16860,plain,
% 9.09/9.31 ($false),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 16859, 16852])).
% 9.09/9.31 tff(16861,plain,((~b(s(s(s(s(z)))), elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.31 tff(16862,plain,
% 9.09/9.31 (~b(s(s(s(s(z)))), elem!1)),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[16861, 3447, 3363, 184, 900, 448])).
% 9.09/9.31 tff(16863,plain,
% 9.09/9.31 (s(s(s(s(z)))) = elem!1),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[762, 16862, 16835])).
% 9.09/9.31 tff(16864,plain,
% 9.09/9.31 (~b(s(s(s(s(z)))), s(z))),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[11186, 16863, 31])).
% 9.09/9.31 tff(16865,plain,
% 9.09/9.31 (r(s(s(s(s(z)))), s(z))),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[749, 16864])).
% 9.09/9.31 tff(16866,plain,
% 9.09/9.31 (~b(s(z), elem!1)),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[6252, 16863, 2881])).
% 9.09/9.31 tff(16867,plain,
% 9.09/9.31 (r(s(z), elem!1)),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[632, 16866, 150])).
% 9.09/9.31 tff(16868,plain,
% 9.09/9.31 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 9.09/9.31 inference(monotonicity,[status(thm)],[16863])).
% 9.09/9.31 tff(16869,plain,
% 9.09/9.31 (~b(z, s(s(s(s(z)))))),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[16124, 16863, 89])).
% 9.09/9.31 tff(16870,plain,
% 9.09/9.31 (r(z, s(s(s(s(z)))))),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[800, 16869])).
% 9.09/9.31 tff(16871,plain,
% 9.09/9.31 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[16415, 16870, 664, 16865, 590, 2913])).
% 9.09/9.31 tff(16872,plain,
% 9.09/9.31 (b(s(s(z)), s(s(s(s(z)))))),
% 9.09/9.31 inference(unit_resolution,[status(thm)],[3652, 16871])).
% 9.09/9.31 tff(16873,plain,
% 9.09/9.31 (b(s(s(z)), elem!1)),
% 9.09/9.31 inference(modus_ponens,[status(thm)],[16872, 16868])).
% 9.09/9.31 tff(16874,plain,
% 9.09/9.31 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 9.09/9.31 inference(rewrite,[status(thm)],[])).
% 9.09/9.31 tff(16875,plain,
% 9.09/9.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))))),
% 9.09/9.31 inference(monotonicity,[status(thm)],[16874])).
% 9.09/9.31 tff(16876,plain,
% 9.09/9.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 9.09/9.31 inference(transitivity,[status(thm)],[16875, 15432])).
% 9.09/9.32 tff(16877,plain,
% 9.09/9.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.09/9.32 inference(quant_inst,[status(thm)],[])).
% 9.09/9.32 tff(16878,plain,
% 9.09/9.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))),
% 9.09/9.32 inference(modus_ponens,[status(thm)],[16877, 16876])).
% 9.09/9.32 tff(16879,plain,
% 9.09/9.32 (~b(s(s(z)), s(s(s(elem!1))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[16878, 391, 900, 448, 16873])).
% 9.09/9.32 tff(16880,plain,
% 9.09/9.32 (r(s(s(z)), s(s(s(elem!1))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[11041, 16879])).
% 9.09/9.32 tff(16881,plain,
% 9.09/9.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.09/9.32 inference(rewrite,[status(thm)],[])).
% 9.09/9.32 tff(16882,plain,
% 9.09/9.32 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.09/9.32 inference(rewrite,[status(thm)],[])).
% 9.09/9.32 tff(16883,plain,
% 9.09/9.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 9.09/9.32 inference(monotonicity,[status(thm)],[16882])).
% 9.09/9.32 tff(16884,plain,
% 9.09/9.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.09/9.32 inference(transitivity,[status(thm)],[16883, 16881])).
% 9.09/9.32 tff(16885,plain,
% 9.09/9.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.09/9.32 inference(quant_inst,[status(thm)],[])).
% 9.09/9.32 tff(16886,plain,
% 9.09/9.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 9.09/9.32 inference(modus_ponens,[status(thm)],[16885, 16884])).
% 9.09/9.32 tff(16887,plain,
% 9.09/9.32 (~b(s(s(s(elem!1))), s(s(z)))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[16886, 391, 900, 448, 16873])).
% 9.09/9.32 tff(16888,plain,
% 9.09/9.32 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[10713, 42, 16887])).
% 9.09/9.32 tff(16889,plain,
% 9.09/9.32 (r(s(s(s(elem!1))), s(s(z)))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[16888, 10703])).
% 9.09/9.32 tff(16890,plain,
% 9.09/9.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 9.09/9.32 inference(rewrite,[status(thm)],[])).
% 9.09/9.32 tff(16891,plain,
% 9.09/9.32 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 9.09/9.32 inference(rewrite,[status(thm)],[])).
% 9.09/9.32 tff(16892,plain,
% 9.09/9.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 9.09/9.32 inference(monotonicity,[status(thm)],[16891])).
% 9.09/9.32 tff(16893,plain,
% 9.09/9.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 9.09/9.32 inference(transitivity,[status(thm)],[16892, 16890])).
% 9.09/9.32 tff(16894,plain,
% 9.09/9.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 9.09/9.32 inference(quant_inst,[status(thm)],[])).
% 9.09/9.32 tff(16895,plain,
% 9.09/9.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 9.09/9.32 inference(modus_ponens,[status(thm)],[16894, 16893])).
% 9.09/9.32 tff(16896,plain,
% 9.09/9.32 (~r(s(s(z)), z)),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[16895, 194, 184, 16889, 16880])).
% 9.09/9.32 tff(16897,plain,
% 9.09/9.32 (b(s(s(z)), z)),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[1211, 16896])).
% 9.09/9.32 tff(16898,plain,
% 9.09/9.32 (~b(s(s(z)), s(z))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[10658, 391, 16897, 664, 590])).
% 9.09/9.32 tff(16899,plain,
% 9.09/9.32 (r(s(s(z)), s(z))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[3778, 16898])).
% 9.09/9.32 tff(16900,plain,
% 9.09/9.32 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[2429, 16899, 16867, 16865])).
% 9.09/9.32 tff(16901,plain,
% 9.09/9.32 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[10090, 16870, 3447, 184])).
% 9.09/9.32 tff(16902,plain,
% 9.09/9.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[11148, 16899, 448, 16865, 15376, 118, 16872, 590, 838, 2, 3446, 411, 16901, 2881, 184])).
% 9.09/9.32 tff(16903,plain,
% 9.09/9.32 ($false),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[1714, 16902, 16900])).
% 9.09/9.32 tff(16904,plain,(b(s(s(s(s(z)))), z) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (elem!1 = z) | (~r(z, elem!1)) | b(s(z), s(s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (s(z) = elem!1) | b(z, elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.32 tff(16905,plain,
% 9.09/9.32 (b(s(s(s(s(z)))), z)),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[16904, 16814, 10550, 2, 8232, 2881, 59, 16829, 16816, 150, 16834, 31])).
% 9.09/9.32 tff(16906,plain,
% 9.09/9.32 (~(elem!1 = s(s(s(s(z)))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[16358, 16905, 484])).
% 9.09/9.32 tff(16907,plain,
% 9.09/9.32 ($false),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[8922, 14460])).
% 9.09/9.32 tff(16908,plain,((~(s(s(s(s(z)))) = elem!1)) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.32 tff(16909,plain,
% 9.09/9.32 (~(s(s(s(s(z)))) = elem!1)),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[16908, 16906])).
% 9.09/9.32 tff(16910,plain,
% 9.09/9.32 (~b(s(s(s(s(z)))), s(z))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[5575, 391, 16905, 16829, 10550])).
% 9.09/9.32 tff(16911,plain,
% 9.09/9.32 (r(s(s(s(s(z)))), s(z))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[749, 16910])).
% 9.09/9.32 tff(16912,plain,
% 9.09/9.32 (~r(s(s(s(s(z)))), elem!1)),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[10824, 194, 838, 2913, 16911])).
% 9.09/9.32 tff(16913,plain,
% 9.09/9.32 (b(s(s(s(s(z)))), elem!1)),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[762, 16912, 16909])).
% 9.09/9.32 tff(16914,plain,
% 9.09/9.32 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[16841, 391, 16816, 16814, 16913])).
% 9.09/9.32 tff(16915,plain,
% 9.09/9.32 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[15351, 16914, 16830])).
% 9.09/9.32 tff(16916,plain,
% 9.09/9.32 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[16858, 391, 16816, 16814, 16913])).
% 9.09/9.32 tff(16917,plain,
% 9.09/9.32 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[2853, 42, 3363, 16916])).
% 9.09/9.32 tff(16918,plain,
% 9.09/9.32 (~r(z, s(s(s(s(z)))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[3850, 194, 59, 16917, 16915])).
% 9.09/9.32 tff(16919,plain,
% 9.09/9.32 (b(z, s(s(s(s(z)))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[800, 16918])).
% 9.09/9.32 tff(16920,plain,
% 9.09/9.32 (~r(elem!1, s(s(s(s(z)))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[6347, 16911, 2913, 838])).
% 9.09/9.32 tff(16921,plain,
% 9.09/9.32 (b(elem!1, s(s(s(s(z)))))),
% 9.09/9.32 inference(unit_resolution,[status(thm)],[781, 16920, 16906])).
% 9.09/9.32 tff(16922,plain,
% 9.09/9.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.32 inference(rewrite,[status(thm)],[])).
% 9.09/9.32 tff(16923,plain,
% 9.09/9.32 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.32 inference(rewrite,[status(thm)],[])).
% 9.09/9.32 tff(16924,plain,
% 9.09/9.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.09/9.32 inference(monotonicity,[status(thm)],[16923])).
% 9.09/9.32 tff(16925,plain,
% 9.09/9.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.32 inference(transitivity,[status(thm)],[16924, 16922])).
% 9.09/9.32 tff(16926,plain,
% 9.09/9.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 9.09/9.32 inference(quant_inst,[status(thm)],[])).
% 9.09/9.32 tff(16927,plain,
% 9.09/9.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.09/9.33 inference(modus_ponens,[status(thm)],[16926, 16925])).
% 9.09/9.33 tff(16928,plain,
% 9.09/9.33 (~r(s(z), s(s(s(elem!1))))),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[16927, 194, 2913, 16917, 16915])).
% 9.09/9.33 tff(16929,plain,
% 9.09/9.33 (b(s(z), s(s(s(elem!1))))),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[247, 16928])).
% 9.09/9.33 tff(16930,plain,
% 9.09/9.33 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[8251, 16815])).
% 9.09/9.33 tff(16931,plain,
% 9.09/9.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.33 inference(rewrite,[status(thm)],[])).
% 9.09/9.33 tff(16932,plain,
% 9.09/9.33 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.33 inference(rewrite,[status(thm)],[])).
% 9.09/9.33 tff(16933,plain,
% 9.09/9.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.09/9.33 inference(monotonicity,[status(thm)],[16932])).
% 9.09/9.33 tff(16934,plain,
% 9.09/9.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.33 inference(transitivity,[status(thm)],[16933, 16931])).
% 9.09/9.33 tff(16935,plain,
% 9.09/9.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.09/9.33 inference(quant_inst,[status(thm)],[])).
% 9.09/9.33 tff(16936,plain,
% 9.09/9.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.09/9.33 inference(modus_ponens,[status(thm)],[16935, 16934])).
% 9.09/9.33 tff(16937,plain,
% 9.09/9.33 (~r(s(s(s(elem!1))), s(z))),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[16936, 194, 2913, 16917, 16915])).
% 9.09/9.33 tff(16938,plain,
% 9.09/9.33 (b(s(s(s(elem!1))), s(z))),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[223, 16937])).
% 9.09/9.33 tff(16939,plain,
% 9.09/9.33 (~b(s(z), elem!1)),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[4026, 16929, 16814, 16938])).
% 9.09/9.33 tff(16940,plain,
% 9.09/9.33 (r(s(z), elem!1)),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[632, 16939, 150])).
% 9.09/9.33 tff(16941,plain,
% 9.09/9.33 (~r(s(s(elem!1)), elem!1)),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[6047, 16940, 59, 10550, 16930, 16929, 3618, 838])).
% 9.09/9.33 tff(16942,plain,
% 9.09/9.33 (~b(s(s(s(elem!1))), z)),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[6325, 16938, 10550, 16905, 16919])).
% 9.09/9.33 tff(16943,plain,
% 9.09/9.33 (r(s(s(s(elem!1))), z)),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[377, 16942])).
% 9.09/9.33 tff(16944,plain,
% 9.09/9.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 9.09/9.33 inference(rewrite,[status(thm)],[])).
% 9.09/9.33 tff(16945,plain,
% 9.09/9.33 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~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)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 9.09/9.33 inference(rewrite,[status(thm)],[])).
% 9.09/9.33 tff(16946,plain,
% 9.09/9.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 9.09/9.33 inference(monotonicity,[status(thm)],[16945])).
% 9.09/9.33 tff(16947,plain,
% 9.09/9.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 9.09/9.33 inference(transitivity,[status(thm)],[16946, 16944])).
% 9.09/9.33 tff(16948,plain,
% 9.09/9.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 9.09/9.33 inference(quant_inst,[status(thm)],[])).
% 9.09/9.33 tff(16949,plain,
% 9.09/9.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 9.09/9.33 inference(modus_ponens,[status(thm)],[16948, 16947])).
% 9.09/9.33 tff(16950,plain,
% 9.09/9.33 (~b(s(s(z)), elem!1)),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[16949, 391, 3823, 90, 2064, 1686])).
% 9.09/9.33 tff(16951,plain,
% 9.09/9.33 (~r(s(s(z)), elem!1)),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[15383, 194, 411, 530, 16450])).
% 9.09/9.33 tff(16952,plain,
% 9.09/9.33 (s(s(z)) = elem!1),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[4730, 16951, 16950])).
% 9.09/9.33 tff(16953,plain,
% 9.09/9.33 (s(s(s(z))) = s(elem!1)),
% 9.09/9.33 inference(monotonicity,[status(thm)],[16952])).
% 9.09/9.33 tff(16954,plain,
% 9.09/9.33 (s(s(s(s(z)))) = s(s(elem!1))),
% 9.09/9.33 inference(monotonicity,[status(thm)],[16953])).
% 9.09/9.33 tff(16955,plain,
% 9.09/9.33 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 9.09/9.33 inference(monotonicity,[status(thm)],[16954])).
% 9.09/9.33 tff(16956,plain,
% 9.09/9.33 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 9.09/9.33 inference(monotonicity,[status(thm)],[16953, 16955])).
% 9.09/9.33 tff(16957,plain,
% 9.09/9.33 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 9.09/9.33 inference(monotonicity,[status(thm)],[16953, 16955])).
% 9.09/9.33 tff(16958,plain,
% 9.09/9.33 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 9.09/9.33 inference(symmetry,[status(thm)],[16957])).
% 9.09/9.33 tff(16959,plain,
% 9.09/9.33 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 9.09/9.33 inference(monotonicity,[status(thm)],[16958])).
% 9.09/9.33 tff(16960,plain,
% 9.09/9.33 (~(s(s(s(elem!1))) = s(elem!1))),
% 9.09/9.33 inference(unit_resolution,[status(thm)],[4584, 16952, 121])).
% 9.09/9.34 tff(16961,plain,
% 9.09/9.34 (~(s(s(elem!1)) = elem!1)),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[451, 16960])).
% 9.09/9.34 tff(16962,plain,
% 9.09/9.34 (b(s(s(elem!1)), elem!1)),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[872, 16961, 888])).
% 9.09/9.34 tff(16963,plain,
% 9.09/9.34 (~r(s(s(s(elem!1))), elem!1)),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[8289, 530, 184, 411])).
% 9.09/9.34 tff(16964,plain,
% 9.09/9.34 (b(s(s(s(elem!1))), elem!1)),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[230, 15376, 16963])).
% 9.09/9.34 tff(16965,plain,
% 9.09/9.34 (~(elem!1 = s(s(elem!1)))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[1292, 16961])).
% 9.09/9.34 tff(16966,plain,
% 9.09/9.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 9.09/9.34 inference(rewrite,[status(thm)],[])).
% 9.09/9.34 tff(16967,plain,
% 9.09/9.34 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 9.09/9.34 inference(rewrite,[status(thm)],[])).
% 9.09/9.34 tff(16968,plain,
% 9.09/9.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 9.09/9.34 inference(monotonicity,[status(thm)],[16967])).
% 9.09/9.34 tff(16969,plain,
% 9.09/9.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 9.09/9.34 inference(transitivity,[status(thm)],[16968, 16966])).
% 9.09/9.34 tff(16970,plain,
% 9.09/9.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 9.09/9.34 inference(quant_inst,[status(thm)],[])).
% 9.09/9.34 tff(16971,plain,
% 9.09/9.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 9.09/9.34 inference(modus_ponens,[status(thm)],[16970, 16969])).
% 9.09/9.34 tff(16972,plain,
% 9.09/9.34 (~b(elem!1, s(s(z)))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[16971, 391, 3823, 90, 2064, 1686])).
% 9.09/9.34 tff(16973,plain,
% 9.09/9.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 9.09/9.34 inference(rewrite,[status(thm)],[])).
% 9.09/9.34 tff(16974,plain,
% 9.09/9.34 (((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 9.09/9.34 inference(rewrite,[status(thm)],[])).
% 9.09/9.34 tff(16975,plain,
% 9.09/9.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))))),
% 9.09/9.34 inference(monotonicity,[status(thm)],[16974])).
% 9.09/9.34 tff(16976,plain,
% 9.09/9.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 9.09/9.34 inference(transitivity,[status(thm)],[16975, 16973])).
% 9.09/9.34 tff(16977,plain,
% 9.09/9.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))),
% 9.09/9.34 inference(quant_inst,[status(thm)],[])).
% 9.09/9.34 tff(16978,plain,
% 9.09/9.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))),
% 9.09/9.34 inference(modus_ponens,[status(thm)],[16977, 16976])).
% 9.09/9.34 tff(16979,plain,
% 9.09/9.34 (~r(elem!1, s(s(z)))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[16978, 194, 411, 530, 16450])).
% 9.09/9.34 tff(16980,plain,
% 9.09/9.34 (elem!1 = s(s(z))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[3394, 16979, 16972])).
% 9.09/9.34 tff(16981,plain,
% 9.09/9.34 (~b(s(s(elem!1)), s(z))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[9032, 16980, 16385])).
% 9.09/9.34 tff(16982,plain,
% 9.09/9.34 (r(s(s(elem!1)), s(z))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[362, 16981])).
% 9.09/9.34 tff(16983,plain,
% 9.09/9.34 (~r(elem!1, s(s(elem!1)))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[6408, 16982, 1216, 847])).
% 9.09/9.34 tff(16984,plain,
% 9.09/9.34 (b(elem!1, s(s(elem!1)))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[1307, 16983, 16965])).
% 9.09/9.34 tff(16985,plain,
% 9.09/9.34 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[1467, 16984, 16964, 16962])).
% 9.09/9.34 tff(16986,plain,
% 9.09/9.34 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[1370, 16985, 16094])).
% 9.09/9.34 tff(16987,plain,
% 9.09/9.34 (~(s(s(elem!1)) = s(elem!1))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[2279, 16960])).
% 9.09/9.34 tff(16988,plain,
% 9.09/9.34 (~(s(elem!1) = s(s(elem!1)))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[9802, 16987])).
% 9.09/9.34 tff(16989,plain,
% 9.09/9.34 (~(s(elem!1) = elem!1)),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[158, 15376])).
% 9.09/9.34 tff(16990,plain,
% 9.09/9.34 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[6001, 16962, 16964, 448])).
% 9.09/9.34 tff(16991,plain,
% 9.09/9.34 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[1356, 16990, 16095])).
% 9.09/9.34 tff(16992,plain,
% 9.09/9.34 (~r(z, s(s(elem!1)))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[1450, 16991, 184, 174])).
% 9.09/9.34 tff(16993,plain,
% 9.09/9.34 (b(z, s(s(elem!1)))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[324, 16992])).
% 9.09/9.34 tff(16994,plain,
% 9.09/9.34 (~r(s(elem!1), elem!1)),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[9873, 16993, 411, 121, 530, 1484, 16962])).
% 9.09/9.34 tff(16995,plain,
% 9.09/9.34 (b(s(elem!1), elem!1)),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[2168, 16994, 16989])).
% 9.09/9.34 tff(16996,plain,
% 9.09/9.34 (~r(s(elem!1), s(s(s(elem!1))))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[8697, 16995, 16964, 16988, 16987, 448, 16962, 16986])).
% 9.09/9.34 tff(16997,plain,
% 9.09/9.34 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 9.09/9.34 inference(modus_ponens,[status(thm)],[16996, 16959])).
% 9.09/9.34 tff(16998,plain,
% 9.09/9.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(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(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 9.09/9.34 inference(rewrite,[status(thm)],[])).
% 9.09/9.34 tff(16999,plain,
% 9.09/9.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 9.09/9.34 inference(quant_inst,[status(thm)],[])).
% 9.09/9.34 tff(17000,plain,
% 9.09/9.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 9.09/9.34 inference(modus_ponens,[status(thm)],[16999, 16998])).
% 9.09/9.34 tff(17001,plain,
% 9.09/9.34 ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[17000, 42])).
% 9.09/9.34 tff(17002,plain,
% 9.09/9.34 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[17001, 16997, 8593])).
% 9.09/9.34 tff(17003,plain,
% 9.09/9.34 (b(s(elem!1), s(s(s(elem!1))))),
% 9.09/9.34 inference(modus_ponens,[status(thm)],[17002, 16956])).
% 9.09/9.34 tff(17004,plain,
% 9.09/9.34 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(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))))))),
% 9.09/9.34 inference(rewrite,[status(thm)],[])).
% 9.09/9.34 tff(17005,plain,
% 9.09/9.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(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)))))))),
% 9.09/9.34 inference(monotonicity,[status(thm)],[17004])).
% 9.09/9.34 tff(17006,plain,
% 9.09/9.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(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))))))),
% 9.09/9.34 inference(transitivity,[status(thm)],[17005, 6885])).
% 9.09/9.34 tff(17007,plain,
% 9.09/9.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 9.09/9.34 inference(quant_inst,[status(thm)],[])).
% 9.09/9.34 tff(17008,plain,
% 9.09/9.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 9.09/9.34 inference(modus_ponens,[status(thm)],[17007, 17006])).
% 9.09/9.34 tff(17009,plain,
% 9.09/9.34 ($false),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[17008, 391, 16964, 448, 16995, 17003])).
% 9.09/9.34 tff(17010,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | r(s(s(elem!1)), elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.34 tff(17011,plain,
% 9.09/9.34 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[17010, 16814, 8232, 118, 3618, 16940, 59, 16943, 2913, 838, 16941, 16905, 16921, 16919, 16829, 10550])).
% 9.09/9.34 tff(17012,plain,
% 9.09/9.34 (r(s(s(z)), s(s(s(s(z)))))),
% 9.09/9.34 inference(unit_resolution,[status(thm)],[3652, 17011])).
% 9.09/9.34 tff(17013,plain,
% 9.09/9.35 (~r(s(s(z)), s(z))),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[5585, 17012, 10550, 16829, 2913])).
% 9.09/9.35 tff(17014,plain,
% 9.09/9.35 (b(s(s(z)), s(z))),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[3778, 17013])).
% 9.09/9.35 tff(17015,plain,
% 9.09/9.35 (~r(s(z), s(s(z)))),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[16396, 17012, 2913, 16911])).
% 9.09/9.35 tff(17016,plain,
% 9.09/9.35 (b(s(z), s(s(z)))),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[1788, 17015])).
% 9.09/9.35 tff(17017,plain,
% 9.09/9.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.09/9.35 inference(rewrite,[status(thm)],[])).
% 9.09/9.35 tff(17018,plain,
% 9.09/9.35 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.09/9.35 inference(rewrite,[status(thm)],[])).
% 9.09/9.35 tff(17019,plain,
% 9.09/9.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 9.09/9.35 inference(monotonicity,[status(thm)],[17018])).
% 9.09/9.35 tff(17020,plain,
% 9.09/9.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.09/9.35 inference(transitivity,[status(thm)],[17019, 17017])).
% 9.09/9.35 tff(17021,plain,
% 9.09/9.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.09/9.35 inference(quant_inst,[status(thm)],[])).
% 9.09/9.35 tff(17022,plain,
% 9.09/9.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 9.09/9.35 inference(modus_ponens,[status(thm)],[17021, 17020])).
% 9.09/9.35 tff(17023,plain,
% 9.09/9.35 (~b(s(s(z)), s(s(s(elem!1))))),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[17022, 391, 16938, 17016, 17014])).
% 9.09/9.35 tff(17024,plain,
% 9.09/9.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.35 inference(rewrite,[status(thm)],[])).
% 9.09/9.35 tff(17025,plain,
% 9.09/9.35 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), 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(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.35 inference(rewrite,[status(thm)],[])).
% 9.09/9.35 tff(17026,plain,
% 9.09/9.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.09/9.35 inference(monotonicity,[status(thm)],[17025])).
% 9.09/9.35 tff(17027,plain,
% 9.09/9.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.09/9.35 inference(transitivity,[status(thm)],[17026, 17024])).
% 9.09/9.35 tff(17028,plain,
% 9.09/9.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 9.09/9.35 inference(quant_inst,[status(thm)],[])).
% 9.09/9.35 tff(17029,plain,
% 9.09/9.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.09/9.35 inference(modus_ponens,[status(thm)],[17028, 17027])).
% 9.09/9.35 tff(17030,plain,
% 9.09/9.35 (~r(s(s(z)), s(s(s(elem!1))))),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[17029, 194, 17012, 16911, 16915])).
% 9.09/9.35 tff(17031,plain,
% 9.09/9.35 ($false),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[11041, 17030, 17023])).
% 9.09/9.35 tff(17032,plain,(b(s(z), s(s(s(s(z))))) | (s(z) = elem!1) | b(elem!1, z) | (elem!1 = z) | b(elem!1, s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.35 tff(17033,plain,
% 9.09/9.35 (b(s(z), s(s(s(s(z)))))),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[17032, 150, 484, 2, 31, 10])).
% 9.09/9.35 tff(17034,plain,
% 9.09/9.35 (~r(s(s(s(s(z)))), elem!1)),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[10408, 3447, 838, 8232])).
% 9.09/9.35 tff(17035,plain,
% 9.09/9.35 (~r(s(z), elem!1)),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[16803, 722, 3618, 8232])).
% 9.09/9.35 tff(17036,plain,
% 9.09/9.35 (b(s(z), s(s(s(s(z)))))),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[16257, 31, 8329, 115, 3446])).
% 9.09/9.35 tff(17037,plain,
% 9.09/9.35 (~(s(z) = elem!1)),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[8542, 4028, 1234])).
% 9.09/9.35 tff(17038,plain,
% 9.09/9.35 (~r(z, s(s(z)))),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[10160, 194, 1749, 2053, 719])).
% 9.09/9.35 tff(17039,plain,
% 9.09/9.35 (b(z, s(s(z)))),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[10164, 42, 17038, 8912])).
% 9.09/9.35 tff(17040,plain,
% 9.09/9.35 (~r(s(s(s(elem!1))), z)),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[8380, 15899, 8849, 59])).
% 9.09/9.35 tff(17041,plain,
% 9.09/9.35 (b(s(s(s(elem!1))), z)),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[377, 17040])).
% 9.09/9.35 tff(17042,plain,
% 9.09/9.35 (b(s(s(s(elem!1))), elem!1)),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[10519, 15899, 4028, 1, 59])).
% 9.09/9.35 tff(17043,plain,
% 9.09/9.35 (~r(elem!1, z)),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[6153, 59, 8849, 327])).
% 9.09/9.35 tff(17044,plain,
% 9.09/9.35 (b(elem!1, z)),
% 9.09/9.35 inference(unit_resolution,[status(thm)],[526, 17043, 2])).
% 9.09/9.35 tff(17045,plain,
% 9.09/9.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 9.09/9.35 inference(rewrite,[status(thm)],[])).
% 9.09/9.35 tff(17046,plain,
% 9.09/9.35 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 9.09/9.36 inference(rewrite,[status(thm)],[])).
% 9.09/9.36 tff(17047,plain,
% 9.09/9.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))))),
% 9.09/9.36 inference(monotonicity,[status(thm)],[17046])).
% 9.09/9.36 tff(17048,plain,
% 9.09/9.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 9.09/9.36 inference(transitivity,[status(thm)],[17047, 17045])).
% 9.09/9.36 tff(17049,plain,
% 9.09/9.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 9.09/9.36 inference(quant_inst,[status(thm)],[])).
% 9.09/9.36 tff(17050,plain,
% 9.09/9.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))),
% 9.09/9.36 inference(modus_ponens,[status(thm)],[17049, 17048])).
% 9.09/9.36 tff(17051,plain,
% 9.09/9.36 ($false),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[17050, 391, 17044, 17042, 17041, 1235, 15045])).
% 9.09/9.36 tff(17052,plain,(b(z, s(s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (elem!1 = z) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.36 tff(17053,plain,
% 9.09/9.36 (b(z, s(s(s(elem!1))))),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[17052, 15045, 1235, 10680, 4028, 4029, 327])).
% 9.09/9.36 tff(17054,plain,
% 9.09/9.36 (~r(z, elem!1)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[845, 182, 722, 847])).
% 9.09/9.36 tff(17055,plain,
% 9.09/9.36 (b(z, elem!1)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[141, 17054, 115])).
% 9.09/9.36 tff(17056,plain,
% 9.09/9.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 9.09/9.36 inference(rewrite,[status(thm)],[])).
% 9.09/9.36 tff(17057,plain,
% 9.09/9.36 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 9.09/9.36 inference(rewrite,[status(thm)],[])).
% 9.09/9.36 tff(17058,plain,
% 9.09/9.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(z))))))))),
% 9.09/9.36 inference(monotonicity,[status(thm)],[17057])).
% 9.09/9.36 tff(17059,plain,
% 9.09/9.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 9.09/9.36 inference(transitivity,[status(thm)],[17058, 17056])).
% 9.09/9.36 tff(17060,plain,
% 9.09/9.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 9.09/9.36 inference(quant_inst,[status(thm)],[])).
% 9.09/9.36 tff(17061,plain,
% 9.09/9.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(z))))))),
% 9.09/9.36 inference(modus_ponens,[status(thm)],[17060, 17059])).
% 9.09/9.36 tff(17062,plain,
% 9.09/9.36 ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(z))))))),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[17061, 194])).
% 9.09/9.36 tff(17063,plain,
% 9.09/9.36 (~r(elem!1, z)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[17062, 182, 719, 847])).
% 9.09/9.36 tff(17064,plain,
% 9.09/9.36 (b(elem!1, z)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[526, 17063, 10680])).
% 9.09/9.36 tff(17065,plain,
% 9.09/9.36 (~b(s(s(s(elem!1))), elem!1)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[10743, 17055, 10682, 17064])).
% 9.09/9.36 tff(17066,plain,
% 9.09/9.36 (b(s(elem!1), elem!1)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[14657, 17055, 150, 17063, 10682, 17065, 10680])).
% 9.09/9.36 tff(17067,plain,
% 9.09/9.36 (~(s(s(s(elem!1))) = s(elem!1))),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[14662, 17066, 17065])).
% 9.09/9.36 tff(17068,plain,
% 9.09/9.36 (~(s(s(elem!1)) = s(elem!1))),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[2279, 17067])).
% 9.09/9.36 tff(17069,plain,
% 9.09/9.36 (~r(s(s(elem!1)), elem!1)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[4039, 17065, 4028, 327, 127])).
% 9.09/9.36 tff(17070,plain,
% 9.09/9.36 (~(s(s(elem!1)) = elem!1)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[451, 17067])).
% 9.09/9.36 tff(17071,plain,
% 9.09/9.36 (b(s(s(elem!1)), elem!1)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[872, 17070, 17069])).
% 9.09/9.36 tff(17072,plain,
% 9.09/9.36 ($false),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[5286, 17071, 17068, 17064, 17066, 17055])).
% 9.09/9.36 tff(17073,plain,((~r(s(z), z)) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | (z = elem!1) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.36 tff(17074,plain,
% 9.09/9.36 (~r(s(z), z)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[17073, 1496, 327, 127, 4028, 17053, 115, 722, 1810, 719])).
% 9.09/9.36 tff(17075,plain,
% 9.09/9.36 (b(s(z), z)),
% 9.09/9.36 inference(unit_resolution,[status(thm)],[180, 17074])).
% 9.09/9.36 tff(17076,plain,
% 9.09/9.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 9.09/9.36 inference(rewrite,[status(thm)],[])).
% 9.09/9.36 tff(17077,plain,
% 9.09/9.36 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 9.09/9.36 inference(rewrite,[status(thm)],[])).
% 9.09/9.36 tff(17078,plain,
% 9.09/9.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 9.09/9.36 inference(monotonicity,[status(thm)],[17077])).
% 9.09/9.36 tff(17079,plain,
% 9.09/9.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 9.09/9.37 inference(transitivity,[status(thm)],[17078, 17076])).
% 9.09/9.37 tff(17080,plain,
% 9.09/9.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 9.09/9.37 inference(quant_inst,[status(thm)],[])).
% 9.09/9.37 tff(17081,plain,
% 9.09/9.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 9.09/9.37 inference(modus_ponens,[status(thm)],[17080, 17079])).
% 9.09/9.37 tff(17082,plain,
% 9.09/9.37 (~b(s(s(z)), s(z))),
% 9.09/9.37 inference(unit_resolution,[status(thm)],[17081, 391, 1235, 17075, 15045])).
% 9.09/9.37 tff(17083,plain,
% 9.09/9.37 (r(s(s(z)), s(z))),
% 9.09/9.37 inference(unit_resolution,[status(thm)],[3778, 17082])).
% 9.09/9.37 tff(17084,plain,
% 9.09/9.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 9.09/9.37 inference(rewrite,[status(thm)],[])).
% 9.09/9.37 tff(17085,plain,
% 9.09/9.37 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 9.09/9.37 inference(rewrite,[status(thm)],[])).
% 9.09/9.37 tff(17086,plain,
% 9.09/9.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 9.09/9.37 inference(monotonicity,[status(thm)],[17085])).
% 9.09/9.37 tff(17087,plain,
% 9.09/9.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 9.09/9.37 inference(transitivity,[status(thm)],[17086, 17084])).
% 9.09/9.37 tff(17088,plain,
% 9.09/9.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 9.09/9.37 inference(quant_inst,[status(thm)],[])).
% 9.09/9.37 tff(17089,plain,
% 9.09/9.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 9.09/9.37 inference(modus_ponens,[status(thm)],[17088, 17087])).
% 9.09/9.37 tff(17090,plain,
% 9.09/9.37 (~b(s(z), s(s(z)))),
% 9.09/9.37 inference(unit_resolution,[status(thm)],[17089, 391, 1235, 17075, 15045])).
% 9.09/9.37 tff(17091,plain,
% 9.09/9.37 (r(s(z), s(s(z)))),
% 9.09/9.37 inference(unit_resolution,[status(thm)],[1788, 17090])).
% 9.09/9.37 tff(17092,plain,
% 9.09/9.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 9.09/9.37 inference(rewrite,[status(thm)],[])).
% 9.09/9.37 tff(17093,plain,
% 9.09/9.37 (((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 9.09/9.37 inference(rewrite,[status(thm)],[])).
% 9.09/9.37 tff(17094,plain,
% 9.09/9.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))))),
% 9.09/9.37 inference(monotonicity,[status(thm)],[17093])).
% 9.09/9.37 tff(17095,plain,
% 9.09/9.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 9.09/9.37 inference(transitivity,[status(thm)],[17094, 17092])).
% 9.09/9.37 tff(17096,plain,
% 9.09/9.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 9.09/9.37 inference(quant_inst,[status(thm)],[])).
% 9.09/9.37 tff(17097,plain,
% 9.09/9.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))),
% 9.09/9.37 inference(modus_ponens,[status(thm)],[17096, 17095])).
% 9.09/9.37 tff(17098,plain,
% 9.09/9.37 (~r(elem!1, s(s(z)))),
% 9.09/9.37 inference(unit_resolution,[status(thm)],[17097, 194, 1810, 17091, 17083])).
% 9.09/9.37 tff(17099,plain,
% 9.09/9.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 9.09/9.37 inference(rewrite,[status(thm)],[])).
% 9.09/9.37 tff(17100,plain,
% 9.09/9.37 (((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 9.09/9.37 inference(rewrite,[status(thm)],[])).
% 9.09/9.37 tff(17101,plain,
% 9.09/9.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))))),
% 9.09/9.37 inference(monotonicity,[status(thm)],[17100])).
% 9.09/9.37 tff(17102,plain,
% 9.09/9.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 9.09/9.37 inference(transitivity,[status(thm)],[17101, 17099])).
% 9.09/9.37 tff(17103,plain,
% 9.09/9.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 9.09/9.37 inference(quant_inst,[status(thm)],[])).
% 9.09/9.37 tff(17104,plain,
% 9.09/9.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 9.09/9.37 inference(modus_ponens,[status(thm)],[17103, 17102])).
% 9.09/9.37 tff(17105,plain,
% 9.09/9.37 (~r(s(s(z)), elem!1)),
% 9.09/9.37 inference(unit_resolution,[status(thm)],[17104, 194, 1810, 17091, 17083])).
% 9.09/9.37 tff(17106,plain,
% 9.09/9.37 (~(s(s(s(s(z)))) = elem!1)),
% 9.09/9.37 inference(unit_resolution,[status(thm)],[5152, 17105, 1749])).
% 9.09/9.37 tff(17107,plain,
% 9.09/9.37 (r(s(z), s(s(z)))),
% 9.09/9.37 inference(unit_resolution,[status(thm)],[1788, 11250])).
% 9.09/9.38 tff(17108,plain,
% 9.09/9.38 (~r(elem!1, s(s(z)))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[17097, 194, 847, 17107, 2405])).
% 9.09/9.38 tff(17109,plain,
% 9.09/9.38 (~r(s(z), elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[14725, 411, 722, 847])).
% 9.09/9.38 tff(17110,plain,
% 9.09/9.38 (b(s(z), elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[632, 17109, 150])).
% 9.09/9.38 tff(17111,plain,
% 9.09/9.38 (~(elem!1 = s(s(z)))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[11253, 17110, 11250])).
% 9.09/9.38 tff(17112,plain,
% 9.09/9.38 (b(elem!1, s(s(z)))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[3394, 17111, 17108])).
% 9.09/9.38 tff(17113,plain,
% 9.09/9.38 (~r(s(s(s(s(z)))), elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[8972, 411, 719, 410])).
% 9.09/9.38 tff(17114,plain,
% 9.09/9.38 (b(s(s(s(s(z)))), elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[762, 17113, 720])).
% 9.09/9.38 tff(17115,plain,
% 9.09/9.38 (~r(s(s(z)), elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[17104, 194, 847, 17107, 2405])).
% 9.09/9.38 tff(17116,plain,
% 9.09/9.38 (~(s(s(z)) = elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[11003, 17111])).
% 9.09/9.38 tff(17117,plain,
% 9.09/9.38 (b(s(s(z)), elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[4730, 17116, 17115])).
% 9.09/9.38 tff(17118,plain,
% 9.09/9.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[11012, 17117, 17114, 17112])).
% 9.09/9.38 tff(17119,plain,
% 9.09/9.38 (r(s(s(s(s(z)))), s(s(z)))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[1714, 17118])).
% 9.09/9.38 tff(17120,plain,
% 9.09/9.38 (~r(s(s(s(s(z)))), s(z))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[10673, 17119, 17107, 2405])).
% 9.09/9.38 tff(17121,plain,
% 9.09/9.38 (b(s(s(s(s(z)))), s(z))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[749, 17120])).
% 9.09/9.38 tff(17122,plain,
% 9.09/9.38 (~r(elem!1, s(s(s(s(z)))))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[15016, 17119, 719, 411])).
% 9.09/9.38 tff(17123,plain,
% 9.09/9.38 (b(elem!1, s(s(s(s(z)))))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[781, 17122, 770])).
% 9.09/9.38 tff(17124,plain,
% 9.09/9.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.09/9.38 inference(rewrite,[status(thm)],[])).
% 9.09/9.38 tff(17125,plain,
% 9.09/9.38 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.09/9.38 inference(rewrite,[status(thm)],[])).
% 9.09/9.38 tff(17126,plain,
% 9.09/9.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 9.09/9.38 inference(monotonicity,[status(thm)],[17125])).
% 9.09/9.38 tff(17127,plain,
% 9.09/9.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.09/9.38 inference(transitivity,[status(thm)],[17126, 17124])).
% 9.09/9.38 tff(17128,plain,
% 9.09/9.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.09/9.38 inference(quant_inst,[status(thm)],[])).
% 9.09/9.38 tff(17129,plain,
% 9.09/9.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 9.09/9.38 inference(modus_ponens,[status(thm)],[17128, 17127])).
% 9.09/9.38 tff(17130,plain,
% 9.09/9.38 ($false),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[17129, 391, 17110, 17123, 17114, 17121])).
% 9.09/9.38 tff(17131,plain,((~r(z, elem!1)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(z)))))) | b(s(z), s(s(z))) | (s(z) = elem!1) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.09/9.38 tff(17132,plain,
% 9.09/9.38 (~r(z, elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[17131, 17083, 719, 17090, 1496, 17106, 722, 1810, 4030])).
% 9.09/9.38 tff(17133,plain,
% 9.09/9.38 (b(z, elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[141, 17132, 115])).
% 9.09/9.38 tff(17134,plain,
% 9.09/9.38 (~r(s(s(elem!1)), elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[4039, 168, 4028, 327, 127])).
% 9.09/9.38 tff(17135,plain,
% 9.09/9.38 (b(s(elem!1), elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[14657, 2282, 150, 133, 10682, 168, 2])).
% 9.09/9.38 tff(17136,plain,
% 9.09/9.38 (~(s(s(s(elem!1))) = s(elem!1))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[14662, 17135, 168])).
% 9.09/9.38 tff(17137,plain,
% 9.09/9.38 (~(s(s(elem!1)) = elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[451, 17136])).
% 9.09/9.38 tff(17138,plain,
% 9.09/9.38 (b(s(s(s(elem!1))), z)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[12783, 17137, 121, 150, 590, 133, 168, 11936])).
% 9.09/9.38 tff(17139,plain,
% 9.09/9.38 (~(s(s(elem!1)) = s(elem!1))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[2279, 17136])).
% 9.09/9.38 tff(17140,plain,
% 9.09/9.38 (b(s(s(elem!1)), elem!1)),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[872, 17137, 888])).
% 9.09/9.38 tff(17141,plain,
% 9.09/9.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.09/9.38 inference(rewrite,[status(thm)],[])).
% 9.09/9.38 tff(17142,plain,
% 9.09/9.38 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.09/9.38 inference(rewrite,[status(thm)],[])).
% 9.09/9.38 tff(17143,plain,
% 9.09/9.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 9.09/9.38 inference(monotonicity,[status(thm)],[17142])).
% 9.09/9.38 tff(17144,plain,
% 9.09/9.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.09/9.38 inference(transitivity,[status(thm)],[17143, 17141])).
% 9.09/9.38 tff(17145,plain,
% 9.09/9.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.09/9.38 inference(quant_inst,[status(thm)],[])).
% 9.09/9.38 tff(17146,plain,
% 9.09/9.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 9.09/9.38 inference(modus_ponens,[status(thm)],[17145, 17144])).
% 9.09/9.38 tff(17147,plain,
% 9.09/9.38 (~b(s(s(s(elem!1))), s(z))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[17146, 391, 380, 10682, 590])).
% 9.09/9.38 tff(17148,plain,
% 9.09/9.38 (r(s(s(s(elem!1))), s(z))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[223, 17147])).
% 9.09/9.38 tff(17149,plain,
% 9.09/9.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 9.09/9.38 inference(rewrite,[status(thm)],[])).
% 9.09/9.38 tff(17150,plain,
% 9.09/9.38 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, 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(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 9.09/9.38 inference(rewrite,[status(thm)],[])).
% 9.09/9.38 tff(17151,plain,
% 9.09/9.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))))),
% 9.09/9.38 inference(monotonicity,[status(thm)],[17150])).
% 9.09/9.38 tff(17152,plain,
% 9.09/9.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 9.09/9.38 inference(transitivity,[status(thm)],[17151, 17149])).
% 9.09/9.38 tff(17153,plain,
% 9.09/9.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 9.09/9.38 inference(quant_inst,[status(thm)],[])).
% 9.09/9.38 tff(17154,plain,
% 9.09/9.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))),
% 9.09/9.38 inference(modus_ponens,[status(thm)],[17153, 17152])).
% 9.09/9.38 tff(17155,plain,
% 9.09/9.38 (~r(elem!1, s(z))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[17154, 194, 410, 12811, 17148])).
% 9.09/9.38 tff(17156,plain,
% 9.09/9.38 ((elem!1 = s(z)) | b(elem!1, s(z))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[835, 42, 17155])).
% 9.09/9.38 tff(17157,plain,
% 9.09/9.38 (b(elem!1, s(z))),
% 9.09/9.38 inference(unit_resolution,[status(thm)],[17156, 1746])).
% 9.09/9.38 tff(17158,plain,
% 9.09/9.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.09/9.38 inference(rewrite,[status(thm)],[])).
% 9.09/9.38 tff(17159,plain,
% 9.09/9.38 (((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.09/9.39 inference(rewrite,[status(thm)],[])).
% 9.09/9.39 tff(17160,plain,
% 9.09/9.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 9.09/9.39 inference(monotonicity,[status(thm)],[17159])).
% 9.09/9.39 tff(17161,plain,
% 9.09/9.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.09/9.39 inference(transitivity,[status(thm)],[17160, 17158])).
% 9.09/9.39 tff(17162,plain,
% 9.09/9.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 9.09/9.39 inference(quant_inst,[status(thm)],[])).
% 9.09/9.39 tff(17163,plain,
% 9.09/9.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 9.09/9.39 inference(modus_ponens,[status(thm)],[17162, 17161])).
% 9.09/9.39 tff(17164,plain,
% 9.09/9.39 (~r(s(z), elem!1)),
% 9.09/9.39 inference(unit_resolution,[status(thm)],[17163, 194, 410, 12811, 17148])).
% 9.09/9.39 tff(17165,plain,
% 9.09/9.39 (b(s(z), elem!1)),
% 9.09/9.39 inference(unit_resolution,[status(thm)],[632, 17164, 150])).
% 9.09/9.39 tff(17166,plain,
% 9.09/9.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 9.09/9.39 inference(rewrite,[status(thm)],[])).
% 9.09/9.39 tff(17167,plain,
% 9.09/9.39 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 9.09/9.39 inference(rewrite,[status(thm)],[])).
% 9.09/9.39 tff(17168,plain,
% 9.09/9.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 9.09/9.39 inference(monotonicity,[status(thm)],[17167])).
% 9.09/9.39 tff(17169,plain,
% 9.09/9.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 9.09/9.39 inference(transitivity,[status(thm)],[17168, 17166])).
% 9.09/9.39 tff(17170,plain,
% 9.09/9.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 9.09/9.39 inference(quant_inst,[status(thm)],[])).
% 9.09/9.39 tff(17171,plain,
% 9.09/9.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 9.09/9.39 inference(modus_ponens,[status(thm)],[17170, 17169])).
% 9.09/9.39 tff(17172,plain,
% 9.09/9.39 (~b(s(z), s(elem!1))),
% 9.09/9.39 inference(unit_resolution,[status(thm)],[17171, 391, 17165, 2122, 17157])).
% 9.09/9.39 tff(17173,plain,
% 9.09/9.39 (r(s(z), s(elem!1))),
% 9.09/9.39 inference(unit_resolution,[status(thm)],[602, 42, 121, 17172])).
% 9.09/9.39 tff(17174,plain,
% 9.09/9.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 9.09/9.39 inference(rewrite,[status(thm)],[])).
% 9.09/9.39 tff(17175,plain,
% 9.09/9.39 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 9.09/9.39 inference(rewrite,[status(thm)],[])).
% 9.09/9.39 tff(17176,plain,
% 9.09/9.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))))),
% 9.09/9.39 inference(monotonicity,[status(thm)],[17175])).
% 9.09/9.39 tff(17177,plain,
% 9.09/9.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 9.09/9.39 inference(transitivity,[status(thm)],[17176, 17174])).
% 9.09/9.39 tff(17178,plain,
% 9.09/9.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 9.09/9.39 inference(quant_inst,[status(thm)],[])).
% 9.09/9.39 tff(17179,plain,
% 9.09/9.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))),
% 9.09/9.39 inference(modus_ponens,[status(thm)],[17178, 17177])).
% 9.09/9.39 tff(17180,plain,
% 9.09/9.39 (~b(s(elem!1), s(s(elem!1)))),
% 9.09/9.39 inference(unit_resolution,[status(thm)],[17179, 391, 973, 17165, 2122, 17157])).
% 9.09/9.39 tff(17181,plain,
% 9.09/9.39 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 9.09/9.39 inference(unit_resolution,[status(thm)],[1111, 42, 17180])).
% 9.09/9.39 tff(17182,plain,
% 9.09/9.39 (r(s(elem!1), s(s(elem!1)))),
% 9.09/9.39 inference(unit_resolution,[status(thm)],[17181, 1100])).
% 9.09/9.39 tff(17183,plain,
% 9.09/9.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 9.09/9.40 inference(rewrite,[status(thm)],[])).
% 9.09/9.40 tff(17184,plain,
% 9.09/9.40 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 9.09/9.40 inference(rewrite,[status(thm)],[])).
% 9.09/9.40 tff(17185,plain,
% 9.09/9.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))))),
% 9.09/9.40 inference(monotonicity,[status(thm)],[17184])).
% 9.09/9.40 tff(17186,plain,
% 9.09/9.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 9.09/9.40 inference(transitivity,[status(thm)],[17185, 17183])).
% 9.09/9.40 tff(17187,plain,
% 9.09/9.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 9.09/9.40 inference(quant_inst,[status(thm)],[])).
% 9.09/9.40 tff(17188,plain,
% 9.09/9.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))),
% 9.09/9.40 inference(modus_ponens,[status(thm)],[17187, 17186])).
% 9.09/9.40 tff(17189,plain,
% 9.09/9.40 (~b(s(z), s(s(elem!1)))),
% 9.09/9.40 inference(unit_resolution,[status(thm)],[17188, 391, 973, 17165, 17157])).
% 9.09/9.40 tff(17190,plain,
% 9.09/9.40 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 9.09/9.40 inference(unit_resolution,[status(thm)],[3414, 42, 17189])).
% 9.09/9.40 tff(17191,plain,
% 9.09/9.40 (r(s(z), s(s(elem!1)))),
% 9.09/9.40 inference(unit_resolution,[status(thm)],[17190, 3404])).
% 9.09/9.40 tff(17192,plain,
% 9.09/9.40 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 9.09/9.40 inference(rewrite,[status(thm)],[])).
% 9.09/9.40 tff(17193,plain,
% 9.09/9.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))))),
% 9.09/9.40 inference(monotonicity,[status(thm)],[17192])).
% 9.09/9.40 tff(17194,plain,
% 9.09/9.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 9.09/9.40 inference(transitivity,[status(thm)],[17193, 874])).
% 9.09/9.40 tff(17195,plain,
% 9.09/9.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 9.09/9.40 inference(quant_inst,[status(thm)],[])).
% 9.19/9.40 tff(17196,plain,
% 9.19/9.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))),
% 9.19/9.40 inference(modus_ponens,[status(thm)],[17195, 17194])).
% 9.19/9.40 tff(17197,plain,
% 9.19/9.40 (~b(s(s(elem!1)), s(z))),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[17196, 391, 973, 17165, 17157])).
% 9.19/9.40 tff(17198,plain,
% 9.19/9.40 (r(s(s(elem!1)), s(z))),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[362, 17197])).
% 9.19/9.40 tff(17199,plain,
% 9.19/9.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 9.19/9.40 inference(rewrite,[status(thm)],[])).
% 9.19/9.40 tff(17200,plain,
% 9.19/9.40 (((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(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(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 9.19/9.40 inference(rewrite,[status(thm)],[])).
% 9.19/9.40 tff(17201,plain,
% 9.19/9.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1)))))),
% 9.19/9.40 inference(monotonicity,[status(thm)],[17200])).
% 9.19/9.40 tff(17202,plain,
% 9.19/9.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 9.19/9.40 inference(transitivity,[status(thm)],[17201, 17199])).
% 9.19/9.40 tff(17203,plain,
% 9.19/9.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 9.19/9.40 inference(quant_inst,[status(thm)],[])).
% 9.19/9.40 tff(17204,plain,
% 9.19/9.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1)))),
% 9.19/9.40 inference(modus_ponens,[status(thm)],[17203, 17202])).
% 9.19/9.40 tff(17205,plain,
% 9.19/9.40 ($false),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[17204, 194, 17198, 17191, 17182, 17173])).
% 9.19/9.40 tff(17206,plain,((~b(s(z), z)) | (s(s(elem!1)) = s(elem!1)) | (s(z) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.40 tff(17207,plain,
% 9.19/9.40 ($false),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[17206, 17140, 17139, 121, 410, 150, 10682, 590, 17135, 17138])).
% 9.19/9.40 tff(17208,plain,(r(elem!1, z) | (s(z) = s(elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, elem!1)) | b(s(s(s(elem!1))), elem!1) | r(s(s(elem!1)), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.40 tff(17209,plain,
% 9.19/9.40 (r(elem!1, z)),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[17208, 168, 4030, 150, 10682, 590, 133, 121, 17134, 2])).
% 9.19/9.40 tff(17210,plain,
% 9.19/9.40 (~r(s(s(s(elem!1))), z)),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[4113, 17209, 722, 4486])).
% 9.19/9.40 tff(17211,plain,
% 9.19/9.40 (b(s(s(s(elem!1))), z)),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[377, 17210])).
% 9.19/9.40 tff(17212,plain,
% 9.19/9.40 (~b(s(z), s(s(s(elem!1))))),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[11303, 17211, 590, 10682])).
% 9.19/9.40 tff(17213,plain,
% 9.19/9.40 (r(s(z), s(s(s(elem!1))))),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[247, 17212])).
% 9.19/9.40 tff(17214,plain,
% 9.19/9.40 ($false),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[15569, 194, 4486, 4030, 17213, 847])).
% 9.19/9.40 tff(17215,plain,(b(s(s(s(elem!1))), elem!1) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (s(z) = elem!1) | (~b(z, elem!1)) | (s(z) = s(elem!1)) | (elem!1 = z) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.40 tff(17216,plain,
% 9.19/9.40 (b(s(s(s(elem!1))), elem!1)),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[17215, 1810, 17075, 17053, 722, 1496, 17133, 10968, 10680, 4028, 327, 127])).
% 9.19/9.40 tff(17217,plain,
% 9.19/9.40 (~b(elem!1, z)),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[10743, 17216, 17053, 17133])).
% 9.19/9.40 tff(17218,plain,
% 9.19/9.40 (~(elem!1 = s(s(z)))),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[3589, 17217, 1235])).
% 9.19/9.40 tff(17219,plain,
% 9.19/9.40 (b(elem!1, s(s(z)))),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[3394, 17218, 17098])).
% 9.19/9.40 tff(17220,plain,
% 9.19/9.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 9.19/9.40 inference(rewrite,[status(thm)],[])).
% 9.19/9.40 tff(17221,plain,
% 9.19/9.40 (((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 9.19/9.40 inference(rewrite,[status(thm)],[])).
% 9.19/9.40 tff(17222,plain,
% 9.19/9.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 9.19/9.40 inference(monotonicity,[status(thm)],[17221])).
% 9.19/9.40 tff(17223,plain,
% 9.19/9.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 9.19/9.40 inference(transitivity,[status(thm)],[17222, 17220])).
% 9.19/9.40 tff(17224,plain,
% 9.19/9.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 9.19/9.40 inference(quant_inst,[status(thm)],[])).
% 9.19/9.40 tff(17225,plain,
% 9.19/9.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 9.19/9.40 inference(modus_ponens,[status(thm)],[17224, 17223])).
% 9.19/9.40 tff(17226,plain,
% 9.19/9.40 ($false),
% 9.19/9.40 inference(unit_resolution,[status(thm)],[17225, 391, 17133, 17216, 17053, 1235, 17219])).
% 9.19/9.40 tff(17227,plain,((elem!1 = s(z)) | (~b(s(s(z)), z)) | (~r(z, s(z))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (z = elem!1) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.41 tff(17228,plain,
% 9.19/9.41 (elem!1 = s(z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17227, 719, 722, 4028, 327, 127, 115, 10584, 1749, 17039, 31])).
% 9.19/9.41 tff(17229,plain,
% 9.19/9.41 (s(z) = elem!1),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[172, 17228])).
% 9.19/9.41 tff(17230,plain,
% 9.19/9.41 ((~r(z, elem!1)) <=> (~r(z, s(z)))),
% 9.19/9.41 inference(monotonicity,[status(thm)],[814])).
% 9.19/9.41 tff(17231,plain,
% 9.19/9.41 (~r(z, s(z))),
% 9.19/9.41 inference(modus_ponens,[status(thm)],[80, 17230])).
% 9.19/9.41 tff(17232,plain,
% 9.19/9.41 ($false),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[722, 17231])).
% 9.19/9.41 tff(17233,plain,((~(s(z) = elem!1)) | (~r(z, s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.41 tff(17234,plain,
% 9.19/9.41 (r(z, elem!1)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17233, 17229, 722])).
% 9.19/9.41 tff(17235,plain,
% 9.19/9.41 (r(z, s(s(s(elem!1))))),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[10733, 17229, 719])).
% 9.19/9.41 tff(17236,plain,
% 9.19/9.41 (b(s(s(s(elem!1))), elem!1)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[10519, 17235, 4028, 4029, 17234])).
% 9.19/9.41 tff(17237,plain,
% 9.19/9.41 (b(z, s(s(s(elem!1))))),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17052, 17039, 10584, 10680, 4028, 4029, 327])).
% 9.19/9.41 tff(17238,plain,
% 9.19/9.41 (~r(elem!1, z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[6153, 17235, 4030, 327])).
% 9.19/9.41 tff(17239,plain,
% 9.19/9.41 (b(elem!1, z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[526, 17238, 10680])).
% 9.19/9.41 tff(17240,plain,
% 9.19/9.41 (~r(s(s(s(elem!1))), z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[8380, 17235, 4030, 17234])).
% 9.19/9.41 tff(17241,plain,
% 9.19/9.41 (b(s(s(s(elem!1))), z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[377, 17240])).
% 9.19/9.41 tff(17242,plain,
% 9.19/9.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 9.19/9.41 inference(rewrite,[status(thm)],[])).
% 9.19/9.41 tff(17243,plain,
% 9.19/9.41 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 9.19/9.41 inference(rewrite,[status(thm)],[])).
% 9.19/9.41 tff(17244,plain,
% 9.19/9.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 9.19/9.41 inference(monotonicity,[status(thm)],[17243])).
% 9.19/9.41 tff(17245,plain,
% 9.19/9.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 9.19/9.41 inference(transitivity,[status(thm)],[17244, 17242])).
% 9.19/9.41 tff(17246,plain,
% 9.19/9.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 9.19/9.41 inference(quant_inst,[status(thm)],[])).
% 9.19/9.41 tff(17247,plain,
% 9.19/9.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 9.19/9.41 inference(modus_ponens,[status(thm)],[17246, 17245])).
% 9.19/9.41 tff(17248,plain,
% 9.19/9.41 ($false),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17247, 391, 665, 380, 10682, 900])).
% 9.19/9.41 tff(17249,plain,((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.41 tff(17250,plain,
% 9.19/9.41 ($false),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17249, 17241, 17239, 17237, 17236])).
% 9.19/9.41 tff(17251,plain,((~r(z, s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (s(s(s(elem!1))) = elem!1) | (z = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.41 tff(17252,plain,
% 9.19/9.41 (~r(z, s(s(s(s(z)))))),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17251, 327, 4028, 722, 127, 115, 1749, 31, 2053])).
% 9.19/9.41 tff(17253,plain,
% 9.19/9.41 (b(z, s(s(s(s(z)))))),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[800, 17252])).
% 9.19/9.41 tff(17254,plain,
% 9.19/9.41 ($false),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[1254, 194, 15899, 59, 410, 327])).
% 9.19/9.41 tff(17255,plain,(b(z, s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.41 tff(17256,plain,
% 9.19/9.41 (b(z, s(s(s(elem!1))))),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17255, 4030, 327, 2])).
% 9.19/9.41 tff(17257,plain,
% 9.19/9.41 (~b(s(z), z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17215, 168, 847, 17256, 722, 150, 133, 121, 2, 4028, 327, 127])).
% 9.19/9.41 tff(17258,plain,
% 9.19/9.41 (r(s(z), z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[180, 17257])).
% 9.19/9.41 tff(17259,plain,
% 9.19/9.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 9.19/9.41 inference(rewrite,[status(thm)],[])).
% 9.19/9.41 tff(17260,plain,
% 9.19/9.41 (((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 9.19/9.41 inference(rewrite,[status(thm)],[])).
% 9.19/9.41 tff(17261,plain,
% 9.19/9.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z)))))),
% 9.19/9.41 inference(monotonicity,[status(thm)],[17260])).
% 9.19/9.41 tff(17262,plain,
% 9.19/9.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 9.19/9.41 inference(transitivity,[status(thm)],[17261, 17259])).
% 9.19/9.41 tff(17263,plain,
% 9.19/9.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 9.19/9.41 inference(quant_inst,[status(thm)],[])).
% 9.19/9.41 tff(17264,plain,
% 9.19/9.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 9.19/9.41 inference(modus_ponens,[status(thm)],[17263, 17262])).
% 9.19/9.41 tff(17265,plain,
% 9.19/9.41 ($false),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17264, 194, 530, 722, 847, 182])).
% 9.19/9.41 tff(17266,plain,((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.41 tff(17267,plain,
% 9.19/9.41 (~r(elem!1, z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17266, 17258, 722, 847])).
% 9.19/9.41 tff(17268,plain,
% 9.19/9.41 (b(s(elem!1), elem!1)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[14657, 17267, 150, 133, 17256, 168, 2])).
% 9.19/9.41 tff(17269,plain,
% 9.19/9.41 (b(elem!1, z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[526, 17267, 2])).
% 9.19/9.41 tff(17270,plain,
% 9.19/9.41 (~(s(s(s(elem!1))) = s(elem!1))),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[14662, 17268, 168])).
% 9.19/9.41 tff(17271,plain,
% 9.19/9.41 (~(s(s(elem!1)) = s(elem!1))),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[2279, 17270])).
% 9.19/9.41 tff(17272,plain,
% 9.19/9.41 (~(s(s(elem!1)) = elem!1)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[451, 17270])).
% 9.19/9.41 tff(17273,plain,
% 9.19/9.41 (b(s(s(elem!1)), elem!1)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[872, 17272, 17134])).
% 9.19/9.41 tff(17274,plain,
% 9.19/9.41 ($false),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[5286, 17273, 17271, 17269, 17268, 133])).
% 9.19/9.41 tff(17275,plain,(b(s(s(s(elem!1))), elem!1) | (~b(z, elem!1)) | (s(z) = elem!1) | (elem!1 = z) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (s(z) = s(elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.41 tff(17276,plain,
% 9.19/9.41 (b(s(s(s(elem!1))), elem!1)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17275, 133, 150, 2, 722, 847, 121, 4028, 327, 127])).
% 9.19/9.41 tff(17277,plain,
% 9.19/9.41 (~b(elem!1, z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[10743, 17276, 17256, 133])).
% 9.19/9.41 tff(17278,plain,
% 9.19/9.41 (r(elem!1, z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[526, 17277, 2])).
% 9.19/9.41 tff(17279,plain,
% 9.19/9.41 (~r(s(z), z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[17266, 17278, 722, 847])).
% 9.19/9.41 tff(17280,plain,
% 9.19/9.41 (b(s(z), z)),
% 9.19/9.41 inference(unit_resolution,[status(thm)],[180, 17279])).
% 9.19/9.41 tff(17281,plain,
% 9.19/9.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.19/9.41 inference(rewrite,[status(thm)],[])).
% 9.19/9.41 tff(17282,plain,
% 9.19/9.41 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.19/9.41 inference(rewrite,[status(thm)],[])).
% 9.19/9.41 tff(17283,plain,
% 9.19/9.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 9.19/9.41 inference(monotonicity,[status(thm)],[17282])).
% 9.19/9.41 tff(17284,plain,
% 9.19/9.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.19/9.41 inference(transitivity,[status(thm)],[17283, 17281])).
% 9.19/9.41 tff(17285,plain,
% 9.19/9.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 9.19/9.41 inference(quant_inst,[status(thm)],[])).
% 9.19/9.41 tff(17286,plain,
% 9.19/9.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 9.19/9.42 inference(modus_ponens,[status(thm)],[17285, 17284])).
% 9.19/9.42 tff(17287,plain,
% 9.19/9.42 ($false),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[17286, 391, 1235, 1234, 3563, 1686, 590])).
% 9.19/9.42 tff(17288,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.42 tff(17289,plain,
% 9.19/9.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[17288, 17280, 1234, 1235, 1686])).
% 9.19/9.42 tff(17290,plain,
% 9.19/9.42 (r(s(s(s(s(z)))), s(s(z)))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[1714, 17289])).
% 9.19/9.42 tff(17291,plain,
% 9.19/9.42 ($false),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[10054, 391, 1234, 1759, 1686, 590])).
% 9.19/9.42 tff(17292,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.42 tff(17293,plain,
% 9.19/9.42 (~b(s(s(s(s(z)))), s(z))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[17292, 17280, 1686, 1234])).
% 9.19/9.42 tff(17294,plain,
% 9.19/9.42 (r(s(s(s(s(z)))), s(z))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[749, 17293])).
% 9.19/9.42 tff(17295,plain,
% 9.19/9.42 (~r(s(z), s(s(z)))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[9076, 17294, 1749, 17290])).
% 9.19/9.42 tff(17296,plain,
% 9.19/9.42 (b(s(z), s(s(z)))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[1788, 17295])).
% 9.19/9.42 tff(17297,plain,
% 9.19/9.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 9.19/9.42 inference(rewrite,[status(thm)],[])).
% 9.19/9.42 tff(17298,plain,
% 9.19/9.42 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 9.19/9.42 inference(rewrite,[status(thm)],[])).
% 9.19/9.42 tff(17299,plain,
% 9.19/9.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 9.19/9.42 inference(monotonicity,[status(thm)],[17298])).
% 9.19/9.42 tff(17300,plain,
% 9.19/9.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 9.19/9.42 inference(transitivity,[status(thm)],[17299, 17297])).
% 9.19/9.42 tff(17301,plain,
% 9.19/9.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 9.19/9.42 inference(quant_inst,[status(thm)],[])).
% 9.19/9.42 tff(17302,plain,
% 9.19/9.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 9.19/9.42 inference(modus_ponens,[status(thm)],[17301, 17300])).
% 9.19/9.42 tff(17303,plain,
% 9.19/9.42 ($false),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[17302, 391, 17276, 17256, 1235, 17296, 17280])).
% 9.19/9.42 tff(17304,plain,((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (elem!1 = z) | (s(z) = elem!1) | (s(z) = s(elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.42 tff(17305,plain,
% 9.19/9.42 (~b(z, elem!1)),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[17304, 838, 1749, 17253, 1234, 722, 10584, 10680, 150, 10968, 4028, 327, 127])).
% 9.19/9.42 tff(17306,plain,
% 9.19/9.42 (r(z, elem!1)),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[141, 17305, 115])).
% 9.19/9.42 tff(17307,plain,
% 9.19/9.42 (~r(s(z), z)),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[845, 17306, 722, 838])).
% 9.19/9.42 tff(17308,plain,
% 9.19/9.42 (b(s(z), z)),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[180, 17307])).
% 9.19/9.42 tff(17309,plain,
% 9.19/9.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[17288, 17308, 1234, 10584, 17253])).
% 9.19/9.42 tff(17310,plain,
% 9.19/9.42 (r(s(s(s(s(z)))), s(s(z)))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[1714, 17309])).
% 9.19/9.42 tff(17311,plain,
% 9.19/9.42 (~b(s(s(s(s(z)))), s(z))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[17292, 17308, 17253, 1234])).
% 9.19/9.42 tff(17312,plain,
% 9.19/9.42 (r(s(s(s(s(z)))), s(z))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[749, 17311])).
% 9.19/9.42 tff(17313,plain,
% 9.19/9.42 (~r(s(z), s(s(z)))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[9076, 17312, 1749, 17310])).
% 9.19/9.42 tff(17314,plain,
% 9.19/9.42 (b(s(z), s(s(z)))),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[1788, 17313])).
% 9.19/9.42 tff(17315,plain,
% 9.19/9.42 (~(s(s(s(s(z)))) = elem!1)),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[16124, 17305, 17253])).
% 9.19/9.42 tff(17316,plain,
% 9.19/9.42 (~r(s(s(s(s(z)))), elem!1)),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[10408, 17306, 2053, 838])).
% 9.19/9.42 tff(17317,plain,
% 9.19/9.42 (b(s(s(s(s(z)))), elem!1)),
% 9.19/9.42 inference(unit_resolution,[status(thm)],[762, 17316, 17315])).
% 9.19/9.42 tff(17318,plain,
% 9.19/9.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 9.19/9.42 inference(rewrite,[status(thm)],[])).
% 9.19/9.42 tff(17319,plain,
% 9.19/9.42 (((~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 9.19/9.42 inference(rewrite,[status(thm)],[])).
% 9.19/9.42 tff(17320,plain,
% 9.19/9.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z))))))),
% 9.19/9.42 inference(monotonicity,[status(thm)],[17319])).
% 9.19/9.42 tff(17321,plain,
% 9.19/9.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 9.19/9.42 inference(transitivity,[status(thm)],[17320, 17318])).
% 9.19/9.42 tff(17322,plain,
% 9.19/9.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 9.19/9.43 inference(quant_inst,[status(thm)],[])).
% 9.19/9.43 tff(17323,plain,
% 9.19/9.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z))))),
% 9.19/9.43 inference(modus_ponens,[status(thm)],[17322, 17321])).
% 9.19/9.43 tff(17324,plain,
% 9.19/9.43 ($false),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[17323, 391, 10584, 17317, 17314, 17253, 17308])).
% 9.19/9.43 tff(17325,plain,((s(z) = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (z = elem!1) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.43 tff(17326,plain,
% 9.19/9.43 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[17325, 127, 1234, 2053, 722, 115, 4028, 1749, 17037, 31])).
% 9.19/9.43 tff(17327,plain,
% 9.19/9.43 ($false),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[1370, 17326, 15838, 8329])).
% 9.19/9.43 tff(17328,plain,((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (z = elem!1) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.43 tff(17329,plain,
% 9.19/9.43 (s(s(s(elem!1))) = elem!1),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[17328, 4028, 1234, 2053, 722, 115, 8329, 1749, 31])).
% 9.19/9.43 tff(17330,plain,
% 9.19/9.43 (~(s(s(s(s(z)))) = elem!1)),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[1436, 17329])).
% 9.19/9.43 tff(17331,plain,
% 9.19/9.43 (~(elem!1 = s(s(s(s(z)))))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[769, 17330])).
% 9.19/9.43 tff(17332,plain,
% 9.19/9.43 (elem!1 = s(s(s(elem!1)))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[8, 17329])).
% 9.19/9.43 tff(17333,plain,
% 9.19/9.43 (s(s(s(elem!1))) = elem!1),
% 9.19/9.43 inference(symmetry,[status(thm)],[17332])).
% 9.19/9.43 tff(17334,plain,
% 9.19/9.43 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 9.19/9.43 inference(monotonicity,[status(thm)],[17333])).
% 9.19/9.43 tff(17335,plain,
% 9.19/9.43 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 9.19/9.43 inference(transitivity,[status(thm)],[17334, 698])).
% 9.19/9.43 tff(17336,plain,
% 9.19/9.43 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 9.19/9.43 inference(monotonicity,[status(thm)],[17335])).
% 9.19/9.43 tff(17337,plain,
% 9.19/9.43 (~(elem!1 = s(s(z)))),
% 9.19/9.43 inference(modus_ponens,[status(thm)],[1397, 17336])).
% 9.19/9.43 tff(17338,plain,
% 9.19/9.43 (~(elem!1 = s(z))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[172, 17037])).
% 9.19/9.43 tff(17339,plain,
% 9.19/9.43 (r(elem!1, s(z))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[837, 17338, 31])).
% 9.19/9.43 tff(17340,plain,
% 9.19/9.43 (~b(s(s(s(elem!1))), s(z))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[8400, 17329, 31])).
% 9.19/9.43 tff(17341,plain,
% 9.19/9.43 (r(s(s(s(elem!1))), s(z))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[223, 17340])).
% 9.19/9.43 tff(17342,plain,
% 9.19/9.43 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[6956, 194, 15972, 59, 2053])).
% 9.19/9.43 tff(17343,plain,
% 9.19/9.43 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[15351, 17342, 16830])).
% 9.19/9.43 tff(17344,plain,
% 9.19/9.43 (~r(s(z), elem!1)),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[14725, 15899, 722, 847])).
% 9.19/9.43 tff(17345,plain,
% 9.19/9.43 (b(s(z), elem!1)),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[632, 17344, 150])).
% 9.19/9.43 tff(17346,plain,
% 9.19/9.43 (b(s(z), s(s(s(elem!1))))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[14872, 17345, 5])).
% 9.19/9.43 tff(17347,plain,
% 9.19/9.43 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.19/9.43 inference(rewrite,[status(thm)],[])).
% 9.19/9.43 tff(17348,plain,
% 9.19/9.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.19/9.43 inference(monotonicity,[status(thm)],[17347])).
% 9.19/9.43 tff(17349,plain,
% 9.19/9.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.19/9.43 inference(transitivity,[status(thm)],[17348, 11076])).
% 9.19/9.43 tff(17350,plain,
% 9.19/9.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.19/9.43 inference(quant_inst,[status(thm)],[])).
% 9.19/9.43 tff(17351,plain,
% 9.19/9.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.19/9.43 inference(modus_ponens,[status(thm)],[17350, 17349])).
% 9.19/9.43 tff(17352,plain,
% 9.19/9.43 ($false),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[17351, 391, 17346, 1234, 15902, 17343])).
% 9.19/9.43 tff(17353,plain,(b(z, s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~(s(s(s(elem!1))) = elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.43 tff(17354,plain,
% 9.19/9.43 (b(z, s(s(s(elem!1))))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[17353, 17329, 2053, 1234, 17037, 17339, 722, 17341, 10680])).
% 9.19/9.43 tff(17355,plain,
% 9.19/9.43 (~(s(elem!1) = s(z))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[123, 10968])).
% 9.19/9.43 tff(17356,plain,
% 9.19/9.43 (~(s(elem!1) = s(s(s(s(z)))))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[1965, 17329])).
% 9.19/9.43 tff(17357,plain,
% 9.19/9.43 (s(s(s(s(elem!1)))) = s(elem!1)),
% 9.19/9.43 inference(symmetry,[status(thm)],[3065])).
% 9.19/9.43 tff(17358,plain,
% 9.19/9.43 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(elem!1), s(z))),
% 9.19/9.43 inference(monotonicity,[status(thm)],[17357])).
% 9.19/9.43 tff(17359,plain,
% 9.19/9.43 (b(s(elem!1), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 9.19/9.43 inference(symmetry,[status(thm)],[17358])).
% 9.19/9.43 tff(17360,plain,
% 9.19/9.43 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 9.19/9.43 inference(monotonicity,[status(thm)],[125])).
% 9.19/9.43 tff(17361,plain,
% 9.19/9.43 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 9.19/9.43 inference(symmetry,[status(thm)],[17360])).
% 9.19/9.43 tff(17362,plain,
% 9.19/9.43 (b(z, elem!1)),
% 9.19/9.43 inference(modus_ponens,[status(thm)],[10682, 17361])).
% 9.19/9.43 tff(17363,plain,
% 9.19/9.43 (~r(elem!1, z)),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[17266, 182, 722, 847])).
% 9.19/9.43 tff(17364,plain,
% 9.19/9.43 (b(elem!1, z)),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[526, 17363, 2])).
% 9.19/9.43 tff(17365,plain,
% 9.19/9.43 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 9.19/9.43 inference(monotonicity,[status(thm)],[125])).
% 9.19/9.43 tff(17366,plain,
% 9.19/9.43 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), elem!1)),
% 9.19/9.43 inference(symmetry,[status(thm)],[17365])).
% 9.19/9.43 tff(17367,plain,
% 9.19/9.43 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 9.19/9.43 inference(monotonicity,[status(thm)],[17366])).
% 9.19/9.43 tff(17368,plain,
% 9.19/9.43 (~b(s(s(s(elem!1))), elem!1)),
% 9.19/9.43 inference(modus_ponens,[status(thm)],[463, 17367])).
% 9.19/9.43 tff(17369,plain,
% 9.19/9.43 (b(s(elem!1), elem!1)),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[14657, 17363, 150, 17362, 10682, 17368, 2])).
% 9.19/9.43 tff(17370,plain,
% 9.19/9.43 (~b(s(elem!1), z)),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[7777, 17369, 17364, 17362])).
% 9.19/9.43 tff(17371,plain,
% 9.19/9.43 (r(s(elem!1), z)),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[549, 17370])).
% 9.19/9.43 tff(17372,plain,
% 9.19/9.43 (~b(z, s(elem!1))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[6555, 17369, 17362, 17364])).
% 9.19/9.43 tff(17373,plain,
% 9.19/9.43 (r(z, s(elem!1))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[566, 17372])).
% 9.19/9.43 tff(17374,plain,
% 9.19/9.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 9.19/9.43 inference(rewrite,[status(thm)],[])).
% 9.19/9.43 tff(17375,plain,
% 9.19/9.43 (((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 9.19/9.43 inference(rewrite,[status(thm)],[])).
% 9.19/9.43 tff(17376,plain,
% 9.19/9.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 9.19/9.43 inference(monotonicity,[status(thm)],[17375])).
% 9.19/9.43 tff(17377,plain,
% 9.19/9.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 9.19/9.43 inference(transitivity,[status(thm)],[17376, 17374])).
% 9.19/9.43 tff(17378,plain,
% 9.19/9.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 9.19/9.43 inference(quant_inst,[status(thm)],[])).
% 9.19/9.43 tff(17379,plain,
% 9.19/9.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 9.19/9.43 inference(modus_ponens,[status(thm)],[17378, 17377])).
% 9.19/9.43 tff(17380,plain,
% 9.19/9.43 ($false),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[17379, 194, 1628, 2144, 182, 13481])).
% 9.19/9.43 tff(17381,plain,((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.43 tff(17382,plain,
% 9.19/9.43 (~r(s(elem!1), s(z))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[17381, 17373, 182, 17371])).
% 9.19/9.43 tff(17383,plain,
% 9.19/9.43 (b(s(elem!1), s(z))),
% 9.19/9.43 inference(unit_resolution,[status(thm)],[13479, 17382, 11964])).
% 9.19/9.43 tff(17384,plain,
% 9.19/9.43 (b(s(s(s(s(elem!1)))), s(z))),
% 9.19/9.43 inference(modus_ponens,[status(thm)],[17383, 17359])).
% 9.19/9.43 tff(17385,plain,
% 9.19/9.43 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 9.19/9.43 inference(monotonicity,[status(thm)],[17357])).
% 9.19/9.43 tff(17386,plain,
% 9.19/9.43 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 9.19/9.43 inference(transitivity,[status(thm)],[17385, 2123])).
% 9.19/9.43 tff(17387,plain,
% 9.19/9.43 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 9.19/9.43 inference(symmetry,[status(thm)],[17386])).
% 9.19/9.43 tff(17388,plain,
% 9.19/9.43 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(elem!1))))))),
% 9.19/9.43 inference(monotonicity,[status(thm)],[17387])).
% 9.19/9.43 tff(17389,plain,
% 9.19/9.43 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 9.19/9.43 inference(modus_ponens,[status(thm)],[2121, 17388])).
% 9.19/9.43 tff(17390,plain,
% 9.19/9.43 (b(s(elem!1), z) <=> b(s(s(s(s(elem!1)))), z)),
% 9.19/9.43 inference(monotonicity,[status(thm)],[3065])).
% 9.19/9.43 tff(17391,plain,
% 9.19/9.43 ((~b(s(elem!1), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 9.19/9.44 inference(monotonicity,[status(thm)],[17390])).
% 9.19/9.44 tff(17392,plain,
% 9.19/9.44 (~b(s(s(s(s(elem!1)))), z)),
% 9.19/9.44 inference(modus_ponens,[status(thm)],[17370, 17391])).
% 9.19/9.44 tff(17393,plain,
% 9.19/9.44 (r(s(s(s(s(elem!1)))), z)),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[1626, 17392])).
% 9.19/9.44 tff(17394,plain,
% 9.19/9.44 (r(z, s(elem!1)) <=> r(z, s(s(s(s(elem!1)))))),
% 9.19/9.44 inference(monotonicity,[status(thm)],[3065])).
% 9.19/9.44 tff(17395,plain,
% 9.19/9.44 (r(z, s(s(s(s(elem!1)))))),
% 9.19/9.44 inference(modus_ponens,[status(thm)],[17373, 17394])).
% 9.19/9.44 tff(17396,plain,
% 9.19/9.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 9.19/9.44 inference(rewrite,[status(thm)],[])).
% 9.19/9.44 tff(17397,plain,
% 9.19/9.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 9.19/9.44 inference(quant_inst,[status(thm)],[])).
% 9.19/9.44 tff(17398,plain,
% 9.19/9.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 9.19/9.44 inference(modus_ponens,[status(thm)],[17397, 17396])).
% 9.19/9.44 tff(17399,plain,
% 9.19/9.44 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[17398, 194, 17395, 17393, 2053])).
% 9.19/9.44 tff(17400,plain,
% 9.19/9.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 9.19/9.44 inference(rewrite,[status(thm)],[])).
% 9.19/9.44 tff(17401,plain,
% 9.19/9.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 9.19/9.44 inference(quant_inst,[status(thm)],[])).
% 9.19/9.44 tff(17402,plain,
% 9.19/9.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 9.19/9.44 inference(modus_ponens,[status(thm)],[17401, 17400])).
% 9.19/9.44 tff(17403,plain,
% 9.19/9.44 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[17402, 42, 17399])).
% 9.19/9.44 tff(17404,plain,
% 9.19/9.44 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[17403, 17389])).
% 9.19/9.44 tff(17405,plain,
% 9.19/9.44 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 9.19/9.44 inference(monotonicity,[status(thm)],[17357])).
% 9.19/9.44 tff(17406,plain,
% 9.19/9.44 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 9.19/9.44 inference(symmetry,[status(thm)],[17405])).
% 9.19/9.44 tff(17407,plain,
% 9.19/9.44 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))),
% 9.19/9.44 inference(monotonicity,[status(thm)],[17406])).
% 9.19/9.44 tff(17408,plain,
% 9.19/9.44 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 9.19/9.44 inference(modus_ponens,[status(thm)],[2121, 17407])).
% 9.19/9.44 tff(17409,plain,
% 9.19/9.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 9.19/9.44 inference(rewrite,[status(thm)],[])).
% 9.19/9.44 tff(17410,plain,
% 9.19/9.44 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 9.19/9.44 inference(rewrite,[status(thm)],[])).
% 9.19/9.44 tff(17411,plain,
% 9.19/9.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 9.19/9.44 inference(monotonicity,[status(thm)],[17410])).
% 9.19/9.44 tff(17412,plain,
% 9.19/9.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 9.19/9.44 inference(transitivity,[status(thm)],[17411, 17409])).
% 9.19/9.44 tff(17413,plain,
% 9.19/9.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 9.19/9.44 inference(quant_inst,[status(thm)],[])).
% 9.19/9.44 tff(17414,plain,
% 9.19/9.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 9.19/9.44 inference(modus_ponens,[status(thm)],[17413, 17412])).
% 9.19/9.44 tff(17415,plain,
% 9.19/9.44 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[17414, 194, 17395, 17393, 2053])).
% 9.19/9.44 tff(17416,plain,
% 9.19/9.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 9.19/9.44 inference(rewrite,[status(thm)],[])).
% 9.19/9.44 tff(17417,plain,
% 9.19/9.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 9.19/9.44 inference(quant_inst,[status(thm)],[])).
% 9.19/9.44 tff(17418,plain,
% 9.19/9.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 9.19/9.44 inference(modus_ponens,[status(thm)],[17417, 17416])).
% 9.19/9.44 tff(17419,plain,
% 9.19/9.44 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[17418, 42, 17415])).
% 9.19/9.44 tff(17420,plain,
% 9.19/9.44 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[17419, 17408])).
% 9.19/9.44 tff(17421,plain,
% 9.19/9.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 9.19/9.44 inference(rewrite,[status(thm)],[])).
% 9.19/9.44 tff(17422,plain,
% 9.19/9.44 (((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 9.19/9.44 inference(rewrite,[status(thm)],[])).
% 9.19/9.44 tff(17423,plain,
% 9.19/9.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 9.19/9.44 inference(monotonicity,[status(thm)],[17422])).
% 9.19/9.44 tff(17424,plain,
% 9.19/9.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 9.19/9.44 inference(transitivity,[status(thm)],[17423, 17421])).
% 9.19/9.44 tff(17425,plain,
% 9.19/9.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 9.19/9.44 inference(quant_inst,[status(thm)],[])).
% 9.19/9.44 tff(17426,plain,
% 9.19/9.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 9.19/9.44 inference(modus_ponens,[status(thm)],[17425, 17424])).
% 9.19/9.44 tff(17427,plain,
% 9.19/9.44 (~b(s(s(s(s(elem!1)))), s(z))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[17426, 391, 1234, 17420, 17404])).
% 9.19/9.44 tff(17428,plain,
% 9.19/9.44 ($false),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[17427, 17384])).
% 9.19/9.44 tff(17429,plain,((~r(s(z), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (s(elem!1) = s(z)) | (s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (~r(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.44 tff(17430,plain,
% 9.19/9.44 (~r(s(z), z)),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[17429, 17332, 1234, 17356, 2053, 17355, 17037, 17354, 10680, 722, 17339])).
% 9.19/9.44 tff(17431,plain,
% 9.19/9.44 (b(s(z), z)),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[180, 17430])).
% 9.19/9.44 tff(17432,plain,
% 9.19/9.44 (b(s(s(s(elem!1))), z)),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[9553, 665, 125])).
% 9.19/9.44 tff(17433,plain,
% 9.19/9.44 (~b(s(z), s(s(s(elem!1))))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[11303, 17432, 10682, 590])).
% 9.19/9.44 tff(17434,plain,
% 9.19/9.44 (r(s(z), s(s(s(elem!1))))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[247, 17433])).
% 9.19/9.44 tff(17435,plain,
% 9.19/9.44 (~b(elem!1, s(s(z)))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[13448, 665, 1235, 17362])).
% 9.19/9.44 tff(17436,plain,
% 9.19/9.44 (r(elem!1, s(s(z)))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[3394, 17435, 3820])).
% 9.19/9.44 tff(17437,plain,
% 9.19/9.44 (r(s(s(s(elem!1))), s(s(z)))),
% 9.19/9.44 inference(unit_resolution,[status(thm)],[10022, 17436, 125])).
% 9.19/9.44 tff(17438,plain,
% 9.19/9.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 9.19/9.45 inference(rewrite,[status(thm)],[])).
% 9.19/9.45 tff(17439,plain,
% 9.19/9.45 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 9.19/9.45 inference(rewrite,[status(thm)],[])).
% 9.19/9.45 tff(17440,plain,
% 9.19/9.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 9.19/9.45 inference(monotonicity,[status(thm)],[17439])).
% 9.19/9.45 tff(17441,plain,
% 9.19/9.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 9.19/9.45 inference(transitivity,[status(thm)],[17440, 17438])).
% 9.19/9.45 tff(17442,plain,
% 9.19/9.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 9.19/9.45 inference(quant_inst,[status(thm)],[])).
% 9.19/9.45 tff(17443,plain,
% 9.19/9.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 9.19/9.45 inference(modus_ponens,[status(thm)],[17442, 17441])).
% 9.19/9.45 tff(17444,plain,
% 9.19/9.45 (~b(s(z), s(s(z)))),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[17443, 391, 17432, 10682, 1235, 590])).
% 9.19/9.45 tff(17445,plain,
% 9.19/9.45 (r(s(z), s(s(z)))),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[1788, 17444])).
% 9.19/9.45 tff(17446,plain,
% 9.19/9.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 9.19/9.45 inference(rewrite,[status(thm)],[])).
% 9.19/9.45 tff(17447,plain,
% 9.19/9.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 9.19/9.45 inference(quant_inst,[status(thm)],[])).
% 9.19/9.45 tff(17448,plain,
% 9.19/9.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 9.19/9.45 inference(modus_ponens,[status(thm)],[17447, 17446])).
% 9.19/9.45 tff(17449,plain,
% 9.19/9.45 (~b(s(s(z)), s(z))),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[17448, 391, 17432, 10682, 1235, 590])).
% 9.19/9.45 tff(17450,plain,
% 9.19/9.45 (r(s(s(z)), s(z))),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[3778, 17449])).
% 9.19/9.45 tff(17451,plain,
% 9.19/9.45 ($false),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[11551, 17450, 17445, 17437, 17434])).
% 9.19/9.45 tff(17452,plain,((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.45 tff(17453,plain,
% 9.19/9.45 (~b(elem!1, z)),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[17452, 17354, 10584, 17431, 17332])).
% 9.19/9.45 tff(17454,plain,
% 9.19/9.45 (r(elem!1, z)),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[526, 17453, 10680])).
% 9.19/9.45 tff(17455,plain,
% 9.19/9.45 (r(s(s(s(elem!1))), z)),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[533, 17454, 17329])).
% 9.19/9.45 tff(17456,plain,
% 9.19/9.45 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[2849, 17037])).
% 9.19/9.45 tff(17457,plain,
% 9.19/9.45 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[10940, 17456])).
% 9.19/9.45 tff(17458,plain,
% 9.19/9.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 9.19/9.45 inference(rewrite,[status(thm)],[])).
% 9.19/9.45 tff(17459,plain,
% 9.19/9.45 (((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 9.19/9.45 inference(rewrite,[status(thm)],[])).
% 9.19/9.45 tff(17460,plain,
% 9.19/9.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))))),
% 9.19/9.45 inference(monotonicity,[status(thm)],[17459])).
% 9.19/9.45 tff(17461,plain,
% 9.19/9.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 9.19/9.45 inference(transitivity,[status(thm)],[17460, 17458])).
% 9.19/9.45 tff(17462,plain,
% 9.19/9.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 9.19/9.45 inference(quant_inst,[status(thm)],[])).
% 9.19/9.45 tff(17463,plain,
% 9.19/9.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 9.19/9.45 inference(modus_ponens,[status(thm)],[17462, 17461])).
% 9.19/9.45 tff(17464,plain,
% 9.19/9.45 ($false),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[17463, 194, 174, 1484, 183, 722])).
% 9.19/9.45 tff(17465,plain,((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.45 tff(17466,plain,
% 9.19/9.45 (~r(s(z), elem!1)),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[17465, 17455, 722, 17341])).
% 9.19/9.45 tff(17467,plain,
% 9.19/9.45 (b(s(z), elem!1)),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[632, 17466, 17037])).
% 9.19/9.45 tff(17468,plain,
% 9.19/9.45 (b(s(z), s(s(s(elem!1))))),
% 9.19/9.45 inference(unit_resolution,[status(thm)],[14872, 17467, 17329])).
% 9.19/9.45 tff(17469,plain,
% 9.19/9.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.19/9.45 inference(rewrite,[status(thm)],[])).
% 9.19/9.45 tff(17470,plain,
% 9.19/9.45 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.19/9.45 inference(rewrite,[status(thm)],[])).
% 9.19/9.45 tff(17471,plain,
% 9.19/9.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 9.19/9.45 inference(monotonicity,[status(thm)],[17470])).
% 9.19/9.45 tff(17472,plain,
% 9.19/9.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.19/9.46 inference(transitivity,[status(thm)],[17471, 17469])).
% 9.19/9.46 tff(17473,plain,
% 9.19/9.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.19/9.46 inference(quant_inst,[status(thm)],[])).
% 9.19/9.46 tff(17474,plain,
% 9.19/9.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 9.19/9.46 inference(modus_ponens,[status(thm)],[17473, 17472])).
% 9.19/9.46 tff(17475,plain,
% 9.19/9.46 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[17474, 194, 174, 2053, 719])).
% 9.19/9.46 tff(17476,plain,
% 9.19/9.46 (b(s(s(s(s(z)))), elem!1)),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[2694, 17475, 5])).
% 9.19/9.46 tff(17477,plain,
% 9.19/9.46 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.19/9.46 inference(modus_ponens,[status(thm)],[17476, 15898])).
% 9.19/9.46 tff(17478,plain,
% 9.19/9.46 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[10884, 194, 174, 2053, 719])).
% 9.19/9.46 tff(17479,plain,
% 9.19/9.46 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[15351, 17478, 15348])).
% 9.19/9.46 tff(17480,plain,
% 9.19/9.46 ($false),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[11292, 391, 10682, 379, 590, 3325, 1669])).
% 9.19/9.46 tff(17481,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.46 tff(17482,plain,
% 9.19/9.46 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[17481, 17479, 10682, 590, 379])).
% 9.19/9.46 tff(17483,plain,
% 9.19/9.46 ($false),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[17482, 17477])).
% 9.19/9.46 tff(17484,plain,((~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.46 tff(17485,plain,
% 9.19/9.46 (~r(z, s(s(s(s(z)))))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[17484, 17354, 17431, 17468, 17457, 17329, 17455, 2053])).
% 9.19/9.46 tff(17486,plain,
% 9.19/9.46 (b(z, s(s(s(s(z)))))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[800, 17485])).
% 9.19/9.46 tff(17487,plain,
% 9.19/9.46 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[17288, 17486, 1234, 10584, 17431])).
% 9.19/9.46 tff(17488,plain,
% 9.19/9.46 (r(s(s(s(s(z)))), s(s(z)))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[1714, 17487])).
% 9.19/9.46 tff(17489,plain,
% 9.19/9.46 (~b(s(s(s(s(z)))), s(z))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[17292, 17486, 17431, 1234])).
% 9.19/9.46 tff(17490,plain,
% 9.19/9.46 (r(s(s(s(s(z)))), s(z))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[749, 17489])).
% 9.19/9.46 tff(17491,plain,
% 9.19/9.46 (~r(s(z), s(s(z)))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[9076, 17490, 1749, 17488])).
% 9.19/9.46 tff(17492,plain,
% 9.19/9.46 (b(s(z), s(s(z)))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[1788, 17491])).
% 9.19/9.46 tff(17493,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 9.19/9.46 tff(17494,plain,
% 9.19/9.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.19/9.46 inference(rewrite,[status(thm)],[])).
% 9.19/9.46 tff(17495,plain,
% 9.19/9.46 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.19/9.46 inference(rewrite,[status(thm)],[])).
% 9.19/9.46 tff(17496,plain,
% 9.19/9.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 9.19/9.46 inference(monotonicity,[status(thm)],[17495])).
% 9.19/9.46 tff(17497,plain,
% 9.19/9.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.19/9.46 inference(transitivity,[status(thm)],[17496, 17494])).
% 9.19/9.46 tff(17498,plain,
% 9.19/9.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.19/9.46 inference(quant_inst,[status(thm)],[])).
% 9.19/9.46 tff(17499,plain,
% 9.19/9.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 9.19/9.46 inference(modus_ponens,[status(thm)],[17498, 17497])).
% 9.19/9.46 tff(17500,plain,
% 9.19/9.46 ($false),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[17499, 391, 379, 1235, 2439, 1686, 17493])).
% 9.19/9.46 tff(17501,plain,((~b(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.46 tff(17502,plain,
% 9.19/9.46 (~b(s(s(s(elem!1))), s(s(z)))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[17501, 17492, 10584, 17468, 17486])).
% 9.19/9.46 tff(17503,plain,
% 9.19/9.46 (~b(elem!1, s(s(z)))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[16425, 17502, 17332])).
% 9.19/9.46 tff(17504,plain,
% 9.19/9.46 (r(elem!1, s(s(z)))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[3394, 17503, 17337])).
% 9.19/9.46 tff(17505,plain,
% 9.19/9.46 (r(s(s(s(elem!1))), s(s(z)))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[10022, 17504, 17332])).
% 9.19/9.46 tff(17506,plain,
% 9.19/9.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.19/9.46 inference(rewrite,[status(thm)],[])).
% 9.19/9.46 tff(17507,plain,
% 9.19/9.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.19/9.46 inference(quant_inst,[status(thm)],[])).
% 9.19/9.46 tff(17508,plain,
% 9.19/9.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.19/9.46 inference(modus_ponens,[status(thm)],[17507, 17506])).
% 9.19/9.46 tff(17509,plain,
% 9.19/9.46 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[17508, 194, 1749, 17488, 17505])).
% 9.19/9.46 tff(17510,plain,
% 9.19/9.46 (~r(elem!1, s(s(s(s(z)))))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[14788, 17509, 17332])).
% 9.19/9.46 tff(17511,plain,
% 9.19/9.46 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 9.19/9.46 inference(monotonicity,[status(thm)],[17332])).
% 9.19/9.46 tff(17512,plain,
% 9.19/9.46 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 9.19/9.46 inference(symmetry,[status(thm)],[17511])).
% 9.19/9.46 tff(17513,plain,
% 9.19/9.46 (b(z, elem!1)),
% 9.19/9.46 inference(modus_ponens,[status(thm)],[17354, 17512])).
% 9.19/9.46 tff(17514,plain,
% 9.19/9.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.19/9.46 inference(rewrite,[status(thm)],[])).
% 9.19/9.46 tff(17515,plain,
% 9.19/9.46 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.19/9.46 inference(rewrite,[status(thm)],[])).
% 9.19/9.46 tff(17516,plain,
% 9.19/9.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 9.19/9.46 inference(monotonicity,[status(thm)],[17515])).
% 9.19/9.46 tff(17517,plain,
% 9.19/9.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.19/9.46 inference(transitivity,[status(thm)],[17516, 17514])).
% 9.19/9.46 tff(17518,plain,
% 9.19/9.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.19/9.46 inference(quant_inst,[status(thm)],[])).
% 9.19/9.46 tff(17519,plain,
% 9.19/9.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 9.19/9.46 inference(modus_ponens,[status(thm)],[17518, 17517])).
% 9.19/9.46 tff(17520,plain,
% 9.19/9.46 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.19/9.46 inference(unit_resolution,[status(thm)],[17519, 194, 1749, 17488, 17505])).
% 9.19/9.47 tff(17521,plain,
% 9.19/9.47 (b(s(s(s(s(z)))), elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[2694, 17520, 17329])).
% 9.19/9.47 tff(17522,plain,
% 9.19/9.47 (~b(elem!1, s(s(s(s(z)))))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[15860, 17521, 17513, 17486])).
% 9.19/9.47 tff(17523,plain,
% 9.19/9.47 ($false),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[781, 17522, 17510, 17331])).
% 9.19/9.47 tff(17524,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | b(elem!1, s(z)) | (z = elem!1) | b(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.47 tff(17525,plain,
% 9.19/9.47 (b(elem!1, s(s(s(elem!1))))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[17524, 1749, 17036, 3447, 722, 31, 115, 8329])).
% 9.19/9.47 tff(17526,plain,
% 9.19/9.47 (~(elem!1 = s(elem!1))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[166, 16989])).
% 9.19/9.47 tff(17527,plain,
% 9.19/9.47 (~r(s(s(s(s(z)))), elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[10408, 838, 3447, 411])).
% 9.19/9.47 tff(17528,plain,
% 9.19/9.47 (~r(s(z), z)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[845, 838, 722, 411])).
% 9.19/9.47 tff(17529,plain,
% 9.19/9.47 (b(s(z), z)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[180, 17528])).
% 9.19/9.47 tff(17530,plain,
% 9.19/9.47 (~r(s(s(z)), z)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[9635, 1749, 3447, 722])).
% 9.19/9.47 tff(17531,plain,
% 9.19/9.47 (b(s(s(z)), z)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[1211, 17530])).
% 9.19/9.47 tff(17532,plain,
% 9.19/9.47 (~r(s(z), elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[14725, 838, 722, 411])).
% 9.19/9.47 tff(17533,plain,
% 9.19/9.47 (b(s(z), elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[632, 17532, 150])).
% 9.19/9.47 tff(17534,plain,
% 9.19/9.47 (~(s(s(s(s(z)))) = elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[6966, 665, 3446])).
% 9.19/9.47 tff(17535,plain,
% 9.19/9.47 (b(s(s(s(s(z)))), elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[762, 17534, 6221])).
% 9.19/9.47 tff(17536,plain,
% 9.19/9.47 (~b(z, s(s(s(s(z)))))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[14799, 17535, 1234, 665, 590])).
% 9.19/9.47 tff(17537,plain,
% 9.19/9.47 (r(z, s(s(s(s(z)))))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[800, 17536])).
% 9.19/9.47 tff(17538,plain,
% 9.19/9.47 (~(elem!1 = s(s(s(s(z)))))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[769, 17534])).
% 9.19/9.47 tff(17539,plain,
% 9.19/9.47 (~b(elem!1, s(s(s(s(z)))))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[10491, 17535, 1234, 644, 665])).
% 9.19/9.47 tff(17540,plain,
% 9.19/9.47 (r(elem!1, s(s(s(s(z)))))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[781, 17539, 17538])).
% 9.19/9.47 tff(17541,plain,
% 9.19/9.47 ($false),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[10499, 194, 411, 3447, 17540, 17537])).
% 9.19/9.47 tff(17542,plain,((~b(elem!1, z)) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | r(s(s(s(s(z)))), elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.47 tff(17543,plain,
% 9.19/9.47 (~b(elem!1, z)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[17542, 17533, 1234, 411, 17529, 17527, 3446])).
% 9.19/9.47 tff(17544,plain,
% 9.19/9.47 (~(elem!1 = s(s(z)))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[3589, 17543, 17531])).
% 9.19/9.47 tff(17545,plain,
% 9.19/9.47 (~(s(s(z)) = elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[11003, 1405])).
% 9.19/9.47 tff(17546,plain,
% 9.19/9.47 (~b(s(s(z)), s(z))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[17081, 391, 1235, 590, 15045])).
% 9.19/9.47 tff(17547,plain,
% 9.19/9.47 (r(s(s(z)), s(z))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[3778, 17546])).
% 9.19/9.47 tff(17548,plain,
% 9.19/9.47 (~b(s(z), s(s(z)))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[17089, 391, 1235, 590, 15045])).
% 9.19/9.47 tff(17549,plain,
% 9.19/9.47 (r(s(z), s(s(z)))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[1788, 17548])).
% 9.19/9.47 tff(17550,plain,
% 9.19/9.47 (~r(s(s(z)), elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[17104, 194, 847, 17549, 17547])).
% 9.19/9.47 tff(17551,plain,
% 9.19/9.47 (b(s(s(z)), elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[4730, 17550, 17545])).
% 9.19/9.47 tff(17552,plain,
% 9.19/9.47 (~(s(s(s(s(z)))) = elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[5152, 17550, 1749])).
% 9.19/9.47 tff(17553,plain,
% 9.19/9.47 (b(s(s(s(s(z)))), elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[762, 17552, 6221])).
% 9.19/9.47 tff(17554,plain,
% 9.19/9.47 (~r(elem!1, s(s(z)))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[17097, 194, 847, 17549, 17547])).
% 9.19/9.47 tff(17555,plain,
% 9.19/9.47 (b(elem!1, s(s(z)))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[3394, 17554, 1405])).
% 9.19/9.47 tff(17556,plain,
% 9.19/9.47 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[11012, 17555, 17553, 17551])).
% 9.19/9.47 tff(17557,plain,
% 9.19/9.47 (r(s(s(s(s(z)))), s(s(z)))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[1714, 17556])).
% 9.19/9.47 tff(17558,plain,
% 9.19/9.47 (~r(s(s(s(s(z)))), s(z))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[10673, 17557, 17549, 17547])).
% 9.19/9.47 tff(17559,plain,
% 9.19/9.47 (b(s(s(s(s(z)))), s(z))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[749, 17558])).
% 9.19/9.47 tff(17560,plain,
% 9.19/9.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 9.19/9.47 inference(rewrite,[status(thm)],[])).
% 9.19/9.47 tff(17561,plain,
% 9.19/9.47 (((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 9.19/9.47 inference(rewrite,[status(thm)],[])).
% 9.19/9.47 tff(17562,plain,
% 9.19/9.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))))),
% 9.19/9.47 inference(monotonicity,[status(thm)],[17561])).
% 9.19/9.47 tff(17563,plain,
% 9.19/9.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 9.19/9.47 inference(transitivity,[status(thm)],[17562, 17560])).
% 9.19/9.47 tff(17564,plain,
% 9.19/9.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.19/9.47 inference(quant_inst,[status(thm)],[])).
% 9.19/9.47 tff(17565,plain,
% 9.19/9.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))),
% 9.19/9.47 inference(modus_ponens,[status(thm)],[17564, 17563])).
% 9.19/9.47 tff(17566,plain,
% 9.19/9.47 ($false),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[17565, 391, 644, 17555, 17553, 17559, 17551])).
% 9.19/9.47 tff(17567,plain,((~b(z, s(s(z)))) | (~b(s(z), elem!1)) | r(s(s(s(s(z)))), elem!1) | (elem!1 = s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.47 tff(17568,plain,
% 9.19/9.47 (~b(z, s(s(z)))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[17567, 17533, 17527, 17544, 1749, 838, 17531, 17529])).
% 9.19/9.47 tff(17569,plain,
% 9.19/9.47 (r(z, s(s(z)))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[10164, 42, 17568, 8912])).
% 9.19/9.47 tff(17570,plain,
% 9.19/9.47 (r(elem!1, z)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[526, 17543, 2])).
% 9.19/9.47 tff(17571,plain,
% 9.19/9.47 (~r(s(s(z)), elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[8513, 17570, 411, 17569])).
% 9.19/9.47 tff(17572,plain,
% 9.19/9.47 (~(s(s(s(s(z)))) = elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[5152, 17571, 1749])).
% 9.19/9.47 tff(17573,plain,
% 9.19/9.47 (b(s(s(s(s(z)))), elem!1)),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[762, 17572, 17527])).
% 9.19/9.47 tff(17574,plain,
% 9.19/9.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 9.19/9.47 inference(rewrite,[status(thm)],[])).
% 9.19/9.47 tff(17575,plain,
% 9.19/9.47 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 9.19/9.47 inference(rewrite,[status(thm)],[])).
% 9.19/9.47 tff(17576,plain,
% 9.19/9.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))))),
% 9.19/9.47 inference(monotonicity,[status(thm)],[17575])).
% 9.19/9.47 tff(17577,plain,
% 9.19/9.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 9.19/9.47 inference(transitivity,[status(thm)],[17576, 17574])).
% 9.19/9.47 tff(17578,plain,
% 9.19/9.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 9.19/9.47 inference(quant_inst,[status(thm)],[])).
% 9.19/9.47 tff(17579,plain,
% 9.19/9.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))),
% 9.19/9.47 inference(modus_ponens,[status(thm)],[17578, 17577])).
% 9.19/9.47 tff(17580,plain,
% 9.19/9.47 (~r(elem!1, s(s(s(s(z)))))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[17579, 194, 411, 17570, 3447])).
% 9.19/9.47 tff(17581,plain,
% 9.19/9.47 (~(elem!1 = s(s(s(s(z)))))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[769, 17572])).
% 9.19/9.47 tff(17582,plain,
% 9.19/9.47 (b(elem!1, s(s(s(s(z)))))),
% 9.19/9.47 inference(unit_resolution,[status(thm)],[781, 17581, 17580])).
% 9.19/9.47 tff(17583,plain,
% 9.19/9.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.19/9.47 inference(rewrite,[status(thm)],[])).
% 9.19/9.47 tff(17584,plain,
% 9.19/9.47 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.19/9.47 inference(rewrite,[status(thm)],[])).
% 9.19/9.47 tff(17585,plain,
% 9.19/9.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 9.19/9.48 inference(monotonicity,[status(thm)],[17584])).
% 9.19/9.48 tff(17586,plain,
% 9.19/9.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.19/9.48 inference(transitivity,[status(thm)],[17585, 17583])).
% 9.19/9.48 tff(17587,plain,
% 9.19/9.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.19/9.48 inference(quant_inst,[status(thm)],[])).
% 9.19/9.48 tff(17588,plain,
% 9.19/9.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 9.19/9.48 inference(modus_ponens,[status(thm)],[17587, 17586])).
% 9.19/9.48 tff(17589,plain,
% 9.19/9.48 ($false),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[17588, 391, 17533, 17582, 17573, 1234])).
% 9.19/9.48 tff(17590,plain,((s(z) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, elem!1)) | (elem!1 = z) | b(s(s(s(s(z)))), z) | (~r(z, s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.48 tff(17591,plain,
% 9.19/9.48 (s(z) = elem!1),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[17590, 15899, 1749, 1234, 2, 3446, 722, 31])).
% 9.19/9.48 tff(17592,plain,
% 9.19/9.48 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 9.19/9.48 inference(monotonicity,[status(thm)],[17591])).
% 9.19/9.48 tff(17593,plain,
% 9.19/9.48 (elem!1 = s(z)),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[1495, 17591])).
% 9.19/9.48 tff(17594,plain,
% 9.19/9.48 (~b(s(z), elem!1)),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[8805, 17593])).
% 9.19/9.48 tff(17595,plain,
% 9.19/9.48 (r(elem!1, s(z))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[10383, 2829, 1234, 10, 8814, 3446])).
% 9.19/9.48 tff(17596,plain,
% 9.19/9.48 (~r(s(z), z)),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[2475, 411, 847, 1484])).
% 9.19/9.48 tff(17597,plain,
% 9.19/9.48 (b(s(z), z)),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[180, 17596])).
% 9.19/9.48 tff(17598,plain,
% 9.19/9.48 (~r(z, s(z))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[14725, 411, 847, 1484])).
% 9.19/9.48 tff(17599,plain,
% 9.19/9.48 (b(z, s(z))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[678, 17598])).
% 9.19/9.48 tff(17600,plain,
% 9.19/9.48 (~b(s(s(s(elem!1))), z)),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[10633, 391, 1526, 17599, 17597])).
% 9.19/9.48 tff(17601,plain,
% 9.19/9.48 (r(s(s(s(elem!1))), z)),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[377, 17600])).
% 9.19/9.48 tff(17602,plain,
% 9.19/9.48 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[11060, 194, 411, 17601, 2053])).
% 9.19/9.48 tff(17603,plain,
% 9.19/9.48 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[4313, 42, 17602, 16058])).
% 9.19/9.48 tff(17604,plain,
% 9.19/9.48 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[11066, 194, 411, 17601, 2053])).
% 9.19/9.48 tff(17605,plain,
% 9.19/9.48 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 17604])).
% 9.19/9.48 tff(17606,plain,
% 9.19/9.48 ($false),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[10108, 17605, 17603, 1234, 1526])).
% 9.19/9.48 tff(17607,plain,((~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.48 tff(17608,plain,
% 9.19/9.48 (~r(z, elem!1)),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[17607, 3363, 1526, 1234, 3447, 847, 5238])).
% 9.19/9.48 tff(17609,plain,
% 9.19/9.48 (~(elem!1 = s(s(s(elem!1))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[147, 17608, 10])).
% 9.19/9.48 tff(17610,plain,
% 9.19/9.48 (~(s(s(s(elem!1))) = elem!1)),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[8, 17609])).
% 9.19/9.48 tff(17611,plain,
% 9.19/9.48 (elem!1 = z),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[8231, 17608, 10])).
% 9.19/9.48 tff(17612,plain,
% 9.19/9.48 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.19/9.48 inference(monotonicity,[status(thm)],[491])).
% 9.19/9.48 tff(17613,plain,
% 9.19/9.48 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 9.19/9.48 inference(symmetry,[status(thm)],[17612])).
% 9.19/9.48 tff(17614,plain,
% 9.19/9.48 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.19/9.48 inference(monotonicity,[status(thm)],[2401])).
% 9.19/9.48 tff(17615,plain,
% 9.19/9.48 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[8883, 11])).
% 9.19/9.48 tff(17616,plain,
% 9.19/9.48 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[307, 17615])).
% 9.19/9.48 tff(17617,plain,
% 9.19/9.48 (r(s(z), z) <=> r(s(elem!1), z)),
% 9.19/9.48 inference(symmetry,[status(thm)],[509])).
% 9.19/9.48 tff(17618,plain,
% 9.19/9.48 (z = elem!1),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[5453, 11])).
% 9.19/9.48 tff(17619,plain,
% 9.19/9.48 (r(s(z), z)),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[5433, 17618, 1484])).
% 9.19/9.48 tff(17620,plain,
% 9.19/9.48 (r(s(elem!1), z)),
% 9.19/9.48 inference(modus_ponens,[status(thm)],[17619, 17617])).
% 9.19/9.48 tff(17621,plain,
% 9.19/9.48 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 9.19/9.48 inference(symmetry,[status(thm)],[1604])).
% 9.19/9.48 tff(17622,plain,
% 9.19/9.48 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(s(z)))), elem!1))),
% 9.19/9.48 inference(monotonicity,[status(thm)],[17621])).
% 9.19/9.48 tff(17623,plain,
% 9.19/9.48 (~b(s(s(s(s(z)))), elem!1)),
% 9.19/9.48 inference(modus_ponens,[status(thm)],[3446, 17622])).
% 9.19/9.48 tff(17624,plain,
% 9.19/9.48 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 9.19/9.48 inference(symmetry,[status(thm)],[494])).
% 9.19/9.48 tff(17625,plain,
% 9.19/9.48 (b(s(s(s(elem!1))), s(elem!1))),
% 9.19/9.48 inference(modus_ponens,[status(thm)],[1526, 17624])).
% 9.19/9.48 tff(17626,plain,
% 9.19/9.48 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 9.19/9.48 inference(symmetry,[status(thm)],[510])).
% 9.19/9.48 tff(17627,plain,
% 9.19/9.48 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 9.19/9.48 inference(transitivity,[status(thm)],[17617, 17626])).
% 9.19/9.48 tff(17628,plain,
% 9.19/9.48 (r(s(elem!1), elem!1)),
% 9.19/9.48 inference(modus_ponens,[status(thm)],[17619, 17627])).
% 9.19/9.48 tff(17629,plain,
% 9.19/9.48 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[1648, 17628, 11, 17625, 184, 957, 17623, 17620])).
% 9.19/9.48 tff(17630,plain,
% 9.19/9.48 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[1164, 17629, 17616])).
% 9.19/9.48 tff(17631,plain,
% 9.19/9.48 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.19/9.48 inference(modus_ponens,[status(thm)],[17630, 17614])).
% 9.19/9.48 tff(17632,plain,
% 9.19/9.48 (r(s(s(s(z))), s(s(s(s(z)))))),
% 9.19/9.48 inference(modus_ponens,[status(thm)],[17631, 17613])).
% 9.19/9.48 tff(17633,plain,
% 9.19/9.48 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[4402, 11, 3843])).
% 9.19/9.48 tff(17634,plain,
% 9.19/9.48 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 9.19/9.48 inference(monotonicity,[status(thm)],[491])).
% 9.19/9.48 tff(17635,plain,
% 9.19/9.48 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 9.19/9.48 inference(symmetry,[status(thm)],[17634])).
% 9.19/9.48 tff(17636,plain,
% 9.19/9.48 (b(s(s(s(z))), s(z))),
% 9.19/9.48 inference(modus_ponens,[status(thm)],[1526, 17635])).
% 9.19/9.48 tff(17637,plain,
% 9.19/9.48 (r(z, s(z))),
% 9.19/9.48 inference(modus_ponens,[status(thm)],[847, 8826])).
% 9.19/9.48 tff(17638,plain,
% 9.19/9.48 (~r(s(s(s(s(z)))), s(z))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[11989, 194, 17637, 17619, 3447])).
% 9.19/9.48 tff(17639,plain,
% 9.19/9.48 (b(s(s(s(s(z)))), s(z))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[749, 17638])).
% 9.19/9.48 tff(17640,plain,
% 9.19/9.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.19/9.48 inference(rewrite,[status(thm)],[])).
% 9.19/9.48 tff(17641,plain,
% 9.19/9.48 (((~b(s(s(s(s(z)))), s(z))) | (~b(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(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))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.19/9.48 inference(rewrite,[status(thm)],[])).
% 9.19/9.48 tff(17642,plain,
% 9.19/9.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(z), s(s(s(s(z))))))))),
% 9.19/9.48 inference(monotonicity,[status(thm)],[17641])).
% 9.19/9.48 tff(17643,plain,
% 9.19/9.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.19/9.48 inference(transitivity,[status(thm)],[17642, 17640])).
% 9.19/9.48 tff(17644,plain,
% 9.19/9.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(z)))), s(s(s(z))))))),
% 9.19/9.48 inference(quant_inst,[status(thm)],[])).
% 9.19/9.48 tff(17645,plain,
% 9.19/9.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))) | (~b(s(z), s(s(s(s(z))))))),
% 9.19/9.48 inference(modus_ponens,[status(thm)],[17644, 17643])).
% 9.19/9.48 tff(17646,plain,
% 9.19/9.48 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[17645, 391, 1234, 17639, 17636])).
% 9.19/9.48 tff(17647,plain,
% 9.19/9.48 (r(s(s(s(s(z)))), s(s(s(z))))),
% 9.19/9.48 inference(unit_resolution,[status(thm)],[4426, 42, 17646, 17633])).
% 9.19/9.48 tff(17648,plain,
% 9.19/9.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(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))))))),
% 9.19/9.48 inference(rewrite,[status(thm)],[])).
% 9.19/9.48 tff(17649,plain,
% 9.19/9.48 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(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)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 9.19/9.48 inference(rewrite,[status(thm)],[])).
% 9.19/9.48 tff(17650,plain,
% 9.19/9.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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)))))))),
% 9.19/9.48 inference(monotonicity,[status(thm)],[17649])).
% 9.19/9.48 tff(17651,plain,
% 9.19/9.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(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))))))),
% 9.19/9.49 inference(transitivity,[status(thm)],[17650, 17648])).
% 9.19/9.49 tff(17652,plain,
% 9.19/9.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 9.19/9.49 inference(quant_inst,[status(thm)],[])).
% 9.19/9.49 tff(17653,plain,
% 9.19/9.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 9.19/9.49 inference(modus_ponens,[status(thm)],[17652, 17651])).
% 9.19/9.49 tff(17654,plain,
% 9.19/9.49 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17653, 194, 3447, 501, 17647])).
% 9.19/9.49 tff(17655,plain,
% 9.19/9.49 ($false),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17654, 17632])).
% 9.19/9.49 tff(17656,plain,((~(elem!1 = z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(z)))), z) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.49 tff(17657,plain,
% 9.19/9.49 (s(s(s(s(elem!1)))) = s(elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17656, 17611, 59, 1234, 1526, 3446, 847, 5238, 3363])).
% 9.19/9.49 tff(17658,plain,
% 9.19/9.49 ($false),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[929, 17657, 17610])).
% 9.19/9.49 tff(17659,plain,((s(z) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(z)))), z) | (~r(elem!1, s(z))) | b(z, s(s(s(elem!1)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.49 tff(17660,plain,
% 9.19/9.49 (s(z) = elem!1),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17659, 17595, 8815, 3446, 1234, 10, 2829])).
% 9.19/9.49 tff(17661,plain,
% 9.19/9.49 (r(elem!1, s(z)) <=> r(elem!1, elem!1)),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17660])).
% 9.19/9.49 tff(17662,plain,
% 9.19/9.49 (r(elem!1, elem!1) <=> r(elem!1, s(z))),
% 9.19/9.49 inference(symmetry,[status(thm)],[17661])).
% 9.19/9.49 tff(17663,plain,
% 9.19/9.49 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(z)))),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17662])).
% 9.19/9.49 tff(17664,plain,
% 9.19/9.49 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 9.19/9.49 inference(quant_inst,[status(thm)],[])).
% 9.19/9.49 tff(17665,plain,
% 9.19/9.49 (~r(elem!1, elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17664, 76])).
% 9.19/9.49 tff(17666,plain,
% 9.19/9.49 (~r(elem!1, s(z))),
% 9.19/9.49 inference(modus_ponens,[status(thm)],[17665, 17663])).
% 9.19/9.49 tff(17667,plain,
% 9.19/9.49 ($false),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17595, 17666])).
% 9.19/9.49 tff(17668,plain,(b(s(z), elem!1) | b(s(s(s(s(z)))), z) | (~b(s(z), s(s(s(s(z)))))) | b(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.49 tff(17669,plain,
% 9.19/9.49 (r(s(s(s(elem!1))), s(z))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17668, 17594, 3446, 1234, 10])).
% 9.19/9.49 tff(17670,plain,
% 9.19/9.49 (r(s(s(s(elem!1))), elem!1)),
% 9.19/9.49 inference(modus_ponens,[status(thm)],[17669, 17592])).
% 9.19/9.49 tff(17671,plain,
% 9.19/9.49 (~r(elem!1, s(elem!1))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[434, 17670, 15899, 59])).
% 9.19/9.49 tff(17672,plain,
% 9.19/9.49 (b(elem!1, s(elem!1))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[443, 17671, 437])).
% 9.19/9.49 tff(17673,plain,
% 9.19/9.49 (s(s(z)) = s(elem!1)),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17591])).
% 9.19/9.49 tff(17674,plain,
% 9.19/9.49 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17673])).
% 9.19/9.49 tff(17675,plain,
% 9.19/9.49 (b(s(elem!1), z)),
% 9.19/9.49 inference(modus_ponens,[status(thm)],[17531, 17674])).
% 9.19/9.49 tff(17676,plain,
% 9.19/9.49 (r(s(elem!1), s(s(s(elem!1))))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[3614, 17591, 1749])).
% 9.19/9.49 tff(17677,plain,
% 9.19/9.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 9.19/9.49 inference(rewrite,[status(thm)],[])).
% 9.19/9.49 tff(17678,plain,
% 9.19/9.49 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 9.19/9.49 inference(rewrite,[status(thm)],[])).
% 9.19/9.49 tff(17679,plain,
% 9.19/9.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17678])).
% 9.19/9.49 tff(17680,plain,
% 9.19/9.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 9.19/9.49 inference(transitivity,[status(thm)],[17679, 17677])).
% 9.19/9.49 tff(17681,plain,
% 9.19/9.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 9.19/9.49 inference(quant_inst,[status(thm)],[])).
% 9.19/9.49 tff(17682,plain,
% 9.19/9.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 9.19/9.49 inference(modus_ponens,[status(thm)],[17681, 17680])).
% 9.19/9.49 tff(17683,plain,
% 9.19/9.49 (~r(z, s(elem!1))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17682, 194, 17670, 59, 17676])).
% 9.19/9.49 tff(17684,plain,
% 9.19/9.49 (b(z, s(elem!1))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[566, 17683])).
% 9.19/9.49 tff(17685,plain,
% 9.19/9.49 (~r(s(z), z)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[829, 17670, 15899, 59, 17591])).
% 9.19/9.49 tff(17686,plain,
% 9.19/9.49 (b(elem!1, z)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[7485, 17685, 17591])).
% 9.19/9.49 tff(17687,plain,
% 9.19/9.49 ($false),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[1939, 17686, 17684, 17675, 17672])).
% 9.19/9.49 tff(17688,plain,(b(z, s(s(s(elem!1)))) | (elem!1 = s(elem!1)) | b(s(s(s(s(z)))), z) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = z) | (~r(z, s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.19/9.49 tff(17689,plain,
% 9.19/9.49 (b(z, s(s(s(elem!1))))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17688, 17526, 3446, 1234, 1749, 10680, 722, 31])).
% 9.19/9.49 tff(17690,plain,
% 9.19/9.49 (~r(z, elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17590, 150, 1749, 1234, 10680, 3446, 722, 31])).
% 9.19/9.49 tff(17691,plain,
% 9.19/9.49 (b(z, elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[141, 17690, 115])).
% 9.19/9.49 tff(17692,plain,
% 9.19/9.49 (~b(s(s(s(elem!1))), elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[10845, 17691, 448, 17689])).
% 9.19/9.49 tff(17693,plain,
% 9.19/9.49 (r(s(s(s(elem!1))), elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[230, 17692, 15376])).
% 9.19/9.49 tff(17694,plain,
% 9.19/9.49 (~b(s(s(s(elem!1))), z)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[10876, 11936, 448, 133])).
% 9.19/9.49 tff(17695,plain,
% 9.19/9.49 (r(s(s(s(elem!1))), z)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[377, 17694])).
% 9.19/9.49 tff(17696,plain,
% 9.19/9.49 (b(s(elem!1), elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[14657, 2282, 150, 133, 10682, 16101, 2])).
% 9.19/9.49 tff(17697,plain,
% 9.19/9.49 (~b(z, s(elem!1))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[6555, 17696, 133, 11936])).
% 9.19/9.49 tff(17698,plain,
% 9.19/9.49 (r(z, s(elem!1))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[566, 17697])).
% 9.19/9.49 tff(17699,plain,
% 9.19/9.49 ($false),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[12988, 17698, 17695, 448, 2053, 3363, 11936, 10682])).
% 9.19/9.49 tff(17700,plain,(r(elem!1, z) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(z) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.49 tff(17701,plain,
% 9.19/9.49 (r(elem!1, z)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17700, 17691, 3447, 17689, 448, 150, 10680])).
% 9.19/9.49 tff(17702,plain,
% 9.19/9.49 (~r(s(z), z)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17266, 17701, 722, 838])).
% 9.19/9.49 tff(17703,plain,
% 9.19/9.49 (b(s(z), z)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[180, 17702])).
% 9.19/9.49 tff(17704,plain,
% 9.19/9.49 (~r(s(s(s(elem!1))), z)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[4113, 17701, 722, 17693])).
% 9.19/9.49 tff(17705,plain,
% 9.19/9.49 (b(s(s(s(elem!1))), z)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[377, 17704])).
% 9.19/9.49 tff(17706,plain,
% 9.19/9.49 (~b(s(z), elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[4929, 17705, 448, 17691, 17703])).
% 9.19/9.49 tff(17707,plain,
% 9.19/9.49 (~b(s(z), s(s(s(elem!1))))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[11303, 17705, 17689, 17703])).
% 9.19/9.49 tff(17708,plain,
% 9.19/9.49 (r(s(z), s(s(s(elem!1))))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[247, 17707])).
% 9.19/9.49 tff(17709,plain,
% 9.19/9.49 ($false),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[5246, 17708, 17706, 31, 150, 17693])).
% 9.19/9.49 tff(17710,plain,((s(z) = elem!1) | b(elem!1, s(z)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (z = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 9.19/9.49 tff(17711,plain,
% 9.19/9.49 (s(z) = elem!1),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17710, 17525, 31, 722, 115, 1749, 17036, 3446])).
% 9.19/9.49 tff(17712,plain,
% 9.19/9.49 (s(s(z)) = s(elem!1)),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17711])).
% 9.19/9.49 tff(17713,plain,
% 9.19/9.49 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17712])).
% 9.19/9.49 tff(17714,plain,
% 9.19/9.49 (s(s(s(z))) = s(s(elem!1))),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17712])).
% 9.19/9.49 tff(17715,plain,
% 9.19/9.49 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17714])).
% 9.19/9.49 tff(17716,plain,
% 9.19/9.49 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17715])).
% 9.19/9.49 tff(17717,plain,
% 9.19/9.49 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 9.19/9.49 inference(symmetry,[status(thm)],[17716])).
% 9.19/9.49 tff(17718,plain,
% 9.19/9.49 (~(s(s(s(elem!1))) = elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[15370, 17525])).
% 9.19/9.49 tff(17719,plain,
% 9.19/9.49 (~(s(elem!1) = elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[158, 17718])).
% 9.19/9.49 tff(17720,plain,
% 9.19/9.49 (~(elem!1 = s(elem!1))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[166, 17719])).
% 9.19/9.49 tff(17721,plain,
% 9.19/9.49 (b(z, s(s(s(elem!1))))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17688, 17720, 3446, 17036, 1749, 10680, 722, 31])).
% 9.19/9.49 tff(17722,plain,
% 9.19/9.49 (b(z, s(s(s(s(z)))))),
% 9.19/9.49 inference(modus_ponens,[status(thm)],[17721, 17717])).
% 9.19/9.49 tff(17723,plain,
% 9.19/9.49 (r(z, elem!1)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[17233, 17711, 722])).
% 9.19/9.49 tff(17724,plain,
% 9.19/9.49 (elem!1 = s(z)),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[1495, 17711])).
% 9.19/9.49 tff(17725,plain,
% 9.19/9.49 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[8251, 17718])).
% 9.19/9.49 tff(17726,plain,
% 9.19/9.49 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.19/9.49 inference(unit_resolution,[status(thm)],[1370, 17725, 8329])).
% 9.19/9.49 tff(17727,plain,
% 9.19/9.49 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17712])).
% 9.19/9.49 tff(17728,plain,
% 9.19/9.49 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17727])).
% 9.19/9.49 tff(17729,plain,
% 9.19/9.49 (~(s(s(elem!1)) = s(elem!1))),
% 9.19/9.49 inference(modus_ponens,[status(thm)],[11335, 17728])).
% 9.19/9.49 tff(17730,plain,
% 9.19/9.49 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 9.19/9.49 inference(transitivity,[status(thm)],[17727, 1098])).
% 9.19/9.49 tff(17731,plain,
% 9.19/9.49 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 9.19/9.49 inference(monotonicity,[status(thm)],[17730])).
% 9.19/9.49 tff(17732,plain,
% 9.19/9.49 (~(s(elem!1) = s(s(elem!1)))),
% 9.19/9.49 inference(modus_ponens,[status(thm)],[11335, 17731])).
% 9.19/9.50 tff(17733,plain,
% 9.19/9.50 (r(s(elem!1), s(s(s(elem!1))))),
% 9.19/9.50 inference(unit_resolution,[status(thm)],[3614, 17711, 1749])).
% 9.19/9.50 tff(17734,plain,
% 9.19/9.50 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 9.19/9.50 inference(symmetry,[status(thm)],[17715])).
% 9.19/9.50 tff(17735,plain,
% 9.19/9.50 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 9.19/9.50 inference(monotonicity,[status(thm)],[17734])).
% 9.19/9.50 tff(17736,plain,
% 9.19/9.50 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 9.19/9.50 inference(modus_ponens,[status(thm)],[17726, 17735])).
% 9.19/9.50 tff(17737,plain,
% 9.19/9.50 (~r(s(s(elem!1)), z)),
% 9.19/9.50 inference(unit_resolution,[status(thm)],[9362, 17736, 722, 3447])).
% 9.19/9.50 tff(17738,plain,
% 9.19/9.50 (b(s(s(elem!1)), z)),
% 9.19/9.50 inference(unit_resolution,[status(thm)],[2629, 17737])).
% 9.19/9.50 tff(17739,plain,
% 9.19/9.50 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 9.19/9.50 inference(monotonicity,[status(thm)],[17712])).
% 9.19/9.50 tff(17740,plain,
% 9.19/9.50 (b(s(elem!1), z)),
% 9.19/9.50 inference(modus_ponens,[status(thm)],[17531, 17739])).
% 9.19/9.50 tff(17741,plain,
% 9.19/9.50 (r(s(s(elem!1)), s(elem!1))),
% 9.19/9.50 inference(unit_resolution,[status(thm)],[1135, 1031, 285])).
% 9.28/9.50 tff(17742,plain,
% 9.28/9.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 9.28/9.50 inference(rewrite,[status(thm)],[])).
% 9.28/9.50 tff(17743,plain,
% 9.28/9.50 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 9.28/9.50 inference(rewrite,[status(thm)],[])).
% 9.28/9.50 tff(17744,plain,
% 9.28/9.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 9.28/9.50 inference(monotonicity,[status(thm)],[17743])).
% 9.28/9.50 tff(17745,plain,
% 9.28/9.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 9.28/9.50 inference(transitivity,[status(thm)],[17744, 17742])).
% 9.28/9.50 tff(17746,plain,
% 9.28/9.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 9.28/9.50 inference(quant_inst,[status(thm)],[])).
% 9.28/9.50 tff(17747,plain,
% 9.28/9.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 9.28/9.50 inference(modus_ponens,[status(thm)],[17746, 17745])).
% 9.28/9.50 tff(17748,plain,
% 9.28/9.50 (~b(s(elem!1), s(s(elem!1)))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[17747, 391, 900, 10682, 591, 2641])).
% 9.28/9.50 tff(17749,plain,
% 9.28/9.50 (r(s(elem!1), s(s(elem!1)))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[8644, 17748, 8611])).
% 9.28/9.50 tff(17750,plain,
% 9.28/9.50 ($false),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[8653, 17749, 17741, 327, 604])).
% 9.28/9.50 tff(17751,plain,(b(s(s(elem!1)), s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.50 tff(17752,plain,
% 9.28/9.50 (b(s(s(elem!1)), s(elem!1))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[17751, 900, 604, 8611, 285, 327, 10682, 591, 2641])).
% 9.28/9.50 tff(17753,plain,
% 9.28/9.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 9.28/9.50 inference(rewrite,[status(thm)],[])).
% 9.28/9.50 tff(17754,plain,
% 9.28/9.50 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 9.28/9.50 inference(rewrite,[status(thm)],[])).
% 9.28/9.50 tff(17755,plain,
% 9.28/9.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))))),
% 9.28/9.50 inference(monotonicity,[status(thm)],[17754])).
% 9.28/9.50 tff(17756,plain,
% 9.28/9.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 9.28/9.50 inference(transitivity,[status(thm)],[17755, 17753])).
% 9.28/9.50 tff(17757,plain,
% 9.28/9.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 9.28/9.50 inference(quant_inst,[status(thm)],[])).
% 9.28/9.50 tff(17758,plain,
% 9.28/9.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))),
% 9.28/9.50 inference(modus_ponens,[status(thm)],[17757, 17756])).
% 9.28/9.50 tff(17759,plain,
% 9.28/9.50 ($false),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[17758, 391, 900, 10682, 591, 2641, 17752])).
% 9.28/9.50 tff(17760,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.50 tff(17761,plain,
% 9.28/9.50 (~b(s(s(s(elem!1))), elem!1)),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[17760, 17721, 17740, 17738, 17733, 17732, 17729, 17726])).
% 9.28/9.50 tff(17762,plain,
% 9.28/9.50 (~b(s(s(s(elem!1))), s(z))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[3938, 17761, 17711])).
% 9.28/9.50 tff(17763,plain,
% 9.28/9.50 (~b(s(s(s(s(z)))), s(z))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[11177, 17762, 17724])).
% 9.28/9.50 tff(17764,plain,
% 9.28/9.50 (r(s(s(s(s(z)))), s(z))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[749, 17763])).
% 9.28/9.50 tff(17765,plain,
% 9.28/9.50 (~r(s(z), z)),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[3243, 17764, 3447, 17723])).
% 9.28/9.50 tff(17766,plain,
% 9.28/9.50 (b(s(z), z)),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[180, 17765])).
% 9.28/9.50 tff(17767,plain,
% 9.28/9.50 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[17288, 17766, 17036, 17531, 17722])).
% 9.28/9.50 tff(17768,plain,
% 9.28/9.50 (r(s(s(s(s(z)))), s(s(z)))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[1714, 17767])).
% 9.28/9.50 tff(17769,plain,
% 9.28/9.50 (r(s(s(s(s(z)))), s(elem!1))),
% 9.28/9.50 inference(modus_ponens,[status(thm)],[17768, 17713])).
% 9.28/9.50 tff(17770,plain,
% 9.28/9.50 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 9.28/9.50 inference(monotonicity,[status(thm)],[17715])).
% 9.28/9.50 tff(17771,plain,
% 9.28/9.50 (r(s(s(s(elem!1))), z)),
% 9.28/9.50 inference(modus_ponens,[status(thm)],[3447, 17770])).
% 9.28/9.50 tff(17772,plain,
% 9.28/9.50 (r(s(s(s(elem!1))), elem!1)),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[230, 17761, 17718])).
% 9.28/9.50 tff(17773,plain,
% 9.28/9.50 (~r(elem!1, z)),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[4113, 17772, 722, 17771])).
% 9.28/9.50 tff(17774,plain,
% 9.28/9.50 (b(elem!1, z)),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[526, 17773, 10680])).
% 9.28/9.50 tff(17775,plain,
% 9.28/9.50 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 9.28/9.50 inference(monotonicity,[status(thm)],[17711])).
% 9.28/9.50 tff(17776,plain,
% 9.28/9.50 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 9.28/9.50 inference(transitivity,[status(thm)],[17775, 2206])).
% 9.28/9.50 tff(17777,plain,
% 9.28/9.50 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 9.28/9.50 inference(monotonicity,[status(thm)],[17776])).
% 9.28/9.50 tff(17778,plain,
% 9.28/9.50 (~(elem!1 = s(s(elem!1)))),
% 9.28/9.50 inference(modus_ponens,[status(thm)],[357, 17777])).
% 9.28/9.50 tff(17779,plain,
% 9.28/9.50 (~r(s(z), s(s(elem!1)))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[5500, 17764, 722, 3447])).
% 9.28/9.50 tff(17780,plain,
% 9.28/9.50 (~r(elem!1, s(s(elem!1)))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[15602, 17779, 17724])).
% 9.28/9.50 tff(17781,plain,
% 9.28/9.50 (b(elem!1, s(s(elem!1)))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[1307, 17780, 17778])).
% 9.28/9.50 tff(17782,plain,
% 9.28/9.50 (~b(z, s(elem!1))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[9660, 17781, 17740, 17738, 17774])).
% 9.28/9.50 tff(17783,plain,
% 9.28/9.50 (r(z, s(elem!1))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[566, 17782])).
% 9.28/9.50 tff(17784,plain,
% 9.28/9.50 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 9.28/9.50 inference(monotonicity,[status(thm)],[17712])).
% 9.28/9.50 tff(17785,plain,
% 9.28/9.50 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 9.28/9.50 inference(transitivity,[status(thm)],[17784, 582])).
% 9.28/9.50 tff(17786,plain,
% 9.28/9.50 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 9.28/9.50 inference(monotonicity,[status(thm)],[17785])).
% 9.28/9.50 tff(17787,plain,
% 9.28/9.50 (~(s(s(s(elem!1))) = s(elem!1))),
% 9.28/9.50 inference(modus_ponens,[status(thm)],[1397, 17786])).
% 9.28/9.50 tff(17788,plain,
% 9.28/9.50 (~r(s(s(s(elem!1))), s(elem!1))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[6881, 17783, 17733, 17771])).
% 9.28/9.50 tff(17789,plain,
% 9.28/9.50 (b(s(s(s(elem!1))), s(elem!1))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[588, 17788, 17787])).
% 9.28/9.50 tff(17790,plain,
% 9.28/9.50 (~b(s(elem!1), s(s(elem!1)))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[14314, 17789, 17525, 17774, 17721])).
% 9.28/9.50 tff(17791,plain,
% 9.28/9.50 (r(s(elem!1), s(s(elem!1)))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[8644, 17790, 17732])).
% 9.28/9.50 tff(17792,plain,
% 9.28/9.50 (~r(s(s(elem!1)), s(elem!1))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[8653, 17791, 17726, 17733])).
% 9.28/9.50 tff(17793,plain,
% 9.28/9.50 (b(s(s(elem!1)), s(elem!1))),
% 9.28/9.50 inference(unit_resolution,[status(thm)],[1135, 17792, 17729])).
% 9.28/9.50 tff(17794,plain,
% 9.28/9.50 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 9.28/9.50 inference(monotonicity,[status(thm)],[17775])).
% 9.28/9.50 tff(17795,plain,
% 9.28/9.50 (~(s(s(elem!1)) = elem!1)),
% 9.28/9.50 inference(modus_ponens,[status(thm)],[357, 17794])).
% 9.28/9.50 tff(17796,plain,
% 9.28/9.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))))),
% 9.28/9.51 inference(rewrite,[status(thm)],[])).
% 9.28/9.51 tff(17797,plain,
% 9.28/9.51 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))))),
% 9.28/9.51 inference(rewrite,[status(thm)],[])).
% 9.28/9.51 tff(17798,plain,
% 9.28/9.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1))))))),
% 9.28/9.51 inference(monotonicity,[status(thm)],[17797])).
% 9.28/9.51 tff(17799,plain,
% 9.28/9.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))))),
% 9.28/9.51 inference(transitivity,[status(thm)],[17798, 17796])).
% 9.28/9.51 tff(17800,plain,
% 9.28/9.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 9.28/9.51 inference(quant_inst,[status(thm)],[])).
% 9.28/9.51 tff(17801,plain,
% 9.28/9.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1))))),
% 9.28/9.51 inference(modus_ponens,[status(thm)],[17800, 17799])).
% 9.28/9.51 tff(17802,plain,
% 9.28/9.51 ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1))))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[17801, 391])).
% 9.28/9.51 tff(17803,plain,
% 9.28/9.51 (~b(z, s(s(elem!1)))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[17802, 17793, 17740, 17774, 17781])).
% 9.28/9.51 tff(17804,plain,
% 9.28/9.51 (r(z, s(s(elem!1)))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[324, 17803])).
% 9.28/9.51 tff(17805,plain,
% 9.28/9.51 (~r(s(s(elem!1)), elem!1)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[13828, 17804, 17771, 17726])).
% 9.28/9.51 tff(17806,plain,
% 9.28/9.51 (b(s(s(elem!1)), elem!1)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[872, 17805, 17795])).
% 9.28/9.51 tff(17807,plain,
% 9.28/9.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 9.28/9.51 inference(rewrite,[status(thm)],[])).
% 9.28/9.51 tff(17808,plain,
% 9.28/9.51 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 9.28/9.51 inference(rewrite,[status(thm)],[])).
% 9.28/9.51 tff(17809,plain,
% 9.28/9.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 9.28/9.51 inference(monotonicity,[status(thm)],[17808])).
% 9.28/9.51 tff(17810,plain,
% 9.28/9.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 9.28/9.51 inference(transitivity,[status(thm)],[17809, 17807])).
% 9.28/9.51 tff(17811,plain,
% 9.28/9.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 9.28/9.51 inference(quant_inst,[status(thm)],[])).
% 9.28/9.51 tff(17812,plain,
% 9.28/9.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 9.28/9.51 inference(modus_ponens,[status(thm)],[17811, 17810])).
% 9.28/9.51 tff(17813,plain,
% 9.28/9.51 ($false),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[17812, 391, 665, 10682, 973, 1037, 2122])).
% 9.28/9.51 tff(17814,plain,((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.51 tff(17815,plain,
% 9.28/9.51 (~b(s(elem!1), elem!1)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[17814, 17806, 17774, 17721, 17793])).
% 9.28/9.51 tff(17816,plain,
% 9.28/9.51 (r(s(elem!1), elem!1)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[2168, 17815, 17719])).
% 9.28/9.51 tff(17817,plain,
% 9.28/9.51 (~r(s(s(s(s(z)))), s(elem!1))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[5914, 17816, 17783, 3447])).
% 9.28/9.51 tff(17818,plain,
% 9.28/9.51 ($false),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[17817, 17769])).
% 9.28/9.51 tff(17819,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z))) | b(elem!1, s(z)) | (z = elem!1) | b(s(s(s(s(z)))), z) | b(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.51 tff(17820,plain,
% 9.28/9.51 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[17819, 722, 31, 115, 3446, 8329])).
% 9.28/9.51 tff(17821,plain,
% 9.28/9.51 (b(s(s(z)), s(s(s(s(z)))))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[3652, 17820])).
% 9.28/9.51 tff(17822,plain,
% 9.28/9.51 (~r(s(z), elem!1)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[14725, 838, 722, 15899])).
% 9.28/9.51 tff(17823,plain,
% 9.28/9.51 (b(s(z), elem!1)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[632, 17822, 150])).
% 9.28/9.51 tff(17824,plain,
% 9.28/9.51 (~b(s(s(s(elem!1))), s(z))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[8400, 5, 31])).
% 9.28/9.51 tff(17825,plain,
% 9.28/9.51 (~r(s(s(s(elem!1))), s(z))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[17353, 5, 2053, 1234, 10, 150, 722, 838, 2])).
% 9.28/9.51 tff(17826,plain,
% 9.28/9.51 ($false),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[223, 17825, 17824])).
% 9.28/9.51 tff(17827,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | b(z, s(s(s(elem!1)))) | (s(z) = elem!1) | (~r(z, s(z))) | (elem!1 = z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.51 tff(17828,plain,
% 9.28/9.51 (~(s(s(s(elem!1))) = elem!1)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[17827, 150, 1234, 10, 3447, 722, 2, 31])).
% 9.28/9.51 tff(17829,plain,
% 9.28/9.51 (~(elem!1 = s(s(s(elem!1))))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[129, 17828])).
% 9.28/9.51 tff(17830,plain,
% 9.28/9.51 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[8251, 17828])).
% 9.28/9.51 tff(17831,plain,
% 9.28/9.51 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[1370, 17830, 8329])).
% 9.28/9.51 tff(17832,plain,
% 9.28/9.51 (~r(elem!1, s(s(s(elem!1))))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[17255, 17831, 10, 2])).
% 9.28/9.51 tff(17833,plain,
% 9.28/9.51 (b(elem!1, s(s(s(elem!1))))),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[424, 17832, 17829])).
% 9.28/9.51 tff(17834,plain,
% 9.28/9.51 (~r(s(s(s(s(z)))), elem!1)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[10408, 838, 3447, 15899])).
% 9.28/9.51 tff(17835,plain,
% 9.28/9.51 (~r(s(z), z)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[845, 838, 722, 15899])).
% 9.28/9.51 tff(17836,plain,
% 9.28/9.51 (b(s(z), z)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[180, 17835])).
% 9.28/9.51 tff(17837,plain,
% 9.28/9.51 (~b(elem!1, z)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[17542, 17823, 1234, 15899, 17836, 17834, 3446])).
% 9.28/9.51 tff(17838,plain,
% 9.28/9.51 (r(elem!1, z)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[526, 17837, 2])).
% 9.28/9.51 tff(17839,plain,
% 9.28/9.51 (~r(s(s(s(elem!1))), elem!1)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[8289, 17838, 15899, 59])).
% 9.28/9.51 tff(17840,plain,
% 9.28/9.51 (b(s(s(s(elem!1))), elem!1)),
% 9.28/9.51 inference(unit_resolution,[status(thm)],[230, 17839, 17828])).
% 9.28/9.51 tff(17841,plain,
% 9.28/9.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.28/9.51 inference(rewrite,[status(thm)],[])).
% 9.28/9.51 tff(17842,plain,
% 9.28/9.51 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.28/9.51 inference(rewrite,[status(thm)],[])).
% 9.28/9.51 tff(17843,plain,
% 9.28/9.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 9.28/9.51 inference(monotonicity,[status(thm)],[17842])).
% 9.28/9.51 tff(17844,plain,
% 9.28/9.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.28/9.51 inference(transitivity,[status(thm)],[17843, 17841])).
% 9.28/9.51 tff(17845,plain,
% 9.28/9.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.28/9.51 inference(quant_inst,[status(thm)],[])).
% 9.28/9.51 tff(17846,plain,
% 9.28/9.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 9.28/9.51 inference(modus_ponens,[status(thm)],[17845, 17844])).
% 9.28/9.51 tff(17847,plain,
% 9.28/9.51 (~b(s(s(s(elem!1))), s(z))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[17846, 391, 17840, 17833, 17823])).
% 9.28/9.52 tff(17848,plain,
% 9.28/9.52 (r(s(s(s(elem!1))), s(z))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[223, 17847])).
% 9.28/9.52 tff(17849,plain,
% 9.28/9.52 (~b(s(z), s(s(s(elem!1))))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[16825, 391, 17840, 17833, 17823])).
% 9.28/9.52 tff(17850,plain,
% 9.28/9.52 (r(s(z), s(s(s(elem!1))))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[247, 17849])).
% 9.28/9.52 tff(17851,plain,
% 9.28/9.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.28/9.52 inference(rewrite,[status(thm)],[])).
% 9.28/9.52 tff(17852,plain,
% 9.28/9.52 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.28/9.52 inference(rewrite,[status(thm)],[])).
% 9.28/9.52 tff(17853,plain,
% 9.28/9.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17852])).
% 9.28/9.52 tff(17854,plain,
% 9.28/9.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.28/9.52 inference(transitivity,[status(thm)],[17853, 17851])).
% 9.28/9.52 tff(17855,plain,
% 9.28/9.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 9.28/9.52 inference(quant_inst,[status(thm)],[])).
% 9.28/9.52 tff(17856,plain,
% 9.28/9.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 9.28/9.52 inference(modus_ponens,[status(thm)],[17855, 17854])).
% 9.28/9.52 tff(17857,plain,
% 9.28/9.52 ($false),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[17856, 194, 59, 17850, 17848, 722])).
% 9.28/9.52 tff(17858,plain,((s(z) = elem!1) | (~r(z, s(z))) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | b(elem!1, s(z)) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 9.28/9.52 tff(17859,plain,
% 9.28/9.52 (s(z) = elem!1),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[17858, 10, 722, 2, 8329, 1234, 31, 3446])).
% 9.28/9.52 tff(17860,plain,
% 9.28/9.52 (b(elem!1, s(s(s(elem!1))))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[8542, 17859, 1234])).
% 9.28/9.52 tff(17861,plain,
% 9.28/9.52 (~(s(s(s(elem!1))) = elem!1)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[15370, 17860])).
% 9.28/9.52 tff(17862,plain,
% 9.28/9.52 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[8251, 17861])).
% 9.28/9.52 tff(17863,plain,
% 9.28/9.52 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[299, 17862])).
% 9.28/9.52 tff(17864,plain,
% 9.28/9.52 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[307, 17863])).
% 9.28/9.52 tff(17865,plain,
% 9.28/9.52 (s(s(z)) = s(elem!1)),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17859])).
% 9.28/9.52 tff(17866,plain,
% 9.28/9.52 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17865])).
% 9.28/9.52 tff(17867,plain,
% 9.28/9.52 (b(s(s(z)), s(s(s(elem!1))))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[8551, 17859, 3823])).
% 9.28/9.52 tff(17868,plain,
% 9.28/9.52 (b(s(elem!1), s(s(s(elem!1))))),
% 9.28/9.52 inference(modus_ponens,[status(thm)],[17867, 17866])).
% 9.28/9.52 tff(17869,plain,
% 9.28/9.52 (s(s(s(z))) = s(s(elem!1))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17865])).
% 9.28/9.52 tff(17870,plain,
% 9.28/9.52 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17869])).
% 9.28/9.52 tff(17871,plain,
% 9.28/9.52 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17870])).
% 9.28/9.52 tff(17872,plain,
% 9.28/9.52 (r(s(s(s(elem!1))), z)),
% 9.28/9.52 inference(modus_ponens,[status(thm)],[3447, 17871])).
% 9.28/9.52 tff(17873,plain,
% 9.28/9.52 (~(s(elem!1) = elem!1)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[158, 17861])).
% 9.28/9.52 tff(17874,plain,
% 9.28/9.52 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17865])).
% 9.28/9.52 tff(17875,plain,
% 9.28/9.52 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17859])).
% 9.28/9.52 tff(17876,plain,
% 9.28/9.52 (r(elem!1, s(s(z))) <=> r(s(z), s(s(z)))),
% 9.28/9.52 inference(symmetry,[status(thm)],[17875])).
% 9.28/9.52 tff(17877,plain,
% 9.28/9.52 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17865])).
% 9.28/9.52 tff(17878,plain,
% 9.28/9.52 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 9.28/9.52 inference(symmetry,[status(thm)],[17877])).
% 9.28/9.52 tff(17879,plain,
% 9.28/9.52 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 9.28/9.52 inference(transitivity,[status(thm)],[17878, 17876])).
% 9.28/9.52 tff(17880,plain,
% 9.28/9.52 ((~r(elem!1, s(elem!1))) <=> (~r(s(z), s(s(z))))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17879])).
% 9.28/9.52 tff(17881,plain,
% 9.28/9.52 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17859])).
% 9.28/9.52 tff(17882,plain,
% 9.28/9.52 (elem!1 = s(z)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[1495, 17859])).
% 9.28/9.52 tff(17883,plain,
% 9.28/9.52 (~b(s(z), elem!1)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[8805, 17882])).
% 9.28/9.52 tff(17884,plain,
% 9.28/9.52 (r(s(s(s(elem!1))), s(z))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[17668, 17883, 3446, 1234, 10])).
% 9.28/9.52 tff(17885,plain,
% 9.28/9.52 (r(s(s(s(elem!1))), elem!1)),
% 9.28/9.52 inference(modus_ponens,[status(thm)],[17884, 17881])).
% 9.28/9.52 tff(17886,plain,
% 9.28/9.52 (~r(elem!1, s(elem!1))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[434, 17885, 15899, 59])).
% 9.28/9.52 tff(17887,plain,
% 9.28/9.52 (~r(s(z), s(s(z)))),
% 9.28/9.52 inference(modus_ponens,[status(thm)],[17886, 17880])).
% 9.28/9.52 tff(17888,plain,
% 9.28/9.52 (b(s(z), s(s(z)))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[1788, 17887])).
% 9.28/9.52 tff(17889,plain,
% 9.28/9.52 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[6275, 17888, 1234, 3823])).
% 9.28/9.52 tff(17890,plain,
% 9.28/9.52 (r(s(s(s(s(z)))), s(s(z)))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[1714, 17889])).
% 9.28/9.52 tff(17891,plain,
% 9.28/9.52 (r(s(s(s(s(z)))), s(elem!1))),
% 9.28/9.52 inference(modus_ponens,[status(thm)],[17890, 17874])).
% 9.28/9.52 tff(17892,plain,
% 9.28/9.52 (~r(s(z), z)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[829, 17885, 15899, 59, 17859])).
% 9.28/9.52 tff(17893,plain,
% 9.28/9.52 (b(elem!1, z)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[7485, 17892, 17859])).
% 9.28/9.52 tff(17894,plain,
% 9.28/9.52 (~(elem!1 = s(elem!1))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[166, 17873])).
% 9.28/9.52 tff(17895,plain,
% 9.28/9.52 (b(elem!1, s(elem!1))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[443, 17886, 17894])).
% 9.28/9.52 tff(17896,plain,
% 9.28/9.52 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17865])).
% 9.28/9.52 tff(17897,plain,
% 9.28/9.52 (b(elem!1, s(s(s(s(z)))))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[8539, 17859, 1234])).
% 9.28/9.52 tff(17898,plain,
% 9.28/9.52 ((s(z) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17859])).
% 9.28/9.52 tff(17899,plain,
% 9.28/9.52 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17898])).
% 9.28/9.52 tff(17900,plain,
% 9.28/9.52 (~(elem!1 = s(s(z)))),
% 9.28/9.52 inference(modus_ponens,[status(thm)],[1783, 17899])).
% 9.28/9.52 tff(17901,plain,
% 9.28/9.52 ((~r(elem!1, s(elem!1))) <=> (~r(elem!1, s(s(z))))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17878])).
% 9.28/9.52 tff(17902,plain,
% 9.28/9.52 (~r(elem!1, s(s(z)))),
% 9.28/9.52 inference(modus_ponens,[status(thm)],[17886, 17901])).
% 9.28/9.52 tff(17903,plain,
% 9.28/9.52 (b(elem!1, s(s(z)))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[3394, 17902, 17900])).
% 9.28/9.52 tff(17904,plain,
% 9.28/9.52 (~r(s(s(z)), z)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[14773, 17903, 3447, 17897, 59])).
% 9.28/9.52 tff(17905,plain,
% 9.28/9.52 (b(s(s(z)), z)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[1211, 17904])).
% 9.28/9.52 tff(17906,plain,
% 9.28/9.52 (b(s(elem!1), z)),
% 9.28/9.52 inference(modus_ponens,[status(thm)],[17905, 17896])).
% 9.28/9.52 tff(17907,plain,
% 9.28/9.52 (~b(z, s(elem!1))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[1939, 17906, 17895, 17893])).
% 9.28/9.52 tff(17908,plain,
% 9.28/9.52 (r(z, s(elem!1))),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[566, 17907])).
% 9.28/9.52 tff(17909,plain,
% 9.28/9.52 (~r(s(elem!1), elem!1)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[5914, 17908, 17891, 3447])).
% 9.28/9.52 tff(17910,plain,
% 9.28/9.52 (b(s(elem!1), elem!1)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[2168, 17909, 17873])).
% 9.28/9.52 tff(17911,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 9.28/9.52 tff(17912,plain,
% 9.28/9.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.28/9.52 inference(rewrite,[status(thm)],[])).
% 9.28/9.52 tff(17913,plain,
% 9.28/9.52 (((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.28/9.52 inference(rewrite,[status(thm)],[])).
% 9.28/9.52 tff(17914,plain,
% 9.28/9.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))))),
% 9.28/9.52 inference(monotonicity,[status(thm)],[17913])).
% 9.28/9.52 tff(17915,plain,
% 9.28/9.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.28/9.52 inference(transitivity,[status(thm)],[17914, 17912])).
% 9.28/9.52 tff(17916,plain,
% 9.28/9.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 9.28/9.52 inference(quant_inst,[status(thm)],[])).
% 9.28/9.52 tff(17917,plain,
% 9.28/9.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))),
% 9.28/9.52 inference(modus_ponens,[status(thm)],[17916, 17915])).
% 9.28/9.52 tff(17918,plain,
% 9.28/9.52 ($false),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[17917, 391, 665, 591, 2122, 2781, 17911])).
% 9.28/9.52 tff(17919,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.52 tff(17920,plain,
% 9.28/9.52 (~b(s(s(s(s(elem!1)))), z)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[17919, 2781, 591, 2122, 665])).
% 9.28/9.52 tff(17921,plain,
% 9.28/9.52 (r(s(s(s(s(elem!1)))), z)),
% 9.28/9.52 inference(unit_resolution,[status(thm)],[1626, 17920])).
% 9.28/9.53 tff(17922,plain,
% 9.28/9.53 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[9915, 194, 411, 174, 17921])).
% 9.28/9.53 tff(17923,plain,
% 9.28/9.53 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[1095, 17922, 305])).
% 9.28/9.53 tff(17924,plain,
% 9.28/9.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 9.28/9.53 inference(rewrite,[status(thm)],[])).
% 9.28/9.53 tff(17925,plain,
% 9.28/9.53 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 9.28/9.53 inference(rewrite,[status(thm)],[])).
% 9.28/9.53 tff(17926,plain,
% 9.28/9.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 9.28/9.53 inference(monotonicity,[status(thm)],[17925])).
% 9.28/9.53 tff(17927,plain,
% 9.28/9.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 9.28/9.53 inference(transitivity,[status(thm)],[17926, 17924])).
% 9.28/9.53 tff(17928,plain,
% 9.28/9.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 9.28/9.53 inference(quant_inst,[status(thm)],[])).
% 9.28/9.53 tff(17929,plain,
% 9.28/9.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 9.28/9.53 inference(modus_ponens,[status(thm)],[17928, 17927])).
% 9.28/9.53 tff(17930,plain,
% 9.28/9.53 ($false),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[17929, 391, 665, 591, 2122, 2781, 17923])).
% 9.28/9.53 tff(17931,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.53 tff(17932,plain,
% 9.28/9.53 (~b(z, s(s(s(s(elem!1)))))),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[17931, 17893, 17906, 17910, 17863, 15899, 17872])).
% 9.28/9.53 tff(17933,plain,
% 9.28/9.53 (r(z, s(s(s(s(elem!1)))))),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[2767, 17932])).
% 9.28/9.53 tff(17934,plain,
% 9.28/9.53 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 9.28/9.53 inference(monotonicity,[status(thm)],[17870])).
% 9.28/9.53 tff(17935,plain,
% 9.28/9.53 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 9.28/9.53 inference(transitivity,[status(thm)],[17874, 17934])).
% 9.28/9.53 tff(17936,plain,
% 9.28/9.53 (r(s(s(s(elem!1))), s(elem!1))),
% 9.28/9.53 inference(modus_ponens,[status(thm)],[17890, 17935])).
% 9.28/9.53 tff(17937,plain,
% 9.28/9.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 9.28/9.53 inference(rewrite,[status(thm)],[])).
% 9.28/9.53 tff(17938,plain,
% 9.28/9.53 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 9.28/9.53 inference(rewrite,[status(thm)],[])).
% 9.28/9.53 tff(17939,plain,
% 9.28/9.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 9.28/9.53 inference(monotonicity,[status(thm)],[17938])).
% 9.28/9.53 tff(17940,plain,
% 9.28/9.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 9.28/9.53 inference(transitivity,[status(thm)],[17939, 17937])).
% 9.28/9.53 tff(17941,plain,
% 9.28/9.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 9.28/9.53 inference(quant_inst,[status(thm)],[])).
% 9.28/9.53 tff(17942,plain,
% 9.28/9.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))),
% 9.28/9.53 inference(modus_ponens,[status(thm)],[17941, 17940])).
% 9.28/9.53 tff(17943,plain,
% 9.28/9.53 ($false),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[17942, 194, 613, 184, 2792, 1082])).
% 9.28/9.53 tff(17944,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.53 tff(17945,plain,
% 9.28/9.53 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[17944, 17936, 59, 17933])).
% 9.28/9.53 tff(17946,plain,
% 9.28/9.53 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[1095, 17945, 17863])).
% 9.28/9.53 tff(17947,plain,
% 9.28/9.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 9.28/9.53 inference(rewrite,[status(thm)],[])).
% 9.28/9.53 tff(17948,plain,
% 9.28/9.53 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 9.28/9.53 inference(rewrite,[status(thm)],[])).
% 9.28/9.53 tff(17949,plain,
% 9.28/9.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 9.28/9.53 inference(monotonicity,[status(thm)],[17948])).
% 9.28/9.53 tff(17950,plain,
% 9.28/9.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 9.28/9.53 inference(transitivity,[status(thm)],[17949, 17947])).
% 9.28/9.53 tff(17951,plain,
% 9.28/9.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 9.28/9.53 inference(quant_inst,[status(thm)],[])).
% 9.28/9.53 tff(17952,plain,
% 9.28/9.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 9.28/9.53 inference(modus_ponens,[status(thm)],[17951, 17950])).
% 9.28/9.53 tff(17953,plain,
% 9.28/9.53 ($false),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[17952, 391, 448, 2122, 1573, 1114, 1036])).
% 9.28/9.53 tff(17954,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.53 tff(17955,plain,
% 9.28/9.53 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[17954, 17860, 17910, 17946, 17868])).
% 9.28/9.53 tff(17956,plain,
% 9.28/9.53 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[1164, 17955, 17864])).
% 9.28/9.53 tff(17957,plain,
% 9.28/9.53 (~(s(s(s(s(elem!1)))) = elem!1)),
% 9.28/9.53 inference(unit_resolution,[status(thm)],[7472, 17859])).
% 9.28/9.53 tff(17958,plain,
% 9.28/9.53 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 9.28/9.53 inference(monotonicity,[status(thm)],[17870])).
% 9.28/9.53 tff(17959,plain,
% 9.28/9.53 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 9.28/9.53 inference(monotonicity,[status(thm)],[17958, 17865])).
% 9.28/9.53 tff(17960,plain,
% 9.28/9.53 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 9.28/9.53 inference(transitivity,[status(thm)],[17959, 8665])).
% 9.28/9.53 tff(17961,plain,
% 9.28/9.53 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 9.28/9.53 inference(monotonicity,[status(thm)],[17960])).
% 9.28/9.53 tff(17962,plain,
% 9.28/9.53 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 9.28/9.53 inference(modus_ponens,[status(thm)],[8678, 17961])).
% 9.28/9.53 tff(17963,assumption,(r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 9.28/9.53 tff(17964,plain,
% 9.28/9.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 9.28/9.54 inference(rewrite,[status(thm)],[])).
% 9.28/9.54 tff(17965,plain,
% 9.28/9.54 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 9.28/9.54 inference(rewrite,[status(thm)],[])).
% 9.28/9.54 tff(17966,plain,
% 9.28/9.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 9.28/9.54 inference(monotonicity,[status(thm)],[17965])).
% 9.28/9.54 tff(17967,plain,
% 9.28/9.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 9.28/9.54 inference(transitivity,[status(thm)],[17966, 17964])).
% 9.28/9.54 tff(17968,plain,
% 9.28/9.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 9.28/9.54 inference(quant_inst,[status(thm)],[])).
% 9.28/9.54 tff(17969,plain,
% 9.28/9.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 9.28/9.54 inference(modus_ponens,[status(thm)],[17968, 17967])).
% 9.28/9.54 tff(17970,plain,
% 9.28/9.54 ($false),
% 9.28/9.54 inference(unit_resolution,[status(thm)],[17969, 194, 613, 2144, 184, 17963])).
% 9.28/9.54 tff(17971,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.54 tff(17972,plain,
% 9.28/9.54 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 9.28/9.54 inference(unit_resolution,[status(thm)],[17971, 17936, 17908, 59])).
% 9.28/9.54 tff(17973,plain,
% 9.28/9.54 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 9.28/9.54 inference(unit_resolution,[status(thm)],[1639, 17972, 17962])).
% 9.28/9.54 tff(17974,assumption,(b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 9.28/9.54 tff(17975,plain,
% 9.28/9.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 9.28/9.54 inference(rewrite,[status(thm)],[])).
% 9.28/9.54 tff(17976,plain,
% 9.28/9.54 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 9.28/9.54 inference(rewrite,[status(thm)],[])).
% 9.28/9.54 tff(17977,plain,
% 9.28/9.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 9.28/9.54 inference(monotonicity,[status(thm)],[17976])).
% 9.28/9.54 tff(17978,plain,
% 9.28/9.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 9.28/9.54 inference(transitivity,[status(thm)],[17977, 17975])).
% 9.28/9.54 tff(17979,plain,
% 9.28/9.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 9.28/9.54 inference(quant_inst,[status(thm)],[])).
% 9.28/9.54 tff(17980,plain,
% 9.28/9.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 9.28/9.54 inference(modus_ponens,[status(thm)],[17979, 17978])).
% 9.28/9.54 tff(17981,plain,
% 9.28/9.54 ($false),
% 9.28/9.54 inference(unit_resolution,[status(thm)],[17980, 391, 802, 2122, 2698, 17974])).
% 9.28/9.54 tff(17982,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.54 tff(17983,plain,
% 9.28/9.54 (~b(s(s(s(s(elem!1)))), elem!1)),
% 9.28/9.54 inference(unit_resolution,[status(thm)],[17982, 17973, 17895, 17910])).
% 9.28/9.54 tff(17984,plain,
% 9.28/9.54 (r(s(s(s(s(elem!1)))), elem!1)),
% 9.28/9.54 inference(unit_resolution,[status(thm)],[1004, 17983, 17957])).
% 9.28/9.54 tff(17985,plain,
% 9.28/9.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.28/9.54 inference(rewrite,[status(thm)],[])).
% 9.28/9.54 tff(17986,plain,
% 9.28/9.54 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.28/9.54 inference(rewrite,[status(thm)],[])).
% 9.28/9.54 tff(17987,plain,
% 9.28/9.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 9.28/9.54 inference(monotonicity,[status(thm)],[17986])).
% 9.28/9.54 tff(17988,plain,
% 9.28/9.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.28/9.55 inference(transitivity,[status(thm)],[17987, 17985])).
% 9.28/9.55 tff(17989,plain,
% 9.28/9.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 9.28/9.55 inference(quant_inst,[status(thm)],[])).
% 9.28/9.55 tff(17990,plain,
% 9.28/9.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 9.28/9.55 inference(modus_ponens,[status(thm)],[17989, 17988])).
% 9.28/9.55 tff(17991,plain,
% 9.28/9.55 ($false),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[17990, 194, 17872, 17984, 17933, 17956])).
% 9.28/9.55 tff(17992,plain,(b(z, s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(s(s(z)))), z) | (~r(z, s(z))) | (elem!1 = z) | b(s(s(s(elem!1))), s(s(elem!1))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.55 tff(17993,plain,
% 9.28/9.55 (b(z, s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[17992, 17821, 17036, 3446, 722, 10680, 8329, 31])).
% 9.28/9.55 tff(17994,plain,
% 9.28/9.55 (r(elem!1, z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[526, 484, 10680])).
% 9.28/9.55 tff(17995,plain,
% 9.28/9.55 (~r(s(z), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[17266, 838, 722, 530])).
% 9.28/9.55 tff(17996,plain,
% 9.28/9.55 (b(s(z), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[180, 17995])).
% 9.28/9.55 tff(17997,plain,
% 9.28/9.55 (~r(s(z), s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[16770, 838, 722, 530])).
% 9.28/9.55 tff(17998,plain,
% 9.28/9.55 (b(s(z), s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[247, 17997])).
% 9.28/9.55 tff(17999,plain,
% 9.28/9.55 (~b(s(s(s(elem!1))), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[11303, 17998, 10682, 17996])).
% 9.28/9.55 tff(18000,plain,
% 9.28/9.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 9.28/9.55 inference(rewrite,[status(thm)],[])).
% 9.28/9.55 tff(18001,plain,
% 9.28/9.55 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 9.28/9.55 inference(rewrite,[status(thm)],[])).
% 9.28/9.55 tff(18002,plain,
% 9.28/9.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))))),
% 9.28/9.55 inference(monotonicity,[status(thm)],[18001])).
% 9.28/9.55 tff(18003,plain,
% 9.28/9.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 9.28/9.55 inference(transitivity,[status(thm)],[18002, 18000])).
% 9.28/9.55 tff(18004,plain,
% 9.28/9.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 9.28/9.55 inference(quant_inst,[status(thm)],[])).
% 9.28/9.55 tff(18005,plain,
% 9.28/9.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))),
% 9.28/9.55 inference(modus_ponens,[status(thm)],[18004, 18003])).
% 9.28/9.55 tff(18006,plain,
% 9.28/9.55 (~r(elem!1, s(s(s(s(z)))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[18005, 194, 530, 722, 2053])).
% 9.28/9.55 tff(18007,plain,
% 9.28/9.55 (b(elem!1, s(s(s(s(z)))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[781, 3696, 18006])).
% 9.28/9.55 tff(18008,plain,
% 9.28/9.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 9.28/9.55 inference(rewrite,[status(thm)],[])).
% 9.28/9.55 tff(18009,plain,
% 9.28/9.55 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 9.28/9.55 inference(rewrite,[status(thm)],[])).
% 9.28/9.55 tff(18010,plain,
% 9.28/9.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 9.28/9.55 inference(monotonicity,[status(thm)],[18009])).
% 9.28/9.55 tff(18011,plain,
% 9.28/9.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 9.28/9.55 inference(transitivity,[status(thm)],[18010, 18008])).
% 9.28/9.55 tff(18012,plain,
% 9.28/9.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 9.28/9.55 inference(quant_inst,[status(thm)],[])).
% 9.28/9.55 tff(18013,plain,
% 9.28/9.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 9.28/9.55 inference(modus_ponens,[status(thm)],[18012, 18011])).
% 9.28/9.55 tff(18014,plain,
% 9.28/9.55 (~r(s(s(s(s(z)))), elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[18013, 194, 530, 722, 2053])).
% 9.28/9.55 tff(18015,plain,
% 9.28/9.55 (b(s(s(s(s(z)))), elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[762, 2691, 18014])).
% 9.28/9.55 tff(18016,plain,
% 9.28/9.55 (r(s(s(s(elem!1))), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[533, 5, 530])).
% 9.28/9.55 tff(18017,plain,
% 9.28/9.55 (r(s(s(s(elem!1))), s(z))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[223, 17824])).
% 9.28/9.55 tff(18018,plain,
% 9.28/9.55 (~r(s(z), elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[17465, 18017, 722, 18016])).
% 9.28/9.55 tff(18019,plain,
% 9.28/9.55 (b(s(z), elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[632, 18018, 150])).
% 9.28/9.55 tff(18020,plain,
% 9.28/9.55 (b(s(z), s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[14872, 18019, 5])).
% 9.28/9.55 tff(18021,plain,
% 9.28/9.55 (~r(z, elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[11294, 18020, 10682, 2053, 3363, 17996, 18016])).
% 9.28/9.55 tff(18022,plain,
% 9.28/9.55 (b(z, elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[141, 18021, 115])).
% 9.28/9.55 tff(18023,plain,
% 9.28/9.55 (~r(z, s(s(s(s(z)))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[17484, 18020, 10682, 16830, 17996, 5, 18016, 2053])).
% 9.28/9.55 tff(18024,plain,
% 9.28/9.55 (b(z, s(s(s(s(z)))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[800, 18023])).
% 9.28/9.55 tff(18025,plain,
% 9.28/9.55 ($false),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[15860, 18024, 18022, 18015, 18007])).
% 9.28/9.55 tff(18026,plain,((~(s(s(s(elem!1))) = elem!1)) | (z = elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (s(z) = elem!1) | (~r(z, s(z))) | (~r(elem!1, z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.55 tff(18027,plain,
% 9.28/9.55 (~(s(s(s(elem!1))) = elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[18026, 150, 10682, 2053, 115, 722, 530, 31])).
% 9.28/9.55 tff(18028,plain,
% 9.28/9.55 (~r(s(z), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[17266, 847, 722, 530])).
% 9.28/9.55 tff(18029,plain,
% 9.28/9.55 (b(s(z), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[180, 18028])).
% 9.28/9.55 tff(18030,plain,
% 9.28/9.55 ($false),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[15845, 194, 410, 327, 232, 847])).
% 9.28/9.55 tff(18031,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.55 tff(18032,plain,
% 9.28/9.55 (~r(s(z), s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[18031, 4030, 15839, 847])).
% 9.28/9.55 tff(18033,plain,
% 9.28/9.55 (b(s(z), s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[247, 18032])).
% 9.28/9.55 tff(18034,plain,
% 9.28/9.55 (~b(s(s(s(elem!1))), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[11303, 18033, 10682, 18029])).
% 9.28/9.55 tff(18035,plain,
% 9.28/9.55 (r(s(s(s(elem!1))), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[377, 18034])).
% 9.28/9.55 tff(18036,plain,
% 9.28/9.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 9.28/9.55 inference(rewrite,[status(thm)],[])).
% 9.28/9.55 tff(18037,plain,
% 9.28/9.55 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 9.28/9.55 inference(rewrite,[status(thm)],[])).
% 9.28/9.55 tff(18038,plain,
% 9.28/9.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z)))))),
% 9.28/9.55 inference(monotonicity,[status(thm)],[18037])).
% 9.28/9.55 tff(18039,plain,
% 9.28/9.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 9.28/9.55 inference(transitivity,[status(thm)],[18038, 18036])).
% 9.28/9.55 tff(18040,plain,
% 9.28/9.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 9.28/9.55 inference(quant_inst,[status(thm)],[])).
% 9.28/9.55 tff(18041,plain,
% 9.28/9.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z)))),
% 9.28/9.55 inference(modus_ponens,[status(thm)],[18040, 18039])).
% 9.28/9.55 tff(18042,plain,
% 9.28/9.55 ($false),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[18041, 194, 530, 18035, 4030, 722])).
% 9.28/9.55 tff(18043,plain,((s(s(s(elem!1))) = elem!1) | (~r(elem!1, z)) | (~r(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.55 tff(18044,plain,
% 9.28/9.55 (b(elem!1, s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[18043, 18027, 722, 10682, 838, 8329, 530])).
% 9.28/9.55 tff(18045,plain,
% 9.28/9.55 (r(s(s(s(elem!1))), elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[230, 16101, 127])).
% 9.28/9.55 tff(18046,plain,
% 9.28/9.55 (~r(s(s(s(elem!1))), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[4113, 18045, 722, 530])).
% 9.28/9.55 tff(18047,plain,
% 9.28/9.55 (b(s(s(s(elem!1))), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[377, 18046])).
% 9.28/9.55 tff(18048,plain,
% 9.28/9.55 (~b(s(z), elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[4929, 18047, 448, 133, 17996])).
% 9.28/9.55 tff(18049,plain,
% 9.28/9.55 (~b(s(z), s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[11303, 18047, 10682, 17996])).
% 9.28/9.55 tff(18050,plain,
% 9.28/9.55 (r(s(z), s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[247, 18049])).
% 9.28/9.55 tff(18051,plain,
% 9.28/9.55 ($false),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[5246, 18050, 18048, 31, 150, 18045])).
% 9.28/9.55 tff(18052,plain,((~b(z, elem!1)) | b(elem!1, s(z)) | (s(z) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(elem!1, z)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.28/9.55 tff(18053,plain,
% 9.28/9.55 (~b(z, elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[18052, 150, 31, 18044, 10682, 722, 530, 18027])).
% 9.28/9.55 tff(18054,plain,
% 9.28/9.55 (r(z, elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[141, 18053, 115])).
% 9.28/9.55 tff(18055,plain,
% 9.28/9.55 (~r(s(s(s(elem!1))), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[11294, 17998, 10682, 2053, 3363, 17996, 18054])).
% 9.28/9.55 tff(18056,plain,
% 9.28/9.55 ($false),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[377, 18055, 17999])).
% 9.28/9.55 tff(18057,plain,((s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(elem!1, z)) | (z = elem!1) | b(elem!1, s(z)) | b(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.55 tff(18058,plain,
% 9.28/9.55 (s(z) = elem!1),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[18057, 17994, 2053, 722, 10682, 115, 31, 8329])).
% 9.28/9.55 tff(18059,plain,
% 9.28/9.55 (s(s(z)) = s(elem!1)),
% 9.28/9.55 inference(monotonicity,[status(thm)],[18058])).
% 9.28/9.55 tff(18060,plain,
% 9.28/9.55 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 9.28/9.55 inference(monotonicity,[status(thm)],[18059])).
% 9.28/9.55 tff(18061,plain,
% 9.28/9.55 (b(s(s(z)), s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[8551, 18058, 3823])).
% 9.28/9.55 tff(18062,plain,
% 9.28/9.55 (b(s(elem!1), s(s(s(elem!1))))),
% 9.28/9.55 inference(modus_ponens,[status(thm)],[18061, 18060])).
% 9.28/9.55 tff(18063,plain,
% 9.28/9.55 (r(z, elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[17233, 18058, 722])).
% 9.28/9.55 tff(18064,plain,
% 9.28/9.55 (r(s(z), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[7485, 18058, 484])).
% 9.28/9.55 tff(18065,plain,
% 9.28/9.55 (~r(s(s(s(s(z)))), s(z))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[3243, 18064, 2053, 18063])).
% 9.28/9.55 tff(18066,plain,
% 9.28/9.55 (b(s(s(s(s(z)))), s(z))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[749, 18065])).
% 9.28/9.55 tff(18067,plain,
% 9.28/9.55 (~b(s(s(z)), s(z))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[5108, 18066, 1234, 3823])).
% 9.28/9.55 tff(18068,plain,
% 9.28/9.55 (r(s(s(z)), s(z))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[3778, 18067])).
% 9.28/9.55 tff(18069,plain,
% 9.28/9.55 (r(s(elem!1), elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[9729, 18068, 18058])).
% 9.28/9.55 tff(18070,plain,
% 9.28/9.55 (~r(s(elem!1), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[541, 18069, 17994, 18063])).
% 9.28/9.55 tff(18071,plain,
% 9.28/9.55 (b(s(elem!1), z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[549, 18070])).
% 9.28/9.55 tff(18072,plain,
% 9.28/9.55 (b(elem!1, s(s(s(elem!1))))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[8542, 18058, 1234])).
% 9.28/9.55 tff(18073,plain,
% 9.28/9.55 (elem!1 = s(z)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[1495, 18058])).
% 9.28/9.55 tff(18074,plain,
% 9.28/9.55 (b(s(s(s(elem!1))), s(z))),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[11177, 18066, 18073])).
% 9.28/9.55 tff(18075,plain,
% 9.28/9.55 (b(s(s(s(elem!1))), elem!1)),
% 9.28/9.55 inference(unit_resolution,[status(thm)],[3938, 18074, 18058])).
% 9.28/9.55 tff(18076,plain,
% 9.28/9.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 9.28/9.55 inference(rewrite,[status(thm)],[])).
% 9.28/9.55 tff(18077,plain,
% 9.28/9.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 9.28/9.56 inference(quant_inst,[status(thm)],[])).
% 9.28/9.56 tff(18078,plain,
% 9.28/9.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 9.28/9.56 inference(modus_ponens,[status(thm)],[18077, 18076])).
% 9.28/9.56 tff(18079,plain,
% 9.28/9.56 ($false),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[18078, 391, 18075, 10682, 18072, 18071, 18062])).
% 9.28/9.56 tff(18080,plain,(b(elem!1, z) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (z = elem!1) | b(elem!1, s(z)) | b(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.56 tff(18081,plain,
% 9.28/9.56 (b(elem!1, z)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[18080, 17993, 17036, 17821, 3447, 722, 115, 31, 8329])).
% 9.28/9.56 tff(18082,plain,
% 9.28/9.56 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 9.28/9.56 inference(monotonicity,[status(thm)],[8079, 818])).
% 9.28/9.56 tff(18083,plain,
% 9.28/9.56 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 9.28/9.56 inference(transitivity,[status(thm)],[18082, 8665])).
% 9.28/9.56 tff(18084,plain,
% 9.28/9.56 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 9.28/9.56 inference(monotonicity,[status(thm)],[18083])).
% 9.28/9.56 tff(18085,plain,
% 9.28/9.56 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 9.28/9.56 inference(modus_ponens,[status(thm)],[8678, 18084])).
% 9.28/9.56 tff(18086,plain,
% 9.28/9.56 (b(elem!1, s(s(s(elem!1))))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[8542, 812, 1234])).
% 9.28/9.56 tff(18087,plain,
% 9.28/9.56 (~(s(s(s(elem!1))) = elem!1)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[15370, 18086])).
% 9.28/9.56 tff(18088,plain,
% 9.28/9.56 (~(s(elem!1) = elem!1)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[158, 18087])).
% 9.28/9.56 tff(18089,plain,
% 9.28/9.56 (b(s(s(z)), s(s(s(elem!1))))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[8551, 812, 3823])).
% 9.28/9.56 tff(18090,plain,
% 9.28/9.56 (b(s(elem!1), s(s(s(elem!1))))),
% 9.28/9.56 inference(modus_ponens,[status(thm)],[18089, 8544])).
% 9.28/9.56 tff(18091,plain,
% 9.28/9.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 9.28/9.56 inference(rewrite,[status(thm)],[])).
% 9.28/9.56 tff(18092,plain,
% 9.28/9.56 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 9.28/9.56 inference(rewrite,[status(thm)],[])).
% 9.28/9.56 tff(18093,plain,
% 9.28/9.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 9.28/9.56 inference(monotonicity,[status(thm)],[18092])).
% 9.28/9.56 tff(18094,plain,
% 9.28/9.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 9.28/9.56 inference(transitivity,[status(thm)],[18093, 18091])).
% 9.28/9.56 tff(18095,plain,
% 9.28/9.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 9.28/9.56 inference(quant_inst,[status(thm)],[])).
% 9.28/9.56 tff(18096,plain,
% 9.28/9.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 9.28/9.56 inference(modus_ponens,[status(thm)],[18095, 18094])).
% 9.28/9.56 tff(18097,plain,
% 9.28/9.56 ($false),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[18096, 391, 665, 1101, 10682, 448, 1036])).
% 9.28/9.56 tff(18098,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.56 tff(18099,plain,
% 9.28/9.56 (~b(s(s(s(elem!1))), s(elem!1))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[18098, 18086, 10682, 665, 18090])).
% 9.28/9.56 tff(18100,plain,
% 9.28/9.56 (r(s(s(s(elem!1))), s(elem!1))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[588, 18099, 7433])).
% 9.28/9.56 tff(18101,plain,
% 9.28/9.56 (r(s(s(s(s(z)))), s(elem!1))),
% 9.28/9.56 inference(modus_ponens,[status(thm)],[18100, 7983])).
% 9.28/9.56 tff(18102,plain,
% 9.28/9.56 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 9.28/9.56 inference(monotonicity,[status(thm)],[820])).
% 9.28/9.56 tff(18103,plain,
% 9.28/9.56 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 9.28/9.56 inference(symmetry,[status(thm)],[18102])).
% 9.28/9.56 tff(18104,plain,
% 9.28/9.56 (b(z, s(s(s(s(z)))))),
% 9.28/9.56 inference(modus_ponens,[status(thm)],[10682, 18103])).
% 9.28/9.56 tff(18105,plain,
% 9.28/9.56 (~b(s(s(s(s(z)))), s(z))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[17292, 18104, 10388, 1234])).
% 9.28/9.56 tff(18106,plain,
% 9.28/9.56 (r(s(s(s(s(z)))), s(z))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[749, 18105])).
% 9.28/9.56 tff(18107,plain,
% 9.28/9.56 (~r(s(z), s(s(elem!1)))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[5500, 18106, 722, 2053])).
% 9.28/9.56 tff(18108,plain,
% 9.28/9.56 (~r(elem!1, s(s(elem!1)))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[15602, 18107, 7866])).
% 9.28/9.56 tff(18109,plain,
% 9.28/9.56 (b(elem!1, s(s(elem!1)))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[1307, 18108, 9651])).
% 9.28/9.56 tff(18110,plain,
% 9.28/9.56 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[8251, 18087])).
% 9.28/9.56 tff(18111,plain,
% 9.28/9.56 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[1370, 18110, 8329])).
% 9.28/9.56 tff(18112,plain,
% 9.28/9.56 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 9.28/9.56 inference(modus_ponens,[status(thm)],[18111, 9598])).
% 9.28/9.56 tff(18113,plain,
% 9.28/9.56 (~r(s(s(elem!1)), z)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[9362, 18112, 722, 2053])).
% 9.28/9.56 tff(18114,plain,
% 9.28/9.56 (b(s(s(elem!1)), z)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[2629, 18113])).
% 9.28/9.56 tff(18115,plain,
% 9.28/9.56 (r(z, elem!1)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[17233, 812, 722])).
% 9.28/9.56 tff(18116,plain,
% 9.28/9.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 9.28/9.56 inference(rewrite,[status(thm)],[])).
% 9.28/9.56 tff(18117,plain,
% 9.28/9.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 9.28/9.56 inference(quant_inst,[status(thm)],[])).
% 9.28/9.56 tff(18118,plain,
% 9.28/9.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 9.28/9.56 inference(modus_ponens,[status(thm)],[18117, 18116])).
% 9.28/9.56 tff(18119,plain,
% 9.28/9.56 ($false),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[18118, 194, 411, 613, 1628, 174])).
% 9.28/9.56 tff(18120,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.56 tff(18121,plain,
% 9.28/9.56 (~r(s(elem!1), z)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[18120, 18115, 18100, 9621])).
% 9.28/9.56 tff(18122,plain,
% 9.28/9.56 (b(s(elem!1), z)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[549, 18121])).
% 9.28/9.56 tff(18123,plain,
% 9.28/9.56 (~b(z, s(elem!1))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[9660, 18122, 18114, 18109, 665])).
% 9.28/9.56 tff(18124,plain,
% 9.28/9.56 (r(z, s(elem!1))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[566, 18123])).
% 9.28/9.56 tff(18125,plain,
% 9.28/9.56 (~r(s(elem!1), elem!1)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[5914, 18124, 18101, 2053])).
% 9.28/9.56 tff(18126,plain,
% 9.28/9.56 (b(s(elem!1), elem!1)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[2168, 18125, 18088])).
% 9.28/9.56 tff(18127,plain,
% 9.28/9.56 (~(elem!1 = s(elem!1))),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[166, 18088])).
% 9.28/9.56 tff(18128,plain,
% 9.28/9.56 (~b(s(s(s(s(z)))), elem!1)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[14799, 18104, 1234, 665, 10388])).
% 9.28/9.56 tff(18129,plain,
% 9.28/9.56 (~b(s(s(s(elem!1))), elem!1)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[1563, 18128, 7866])).
% 9.28/9.56 tff(18130,plain,
% 9.28/9.56 (r(s(s(s(elem!1))), elem!1)),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[230, 18129, 18087])).
% 9.28/9.56 tff(18131,plain,
% 9.28/9.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 9.28/9.56 inference(rewrite,[status(thm)],[])).
% 9.28/9.56 tff(18132,plain,
% 9.28/9.56 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 9.28/9.56 inference(rewrite,[status(thm)],[])).
% 9.28/9.56 tff(18133,plain,
% 9.28/9.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))))),
% 9.28/9.56 inference(monotonicity,[status(thm)],[18132])).
% 9.28/9.56 tff(18134,plain,
% 9.28/9.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 9.28/9.56 inference(transitivity,[status(thm)],[18133, 18131])).
% 9.28/9.56 tff(18135,plain,
% 9.28/9.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 9.28/9.56 inference(quant_inst,[status(thm)],[])).
% 9.28/9.56 tff(18136,plain,
% 9.28/9.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))),
% 9.28/9.56 inference(modus_ponens,[status(thm)],[18135, 18134])).
% 9.28/9.56 tff(18137,plain,
% 9.28/9.56 ($false),
% 9.28/9.56 inference(unit_resolution,[status(thm)],[18136, 194, 411, 174, 233, 2251])).
% 9.28/9.57 tff(18138,plain,((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.57 tff(18139,plain,
% 9.28/9.57 (~r(elem!1, s(elem!1))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[18138, 18115, 9621, 18130])).
% 9.28/9.57 tff(18140,plain,
% 9.28/9.57 (b(elem!1, s(elem!1))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[443, 18139, 18127])).
% 9.28/9.57 tff(18141,plain,
% 9.28/9.57 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[299, 18110])).
% 9.28/9.57 tff(18142,plain,
% 9.28/9.57 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[307, 18141])).
% 9.28/9.57 tff(18143,plain,
% 9.28/9.57 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[299, 16094])).
% 9.28/9.57 tff(18144,plain,
% 9.28/9.57 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[9915, 194, 411, 174, 12854])).
% 9.28/9.57 tff(18145,plain,
% 9.28/9.57 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[1095, 18144, 18143])).
% 9.28/9.57 tff(18146,plain,
% 9.28/9.57 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[307, 18143])).
% 9.28/9.57 tff(18147,plain,
% 9.28/9.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 9.28/9.57 inference(rewrite,[status(thm)],[])).
% 9.28/9.57 tff(18148,plain,
% 9.28/9.57 (((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 9.28/9.57 inference(rewrite,[status(thm)],[])).
% 9.28/9.57 tff(18149,plain,
% 9.28/9.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 9.28/9.57 inference(monotonicity,[status(thm)],[18148])).
% 9.28/9.57 tff(18150,plain,
% 9.28/9.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 9.28/9.57 inference(transitivity,[status(thm)],[18149, 18147])).
% 9.28/9.57 tff(18151,plain,
% 9.28/9.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.28/9.57 inference(quant_inst,[status(thm)],[])).
% 9.28/9.57 tff(18152,plain,
% 9.28/9.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 9.28/9.57 inference(modus_ponens,[status(thm)],[18151, 18150])).
% 9.28/9.57 tff(18153,plain,
% 9.28/9.57 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[18152, 194, 411, 174, 12854])).
% 9.28/9.57 tff(18154,plain,
% 9.28/9.57 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[1164, 18153, 18146])).
% 9.28/9.57 tff(18155,plain,
% 9.28/9.57 ($false),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[17952, 391, 448, 2122, 18154, 18145, 1036])).
% 9.28/9.57 tff(18156,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.57 tff(18157,plain,
% 9.28/9.57 (~r(s(s(s(s(elem!1)))), z)),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[18156, 18126, 18086, 18090, 18115, 9621])).
% 9.28/9.57 tff(18158,plain,
% 9.28/9.57 (b(s(s(s(s(elem!1)))), z)),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[1626, 18157])).
% 9.28/9.57 tff(18159,plain,
% 9.28/9.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.28/9.57 inference(rewrite,[status(thm)],[])).
% 9.28/9.57 tff(18160,plain,
% 9.28/9.57 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.28/9.57 inference(rewrite,[status(thm)],[])).
% 9.28/9.57 tff(18161,plain,
% 9.28/9.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 9.28/9.57 inference(monotonicity,[status(thm)],[18160])).
% 9.28/9.57 tff(18162,plain,
% 9.28/9.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.28/9.57 inference(transitivity,[status(thm)],[18161, 18159])).
% 9.28/9.57 tff(18163,plain,
% 9.28/9.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 9.28/9.57 inference(quant_inst,[status(thm)],[])).
% 9.28/9.57 tff(18164,plain,
% 9.28/9.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 9.28/9.57 inference(modus_ponens,[status(thm)],[18163, 18162])).
% 9.28/9.57 tff(18165,plain,
% 9.28/9.57 ($false),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[18164, 391, 665, 10682, 448, 1573, 17911])).
% 9.28/9.57 tff(18166,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.57 tff(18167,plain,
% 9.28/9.57 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[18166, 18086, 10682, 665, 18158])).
% 9.28/9.57 tff(18168,plain,
% 9.28/9.57 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.28/9.57 inference(unit_resolution,[status(thm)],[1164, 18167, 18142])).
% 9.28/9.57 tff(18169,plain,
% 9.28/9.57 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.28/9.58 inference(monotonicity,[status(thm)],[819, 8079])).
% 9.28/9.58 tff(18170,plain,
% 9.28/9.58 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 9.28/9.58 inference(monotonicity,[status(thm)],[18169])).
% 9.28/9.58 tff(18171,plain,
% 9.28/9.58 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 9.28/9.58 inference(monotonicity,[status(thm)],[8079])).
% 9.28/9.58 tff(18172,plain,
% 9.28/9.58 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 9.28/9.58 inference(symmetry,[status(thm)],[18171])).
% 9.28/9.58 tff(18173,plain,
% 9.28/9.58 (b(s(s(s(s(s(z))))), z)),
% 9.28/9.58 inference(modus_ponens,[status(thm)],[18158, 18172])).
% 9.28/9.58 tff(18174,plain,
% 9.28/9.58 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 9.28/9.58 inference(symmetry,[status(thm)],[8079])).
% 9.28/9.58 tff(18175,plain,
% 9.28/9.58 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 9.28/9.58 inference(monotonicity,[status(thm)],[18174])).
% 9.28/9.58 tff(18176,plain,
% 9.28/9.58 (~(elem!1 = s(s(s(s(elem!1)))))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[15610, 7473])).
% 9.28/9.58 tff(18177,plain,
% 9.28/9.58 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[314, 18110])).
% 9.28/9.58 tff(18178,plain,
% 9.28/9.58 (~(s(s(elem!1)) = s(elem!1))),
% 9.28/9.58 inference(modus_ponens,[status(thm)],[2689, 7411])).
% 9.28/9.58 tff(18179,plain,
% 9.28/9.58 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 9.28/9.58 inference(transitivity,[status(thm)],[7410, 1098])).
% 9.28/9.58 tff(18180,plain,
% 9.28/9.58 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 9.28/9.58 inference(monotonicity,[status(thm)],[18179])).
% 9.28/9.58 tff(18181,plain,
% 9.28/9.58 (~(s(elem!1) = s(s(elem!1)))),
% 9.28/9.58 inference(modus_ponens,[status(thm)],[2689, 18180])).
% 9.28/9.58 tff(18182,plain,
% 9.28/9.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 9.28/9.58 inference(rewrite,[status(thm)],[])).
% 9.28/9.58 tff(18183,plain,
% 9.28/9.58 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 9.28/9.58 inference(rewrite,[status(thm)],[])).
% 9.28/9.58 tff(18184,plain,
% 9.28/9.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 9.28/9.58 inference(monotonicity,[status(thm)],[18183])).
% 9.28/9.58 tff(18185,plain,
% 9.28/9.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 9.28/9.58 inference(transitivity,[status(thm)],[18184, 18182])).
% 9.28/9.58 tff(18186,plain,
% 9.28/9.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 9.28/9.58 inference(quant_inst,[status(thm)],[])).
% 9.28/9.58 tff(18187,plain,
% 9.28/9.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 9.28/9.58 inference(modus_ponens,[status(thm)],[18186, 18185])).
% 9.28/9.58 tff(18188,plain,
% 9.28/9.58 (~b(s(elem!1), s(s(elem!1)))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[18187, 391, 665, 10682, 973, 2122])).
% 9.28/9.58 tff(18189,plain,
% 9.28/9.58 (r(s(elem!1), s(s(elem!1)))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[8644, 18188, 8611])).
% 9.28/9.58 tff(18190,plain,
% 9.28/9.58 (~b(s(s(elem!1)), s(elem!1))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[17814, 973, 10682, 665, 2122])).
% 9.28/9.58 tff(18191,plain,
% 9.28/9.58 (r(s(s(elem!1)), s(elem!1))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[1135, 18190, 285])).
% 9.28/9.58 tff(18192,plain,
% 9.28/9.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 9.28/9.58 inference(rewrite,[status(thm)],[])).
% 9.28/9.58 tff(18193,plain,
% 9.28/9.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 9.28/9.58 inference(quant_inst,[status(thm)],[])).
% 9.28/9.58 tff(18194,plain,
% 9.28/9.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 9.28/9.58 inference(modus_ponens,[status(thm)],[18193, 18192])).
% 9.28/9.58 tff(18195,plain,
% 9.28/9.58 ($false),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[18194, 194, 613, 327, 18191, 18189])).
% 9.28/9.58 tff(18196,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.58 tff(18197,plain,
% 9.28/9.58 (~b(s(s(elem!1)), elem!1)),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[18196, 18100, 18111, 18181, 665, 10682, 18126, 18178])).
% 9.28/9.58 tff(18198,plain,
% 9.28/9.58 (r(s(s(elem!1)), elem!1)),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[872, 18197, 7422])).
% 9.28/9.58 tff(18199,plain,
% 9.28/9.58 (~r(z, s(s(elem!1)))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[13828, 18198, 9621, 18111])).
% 9.28/9.58 tff(18200,plain,
% 9.28/9.58 (b(z, s(s(elem!1)))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[324, 18199])).
% 9.28/9.58 tff(18201,plain,
% 9.28/9.58 (~r(elem!1, s(s(s(s(elem!1)))))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[14223, 18200, 10682, 18130, 18198, 18110, 18177])).
% 9.28/9.58 tff(18202,plain,
% 9.28/9.58 (b(elem!1, s(s(s(s(elem!1)))))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[1018, 18201, 18176])).
% 9.28/9.58 tff(18203,plain,
% 9.28/9.58 (b(elem!1, s(s(s(s(s(z))))))),
% 9.28/9.58 inference(modus_ponens,[status(thm)],[18202, 18175])).
% 9.28/9.58 tff(18204,plain,
% 9.28/9.58 (b(z, s(s(s(z))))),
% 9.28/9.58 inference(modus_ponens,[status(thm)],[18200, 7862])).
% 9.28/9.58 tff(18205,plain,
% 9.28/9.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 9.28/9.58 inference(rewrite,[status(thm)],[])).
% 9.28/9.58 tff(18206,plain,
% 9.28/9.58 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 9.28/9.58 inference(rewrite,[status(thm)],[])).
% 9.28/9.58 tff(18207,plain,
% 9.28/9.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 9.28/9.58 inference(monotonicity,[status(thm)],[18206])).
% 9.28/9.58 tff(18208,plain,
% 9.28/9.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 9.28/9.58 inference(transitivity,[status(thm)],[18207, 18205])).
% 9.28/9.58 tff(18209,plain,
% 9.28/9.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 9.28/9.58 inference(quant_inst,[status(thm)],[])).
% 9.28/9.58 tff(18210,plain,
% 9.28/9.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 9.28/9.58 inference(modus_ponens,[status(thm)],[18209, 18208])).
% 9.28/9.58 tff(18211,plain,
% 9.28/9.58 ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[18210, 391])).
% 9.28/9.58 tff(18212,plain,
% 9.28/9.58 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[18211, 18204, 665, 18203, 18173])).
% 9.28/9.58 tff(18213,plain,
% 9.28/9.58 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.28/9.58 inference(modus_ponens,[status(thm)],[18212, 18170])).
% 9.28/9.58 tff(18214,plain,
% 9.28/9.58 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[1048, 18213, 7435])).
% 9.28/9.58 tff(18215,plain,
% 9.28/9.58 (~r(s(s(s(s(elem!1)))), elem!1)),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[14274, 18214, 18111, 18168])).
% 9.28/9.58 tff(18216,plain,
% 9.28/9.58 (b(s(s(s(s(elem!1)))), elem!1)),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[1004, 18215, 7473])).
% 9.28/9.58 tff(18217,plain,
% 9.28/9.58 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[17982, 18216, 18140, 18126])).
% 9.28/9.58 tff(18218,plain,
% 9.28/9.58 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 9.28/9.58 inference(unit_resolution,[status(thm)],[1639, 18217, 18085])).
% 9.28/9.58 tff(18219,plain,
% 9.28/9.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 9.28/9.58 inference(rewrite,[status(thm)],[])).
% 9.28/9.58 tff(18220,plain,
% 9.28/9.58 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 9.28/9.58 inference(rewrite,[status(thm)],[])).
% 9.28/9.58 tff(18221,plain,
% 9.28/9.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 9.28/9.59 inference(monotonicity,[status(thm)],[18220])).
% 9.28/9.59 tff(18222,plain,
% 9.28/9.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 9.28/9.59 inference(transitivity,[status(thm)],[18221, 18219])).
% 9.28/9.59 tff(18223,plain,
% 9.28/9.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 9.28/9.59 inference(quant_inst,[status(thm)],[])).
% 9.28/9.59 tff(18224,plain,
% 9.28/9.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 9.28/9.59 inference(modus_ponens,[status(thm)],[18223, 18222])).
% 9.28/9.59 tff(18225,plain,
% 9.28/9.59 ($false),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[18224, 194, 18100, 9621, 18124, 18218])).
% 9.28/9.59 tff(18226,plain,((~(s(z) = elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.59 tff(18227,plain,
% 9.28/9.59 (~(s(z) = elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[18226, 18081, 17993, 3447, 722, 17036, 11335, 8329, 17821])).
% 9.28/9.59 tff(18228,plain,
% 9.28/9.59 (~r(elem!1, z)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[18057, 18227, 3447, 722, 17993, 115, 31, 8329])).
% 9.28/9.59 tff(18229,plain,
% 9.28/9.59 (~(s(s(s(s(z)))) = elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[6966, 18081, 3446])).
% 9.28/9.59 tff(18230,plain,
% 9.28/9.59 (~r(s(s(s(s(z)))), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[10408, 411, 3447, 847])).
% 9.28/9.59 tff(18231,plain,
% 9.28/9.59 (~r(s(z), z)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[845, 411, 722, 847])).
% 9.28/9.59 tff(18232,plain,
% 9.28/9.59 (b(s(z), z)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[180, 18231])).
% 9.28/9.59 tff(18233,plain,
% 9.28/9.59 ($false),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[17542, 18232, 17110, 1234, 665, 411, 18230, 3446])).
% 9.28/9.59 tff(18234,plain,((~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, z)) | b(s(s(s(s(z)))), z) | (s(z) = elem!1) | (~r(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.59 tff(18235,plain,
% 9.28/9.59 (~r(z, elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[18234, 150, 18081, 3446, 17036, 722, 838])).
% 9.28/9.59 tff(18236,plain,
% 9.28/9.59 (b(z, elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[141, 18235, 115])).
% 9.28/9.59 tff(18237,plain,
% 9.28/9.59 (~b(elem!1, s(s(s(elem!1))))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[17700, 18236, 3447, 17993, 2282, 150, 10680])).
% 9.28/9.59 tff(18238,plain,
% 9.28/9.59 (~b(s(s(s(elem!1))), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[10743, 133, 10682, 665])).
% 9.28/9.59 tff(18239,plain,
% 9.28/9.59 (b(s(elem!1), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[14657, 133, 2282, 150, 10682, 18238, 2])).
% 9.28/9.59 tff(18240,plain,
% 9.28/9.59 (~(s(s(s(elem!1))) = s(elem!1))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[14662, 18239, 18238])).
% 9.28/9.59 tff(18241,plain,
% 9.28/9.59 (~(s(s(elem!1)) = s(elem!1))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[2279, 18240])).
% 9.28/9.59 tff(18242,plain,
% 9.28/9.59 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[287, 18241])).
% 9.28/9.59 tff(18243,plain,
% 9.28/9.59 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[1370, 18242, 8329])).
% 9.28/9.59 tff(18244,plain,
% 9.28/9.59 (s(s(s(elem!1))) = elem!1),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[17275, 18243, 4028, 2, 722, 150, 121, 847, 133, 18238])).
% 9.28/9.59 tff(18245,plain,
% 9.28/9.59 (elem!1 = s(s(s(elem!1)))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[8, 18244])).
% 9.28/9.59 tff(18246,plain,
% 9.28/9.59 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.28/9.59 inference(monotonicity,[status(thm)],[18245])).
% 9.28/9.59 tff(18247,plain,
% 9.28/9.59 (~(s(elem!1) = s(s(s(s(z)))))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[1965, 18244])).
% 9.28/9.59 tff(18248,plain,
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% 9.28/9.59 inference(unit_resolution,[status(thm)],[17429, 18247, 1234, 18245, 2053, 11956, 150, 10682, 2, 722, 847])).
% 9.28/9.59 tff(18249,plain,
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% 9.28/9.59 tff(18250,plain,
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% 9.28/9.59 inference(unit_resolution,[status(thm)],[5231, 18249, 665, 133])).
% 9.28/9.59 tff(18251,plain,
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% 9.28/9.59 inference(unit_resolution,[status(thm)],[632, 18250, 150])).
% 9.28/9.59 tff(18252,plain,
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% 9.28/9.59 inference(unit_resolution,[status(thm)],[17452, 18249, 665, 10682, 18245])).
% 9.28/9.59 tff(18253,plain,
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% 9.28/9.59 inference(unit_resolution,[status(thm)],[1211, 18252])).
% 9.28/9.59 tff(18254,plain,
% 9.28/9.59 (~r(s(s(z)), s(z))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[4462, 18253, 722, 18251])).
% 9.28/9.59 tff(18255,plain,
% 9.28/9.59 (~(elem!1 = s(s(z)))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[15394, 18254, 847])).
% 9.28/9.59 tff(18256,plain,
% 9.28/9.59 (b(s(s(z)), s(z))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[3778, 18254])).
% 9.28/9.59 tff(18257,plain,
% 9.28/9.59 (~b(s(s(s(s(z)))), s(z))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[5108, 18256, 1234, 3823])).
% 9.28/9.59 tff(18258,plain,
% 9.28/9.59 (r(s(s(s(s(z)))), s(z))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[749, 18257])).
% 9.28/9.59 tff(18259,plain,
% 9.28/9.59 (~r(s(s(s(s(z)))), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[13589, 18258, 1234, 665, 133, 173, 18255, 18251, 770])).
% 9.28/9.59 tff(18260,plain,
% 9.28/9.59 (b(s(s(s(s(z)))), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[762, 18259, 720])).
% 9.28/9.59 tff(18261,plain,
% 9.28/9.59 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.28/9.59 inference(modus_ponens,[status(thm)],[18260, 18246])).
% 9.28/9.59 tff(18262,plain,
% 9.28/9.59 (b(s(s(s(elem!1))), z)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[9553, 18245, 665])).
% 9.28/9.59 tff(18263,plain,
% 9.28/9.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.28/9.59 inference(rewrite,[status(thm)],[])).
% 9.28/9.59 tff(18264,plain,
% 9.28/9.59 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.28/9.59 inference(rewrite,[status(thm)],[])).
% 9.28/9.59 tff(18265,plain,
% 9.28/9.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 9.28/9.59 inference(monotonicity,[status(thm)],[18264])).
% 9.28/9.59 tff(18266,plain,
% 9.28/9.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.28/9.59 inference(transitivity,[status(thm)],[18265, 18263])).
% 9.28/9.59 tff(18267,plain,
% 9.28/9.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 9.28/9.59 inference(quant_inst,[status(thm)],[])).
% 9.28/9.59 tff(18268,plain,
% 9.28/9.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 9.28/9.59 inference(modus_ponens,[status(thm)],[18267, 18266])).
% 9.28/9.59 tff(18269,plain,
% 9.28/9.59 ($false),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[18268, 391, 18262, 3823, 1234, 18256, 18261])).
% 9.28/9.59 tff(18270,plain,((~b(z, elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = z) | b(elem!1, s(s(s(elem!1)))) | (s(z) = s(elem!1)) | b(s(s(s(elem!1))), s(s(elem!1))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 9.28/9.59 tff(18271,plain,
% 9.28/9.59 ($false),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[18270, 18237, 18236, 17036, 18229, 18081, 838, 722, 150, 17993, 3447, 10680, 17821, 10968, 8329, 2282])).
% 9.28/9.59 tff(18272,plain,((s(z) = elem!1) | (~r(z, s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(elem!1, z) | (z = elem!1) | b(s(s(s(s(z)))), z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.59 tff(18273,plain,
% 9.28/9.59 ($false),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[18272, 18228, 18227, 8329, 722, 115, 3446, 31])).
% 9.28/9.59 tff(18274,plain,((~r(z, s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | (z = elem!1) | b(s(s(s(s(z)))), z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.28/9.59 tff(18275,plain,
% 9.28/9.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[18274, 3446, 98, 31, 722])).
% 9.28/9.59 tff(18276,plain,
% 9.28/9.59 (~(s(s(s(elem!1))) = elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[17827, 3447, 17033, 10, 722, 150, 2, 31])).
% 9.28/9.59 tff(18277,plain,
% 9.28/9.59 (b(s(s(s(elem!1))), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[230, 18276, 8290])).
% 9.28/9.59 tff(18278,plain,
% 9.28/9.59 (~b(elem!1, s(s(s(elem!1))))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[16827, 18277, 722, 150, 3618, 838, 8232])).
% 9.28/9.59 tff(18279,plain,
% 9.28/9.59 (~r(s(s(elem!1)), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[8459, 18278, 10, 2, 484, 31, 18275, 17035])).
% 9.28/9.59 tff(18280,plain,
% 9.28/9.59 (~(elem!1 = s(s(s(elem!1))))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[129, 18276])).
% 9.28/9.59 tff(18281,plain,
% 9.28/9.59 (~(s(elem!1) = elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[158, 18276])).
% 9.28/9.59 tff(18282,plain,
% 9.28/9.59 (~(elem!1 = s(elem!1))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[166, 18281])).
% 9.28/9.59 tff(18283,plain,
% 9.28/9.59 (~b(z, elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[6505, 18277, 59, 150, 484, 18282, 18280, 2])).
% 9.28/9.59 tff(18284,plain,
% 9.28/9.59 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[8251, 18276])).
% 9.28/9.59 tff(18285,plain,
% 9.28/9.59 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[299, 18284])).
% 9.28/9.59 tff(18286,plain,
% 9.28/9.59 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[307, 18285])).
% 9.28/9.59 tff(18287,plain,
% 9.28/9.59 (b(s(z), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[632, 17035, 150])).
% 9.28/9.59 tff(18288,plain,
% 9.28/9.59 (r(elem!1, s(s(s(elem!1))))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[424, 18278, 18280])).
% 9.28/9.59 tff(18289,plain,
% 9.28/9.59 (~r(s(s(s(elem!1))), s(z))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[6132, 18288, 59, 3618])).
% 9.28/9.59 tff(18290,plain,
% 9.28/9.59 (b(s(s(s(elem!1))), s(z))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[223, 18289])).
% 9.28/9.59 tff(18291,plain,
% 9.28/9.59 (b(s(s(elem!1)), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[872, 5625, 888])).
% 9.28/9.59 tff(18292,plain,
% 9.28/9.59 (b(s(s(s(elem!1))), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[230, 10623, 225])).
% 9.28/9.59 tff(18293,plain,
% 9.28/9.59 (~b(elem!1, s(s(elem!1)))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[1467, 18292, 1374, 973])).
% 9.28/9.59 tff(18294,plain,
% 9.28/9.59 (r(elem!1, s(s(elem!1)))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[1307, 18293, 1457])).
% 9.28/9.59 tff(18295,plain,
% 9.28/9.59 (~r(s(s(elem!1)), s(z))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[6179, 232, 847, 1064])).
% 9.28/9.59 tff(18296,plain,
% 9.28/9.59 (b(s(s(elem!1)), s(z))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[362, 18295])).
% 9.28/9.59 tff(18297,plain,
% 9.28/9.59 (~b(s(s(s(s(z)))), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[1660, 18296, 1234, 1374, 1526])).
% 9.28/9.59 tff(18298,plain,
% 9.28/9.59 (~b(s(s(s(s(z)))), s(z))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[3263, 18296, 1374, 1234, 1526])).
% 9.28/9.59 tff(18299,plain,
% 9.28/9.59 (r(s(s(s(s(z)))), s(z))),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[749, 18298])).
% 9.28/9.59 tff(18300,plain,
% 9.28/9.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 9.28/9.59 inference(rewrite,[status(thm)],[])).
% 9.28/9.59 tff(18301,plain,
% 9.28/9.59 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 9.28/9.59 inference(rewrite,[status(thm)],[])).
% 9.28/9.59 tff(18302,plain,
% 9.28/9.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 9.28/9.59 inference(monotonicity,[status(thm)],[18301])).
% 9.28/9.59 tff(18303,plain,
% 9.28/9.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 9.28/9.59 inference(transitivity,[status(thm)],[18302, 18300])).
% 9.28/9.59 tff(18304,plain,
% 9.28/9.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 9.28/9.59 inference(quant_inst,[status(thm)],[])).
% 9.28/9.59 tff(18305,plain,
% 9.28/9.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 9.28/9.59 inference(modus_ponens,[status(thm)],[18304, 18303])).
% 9.28/9.59 tff(18306,plain,
% 9.28/9.59 (~r(s(s(s(s(z)))), elem!1)),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[18305, 194, 232, 847, 18299])).
% 9.28/9.59 tff(18307,plain,
% 9.28/9.59 (s(s(s(s(z)))) = elem!1),
% 9.28/9.59 inference(unit_resolution,[status(thm)],[762, 18306, 18297])).
% 9.28/9.59 tff(18308,plain,
% 9.28/9.59 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 9.28/9.59 inference(monotonicity,[status(thm)],[18307])).
% 9.28/9.59 tff(18309,plain,
% 9.28/9.59 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 9.28/9.59 inference(symmetry,[status(thm)],[18308])).
% 9.28/9.59 tff(18310,plain,
% 9.28/9.59 ((~b(elem!1, z)) <=> (~b(s(s(s(s(z)))), z))),
% 9.28/9.59 inference(monotonicity,[status(thm)],[18309])).
% 9.38/9.60 tff(18311,plain,
% 9.38/9.60 (~b(s(s(s(s(z)))), z)),
% 9.38/9.60 inference(modus_ponens,[status(thm)],[484, 18310])).
% 9.38/9.60 tff(18312,plain,
% 9.38/9.60 (r(s(s(s(s(z)))), z)),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[87, 18311])).
% 9.38/9.60 tff(18313,plain,
% 9.38/9.60 ((s(s(s(s(z)))) = z) <=> (elem!1 = z)),
% 9.38/9.60 inference(monotonicity,[status(thm)],[18307])).
% 9.38/9.60 tff(18314,plain,
% 9.38/9.60 ((s(s(s(s(z)))) = z) <=> (z = elem!1)),
% 9.38/9.60 inference(transitivity,[status(thm)],[18313, 92])).
% 9.38/9.60 tff(18315,plain,
% 9.38/9.60 ((~(s(s(s(s(z)))) = z)) <=> (~(z = elem!1))),
% 9.38/9.60 inference(monotonicity,[status(thm)],[18314])).
% 9.38/9.60 tff(18316,plain,
% 9.38/9.60 (~(z = elem!1)),
% 9.38/9.60 inference(modus_ponens,[status(thm)],[83, 18315])).
% 9.38/9.60 tff(18317,plain,
% 9.38/9.60 (r(z, elem!1)),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[141, 18316, 89])).
% 9.38/9.60 tff(18318,plain,
% 9.38/9.60 (~r(s(z), z)),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[3243, 18317, 18299, 18312])).
% 9.38/9.60 tff(18319,plain,
% 9.38/9.60 (b(s(z), z)),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[180, 18318])).
% 9.38/9.60 tff(18320,plain,
% 9.38/9.60 (s(s(s(s(s(z))))) = s(elem!1)),
% 9.38/9.60 inference(monotonicity,[status(thm)],[18307])).
% 9.38/9.60 tff(18321,plain,
% 9.38/9.60 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 9.38/9.60 inference(monotonicity,[status(thm)],[18320])).
% 9.38/9.60 tff(18322,plain,
% 9.38/9.60 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 9.38/9.60 inference(monotonicity,[status(thm)],[18321])).
% 9.38/9.60 tff(18323,plain,
% 9.38/9.60 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 9.38/9.60 inference(monotonicity,[status(thm)],[18322])).
% 9.38/9.60 tff(18324,plain,
% 9.38/9.60 (~(s(s(elem!1)) = s(s(z)))),
% 9.38/9.60 inference(modus_ponens,[status(thm)],[5009, 18323])).
% 9.38/9.60 tff(18325,plain,
% 9.38/9.60 (~(elem!1 = s(s(s(s(elem!1)))))),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[14423, 18324, 18307])).
% 9.38/9.60 tff(18326,plain,
% 9.38/9.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.38/9.60 inference(rewrite,[status(thm)],[])).
% 9.38/9.60 tff(18327,plain,
% 9.38/9.60 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), 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))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.38/9.60 inference(rewrite,[status(thm)],[])).
% 9.38/9.60 tff(18328,plain,
% 9.38/9.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 9.38/9.60 inference(monotonicity,[status(thm)],[18327])).
% 9.38/9.60 tff(18329,plain,
% 9.38/9.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.38/9.60 inference(transitivity,[status(thm)],[18328, 18326])).
% 9.38/9.60 tff(18330,plain,
% 9.38/9.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), 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)))))),
% 9.38/9.60 inference(quant_inst,[status(thm)],[])).
% 9.38/9.60 tff(18331,plain,
% 9.38/9.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 9.38/9.60 inference(modus_ponens,[status(thm)],[18330, 18329])).
% 9.38/9.60 tff(18332,plain,
% 9.38/9.60 ($false),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[18331, 391, 381, 1374, 644, 1526, 974])).
% 9.38/9.60 tff(18333,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.60 tff(18334,plain,
% 9.38/9.60 (~b(elem!1, s(s(s(s(elem!1)))))),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[18333, 18296, 1374, 644, 1526])).
% 9.38/9.60 tff(18335,plain,
% 9.38/9.60 (r(elem!1, s(s(s(s(elem!1)))))),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[1018, 18334, 18325])).
% 9.38/9.60 tff(18336,plain,
% 9.38/9.60 ((s(s(s(s(z)))) = z) <=> (elem!1 = z)),
% 9.38/9.60 inference(transitivity,[status(thm)],[18314, 93])).
% 9.38/9.60 tff(18337,plain,
% 9.38/9.60 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = z))),
% 9.38/9.60 inference(monotonicity,[status(thm)],[18336])).
% 9.38/9.60 tff(18338,plain,
% 9.38/9.60 (~(elem!1 = z)),
% 9.38/9.60 inference(modus_ponens,[status(thm)],[83, 18337])).
% 9.38/9.60 tff(18339,plain,
% 9.38/9.60 (r(elem!1, z)),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[526, 18338, 484])).
% 9.38/9.60 tff(18340,plain,
% 9.38/9.60 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[4052, 18339, 184, 410])).
% 9.38/9.60 tff(18341,plain,
% 9.38/9.60 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.38/9.60 inference(unit_resolution,[status(thm)],[1164, 18340, 1373])).
% 9.38/9.60 tff(18342,plain,
% 9.38/9.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.38/9.60 inference(rewrite,[status(thm)],[])).
% 9.38/9.60 tff(18343,plain,
% 9.38/9.60 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(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(elem!1))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.38/9.60 inference(rewrite,[status(thm)],[])).
% 9.38/9.60 tff(18344,plain,
% 9.38/9.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 9.38/9.60 inference(monotonicity,[status(thm)],[18343])).
% 9.38/9.60 tff(18345,plain,
% 9.38/9.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.38/9.61 inference(transitivity,[status(thm)],[18344, 18342])).
% 9.38/9.61 tff(18346,plain,
% 9.38/9.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(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(elem!1)))))))),
% 9.38/9.61 inference(quant_inst,[status(thm)],[])).
% 9.38/9.61 tff(18347,plain,
% 9.38/9.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 9.38/9.61 inference(modus_ponens,[status(thm)],[18346, 18345])).
% 9.38/9.61 tff(18348,plain,
% 9.38/9.61 ($false),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[18347, 391, 381, 1374, 644, 1733, 1573])).
% 9.38/9.61 tff(18349,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.61 tff(18350,plain,
% 9.38/9.61 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[18349, 18296, 1374, 644, 18341])).
% 9.38/9.61 tff(18351,plain,
% 9.38/9.61 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[1061, 18350, 1050])).
% 9.38/9.61 tff(18352,plain,
% 9.38/9.61 (~r(z, s(s(s(s(elem!1)))))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[15669, 18351, 18339, 18335])).
% 9.38/9.61 tff(18353,plain,
% 9.38/9.61 (b(z, s(s(s(s(elem!1)))))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[2767, 18352])).
% 9.38/9.61 tff(18354,plain,
% 9.38/9.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.38/9.61 inference(rewrite,[status(thm)],[])).
% 9.38/9.61 tff(18355,plain,
% 9.38/9.61 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~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))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.38/9.61 inference(rewrite,[status(thm)],[])).
% 9.38/9.61 tff(18356,plain,
% 9.38/9.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1))))))))),
% 9.38/9.61 inference(monotonicity,[status(thm)],[18355])).
% 9.38/9.61 tff(18357,plain,
% 9.38/9.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.38/9.61 inference(transitivity,[status(thm)],[18356, 18354])).
% 9.38/9.61 tff(18358,plain,
% 9.38/9.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~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)))))),
% 9.38/9.61 inference(quant_inst,[status(thm)],[])).
% 9.38/9.61 tff(18359,plain,
% 9.38/9.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1))))))),
% 9.38/9.61 inference(modus_ponens,[status(thm)],[18358, 18357])).
% 9.38/9.61 tff(18360,plain,
% 9.38/9.61 ($false),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[18359, 391, 18296, 1374, 1526, 18353, 18319])).
% 9.38/9.61 tff(18361,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(z), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, z) | b(z, elem!1) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.61 tff(18362,plain,
% 9.38/9.61 (~r(s(z), s(s(s(elem!1))))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[18361, 1526, 1374, 2712, 644, 1373, 59, 10625, 484, 89, 847, 1234, 18294])).
% 9.38/9.61 tff(18363,plain,
% 9.38/9.61 (b(s(z), s(s(s(elem!1))))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[247, 18362])).
% 9.38/9.61 tff(18364,plain,
% 9.38/9.61 (~b(s(s(elem!1)), s(z))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[4762, 18363, 1526, 1374])).
% 9.38/9.61 tff(18365,plain,
% 9.38/9.61 (r(s(s(elem!1)), s(z))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[362, 18364])).
% 9.38/9.61 tff(18366,plain,
% 9.38/9.61 (~r(s(z), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[5941, 1482, 59, 847])).
% 9.38/9.61 tff(18367,plain,
% 9.38/9.61 (b(s(z), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[180, 18366])).
% 9.38/9.61 tff(18368,plain,
% 9.38/9.61 (~r(s(s(s(elem!1))), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[8380, 8232, 59, 410])).
% 9.38/9.61 tff(18369,plain,
% 9.38/9.61 (b(s(s(s(elem!1))), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[377, 18368])).
% 9.38/9.61 tff(18370,plain,
% 9.38/9.61 (~r(z, s(s(elem!1)))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[2549, 8232, 1064, 340])).
% 9.38/9.61 tff(18371,plain,
% 9.38/9.61 (b(z, s(s(elem!1)))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[324, 18370])).
% 9.38/9.61 tff(18372,plain,
% 9.38/9.61 ($false),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[6210, 18371, 18369, 973, 1526, 18367])).
% 9.38/9.61 tff(18373,plain,((elem!1 = z) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.61 tff(18374,plain,
% 9.38/9.61 (elem!1 = z),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[18373, 1526, 973, 847, 18294, 18365, 10625, 484, 10])).
% 9.38/9.61 tff(18375,plain,
% 9.38/9.61 (s(elem!1) = s(z)),
% 9.38/9.61 inference(monotonicity,[status(thm)],[18374])).
% 9.38/9.61 tff(18376,plain,
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% 9.38/9.61 inference(monotonicity,[status(thm)],[18375])).
% 9.38/9.61 tff(18377,plain,
% 9.38/9.61 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 9.38/9.61 inference(monotonicity,[status(thm)],[18376])).
% 9.38/9.61 tff(18378,plain,
% 9.38/9.61 (b(s(z), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[3200, 18374, 644])).
% 9.38/9.61 tff(18379,plain,
% 9.38/9.61 (z = elem!1),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[5453, 18374])).
% 9.38/9.61 tff(18380,plain,
% 9.38/9.61 (~r(s(s(s(elem!1))), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[9853, 18379, 225])).
% 9.38/9.61 tff(18381,plain,
% 9.38/9.61 (b(s(s(s(elem!1))), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[377, 18380])).
% 9.38/9.61 tff(18382,plain,
% 9.38/9.61 (~b(z, s(s(elem!1)))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[6210, 18381, 973, 1526, 18378])).
% 9.38/9.61 tff(18383,plain,
% 9.38/9.61 (r(z, s(s(elem!1)))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[324, 18382])).
% 9.38/9.61 tff(18384,plain,
% 9.38/9.61 (r(z, s(s(z)))),
% 9.38/9.61 inference(modus_ponens,[status(thm)],[18383, 18377])).
% 9.38/9.61 tff(18385,plain,
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% 9.38/9.61 inference(symmetry,[status(thm)],[18376])).
% 9.38/9.61 tff(18386,plain,
% 9.38/9.61 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 9.38/9.61 inference(monotonicity,[status(thm)],[18385])).
% 9.38/9.61 tff(18387,plain,
% 9.38/9.61 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 9.38/9.61 inference(symmetry,[status(thm)],[18386])).
% 9.38/9.61 tff(18388,plain,
% 9.38/9.61 (r(s(s(z)), s(z))),
% 9.38/9.61 inference(modus_ponens,[status(thm)],[18365, 18387])).
% 9.38/9.61 tff(18389,plain,
% 9.38/9.61 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.38/9.61 inference(symmetry,[status(thm)],[3504])).
% 9.38/9.61 tff(18390,plain,
% 9.38/9.61 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 9.38/9.61 inference(monotonicity,[status(thm)],[18389])).
% 9.38/9.61 tff(18391,plain,
% 9.38/9.61 (b(s(z), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[3200, 11, 644])).
% 9.38/9.61 tff(18392,plain,
% 9.38/9.61 (~r(s(s(s(elem!1))), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[9853, 17618, 225])).
% 9.38/9.61 tff(18393,plain,
% 9.38/9.61 (b(s(s(s(elem!1))), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[377, 18392])).
% 9.38/9.61 tff(18394,plain,
% 9.38/9.61 (~b(z, s(s(elem!1)))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[6210, 18393, 973, 1526, 18391])).
% 9.38/9.61 tff(18395,plain,
% 9.38/9.61 (r(z, s(s(elem!1)))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[324, 18394])).
% 9.38/9.61 tff(18396,plain,
% 9.38/9.61 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 9.38/9.61 inference(monotonicity,[status(thm)],[2980])).
% 9.38/9.61 tff(18397,plain,
% 9.38/9.61 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 9.38/9.61 inference(symmetry,[status(thm)],[18396])).
% 9.38/9.61 tff(18398,plain,
% 9.38/9.61 (r(s(s(z)), s(z))),
% 9.38/9.61 inference(modus_ponens,[status(thm)],[340, 18397])).
% 9.38/9.61 tff(18399,plain,
% 9.38/9.61 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(z, s(s(s(s(z))))))),
% 9.38/9.61 inference(monotonicity,[status(thm)],[60])).
% 9.38/9.61 tff(18400,plain,
% 9.38/9.61 (~r(z, s(s(s(s(z)))))),
% 9.38/9.61 inference(modus_ponens,[status(thm)],[3222, 18399])).
% 9.38/9.61 tff(18401,plain,
% 9.38/9.61 (b(z, s(s(s(s(z)))))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[800, 18400])).
% 9.38/9.61 tff(18402,plain,
% 9.38/9.61 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 9.38/9.61 inference(monotonicity,[status(thm)],[489])).
% 9.38/9.61 tff(18403,plain,
% 9.38/9.61 (r(z, s(s(z)))),
% 9.38/9.61 inference(modus_ponens,[status(thm)],[326, 18402])).
% 9.38/9.61 tff(18404,plain,
% 9.38/9.61 ((~r(s(z), s(s(s(z))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 9.38/9.61 inference(monotonicity,[status(thm)],[502])).
% 9.38/9.61 tff(18405,plain,
% 9.38/9.61 (b(s(elem!1), z) <=> b(s(z), z)),
% 9.38/9.61 inference(monotonicity,[status(thm)],[488])).
% 9.38/9.61 tff(18406,plain,
% 9.38/9.61 (b(s(z), z) <=> b(s(elem!1), z)),
% 9.38/9.61 inference(symmetry,[status(thm)],[18405])).
% 9.38/9.61 tff(18407,plain,
% 9.38/9.61 (b(s(elem!1), z)),
% 9.38/9.61 inference(modus_ponens,[status(thm)],[590, 18406])).
% 9.38/9.61 tff(18408,plain,
% 9.38/9.61 (~b(s(s(s(s(z)))), s(z))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[2638, 18401, 17625, 18393, 18407])).
% 9.38/9.61 tff(18409,plain,
% 9.38/9.61 (r(s(s(s(s(z)))), s(z))),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[749, 18408])).
% 9.38/9.61 tff(18410,plain,
% 9.38/9.61 (~b(s(s(s(s(z)))), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[6325, 18401, 1526, 590, 18393])).
% 9.38/9.61 tff(18411,plain,
% 9.38/9.61 (r(s(s(s(s(z)))), z)),
% 9.38/9.61 inference(unit_resolution,[status(thm)],[87, 18410])).
% 9.38/9.61 tff(18412,plain,
% 9.38/9.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 9.38/9.61 inference(rewrite,[status(thm)],[])).
% 9.38/9.61 tff(18413,plain,
% 9.38/9.61 (((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 9.38/9.61 inference(rewrite,[status(thm)],[])).
% 9.38/9.61 tff(18414,plain,
% 9.38/9.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 9.38/9.61 inference(monotonicity,[status(thm)],[18413])).
% 9.38/9.61 tff(18415,plain,
% 9.38/9.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 9.38/9.62 inference(transitivity,[status(thm)],[18414, 18412])).
% 9.38/9.62 tff(18416,plain,
% 9.38/9.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 9.38/9.62 inference(quant_inst,[status(thm)],[])).
% 9.38/9.62 tff(18417,plain,
% 9.38/9.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 9.38/9.62 inference(modus_ponens,[status(thm)],[18416, 18415])).
% 9.38/9.62 tff(18418,plain,
% 9.38/9.62 ($false),
% 9.38/9.62 inference(unit_resolution,[status(thm)],[18417, 194, 722, 2053, 723, 15705])).
% 9.38/9.62 tff(18419,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.62 tff(18420,plain,
% 9.38/9.62 (~r(s(z), s(s(s(z))))),
% 9.38/9.62 inference(unit_resolution,[status(thm)],[18419, 17637, 18411, 18409])).
% 9.38/9.62 tff(18421,plain,
% 9.38/9.62 (~r(s(z), s(s(s(elem!1))))),
% 9.38/9.62 inference(modus_ponens,[status(thm)],[18420, 18404])).
% 9.38/9.62 tff(18422,plain,
% 9.38/9.62 (b(s(z), s(s(s(elem!1))))),
% 9.38/9.62 inference(unit_resolution,[status(thm)],[247, 18421])).
% 9.38/9.62 tff(18423,plain,
% 9.38/9.62 (~b(s(s(elem!1)), s(z))),
% 9.38/9.62 inference(unit_resolution,[status(thm)],[1534, 18422, 1374, 18393, 1526])).
% 9.38/9.62 tff(18424,plain,
% 9.38/9.62 (r(s(s(elem!1)), s(z))),
% 9.38/9.62 inference(unit_resolution,[status(thm)],[362, 18423])).
% 9.38/9.62 tff(18425,plain,
% 9.38/9.62 (r(s(s(z)), s(z))),
% 9.38/9.62 inference(modus_ponens,[status(thm)],[18424, 18397])).
% 9.38/9.62 tff(18426,plain,
% 9.38/9.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 9.38/9.62 inference(rewrite,[status(thm)],[])).
% 9.38/9.62 tff(18427,plain,
% 9.38/9.62 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 9.38/9.62 inference(rewrite,[status(thm)],[])).
% 9.38/9.62 tff(18428,plain,
% 9.38/9.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 9.38/9.62 inference(monotonicity,[status(thm)],[18427])).
% 9.38/9.62 tff(18429,plain,
% 9.38/9.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 9.38/9.62 inference(transitivity,[status(thm)],[18428, 18426])).
% 9.38/9.62 tff(18430,plain,
% 9.38/9.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 9.38/9.62 inference(quant_inst,[status(thm)],[])).
% 9.38/9.62 tff(18431,plain,
% 9.38/9.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 9.38/9.62 inference(modus_ponens,[status(thm)],[18430, 18429])).
% 9.38/9.62 tff(18432,plain,
% 9.38/9.62 ($false),
% 9.38/9.62 inference(unit_resolution,[status(thm)],[18431, 194, 2053, 1697, 2405, 8505])).
% 9.38/9.62 tff(18433,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.62 tff(18434,plain,
% 9.38/9.62 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.38/9.62 inference(unit_resolution,[status(thm)],[18433, 18411, 18425, 18403])).
% 9.38/9.62 tff(18435,plain,
% 9.38/9.62 (b(s(s(s(s(z)))), s(s(z)))),
% 9.38/9.62 inference(unit_resolution,[status(thm)],[1714, 18434])).
% 9.38/9.62 tff(18436,plain,
% 9.38/9.62 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 9.38/9.62 inference(monotonicity,[status(thm)],[489])).
% 9.38/9.62 tff(18437,plain,
% 9.38/9.62 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 9.38/9.62 inference(monotonicity,[status(thm)],[11])).
% 9.38/9.62 tff(18438,plain,
% 9.38/9.62 (b(s(s(elem!1)), z)),
% 9.38/9.62 inference(modus_ponens,[status(thm)],[973, 18437])).
% 9.38/9.62 tff(18439,plain,
% 9.38/9.62 (b(s(s(z)), z)),
% 9.38/9.62 inference(modus_ponens,[status(thm)],[18438, 18436])).
% 9.38/9.62 tff(18440,plain,
% 9.38/9.62 ($false),
% 9.38/9.62 inference(unit_resolution,[status(thm)],[17286, 391, 18439, 1234, 18435, 18401, 590])).
% 9.38/9.62 tff(18441,plain,((~(elem!1 = z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | r(elem!1, s(s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.38/9.62 tff(18442,plain,
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% 9.38/9.62 tff(18443,plain,
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% 9.38/9.62 tff(18445,plain,
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% 9.38/9.62 inference(quant_inst,[status(thm)],[])).
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% 9.38/9.62 inference(modus_ponens,[status(thm)],[18448, 18447])).
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% 9.38/9.62 tff(18452,plain,
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% 9.38/9.62 tff(18453,plain,
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% 9.38/9.62 inference(unit_resolution,[status(thm)],[1714, 18452])).
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% 9.38/9.62 inference(modus_ponens,[status(thm)],[18453, 2421])).
% 9.38/9.62 tff(18455,plain,
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% 9.38/9.62 tff(18456,plain,
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% 9.38/9.62 tff(18457,plain,
% 9.38/9.62 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
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% 9.38/9.62 tff(18458,plain,
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% 9.38/9.62 tff(18459,plain,
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% 9.38/9.62 tff(18460,plain,
% 9.38/9.62 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 9.38/9.62 inference(monotonicity,[status(thm)],[2401, 488])).
% 9.38/9.62 tff(18461,plain,
% 9.38/9.62 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
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% 9.38/9.62 tff(18462,plain,
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% 9.38/9.62 tff(18463,plain,
% 9.38/9.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
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% 9.38/9.62 tff(18464,plain,
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% 9.38/9.62 inference(rewrite,[status(thm)],[])).
% 9.38/9.62 tff(18465,plain,
% 9.38/9.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 9.38/9.62 inference(monotonicity,[status(thm)],[18464])).
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% 9.38/9.62 inference(quant_inst,[status(thm)],[])).
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% 9.38/9.62 inference(modus_ponens,[status(thm)],[18467, 18466])).
% 9.38/9.62 tff(18469,plain,
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% 9.38/9.62 tff(18470,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.62 tff(18471,plain,
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% 9.38/9.62 tff(18472,plain,
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% 9.38/9.62 tff(18473,plain,
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% 9.38/9.62 tff(18474,plain,
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% 9.38/9.62 tff(18475,plain,
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% 9.38/9.62 inference(modus_ponens,[status(thm)],[18474, 17614])).
% 9.38/9.62 tff(18476,plain,
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% 9.38/9.62 inference(modus_ponens,[status(thm)],[18475, 17613])).
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% 9.38/9.63 tff(18478,plain,
% 9.38/9.63 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
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% 9.38/9.63 inference(transitivity,[status(thm)],[18479, 18477])).
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% 9.38/9.63 inference(modus_ponens,[status(thm)],[18481, 18480])).
% 9.38/9.63 tff(18483,plain,
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% 9.38/9.63 inference(unit_resolution,[status(thm)],[18482, 194, 723, 719, 15510])).
% 9.38/9.63 tff(18484,plain,
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% 9.38/9.63 tff(18485,plain,((~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.63 tff(18486,plain,
% 9.38/9.63 (~r(s(s(s(s(z)))), s(z))),
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% 9.38/9.63 tff(18487,plain,
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% 9.38/9.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.63 inference(rewrite,[status(thm)],[])).
% 9.38/9.63 tff(18489,plain,
% 9.38/9.63 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.63 inference(rewrite,[status(thm)],[])).
% 9.38/9.63 tff(18490,plain,
% 9.38/9.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 9.38/9.63 inference(monotonicity,[status(thm)],[18489])).
% 9.38/9.63 tff(18491,plain,
% 9.38/9.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.63 inference(transitivity,[status(thm)],[18490, 18488])).
% 9.38/9.63 tff(18492,plain,
% 9.38/9.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 9.38/9.63 inference(quant_inst,[status(thm)],[])).
% 9.38/9.63 tff(18493,plain,
% 9.38/9.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 9.38/9.63 inference(modus_ponens,[status(thm)],[18492, 18491])).
% 9.38/9.63 tff(18494,plain,
% 9.38/9.63 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 9.38/9.63 inference(unit_resolution,[status(thm)],[18493, 391, 90, 1234, 18487, 17636])).
% 9.38/9.63 tff(18495,plain,
% 9.38/9.63 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.38/9.63 inference(modus_ponens,[status(thm)],[18494, 18390])).
% 9.38/9.63 tff(18496,plain,
% 9.38/9.63 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.38/9.63 inference(unit_resolution,[status(thm)],[1164, 18495, 1373])).
% 9.38/9.63 tff(18497,plain,
% 9.38/9.63 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.38/9.63 inference(modus_ponens,[status(thm)],[18496, 17614])).
% 9.38/9.63 tff(18498,plain,
% 9.38/9.63 (r(s(s(s(z))), s(s(s(s(z)))))),
% 9.38/9.63 inference(modus_ponens,[status(thm)],[18497, 17613])).
% 9.38/9.63 tff(18499,plain,
% 9.38/9.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), 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))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.63 inference(rewrite,[status(thm)],[])).
% 9.38/9.63 tff(18500,plain,
% 9.38/9.63 (((~b(s(s(s(s(z)))), z)) | (~b(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(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), 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))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.63 inference(rewrite,[status(thm)],[])).
% 9.38/9.63 tff(18501,plain,
% 9.38/9.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(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(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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))) | (~b(s(z), s(s(s(s(z))))))))),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18500])).
% 9.38/9.64 tff(18502,plain,
% 9.38/9.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(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(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), 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))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.64 inference(transitivity,[status(thm)],[18501, 18499])).
% 9.38/9.64 tff(18503,plain,
% 9.38/9.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(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(s(z)))), s(s(s(z))))))),
% 9.38/9.64 inference(quant_inst,[status(thm)],[])).
% 9.38/9.64 tff(18504,plain,
% 9.38/9.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), 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))) | (~b(s(z), s(s(s(s(z))))))),
% 9.38/9.64 inference(modus_ponens,[status(thm)],[18503, 18502])).
% 9.38/9.64 tff(18505,plain,
% 9.38/9.64 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[18504, 391, 90, 1234, 18487, 17636])).
% 9.38/9.64 tff(18506,plain,
% 9.38/9.64 (r(s(s(s(s(z)))), s(s(s(z))))),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[4426, 42, 18505, 17633])).
% 9.38/9.64 tff(18507,plain,
% 9.38/9.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 9.38/9.64 inference(rewrite,[status(thm)],[])).
% 9.38/9.64 tff(18508,plain,
% 9.38/9.64 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, 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(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 9.38/9.64 inference(rewrite,[status(thm)],[])).
% 9.38/9.64 tff(18509,plain,
% 9.38/9.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18508])).
% 9.38/9.64 tff(18510,plain,
% 9.38/9.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 9.38/9.64 inference(transitivity,[status(thm)],[18509, 18507])).
% 9.38/9.64 tff(18511,plain,
% 9.38/9.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 9.38/9.64 inference(quant_inst,[status(thm)],[])).
% 9.38/9.64 tff(18512,plain,
% 9.38/9.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 9.38/9.64 inference(modus_ponens,[status(thm)],[18511, 18510])).
% 9.38/9.64 tff(18513,plain,
% 9.38/9.64 ($false),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[18512, 194, 18456, 501, 18506, 18498])).
% 9.38/9.64 tff(18514,plain,((~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | r(s(s(s(elem!1))), elem!1) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.64 tff(18515,plain,
% 9.38/9.64 (~b(s(s(s(s(z)))), z)),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[18514, 18374, 1373, 1234, 1374, 1035, 1526, 59, 18365, 847, 973, 225, 3843, 644])).
% 9.38/9.64 tff(18516,plain,
% 9.38/9.64 (r(s(s(s(s(z)))), z)),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[87, 18515])).
% 9.38/9.64 tff(18517,plain,
% 9.38/9.64 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[18433, 18388, 18516, 18384])).
% 9.38/9.64 tff(18518,plain,
% 9.38/9.64 (b(s(s(s(s(z)))), s(s(z)))),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[1714, 18517])).
% 9.38/9.64 tff(18519,plain,
% 9.38/9.64 (s(s(s(elem!1))) = s(s(s(z)))),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18376])).
% 9.38/9.64 tff(18520,plain,
% 9.38/9.64 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18519])).
% 9.38/9.64 tff(18521,plain,
% 9.38/9.64 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18376, 18520])).
% 9.38/9.64 tff(18522,plain,
% 9.38/9.64 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18520])).
% 9.38/9.64 tff(18523,plain,
% 9.38/9.64 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(s(elem!1)))))),
% 9.38/9.64 inference(symmetry,[status(thm)],[18522])).
% 9.38/9.64 tff(18524,plain,
% 9.38/9.64 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18374])).
% 9.38/9.64 tff(18525,plain,
% 9.38/9.64 (r(elem!1, s(s(s(s(z)))))),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[18441, 18383, 18374, 1374, 1526, 18378, 1234, 847, 973, 225])).
% 9.38/9.64 tff(18526,plain,
% 9.38/9.64 (r(z, s(s(s(s(z)))))),
% 9.38/9.64 inference(modus_ponens,[status(thm)],[18525, 18524])).
% 9.38/9.64 tff(18527,plain,
% 9.38/9.64 (r(z, s(s(s(s(elem!1)))))),
% 9.38/9.64 inference(modus_ponens,[status(thm)],[18526, 18523])).
% 9.38/9.64 tff(18528,plain,
% 9.38/9.64 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18374])).
% 9.38/9.64 tff(18529,plain,
% 9.38/9.64 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 9.38/9.64 inference(symmetry,[status(thm)],[18528])).
% 9.38/9.64 tff(18530,plain,
% 9.38/9.64 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18520])).
% 9.38/9.64 tff(18531,plain,
% 9.38/9.64 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 9.38/9.64 inference(symmetry,[status(thm)],[18530])).
% 9.38/9.64 tff(18532,plain,
% 9.38/9.64 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 9.38/9.64 inference(transitivity,[status(thm)],[18531, 18529])).
% 9.38/9.64 tff(18533,plain,
% 9.38/9.64 (r(s(s(s(s(elem!1)))), elem!1)),
% 9.38/9.64 inference(modus_ponens,[status(thm)],[18516, 18532])).
% 9.38/9.64 tff(18534,plain,
% 9.38/9.64 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[2800, 18533, 18383, 18527])).
% 9.38/9.64 tff(18535,plain,
% 9.38/9.64 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[1048, 18534, 1035])).
% 9.38/9.64 tff(18536,plain,
% 9.38/9.64 (b(s(s(z)), s(s(s(s(z)))))),
% 9.38/9.64 inference(modus_ponens,[status(thm)],[18535, 18521])).
% 9.38/9.64 tff(18537,plain,
% 9.38/9.64 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.64 inference(rewrite,[status(thm)],[])).
% 9.38/9.64 tff(18538,plain,
% 9.38/9.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18537])).
% 9.38/9.64 tff(18539,plain,
% 9.38/9.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.64 inference(transitivity,[status(thm)],[18538, 6268])).
% 9.38/9.64 tff(18540,plain,
% 9.38/9.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 9.38/9.64 inference(quant_inst,[status(thm)],[])).
% 9.38/9.64 tff(18541,plain,
% 9.38/9.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 9.38/9.64 inference(modus_ponens,[status(thm)],[18540, 18539])).
% 9.38/9.64 tff(18542,plain,
% 9.38/9.64 (~b(s(z), s(s(z)))),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[18541, 391, 18536, 1234, 18518])).
% 9.38/9.64 tff(18543,plain,
% 9.38/9.64 (r(s(z), s(s(z)))),
% 9.38/9.64 inference(unit_resolution,[status(thm)],[1788, 18542])).
% 9.38/9.64 tff(18544,plain,
% 9.38/9.64 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 9.38/9.64 inference(monotonicity,[status(thm)],[491])).
% 9.38/9.64 tff(18545,plain,
% 9.38/9.64 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 9.38/9.64 inference(symmetry,[status(thm)],[18544])).
% 9.38/9.64 tff(18546,plain,
% 9.38/9.64 (b(s(z), s(s(s(z))))),
% 9.38/9.64 inference(modus_ponens,[status(thm)],[379, 18545])).
% 9.38/9.64 tff(18547,plain,
% 9.38/9.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 9.38/9.64 inference(rewrite,[status(thm)],[])).
% 9.38/9.64 tff(18548,plain,
% 9.38/9.64 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 9.38/9.64 inference(rewrite,[status(thm)],[])).
% 9.38/9.64 tff(18549,plain,
% 9.38/9.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 9.38/9.64 inference(monotonicity,[status(thm)],[18548])).
% 9.38/9.64 tff(18550,plain,
% 9.38/9.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 9.38/9.64 inference(transitivity,[status(thm)],[18549, 18547])).
% 9.38/9.64 tff(18551,plain,
% 9.38/9.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 9.38/9.64 inference(quant_inst,[status(thm)],[])).
% 9.38/9.64 tff(18552,plain,
% 9.38/9.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 9.38/9.65 inference(modus_ponens,[status(thm)],[18551, 18550])).
% 9.38/9.65 tff(18553,plain,
% 9.38/9.65 ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18552, 391])).
% 9.38/9.65 tff(18554,plain,
% 9.38/9.65 ($false),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18553, 3198, 664, 1677, 18546])).
% 9.38/9.65 tff(18555,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~(elem!1 = z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.65 tff(18556,plain,
% 9.38/9.65 (~b(z, s(z))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18555, 18381, 644, 18363, 18374])).
% 9.38/9.65 tff(18557,plain,
% 9.38/9.65 (r(z, s(z))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[678, 18556])).
% 9.38/9.65 tff(18558,plain,
% 9.38/9.65 ($false),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[9718, 194, 18557, 18543, 18388, 18384])).
% 9.38/9.65 tff(18559,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(s(z), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(elem!1, z) | b(z, s(s(s(elem!1)))) | b(z, elem!1) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.65 tff(18560,plain,
% 9.38/9.65 ($false),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18559, 18291, 9895, 847, 1234, 1374, 1526, 225, 644, 1373, 3843, 484, 10, 89, 6460, 4028, 31])).
% 9.38/9.65 tff(18561,plain,((s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | r(s(s(s(elem!1))), elem!1) | (~b(s(z), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(elem!1, z) | b(z, s(s(s(elem!1)))) | b(z, elem!1) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.38/9.65 tff(18562,plain,
% 9.38/9.65 (s(s(s(elem!1))) = s(elem!1)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18561, 18275, 17033, 838, 18290, 8290, 18287, 18286, 3363, 484, 10, 18283, 18278, 31, 18279])).
% 9.38/9.65 tff(18563,plain,
% 9.38/9.65 (~(s(s(s(s(z)))) = elem!1)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[717, 18562])).
% 9.38/9.65 tff(18564,plain,
% 9.38/9.65 (b(s(s(s(s(z)))), elem!1)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[762, 18563, 17034])).
% 9.38/9.65 tff(18565,plain,
% 9.38/9.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[6136, 18288, 59, 3618])).
% 9.38/9.65 tff(18566,plain,
% 9.38/9.65 (~r(s(s(s(elem!1))), z)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[8380, 18288, 59, 8232])).
% 9.38/9.65 tff(18567,plain,
% 9.38/9.65 (b(s(s(s(elem!1))), z)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[377, 18566])).
% 9.38/9.65 tff(18568,plain,
% 9.38/9.65 (~r(s(elem!1), z)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[6142, 18565, 59, 3618, 18282, 18278, 18277])).
% 9.38/9.65 tff(18569,plain,
% 9.38/9.65 (b(s(elem!1), z)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[549, 18568])).
% 9.38/9.65 tff(18570,plain,
% 9.38/9.65 (r(z, s(elem!1))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[2614, 18569, 18567, 18565, 59])).
% 9.38/9.65 tff(18571,plain,
% 9.38/9.65 (~r(elem!1, s(s(s(s(z)))))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[6444, 18570, 3618, 3447])).
% 9.38/9.65 tff(18572,plain,
% 9.38/9.65 (~(elem!1 = s(s(s(s(z)))))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[769, 18563])).
% 9.38/9.65 tff(18573,plain,
% 9.38/9.65 (b(elem!1, s(s(s(s(z)))))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[781, 18572, 18571])).
% 9.38/9.65 tff(18574,plain,
% 9.38/9.65 ($false),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[17588, 391, 18287, 18573, 18564, 17033])).
% 9.38/9.65 tff(18575,plain,(b(s(s(s(s(z)))), z) | b(elem!1, z) | b(z, s(s(s(elem!1)))) | b(elem!1, s(z)) | (elem!1 = z) | (~r(z, s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.38/9.65 tff(18576,plain,
% 9.38/9.65 (b(s(s(s(s(z)))), z)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18575, 722, 10, 31, 2, 484, 150])).
% 9.38/9.65 tff(18577,plain,
% 9.38/9.65 (~b(z, s(s(s(s(z)))))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[10438, 18576, 17033, 8232, 838])).
% 9.38/9.65 tff(18578,plain,
% 9.38/9.65 (r(z, s(s(s(s(z)))))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[800, 18577])).
% 9.38/9.65 tff(18579,plain,
% 9.38/9.65 (~(elem!1 = s(s(s(s(z)))))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[16358, 18576, 484])).
% 9.38/9.65 tff(18580,plain,
% 9.38/9.65 (~(s(s(s(s(z)))) = elem!1)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[16908, 18579])).
% 9.38/9.65 tff(18581,plain,
% 9.38/9.65 (~r(s(s(s(s(z)))), elem!1)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[10418, 18578, 838, 8232])).
% 9.38/9.65 tff(18582,plain,
% 9.38/9.65 (b(s(s(s(s(z)))), elem!1)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[762, 18581, 18580])).
% 9.38/9.65 tff(18583,plain,
% 9.38/9.65 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.65 inference(rewrite,[status(thm)],[])).
% 9.38/9.65 tff(18584,plain,
% 9.38/9.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 9.38/9.65 inference(monotonicity,[status(thm)],[18583])).
% 9.38/9.65 tff(18585,plain,
% 9.38/9.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.65 inference(transitivity,[status(thm)],[18584, 17583])).
% 9.38/9.65 tff(18586,plain,
% 9.38/9.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))),
% 9.38/9.65 inference(quant_inst,[status(thm)],[])).
% 9.38/9.65 tff(18587,plain,
% 9.38/9.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 9.38/9.65 inference(modus_ponens,[status(thm)],[18586, 18585])).
% 9.38/9.65 tff(18588,plain,
% 9.38/9.65 ($false),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18587, 391, 644, 2064, 1652, 1234])).
% 9.38/9.65 tff(18589,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.65 tff(18590,plain,
% 9.38/9.65 (~b(elem!1, s(s(s(s(z)))))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18589, 18287, 18582, 17033])).
% 9.38/9.65 tff(18591,plain,
% 9.38/9.65 (r(elem!1, s(s(s(s(z)))))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[781, 18590, 18579])).
% 9.38/9.65 tff(18592,plain,
% 9.38/9.65 (~r(s(s(s(s(z)))), s(z))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[15063, 18591, 8232, 18578])).
% 9.38/9.65 tff(18593,plain,
% 9.38/9.65 (b(s(s(s(s(z)))), s(z))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[749, 18592])).
% 9.38/9.65 tff(18594,plain,
% 9.38/9.65 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[15016, 18591, 8232, 18578])).
% 9.38/9.65 tff(18595,plain,
% 9.38/9.65 (b(s(s(s(s(z)))), s(s(z)))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[1714, 18594])).
% 9.38/9.65 tff(18596,plain,
% 9.38/9.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 9.38/9.65 inference(rewrite,[status(thm)],[])).
% 9.38/9.65 tff(18597,plain,
% 9.38/9.65 (((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 9.38/9.65 inference(rewrite,[status(thm)],[])).
% 9.38/9.65 tff(18598,plain,
% 9.38/9.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))))),
% 9.38/9.65 inference(monotonicity,[status(thm)],[18597])).
% 9.38/9.65 tff(18599,plain,
% 9.38/9.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 9.38/9.65 inference(transitivity,[status(thm)],[18598, 18596])).
% 9.38/9.65 tff(18600,plain,
% 9.38/9.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))),
% 9.38/9.65 inference(quant_inst,[status(thm)],[])).
% 9.38/9.65 tff(18601,plain,
% 9.38/9.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))),
% 9.38/9.65 inference(modus_ponens,[status(thm)],[18600, 18599])).
% 9.38/9.65 tff(18602,plain,
% 9.38/9.65 ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18601, 194])).
% 9.38/9.65 tff(18603,plain,
% 9.38/9.65 (~r(elem!1, s(s(z)))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18602, 3557, 530, 722])).
% 9.38/9.65 tff(18604,plain,
% 9.38/9.65 (b(elem!1, s(s(z)))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[3394, 18603, 1405])).
% 9.38/9.65 tff(18605,plain,
% 9.38/9.65 (~b(s(s(z)), elem!1)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[11012, 18604, 1652, 3563])).
% 9.38/9.65 tff(18606,plain,
% 9.38/9.65 (r(s(s(z)), elem!1)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[4730, 18605, 5547])).
% 9.38/9.65 tff(18607,plain,
% 9.38/9.65 ($false),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[15383, 194, 411, 530, 3557, 18606])).
% 9.38/9.65 tff(18608,plain,((~r(s(s(z)), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(s(z)) = elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.65 tff(18609,plain,
% 9.38/9.65 (~r(s(s(z)), z)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18608, 14710, 530, 411, 1652, 3563, 3694, 722])).
% 9.38/9.65 tff(18610,plain,
% 9.38/9.65 (b(s(s(z)), z)),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[1211, 18609])).
% 9.38/9.65 tff(18611,plain,
% 9.38/9.65 (~b(z, s(s(z)))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[15053, 18610, 90, 3563])).
% 9.38/9.65 tff(18612,plain,
% 9.38/9.65 ($false),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[10164, 42, 8518, 3373, 8912])).
% 9.38/9.65 tff(18613,plain,(r(z, s(s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.65 tff(18614,plain,
% 9.38/9.65 (r(z, s(s(z)))),
% 9.38/9.65 inference(unit_resolution,[status(thm)],[18613, 18611])).
% 9.38/9.65 tff(18615,plain,
% 9.38/9.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.38/9.65 inference(rewrite,[status(thm)],[])).
% 9.38/9.65 tff(18616,plain,
% 9.38/9.65 (((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.38/9.65 inference(rewrite,[status(thm)],[])).
% 9.38/9.65 tff(18617,plain,
% 9.38/9.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 9.38/9.66 inference(monotonicity,[status(thm)],[18616])).
% 9.38/9.66 tff(18618,plain,
% 9.38/9.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.38/9.66 inference(transitivity,[status(thm)],[18617, 18615])).
% 9.38/9.66 tff(18619,plain,
% 9.38/9.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.38/9.66 inference(quant_inst,[status(thm)],[])).
% 9.38/9.66 tff(18620,plain,
% 9.38/9.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 9.38/9.66 inference(modus_ponens,[status(thm)],[18619, 18618])).
% 9.38/9.66 tff(18621,plain,
% 9.38/9.66 ($false),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[18620, 391, 644, 1235, 3369, 1652, 1759])).
% 9.38/9.66 tff(18622,plain,((~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.66 tff(18623,plain,
% 9.38/9.66 (~b(elem!1, s(s(z)))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[18622, 18610, 644, 1652, 1759])).
% 9.38/9.66 tff(18624,plain,
% 9.38/9.66 (r(elem!1, s(s(z)))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[3394, 18623, 3694])).
% 9.38/9.66 tff(18625,plain,
% 9.38/9.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 9.38/9.66 inference(rewrite,[status(thm)],[])).
% 9.38/9.66 tff(18626,plain,
% 9.38/9.66 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 9.38/9.66 inference(rewrite,[status(thm)],[])).
% 9.38/9.66 tff(18627,plain,
% 9.38/9.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))))),
% 9.38/9.66 inference(monotonicity,[status(thm)],[18626])).
% 9.38/9.66 tff(18628,plain,
% 9.38/9.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 9.38/9.66 inference(transitivity,[status(thm)],[18627, 18625])).
% 9.38/9.66 tff(18629,plain,
% 9.38/9.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1)))),
% 9.38/9.66 inference(quant_inst,[status(thm)],[])).
% 9.38/9.66 tff(18630,plain,
% 9.38/9.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))),
% 9.38/9.66 inference(modus_ponens,[status(thm)],[18629, 18628])).
% 9.38/9.66 tff(18631,plain,
% 9.38/9.66 ($false),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[18630, 194, 411, 1749, 1748, 8505])).
% 9.38/9.66 tff(18632,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.66 tff(18633,plain,
% 9.38/9.66 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[18632, 18624, 411, 18614])).
% 9.38/9.66 tff(18634,plain,
% 9.38/9.66 (b(s(s(z)), s(s(s(s(z)))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[3652, 18633])).
% 9.38/9.66 tff(18635,plain,
% 9.38/9.66 (~b(s(z), s(s(z)))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[6275, 18634, 1234, 3563])).
% 9.38/9.66 tff(18636,plain,
% 9.38/9.66 (r(s(z), s(s(z)))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[1788, 18635])).
% 9.38/9.66 tff(18637,plain,
% 9.38/9.66 (~b(s(s(z)), s(z))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[9374, 18634, 1234, 3563])).
% 9.38/9.66 tff(18638,plain,
% 9.38/9.66 (r(s(s(z)), s(z))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[3778, 18637])).
% 9.38/9.66 tff(18639,plain,
% 9.38/9.66 ($false),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[9720, 18638, 18636, 722, 18614])).
% 9.38/9.66 tff(18640,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.66 tff(18641,plain,
% 9.38/9.66 (~(s(s(s(elem!1))) = elem!1)),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[18640, 722, 17033, 18595, 8232, 18287, 18582, 18593, 18576, 3618])).
% 9.38/9.66 tff(18642,plain,
% 9.38/9.66 (b(s(s(s(elem!1))), elem!1)),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[230, 18641, 8290])).
% 9.38/9.66 tff(18643,plain,
% 9.38/9.66 (~r(s(z), s(s(s(elem!1))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[16770, 722, 3618, 838])).
% 9.38/9.66 tff(18644,plain,
% 9.38/9.66 (b(s(z), s(s(s(elem!1))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[247, 18643])).
% 9.38/9.66 tff(18645,plain,
% 9.38/9.66 (b(s(s(s(elem!1))), elem!1)),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[230, 127, 225])).
% 9.38/9.66 tff(18646,plain,
% 9.38/9.66 (~b(s(s(s(elem!1))), s(z))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[16792, 18645, 184, 3843, 719, 379, 1759])).
% 9.38/9.66 tff(18647,plain,
% 9.38/9.66 (~r(s(s(s(elem!1))), s(z))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[6132, 4030, 184, 530])).
% 9.38/9.66 tff(18648,plain,
% 9.38/9.66 ($false),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[223, 18647, 18646])).
% 9.38/9.66 tff(18649,plain,((s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | b(elem!1, s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.38/9.66 tff(18650,plain,
% 9.38/9.66 (b(elem!1, s(s(s(elem!1))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[18649, 18641, 3618, 3363, 18578, 18644, 18593, 59, 8290])).
% 9.38/9.66 tff(18651,plain,
% 9.38/9.66 ($false),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[16827, 18650, 18642, 722, 150, 3618, 838, 8232])).
% 9.38/9.66 tff(18652,plain,((~r(z, s(z))) | (s(z) = elem!1) | b(elem!1, z) | b(z, s(s(s(elem!1)))) | b(elem!1, s(z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 9.38/9.66 tff(18653,plain,
% 9.38/9.66 (~r(z, s(z))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[18652, 150, 484, 10, 31, 2])).
% 9.38/9.66 tff(18654,plain,
% 9.38/9.66 (b(z, s(z))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[678, 18653])).
% 9.38/9.66 tff(18655,plain,
% 9.38/9.66 (~r(elem!1, s(s(s(s(z)))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[17579, 194, 8232, 3618, 3447])).
% 9.38/9.66 tff(18656,plain,
% 9.38/9.66 (b(s(s(s(s(z)))), elem!1)),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[762, 8917, 6221])).
% 9.38/9.66 tff(18657,plain,
% 9.38/9.66 (r(s(s(s(elem!1))), s(z))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[17668, 2829, 1234, 3446, 10])).
% 9.38/9.66 tff(18658,plain,
% 9.38/9.66 (~r(elem!1, s(s(s(elem!1))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[6132, 18657, 59, 530])).
% 9.38/9.66 tff(18659,plain,
% 9.38/9.66 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[5792, 9968, 16441, 59])).
% 9.38/9.66 tff(18660,plain,
% 9.38/9.66 (~(s(s(s(s(z)))) = elem!1)),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[16124, 1686, 89])).
% 9.38/9.66 tff(18661,plain,
% 9.38/9.66 (b(s(s(s(s(z)))), elem!1)),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[762, 18660, 6221])).
% 9.38/9.66 tff(18662,plain,
% 9.38/9.66 (~(elem!1 = s(s(s(s(z)))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[769, 18660])).
% 9.38/9.66 tff(18663,plain,
% 9.38/9.66 (b(elem!1, s(s(s(s(z)))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[781, 18662, 3222])).
% 9.38/9.66 tff(18664,plain,
% 9.38/9.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.66 inference(rewrite,[status(thm)],[])).
% 9.38/9.66 tff(18665,plain,
% 9.38/9.66 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.66 inference(rewrite,[status(thm)],[])).
% 9.38/9.66 tff(18666,plain,
% 9.38/9.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 9.38/9.66 inference(monotonicity,[status(thm)],[18665])).
% 9.38/9.66 tff(18667,plain,
% 9.38/9.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.66 inference(transitivity,[status(thm)],[18666, 18664])).
% 9.38/9.66 tff(18668,plain,
% 9.38/9.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 9.38/9.66 inference(quant_inst,[status(thm)],[])).
% 9.38/9.66 tff(18669,plain,
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% 9.38/9.66 inference(modus_ponens,[status(thm)],[18668, 18667])).
% 9.38/9.66 tff(18670,plain,
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% 9.38/9.66 inference(unit_resolution,[status(thm)],[18669, 391, 18663, 18661, 1234, 1686, 590])).
% 9.38/9.66 tff(18671,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.38/9.66 tff(18672,plain,
% 9.38/9.66 (~b(z, s(s(s(s(z)))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[18671, 137, 590, 1234, 6221, 3222])).
% 9.38/9.66 tff(18673,plain,
% 9.38/9.66 (r(z, s(s(s(s(z)))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[800, 18672])).
% 9.38/9.66 tff(18674,plain,
% 9.38/9.66 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.38/9.66 inference(unit_resolution,[status(thm)],[10090, 18673, 2053, 59])).
% 9.38/9.66 tff(18675,plain,
% 9.38/9.66 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.38/9.67 inference(unit_resolution,[status(thm)],[15351, 18674, 15348])).
% 9.38/9.67 tff(18676,plain,
% 9.38/9.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.38/9.67 inference(rewrite,[status(thm)],[])).
% 9.38/9.67 tff(18677,plain,
% 9.38/9.67 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.38/9.67 inference(rewrite,[status(thm)],[])).
% 9.38/9.67 tff(18678,plain,
% 9.38/9.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.38/9.67 inference(monotonicity,[status(thm)],[18677])).
% 9.38/9.67 tff(18679,plain,
% 9.38/9.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.38/9.67 inference(transitivity,[status(thm)],[18678, 18676])).
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% 9.38/9.67 inference(quant_inst,[status(thm)],[])).
% 9.38/9.67 tff(18681,plain,
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% 9.38/9.67 inference(modus_ponens,[status(thm)],[18680, 18679])).
% 9.38/9.67 tff(18682,plain,
% 9.38/9.67 (~b(s(s(z)), s(z))),
% 9.38/9.67 inference(unit_resolution,[status(thm)],[18681, 391, 3823, 1234, 3325, 1669])).
% 9.38/9.67 tff(18683,plain,
% 9.38/9.67 (r(s(s(z)), s(z))),
% 9.38/9.67 inference(unit_resolution,[status(thm)],[3778, 18682])).
% 9.38/9.67 tff(18684,plain,
% 9.38/9.67 (~b(s(s(z)), s(s(s(elem!1))))),
% 9.38/9.67 inference(unit_resolution,[status(thm)],[15908, 391, 3823, 3325, 1669])).
% 9.38/9.67 tff(18685,plain,
% 9.38/9.67 (r(s(s(z)), s(s(s(elem!1))))),
% 9.38/9.67 inference(unit_resolution,[status(thm)],[11041, 18684])).
% 9.38/9.67 tff(18686,plain,
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% 9.38/9.67 inference(unit_resolution,[status(thm)],[11050, 18685, 18683, 174, 232])).
% 9.38/9.67 tff(18687,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.67 tff(18688,plain,
% 9.38/9.67 (~b(s(s(z)), s(s(s(s(z)))))),
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% 9.38/9.67 tff(18689,plain,
% 9.38/9.67 (r(s(s(z)), s(s(s(s(z)))))),
% 9.38/9.67 inference(unit_resolution,[status(thm)],[3652, 18688])).
% 9.38/9.67 tff(18690,plain,
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% 9.38/9.67 tff(18691,plain,
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% 9.38/9.67 inference(unit_resolution,[status(thm)],[1211, 18690])).
% 9.38/9.67 tff(18692,plain,
% 9.38/9.67 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
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% 9.38/9.67 tff(18693,plain,
% 9.38/9.67 ((s(s(elem!1)) = elem!1) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
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% 9.38/9.67 tff(18694,plain,
% 9.38/9.67 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 9.38/9.67 inference(transitivity,[status(thm)],[250, 18693, 268])).
% 9.38/9.67 tff(18695,plain,
% 9.38/9.67 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
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% 9.38/9.67 tff(18696,plain,
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% 9.38/9.67 tff(18697,plain,
% 9.38/9.67 ((~b(s(s(s(s(s(elem!1))))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
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% 9.38/9.67 tff(18698,plain,
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% 9.38/9.67 tff(18699,plain,
% 9.38/9.67 (~r(s(s(s(s(s(elem!1))))), z)),
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% 9.38/9.67 tff(18700,assumption,(~r(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 9.38/9.67 tff(18701,assumption,(~b(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 9.38/9.67 tff(18702,plain,
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% 9.38/9.67 inference(unit_resolution,[status(thm)],[8165, 42, 8162, 18701, 18700])).
% 9.38/9.67 tff(18703,plain,(b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z)), inference(lemma,lemma(discharge,[]))).
% 9.38/9.67 tff(18704,plain,
% 9.38/9.67 (b(s(s(s(s(s(elem!1))))), z)),
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% 9.38/9.67 tff(18705,plain,
% 9.38/9.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 9.38/9.67 inference(rewrite,[status(thm)],[])).
% 9.38/9.67 tff(18706,plain,
% 9.38/9.67 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 9.38/9.67 inference(rewrite,[status(thm)],[])).
% 9.38/9.67 tff(18707,plain,
% 9.38/9.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 9.38/9.67 inference(monotonicity,[status(thm)],[18706])).
% 9.38/9.67 tff(18708,plain,
% 9.38/9.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 9.38/9.67 inference(transitivity,[status(thm)],[18707, 18705])).
% 9.38/9.67 tff(18709,plain,
% 9.38/9.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 9.38/9.68 inference(quant_inst,[status(thm)],[])).
% 9.38/9.68 tff(18710,plain,
% 9.38/9.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 9.38/9.68 inference(modus_ponens,[status(thm)],[18709, 18708])).
% 9.38/9.68 tff(18711,plain,
% 9.38/9.68 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[18710, 391, 1234, 664, 590, 18704])).
% 9.38/9.68 tff(18712,plain,
% 9.38/9.68 (~b(s(s(elem!1)), s(z))),
% 9.38/9.68 inference(modus_ponens,[status(thm)],[18711, 18697])).
% 9.38/9.68 tff(18713,plain,
% 9.38/9.68 (r(s(s(elem!1)), s(z))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[362, 18712])).
% 9.38/9.68 tff(18714,plain,
% 9.38/9.68 (~r(elem!1, s(s(elem!1)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[6179, 18713, 847, 9968])).
% 9.38/9.68 tff(18715,plain,
% 9.38/9.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.68 inference(rewrite,[status(thm)],[])).
% 9.38/9.68 tff(18716,plain,
% 9.38/9.68 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.68 inference(rewrite,[status(thm)],[])).
% 9.38/9.68 tff(18717,plain,
% 9.38/9.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 9.38/9.68 inference(monotonicity,[status(thm)],[18716])).
% 9.38/9.68 tff(18718,plain,
% 9.38/9.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.68 inference(transitivity,[status(thm)],[18717, 18715])).
% 9.38/9.68 tff(18719,plain,
% 9.38/9.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 9.38/9.68 inference(quant_inst,[status(thm)],[])).
% 9.38/9.68 tff(18720,plain,
% 9.38/9.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 9.38/9.68 inference(modus_ponens,[status(thm)],[18719, 18718])).
% 9.38/9.68 tff(18721,plain,
% 9.38/9.68 (~b(s(s(z)), s(z))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[18720, 391, 1235, 1234, 664, 590])).
% 9.38/9.68 tff(18722,plain,
% 9.38/9.68 (r(s(s(z)), s(z))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[3778, 18721])).
% 9.38/9.68 tff(18723,plain,
% 9.38/9.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.68 inference(rewrite,[status(thm)],[])).
% 9.38/9.68 tff(18724,plain,
% 9.38/9.68 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.68 inference(rewrite,[status(thm)],[])).
% 9.38/9.68 tff(18725,plain,
% 9.38/9.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 9.38/9.68 inference(monotonicity,[status(thm)],[18724])).
% 9.38/9.68 tff(18726,plain,
% 9.38/9.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.38/9.68 inference(transitivity,[status(thm)],[18725, 18723])).
% 9.38/9.68 tff(18727,plain,
% 9.38/9.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 9.38/9.68 inference(quant_inst,[status(thm)],[])).
% 9.38/9.68 tff(18728,plain,
% 9.38/9.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 9.38/9.68 inference(modus_ponens,[status(thm)],[18727, 18726])).
% 9.38/9.68 tff(18729,plain,
% 9.38/9.68 (~b(s(z), s(s(z)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[18728, 391, 1235, 1234, 664, 590])).
% 9.38/9.68 tff(18730,plain,
% 9.38/9.68 (r(s(z), s(s(z)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[1788, 18729])).
% 9.38/9.68 tff(18731,plain,
% 9.38/9.68 (~r(s(s(s(elem!1))), s(s(z)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[11551, 18722, 9968, 18730])).
% 9.38/9.68 tff(18732,plain,
% 9.38/9.68 (~r(elem!1, s(s(z)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[10022, 18731, 125])).
% 9.38/9.68 tff(18733,plain,
% 9.38/9.68 (b(elem!1, s(s(z)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[3394, 18732, 3820])).
% 9.38/9.68 tff(18734,plain,
% 9.38/9.68 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 9.38/9.68 inference(symmetry,[status(thm)],[9482])).
% 9.38/9.68 tff(18735,plain,
% 9.38/9.68 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 9.38/9.68 inference(monotonicity,[status(thm)],[18734])).
% 9.38/9.68 tff(18736,plain,
% 9.38/9.68 (~(s(s(z)) = s(s(elem!1)))),
% 9.38/9.68 inference(modus_ponens,[status(thm)],[2689, 18735])).
% 9.38/9.68 tff(18737,plain,
% 9.38/9.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 9.38/9.68 inference(rewrite,[status(thm)],[])).
% 9.38/9.68 tff(18738,plain,
% 9.38/9.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 9.38/9.68 inference(quant_inst,[status(thm)],[])).
% 9.38/9.68 tff(18739,plain,
% 9.38/9.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 9.38/9.68 inference(modus_ponens,[status(thm)],[18738, 18737])).
% 9.38/9.68 tff(18740,plain,
% 9.38/9.68 (~r(s(s(z)), s(s(elem!1)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[18739, 194, 340, 1484, 2405])).
% 9.38/9.68 tff(18741,plain,
% 9.38/9.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 9.38/9.68 inference(rewrite,[status(thm)],[])).
% 9.38/9.68 tff(18742,plain,
% 9.38/9.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 9.38/9.68 inference(quant_inst,[status(thm)],[])).
% 9.38/9.68 tff(18743,plain,
% 9.38/9.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 9.38/9.68 inference(modus_ponens,[status(thm)],[18742, 18741])).
% 9.38/9.68 tff(18744,plain,
% 9.38/9.68 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[18743, 42, 18740])).
% 9.38/9.68 tff(18745,plain,
% 9.38/9.68 (b(s(s(z)), s(s(elem!1)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[18744, 18736])).
% 9.38/9.68 tff(18746,plain,
% 9.38/9.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 9.38/9.68 inference(rewrite,[status(thm)],[])).
% 9.38/9.68 tff(18747,plain,
% 9.38/9.68 (((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 9.38/9.68 inference(rewrite,[status(thm)],[])).
% 9.38/9.68 tff(18748,plain,
% 9.38/9.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 9.38/9.68 inference(monotonicity,[status(thm)],[18747])).
% 9.38/9.68 tff(18749,plain,
% 9.38/9.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 9.38/9.68 inference(transitivity,[status(thm)],[18748, 18746])).
% 9.38/9.68 tff(18750,plain,
% 9.38/9.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 9.38/9.68 inference(quant_inst,[status(thm)],[])).
% 9.38/9.68 tff(18751,plain,
% 9.38/9.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 9.38/9.68 inference(modus_ponens,[status(thm)],[18750, 18749])).
% 9.38/9.68 tff(18752,plain,
% 9.38/9.68 (~r(s(s(elem!1)), s(s(z)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[18751, 194, 340, 1484, 2405])).
% 9.38/9.68 tff(18753,plain,
% 9.38/9.68 (b(s(s(elem!1)), s(s(z)))),
% 9.38/9.68 inference(unit_resolution,[status(thm)],[5174, 42, 18752, 2689])).
% 9.38/9.68 tff(18754,plain,
% 9.38/9.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 9.38/9.69 inference(rewrite,[status(thm)],[])).
% 9.38/9.69 tff(18755,plain,
% 9.38/9.69 (((~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 9.38/9.69 inference(rewrite,[status(thm)],[])).
% 9.38/9.69 tff(18756,plain,
% 9.38/9.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 9.38/9.69 inference(monotonicity,[status(thm)],[18755])).
% 9.38/9.69 tff(18757,plain,
% 9.38/9.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 9.38/9.69 inference(transitivity,[status(thm)],[18756, 18754])).
% 9.38/9.69 tff(18758,plain,
% 9.38/9.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z)))))),
% 9.38/9.69 inference(quant_inst,[status(thm)],[])).
% 9.38/9.69 tff(18759,plain,
% 9.38/9.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 9.38/9.69 inference(modus_ponens,[status(thm)],[18758, 18757])).
% 9.38/9.69 tff(18760,plain,
% 9.38/9.69 ($false),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[18759, 391, 1294, 1235, 3369, 18753, 18745])).
% 9.38/9.69 tff(18761,plain,((~r(s(s(z)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.69 tff(18762,plain,
% 9.38/9.69 (~b(elem!1, s(s(elem!1)))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[18761, 18713, 2689, 1484, 1235, 18733, 18722])).
% 9.38/9.69 tff(18763,plain,
% 9.38/9.69 (elem!1 = s(s(elem!1))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[1307, 18762, 18714])).
% 9.38/9.69 tff(18764,plain,
% 9.38/9.69 (s(s(elem!1)) = s(s(s(elem!1)))),
% 9.38/9.69 inference(modus_ponens,[status(thm)],[18763, 18694])).
% 9.38/9.69 tff(18765,plain,
% 9.38/9.69 ($false),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[270, 18764])).
% 9.38/9.69 tff(18766,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(z))) | (~r(s(z), elem!1)) | (~b(s(s(z)), z)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.69 tff(18767,plain,
% 9.38/9.69 (s(s(elem!1)) = s(s(s(elem!1)))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[18766, 125, 2689, 1484, 18691, 847, 1234, 664, 590, 18675, 9970, 59, 2053, 18659])).
% 9.38/9.69 tff(18768,plain,
% 9.38/9.69 (s(s(s(elem!1))) = s(s(elem!1))),
% 9.38/9.69 inference(symmetry,[status(thm)],[18767])).
% 9.38/9.69 tff(18769,plain,
% 9.38/9.69 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 9.38/9.69 inference(monotonicity,[status(thm)],[18768])).
% 9.38/9.69 tff(18770,plain,
% 9.38/9.69 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 9.38/9.69 inference(symmetry,[status(thm)],[18769])).
% 9.38/9.69 tff(18771,plain,
% 9.38/9.69 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 9.38/9.69 inference(monotonicity,[status(thm)],[18770])).
% 9.38/9.69 tff(18772,plain,
% 9.38/9.69 (s(s(s(elem!1))) = s(s(elem!1))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[314, 18767])).
% 9.38/9.69 tff(18773,plain,
% 9.38/9.69 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[16476, 18772])).
% 9.38/9.69 tff(18774,plain,
% 9.38/9.69 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 9.38/9.69 inference(modus_ponens,[status(thm)],[18773, 18771])).
% 9.38/9.69 tff(18775,plain,
% 9.38/9.69 (~r(z, s(s(z)))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[10160, 194, 18689, 2053, 18673])).
% 9.38/9.69 tff(18776,plain,
% 9.38/9.69 (b(z, s(s(z)))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[18613, 18775])).
% 9.38/9.69 tff(18777,plain,
% 9.38/9.69 (~b(s(z), s(s(z)))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[18728, 391, 18691, 1234, 664, 590])).
% 9.38/9.69 tff(18778,plain,
% 9.38/9.69 (r(s(z), s(s(z)))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[1788, 18777])).
% 9.38/9.69 tff(18779,plain,
% 9.38/9.69 (~b(s(s(z)), s(z))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[18720, 391, 18691, 1234, 664, 590])).
% 9.38/9.69 tff(18780,plain,
% 9.38/9.69 (r(s(s(z)), s(z))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[3778, 18779])).
% 9.38/9.69 tff(18781,plain,
% 9.38/9.69 (~r(s(s(s(s(z)))), s(z))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[9149, 18780, 1484, 18689])).
% 9.38/9.69 tff(18782,plain,
% 9.38/9.69 (b(s(s(s(s(z)))), s(z))),
% 9.38/9.69 inference(unit_resolution,[status(thm)],[749, 18781])).
% 9.38/9.69 tff(18783,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 9.38/9.69 tff(18784,assumption,(b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 9.38/9.69 tff(18785,plain,
% 9.38/9.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 9.38/9.69 inference(rewrite,[status(thm)],[])).
% 9.38/9.69 tff(18786,plain,
% 9.38/9.69 (((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 9.38/9.69 inference(rewrite,[status(thm)],[])).
% 9.38/9.69 tff(18787,plain,
% 9.38/9.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 9.38/9.69 inference(monotonicity,[status(thm)],[18786])).
% 9.38/9.69 tff(18788,plain,
% 9.38/9.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 9.38/9.69 inference(transitivity,[status(thm)],[18787, 18785])).
% 9.38/9.69 tff(18789,plain,
% 9.38/9.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 9.38/9.69 inference(quant_inst,[status(thm)],[])).
% 9.38/9.69 tff(18790,plain,
% 9.38/9.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 9.38/9.70 inference(modus_ponens,[status(thm)],[18789, 18788])).
% 9.38/9.70 tff(18791,plain,
% 9.38/9.70 ($false),
% 9.38/9.70 inference(unit_resolution,[status(thm)],[18790, 391, 1235, 664, 15045, 18783, 18784])).
% 9.38/9.70 tff(18792,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 9.38/9.70 tff(18793,plain,
% 9.38/9.70 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 9.38/9.70 inference(unit_resolution,[status(thm)],[18792, 18783, 664, 15045, 1235])).
% 9.38/9.70 tff(18794,plain,
% 9.38/9.70 (r(s(s(s(s(s(z))))), s(s(z)))),
% 9.38/9.70 inference(unit_resolution,[status(thm)],[16516, 42, 18793, 8678])).
% 9.38/9.70 tff(18795,plain,
% 9.38/9.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 9.38/9.70 inference(rewrite,[status(thm)],[])).
% 9.38/9.70 tff(18796,plain,
% 9.38/9.70 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 9.38/9.70 inference(rewrite,[status(thm)],[])).
% 9.38/9.70 tff(18797,plain,
% 9.38/9.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 9.38/9.70 inference(monotonicity,[status(thm)],[18796])).
% 9.38/9.70 tff(18798,plain,
% 9.38/9.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 9.38/9.70 inference(transitivity,[status(thm)],[18797, 18795])).
% 9.38/9.70 tff(18799,plain,
% 9.38/9.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 9.38/9.70 inference(quant_inst,[status(thm)],[])).
% 9.38/9.70 tff(18800,plain,
% 9.38/9.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 9.38/9.70 inference(modus_ponens,[status(thm)],[18799, 18798])).
% 9.38/9.70 tff(18801,plain,
% 9.38/9.70 (~r(s(s(s(s(s(z))))), s(z))),
% 9.38/9.70 inference(unit_resolution,[status(thm)],[18800, 194, 1749, 1747, 18794])).
% 9.38/9.70 tff(18802,plain,
% 9.38/9.70 (b(s(s(s(s(s(z))))), s(z))),
% 9.38/9.70 inference(unit_resolution,[status(thm)],[15766, 42, 15763, 18801])).
% 9.38/9.70 tff(18803,plain,
% 9.38/9.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 9.38/9.70 inference(rewrite,[status(thm)],[])).
% 9.38/9.70 tff(18804,plain,
% 9.38/9.70 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 9.48/9.70 inference(rewrite,[status(thm)],[])).
% 9.48/9.70 tff(18805,plain,
% 9.48/9.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 9.48/9.70 inference(monotonicity,[status(thm)],[18804])).
% 9.48/9.70 tff(18806,plain,
% 9.48/9.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 9.48/9.70 inference(transitivity,[status(thm)],[18805, 18803])).
% 9.48/9.70 tff(18807,plain,
% 9.48/9.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 9.48/9.70 inference(quant_inst,[status(thm)],[])).
% 9.48/9.70 tff(18808,plain,
% 9.48/9.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 9.48/9.70 inference(modus_ponens,[status(thm)],[18807, 18806])).
% 9.48/9.70 tff(18809,plain,
% 9.48/9.70 ($false),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[18808, 391, 1234, 1759, 664, 18783, 18802])).
% 9.48/9.70 tff(18810,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.70 tff(18811,plain,
% 9.48/9.70 (~b(s(s(s(s(s(z))))), z)),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[18810, 18782, 1234, 664, 18689, 18778, 18776, 18691])).
% 9.48/9.70 tff(18812,plain,
% 9.48/9.70 (r(s(s(s(s(s(z))))), z)),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[16530, 18811])).
% 9.48/9.70 tff(18813,plain,
% 9.48/9.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.48/9.70 inference(rewrite,[status(thm)],[])).
% 9.48/9.70 tff(18814,plain,
% 9.48/9.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.48/9.70 inference(quant_inst,[status(thm)],[])).
% 9.48/9.70 tff(18815,plain,
% 9.48/9.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 9.48/9.70 inference(modus_ponens,[status(thm)],[18814, 18813])).
% 9.48/9.70 tff(18816,plain,
% 9.48/9.70 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[18815, 194, 16441, 59, 18812])).
% 9.48/9.70 tff(18817,plain,
% 9.48/9.70 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 9.48/9.70 inference(transitivity,[status(thm)],[3818, 8492])).
% 9.48/9.70 tff(18818,plain,
% 9.48/9.70 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 9.48/9.70 inference(monotonicity,[status(thm)],[18817])).
% 9.48/9.70 tff(18819,plain,
% 9.48/9.70 (~(s(s(z)) = elem!1)),
% 9.48/9.70 inference(modus_ponens,[status(thm)],[1397, 18818])).
% 9.48/9.70 tff(18820,plain,
% 9.48/9.70 (~r(s(s(z)), elem!1)),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[6674, 18780, 1484, 847])).
% 9.48/9.70 tff(18821,plain,
% 9.48/9.70 (b(s(s(z)), elem!1)),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[4730, 18820, 18819])).
% 9.48/9.70 tff(18822,plain,
% 9.48/9.70 (~r(s(s(s(elem!1))), s(s(z)))),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[11551, 18780, 9968, 18778])).
% 9.48/9.70 tff(18823,plain,
% 9.48/9.70 (~r(elem!1, s(s(z)))),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[10022, 18822, 125])).
% 9.48/9.70 tff(18824,plain,
% 9.48/9.70 (b(elem!1, s(s(z)))),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[3394, 18823, 3820])).
% 9.48/9.70 tff(18825,plain,
% 9.48/9.70 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[11012, 18824, 1652, 18821])).
% 9.48/9.70 tff(18826,plain,
% 9.48/9.70 (r(s(s(s(s(z)))), s(s(z)))),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[1714, 18825])).
% 9.48/9.70 tff(18827,assumption,(r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 9.48/9.70 tff(18828,plain,
% 9.48/9.70 (~r(s(s(s(s(s(z))))), s(z))),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[18800, 194, 1749, 1747, 18827])).
% 9.48/9.70 tff(18829,plain,
% 9.48/9.70 (b(s(s(s(s(s(z))))), s(z))),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[15766, 42, 15763, 18828])).
% 9.48/9.70 tff(18830,plain,
% 9.48/9.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 9.48/9.70 inference(rewrite,[status(thm)],[])).
% 9.48/9.70 tff(18831,plain,
% 9.48/9.70 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 9.48/9.70 inference(rewrite,[status(thm)],[])).
% 9.48/9.70 tff(18832,plain,
% 9.48/9.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 9.48/9.70 inference(monotonicity,[status(thm)],[18831])).
% 9.48/9.70 tff(18833,plain,
% 9.48/9.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 9.48/9.70 inference(transitivity,[status(thm)],[18832, 18830])).
% 9.48/9.70 tff(18834,plain,
% 9.48/9.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 9.48/9.70 inference(quant_inst,[status(thm)],[])).
% 9.48/9.70 tff(18835,plain,
% 9.48/9.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 9.48/9.70 inference(modus_ponens,[status(thm)],[18834, 18833])).
% 9.48/9.70 tff(18836,plain,
% 9.48/9.70 ($false),
% 9.48/9.70 inference(unit_resolution,[status(thm)],[18835, 194, 1749, 1697, 15748, 18827])).
% 9.48/9.71 tff(18837,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.71 tff(18838,plain,
% 9.48/9.71 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18837, 18827, 1697, 1749])).
% 9.48/9.71 tff(18839,plain,
% 9.48/9.71 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[8761, 18838])).
% 9.48/9.71 tff(18840,plain,
% 9.48/9.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 9.48/9.71 inference(rewrite,[status(thm)],[])).
% 9.48/9.71 tff(18841,plain,
% 9.48/9.71 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 9.48/9.71 inference(rewrite,[status(thm)],[])).
% 9.48/9.71 tff(18842,plain,
% 9.48/9.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 9.48/9.71 inference(monotonicity,[status(thm)],[18841])).
% 9.48/9.71 tff(18843,plain,
% 9.48/9.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 9.48/9.71 inference(transitivity,[status(thm)],[18842, 18840])).
% 9.48/9.71 tff(18844,plain,
% 9.48/9.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 9.48/9.71 inference(quant_inst,[status(thm)],[])).
% 9.48/9.71 tff(18845,plain,
% 9.48/9.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 9.48/9.71 inference(modus_ponens,[status(thm)],[18844, 18843])).
% 9.48/9.71 tff(18846,plain,
% 9.48/9.71 ($false),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18845, 391, 1234, 1759, 18839, 18829])).
% 9.48/9.71 tff(18847,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.71 tff(18848,plain,
% 9.48/9.71 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18847, 18782, 1234, 18689, 18778, 18826])).
% 9.48/9.71 tff(18849,plain,
% 9.48/9.71 (b(s(s(s(s(s(z))))), s(s(z)))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[16516, 42, 8678, 18848])).
% 9.48/9.71 tff(18850,plain,
% 9.48/9.71 (b(s(s(s(elem!1))), s(s(z)))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[16425, 18824, 125])).
% 9.48/9.71 tff(18851,plain,
% 9.48/9.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.48/9.71 inference(rewrite,[status(thm)],[])).
% 9.48/9.71 tff(18852,plain,
% 9.48/9.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.48/9.71 inference(quant_inst,[status(thm)],[])).
% 9.48/9.71 tff(18853,plain,
% 9.48/9.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 9.48/9.71 inference(modus_ponens,[status(thm)],[18852, 18851])).
% 9.48/9.71 tff(18854,plain,
% 9.48/9.71 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18853, 391, 18691, 664, 18850, 18849])).
% 9.48/9.71 tff(18855,plain,
% 9.48/9.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 9.48/9.71 inference(rewrite,[status(thm)],[])).
% 9.48/9.71 tff(18856,plain,
% 9.48/9.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 9.48/9.71 inference(quant_inst,[status(thm)],[])).
% 9.48/9.71 tff(18857,plain,
% 9.48/9.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 9.48/9.71 inference(modus_ponens,[status(thm)],[18856, 18855])).
% 9.48/9.71 tff(18858,plain,
% 9.48/9.71 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18857, 42, 18854])).
% 9.48/9.71 tff(18859,plain,
% 9.48/9.71 ($false),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18858, 18816, 18774])).
% 9.48/9.71 tff(18860,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | (~r(elem!1, z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.71 tff(18861,plain,
% 9.48/9.71 (~(elem!1 = s(s(s(elem!1))))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18860, 5429, 1234, 2689, 664, 847, 590, 3447, 18656, 16830, 6221, 3222, 530, 10])).
% 9.48/9.71 tff(18862,plain,
% 9.48/9.71 (b(elem!1, s(s(s(elem!1))))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[424, 18861, 18658])).
% 9.48/9.71 tff(18863,plain,
% 9.48/9.71 (~(s(s(s(elem!1))) = elem!1)),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[8, 18861])).
% 9.48/9.71 tff(18864,plain,
% 9.48/9.71 (b(s(s(s(elem!1))), elem!1)),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[230, 18863, 225])).
% 9.48/9.71 tff(18865,plain,
% 9.48/9.71 ($false),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[16861, 18864, 18862, 3363, 59, 3447, 18656])).
% 9.48/9.71 tff(18866,plain,(b(s(z), elem!1) | r(s(s(s(elem!1))), elem!1) | (~b(s(z), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (~b(s(z), z)) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | (~r(elem!1, z)) | b(z, s(s(s(elem!1)))) | b(s(s(s(s(z)))), z) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.48/9.71 tff(18867,plain,
% 9.48/9.71 (b(s(z), elem!1)),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18866, 17034, 17033, 2680, 18654, 838, 10550, 8290, 18655, 3618, 10, 3446, 150])).
% 9.48/9.71 tff(18868,plain,
% 9.48/9.71 ($false),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18589, 6223, 6222, 644, 1234])).
% 9.48/9.71 tff(18869,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.48/9.71 tff(18870,plain,
% 9.48/9.71 (s(s(s(s(z)))) = elem!1),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18869, 18867, 17033, 18655, 17034])).
% 9.48/9.71 tff(18871,plain,
% 9.48/9.71 (~b(s(s(s(s(z)))), s(z))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[11186, 18870, 31])).
% 9.48/9.71 tff(18872,plain,
% 9.48/9.71 (~r(elem!1, s(s(s(s(z)))))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[17579, 194, 411, 3618, 2053])).
% 9.48/9.71 tff(18873,plain,
% 9.48/9.71 (~(s(s(s(elem!1))) = elem!1)),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[1436, 688])).
% 9.48/9.71 tff(18874,plain,
% 9.48/9.71 (~(elem!1 = s(s(s(elem!1))))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[129, 18873])).
% 9.48/9.71 tff(18875,plain,
% 9.48/9.71 (~(s(elem!1) = elem!1)),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[9227, 688])).
% 9.48/9.71 tff(18876,plain,
% 9.48/9.71 (~(elem!1 = s(elem!1))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[166, 18875])).
% 9.48/9.71 tff(18877,plain,
% 9.48/9.71 (~r(s(s(s(elem!1))), elem!1)),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[8289, 3618, 184, 411])).
% 9.48/9.71 tff(18878,plain,
% 9.48/9.71 (b(s(s(s(elem!1))), elem!1)),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[230, 18873, 18877])).
% 9.48/9.71 tff(18879,plain,
% 9.48/9.71 (~b(z, elem!1)),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[6505, 18878, 184, 150, 484, 18876, 18874, 2])).
% 9.48/9.71 tff(18880,plain,
% 9.48/9.71 (~b(z, s(s(s(s(z)))))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18671, 18879, 590, 1234, 14711, 18872])).
% 9.48/9.71 tff(18881,plain,
% 9.48/9.71 (r(z, s(s(s(s(z)))))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[800, 18880])).
% 9.48/9.71 tff(18882,plain,
% 9.48/9.71 (b(s(s(z)), elem!1)),
% 9.48/9.71 inference(modus_ponens,[status(thm)],[3823, 14383])).
% 9.48/9.71 tff(18883,plain,
% 9.48/9.71 (~r(s(s(s(elem!1))), s(z))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[15362, 3557, 184, 16058, 2053, 3823, 719])).
% 9.48/9.71 tff(18884,plain,
% 9.48/9.71 (b(s(s(s(elem!1))), s(z))),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[223, 18883])).
% 9.48/9.71 tff(18885,plain,
% 9.48/9.71 ($false),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[15345, 14771, 18884, 590, 3843, 664, 2053, 3557])).
% 9.48/9.71 tff(18886,plain,((~r(s(s(z)), z)) | (~b(s(z), z)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.71 tff(18887,plain,
% 9.48/9.71 (~r(s(s(z)), z)),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[18886, 3823, 3843, 664, 2053, 184, 590, 719])).
% 9.48/9.71 tff(18888,plain,
% 9.48/9.71 (b(s(s(z)), z)),
% 9.48/9.71 inference(unit_resolution,[status(thm)],[1211, 18887])).
% 9.48/9.71 tff(18889,plain,
% 9.48/9.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 9.48/9.71 inference(rewrite,[status(thm)],[])).
% 9.48/9.71 tff(18890,plain,
% 9.48/9.71 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 9.48/9.71 inference(rewrite,[status(thm)],[])).
% 9.48/9.71 tff(18891,plain,
% 9.48/9.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 9.48/9.71 inference(monotonicity,[status(thm)],[18890])).
% 9.48/9.71 tff(18892,plain,
% 9.48/9.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 9.48/9.72 inference(transitivity,[status(thm)],[18891, 18889])).
% 9.48/9.72 tff(18893,plain,
% 9.48/9.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 9.48/9.72 inference(quant_inst,[status(thm)],[])).
% 9.48/9.72 tff(18894,plain,
% 9.48/9.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 9.48/9.72 inference(modus_ponens,[status(thm)],[18893, 18892])).
% 9.48/9.72 tff(18895,plain,
% 9.48/9.72 (~b(s(s(z)), s(z))),
% 9.48/9.72 inference(unit_resolution,[status(thm)],[18894, 391, 644, 18888, 664, 590])).
% 9.48/9.72 tff(18896,plain,
% 9.48/9.72 (r(s(s(z)), s(z))),
% 9.48/9.72 inference(unit_resolution,[status(thm)],[3778, 18895])).
% 9.48/9.72 tff(18897,plain,
% 9.48/9.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 9.48/9.72 inference(rewrite,[status(thm)],[])).
% 9.48/9.72 tff(18898,plain,
% 9.48/9.72 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 9.48/9.72 inference(rewrite,[status(thm)],[])).
% 9.48/9.72 tff(18899,plain,
% 9.48/9.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 9.48/9.72 inference(monotonicity,[status(thm)],[18898])).
% 9.48/9.72 tff(18900,plain,
% 9.48/9.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 9.48/9.72 inference(transitivity,[status(thm)],[18899, 18897])).
% 9.48/9.72 tff(18901,plain,
% 9.48/9.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 9.48/9.72 inference(quant_inst,[status(thm)],[])).
% 9.48/9.72 tff(18902,plain,
% 9.48/9.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 9.48/9.72 inference(modus_ponens,[status(thm)],[18901, 18900])).
% 9.48/9.72 tff(18903,plain,
% 9.48/9.72 (~b(s(z), s(s(z)))),
% 9.48/9.72 inference(unit_resolution,[status(thm)],[18902, 391, 644, 18888, 664, 590])).
% 9.48/9.72 tff(18904,plain,
% 9.48/9.72 (r(s(z), s(s(z)))),
% 9.48/9.72 inference(unit_resolution,[status(thm)],[1788, 18903])).
% 9.48/9.72 tff(18905,plain,
% 9.48/9.72 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.48/9.72 inference(unit_resolution,[status(thm)],[10673, 18904, 723, 18896])).
% 9.48/9.72 tff(18906,plain,
% 9.48/9.72 (b(s(s(s(s(z)))), s(s(z)))),
% 9.48/9.72 inference(unit_resolution,[status(thm)],[1714, 18905])).
% 9.48/9.72 tff(18907,plain,
% 9.48/9.72 (b(elem!1, s(s(z)))),
% 9.48/9.72 inference(unit_resolution,[status(thm)],[11029, 18906, 688])).
% 9.48/9.72 tff(18908,plain,
% 9.48/9.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 9.48/9.72 inference(rewrite,[status(thm)],[])).
% 9.48/9.72 tff(18909,plain,
% 9.48/9.72 (((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 9.48/9.72 inference(rewrite,[status(thm)],[])).
% 9.48/9.72 tff(18910,plain,
% 9.48/9.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))))),
% 9.48/9.72 inference(monotonicity,[status(thm)],[18909])).
% 9.48/9.72 tff(18911,plain,
% 9.48/9.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 9.48/9.72 inference(transitivity,[status(thm)],[18910, 18908])).
% 9.48/9.72 tff(18912,plain,
% 9.48/9.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.48/9.72 inference(quant_inst,[status(thm)],[])).
% 9.48/9.72 tff(18913,plain,
% 9.48/9.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))),
% 9.48/9.72 inference(modus_ponens,[status(thm)],[18912, 18911])).
% 9.48/9.72 tff(18914,plain,
% 9.48/9.72 (~b(s(s(z)), s(s(s(elem!1))))),
% 9.48/9.72 inference(unit_resolution,[status(thm)],[18913, 391, 900, 18888, 18907, 18882])).
% 9.48/9.72 tff(18915,plain,
% 9.48/9.72 (r(s(s(z)), s(s(s(elem!1))))),
% 9.48/9.72 inference(unit_resolution,[status(thm)],[11041, 18914])).
% 9.48/9.72 tff(18916,plain,
% 9.48/9.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 9.48/9.72 inference(rewrite,[status(thm)],[])).
% 9.48/9.72 tff(18917,plain,
% 9.48/9.72 (((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 9.48/9.72 inference(rewrite,[status(thm)],[])).
% 9.48/9.72 tff(18918,plain,
% 9.48/9.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 9.48/9.73 inference(monotonicity,[status(thm)],[18917])).
% 9.48/9.73 tff(18919,plain,
% 9.48/9.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 9.48/9.73 inference(transitivity,[status(thm)],[18918, 18916])).
% 9.48/9.73 tff(18920,plain,
% 9.48/9.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.48/9.73 inference(quant_inst,[status(thm)],[])).
% 9.48/9.73 tff(18921,plain,
% 9.48/9.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 9.48/9.73 inference(modus_ponens,[status(thm)],[18920, 18919])).
% 9.48/9.73 tff(18922,plain,
% 9.48/9.73 (~b(s(s(s(elem!1))), s(z))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[18921, 391, 900, 644, 18888, 18907])).
% 9.48/9.73 tff(18923,plain,
% 9.48/9.73 (r(s(s(s(elem!1))), s(z))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[223, 18922])).
% 9.48/9.73 tff(18924,plain,
% 9.48/9.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 9.48/9.73 inference(rewrite,[status(thm)],[])).
% 9.48/9.73 tff(18925,plain,
% 9.48/9.73 (((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 9.48/9.73 inference(rewrite,[status(thm)],[])).
% 9.48/9.73 tff(18926,plain,
% 9.48/9.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))))),
% 9.48/9.73 inference(monotonicity,[status(thm)],[18925])).
% 9.48/9.73 tff(18927,plain,
% 9.48/9.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)))),
% 9.48/9.73 inference(transitivity,[status(thm)],[18926, 18924])).
% 9.48/9.73 tff(18928,plain,
% 9.48/9.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 9.48/9.73 inference(quant_inst,[status(thm)],[])).
% 9.48/9.73 tff(18929,plain,
% 9.48/9.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z))),
% 9.48/9.73 inference(modus_ponens,[status(thm)],[18928, 18927])).
% 9.48/9.73 tff(18930,plain,
% 9.48/9.73 (~b(s(z), s(s(s(elem!1))))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[18929, 391, 900, 644, 18888, 18907])).
% 9.48/9.73 tff(18931,plain,
% 9.48/9.73 (r(s(z), s(s(s(elem!1))))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[247, 18930])).
% 9.48/9.73 tff(18932,plain,
% 9.48/9.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 9.48/9.73 inference(rewrite,[status(thm)],[])).
% 9.48/9.73 tff(18933,plain,
% 9.48/9.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 9.48/9.73 inference(quant_inst,[status(thm)],[])).
% 9.48/9.73 tff(18934,plain,
% 9.48/9.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 9.48/9.73 inference(modus_ponens,[status(thm)],[18933, 18932])).
% 9.48/9.73 tff(18935,plain,
% 9.48/9.73 ($false),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[18934, 194, 18931, 18923, 18896, 18915])).
% 9.48/9.73 tff(18936,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.73 tff(18937,plain,
% 9.48/9.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[18936, 18878, 644, 688, 723, 664, 590, 3363, 2053, 184, 18881])).
% 9.48/9.73 tff(18938,plain,
% 9.48/9.73 (r(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[3652, 18937])).
% 9.48/9.73 tff(18939,plain,
% 9.48/9.73 (r(s(s(z)), elem!1)),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[5152, 18938, 688])).
% 9.48/9.73 tff(18940,plain,
% 9.48/9.73 (~r(z, s(s(z)))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[8513, 18939, 3618, 411])).
% 9.48/9.73 tff(18941,plain,
% 9.48/9.73 (~r(s(s(z)), z)),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[14746, 18938, 2053, 184])).
% 9.48/9.73 tff(18942,plain,
% 9.48/9.73 (b(s(s(z)), z)),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[1211, 18941])).
% 9.48/9.73 tff(18943,plain,
% 9.48/9.73 (~b(z, s(s(z)))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[17567, 18942, 644, 14711, 715, 847, 18938, 590])).
% 9.48/9.73 tff(18944,plain,
% 9.48/9.73 ($false),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[18613, 18943, 18940])).
% 9.48/9.73 tff(18945,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (s(z) = elem!1) | b(elem!1, z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 9.48/9.73 tff(18946,plain,
% 9.48/9.73 (~r(s(s(s(s(z)))), s(z))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[18945, 18870, 838, 10550, 8232, 3447, 59, 18867, 18654, 17033, 150, 484, 2])).
% 9.48/9.73 tff(18947,plain,
% 9.48/9.73 ($false),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[749, 18946, 18871])).
% 9.48/9.73 tff(18948,plain,(b(s(s(s(s(z)))), z) | (s(z) = elem!1) | b(elem!1, z) | (elem!1 = z) | b(elem!1, s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.73 tff(18949,plain,
% 9.48/9.73 (b(s(s(s(s(z)))), z)),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[18948, 150, 484, 2, 31, 10])).
% 9.48/9.73 tff(18950,plain,
% 9.48/9.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.48/9.73 inference(rewrite,[status(thm)],[])).
% 9.48/9.73 tff(18951,plain,
% 9.48/9.73 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.48/9.73 inference(rewrite,[status(thm)],[])).
% 9.48/9.73 tff(18952,plain,
% 9.48/9.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 9.48/9.73 inference(monotonicity,[status(thm)],[18951])).
% 9.48/9.73 tff(18953,plain,
% 9.48/9.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.48/9.73 inference(transitivity,[status(thm)],[18952, 18950])).
% 9.48/9.73 tff(18954,plain,
% 9.48/9.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.48/9.73 inference(quant_inst,[status(thm)],[])).
% 9.48/9.73 tff(18955,plain,
% 9.48/9.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 9.48/9.73 inference(modus_ponens,[status(thm)],[18954, 18953])).
% 9.48/9.73 tff(18956,plain,
% 9.48/9.73 ($false),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[18955, 391, 18949, 17033, 18654, 10550])).
% 9.48/9.73 tff(18957,plain,((s(z) = elem!1) | b(elem!1, z) | (elem!1 = z) | b(elem!1, s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.73 tff(18958,plain,
% 9.48/9.73 (s(z) = elem!1),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[18957, 484, 2, 31, 10])).
% 9.48/9.73 tff(18959,plain,
% 9.48/9.73 (b(s(z), z) <=> b(elem!1, z)),
% 9.48/9.73 inference(monotonicity,[status(thm)],[18958])).
% 9.48/9.73 tff(18960,plain,
% 9.48/9.73 (b(elem!1, z) <=> b(s(z), z)),
% 9.48/9.73 inference(symmetry,[status(thm)],[18959])).
% 9.48/9.73 tff(18961,plain,
% 9.48/9.73 ((~b(elem!1, z)) <=> (~b(s(z), z))),
% 9.48/9.73 inference(monotonicity,[status(thm)],[18960])).
% 9.48/9.73 tff(18962,plain,
% 9.48/9.73 (~b(s(z), z)),
% 9.48/9.73 inference(modus_ponens,[status(thm)],[484, 18961])).
% 9.48/9.73 tff(18963,plain,
% 9.48/9.73 ($false),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[10550, 18962])).
% 9.48/9.73 tff(18964,plain,(b(elem!1, z) | (elem!1 = z) | b(elem!1, s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.73 tff(18965,plain,
% 9.48/9.73 (b(elem!1, z)),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[18964, 31, 2, 10])).
% 9.48/9.73 tff(18966,plain,
% 9.48/9.73 (s(s(s(elem!1))) = elem!1),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[158, 152])).
% 9.48/9.73 tff(18967,plain,
% 9.48/9.73 (~b(s(s(s(elem!1))), s(z))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[8400, 18966, 31])).
% 9.48/9.73 tff(18968,plain,
% 9.48/9.73 (~r(s(s(s(elem!1))), s(z))),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[15095, 9221, 184, 665, 411, 18966])).
% 9.48/9.73 tff(18969,plain,
% 9.48/9.73 ($false),
% 9.48/9.73 inference(unit_resolution,[status(thm)],[223, 18968, 18967])).
% 9.48/9.74 tff(18970,plain,((~(s(elem!1) = elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~r(z, elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.74 tff(18971,plain,
% 9.48/9.74 (~(s(elem!1) = elem!1)),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[18970, 18965, 59, 8232, 31])).
% 9.48/9.74 tff(18972,plain,
% 9.48/9.74 (~b(s(z), s(s(s(elem!1))))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[2884, 7866, 2881])).
% 9.48/9.74 tff(18973,plain,
% 9.48/9.74 (r(s(z), s(s(s(elem!1))))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[247, 18972])).
% 9.48/9.74 tff(18974,plain,
% 9.48/9.74 (r(elem!1, s(s(s(elem!1))))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[2570, 18973, 812])).
% 9.48/9.74 tff(18975,plain,
% 9.48/9.74 (r(z, s(s(s(s(z)))))),
% 9.48/9.74 inference(modus_ponens,[status(thm)],[59, 826])).
% 9.48/9.74 tff(18976,plain,
% 9.48/9.74 (r(elem!1, s(s(s(s(z)))))),
% 9.48/9.74 inference(modus_ponens,[status(thm)],[2913, 7403])).
% 9.48/9.74 tff(18977,plain,
% 9.48/9.74 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[15016, 18976, 8232, 18975])).
% 9.48/9.74 tff(18978,plain,
% 9.48/9.74 (b(s(s(s(s(z)))), s(s(z)))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[1714, 18977])).
% 9.48/9.74 tff(18979,plain,
% 9.48/9.74 (~r(s(s(s(s(z)))), z)),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[10620, 722, 2913])).
% 9.48/9.74 tff(18980,plain,
% 9.48/9.74 (b(s(s(s(s(z)))), z)),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[87, 18979])).
% 9.48/9.74 tff(18981,plain,
% 9.48/9.74 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 9.48/9.74 inference(monotonicity,[status(thm)],[818])).
% 9.48/9.74 tff(18982,plain,
% 9.48/9.74 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 9.48/9.74 inference(symmetry,[status(thm)],[18981])).
% 9.48/9.74 tff(18983,plain,
% 9.48/9.74 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 9.48/9.74 inference(monotonicity,[status(thm)],[820])).
% 9.48/9.74 tff(18984,plain,
% 9.48/9.74 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 9.48/9.74 inference(monotonicity,[status(thm)],[818])).
% 9.48/9.74 tff(18985,plain,
% 9.48/9.74 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 9.48/9.74 inference(transitivity,[status(thm)],[18984, 18983, 18982])).
% 9.48/9.74 tff(18986,plain,
% 9.48/9.74 (b(s(s(s(elem!1))), s(s(z)))),
% 9.48/9.74 inference(modus_ponens,[status(thm)],[18978, 18985])).
% 9.48/9.74 tff(18987,plain,
% 9.48/9.74 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 9.48/9.74 inference(monotonicity,[status(thm)],[812])).
% 9.48/9.74 tff(18988,plain,
% 9.48/9.74 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 9.48/9.74 inference(symmetry,[status(thm)],[18987])).
% 9.48/9.74 tff(18989,plain,
% 9.48/9.74 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), s(z)))),
% 9.48/9.74 inference(monotonicity,[status(thm)],[18988])).
% 9.48/9.74 tff(18990,plain,
% 9.48/9.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 9.48/9.74 inference(rewrite,[status(thm)],[])).
% 9.48/9.74 tff(18991,plain,
% 9.48/9.74 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 9.48/9.74 inference(rewrite,[status(thm)],[])).
% 9.48/9.74 tff(18992,plain,
% 9.48/9.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 9.48/9.74 inference(monotonicity,[status(thm)],[18991])).
% 9.48/9.74 tff(18993,plain,
% 9.48/9.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 9.48/9.74 inference(transitivity,[status(thm)],[18992, 18990])).
% 9.48/9.74 tff(18994,plain,
% 9.48/9.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 9.48/9.74 inference(quant_inst,[status(thm)],[])).
% 9.48/9.74 tff(18995,plain,
% 9.48/9.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 9.48/9.74 inference(modus_ponens,[status(thm)],[18994, 18993])).
% 9.48/9.74 tff(18996,plain,
% 9.48/9.74 ($false),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[18995, 194, 233, 184, 232, 722])).
% 9.48/9.74 tff(18997,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.74 tff(18998,plain,
% 9.48/9.74 (~r(s(s(s(elem!1))), elem!1)),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[18997, 18973, 59, 722])).
% 9.48/9.74 tff(18999,plain,
% 9.48/9.74 (~r(s(s(s(elem!1))), s(z))),
% 9.48/9.74 inference(modus_ponens,[status(thm)],[18998, 18989])).
% 9.48/9.74 tff(19000,plain,
% 9.48/9.74 (b(s(s(s(elem!1))), s(z))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[223, 18999])).
% 9.48/9.74 tff(19001,plain,
% 9.48/9.74 (b(s(s(s(elem!1))), elem!1)),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[228, 42, 18998, 7457])).
% 9.48/9.74 tff(19002,plain,
% 9.48/9.74 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[17255, 18974, 10, 2])).
% 9.48/9.74 tff(19003,plain,
% 9.48/9.74 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[8251, 7457])).
% 9.48/9.74 tff(19004,plain,
% 9.48/9.74 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[1370, 19003, 19002])).
% 9.48/9.74 tff(19005,plain,
% 9.48/9.74 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 9.48/9.74 inference(transitivity,[status(thm)],[18984, 18983])).
% 9.48/9.74 tff(19006,plain,
% 9.48/9.74 (b(s(s(s(elem!1))), s(elem!1))),
% 9.48/9.74 inference(modus_ponens,[status(thm)],[18978, 19005])).
% 9.48/9.74 tff(19007,plain,
% 9.48/9.74 (~r(s(s(z)), s(z))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[10610, 3557, 1216, 722])).
% 9.48/9.74 tff(19008,plain,
% 9.48/9.74 (b(s(s(z)), s(z))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[3778, 19007])).
% 9.48/9.74 tff(19009,plain,
% 9.48/9.74 (b(s(elem!1), elem!1)),
% 9.48/9.74 inference(modus_ponens,[status(thm)],[19008, 7399])).
% 9.48/9.74 tff(19010,plain,
% 9.48/9.74 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 9.48/9.74 inference(transitivity,[status(thm)],[9732, 9731])).
% 9.48/9.74 tff(19011,plain,
% 9.48/9.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.48/9.74 inference(rewrite,[status(thm)],[])).
% 9.48/9.74 tff(19012,plain,
% 9.48/9.74 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.48/9.74 inference(rewrite,[status(thm)],[])).
% 9.48/9.74 tff(19013,plain,
% 9.48/9.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 9.48/9.74 inference(monotonicity,[status(thm)],[19012])).
% 9.48/9.74 tff(19014,plain,
% 9.48/9.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.48/9.74 inference(transitivity,[status(thm)],[19013, 19011])).
% 9.48/9.74 tff(19015,plain,
% 9.48/9.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.48/9.74 inference(quant_inst,[status(thm)],[])).
% 9.48/9.74 tff(19016,plain,
% 9.48/9.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 9.48/9.74 inference(modus_ponens,[status(thm)],[19015, 19014])).
% 9.48/9.74 tff(19017,plain,
% 9.48/9.74 ($false),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[19016, 391, 1526, 2439, 1233, 17493])).
% 9.48/9.74 tff(19018,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.74 tff(19019,plain,
% 9.48/9.74 (~b(s(z), s(s(z)))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[19018, 19008, 1526, 17493])).
% 9.48/9.74 tff(19020,plain,
% 9.48/9.74 (r(s(z), s(s(z)))),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[1788, 19019])).
% 9.48/9.74 tff(19021,plain,
% 9.48/9.74 (r(elem!1, s(elem!1))),
% 9.48/9.74 inference(modus_ponens,[status(thm)],[19020, 19010])).
% 9.48/9.74 tff(19022,plain,
% 9.48/9.74 (r(s(elem!1), z)),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[3560, 3557, 812])).
% 9.48/9.74 tff(19023,plain,
% 9.48/9.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 9.48/9.74 inference(rewrite,[status(thm)],[])).
% 9.48/9.74 tff(19024,plain,
% 9.48/9.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 9.48/9.74 inference(quant_inst,[status(thm)],[])).
% 9.48/9.74 tff(19025,plain,
% 9.48/9.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 9.48/9.74 inference(modus_ponens,[status(thm)],[19024, 19023])).
% 9.48/9.74 tff(19026,plain,
% 9.48/9.74 (~r(s(s(elem!1)), elem!1)),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[19025, 194, 1628, 2251, 2170])).
% 9.48/9.74 tff(19027,plain,
% 9.48/9.74 (b(s(s(elem!1)), elem!1)),
% 9.48/9.74 inference(unit_resolution,[status(thm)],[872, 19026, 249])).
% 9.48/9.74 tff(19028,plain,
% 9.48/9.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 9.48/9.74 inference(rewrite,[status(thm)],[])).
% 9.48/9.74 tff(19029,plain,
% 9.48/9.74 (((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 9.48/9.74 inference(rewrite,[status(thm)],[])).
% 9.48/9.74 tff(19030,plain,
% 9.48/9.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))))),
% 9.48/9.75 inference(monotonicity,[status(thm)],[19029])).
% 9.48/9.75 tff(19031,plain,
% 9.48/9.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 9.48/9.75 inference(transitivity,[status(thm)],[19030, 19028])).
% 9.48/9.75 tff(19032,plain,
% 9.48/9.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 9.48/9.75 inference(quant_inst,[status(thm)],[])).
% 9.48/9.75 tff(19033,plain,
% 9.48/9.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))),
% 9.48/9.75 inference(modus_ponens,[status(thm)],[19032, 19031])).
% 9.48/9.75 tff(19034,plain,
% 9.48/9.75 (~r(elem!1, s(s(elem!1)))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[19033, 194, 1628, 2251, 2170])).
% 9.48/9.75 tff(19035,plain,
% 9.48/9.75 (b(elem!1, s(s(elem!1)))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[1307, 19034, 1457])).
% 9.48/9.75 tff(19036,plain,
% 9.48/9.75 ($false),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[1467, 19035, 19027, 1374, 900])).
% 9.48/9.75 tff(19037,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.75 tff(19038,plain,
% 9.48/9.75 (~r(s(s(elem!1)), s(elem!1))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[19037, 19022, 900, 9651, 7422, 1374, 19021])).
% 9.48/9.75 tff(19039,plain,
% 9.48/9.75 (b(s(s(elem!1)), s(elem!1))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[1135, 19038, 285])).
% 9.48/9.75 tff(19040,plain,
% 9.48/9.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~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)))))),
% 9.48/9.75 inference(rewrite,[status(thm)],[])).
% 9.48/9.75 tff(19041,plain,
% 9.48/9.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~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)))))),
% 9.48/9.75 inference(quant_inst,[status(thm)],[])).
% 9.48/9.75 tff(19042,plain,
% 9.48/9.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 9.48/9.75 inference(modus_ponens,[status(thm)],[19041, 19040])).
% 9.48/9.75 tff(19043,plain,
% 9.48/9.75 ($false),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[19042, 391, 665, 1101, 1374, 19039, 19009])).
% 9.48/9.75 tff(19044,plain,((~r(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.75 tff(19045,plain,
% 9.48/9.75 (~r(s(s(z)), z)),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[19044, 19006, 665, 19004, 7412, 19001, 812, 19000, 18986, 2913, 722])).
% 9.48/9.75 tff(19046,plain,
% 9.48/9.75 (b(s(s(z)), z)),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[1211, 19045])).
% 9.48/9.75 tff(19047,plain,
% 9.48/9.75 (~b(z, s(s(z)))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[15053, 19046, 18980, 18978])).
% 9.48/9.75 tff(19048,plain,
% 9.48/9.75 (~b(z, s(elem!1))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[8527, 19047, 812])).
% 9.48/9.75 tff(19049,plain,
% 9.48/9.75 (r(z, s(elem!1))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[566, 19048])).
% 9.48/9.75 tff(19050,plain,
% 9.48/9.75 (~r(s(s(s(s(z)))), elem!1)),
% 9.48/9.75 inference(modus_ponens,[status(thm)],[18998, 7845])).
% 9.48/9.75 tff(19051,plain,
% 9.48/9.75 (b(s(s(s(s(z)))), elem!1)),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[762, 19050, 7853])).
% 9.48/9.75 tff(19052,plain,
% 9.48/9.75 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 9.48/9.75 inference(monotonicity,[status(thm)],[10746])).
% 9.48/9.75 tff(19053,plain,
% 9.48/9.75 (~(elem!1 = s(s(z)))),
% 9.48/9.75 inference(modus_ponens,[status(thm)],[1783, 19052])).
% 9.48/9.75 tff(19054,plain,
% 9.48/9.75 (r(z, s(s(z)))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[18613, 19047])).
% 9.48/9.75 tff(19055,plain,
% 9.48/9.75 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(s(z)))), s(z)))),
% 9.48/9.75 inference(monotonicity,[status(thm)],[823])).
% 9.48/9.75 tff(19056,plain,
% 9.48/9.75 (~r(s(s(s(s(z)))), s(z))),
% 9.48/9.75 inference(modus_ponens,[status(thm)],[18998, 19055])).
% 9.48/9.75 tff(19057,plain,
% 9.48/9.75 (b(s(s(s(s(z)))), s(z))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[749, 19056])).
% 9.48/9.75 tff(19058,plain,
% 9.48/9.75 (b(s(elem!1), z)),
% 9.48/9.75 inference(modus_ponens,[status(thm)],[19046, 9630])).
% 9.48/9.75 tff(19059,plain,
% 9.48/9.75 (~r(s(s(s(elem!1))), z)),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[5980, 18973, 59, 722])).
% 9.48/9.75 tff(19060,plain,
% 9.48/9.75 (b(s(s(s(elem!1))), z)),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[377, 19059])).
% 9.48/9.75 tff(19061,plain,
% 9.48/9.75 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 9.48/9.75 inference(monotonicity,[status(thm)],[820, 8079])).
% 9.48/9.75 tff(19062,plain,
% 9.48/9.75 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 9.48/9.75 inference(monotonicity,[status(thm)],[19061])).
% 9.48/9.75 tff(19063,plain,
% 9.48/9.75 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 9.48/9.75 inference(modus_ponens,[status(thm)],[8755, 19062])).
% 9.48/9.75 tff(19064,plain,
% 9.48/9.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.48/9.75 inference(rewrite,[status(thm)],[])).
% 9.48/9.75 tff(19065,plain,
% 9.48/9.75 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.48/9.75 inference(rewrite,[status(thm)],[])).
% 9.48/9.75 tff(19066,plain,
% 9.48/9.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 9.48/9.75 inference(monotonicity,[status(thm)],[19065])).
% 9.48/9.75 tff(19067,plain,
% 9.48/9.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.48/9.75 inference(transitivity,[status(thm)],[19066, 19064])).
% 9.48/9.75 tff(19068,plain,
% 9.48/9.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 9.48/9.75 inference(quant_inst,[status(thm)],[])).
% 9.48/9.75 tff(19069,plain,
% 9.48/9.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 9.48/9.75 inference(modus_ponens,[status(thm)],[19068, 19067])).
% 9.48/9.75 tff(19070,plain,
% 9.48/9.75 ($false),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[19069, 194, 411, 184, 410, 1538])).
% 9.48/9.75 tff(19071,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.75 tff(19072,plain,
% 9.48/9.75 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[19071, 18974, 59, 8232])).
% 9.48/9.75 tff(19073,plain,
% 9.48/9.75 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.48/9.75 inference(unit_resolution,[status(thm)],[1164, 19072, 19063])).
% 9.48/9.75 tff(19074,plain,
% 9.48/9.75 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 9.48/9.75 inference(transitivity,[status(thm)],[18083, 8666])).
% 9.48/9.75 tff(19075,plain,
% 9.48/9.75 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 9.48/9.75 inference(monotonicity,[status(thm)],[19074])).
% 9.48/9.75 tff(19076,plain,
% 9.48/9.75 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 9.48/9.75 inference(modus_ponens,[status(thm)],[8678, 19075])).
% 9.48/9.75 tff(19077,plain,
% 9.48/9.75 (b(s(elem!1), s(s(s(elem!1))))),
% 9.48/9.75 inference(modus_ponens,[status(thm)],[3823, 9785])).
% 9.48/9.75 tff(19078,plain,
% 9.48/9.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 9.48/9.76 inference(rewrite,[status(thm)],[])).
% 9.48/9.76 tff(19079,plain,
% 9.48/9.76 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 9.48/9.76 inference(rewrite,[status(thm)],[])).
% 9.48/9.76 tff(19080,plain,
% 9.48/9.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 9.48/9.76 inference(monotonicity,[status(thm)],[19079])).
% 9.48/9.76 tff(19081,plain,
% 9.48/9.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 9.48/9.76 inference(transitivity,[status(thm)],[19080, 19078])).
% 9.48/9.76 tff(19082,plain,
% 9.48/9.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 9.48/9.76 inference(quant_inst,[status(thm)],[])).
% 9.48/9.76 tff(19083,plain,
% 9.48/9.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 9.48/9.76 inference(modus_ponens,[status(thm)],[19082, 19081])).
% 9.48/9.76 tff(19084,plain,
% 9.48/9.76 ($false),
% 9.48/9.76 inference(unit_resolution,[status(thm)],[19083, 391, 3823, 90, 1759, 2439, 3563])).
% 9.48/9.76 tff(19085,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.76 tff(19086,plain,
% 9.48/9.76 (~b(s(z), s(s(z)))),
% 9.48/9.76 inference(unit_resolution,[status(thm)],[19085, 3823, 90, 1759, 3563])).
% 9.48/9.76 tff(19087,plain,
% 9.48/9.76 (r(s(z), s(s(z)))),
% 9.48/9.76 inference(unit_resolution,[status(thm)],[1788, 19086])).
% 9.48/9.76 tff(19088,plain,
% 9.48/9.76 (~r(s(s(z)), s(z))),
% 9.48/9.76 inference(unit_resolution,[status(thm)],[9720, 19087, 722, 8505])).
% 9.48/9.76 tff(19089,plain,
% 9.48/9.76 (b(s(s(z)), s(z))),
% 9.48/9.76 inference(unit_resolution,[status(thm)],[3778, 19088])).
% 9.48/9.76 tff(19090,plain,
% 9.48/9.76 (b(s(elem!1), elem!1)),
% 9.48/9.76 inference(modus_ponens,[status(thm)],[19089, 7399])).
% 9.48/9.76 tff(19091,plain,
% 9.48/9.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 9.48/9.76 inference(rewrite,[status(thm)],[])).
% 9.48/9.76 tff(19092,plain,
% 9.48/9.76 (((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 9.48/9.76 inference(rewrite,[status(thm)],[])).
% 9.48/9.76 tff(19093,plain,
% 9.48/9.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 9.48/9.76 inference(monotonicity,[status(thm)],[19092])).
% 9.48/9.76 tff(19094,plain,
% 9.48/9.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 9.48/9.76 inference(transitivity,[status(thm)],[19093, 19091])).
% 9.48/9.76 tff(19095,plain,
% 9.48/9.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 9.48/9.76 inference(quant_inst,[status(thm)],[])).
% 9.48/9.76 tff(19096,plain,
% 9.48/9.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 9.48/9.76 inference(modus_ponens,[status(thm)],[19095, 19094])).
% 9.48/9.76 tff(19097,plain,
% 9.48/9.76 ($false),
% 9.48/9.76 inference(unit_resolution,[status(thm)],[19096, 391, 665, 900, 3927, 2122, 1036])).
% 9.48/9.76 tff(19098,plain,((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~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,[]))).
% 9.48/9.76 tff(19099,plain,
% 9.48/9.76 (~b(z, s(s(elem!1)))),
% 9.48/9.76 inference(unit_resolution,[status(thm)],[19098, 19090, 900, 665, 19077])).
% 9.48/9.76 tff(19100,plain,
% 9.48/9.76 (r(z, s(s(elem!1)))),
% 9.48/9.76 inference(unit_resolution,[status(thm)],[324, 19099])).
% 9.48/9.76 tff(19101,plain,
% 9.48/9.76 (r(elem!1, s(elem!1))),
% 9.48/9.76 inference(modus_ponens,[status(thm)],[19087, 19010])).
% 9.48/9.76 tff(19102,plain,
% 9.48/9.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.76 inference(rewrite,[status(thm)],[])).
% 9.48/9.76 tff(19103,plain,
% 9.48/9.76 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.76 inference(rewrite,[status(thm)],[])).
% 9.48/9.76 tff(19104,plain,
% 9.48/9.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 9.48/9.76 inference(monotonicity,[status(thm)],[19103])).
% 9.48/9.76 tff(19105,plain,
% 9.48/9.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.76 inference(transitivity,[status(thm)],[19104, 19102])).
% 9.48/9.76 tff(19106,plain,
% 9.48/9.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 9.48/9.76 inference(quant_inst,[status(thm)],[])).
% 9.48/9.76 tff(19107,plain,
% 9.48/9.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 9.48/9.76 inference(modus_ponens,[status(thm)],[19106, 19105])).
% 9.48/9.76 tff(19108,plain,
% 9.48/9.76 (~r(s(s(s(s(elem!1)))), z)),
% 9.48/9.76 inference(unit_resolution,[status(thm)],[19107, 194, 411, 2251, 991])).
% 9.48/9.76 tff(19109,plain,
% 9.48/9.76 (b(s(s(s(s(elem!1)))), z)),
% 9.48/9.76 inference(unit_resolution,[status(thm)],[1626, 19108])).
% 9.48/9.76 tff(19110,plain,
% 9.48/9.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.76 inference(rewrite,[status(thm)],[])).
% 9.48/9.76 tff(19111,plain,
% 9.48/9.76 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.76 inference(rewrite,[status(thm)],[])).
% 9.48/9.76 tff(19112,plain,
% 9.48/9.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 9.48/9.77 inference(monotonicity,[status(thm)],[19111])).
% 9.48/9.77 tff(19113,plain,
% 9.48/9.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.77 inference(transitivity,[status(thm)],[19112, 19110])).
% 9.48/9.77 tff(19114,plain,
% 9.48/9.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 9.48/9.77 inference(quant_inst,[status(thm)],[])).
% 9.48/9.77 tff(19115,plain,
% 9.48/9.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 9.48/9.77 inference(modus_ponens,[status(thm)],[19114, 19113])).
% 9.48/9.77 tff(19116,plain,
% 9.48/9.77 (~r(z, s(s(s(s(elem!1)))))),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[19115, 194, 411, 2251, 991])).
% 9.48/9.77 tff(19117,plain,
% 9.48/9.77 (b(z, s(s(s(s(elem!1)))))),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[2767, 19116])).
% 9.48/9.77 tff(19118,plain,
% 9.48/9.77 ($false),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[17919, 19117, 19109, 665, 2122, 591])).
% 9.48/9.77 tff(19119,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.77 tff(19120,plain,
% 9.48/9.77 (~r(s(s(s(s(elem!1)))), elem!1)),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[19119, 19090, 665, 591, 411, 19101])).
% 9.48/9.77 tff(19121,plain,
% 9.48/9.77 (b(s(s(s(s(elem!1)))), elem!1)),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[1004, 19120, 7473])).
% 9.48/9.77 tff(19122,plain,
% 9.48/9.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.77 inference(rewrite,[status(thm)],[])).
% 9.48/9.77 tff(19123,plain,
% 9.48/9.77 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.77 inference(rewrite,[status(thm)],[])).
% 9.48/9.77 tff(19124,plain,
% 9.48/9.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 9.48/9.77 inference(monotonicity,[status(thm)],[19123])).
% 9.48/9.77 tff(19125,plain,
% 9.48/9.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.77 inference(transitivity,[status(thm)],[19124, 19122])).
% 9.48/9.77 tff(19126,plain,
% 9.48/9.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 9.48/9.77 inference(quant_inst,[status(thm)],[])).
% 9.48/9.77 tff(19127,plain,
% 9.48/9.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 9.48/9.77 inference(modus_ponens,[status(thm)],[19126, 19125])).
% 9.48/9.77 tff(19128,plain,
% 9.48/9.77 ($false),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[19127, 391, 380, 591, 2698, 2781, 1036])).
% 9.48/9.77 tff(19129,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.77 tff(19130,plain,
% 9.48/9.77 (~b(z, s(s(s(s(elem!1)))))),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[19129, 19121, 380, 19077, 591])).
% 9.48/9.77 tff(19131,plain,
% 9.48/9.77 (r(z, s(s(s(s(elem!1)))))),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[2767, 19130])).
% 9.48/9.77 tff(19132,plain,
% 9.48/9.77 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 9.48/9.77 inference(monotonicity,[status(thm)],[8079])).
% 9.48/9.77 tff(19133,plain,
% 9.48/9.77 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 9.48/9.77 inference(transitivity,[status(thm)],[19132, 1021])).
% 9.48/9.77 tff(19134,plain,
% 9.48/9.77 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 9.48/9.77 inference(monotonicity,[status(thm)],[19133])).
% 9.48/9.77 tff(19135,plain,
% 9.48/9.77 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 9.48/9.77 inference(commutativity,[status(thm)],[])).
% 9.48/9.77 tff(19136,plain,
% 9.48/9.77 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 9.48/9.77 inference(monotonicity,[status(thm)],[819])).
% 9.48/9.77 tff(19137,plain,
% 9.48/9.77 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 9.48/9.77 inference(transitivity,[status(thm)],[19136, 19135])).
% 9.48/9.77 tff(19138,plain,
% 9.48/9.77 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(elem!1))))),
% 9.48/9.77 inference(monotonicity,[status(thm)],[19137])).
% 9.48/9.77 tff(19139,plain,
% 9.48/9.77 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 9.48/9.77 inference(modus_ponens,[status(thm)],[8593, 19138])).
% 9.48/9.77 tff(19140,plain,
% 9.48/9.77 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 9.48/9.77 inference(modus_ponens,[status(thm)],[19139, 19134])).
% 9.48/9.77 tff(19141,plain,
% 9.48/9.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.77 inference(rewrite,[status(thm)],[])).
% 9.48/9.77 tff(19142,plain,
% 9.48/9.77 (((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.77 inference(rewrite,[status(thm)],[])).
% 9.48/9.77 tff(19143,plain,
% 9.48/9.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 9.48/9.77 inference(monotonicity,[status(thm)],[19142])).
% 9.48/9.77 tff(19144,plain,
% 9.48/9.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 9.48/9.77 inference(transitivity,[status(thm)],[19143, 19141])).
% 9.48/9.77 tff(19145,plain,
% 9.48/9.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 9.48/9.77 inference(quant_inst,[status(thm)],[])).
% 9.48/9.77 tff(19146,plain,
% 9.48/9.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 9.48/9.77 inference(modus_ponens,[status(thm)],[19145, 19144])).
% 9.48/9.77 tff(19147,plain,
% 9.48/9.77 ($false),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[19146, 391, 665, 1374, 2698, 1573, 1152])).
% 9.48/9.77 tff(19148,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.77 tff(19149,plain,
% 9.48/9.77 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[19148, 19121, 1374, 665, 1573])).
% 9.48/9.77 tff(19150,plain,
% 9.48/9.77 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[1048, 19149, 19140])).
% 9.48/9.77 tff(19151,plain,
% 9.48/9.77 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[18470, 19150, 19131, 19100])).
% 9.48/9.77 tff(19152,plain,
% 9.48/9.77 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 9.48/9.77 inference(unit_resolution,[status(thm)],[988, 19151, 19076])).
% 9.48/9.77 tff(19153,plain,
% 9.48/9.77 (b(s(s(s(elem!1))), s(elem!1))),
% 9.48/9.77 inference(modus_ponens,[status(thm)],[3563, 19005])).
% 9.48/9.77 tff(19154,plain,
% 9.48/9.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.48/9.77 inference(rewrite,[status(thm)],[])).
% 9.48/9.77 tff(19155,plain,
% 9.48/9.77 (((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.48/9.77 inference(rewrite,[status(thm)],[])).
% 9.48/9.77 tff(19156,plain,
% 9.48/9.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 9.48/9.78 inference(monotonicity,[status(thm)],[19155])).
% 9.48/9.78 tff(19157,plain,
% 9.48/9.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.48/9.78 inference(transitivity,[status(thm)],[19156, 19154])).
% 9.48/9.78 tff(19158,plain,
% 9.48/9.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.48/9.78 inference(quant_inst,[status(thm)],[])).
% 9.48/9.78 tff(19159,plain,
% 9.48/9.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 9.48/9.78 inference(modus_ponens,[status(thm)],[19158, 19157])).
% 9.48/9.78 tff(19160,plain,
% 9.48/9.78 ($false),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[19159, 391, 665, 19153, 19090, 1573, 19152])).
% 9.48/9.78 tff(19161,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (~(s(z) = elem!1)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.78 tff(19162,plain,
% 9.48/9.78 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[19161, 19073, 665, 19004, 19001, 19060, 19058, 8232, 812, 722, 19054, 18980, 19057, 18978])).
% 9.48/9.78 tff(19163,plain,
% 9.48/9.78 (r(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[3652, 19162])).
% 9.48/9.78 tff(19164,plain,
% 9.48/9.78 (~r(elem!1, s(s(z)))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[18632, 19163, 8232, 19054])).
% 9.48/9.78 tff(19165,plain,
% 9.48/9.78 (b(elem!1, s(s(z)))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[3394, 19164, 19053])).
% 9.48/9.78 tff(19166,plain,
% 9.48/9.78 (~b(s(s(z)), elem!1)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[11012, 19165, 19051, 18978])).
% 9.48/9.78 tff(19167,plain,
% 9.48/9.78 (r(s(s(z)), elem!1)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[4730, 19166, 10749])).
% 9.48/9.78 tff(19168,plain,
% 9.48/9.78 (r(s(elem!1), elem!1)),
% 9.48/9.78 inference(modus_ponens,[status(thm)],[19167, 9724])).
% 9.48/9.78 tff(19169,plain,
% 9.48/9.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 9.48/9.78 inference(rewrite,[status(thm)],[])).
% 9.48/9.78 tff(19170,plain,
% 9.48/9.78 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 9.48/9.78 inference(rewrite,[status(thm)],[])).
% 9.48/9.78 tff(19171,plain,
% 9.48/9.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 9.48/9.78 inference(monotonicity,[status(thm)],[19170])).
% 9.48/9.78 tff(19172,plain,
% 9.48/9.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 9.48/9.78 inference(transitivity,[status(thm)],[19171, 19169])).
% 9.48/9.78 tff(19173,plain,
% 9.48/9.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 9.48/9.78 inference(quant_inst,[status(thm)],[])).
% 9.48/9.78 tff(19174,plain,
% 9.48/9.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 9.48/9.78 inference(modus_ponens,[status(thm)],[19173, 19172])).
% 9.48/9.78 tff(19175,plain,
% 9.48/9.78 ($false),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[19174, 194, 8232, 19168, 19049, 18974])).
% 9.48/9.78 tff(19176,plain,((~(s(z) = elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.78 tff(19177,plain,
% 9.48/9.78 (~(s(z) = elem!1)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[19176, 722, 18965, 10, 2, 2881])).
% 9.48/9.78 tff(19178,plain,
% 9.48/9.78 (~(elem!1 = s(z))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[172, 19177])).
% 9.48/9.78 tff(19179,plain,
% 9.48/9.78 (r(elem!1, s(z))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[837, 19178, 31])).
% 9.48/9.78 tff(19180,plain,
% 9.48/9.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 9.48/9.78 inference(rewrite,[status(thm)],[])).
% 9.48/9.78 tff(19181,plain,
% 9.48/9.78 (((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 9.48/9.78 inference(rewrite,[status(thm)],[])).
% 9.48/9.78 tff(19182,plain,
% 9.48/9.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 9.48/9.78 inference(monotonicity,[status(thm)],[19181])).
% 9.48/9.78 tff(19183,plain,
% 9.48/9.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 9.48/9.78 inference(transitivity,[status(thm)],[19182, 19180])).
% 9.48/9.78 tff(19184,plain,
% 9.48/9.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 9.48/9.78 inference(quant_inst,[status(thm)],[])).
% 9.48/9.78 tff(19185,plain,
% 9.48/9.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 9.48/9.78 inference(modus_ponens,[status(thm)],[19184, 19183])).
% 9.48/9.78 tff(19186,plain,
% 9.48/9.78 ($false),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[19185, 194, 8232, 722, 19179, 2913])).
% 9.48/9.78 tff(19187,plain,((~r(z, s(z))) | b(elem!1, s(z)) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.78 tff(19188,plain,
% 9.48/9.78 (~r(z, s(z))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[19187, 2881, 10, 2, 31])).
% 9.48/9.78 tff(19189,plain,
% 9.48/9.78 (b(z, s(z))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[678, 19188])).
% 9.48/9.78 tff(19190,plain,
% 9.48/9.78 (~b(s(z), elem!1)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[14831, 391, 665, 664, 590])).
% 9.48/9.78 tff(19191,plain,
% 9.48/9.78 (r(s(z), elem!1)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[632, 150, 19190])).
% 9.48/9.78 tff(19192,plain,
% 9.48/9.78 (~r(s(s(s(s(z)))), elem!1)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[5396, 19191, 2913, 838])).
% 9.48/9.78 tff(19193,plain,
% 9.48/9.78 (~r(s(s(z)), s(z))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[5585, 1749, 590, 1216, 664])).
% 9.48/9.78 tff(19194,plain,
% 9.48/9.78 (~(elem!1 = s(s(z)))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[15394, 19193, 847])).
% 9.48/9.78 tff(19195,plain,
% 9.48/9.78 (~r(s(s(z)), z)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[14746, 1749, 2053, 184])).
% 9.48/9.78 tff(19196,plain,
% 9.48/9.78 (b(s(s(z)), z)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[1211, 19195])).
% 9.48/9.78 tff(19197,plain,
% 9.48/9.78 (s(s(z)) = elem!1),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[14843, 19196, 590, 665, 664, 847, 1484])).
% 9.48/9.78 tff(19198,plain,
% 9.48/9.78 ($false),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[11003, 19197, 19194])).
% 9.48/9.78 tff(19199,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.78 tff(19200,plain,
% 9.48/9.78 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[19199, 3447, 665, 664, 838, 19191, 2913, 590, 184])).
% 9.48/9.78 tff(19201,plain,
% 9.48/9.78 (b(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[3652, 19200])).
% 9.48/9.78 tff(19202,plain,
% 9.48/9.78 (b(elem!1, s(s(s(s(z)))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[781, 16267, 10481])).
% 9.48/9.78 tff(19203,plain,
% 9.48/9.78 (~r(s(s(s(s(z)))), elem!1)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[5396, 1484, 2913, 847])).
% 9.48/9.78 tff(19204,plain,
% 9.48/9.78 (b(s(s(s(s(z)))), elem!1)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[762, 6967, 19203])).
% 9.48/9.78 tff(19205,plain,
% 9.48/9.78 (~b(z, s(s(s(s(z)))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[14821, 19204, 665, 19202])).
% 9.48/9.78 tff(19206,plain,
% 9.48/9.78 (r(z, s(s(s(s(z)))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[800, 19205])).
% 9.48/9.78 tff(19207,plain,
% 9.48/9.78 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[16415, 723, 2913, 664, 590, 19206])).
% 9.48/9.78 tff(19208,plain,
% 9.48/9.78 (b(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[3652, 19207])).
% 9.48/9.78 tff(19209,plain,
% 9.48/9.78 (~r(s(s(z)), z)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[18886, 19208, 3843, 664, 3447, 184, 590, 19206])).
% 9.48/9.78 tff(19210,plain,
% 9.48/9.78 (b(s(s(z)), z)),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[1211, 19209])).
% 9.48/9.78 tff(19211,plain,
% 9.48/9.78 (s(s(z)) = elem!1),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[14843, 19210, 590, 665, 664, 847, 1484])).
% 9.48/9.78 tff(19212,plain,
% 9.48/9.78 (elem!1 = s(s(z))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[11003, 19211])).
% 9.48/9.78 tff(19213,plain,
% 9.48/9.78 (r(s(s(z)), s(z))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[15394, 19212, 847])).
% 9.48/9.78 tff(19214,plain,
% 9.48/9.78 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[2429, 19213, 1484, 723])).
% 9.48/9.78 tff(19215,plain,
% 9.48/9.78 (b(s(s(s(s(z)))), s(s(z)))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[1714, 19214])).
% 9.48/9.78 tff(19216,plain,
% 9.48/9.78 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[10090, 19206, 3447, 184])).
% 9.48/9.78 tff(19217,plain,
% 9.48/9.78 (b(elem!1, s(s(s(elem!1))))),
% 9.48/9.78 inference(unit_resolution,[status(thm)],[11332, 19215, 2913, 3447, 19206, 31, 19213, 19208, 98])).
% 9.48/9.78 tff(19218,plain,
% 9.48/9.78 (~(s(s(s(elem!1))) = elem!1)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[15370, 19217])).
% 9.48/9.79 tff(19219,plain,
% 9.48/9.79 ($false),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[11148, 19218, 19217, 2881, 3446, 723, 118, 19208, 590, 847, 2, 19213, 411, 19216, 19215, 184])).
% 9.48/9.79 tff(19220,plain,((~r(s(s(s(s(z)))), s(z))) | b(s(z), s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (~b(s(z), z)) | (~r(elem!1, s(z))) | (elem!1 = z) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(z)) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.79 tff(19221,plain,
% 9.48/9.79 (~r(s(s(s(s(z)))), s(z))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[19220, 3446, 2881, 590, 838, 2, 411, 184, 31, 19191, 665, 664, 3363])).
% 9.48/9.79 tff(19222,plain,
% 9.48/9.79 (b(s(s(s(s(z)))), s(z))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[749, 19221])).
% 9.48/9.79 tff(19223,plain,
% 9.48/9.79 (~r(elem!1, s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[11195, 3447, 2913, 838])).
% 9.48/9.79 tff(19224,plain,
% 9.48/9.79 (b(elem!1, s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[781, 19223, 10481])).
% 9.48/9.79 tff(19225,plain,
% 9.48/9.79 (b(s(s(s(s(z)))), elem!1)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[762, 6967, 19192])).
% 9.48/9.79 tff(19226,plain,
% 9.48/9.79 (~b(z, s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[14821, 19225, 665, 19224])).
% 9.48/9.79 tff(19227,plain,
% 9.48/9.79 (r(z, s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[800, 19226])).
% 9.48/9.79 tff(19228,plain,
% 9.48/9.79 (~r(s(s(z)), z)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[18886, 19201, 3363, 664, 3447, 184, 590, 19227])).
% 9.48/9.79 tff(19229,plain,
% 9.48/9.79 (b(s(s(z)), z)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[1211, 19228])).
% 9.48/9.79 tff(19230,plain,
% 9.48/9.79 (s(s(z)) = elem!1),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[14843, 19229, 590, 665, 664, 838, 19191])).
% 9.48/9.79 tff(19231,plain,
% 9.48/9.79 (elem!1 = s(s(z))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[11003, 19230])).
% 9.48/9.79 tff(19232,plain,
% 9.48/9.79 (r(s(s(z)), s(z))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[15394, 19231, 838])).
% 9.48/9.79 tff(19233,plain,
% 9.48/9.79 (b(elem!1, s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[11220, 19232, 31, 2, 2913, 3447, 590, 19222, 19201])).
% 9.48/9.79 tff(19234,plain,
% 9.48/9.79 (~(s(s(s(elem!1))) = elem!1)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[15370, 19233])).
% 9.48/9.79 tff(19235,plain,
% 9.48/9.79 (~(elem!1 = s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[129, 19234])).
% 9.48/9.79 tff(19236,plain,
% 9.48/9.79 (r(s(s(s(elem!1))), elem!1)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[230, 19234, 168])).
% 9.48/9.79 tff(19237,plain,
% 9.48/9.79 (~r(s(z), s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[5246, 19236, 31, 150, 19190])).
% 9.48/9.79 tff(19238,plain,
% 9.48/9.79 (b(s(z), s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[247, 19237])).
% 9.48/9.79 tff(19239,plain,
% 9.48/9.79 (~b(elem!1, s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[11099, 3446, 1484, 150, 379, 665, 411, 174])).
% 9.48/9.79 tff(19240,plain,
% 9.48/9.79 (r(elem!1, s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[424, 19239, 1])).
% 9.48/9.79 tff(19241,plain,
% 9.48/9.79 (~b(z, s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[11294, 3447, 379, 590, 3363, 411, 174])).
% 9.48/9.79 tff(19242,plain,
% 9.48/9.79 (r(z, s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[58, 19241])).
% 9.48/9.79 tff(19243,plain,
% 9.48/9.79 ($false),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[8380, 19242, 19240, 174, 411])).
% 9.48/9.79 tff(19244,plain,(b(s(s(s(s(z)))), z) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(z), elem!1)) | (s(z) = elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.79 tff(19245,plain,
% 9.48/9.79 (~r(s(s(s(elem!1))), z)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[19244, 19238, 665, 19191, 3446, 590, 150, 19235, 411])).
% 9.48/9.79 tff(19246,plain,
% 9.48/9.79 (~b(s(s(s(elem!1))), z)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[673, 19238, 665, 664, 19233])).
% 9.48/9.79 tff(19247,plain,
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% 9.48/9.79 inference(unit_resolution,[status(thm)],[377, 19246, 19245])).
% 9.48/9.79 tff(19248,plain,(b(s(s(s(s(z)))), z) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (s(z) = elem!1) | (~r(z, elem!1)) | b(elem!1, s(z)) | b(s(s(s(elem!1))), elem!1) | (elem!1 = z) | (~r(z, s(s(s(elem!1))))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.79 tff(19249,plain,
% 9.48/9.79 (b(s(s(s(s(z)))), z)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[19248, 168, 664, 590, 150, 411, 31, 665, 2, 184, 2881])).
% 9.48/9.79 tff(19250,plain,
% 9.48/9.79 (~b(s(s(s(s(z)))), elem!1)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[14978, 19249, 590, 665, 664])).
% 9.48/9.79 tff(19251,plain,
% 9.48/9.79 (s(s(s(s(z)))) = elem!1),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[762, 19250, 19192])).
% 9.48/9.79 tff(19252,plain,
% 9.48/9.79 (~(s(s(s(elem!1))) = elem!1)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[1436, 19251])).
% 9.48/9.79 tff(19253,plain,
% 9.48/9.79 (r(s(s(s(elem!1))), elem!1)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[230, 19252, 168])).
% 9.48/9.79 tff(19254,plain,
% 9.48/9.79 (~(elem!1 = s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[129, 19252])).
% 9.48/9.79 tff(19255,plain,
% 9.48/9.79 (b(elem!1, s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[10519, 19254, 184, 411, 168])).
% 9.48/9.79 tff(19256,plain,
% 9.48/9.79 (~r(s(z), s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[5246, 19253, 31, 150, 19190])).
% 9.48/9.79 tff(19257,plain,
% 9.48/9.79 (b(s(z), s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[247, 19256])).
% 9.48/9.79 tff(19258,plain,
% 9.48/9.79 (~b(s(s(s(elem!1))), z)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[673, 19257, 665, 664, 19255])).
% 9.48/9.79 tff(19259,plain,
% 9.48/9.79 (r(s(s(s(elem!1))), z)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[377, 19258])).
% 9.48/9.79 tff(19260,plain,
% 9.48/9.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))))),
% 9.48/9.79 inference(rewrite,[status(thm)],[])).
% 9.48/9.79 tff(19261,plain,
% 9.48/9.79 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))))),
% 9.48/9.79 inference(rewrite,[status(thm)],[])).
% 9.48/9.79 tff(19262,plain,
% 9.48/9.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z)))))),
% 9.48/9.79 inference(monotonicity,[status(thm)],[19261])).
% 9.48/9.79 tff(19263,plain,
% 9.48/9.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))))),
% 9.48/9.79 inference(transitivity,[status(thm)],[19262, 19260])).
% 9.48/9.79 tff(19264,plain,
% 9.48/9.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 9.48/9.79 inference(quant_inst,[status(thm)],[])).
% 9.48/9.79 tff(19265,plain,
% 9.48/9.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z)))),
% 9.48/9.79 inference(modus_ponens,[status(thm)],[19264, 19263])).
% 9.48/9.79 tff(19266,plain,
% 9.48/9.79 ($false),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[19265, 194, 411, 19259, 19253, 838])).
% 9.48/9.79 tff(19267,plain,(b(s(s(s(elem!1))), elem!1) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | b(elem!1, s(z)) | (s(z) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (elem!1 = z) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.79 tff(19268,plain,
% 9.48/9.79 (b(s(s(s(elem!1))), elem!1)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[19267, 150, 665, 664, 31, 411, 184, 590, 2, 2881])).
% 9.48/9.79 tff(19269,plain,
% 9.48/9.79 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[19199, 3447, 665, 664, 847, 1484, 2913, 590, 184])).
% 9.48/9.79 tff(19270,plain,
% 9.48/9.79 (b(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[3652, 19269])).
% 9.48/9.79 tff(19271,plain,
% 9.48/9.79 (b(elem!1, s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[781, 10481, 16267])).
% 9.48/9.79 tff(19272,plain,
% 9.48/9.79 (~b(z, s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[14821, 19204, 665, 19271])).
% 9.48/9.79 tff(19273,plain,
% 9.48/9.79 (r(z, s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[800, 19272])).
% 9.48/9.79 tff(19274,plain,
% 9.48/9.79 (~r(s(s(z)), z)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[18886, 19273, 3843, 664, 3447, 184, 590, 19270])).
% 9.48/9.79 tff(19275,plain,
% 9.48/9.79 (b(s(s(z)), z)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[1211, 19274])).
% 9.48/9.79 tff(19276,plain,
% 9.48/9.79 (~r(s(s(s(s(z)))), s(z))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[19220, 3446, 2881, 590, 847, 2, 411, 184, 31, 1484, 665, 664, 3843])).
% 9.48/9.79 tff(19277,plain,
% 9.48/9.79 (b(s(s(s(s(z)))), s(z))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[749, 19276])).
% 9.48/9.79 tff(19278,plain,
% 9.48/9.79 (~b(elem!1, s(s(s(elem!1))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[16861, 19204, 3843, 184, 900, 3447])).
% 9.48/9.79 tff(19279,plain,
% 9.48/9.79 (~r(s(s(z)), s(z))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[11220, 19278, 31, 2, 2913, 3447, 590, 19277, 19270])).
% 9.48/9.79 tff(19280,plain,
% 9.48/9.79 (~(elem!1 = s(s(z)))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[15394, 19279, 847])).
% 9.48/9.79 tff(19281,plain,
% 9.48/9.79 (~(s(s(z)) = elem!1)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[11003, 19280])).
% 9.48/9.79 tff(19282,plain,
% 9.48/9.79 ($false),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[14843, 19281, 19275, 590, 665, 664, 847, 1484])).
% 9.48/9.79 tff(19283,plain,(b(s(s(s(s(z)))), z) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), elem!1)) | b(s(z), s(s(s(s(z))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.48/9.79 tff(19284,plain,
% 9.48/9.79 (b(s(s(s(s(z)))), z)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[19283, 838, 665, 664, 590, 19191, 3363, 184, 31, 2, 19268, 2881, 411])).
% 9.48/9.79 tff(19285,plain,
% 9.48/9.79 (~b(s(s(s(s(z)))), elem!1)),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[14978, 19284, 590, 665, 664])).
% 9.48/9.79 tff(19286,plain,
% 9.48/9.79 (s(s(s(s(z)))) = elem!1),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[762, 19285, 19192])).
% 9.48/9.79 tff(19287,plain,
% 9.48/9.79 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 9.48/9.79 inference(monotonicity,[status(thm)],[19286])).
% 9.48/9.79 tff(19288,plain,
% 9.48/9.79 (~b(s(s(s(s(z)))), s(z))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[11186, 19286, 31])).
% 9.48/9.79 tff(19289,plain,
% 9.48/9.79 (r(s(s(s(s(z)))), s(z))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[749, 19288])).
% 9.48/9.79 tff(19290,plain,
% 9.48/9.79 (r(z, s(s(s(s(z))))) <=> r(z, elem!1)),
% 9.48/9.79 inference(monotonicity,[status(thm)],[19286])).
% 9.48/9.79 tff(19291,plain,
% 9.48/9.79 (r(z, elem!1) <=> r(z, s(s(s(s(z)))))),
% 9.48/9.79 inference(symmetry,[status(thm)],[19290])).
% 9.48/9.79 tff(19292,plain,
% 9.48/9.79 (r(z, s(s(s(s(z)))))),
% 9.48/9.79 inference(modus_ponens,[status(thm)],[411, 19291])).
% 9.48/9.79 tff(19293,plain,
% 9.48/9.79 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[16415, 19292, 2913, 664, 590, 19289])).
% 9.48/9.79 tff(19294,plain,
% 9.48/9.79 (b(s(s(z)), s(s(s(s(z)))))),
% 9.48/9.79 inference(unit_resolution,[status(thm)],[3652, 19293])).
% 9.48/9.79 tff(19295,plain,
% 9.48/9.79 (b(s(s(z)), elem!1)),
% 9.48/9.79 inference(modus_ponens,[status(thm)],[19294, 19287])).
% 9.48/9.79 tff(19296,plain,
% 9.48/9.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 9.58/9.80 inference(rewrite,[status(thm)],[])).
% 9.58/9.80 tff(19297,plain,
% 9.58/9.80 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 9.58/9.80 inference(rewrite,[status(thm)],[])).
% 9.58/9.80 tff(19298,plain,
% 9.58/9.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))))),
% 9.58/9.80 inference(monotonicity,[status(thm)],[19297])).
% 9.58/9.80 tff(19299,plain,
% 9.58/9.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)))),
% 9.58/9.80 inference(transitivity,[status(thm)],[19298, 19296])).
% 9.58/9.80 tff(19300,plain,
% 9.58/9.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.58/9.80 inference(quant_inst,[status(thm)],[])).
% 9.58/9.80 tff(19301,plain,
% 9.58/9.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), elem!1))),
% 9.58/9.80 inference(modus_ponens,[status(thm)],[19300, 19299])).
% 9.58/9.80 tff(19302,plain,
% 9.58/9.80 (~b(s(s(z)), s(s(s(elem!1))))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[19301, 391, 665, 19268, 19295, 664])).
% 9.58/9.80 tff(19303,plain,
% 9.58/9.80 (r(s(s(z)), s(s(s(elem!1))))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[11041, 19302])).
% 9.58/9.80 tff(19304,plain,
% 9.58/9.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.58/9.80 inference(rewrite,[status(thm)],[])).
% 9.58/9.80 tff(19305,plain,
% 9.58/9.80 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.58/9.80 inference(rewrite,[status(thm)],[])).
% 9.58/9.80 tff(19306,plain,
% 9.58/9.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 9.58/9.80 inference(monotonicity,[status(thm)],[19305])).
% 9.58/9.80 tff(19307,plain,
% 9.58/9.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.58/9.80 inference(transitivity,[status(thm)],[19306, 19304])).
% 9.58/9.80 tff(19308,plain,
% 9.58/9.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.58/9.80 inference(quant_inst,[status(thm)],[])).
% 9.58/9.80 tff(19309,plain,
% 9.58/9.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 9.58/9.80 inference(modus_ponens,[status(thm)],[19308, 19307])).
% 9.58/9.80 tff(19310,plain,
% 9.58/9.80 (~b(s(s(s(elem!1))), s(s(z)))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[19309, 391, 665, 19268, 19295, 664])).
% 9.58/9.80 tff(19311,plain,
% 9.58/9.80 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[10713, 42, 19310])).
% 9.58/9.80 tff(19312,plain,
% 9.58/9.80 (r(s(s(s(elem!1))), s(s(z)))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[19311, 10703])).
% 9.58/9.80 tff(19313,plain,
% 9.58/9.80 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 9.58/9.80 inference(monotonicity,[status(thm)],[19286])).
% 9.58/9.80 tff(19314,plain,
% 9.58/9.80 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 9.58/9.80 inference(transitivity,[status(thm)],[19313, 698])).
% 9.58/9.80 tff(19315,plain,
% 9.58/9.80 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 9.58/9.80 inference(transitivity,[status(thm)],[19314, 8492])).
% 9.58/9.80 tff(19316,plain,
% 9.58/9.80 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 9.58/9.80 inference(monotonicity,[status(thm)],[19315])).
% 9.58/9.80 tff(19317,plain,
% 9.58/9.80 (~(s(s(z)) = elem!1)),
% 9.58/9.80 inference(modus_ponens,[status(thm)],[714, 19316])).
% 9.58/9.80 tff(19318,plain,
% 9.58/9.80 (~b(s(s(z)), z)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[14843, 19317, 590, 665, 664, 838, 19191])).
% 9.58/9.80 tff(19319,plain,
% 9.58/9.80 (r(s(s(z)), z)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[1211, 19318])).
% 9.58/9.80 tff(19320,plain,
% 9.58/9.80 ($false),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[16895, 194, 184, 19319, 19312, 19303])).
% 9.58/9.80 tff(19321,plain,((s(z) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | b(elem!1, s(z)) | (elem!1 = z) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.80 tff(19322,plain,
% 9.58/9.80 (s(z) = elem!1),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[19321, 19189, 18965, 59, 10550, 8232, 31, 2, 2881])).
% 9.58/9.80 tff(19323,plain,
% 9.58/9.80 (elem!1 = s(z)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[1495, 19322])).
% 9.58/9.80 tff(19324,plain,
% 9.58/9.80 (~b(s(z), s(s(s(elem!1))))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[2884, 19323, 2881])).
% 9.58/9.80 tff(19325,plain,
% 9.58/9.80 (r(s(z), s(s(s(elem!1))))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[247, 19324])).
% 9.58/9.80 tff(19326,plain,
% 9.58/9.80 (r(elem!1, s(s(s(elem!1))))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[2570, 19325, 19322])).
% 9.58/9.80 tff(19327,plain,
% 9.58/9.80 (~r(s(s(s(elem!1))), elem!1)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[419, 19326, 59, 8232])).
% 9.58/9.80 tff(19328,plain,
% 9.58/9.80 (~b(elem!1, s(s(s(elem!1))))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[8314, 19323, 2881])).
% 9.58/9.80 tff(19329,plain,
% 9.58/9.80 (~b(s(s(s(elem!1))), s(z))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[10635, 19328, 8232, 59, 10550, 19189, 31])).
% 9.58/9.80 tff(19330,plain,
% 9.58/9.80 (~b(s(s(s(s(z)))), s(z))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[11177, 19329, 19323])).
% 9.58/9.80 tff(19331,plain,
% 9.58/9.80 (~b(s(s(s(s(z)))), elem!1)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[9614, 19330, 19322])).
% 9.58/9.80 tff(19332,plain,
% 9.58/9.80 (~b(s(s(s(elem!1))), elem!1)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[1563, 19331, 19323])).
% 9.58/9.80 tff(19333,plain,
% 9.58/9.80 (r(s(s(s(elem!1))), s(z))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[223, 19329])).
% 9.58/9.80 tff(19334,plain,
% 9.58/9.80 (~r(elem!1, s(z))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[10776, 19326, 19333, 2913])).
% 9.58/9.80 tff(19335,plain,
% 9.58/9.80 (~(s(s(s(elem!1))) = elem!1)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[8406, 19334, 19333])).
% 9.58/9.80 tff(19336,plain,
% 9.58/9.80 ($false),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[230, 19335, 19332, 19327])).
% 9.58/9.80 tff(19337,plain,(b(s(z), s(s(s(s(z))))) | b(elem!1, s(z)) | (elem!1 = z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.80 tff(19338,plain,
% 9.58/9.80 (b(s(z), s(s(s(s(z)))))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[19337, 31, 2, 10])).
% 9.58/9.80 tff(19339,plain,
% 9.58/9.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))))),
% 9.58/9.80 inference(rewrite,[status(thm)],[])).
% 9.58/9.80 tff(19340,plain,
% 9.58/9.80 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))))),
% 9.58/9.80 inference(rewrite,[status(thm)],[])).
% 9.58/9.80 tff(19341,plain,
% 9.58/9.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z)))))),
% 9.58/9.80 inference(monotonicity,[status(thm)],[19340])).
% 9.58/9.80 tff(19342,plain,
% 9.58/9.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))))),
% 9.58/9.80 inference(transitivity,[status(thm)],[19341, 19339])).
% 9.58/9.80 tff(19343,plain,
% 9.58/9.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 9.58/9.80 inference(quant_inst,[status(thm)],[])).
% 9.58/9.80 tff(19344,plain,
% 9.58/9.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z)))),
% 9.58/9.80 inference(modus_ponens,[status(thm)],[19343, 19342])).
% 9.58/9.80 tff(19345,plain,
% 9.58/9.80 ($false),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[19344, 194, 411, 233, 184, 847])).
% 9.58/9.80 tff(19346,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.80 tff(19347,plain,
% 9.58/9.80 (~r(s(s(s(elem!1))), elem!1)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[19346, 838, 184, 411])).
% 9.58/9.80 tff(19348,plain,
% 9.58/9.80 (s(s(s(elem!1))) = elem!1),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[230, 19347, 168])).
% 9.58/9.80 tff(19349,plain,
% 9.58/9.80 (~(s(s(s(s(z)))) = elem!1)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[1436, 19348])).
% 9.58/9.80 tff(19350,plain,
% 9.58/9.80 (~(elem!1 = s(s(s(s(z)))))),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[769, 19349])).
% 9.58/9.80 tff(19351,plain,
% 9.58/9.80 (~r(s(s(s(s(z)))), elem!1)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[10450, 19350, 411, 665, 838])).
% 9.58/9.80 tff(19352,plain,
% 9.58/9.80 (b(s(s(s(s(z)))), elem!1)),
% 9.58/9.80 inference(unit_resolution,[status(thm)],[762, 19351, 19349])).
% 9.58/9.80 tff(19353,plain,
% 9.58/9.80 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 9.58/9.80 inference(monotonicity,[status(thm)],[19348])).
% 9.58/9.80 tff(19354,plain,
% 9.58/9.80 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 9.58/9.80 inference(transitivity,[status(thm)],[19353, 698])).
% 9.58/9.80 tff(19355,plain,
% 9.58/9.80 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19354])).
% 9.58/9.81 tff(19356,plain,
% 9.58/9.81 (~(elem!1 = s(s(z)))),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[1397, 19355])).
% 9.58/9.81 tff(19357,plain,
% 9.58/9.81 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 9.58/9.81 inference(transitivity,[status(thm)],[19354, 8492])).
% 9.58/9.81 tff(19358,plain,
% 9.58/9.81 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19357])).
% 9.58/9.81 tff(19359,plain,
% 9.58/9.81 (~(s(s(z)) = elem!1)),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[1397, 19358])).
% 9.58/9.81 tff(19360,plain,
% 9.58/9.81 (~r(s(z), elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[15942, 19359, 665, 411, 1234, 838, 184, 19356, 19352])).
% 9.58/9.81 tff(19361,plain,
% 9.58/9.81 (b(s(z), elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[632, 19360, 150])).
% 9.58/9.81 tff(19362,plain,
% 9.58/9.81 (b(s(s(s(s(z)))), z)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[17542, 19361, 590, 665, 411, 1234, 19351])).
% 9.58/9.81 tff(19363,plain,
% 9.58/9.81 (~b(z, s(z))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[14978, 19362, 590, 665, 19352])).
% 9.58/9.81 tff(19364,plain,
% 9.58/9.81 (~r(z, s(z))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[15079, 19362, 665, 1234, 411, 19356, 838, 19359, 19352, 19350, 150])).
% 9.58/9.81 tff(19365,plain,
% 9.58/9.81 ($false),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[678, 19364, 19363])).
% 9.58/9.81 tff(19366,plain,((s(z) = elem!1) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.81 tff(19367,plain,
% 9.58/9.81 (s(z) = elem!1),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[19366, 168, 19338, 8232, 10550, 59, 18965, 31])).
% 9.58/9.81 tff(19368,plain,
% 9.58/9.81 (b(elem!1, s(s(s(elem!1))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[8542, 19367, 19338])).
% 9.58/9.81 tff(19369,plain,
% 9.58/9.81 (~(s(s(s(elem!1))) = elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[15370, 19368])).
% 9.58/9.81 tff(19370,plain,
% 9.58/9.81 (~(s(elem!1) = elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[158, 19369])).
% 9.58/9.81 tff(19371,plain,
% 9.58/9.81 (~(elem!1 = s(elem!1))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[166, 19370])).
% 9.58/9.81 tff(19372,plain,
% 9.58/9.81 (r(s(s(s(elem!1))), elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[230, 19369, 168])).
% 9.58/9.81 tff(19373,plain,
% 9.58/9.81 (~r(elem!1, s(elem!1))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[434, 19372, 8232, 59])).
% 9.58/9.81 tff(19374,plain,
% 9.58/9.81 (b(elem!1, s(elem!1))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[443, 19373, 19371])).
% 9.58/9.81 tff(19375,plain,
% 9.58/9.81 (b(s(z), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[812])).
% 9.58/9.81 tff(19376,plain,
% 9.58/9.81 ((~b(s(z), s(elem!1))) <=> (~b(elem!1, s(elem!1)))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19375])).
% 9.58/9.81 tff(19377,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 9.58/9.81 tff(19378,plain,
% 9.58/9.81 (~b(elem!1, s(elem!1))),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[19377, 19376])).
% 9.58/9.81 tff(19379,plain,
% 9.58/9.81 ($false),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[802, 19378])).
% 9.58/9.81 tff(19380,plain,((~b(elem!1, s(elem!1))) | b(s(z), s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.81 tff(19381,plain,
% 9.58/9.81 (b(s(z), s(elem!1))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[19380, 19374, 19367])).
% 9.58/9.81 tff(19382,plain,
% 9.58/9.81 (~r(elem!1, s(s(s(elem!1))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[419, 19372, 59, 8232])).
% 9.58/9.81 tff(19383,plain,
% 9.58/9.81 (~r(s(z), s(s(s(elem!1))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[2570, 19382, 19367])).
% 9.58/9.81 tff(19384,plain,
% 9.58/9.81 (b(s(z), s(s(s(elem!1))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[247, 19383])).
% 9.58/9.81 tff(19385,plain,
% 9.58/9.81 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19367])).
% 9.58/9.81 tff(19386,plain,
% 9.58/9.81 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 9.58/9.81 inference(symmetry,[status(thm)],[19385])).
% 9.58/9.81 tff(19387,plain,
% 9.58/9.81 (~(s(s(s(s(elem!1)))) = elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[7472, 19367])).
% 9.58/9.81 tff(19388,plain,
% 9.58/9.81 (~(elem!1 = s(s(s(s(elem!1)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[15610, 19387])).
% 9.58/9.81 tff(19389,plain,
% 9.58/9.81 (s(s(z)) = s(elem!1)),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19367])).
% 9.58/9.81 tff(19390,plain,
% 9.58/9.81 (s(s(s(z))) = s(s(elem!1))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19389])).
% 9.58/9.81 tff(19391,plain,
% 9.58/9.81 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19390])).
% 9.58/9.81 tff(19392,plain,
% 9.58/9.81 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19391])).
% 9.58/9.81 tff(19393,plain,
% 9.58/9.81 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19389])).
% 9.58/9.81 tff(19394,plain,
% 9.58/9.81 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 9.58/9.81 inference(transitivity,[status(thm)],[19393, 19392])).
% 9.58/9.81 tff(19395,plain,
% 9.58/9.81 (b(elem!1, s(s(s(s(z)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[8539, 19367, 19338])).
% 9.58/9.81 tff(19396,plain,
% 9.58/9.81 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19389])).
% 9.58/9.81 tff(19397,plain,
% 9.58/9.81 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19396])).
% 9.58/9.81 tff(19398,plain,
% 9.58/9.81 (~(s(s(elem!1)) = s(elem!1))),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[2680, 19397])).
% 9.58/9.81 tff(19399,plain,
% 9.58/9.81 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 9.58/9.81 inference(transitivity,[status(thm)],[19396, 1098])).
% 9.58/9.81 tff(19400,plain,
% 9.58/9.81 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19399])).
% 9.58/9.81 tff(19401,plain,
% 9.58/9.81 (~(s(elem!1) = s(s(elem!1)))),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[2680, 19400])).
% 9.58/9.81 tff(19402,plain,
% 9.58/9.81 (~b(s(s(s(elem!1))), s(z))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[3938, 19367, 168])).
% 9.58/9.81 tff(19403,plain,
% 9.58/9.81 (elem!1 = s(z)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[1495, 19367])).
% 9.58/9.81 tff(19404,plain,
% 9.58/9.81 (~b(s(s(s(s(z)))), s(z))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[11177, 19403, 19402])).
% 9.58/9.81 tff(19405,plain,
% 9.58/9.81 (r(s(s(s(s(z)))), s(z))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[749, 19404])).
% 9.58/9.81 tff(19406,plain,
% 9.58/9.81 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19391])).
% 9.58/9.81 tff(19407,plain,
% 9.58/9.81 (r(z, s(z))),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[8232, 814])).
% 9.58/9.81 tff(19408,plain,
% 9.58/9.81 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[18274, 3446, 98, 31, 19407])).
% 9.58/9.81 tff(19409,plain,
% 9.58/9.81 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[3482, 19408, 7866])).
% 9.58/9.81 tff(19410,plain,
% 9.58/9.81 (b(elem!1, s(s(s(elem!1))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[8542, 812, 19338])).
% 9.58/9.81 tff(19411,plain,
% 9.58/9.81 (~(s(s(s(elem!1))) = elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[15370, 19410])).
% 9.58/9.81 tff(19412,plain,
% 9.58/9.81 (~(s(elem!1) = elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[158, 19411])).
% 9.58/9.81 tff(19413,plain,
% 9.58/9.81 (~(elem!1 = s(elem!1))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[166, 19412])).
% 9.58/9.81 tff(19414,plain,
% 9.58/9.81 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[17688, 3446, 19407, 19338, 10, 2, 19413, 31])).
% 9.58/9.81 tff(19415,plain,
% 9.58/9.81 (b(s(s(z)), s(s(s(s(z)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[3652, 19414])).
% 9.58/9.81 tff(19416,plain,
% 9.58/9.81 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[818])).
% 9.58/9.81 tff(19417,plain,
% 9.58/9.81 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 9.58/9.81 inference(symmetry,[status(thm)],[19416])).
% 9.58/9.81 tff(19418,plain,
% 9.58/9.81 (b(elem!1, s(s(z)))),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[802, 19417])).
% 9.58/9.81 tff(19419,plain,
% 9.58/9.81 (b(elem!1, s(s(s(s(z)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[8539, 812, 19338])).
% 9.58/9.81 tff(19420,plain,
% 9.58/9.81 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[9127, 19415, 19419, 19418])).
% 9.58/9.81 tff(19421,plain,
% 9.58/9.81 (r(s(s(s(s(z)))), s(s(z)))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[1714, 19420])).
% 9.58/9.81 tff(19422,plain,
% 9.58/9.81 (~r(s(s(z)), z)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[14773, 3447, 19418, 59, 19419])).
% 9.58/9.81 tff(19423,plain,
% 9.58/9.81 (b(s(s(z)), z)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[1211, 19422])).
% 9.58/9.81 tff(19424,plain,
% 9.58/9.81 (b(s(elem!1), z)),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[19423, 9630])).
% 9.58/9.81 tff(19425,plain,
% 9.58/9.81 (~b(z, s(elem!1))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[1939, 19424, 18965, 802])).
% 9.58/9.81 tff(19426,plain,
% 9.58/9.81 (r(z, s(elem!1))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[566, 19425])).
% 9.58/9.81 tff(19427,plain,
% 9.58/9.81 (r(z, s(s(z)))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[8520, 19426, 812])).
% 9.58/9.81 tff(19428,plain,
% 9.58/9.81 (~r(s(s(z)), s(z))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[18433, 19427, 19421, 3447])).
% 9.58/9.81 tff(19429,plain,
% 9.58/9.81 (b(s(s(z)), s(z))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[3778, 19428])).
% 9.58/9.81 tff(19430,plain,
% 9.58/9.81 (~b(s(s(elem!1)), z)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[14756, 19429, 19338, 19415, 19409])).
% 9.58/9.81 tff(19431,plain,
% 9.58/9.81 (r(s(s(elem!1)), z)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[2629, 19430])).
% 9.58/9.81 tff(19432,plain,
% 9.58/9.81 (b(s(elem!1), s(s(s(elem!1))))),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[19415, 9785])).
% 9.58/9.81 tff(19433,plain,
% 9.58/9.81 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[818])).
% 9.58/9.81 tff(19434,plain,
% 9.58/9.81 (r(s(s(s(s(z)))), s(elem!1))),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[19421, 19433])).
% 9.58/9.81 tff(19435,plain,
% 9.58/9.81 (~r(s(elem!1), elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[5914, 19426, 19434, 3447])).
% 9.58/9.81 tff(19436,plain,
% 9.58/9.81 (b(s(elem!1), elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[2168, 19435, 19412])).
% 9.58/9.81 tff(19437,plain,
% 9.58/9.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.58/9.81 inference(rewrite,[status(thm)],[])).
% 9.58/9.81 tff(19438,plain,
% 9.58/9.81 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.58/9.81 inference(rewrite,[status(thm)],[])).
% 9.58/9.81 tff(19439,plain,
% 9.58/9.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19438])).
% 9.58/9.81 tff(19440,plain,
% 9.58/9.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.58/9.81 inference(transitivity,[status(thm)],[19439, 19437])).
% 9.58/9.81 tff(19441,plain,
% 9.58/9.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 9.58/9.81 inference(quant_inst,[status(thm)],[])).
% 9.58/9.81 tff(19442,plain,
% 9.58/9.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[19441, 19440])).
% 9.58/9.81 tff(19443,plain,
% 9.58/9.81 ($false),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[19442, 391, 448, 1374, 2122, 1152, 1036])).
% 9.58/9.81 tff(19444,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.81 tff(19445,plain,
% 9.58/9.81 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[19444, 19436, 19408, 19410, 19432])).
% 9.58/9.81 tff(19446,plain,
% 9.58/9.81 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[1048, 19445, 19140])).
% 9.58/9.81 tff(19447,plain,
% 9.58/9.81 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[8251, 19411])).
% 9.58/9.81 tff(19448,plain,
% 9.58/9.81 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[299, 19447])).
% 9.58/9.81 tff(19449,plain,
% 9.58/9.81 (r(s(s(s(elem!1))), z)),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[3447, 7600])).
% 9.58/9.81 tff(19450,plain,
% 9.58/9.81 (~b(z, s(s(s(s(elem!1)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[17931, 19436, 18965, 19449, 19448, 8232, 19424])).
% 9.58/9.81 tff(19451,plain,
% 9.58/9.81 (r(z, s(s(s(s(elem!1)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[2767, 19450])).
% 9.58/9.81 tff(19452,plain,
% 9.58/9.81 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 9.58/9.81 inference(transitivity,[status(thm)],[19433, 7982])).
% 9.58/9.81 tff(19453,plain,
% 9.58/9.81 (r(s(s(s(elem!1))), s(elem!1))),
% 9.58/9.81 inference(modus_ponens,[status(thm)],[19421, 19452])).
% 9.58/9.81 tff(19454,plain,
% 9.58/9.81 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[17971, 19426, 59, 19453])).
% 9.58/9.81 tff(19455,plain,
% 9.58/9.81 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[1639, 19454, 18085])).
% 9.58/9.81 tff(19456,plain,
% 9.58/9.81 (~b(s(s(s(s(elem!1)))), elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[17982, 19455, 802, 19436])).
% 9.58/9.81 tff(19457,plain,
% 9.58/9.81 (r(s(s(s(s(elem!1)))), elem!1)),
% 9.58/9.81 inference(unit_resolution,[status(thm)],[1004, 19456, 7473])).
% 9.58/9.81 tff(19458,plain,
% 9.58/9.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.58/9.81 inference(rewrite,[status(thm)],[])).
% 9.58/9.81 tff(19459,plain,
% 9.58/9.81 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.58/9.81 inference(rewrite,[status(thm)],[])).
% 9.58/9.81 tff(19460,plain,
% 9.58/9.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 9.58/9.81 inference(monotonicity,[status(thm)],[19459])).
% 9.58/9.81 tff(19461,plain,
% 9.58/9.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 9.58/9.82 inference(transitivity,[status(thm)],[19460, 19458])).
% 9.58/9.82 tff(19462,plain,
% 9.58/9.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)))),
% 9.58/9.82 inference(quant_inst,[status(thm)],[])).
% 9.58/9.82 tff(19463,plain,
% 9.58/9.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 9.58/9.82 inference(modus_ponens,[status(thm)],[19462, 19461])).
% 9.58/9.82 tff(19464,plain,
% 9.58/9.82 ($false),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[19463, 194, 19457, 19451, 19446, 19431])).
% 9.58/9.82 tff(19465,plain,(b(s(s(s(s(z)))), z) | (~b(elem!1, s(elem!1))) | (~(s(z) = elem!1)) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.82 tff(19466,plain,
% 9.58/9.82 (b(s(s(s(s(z)))), z)),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[19465, 19374, 19367, 10, 2, 31])).
% 9.58/9.82 tff(19467,plain,
% 9.58/9.82 (b(s(s(s(elem!1))), z)),
% 9.58/9.82 inference(modus_ponens,[status(thm)],[19466, 19406])).
% 9.58/9.82 tff(19468,plain,
% 9.58/9.82 (b(elem!1, s(elem!1))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[443, 438, 17526])).
% 9.58/9.82 tff(19469,plain,
% 9.58/9.82 (~b(z, s(elem!1))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[1939, 591, 665, 19468])).
% 9.58/9.82 tff(19470,plain,
% 9.58/9.82 (r(z, s(elem!1))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[566, 19469])).
% 9.58/9.82 tff(19471,plain,
% 9.58/9.82 (b(elem!1, s(s(z)))),
% 9.58/9.82 inference(modus_ponens,[status(thm)],[19468, 19417])).
% 9.58/9.82 tff(19472,plain,
% 9.58/9.82 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[9127, 3823, 2064, 19471])).
% 9.58/9.82 tff(19473,plain,
% 9.58/9.82 (r(s(s(s(s(z)))), s(s(z)))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[1714, 19472])).
% 9.58/9.82 tff(19474,plain,
% 9.58/9.82 (r(s(s(s(elem!1))), s(elem!1))),
% 9.58/9.82 inference(modus_ponens,[status(thm)],[19473, 19452])).
% 9.58/9.82 tff(19475,plain,
% 9.58/9.82 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[17971, 613, 184, 19470])).
% 9.58/9.82 tff(19476,plain,
% 9.58/9.82 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[1639, 19475, 18085])).
% 9.58/9.82 tff(19477,plain,
% 9.58/9.82 (~b(s(s(s(s(elem!1)))), elem!1)),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[17982, 2122, 19468, 19476])).
% 9.58/9.82 tff(19478,plain,
% 9.58/9.82 (r(s(s(s(s(elem!1)))), elem!1)),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[1004, 19477, 7473])).
% 9.58/9.82 tff(19479,plain,
% 9.58/9.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 9.58/9.82 inference(rewrite,[status(thm)],[])).
% 9.58/9.82 tff(19480,plain,
% 9.58/9.82 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 9.58/9.82 inference(rewrite,[status(thm)],[])).
% 9.58/9.82 tff(19481,plain,
% 9.58/9.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 9.58/9.82 inference(monotonicity,[status(thm)],[19480])).
% 9.58/9.82 tff(19482,plain,
% 9.58/9.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 9.58/9.82 inference(transitivity,[status(thm)],[19481, 19479])).
% 9.58/9.82 tff(19483,plain,
% 9.58/9.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 9.58/9.82 inference(quant_inst,[status(thm)],[])).
% 9.58/9.82 tff(19484,plain,
% 9.58/9.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 9.58/9.82 inference(modus_ponens,[status(thm)],[19483, 19482])).
% 9.58/9.82 tff(19485,plain,
% 9.58/9.82 (~b(s(elem!1), s(s(elem!1)))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[19484, 391, 380, 973, 448, 2122])).
% 9.58/9.82 tff(19486,plain,
% 9.58/9.82 (r(s(elem!1), s(s(elem!1)))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[8644, 19485, 8611])).
% 9.58/9.82 tff(19487,plain,
% 9.58/9.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 9.58/9.82 inference(rewrite,[status(thm)],[])).
% 9.58/9.82 tff(19488,plain,
% 9.58/9.82 (((~b(s(elem!1), elem!1)) | (~b(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)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 9.58/9.82 inference(rewrite,[status(thm)],[])).
% 9.58/9.82 tff(19489,plain,
% 9.58/9.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 9.58/9.82 inference(monotonicity,[status(thm)],[19488])).
% 9.58/9.82 tff(19490,plain,
% 9.58/9.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 9.58/9.82 inference(transitivity,[status(thm)],[19489, 19487])).
% 9.58/9.82 tff(19491,plain,
% 9.58/9.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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))))),
% 9.58/9.82 inference(quant_inst,[status(thm)],[])).
% 9.58/9.82 tff(19492,plain,
% 9.58/9.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 9.58/9.82 inference(modus_ponens,[status(thm)],[19491, 19490])).
% 9.58/9.82 tff(19493,plain,
% 9.58/9.82 ($false),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[19492, 391, 973, 802, 1037, 2122])).
% 9.58/9.82 tff(19494,plain,((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.82 tff(19495,plain,
% 9.58/9.82 (~b(s(s(elem!1)), s(elem!1))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[19494, 973, 802, 2122])).
% 9.58/9.82 tff(19496,plain,
% 9.58/9.82 (r(s(s(elem!1)), s(elem!1))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[1135, 19495, 285])).
% 9.58/9.82 tff(19497,plain,
% 9.58/9.82 ($false),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[18194, 194, 613, 327, 19496, 19486])).
% 9.58/9.82 tff(19498,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.82 tff(19499,plain,
% 9.58/9.82 (~b(s(s(elem!1)), elem!1)),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[19498, 327, 613, 8611, 380, 448, 2122, 285, 19468])).
% 9.58/9.82 tff(19500,plain,
% 9.58/9.82 (r(s(s(elem!1)), elem!1)),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[872, 19499, 7422])).
% 9.58/9.82 tff(19501,plain,
% 9.58/9.82 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 9.58/9.82 inference(monotonicity,[status(thm)],[19132])).
% 9.58/9.82 tff(19502,plain,
% 9.58/9.82 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 9.58/9.82 inference(modus_ponens,[status(thm)],[19139, 19501])).
% 9.58/9.82 tff(19503,plain,
% 9.58/9.82 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 9.58/9.82 inference(modus_ponens,[status(thm)],[327, 9598])).
% 9.58/9.82 tff(19504,plain,
% 9.58/9.82 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[14274, 1176, 327, 991])).
% 9.58/9.82 tff(19505,plain,
% 9.58/9.82 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.58/9.82 inference(unit_resolution,[status(thm)],[1164, 19504, 18146])).
% 9.58/9.82 tff(19506,plain,
% 9.58/9.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.58/9.82 inference(rewrite,[status(thm)],[])).
% 9.58/9.82 tff(19507,plain,
% 9.58/9.82 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.58/9.82 inference(rewrite,[status(thm)],[])).
% 9.58/9.82 tff(19508,plain,
% 9.58/9.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 9.58/9.82 inference(monotonicity,[status(thm)],[19507])).
% 9.58/9.83 tff(19509,plain,
% 9.58/9.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.58/9.83 inference(transitivity,[status(thm)],[19508, 19506])).
% 9.58/9.83 tff(19510,plain,
% 9.58/9.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 9.58/9.83 inference(quant_inst,[status(thm)],[])).
% 9.58/9.83 tff(19511,plain,
% 9.58/9.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 9.58/9.83 inference(modus_ponens,[status(thm)],[19510, 19509])).
% 9.58/9.83 tff(19512,plain,
% 9.58/9.83 ($false),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[19511, 391, 448, 2122, 1733, 1573, 1036])).
% 9.58/9.83 tff(19513,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.83 tff(19514,plain,
% 9.58/9.83 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[19513, 19505, 448, 2122, 1036])).
% 9.58/9.83 tff(19515,plain,
% 9.58/9.83 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[1061, 19514, 1050])).
% 9.58/9.83 tff(19516,plain,
% 9.58/9.83 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[17954, 19505, 448, 2122, 1036])).
% 9.58/9.83 tff(19517,plain,
% 9.58/9.83 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[1095, 19516, 18143])).
% 9.58/9.83 tff(19518,plain,
% 9.58/9.83 (~r(s(s(elem!1)), elem!1)),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[14240, 19517, 327, 19515])).
% 9.58/9.83 tff(19519,plain,
% 9.58/9.83 (b(s(s(elem!1)), elem!1)),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[872, 19518, 249])).
% 9.58/9.83 tff(19520,plain,
% 9.58/9.83 (~b(z, s(s(elem!1)))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[8483, 19519, 380, 591, 1036])).
% 9.58/9.83 tff(19521,plain,
% 9.58/9.83 (r(z, s(s(elem!1)))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[324, 19520])).
% 9.58/9.83 tff(19522,plain,
% 9.58/9.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.58/9.83 inference(rewrite,[status(thm)],[])).
% 9.58/9.83 tff(19523,plain,
% 9.58/9.83 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.58/9.83 inference(rewrite,[status(thm)],[])).
% 9.58/9.83 tff(19524,plain,
% 9.58/9.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 9.58/9.83 inference(monotonicity,[status(thm)],[19523])).
% 9.58/9.83 tff(19525,plain,
% 9.58/9.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.58/9.83 inference(transitivity,[status(thm)],[19524, 19522])).
% 9.58/9.83 tff(19526,plain,
% 9.58/9.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 9.58/9.83 inference(quant_inst,[status(thm)],[])).
% 9.58/9.83 tff(19527,plain,
% 9.58/9.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 9.58/9.83 inference(modus_ponens,[status(thm)],[19526, 19525])).
% 9.58/9.83 tff(19528,plain,
% 9.58/9.83 ($false),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[19527, 194, 184, 327, 19521, 1176])).
% 9.58/9.83 tff(19529,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.83 tff(19530,plain,
% 9.58/9.83 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[19529, 327, 184, 380, 591, 1036, 7422, 19502, 448, 2122, 19478])).
% 9.58/9.83 tff(19531,plain,
% 9.58/9.83 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[1048, 19530, 19140])).
% 9.58/9.83 tff(19532,plain,
% 9.58/9.83 (~r(z, s(s(s(elem!1))))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[372, 327, 326, 364])).
% 9.58/9.83 tff(19533,plain,
% 9.58/9.83 (b(z, s(s(s(elem!1))))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[58, 19532])).
% 9.58/9.83 tff(19534,plain,
% 9.58/9.83 (~b(s(s(s(elem!1))), elem!1)),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[17249, 19533, 380, 665])).
% 9.58/9.83 tff(19535,plain,
% 9.58/9.83 (~b(s(s(s(elem!1))), s(elem!1))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[12799, 19533, 380, 591])).
% 9.58/9.83 tff(19536,plain,
% 9.58/9.83 (r(s(s(s(elem!1))), s(elem!1))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[588, 19535, 279])).
% 9.58/9.83 tff(19537,plain,
% 9.58/9.83 (~(s(s(s(elem!1))) = elem!1)),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[13062, 19536, 438])).
% 9.58/9.83 tff(19538,plain,
% 9.58/9.83 (b(elem!1, s(s(s(elem!1))))),
% 9.58/9.83 inference(unit_resolution,[status(thm)],[4039, 19537, 364, 327, 19534])).
% 9.58/9.83 tff(19539,plain,
% 9.58/9.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 9.58/9.83 inference(rewrite,[status(thm)],[])).
% 9.58/9.83 tff(19540,plain,
% 9.58/9.83 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 9.58/9.83 inference(rewrite,[status(thm)],[])).
% 9.58/9.83 tff(19541,plain,
% 9.58/9.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 9.58/9.84 inference(monotonicity,[status(thm)],[19540])).
% 9.58/9.84 tff(19542,plain,
% 9.58/9.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 9.58/9.84 inference(transitivity,[status(thm)],[19541, 19539])).
% 9.58/9.84 tff(19543,plain,
% 9.58/9.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 9.58/9.84 inference(quant_inst,[status(thm)],[])).
% 9.58/9.84 tff(19544,plain,
% 9.58/9.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 9.58/9.84 inference(modus_ponens,[status(thm)],[19543, 19542])).
% 9.58/9.84 tff(19545,plain,
% 9.58/9.84 ($false),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[19544, 391, 665, 380, 19533, 19538])).
% 9.58/9.84 tff(19546,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), elem!1)) | r(elem!1, s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.84 tff(19547,plain,
% 9.58/9.84 (~r(z, s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[19546, 364, 665, 438, 380, 279, 327, 591])).
% 9.58/9.84 tff(19548,plain,
% 9.58/9.84 (b(z, s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[324, 19547])).
% 9.58/9.84 tff(19549,plain,
% 9.58/9.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 9.58/9.84 inference(rewrite,[status(thm)],[])).
% 9.58/9.84 tff(19550,plain,
% 9.58/9.84 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 9.58/9.84 inference(rewrite,[status(thm)],[])).
% 9.58/9.84 tff(19551,plain,
% 9.58/9.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 9.58/9.84 inference(monotonicity,[status(thm)],[19550])).
% 9.58/9.84 tff(19552,plain,
% 9.58/9.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 9.58/9.84 inference(transitivity,[status(thm)],[19551, 19549])).
% 9.58/9.84 tff(19553,plain,
% 9.58/9.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 9.58/9.84 inference(quant_inst,[status(thm)],[])).
% 9.58/9.84 tff(19554,plain,
% 9.58/9.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 9.58/9.84 inference(modus_ponens,[status(thm)],[19553, 19552])).
% 9.58/9.84 tff(19555,plain,
% 9.58/9.84 ($false),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[19554, 391, 665, 381, 380, 448, 3927])).
% 9.58/9.84 tff(19556,plain,((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.84 tff(19557,plain,
% 9.58/9.84 (~b(s(s(elem!1)), s(z))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[19556, 19548, 665, 448, 380])).
% 9.58/9.84 tff(19558,plain,
% 9.58/9.84 (r(s(s(elem!1)), s(z))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[362, 19557])).
% 9.58/9.84 tff(19559,plain,
% 9.58/9.84 (~r(s(z), s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[11801, 19558, 723, 6240])).
% 9.58/9.84 tff(19560,plain,
% 9.58/9.84 (~r(elem!1, s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[15602, 19559, 169])).
% 9.58/9.84 tff(19561,plain,
% 9.58/9.84 (b(elem!1, s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[1307, 19560, 1457])).
% 9.58/9.84 tff(19562,plain,
% 9.58/9.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.58/9.84 inference(rewrite,[status(thm)],[])).
% 9.58/9.84 tff(19563,plain,
% 9.58/9.84 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.58/9.84 inference(rewrite,[status(thm)],[])).
% 9.58/9.84 tff(19564,plain,
% 9.58/9.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 9.58/9.84 inference(monotonicity,[status(thm)],[19563])).
% 9.58/9.84 tff(19565,plain,
% 9.58/9.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.58/9.84 inference(transitivity,[status(thm)],[19564, 19562])).
% 9.58/9.84 tff(19566,plain,
% 9.58/9.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 9.58/9.84 inference(quant_inst,[status(thm)],[])).
% 9.58/9.84 tff(19567,plain,
% 9.58/9.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 9.58/9.84 inference(modus_ponens,[status(thm)],[19566, 19565])).
% 9.58/9.84 tff(19568,plain,
% 9.58/9.84 ($false),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[19567, 391, 665, 3927, 1294, 1733, 1152])).
% 9.58/9.84 tff(19569,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.84 tff(19570,plain,
% 9.58/9.84 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[19569, 19561, 1152, 19548, 665])).
% 9.58/9.84 tff(19571,plain,
% 9.58/9.84 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[1061, 19570, 1050])).
% 9.58/9.84 tff(19572,plain,
% 9.58/9.84 ($false),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[14292, 194, 364, 327, 19571, 1538])).
% 9.58/9.84 tff(19573,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (elem!1 = s(s(elem!1))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | r(elem!1, s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.84 tff(19574,plain,
% 9.58/9.84 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[19573, 19500, 327, 19502, 19531, 665, 9651, 7866, 723, 19503, 448, 380, 438, 7433, 591])).
% 9.58/9.84 tff(19575,plain,
% 9.58/9.84 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[1164, 19574, 18146])).
% 9.58/9.84 tff(19576,plain,
% 9.58/9.84 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[19513, 19575, 448, 2122, 1036])).
% 9.58/9.84 tff(19577,plain,
% 9.58/9.84 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[1061, 19576, 19502])).
% 9.58/9.84 tff(19578,plain,
% 9.58/9.84 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[17954, 19575, 448, 2122, 1036])).
% 9.58/9.84 tff(19579,plain,
% 9.58/9.84 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[1095, 19578, 18143])).
% 9.58/9.84 tff(19580,plain,
% 9.58/9.84 ($false),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[14240, 19579, 19577, 327, 19500])).
% 9.58/9.84 tff(19581,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), z)) | r(elem!1, s(elem!1)) | (~b(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.84 tff(19582,plain,
% 9.58/9.84 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[19581, 2122, 448, 1036, 665, 723, 380, 438, 591, 613, 8611, 285, 184, 812])).
% 9.58/9.84 tff(19583,plain,
% 9.58/9.84 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[1370, 19582, 16094])).
% 9.58/9.84 tff(19584,plain,
% 9.58/9.84 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[19444, 19583, 2122, 448, 1036])).
% 9.58/9.84 tff(19585,plain,
% 9.58/9.84 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.58/9.84 inference(unit_resolution,[status(thm)],[1048, 19584, 19140])).
% 9.58/9.84 tff(19586,plain,
% 9.58/9.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.58/9.85 inference(rewrite,[status(thm)],[])).
% 9.58/9.85 tff(19587,plain,
% 9.58/9.85 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.58/9.85 inference(rewrite,[status(thm)],[])).
% 9.58/9.85 tff(19588,plain,
% 9.58/9.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 9.58/9.85 inference(monotonicity,[status(thm)],[19587])).
% 9.58/9.85 tff(19589,plain,
% 9.58/9.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.58/9.85 inference(transitivity,[status(thm)],[19588, 19586])).
% 9.58/9.85 tff(19590,plain,
% 9.58/9.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 9.58/9.85 inference(quant_inst,[status(thm)],[])).
% 9.58/9.85 tff(19591,plain,
% 9.58/9.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))),
% 9.58/9.85 inference(modus_ponens,[status(thm)],[19590, 19589])).
% 9.58/9.85 tff(19592,plain,
% 9.58/9.85 ($false),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[19591, 391, 380, 448, 2122, 2781, 1036])).
% 9.58/9.85 tff(19593,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.85 tff(19594,plain,
% 9.58/9.85 (~b(z, s(s(s(s(elem!1)))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[19593, 2122, 448, 380, 1036])).
% 9.58/9.85 tff(19595,plain,
% 9.58/9.85 (r(z, s(s(s(s(elem!1)))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[2767, 19594])).
% 9.58/9.85 tff(19596,plain,
% 9.58/9.85 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[17944, 19595, 184, 613])).
% 9.58/9.85 tff(19597,plain,
% 9.58/9.85 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[1095, 19596, 18143])).
% 9.58/9.85 tff(19598,plain,
% 9.58/9.85 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[17954, 19597, 448, 2122, 1036])).
% 9.58/9.85 tff(19599,plain,
% 9.58/9.85 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[1164, 19598, 18146])).
% 9.58/9.85 tff(19600,plain,
% 9.58/9.85 (~r(z, s(s(elem!1)))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[2800, 19595, 19478, 19585])).
% 9.58/9.85 tff(19601,plain,
% 9.58/9.85 (b(z, s(s(elem!1)))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[324, 19600])).
% 9.58/9.85 tff(19602,plain,
% 9.58/9.85 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[4893, 19601, 380, 19583])).
% 9.58/9.85 tff(19603,plain,
% 9.58/9.85 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[1356, 19602, 16095])).
% 9.58/9.85 tff(19604,plain,
% 9.58/9.85 ($false),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[14542, 19603, 19599, 19585, 19478])).
% 9.58/9.85 tff(19605,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~r(s(s(s(s(z)))), s(z))) | r(elem!1, s(elem!1)) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.85 tff(19606,plain,
% 9.58/9.85 (~b(s(elem!1), elem!1)),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[19605, 19077, 448, 380, 184, 19474, 665, 723, 438, 591, 8611, 285, 812])).
% 9.58/9.85 tff(19607,plain,
% 9.58/9.85 (r(s(elem!1), elem!1)),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[2168, 19606, 16989])).
% 9.58/9.85 tff(19608,plain,
% 9.58/9.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 9.58/9.85 inference(rewrite,[status(thm)],[])).
% 9.58/9.85 tff(19609,plain,
% 9.58/9.85 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 9.58/9.85 inference(rewrite,[status(thm)],[])).
% 9.58/9.85 tff(19610,plain,
% 9.58/9.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 9.58/9.85 inference(monotonicity,[status(thm)],[19609])).
% 9.58/9.85 tff(19611,plain,
% 9.58/9.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 9.58/9.85 inference(transitivity,[status(thm)],[19610, 19608])).
% 9.58/9.85 tff(19612,plain,
% 9.58/9.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 9.58/9.85 inference(quant_inst,[status(thm)],[])).
% 9.58/9.85 tff(19613,plain,
% 9.58/9.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))),
% 9.58/9.85 inference(modus_ponens,[status(thm)],[19612, 19611])).
% 9.58/9.85 tff(19614,plain,
% 9.58/9.85 ($false),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[19613, 194, 19474, 19607, 19470, 184])).
% 9.58/9.85 tff(19615,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~r(s(s(s(s(z)))), s(z))) | r(elem!1, s(elem!1)) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~(s(z) = elem!1)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.85 tff(19616,plain,
% 9.58/9.85 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[19615, 591, 448, 380, 665, 723, 438, 184, 8611, 285, 812, 2064])).
% 9.58/9.85 tff(19617,plain,
% 9.58/9.85 (r(s(s(z)), s(s(s(s(z)))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[3652, 19616])).
% 9.58/9.85 tff(19618,plain,
% 9.58/9.85 (r(s(elem!1), s(s(s(elem!1))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[3614, 19617, 812])).
% 9.58/9.85 tff(19619,plain,
% 9.58/9.85 ($false),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[17682, 194, 233, 19470, 184, 19618])).
% 9.58/9.85 tff(19620,plain,((~b(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~r(s(s(s(s(z)))), s(z))) | r(elem!1, s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.85 tff(19621,plain,
% 9.58/9.85 (~b(s(elem!1), z)),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[19620, 19372, 59, 19367, 19368, 19467, 18965, 19405, 19373, 19401, 19398, 19395])).
% 9.58/9.85 tff(19622,plain,
% 9.58/9.85 (r(s(elem!1), z)),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[549, 19621])).
% 9.58/9.85 tff(19623,plain,
% 9.58/9.85 (~r(s(elem!1), s(s(s(elem!1))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[7811, 19622, 19372, 59])).
% 9.58/9.85 tff(19624,plain,
% 9.58/9.85 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[3614, 19623, 19367])).
% 9.58/9.85 tff(19625,plain,
% 9.58/9.85 (b(s(s(z)), s(s(s(s(z)))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[3652, 19624])).
% 9.58/9.85 tff(19626,plain,
% 9.58/9.85 (b(s(elem!1), s(s(s(elem!1))))),
% 9.58/9.85 inference(modus_ponens,[status(thm)],[19625, 19394])).
% 9.58/9.85 tff(19627,plain,
% 9.58/9.85 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 9.58/9.85 inference(monotonicity,[status(thm)],[19391])).
% 9.58/9.85 tff(19628,plain,
% 9.58/9.85 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 9.58/9.85 inference(monotonicity,[status(thm)],[19389])).
% 9.58/9.85 tff(19629,plain,
% 9.58/9.85 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 9.58/9.85 inference(transitivity,[status(thm)],[19628, 19627])).
% 9.58/9.85 tff(19630,plain,
% 9.58/9.85 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 9.58/9.85 inference(monotonicity,[status(thm)],[19389])).
% 9.58/9.85 tff(19631,plain,
% 9.58/9.85 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 9.58/9.85 inference(symmetry,[status(thm)],[19630])).
% 9.58/9.85 tff(19632,plain,
% 9.58/9.85 (b(elem!1, s(s(z)))),
% 9.58/9.85 inference(modus_ponens,[status(thm)],[19374, 19631])).
% 9.58/9.85 tff(19633,plain,
% 9.58/9.85 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[9127, 19625, 19395, 19632])).
% 9.58/9.85 tff(19634,plain,
% 9.58/9.85 (r(s(s(s(s(z)))), s(s(z)))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[1714, 19633])).
% 9.58/9.85 tff(19635,plain,
% 9.58/9.85 (r(s(s(s(elem!1))), s(elem!1))),
% 9.58/9.85 inference(modus_ponens,[status(thm)],[19634, 19629])).
% 9.58/9.85 tff(19636,plain,
% 9.58/9.85 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[8251, 19369])).
% 9.58/9.85 tff(19637,plain,
% 9.58/9.85 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 9.58/9.85 inference(unit_resolution,[status(thm)],[299, 19636])).
% 9.58/9.85 tff(19638,plain,
% 9.58/9.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.58/9.85 inference(rewrite,[status(thm)],[])).
% 9.58/9.85 tff(19639,plain,
% 9.58/9.85 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.58/9.85 inference(rewrite,[status(thm)],[])).
% 9.58/9.85 tff(19640,plain,
% 9.58/9.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 9.58/9.86 inference(monotonicity,[status(thm)],[19639])).
% 9.58/9.86 tff(19641,plain,
% 9.58/9.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(transitivity,[status(thm)],[19640, 19638])).
% 9.58/9.86 tff(19642,plain,
% 9.58/9.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 9.58/9.86 inference(quant_inst,[status(thm)],[])).
% 9.58/9.86 tff(19643,plain,
% 9.58/9.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))),
% 9.58/9.86 inference(modus_ponens,[status(thm)],[19642, 19641])).
% 9.58/9.86 tff(19644,plain,
% 9.58/9.86 ($false),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[19643, 391, 380, 448, 802, 2781, 1036])).
% 9.58/9.86 tff(19645,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.86 tff(19646,plain,
% 9.58/9.86 (~b(z, s(s(s(s(elem!1)))))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[19645, 19467, 19368, 19374, 19626])).
% 9.58/9.86 tff(19647,plain,
% 9.58/9.86 (r(z, s(s(s(s(elem!1)))))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[2767, 19646])).
% 9.58/9.86 tff(19648,plain,
% 9.58/9.86 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[17944, 19647, 59, 19635])).
% 9.58/9.86 tff(19649,plain,
% 9.58/9.86 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[1095, 19648, 19637])).
% 9.58/9.86 tff(19650,plain,
% 9.58/9.86 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[929, 15376])).
% 9.58/9.86 tff(19651,plain,
% 9.58/9.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(rewrite,[status(thm)],[])).
% 9.58/9.86 tff(19652,plain,
% 9.58/9.86 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(rewrite,[status(thm)],[])).
% 9.58/9.86 tff(19653,plain,
% 9.58/9.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 9.58/9.86 inference(monotonicity,[status(thm)],[19652])).
% 9.58/9.86 tff(19654,plain,
% 9.58/9.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(transitivity,[status(thm)],[19653, 19651])).
% 9.58/9.86 tff(19655,plain,
% 9.58/9.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 9.58/9.86 inference(quant_inst,[status(thm)],[])).
% 9.58/9.86 tff(19656,plain,
% 9.58/9.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 9.58/9.86 inference(modus_ponens,[status(thm)],[19655, 19654])).
% 9.58/9.86 tff(19657,plain,
% 9.58/9.86 ($false),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[19656, 194, 613, 485, 233, 1063])).
% 9.58/9.86 tff(19658,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.86 tff(19659,plain,
% 9.58/9.86 (~r(elem!1, s(s(s(s(elem!1)))))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[19658, 485, 233, 613])).
% 9.58/9.86 tff(19660,plain,
% 9.58/9.86 (b(elem!1, s(s(s(s(elem!1)))))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[1018, 19659, 14203])).
% 9.58/9.86 tff(19661,plain,
% 9.58/9.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(rewrite,[status(thm)],[])).
% 9.58/9.86 tff(19662,plain,
% 9.58/9.86 (((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(rewrite,[status(thm)],[])).
% 9.58/9.86 tff(19663,plain,
% 9.58/9.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 9.58/9.86 inference(monotonicity,[status(thm)],[19662])).
% 9.58/9.86 tff(19664,plain,
% 9.58/9.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(transitivity,[status(thm)],[19663, 19661])).
% 9.58/9.86 tff(19665,plain,
% 9.58/9.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(quant_inst,[status(thm)],[])).
% 9.58/9.86 tff(19666,plain,
% 9.58/9.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 9.58/9.86 inference(modus_ponens,[status(thm)],[19665, 19664])).
% 9.58/9.86 tff(19667,plain,
% 9.58/9.86 ($false),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[19666, 391, 380, 974, 802, 975, 1036])).
% 9.58/9.86 tff(19668,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.86 tff(19669,plain,
% 9.58/9.86 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[19668, 19660, 380, 802, 1036])).
% 9.58/9.86 tff(19670,plain,
% 9.58/9.86 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[988, 19669, 19650])).
% 9.58/9.86 tff(19671,plain,
% 9.58/9.86 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[1159, 194, 613, 485, 19670])).
% 9.58/9.86 tff(19672,plain,
% 9.58/9.86 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.58/9.86 inference(unit_resolution,[status(thm)],[1164, 19671, 18146])).
% 9.58/9.86 tff(19673,plain,
% 9.58/9.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(rewrite,[status(thm)],[])).
% 9.58/9.86 tff(19674,plain,
% 9.58/9.86 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(rewrite,[status(thm)],[])).
% 9.58/9.86 tff(19675,plain,
% 9.58/9.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 9.58/9.86 inference(monotonicity,[status(thm)],[19674])).
% 9.58/9.86 tff(19676,plain,
% 9.58/9.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.58/9.86 inference(transitivity,[status(thm)],[19675, 19673])).
% 9.58/9.86 tff(19677,plain,
% 9.58/9.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 9.58/9.86 inference(quant_inst,[status(thm)],[])).
% 9.58/9.87 tff(19678,plain,
% 9.58/9.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 9.58/9.87 inference(modus_ponens,[status(thm)],[19677, 19676])).
% 9.58/9.87 tff(19679,plain,
% 9.58/9.87 ($false),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[19678, 391, 380, 448, 19660, 19672, 1114])).
% 9.58/9.87 tff(19680,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.87 tff(19681,plain,
% 9.58/9.87 (~r(s(elem!1), elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[19680, 19467, 19368, 19649, 19635, 19374, 19626, 19388, 19372])).
% 9.58/9.87 tff(19682,plain,
% 9.58/9.87 (b(s(elem!1), elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[2168, 19681, 19370])).
% 9.58/9.87 tff(19683,plain,
% 9.58/9.87 (b(s(elem!1), s(z))),
% 9.58/9.87 inference(modus_ponens,[status(thm)],[19682, 19386])).
% 9.58/9.87 tff(19684,plain,
% 9.58/9.87 (~b(z, s(elem!1))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[7240, 19683, 10550, 19384, 19381])).
% 9.58/9.87 tff(19685,plain,
% 9.58/9.87 (r(z, s(elem!1))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[566, 19684])).
% 9.58/9.87 tff(19686,plain,
% 9.58/9.87 ($false),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[7820, 194, 19635, 19622, 19685, 59])).
% 9.58/9.87 tff(19687,plain,(b(s(s(s(elem!1))), elem!1) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.87 tff(19688,plain,
% 9.58/9.87 (b(s(s(s(elem!1))), elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[19687, 31, 2, 10])).
% 9.58/9.87 tff(19689,plain,
% 9.58/9.87 (~(s(z) = elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[8542, 4028, 19338])).
% 9.58/9.87 tff(19690,plain,
% 9.58/9.87 (~(elem!1 = s(z))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[172, 19689])).
% 9.58/9.87 tff(19691,plain,
% 9.58/9.87 (r(elem!1, s(z))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[837, 19690, 31])).
% 9.58/9.87 tff(19692,plain,
% 9.58/9.87 (~r(elem!1, s(s(s(elem!1))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[8380, 12778, 184, 411])).
% 9.58/9.87 tff(19693,plain,
% 9.58/9.87 ($false),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[424, 19692, 12780, 4028])).
% 9.58/9.87 tff(19694,plain,(b(s(s(s(elem!1))), z) | b(elem!1, s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.87 tff(19695,plain,
% 9.58/9.87 (b(s(s(s(elem!1))), z)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[19694, 4028, 59, 8232, 18965])).
% 9.58/9.87 tff(19696,plain,
% 9.58/9.87 (~b(s(z), elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[17542, 10482, 590, 665, 411, 1234, 3446])).
% 9.58/9.87 tff(19697,plain,
% 9.58/9.87 (r(s(z), elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[632, 19696, 150])).
% 9.58/9.87 tff(19698,plain,
% 9.58/9.87 (~r(z, s(z))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[18234, 3446, 411, 665, 1234, 847, 150])).
% 9.58/9.87 tff(19699,plain,
% 9.58/9.87 (b(z, s(z))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[678, 19698])).
% 9.58/9.87 tff(19700,plain,
% 9.58/9.87 (~b(z, s(s(s(s(z)))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[14799, 10483, 665, 1234, 590])).
% 9.58/9.87 tff(19701,plain,
% 9.58/9.87 (r(z, s(s(s(s(z)))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[800, 19700])).
% 9.58/9.87 tff(19702,plain,
% 9.58/9.87 (r(s(s(s(elem!1))), s(z))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[17668, 19696, 1234, 3446, 10])).
% 9.58/9.87 tff(19703,plain,
% 9.58/9.87 (~b(s(z), elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[17542, 3446, 590, 665, 411, 1234, 6221])).
% 9.58/9.87 tff(19704,plain,
% 9.58/9.87 (r(s(z), elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[632, 19703, 150])).
% 9.58/9.87 tff(19705,plain,
% 9.58/9.87 (~r(s(s(z)), z)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[14746, 3447, 1749, 184])).
% 9.58/9.87 tff(19706,plain,
% 9.58/9.87 (b(s(s(z)), z)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[1211, 19705])).
% 9.58/9.87 tff(19707,plain,
% 9.58/9.87 (s(s(z)) = elem!1),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[14843, 19706, 590, 665, 19699, 847, 19704])).
% 9.58/9.87 tff(19708,plain,
% 9.58/9.87 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 9.58/9.87 inference(monotonicity,[status(thm)],[19707])).
% 9.58/9.87 tff(19709,plain,
% 9.58/9.87 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(z)))),
% 9.58/9.87 inference(symmetry,[status(thm)],[19708])).
% 9.58/9.87 tff(19710,plain,
% 9.58/9.87 (b(s(s(s(elem!1))), s(s(z)))),
% 9.58/9.87 inference(modus_ponens,[status(thm)],[900, 19709])).
% 9.58/9.87 tff(19711,plain,
% 9.58/9.87 (~r(s(s(z)), z)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[14746, 1749, 184, 2053])).
% 9.58/9.87 tff(19712,plain,
% 9.58/9.87 (b(s(s(z)), z)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[1211, 19711])).
% 9.58/9.87 tff(19713,plain,
% 9.58/9.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.58/9.87 inference(rewrite,[status(thm)],[])).
% 9.58/9.87 tff(19714,plain,
% 9.58/9.87 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.58/9.87 inference(rewrite,[status(thm)],[])).
% 9.58/9.87 tff(19715,plain,
% 9.58/9.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 9.58/9.87 inference(monotonicity,[status(thm)],[19714])).
% 9.58/9.87 tff(19716,plain,
% 9.58/9.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.58/9.87 inference(transitivity,[status(thm)],[19715, 19713])).
% 9.58/9.87 tff(19717,plain,
% 9.58/9.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))),
% 9.58/9.87 inference(quant_inst,[status(thm)],[])).
% 9.58/9.87 tff(19718,plain,
% 9.58/9.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 9.58/9.87 inference(modus_ponens,[status(thm)],[19717, 19716])).
% 9.58/9.87 tff(19719,plain,
% 9.58/9.87 ($false),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[19718, 391, 380, 19712, 17039, 17493])).
% 9.58/9.87 tff(19720,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.87 tff(19721,plain,
% 9.58/9.87 (~b(s(s(s(elem!1))), s(s(z)))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[19720, 3447, 380, 184, 1749, 719])).
% 9.58/9.87 tff(19722,plain,
% 9.58/9.87 ($false),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[19721, 19710])).
% 9.58/9.87 tff(19723,plain,(b(s(s(s(s(z)))), z) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.58/9.87 tff(19724,plain,
% 9.58/9.87 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[19723, 19701, 590, 665, 847, 150, 900, 59, 380, 3446, 411, 1234, 10482])).
% 9.58/9.87 tff(19725,plain,
% 9.58/9.87 (b(s(s(z)), s(s(s(s(z)))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[3652, 19724])).
% 9.58/9.87 tff(19726,plain,
% 9.58/9.87 (~r(s(s(z)), z)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[15362, 19725, 59, 16830, 3447, 19702, 19701])).
% 9.58/9.87 tff(19727,plain,
% 9.58/9.87 (b(s(s(z)), z)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[1211, 19726])).
% 9.58/9.87 tff(19728,plain,
% 9.58/9.87 (s(s(z)) = elem!1),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[14843, 19727, 590, 665, 19699, 847, 19697])).
% 9.58/9.87 tff(19729,plain,
% 9.58/9.87 (s(s(s(z))) = s(elem!1)),
% 9.58/9.87 inference(monotonicity,[status(thm)],[19728])).
% 9.58/9.87 tff(19730,plain,
% 9.58/9.87 (s(s(s(s(z)))) = s(s(elem!1))),
% 9.58/9.87 inference(monotonicity,[status(thm)],[19729])).
% 9.58/9.87 tff(19731,plain,
% 9.58/9.87 (s(s(elem!1)) = s(s(s(s(z))))),
% 9.58/9.87 inference(symmetry,[status(thm)],[19730])).
% 9.58/9.87 tff(19732,plain,
% 9.58/9.87 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 9.58/9.87 inference(monotonicity,[status(thm)],[19731])).
% 9.58/9.87 tff(19733,plain,
% 9.58/9.87 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 9.58/9.87 inference(symmetry,[status(thm)],[19732])).
% 9.58/9.87 tff(19734,plain,
% 9.58/9.87 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 9.58/9.87 inference(monotonicity,[status(thm)],[19728])).
% 9.58/9.87 tff(19735,plain,
% 9.58/9.87 (b(elem!1, s(s(s(s(z)))))),
% 9.58/9.87 inference(modus_ponens,[status(thm)],[19725, 19734])).
% 9.58/9.87 tff(19736,plain,
% 9.58/9.87 (b(elem!1, s(s(elem!1)))),
% 9.58/9.87 inference(modus_ponens,[status(thm)],[19735, 19733])).
% 9.58/9.87 tff(19737,plain,
% 9.58/9.87 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.58/9.87 inference(monotonicity,[status(thm)],[19730])).
% 9.58/9.87 tff(19738,plain,
% 9.58/9.87 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[15957, 10483, 665, 1234, 3447, 847, 411, 59])).
% 9.58/9.87 tff(19739,plain,
% 9.58/9.87 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[15351, 19738, 16830])).
% 9.58/9.87 tff(19740,plain,
% 9.58/9.87 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.58/9.87 inference(modus_ponens,[status(thm)],[19739, 19737])).
% 9.58/9.87 tff(19741,plain,
% 9.58/9.87 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 9.58/9.87 inference(monotonicity,[status(thm)],[19730])).
% 9.58/9.87 tff(19742,plain,
% 9.58/9.87 (b(s(s(elem!1)), elem!1)),
% 9.58/9.87 inference(modus_ponens,[status(thm)],[10483, 19741])).
% 9.58/9.87 tff(19743,plain,
% 9.58/9.87 ($false),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[1465, 391, 900, 19742, 19740, 19736])).
% 9.58/9.87 tff(19744,plain,(b(s(s(s(s(z)))), z) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (~b(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.87 tff(19745,plain,
% 9.58/9.87 (b(s(s(s(s(z)))), z)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[19744, 19691, 10550, 18965, 19688, 19689, 19695, 8232, 19338, 10])).
% 9.58/9.87 tff(19746,plain,
% 9.58/9.87 (~b(z, s(s(s(s(z)))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[10438, 19745, 19338, 8232, 19691])).
% 9.58/9.87 tff(19747,plain,
% 9.58/9.87 (r(z, s(s(s(s(z)))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[800, 19746])).
% 9.58/9.87 tff(19748,plain,
% 9.58/9.87 (~r(s(s(s(s(z)))), elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[10418, 19747, 19691, 8232])).
% 9.58/9.87 tff(19749,plain,
% 9.58/9.87 (~b(s(s(s(elem!1))), s(z))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[10635, 664, 411, 184, 590, 4028, 31])).
% 9.58/9.87 tff(19750,plain,
% 9.58/9.87 (r(s(s(s(elem!1))), s(z))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[223, 19749])).
% 9.58/9.87 tff(19751,plain,
% 9.58/9.87 (~b(s(s(s(s(z)))), elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[14978, 664, 590, 665, 90])).
% 9.58/9.87 tff(19752,plain,
% 9.58/9.87 (s(s(s(s(z)))) = elem!1),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[762, 19751, 6221])).
% 9.58/9.87 tff(19753,plain,
% 9.58/9.87 (~(s(s(s(elem!1))) = elem!1)),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[1436, 19752])).
% 9.58/9.87 tff(19754,plain,
% 9.58/9.87 (~(elem!1 = s(s(s(elem!1))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[129, 19753])).
% 9.58/9.87 tff(19755,plain,
% 9.58/9.87 (r(elem!1, s(s(s(elem!1))))),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[424, 19754, 4028])).
% 9.58/9.87 tff(19756,plain,
% 9.58/9.87 ($false),
% 9.58/9.87 inference(unit_resolution,[status(thm)],[10530, 194, 411, 184, 19755, 19750])).
% 9.58/9.87 tff(19757,plain,((~b(z, s(z))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | r(s(s(s(s(z)))), elem!1) | (~b(s(z), z)) | b(elem!1, s(z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.88 tff(19758,plain,
% 9.58/9.88 (~b(z, s(z))),
% 9.58/9.88 inference(unit_resolution,[status(thm)],[19757, 4028, 59, 8232, 19748, 10550, 31, 18965, 19745])).
% 9.58/9.88 tff(19759,plain,
% 9.58/9.88 (r(z, s(z))),
% 9.58/9.88 inference(unit_resolution,[status(thm)],[678, 19758])).
% 9.58/9.88 tff(19760,plain,
% 9.58/9.88 ($false),
% 9.58/9.88 inference(unit_resolution,[status(thm)],[14725, 838, 5238, 722, 411])).
% 9.58/9.88 tff(19761,plain,((s(z) = elem!1) | (~r(z, s(z))) | (~r(z, elem!1)) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.58/9.88 tff(19762,plain,
% 9.58/9.88 (b(s(z), elem!1)),
% 9.58/9.88 inference(unit_resolution,[status(thm)],[19761, 19759, 8232, 31, 19689])).
% 9.58/9.88 tff(19763,plain,
% 9.58/9.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))),
% 9.58/9.88 inference(rewrite,[status(thm)],[])).
% 9.58/9.88 tff(19764,plain,
% 9.58/9.88 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))),
% 9.58/9.88 inference(rewrite,[status(thm)],[])).
% 9.58/9.88 tff(19765,plain,
% 9.58/9.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))))),
% 9.58/9.88 inference(monotonicity,[status(thm)],[19764])).
% 9.58/9.88 tff(19766,plain,
% 9.58/9.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))),
% 9.58/9.88 inference(transitivity,[status(thm)],[19765, 19763])).
% 9.58/9.88 tff(19767,plain,
% 9.58/9.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 9.58/9.88 inference(quant_inst,[status(thm)],[])).
% 9.58/9.88 tff(19768,plain,
% 9.58/9.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))),
% 9.58/9.88 inference(modus_ponens,[status(thm)],[19767, 19766])).
% 9.58/9.88 tff(19769,plain,
% 9.58/9.88 (~r(s(elem!1), z)),
% 9.58/9.88 inference(unit_resolution,[status(thm)],[19768, 194, 411, 485, 847])).
% 9.58/9.88 tff(19770,plain,
% 9.58/9.88 (b(s(elem!1), z)),
% 9.58/9.88 inference(unit_resolution,[status(thm)],[549, 19769])).
% 9.58/9.88 tff(19771,plain,
% 9.58/9.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))),
% 9.58/9.88 inference(rewrite,[status(thm)],[])).
% 9.58/9.88 tff(19772,plain,
% 9.58/9.88 (((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))),
% 9.58/9.88 inference(rewrite,[status(thm)],[])).
% 9.58/9.88 tff(19773,plain,
% 9.58/9.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))))),
% 9.58/9.88 inference(monotonicity,[status(thm)],[19772])).
% 9.58/9.88 tff(19774,plain,
% 9.58/9.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))),
% 9.58/9.88 inference(transitivity,[status(thm)],[19773, 19771])).
% 9.58/9.88 tff(19775,plain,
% 9.58/9.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 9.58/9.88 inference(quant_inst,[status(thm)],[])).
% 9.58/9.88 tff(19776,plain,
% 9.58/9.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))),
% 9.58/9.88 inference(modus_ponens,[status(thm)],[19775, 19774])).
% 9.58/9.88 tff(19777,plain,
% 9.58/9.88 (~r(z, s(elem!1))),
% 9.58/9.88 inference(unit_resolution,[status(thm)],[19776, 194, 411, 485, 847])).
% 9.58/9.88 tff(19778,plain,
% 9.58/9.88 (b(z, s(elem!1))),
% 9.58/9.88 inference(unit_resolution,[status(thm)],[566, 19777])).
% 9.58/9.88 tff(19779,plain,
% 9.58/9.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 9.58/9.88 inference(rewrite,[status(thm)],[])).
% 9.58/9.88 tff(19780,plain,
% 9.58/9.88 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 9.58/9.88 inference(rewrite,[status(thm)],[])).
% 9.58/9.88 tff(19781,plain,
% 9.58/9.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))))),
% 9.58/9.88 inference(monotonicity,[status(thm)],[19780])).
% 9.58/9.88 tff(19782,plain,
% 9.58/9.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 9.58/9.88 inference(transitivity,[status(thm)],[19781, 19779])).
% 9.58/9.88 tff(19783,plain,
% 9.58/9.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 9.58/9.88 inference(quant_inst,[status(thm)],[])).
% 9.58/9.88 tff(19784,plain,
% 9.58/9.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))),
% 9.58/9.88 inference(modus_ponens,[status(thm)],[19783, 19782])).
% 9.58/9.88 tff(19785,plain,
% 9.58/9.89 ($false),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[19784, 391, 665, 900, 380, 19778, 19770])).
% 9.58/9.89 tff(19786,plain,((~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.89 tff(19787,plain,
% 9.58/9.89 (~r(s(elem!1), elem!1)),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[19786, 19695, 19688, 18965, 8232, 19691])).
% 9.58/9.89 tff(19788,plain,
% 9.58/9.89 (~(elem!1 = s(elem!1))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[166, 18971])).
% 9.58/9.89 tff(19789,plain,
% 9.58/9.89 (b(s(elem!1), elem!1)),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[2168, 19787, 18971])).
% 9.58/9.89 tff(19790,plain,
% 9.58/9.89 (b(s(s(s(elem!1))), z)),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[19694, 4028, 59, 8232, 665])).
% 9.58/9.89 tff(19791,plain,
% 9.58/9.89 (r(elem!1, s(s(s(elem!1))))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[424, 18874, 4028])).
% 9.58/9.89 tff(19792,plain,
% 9.58/9.89 (~r(z, s(s(elem!1)))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[2562, 364, 411, 410])).
% 9.58/9.89 tff(19793,plain,
% 9.58/9.89 (b(z, s(s(elem!1)))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[324, 19792])).
% 9.58/9.89 tff(19794,plain,
% 9.58/9.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)))),
% 9.58/9.89 inference(rewrite,[status(thm)],[])).
% 9.58/9.89 tff(19795,plain,
% 9.58/9.89 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)))),
% 9.58/9.89 inference(rewrite,[status(thm)],[])).
% 9.58/9.89 tff(19796,plain,
% 9.58/9.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1))))),
% 9.58/9.89 inference(monotonicity,[status(thm)],[19795])).
% 9.58/9.89 tff(19797,plain,
% 9.58/9.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)))),
% 9.58/9.89 inference(transitivity,[status(thm)],[19796, 19794])).
% 9.58/9.89 tff(19798,plain,
% 9.58/9.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 9.58/9.89 inference(quant_inst,[status(thm)],[])).
% 9.58/9.89 tff(19799,plain,
% 9.58/9.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1))),
% 9.58/9.89 inference(modus_ponens,[status(thm)],[19798, 19797])).
% 9.58/9.89 tff(19800,plain,
% 9.58/9.89 ($false),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[19799, 391, 665, 3927, 644, 2641, 590])).
% 9.58/9.89 tff(19801,plain,((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.89 tff(19802,plain,
% 9.58/9.89 (~b(s(s(elem!1)), z)),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[19801, 19793, 590, 665, 644])).
% 9.58/9.89 tff(19803,plain,
% 9.58/9.89 (r(s(s(elem!1)), z)),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[2629, 19802])).
% 9.58/9.89 tff(19804,plain,
% 9.58/9.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 9.58/9.89 inference(rewrite,[status(thm)],[])).
% 9.58/9.89 tff(19805,plain,
% 9.58/9.89 (((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 9.58/9.89 inference(rewrite,[status(thm)],[])).
% 9.58/9.89 tff(19806,plain,
% 9.58/9.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 9.58/9.89 inference(monotonicity,[status(thm)],[19805])).
% 9.58/9.89 tff(19807,plain,
% 9.58/9.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 9.58/9.89 inference(transitivity,[status(thm)],[19806, 19804])).
% 9.58/9.89 tff(19808,plain,
% 9.58/9.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 9.58/9.89 inference(quant_inst,[status(thm)],[])).
% 9.58/9.89 tff(19809,plain,
% 9.58/9.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 9.58/9.89 inference(modus_ponens,[status(thm)],[19808, 19807])).
% 9.58/9.89 tff(19810,plain,
% 9.58/9.89 ($false),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[19809, 194, 411, 364, 410, 19803])).
% 9.58/9.89 tff(19811,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.89 tff(19812,plain,
% 9.58/9.89 (~r(s(s(elem!1)), elem!1)),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[19811, 19791, 8232, 590, 665, 644])).
% 9.58/9.89 tff(19813,plain,
% 9.58/9.89 (b(s(s(elem!1)), elem!1)),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[872, 19812, 14411])).
% 9.58/9.89 tff(19814,plain,
% 9.58/9.89 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[8251, 18873])).
% 9.58/9.89 tff(19815,plain,
% 9.58/9.89 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[299, 19814])).
% 9.58/9.89 tff(19816,plain,
% 9.58/9.89 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[307, 19815])).
% 9.58/9.89 tff(19817,plain,
% 9.58/9.89 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[19071, 19791, 59, 8232])).
% 9.58/9.89 tff(19818,plain,
% 9.58/9.89 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[1164, 19817, 19816])).
% 9.58/9.89 tff(19819,plain,
% 9.58/9.89 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[17255, 19791, 10, 2])).
% 9.58/9.89 tff(19820,plain,
% 9.58/9.89 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[1370, 19819, 19814])).
% 9.58/9.89 tff(19821,plain,
% 9.58/9.89 (~(elem!1 = s(s(s(s(elem!1)))))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[14423, 688, 2680])).
% 9.58/9.89 tff(19822,plain,
% 9.58/9.89 (~(elem!1 = s(s(elem!1)))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[1292, 14411])).
% 9.58/9.89 tff(19823,plain,
% 9.58/9.89 (~b(elem!1, s(s(elem!1)))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[1467, 19813, 900, 19820])).
% 9.58/9.89 tff(19824,plain,
% 9.58/9.89 (r(elem!1, s(s(elem!1)))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[1307, 19823, 19822])).
% 9.58/9.89 tff(19825,plain,
% 9.58/9.89 (~(s(s(s(s(elem!1)))) = elem!1)),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[14255, 19821])).
% 9.58/9.89 tff(19826,plain,
% 9.58/9.89 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 9.58/9.89 inference(monotonicity,[status(thm)],[688])).
% 9.58/9.89 tff(19827,plain,
% 9.58/9.89 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.58/9.89 inference(symmetry,[status(thm)],[19826])).
% 9.58/9.89 tff(19828,plain,
% 9.58/9.89 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.58/9.89 inference(modus_ponens,[status(thm)],[19791, 19827])).
% 9.58/9.89 tff(19829,plain,
% 9.58/9.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.58/9.89 inference(rewrite,[status(thm)],[])).
% 9.58/9.89 tff(19830,plain,
% 9.58/9.89 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.58/9.89 inference(rewrite,[status(thm)],[])).
% 9.58/9.89 tff(19831,plain,
% 9.58/9.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 9.58/9.89 inference(monotonicity,[status(thm)],[19830])).
% 9.58/9.89 tff(19832,plain,
% 9.58/9.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.58/9.89 inference(transitivity,[status(thm)],[19831, 19829])).
% 9.58/9.89 tff(19833,plain,
% 9.58/9.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 9.58/9.89 inference(quant_inst,[status(thm)],[])).
% 9.58/9.89 tff(19834,plain,
% 9.58/9.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 9.58/9.89 inference(modus_ponens,[status(thm)],[19833, 19832])).
% 9.58/9.89 tff(19835,plain,
% 9.58/9.89 ($false),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[19834, 194, 613, 184, 719, 2100])).
% 9.58/9.89 tff(19836,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.58/9.89 tff(19837,plain,
% 9.58/9.89 (~r(s(s(s(elem!1))), s(elem!1))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[19836, 19828, 59, 719])).
% 9.58/9.89 tff(19838,plain,
% 9.58/9.89 (b(s(s(s(elem!1))), s(elem!1))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[588, 19837, 14410])).
% 9.58/9.89 tff(19839,plain,
% 9.58/9.89 (r(elem!1, s(elem!1))),
% 9.58/9.89 inference(unit_resolution,[status(thm)],[2340, 19838, 900, 437, 469])).
% 9.58/9.89 tff(19840,plain,
% 9.58/9.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))))),
% 9.58/9.90 inference(rewrite,[status(thm)],[])).
% 9.58/9.90 tff(19841,plain,
% 9.58/9.90 (((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))))),
% 9.58/9.90 inference(rewrite,[status(thm)],[])).
% 9.58/9.90 tff(19842,plain,
% 9.58/9.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1)))))),
% 9.68/9.90 inference(monotonicity,[status(thm)],[19841])).
% 9.68/9.90 tff(19843,plain,
% 9.68/9.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))))),
% 9.68/9.90 inference(transitivity,[status(thm)],[19842, 19840])).
% 9.68/9.90 tff(19844,plain,
% 9.68/9.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 9.68/9.90 inference(quant_inst,[status(thm)],[])).
% 9.68/9.90 tff(19845,plain,
% 9.68/9.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1)))),
% 9.68/9.90 inference(modus_ponens,[status(thm)],[19844, 19843])).
% 9.68/9.90 tff(19846,plain,
% 9.68/9.90 ($false),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19845, 391, 665, 900, 380, 592, 2122])).
% 9.68/9.90 tff(19847,plain,((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.90 tff(19848,plain,
% 9.68/9.90 (~b(z, s(elem!1))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19847, 19790, 900, 665, 2122])).
% 9.68/9.90 tff(19849,plain,
% 9.68/9.90 (r(z, s(elem!1))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[566, 19848])).
% 9.68/9.90 tff(19850,plain,
% 9.68/9.90 ($false),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[15292, 194, 411, 1628, 2144, 2251])).
% 9.68/9.90 tff(19851,plain,((~r(z, s(elem!1))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.90 tff(19852,plain,
% 9.68/9.90 (~r(s(elem!1), z)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19851, 19839, 8232, 19849])).
% 9.68/9.90 tff(19853,plain,
% 9.68/9.90 (b(s(elem!1), z)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[549, 19852])).
% 9.68/9.90 tff(19854,plain,
% 9.68/9.90 (~r(s(s(s(s(elem!1)))), elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19119, 19853, 665, 2122, 8232, 19839])).
% 9.68/9.90 tff(19855,plain,
% 9.68/9.90 (b(s(s(s(s(elem!1)))), elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[1004, 19854, 19825])).
% 9.68/9.90 tff(19856,plain,
% 9.68/9.90 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19148, 19855, 19820, 665, 19818])).
% 9.68/9.90 tff(19857,plain,
% 9.68/9.90 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[1048, 19856, 14425])).
% 9.68/9.90 tff(19858,plain,
% 9.68/9.90 (~b(z, s(s(elem!1)))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[6210, 1526, 590, 973, 380])).
% 9.68/9.90 tff(19859,plain,
% 9.68/9.90 (r(z, s(s(elem!1)))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[324, 19858])).
% 9.68/9.90 tff(19860,plain,
% 9.68/9.90 (~r(s(s(elem!1)), s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[2549, 19859, 411, 1064])).
% 9.68/9.90 tff(19861,plain,
% 9.68/9.90 (b(s(s(elem!1)), s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[362, 19860])).
% 9.68/9.90 tff(19862,plain,
% 9.68/9.90 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[18349, 19861, 644, 1573, 1374])).
% 9.68/9.90 tff(19863,plain,
% 9.68/9.90 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[1061, 19862, 1050])).
% 9.68/9.90 tff(19864,plain,
% 9.68/9.90 (~b(elem!1, s(s(s(s(elem!1)))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[18333, 19861, 644, 1526, 1374])).
% 9.68/9.90 tff(19865,plain,
% 9.68/9.90 (r(elem!1, s(s(s(s(elem!1)))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[1018, 19864, 14203])).
% 9.68/9.90 tff(19866,plain,
% 9.68/9.90 ($false),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[1184, 19865, 19863, 1176, 1064])).
% 9.68/9.90 tff(19867,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.90 tff(19868,plain,
% 9.68/9.90 (~b(s(s(s(elem!1))), s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19867, 19857, 19824, 19821, 14527, 644, 19820, 19818, 8232, 590, 19813, 19790])).
% 9.68/9.90 tff(19869,plain,
% 9.68/9.90 (r(s(s(s(elem!1))), s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[223, 19868])).
% 9.68/9.90 tff(19870,plain,
% 9.68/9.90 ($false),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[10530, 194, 8232, 59, 19791, 19869])).
% 9.68/9.90 tff(19871,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | r(s(elem!1), elem!1) | (~r(z, s(s(s(s(z)))))) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.90 tff(19872,plain,
% 9.68/9.90 (~(s(s(s(s(z)))) = elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19871, 19762, 10550, 19688, 18965, 19789, 19788, 19787, 19747, 10, 2, 4028])).
% 9.68/9.90 tff(19873,plain,
% 9.68/9.90 (r(elem!1, s(s(s(s(z)))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[18869, 19872, 19338, 19762, 19748])).
% 9.68/9.90 tff(19874,plain,
% 9.68/9.90 (~r(s(s(s(s(z)))), s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[15063, 19873, 8232, 19747])).
% 9.68/9.90 tff(19875,plain,
% 9.68/9.90 (b(s(s(s(s(z)))), s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[749, 19874])).
% 9.68/9.90 tff(19876,plain,
% 9.68/9.90 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[2849, 19689])).
% 9.68/9.90 tff(19877,plain,
% 9.68/9.90 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[15016, 19873, 8232, 19747])).
% 9.68/9.90 tff(19878,plain,
% 9.68/9.90 (b(s(s(s(s(z)))), s(s(z)))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[1714, 19877])).
% 9.68/9.90 tff(19879,plain,
% 9.68/9.90 (b(s(s(s(s(z)))), elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[762, 19872, 19748])).
% 9.68/9.90 tff(19880,plain,
% 9.68/9.90 (~r(elem!1, z)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[18640, 5, 1234, 722, 411, 644, 1652, 1759, 90, 3563])).
% 9.68/9.90 tff(19881,plain,
% 9.68/9.90 ($false),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[15970, 18017, 19880, 10, 5])).
% 9.68/9.90 tff(19882,plain,((~(s(s(s(elem!1))) = elem!1)) | b(z, s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.90 tff(19883,plain,
% 9.68/9.90 (~(s(s(s(elem!1))) = elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19882, 19759, 19338, 10, 8232, 19762, 19879, 19875, 19745, 19878, 31])).
% 9.68/9.90 tff(19884,plain,
% 9.68/9.90 (~(elem!1 = s(s(s(elem!1))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[129, 19883])).
% 9.68/9.90 tff(19885,plain,
% 9.68/9.90 (r(elem!1, s(s(s(elem!1))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[424, 19884, 4028])).
% 9.68/9.90 tff(19886,plain,
% 9.68/9.90 ($false),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[10530, 194, 411, 184, 410, 183])).
% 9.68/9.90 tff(19887,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.90 tff(19888,plain,
% 9.68/9.90 (~r(s(s(s(elem!1))), s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19887, 19885, 59, 8232])).
% 9.68/9.90 tff(19889,plain,
% 9.68/9.90 (b(s(s(s(elem!1))), s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[223, 19888])).
% 9.68/9.90 tff(19890,plain,
% 9.68/9.90 (~b(s(z), s(s(s(elem!1))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[16792, 19889, 59, 19688, 19876, 19875, 19747])).
% 9.68/9.90 tff(19891,plain,
% 9.68/9.90 (r(s(z), s(s(s(elem!1))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[247, 19890])).
% 9.68/9.90 tff(19892,plain,
% 9.68/9.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 9.68/9.90 inference(rewrite,[status(thm)],[])).
% 9.68/9.90 tff(19893,plain,
% 9.68/9.90 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 9.68/9.90 inference(rewrite,[status(thm)],[])).
% 9.68/9.90 tff(19894,plain,
% 9.68/9.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))))),
% 9.68/9.90 inference(monotonicity,[status(thm)],[19893])).
% 9.68/9.90 tff(19895,plain,
% 9.68/9.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 9.68/9.90 inference(transitivity,[status(thm)],[19894, 19892])).
% 9.68/9.90 tff(19896,plain,
% 9.68/9.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 9.68/9.90 inference(quant_inst,[status(thm)],[])).
% 9.68/9.90 tff(19897,plain,
% 9.68/9.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))),
% 9.68/9.90 inference(modus_ponens,[status(thm)],[19896, 19895])).
% 9.68/9.90 tff(19898,plain,
% 9.68/9.90 ($false),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19897, 194, 8232, 19891, 19759, 19691])).
% 9.68/9.90 tff(19899,plain,(b(elem!1, s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | b(elem!1, s(z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 9.68/9.90 tff(19900,plain,
% 9.68/9.90 (b(elem!1, s(s(s(elem!1))))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19899, 31, 10, 2])).
% 9.68/9.90 tff(19901,plain,
% 9.68/9.90 (~(s(s(s(s(z)))) = elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[8916, 2829, 19338])).
% 9.68/9.90 tff(19902,plain,
% 9.68/9.90 (~b(s(s(s(s(z)))), elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[16861, 3363, 448, 184, 900, 2053])).
% 9.68/9.90 tff(19903,plain,
% 9.68/9.90 (r(s(s(s(s(z)))), elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[762, 19902, 720])).
% 9.68/9.90 tff(19904,plain,
% 9.68/9.90 ($false),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[10450, 19903, 838, 411, 665, 770])).
% 9.68/9.90 tff(19905,plain,((s(z) = elem!1) | (~r(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | b(elem!1, s(z)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.90 tff(19906,plain,
% 9.68/9.90 (s(z) = elem!1),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19905, 3447, 18965, 19901, 31, 19900, 59, 19688, 8232])).
% 9.68/9.90 tff(19907,plain,
% 9.68/9.90 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 9.68/9.90 inference(monotonicity,[status(thm)],[19906])).
% 9.68/9.90 tff(19908,plain,
% 9.68/9.90 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 9.68/9.90 inference(symmetry,[status(thm)],[19907])).
% 9.68/9.90 tff(19909,plain,
% 9.68/9.90 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), s(z)))),
% 9.68/9.90 inference(monotonicity,[status(thm)],[19908])).
% 9.68/9.90 tff(19910,plain,
% 9.68/9.90 (~b(elem!1, s(elem!1))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19465, 19906, 3446, 10, 2, 31])).
% 9.68/9.90 tff(19911,plain,
% 9.68/9.90 (r(elem!1, s(elem!1))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[443, 19910, 19788])).
% 9.68/9.90 tff(19912,plain,
% 9.68/9.90 (~r(s(s(s(elem!1))), elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[434, 19911, 8232, 59])).
% 9.68/9.90 tff(19913,plain,
% 9.68/9.90 (~r(s(s(s(elem!1))), s(z))),
% 9.68/9.90 inference(modus_ponens,[status(thm)],[19912, 19909])).
% 9.68/9.90 tff(19914,plain,
% 9.68/9.90 (r(s(s(s(elem!1))), s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[17668, 3446, 19338, 2829, 10])).
% 9.68/9.90 tff(19915,plain,
% 9.68/9.90 ($false),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19914, 19913])).
% 9.68/9.90 tff(19916,plain,(b(s(s(s(s(z)))), z) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.68/9.90 tff(19917,plain,
% 9.68/9.90 (b(s(s(s(s(z)))), z)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19916, 2829, 2, 31, 10])).
% 9.68/9.90 tff(19918,plain,
% 9.68/9.90 (~r(s(s(s(s(z)))), elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[10450, 838, 411, 665, 770])).
% 9.68/9.90 tff(19919,plain,
% 9.68/9.90 (~r(z, s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19761, 150, 411, 31, 2829])).
% 9.68/9.90 tff(19920,plain,
% 9.68/9.90 (b(z, s(z))),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[678, 19919])).
% 9.68/9.90 tff(19921,plain,
% 9.68/9.90 (~b(s(s(s(s(z)))), elem!1)),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[14978, 19920, 590, 665, 90])).
% 9.68/9.90 tff(19922,plain,
% 9.68/9.90 ($false),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[762, 19921, 19918, 720])).
% 9.68/9.90 tff(19923,plain,((s(z) = elem!1) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.68/9.90 tff(19924,plain,
% 9.68/9.90 (s(z) = elem!1),
% 9.68/9.90 inference(unit_resolution,[status(thm)],[19923, 19901, 10550, 18965, 19917, 8232, 31, 2829])).
% 9.68/9.90 tff(19925,plain,
% 9.68/9.90 (s(s(z)) = s(elem!1)),
% 9.68/9.90 inference(monotonicity,[status(thm)],[19924])).
% 9.68/9.90 tff(19926,plain,
% 9.68/9.90 (s(s(s(z))) = s(s(elem!1))),
% 9.68/9.90 inference(monotonicity,[status(thm)],[19925])).
% 9.68/9.90 tff(19927,plain,
% 9.68/9.90 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 9.68/9.90 inference(monotonicity,[status(thm)],[19926])).
% 9.68/9.90 tff(19928,plain,
% 9.68/9.90 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 9.68/9.90 inference(monotonicity,[status(thm)],[19927])).
% 9.68/9.90 tff(19929,plain,
% 9.68/9.90 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 9.68/9.90 inference(symmetry,[status(thm)],[19928])).
% 9.68/9.90 tff(19930,plain,
% 9.68/9.90 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(s(z)))), z))),
% 9.68/9.90 inference(monotonicity,[status(thm)],[19929])).
% 9.68/9.90 tff(19931,plain,
% 9.68/9.90 (~b(s(s(s(s(z)))), z)),
% 9.68/9.90 inference(modus_ponens,[status(thm)],[9550, 19930])).
% 9.68/9.91 tff(19932,plain,
% 9.68/9.91 ($false),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[19917, 19931])).
% 9.68/9.91 tff(19933,plain,(b(s(z), elem!1) | b(s(s(s(elem!1))), z) | b(elem!1, s(z)) | (elem!1 = z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.91 tff(19934,plain,
% 9.68/9.91 (b(s(z), elem!1)),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[19933, 9550, 31, 2, 10])).
% 9.68/9.91 tff(19935,plain,
% 9.68/9.91 (~b(s(z), s(s(s(elem!1))))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[16825, 391, 19688, 19900, 19934])).
% 9.68/9.91 tff(19936,plain,
% 9.68/9.91 (r(s(z), s(s(s(elem!1))))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[247, 19935])).
% 9.68/9.91 tff(19937,plain,
% 9.68/9.91 (~r(z, s(z))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[5980, 19936, 59, 12778])).
% 9.68/9.91 tff(19938,plain,
% 9.68/9.91 (b(z, s(z))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[678, 19937])).
% 9.68/9.91 tff(19939,plain,
% 9.68/9.91 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 9.68/9.91 inference(rewrite,[status(thm)],[])).
% 9.68/9.91 tff(19940,plain,
% 9.68/9.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 9.68/9.91 inference(monotonicity,[status(thm)],[19939])).
% 9.68/9.91 tff(19941,plain,
% 9.68/9.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 9.68/9.91 inference(transitivity,[status(thm)],[19940, 14826])).
% 9.68/9.91 tff(19942,plain,
% 9.68/9.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 9.68/9.91 inference(quant_inst,[status(thm)],[])).
% 9.68/9.91 tff(19943,plain,
% 9.68/9.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 9.68/9.91 inference(modus_ponens,[status(thm)],[19942, 19941])).
% 9.68/9.91 tff(19944,plain,
% 9.68/9.91 ($false),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[19943, 391, 18965, 19934, 19938, 10550])).
% 9.68/9.91 tff(19945,plain,(b(s(s(s(elem!1))), z) | b(elem!1, s(z)) | (elem!1 = z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.91 tff(19946,plain,
% 9.68/9.91 (b(s(s(s(elem!1))), z)),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[19945, 31, 2, 10])).
% 9.68/9.91 tff(19947,plain,
% 9.68/9.91 (s(z) = elem!1),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[19923, 19917, 10550, 18965, 19901, 8232, 31, 2829])).
% 9.68/9.91 tff(19948,plain,
% 9.68/9.91 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 9.68/9.91 inference(monotonicity,[status(thm)],[19947])).
% 9.68/9.91 tff(19949,plain,
% 9.68/9.91 (r(elem!1, s(s(z))) <=> r(s(z), s(s(z)))),
% 9.68/9.91 inference(symmetry,[status(thm)],[19948])).
% 9.68/9.91 tff(19950,plain,
% 9.68/9.91 (s(s(z)) = s(elem!1)),
% 9.68/9.91 inference(monotonicity,[status(thm)],[19947])).
% 9.68/9.91 tff(19951,plain,
% 9.68/9.91 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 9.68/9.91 inference(monotonicity,[status(thm)],[19950])).
% 9.68/9.91 tff(19952,plain,
% 9.68/9.91 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 9.68/9.91 inference(symmetry,[status(thm)],[19951])).
% 9.68/9.91 tff(19953,plain,
% 9.68/9.91 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 9.68/9.91 inference(transitivity,[status(thm)],[19952, 19949])).
% 9.68/9.91 tff(19954,plain,
% 9.68/9.91 (b(elem!1, s(elem!1))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[443, 438, 437])).
% 9.68/9.91 tff(19955,plain,
% 9.68/9.91 (b(s(s(s(s(z)))), elem!1)),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[1563, 7866, 900])).
% 9.68/9.91 tff(19956,plain,
% 9.68/9.91 (b(s(s(s(s(z)))), s(z))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[9614, 19955, 812])).
% 9.68/9.91 tff(19957,plain,
% 9.68/9.91 (b(s(s(s(elem!1))), s(z))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[11177, 19956, 7866])).
% 9.68/9.91 tff(19958,plain,
% 9.68/9.91 (r(elem!1, s(elem!1))),
% 9.68/9.91 inference(modus_ponens,[status(thm)],[1748, 9731])).
% 9.68/9.91 tff(19959,plain,
% 9.68/9.91 ($false),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[438, 19958])).
% 9.68/9.91 tff(19960,plain,((~r(elem!1, s(s(z)))) | r(elem!1, s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.91 tff(19961,plain,
% 9.68/9.91 (~r(elem!1, s(s(z)))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[19960, 438, 812])).
% 9.68/9.91 tff(19962,plain,
% 9.68/9.91 (b(elem!1, s(s(z)))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[3394, 19961, 19053])).
% 9.68/9.91 tff(19963,plain,
% 9.68/9.91 (~b(s(s(z)), s(s(s(elem!1))))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[8561, 19962, 1234, 448, 19957])).
% 9.68/9.91 tff(19964,plain,
% 9.68/9.91 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[8551, 19963, 812])).
% 9.68/9.91 tff(19965,plain,
% 9.68/9.91 (r(s(s(z)), s(s(s(s(z)))))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[3652, 19964])).
% 9.68/9.91 tff(19966,plain,
% 9.68/9.91 (r(s(elem!1), s(s(s(elem!1))))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[3614, 19965, 812])).
% 9.68/9.91 tff(19967,plain,
% 9.68/9.91 (~r(s(elem!1), z)),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[7955, 194, 613, 184, 604])).
% 9.68/9.91 tff(19968,plain,
% 9.68/9.91 (b(s(elem!1), z)),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[549, 19967])).
% 9.68/9.91 tff(19969,plain,
% 9.68/9.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 9.68/9.91 inference(rewrite,[status(thm)],[])).
% 9.68/9.91 tff(19970,plain,
% 9.68/9.91 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 9.68/9.91 inference(rewrite,[status(thm)],[])).
% 9.68/9.91 tff(19971,plain,
% 9.68/9.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 9.68/9.91 inference(monotonicity,[status(thm)],[19970])).
% 9.68/9.91 tff(19972,plain,
% 9.68/9.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 9.68/9.91 inference(transitivity,[status(thm)],[19971, 19969])).
% 9.68/9.91 tff(19973,plain,
% 9.68/9.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 9.68/9.91 inference(quant_inst,[status(thm)],[])).
% 9.68/9.91 tff(19974,plain,
% 9.68/9.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 9.68/9.91 inference(modus_ponens,[status(thm)],[19973, 19972])).
% 9.68/9.91 tff(19975,plain,
% 9.68/9.91 (~r(z, s(elem!1))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[19974, 194, 613, 184, 604])).
% 9.68/9.91 tff(19976,plain,
% 9.68/9.91 (b(z, s(elem!1))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[566, 19975])).
% 9.68/9.91 tff(19977,plain,
% 9.68/9.91 ($false),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[1939, 19976, 19968, 665, 802])).
% 9.68/9.91 tff(19978,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.91 tff(19979,plain,
% 9.68/9.91 (~r(s(s(s(elem!1))), s(elem!1))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[19978, 19954, 665, 184, 19966])).
% 9.68/9.91 tff(19980,plain,
% 9.68/9.91 (b(s(s(s(elem!1))), s(elem!1))),
% 9.68/9.91 inference(unit_resolution,[status(thm)],[588, 19979, 7433])).
% 9.68/9.91 tff(19981,plain,
% 9.68/9.91 (b(s(z), s(s(s(elem!1))))),
% 9.68/9.91 inference(modus_ponens,[status(thm)],[448, 7582])).
% 9.68/9.91 tff(19982,plain,
% 9.68/9.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 9.68/9.92 inference(rewrite,[status(thm)],[])).
% 9.68/9.92 tff(19983,plain,
% 9.68/9.92 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 9.68/9.92 inference(rewrite,[status(thm)],[])).
% 9.68/9.92 tff(19984,plain,
% 9.68/9.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 9.68/9.92 inference(monotonicity,[status(thm)],[19983])).
% 9.68/9.92 tff(19985,plain,
% 9.68/9.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 9.68/9.92 inference(transitivity,[status(thm)],[19984, 19982])).
% 9.68/9.92 tff(19986,plain,
% 9.68/9.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 9.68/9.92 inference(quant_inst,[status(thm)],[])).
% 9.68/9.92 tff(19987,plain,
% 9.68/9.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 9.68/9.92 inference(modus_ponens,[status(thm)],[19986, 19985])).
% 9.68/9.92 tff(19988,plain,
% 9.68/9.92 ($false),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[19987, 194, 1628, 184, 327, 604])).
% 9.68/9.92 tff(19989,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.92 tff(19990,plain,
% 9.68/9.92 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[19989, 1628, 184, 604])).
% 9.68/9.92 tff(19991,plain,
% 9.68/9.92 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[1370, 19990, 16094])).
% 9.68/9.92 tff(19992,plain,
% 9.68/9.92 (~b(s(s(elem!1)), s(z))),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[4762, 19991, 19981, 19957])).
% 9.68/9.92 tff(19993,plain,
% 9.68/9.92 (r(s(s(elem!1)), s(z))),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[362, 19992])).
% 9.68/9.92 tff(19994,plain,
% 9.68/9.92 (r(s(s(elem!1)), elem!1)),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[2220, 19993, 812])).
% 9.68/9.92 tff(19995,plain,
% 9.68/9.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.68/9.92 inference(rewrite,[status(thm)],[])).
% 9.68/9.92 tff(19996,plain,
% 9.68/9.92 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.68/9.92 inference(rewrite,[status(thm)],[])).
% 9.68/9.92 tff(19997,plain,
% 9.68/9.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 9.68/9.92 inference(monotonicity,[status(thm)],[19996])).
% 9.68/9.92 tff(19998,plain,
% 9.68/9.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.68/9.92 inference(transitivity,[status(thm)],[19997, 19995])).
% 9.68/9.92 tff(19999,plain,
% 9.68/9.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 9.68/9.92 inference(quant_inst,[status(thm)],[])).
% 9.68/9.92 tff(20000,plain,
% 9.68/9.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 9.68/9.92 inference(modus_ponens,[status(thm)],[19999, 19998])).
% 9.68/9.92 tff(20001,plain,
% 9.68/9.92 ($false),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[20000, 194, 1628, 184, 604, 1538])).
% 9.68/9.92 tff(20002,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.92 tff(20003,plain,
% 9.68/9.92 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[20002, 1628, 184, 604])).
% 9.68/9.92 tff(20004,plain,
% 9.68/9.92 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[1164, 20003, 18146])).
% 9.68/9.92 tff(20005,plain,
% 9.68/9.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 9.68/9.92 inference(rewrite,[status(thm)],[])).
% 9.68/9.92 tff(20006,plain,
% 9.68/9.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 9.68/9.92 inference(quant_inst,[status(thm)],[])).
% 9.68/9.92 tff(20007,plain,
% 9.68/9.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 9.68/9.92 inference(modus_ponens,[status(thm)],[20006, 20005])).
% 9.68/9.92 tff(20008,plain,
% 9.68/9.92 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[20007, 194, 411, 1628, 12854])).
% 9.68/9.92 tff(20009,plain,
% 9.68/9.92 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[988, 20008, 957])).
% 9.68/9.92 tff(20010,assumption,(~(s(elem!1) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 9.68/9.92 tff(20011,plain,
% 9.68/9.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 9.68/9.92 inference(rewrite,[status(thm)],[])).
% 9.68/9.92 tff(20012,plain,
% 9.68/9.92 (((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 9.68/9.92 inference(rewrite,[status(thm)],[])).
% 9.68/9.92 tff(20013,plain,
% 9.68/9.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 9.68/9.92 inference(monotonicity,[status(thm)],[20012])).
% 9.68/9.92 tff(20014,plain,
% 9.68/9.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 9.68/9.92 inference(transitivity,[status(thm)],[20013, 20011])).
% 9.68/9.92 tff(20015,plain,
% 9.68/9.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 9.68/9.92 inference(quant_inst,[status(thm)],[])).
% 9.68/9.92 tff(20016,plain,
% 9.68/9.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 9.68/9.92 inference(modus_ponens,[status(thm)],[20015, 20014])).
% 9.68/9.92 tff(20017,plain,
% 9.68/9.92 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[20016, 194, 411, 1628, 12854])).
% 9.68/9.92 tff(20018,plain,
% 9.68/9.92 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 9.68/9.92 inference(unit_resolution,[status(thm)],[1639, 20017, 20010])).
% 9.68/9.92 tff(20019,plain,
% 9.68/9.92 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.68/9.92 inference(rewrite,[status(thm)],[])).
% 9.68/9.92 tff(20020,plain,
% 9.68/9.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 9.68/9.92 inference(monotonicity,[status(thm)],[20019])).
% 9.68/9.92 tff(20021,plain,
% 9.68/9.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.68/9.92 inference(transitivity,[status(thm)],[20020, 1641])).
% 9.68/9.92 tff(20022,plain,
% 9.68/9.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 9.68/9.92 inference(quant_inst,[status(thm)],[])).
% 9.68/9.92 tff(20023,plain,
% 9.68/9.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 9.68/9.93 inference(modus_ponens,[status(thm)],[20022, 20021])).
% 9.68/9.93 tff(20024,plain,
% 9.68/9.93 ($false),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[20023, 391, 1101, 1573, 20018, 20009])).
% 9.68/9.93 tff(20025,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.93 tff(20026,plain,
% 9.68/9.93 (~r(s(s(s(s(elem!1)))), z)),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[20025, 20004, 1101, 18085, 19650, 411, 1628])).
% 9.68/9.93 tff(20027,plain,
% 9.68/9.93 (b(s(s(s(s(elem!1)))), z)),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[1626, 20026])).
% 9.68/9.93 tff(20028,plain,
% 9.68/9.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.68/9.93 inference(rewrite,[status(thm)],[])).
% 9.68/9.93 tff(20029,plain,
% 9.68/9.93 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.68/9.93 inference(rewrite,[status(thm)],[])).
% 9.68/9.93 tff(20030,plain,
% 9.68/9.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 9.68/9.93 inference(monotonicity,[status(thm)],[20029])).
% 9.68/9.93 tff(20031,plain,
% 9.68/9.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.68/9.93 inference(transitivity,[status(thm)],[20030, 20028])).
% 9.68/9.93 tff(20032,plain,
% 9.68/9.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 9.68/9.93 inference(quant_inst,[status(thm)],[])).
% 9.68/9.93 tff(20033,plain,
% 9.68/9.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 9.68/9.93 inference(modus_ponens,[status(thm)],[20032, 20031])).
% 9.68/9.93 tff(20034,plain,
% 9.68/9.93 ($false),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[20033, 391, 380, 1374, 3927, 1152, 17911])).
% 9.68/9.93 tff(20035,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.93 tff(20036,plain,
% 9.68/9.93 (~b(z, s(s(elem!1)))),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[20035, 1152, 1374, 380, 17911])).
% 9.68/9.93 tff(20037,plain,
% 9.68/9.93 (r(z, s(s(elem!1)))),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[324, 20036])).
% 9.68/9.93 tff(20038,plain,
% 9.68/9.93 (~r(elem!1, s(s(elem!1)))),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[1979, 20037, 411, 364])).
% 9.68/9.93 tff(20039,plain,
% 9.68/9.93 (b(elem!1, s(s(elem!1)))),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[1307, 20038, 1457])).
% 9.68/9.93 tff(20040,plain,
% 9.68/9.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.68/9.93 inference(rewrite,[status(thm)],[])).
% 9.68/9.93 tff(20041,plain,
% 9.68/9.93 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.68/9.93 inference(rewrite,[status(thm)],[])).
% 9.68/9.93 tff(20042,plain,
% 9.68/9.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 9.68/9.93 inference(monotonicity,[status(thm)],[20041])).
% 9.68/9.93 tff(20043,plain,
% 9.68/9.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 9.68/9.93 inference(transitivity,[status(thm)],[20042, 20040])).
% 9.68/9.93 tff(20044,plain,
% 9.68/9.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 9.68/9.93 inference(quant_inst,[status(thm)],[])).
% 9.68/9.93 tff(20045,plain,
% 9.68/9.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 9.68/9.93 inference(modus_ponens,[status(thm)],[20044, 20043])).
% 9.68/9.93 tff(20046,plain,
% 9.68/9.93 ($false),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[20045, 391, 448, 1374, 20039, 1152, 17911])).
% 9.68/9.93 tff(20047,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (elem!1 = s(s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.93 tff(20048,plain,
% 9.68/9.93 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[20047, 19991, 448, 20027, 9651, 411, 19994, 380])).
% 9.68/9.93 tff(20049,plain,
% 9.68/9.93 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[1048, 20048, 19140])).
% 9.68/9.93 tff(20050,plain,
% 9.68/9.93 (~b(s(s(s(s(elem!1)))), elem!1)),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[2706, 20004, 448, 900, 1101])).
% 9.68/9.93 tff(20051,plain,
% 9.68/9.93 (r(s(s(s(s(elem!1)))), elem!1)),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[1004, 20050, 7473])).
% 9.68/9.93 tff(20052,plain,
% 9.68/9.93 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[1741, 1733, 1374, 1573])).
% 9.68/9.93 tff(20053,plain,
% 9.68/9.93 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[1048, 20052, 19140])).
% 9.68/9.93 tff(20054,plain,
% 9.68/9.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.68/9.93 inference(rewrite,[status(thm)],[])).
% 9.68/9.93 tff(20055,plain,
% 9.68/9.93 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.68/9.93 inference(rewrite,[status(thm)],[])).
% 9.68/9.93 tff(20056,plain,
% 9.68/9.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))))),
% 9.68/9.93 inference(monotonicity,[status(thm)],[20055])).
% 9.68/9.93 tff(20057,plain,
% 9.68/9.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 9.68/9.93 inference(transitivity,[status(thm)],[20056, 20054])).
% 9.68/9.93 tff(20058,plain,
% 9.68/9.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 9.68/9.93 inference(quant_inst,[status(thm)],[])).
% 9.68/9.93 tff(20059,plain,
% 9.68/9.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))),
% 9.68/9.93 inference(modus_ponens,[status(thm)],[20058, 20057])).
% 9.68/9.93 tff(20060,plain,
% 9.68/9.93 ($false),
% 9.68/9.93 inference(unit_resolution,[status(thm)],[20059, 391, 665, 900, 380, 1733, 2781])).
% 9.68/9.93 tff(20061,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.94 tff(20062,plain,
% 9.68/9.94 (~b(z, s(s(s(s(elem!1)))))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[20061, 1733, 900, 380, 665])).
% 9.68/9.94 tff(20063,plain,
% 9.68/9.94 (r(z, s(s(s(s(elem!1)))))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[2767, 20062])).
% 9.68/9.94 tff(20064,plain,
% 9.68/9.94 (~r(z, s(s(elem!1)))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[2800, 20063, 991, 20053])).
% 9.68/9.94 tff(20065,plain,
% 9.68/9.94 (b(z, s(s(elem!1)))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[324, 20064])).
% 9.68/9.94 tff(20066,plain,
% 9.68/9.94 (b(z, s(s(s(z))))),
% 9.68/9.94 inference(modus_ponens,[status(thm)],[20065, 7862])).
% 9.68/9.94 tff(20067,plain,
% 9.68/9.94 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[3482, 1374, 7866])).
% 9.68/9.94 tff(20068,plain,
% 9.68/9.94 (b(s(s(s(s(z)))), s(s(s(z))))),
% 9.68/9.94 inference(modus_ponens,[status(thm)],[20067, 7865])).
% 9.68/9.94 tff(20069,plain,
% 9.68/9.94 ($false),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[19463, 194, 991, 2792, 1176, 2616])).
% 9.68/9.94 tff(20070,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.94 tff(20071,plain,
% 9.68/9.94 (~r(s(s(elem!1)), z)),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[20070, 20063, 20053, 991])).
% 9.68/9.94 tff(20072,plain,
% 9.68/9.94 (b(s(s(elem!1)), z)),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[2629, 20071])).
% 9.68/9.94 tff(20073,plain,
% 9.68/9.94 (b(s(s(s(z))), z)),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[7886, 20072, 812])).
% 9.68/9.94 tff(20074,plain,
% 9.68/9.94 (~b(z, s(s(s(z))))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[7880, 20073, 20068, 90])).
% 9.68/9.94 tff(20075,plain,
% 9.68/9.94 ($false),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[20074, 20066])).
% 9.68/9.94 tff(20076,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.94 tff(20077,plain,
% 9.68/9.94 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[20076, 20051, 90, 812, 900, 380, 665, 19991, 20004])).
% 9.68/9.94 tff(20078,plain,
% 9.68/9.94 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[1061, 20077, 19502])).
% 9.68/9.94 tff(20079,plain,
% 9.68/9.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 9.68/9.94 inference(rewrite,[status(thm)],[])).
% 9.68/9.94 tff(20080,plain,
% 9.68/9.94 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 9.68/9.94 inference(rewrite,[status(thm)],[])).
% 9.68/9.94 tff(20081,plain,
% 9.68/9.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 9.68/9.94 inference(monotonicity,[status(thm)],[20080])).
% 9.68/9.94 tff(20082,plain,
% 9.68/9.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 9.68/9.94 inference(transitivity,[status(thm)],[20081, 20079])).
% 9.68/9.94 tff(20083,plain,
% 9.68/9.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))),
% 9.68/9.94 inference(quant_inst,[status(thm)],[])).
% 9.68/9.94 tff(20084,plain,
% 9.68/9.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 9.68/9.94 inference(modus_ponens,[status(thm)],[20083, 20082])).
% 9.68/9.94 tff(20085,plain,
% 9.68/9.94 ($false),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[20084, 194, 364, 1063, 1177, 1176])).
% 9.68/9.94 tff(20086,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.94 tff(20087,plain,
% 9.68/9.94 (~r(elem!1, s(s(s(s(elem!1)))))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[20086, 20049, 19994, 20078])).
% 9.68/9.94 tff(20088,plain,
% 9.68/9.94 (b(elem!1, s(s(s(s(elem!1)))))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[1018, 20087, 18176])).
% 9.68/9.94 tff(20089,plain,
% 9.68/9.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.68/9.94 inference(rewrite,[status(thm)],[])).
% 9.68/9.94 tff(20090,plain,
% 9.68/9.94 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.68/9.94 inference(rewrite,[status(thm)],[])).
% 9.68/9.94 tff(20091,plain,
% 9.68/9.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 9.68/9.94 inference(monotonicity,[status(thm)],[20090])).
% 9.68/9.94 tff(20092,plain,
% 9.68/9.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 9.68/9.94 inference(transitivity,[status(thm)],[20091, 20089])).
% 9.68/9.94 tff(20093,plain,
% 9.68/9.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)))),
% 9.68/9.94 inference(quant_inst,[status(thm)],[])).
% 9.68/9.94 tff(20094,plain,
% 9.68/9.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 9.68/9.94 inference(modus_ponens,[status(thm)],[20093, 20092])).
% 9.68/9.94 tff(20095,plain,
% 9.68/9.94 ($false),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[20094, 391, 665, 974, 2781, 17911])).
% 9.68/9.94 tff(20096,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.94 tff(20097,plain,
% 9.68/9.94 (~b(z, s(s(s(s(elem!1)))))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[20096, 20088, 665, 20027])).
% 9.68/9.94 tff(20098,plain,
% 9.68/9.94 (r(z, s(s(s(s(elem!1)))))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[2767, 20097])).
% 9.68/9.94 tff(20099,plain,
% 9.68/9.94 (~r(z, s(s(elem!1)))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[2800, 20098, 20051, 20049])).
% 9.68/9.94 tff(20100,plain,
% 9.68/9.94 (b(z, s(s(elem!1)))),
% 9.68/9.94 inference(unit_resolution,[status(thm)],[324, 20099])).
% 9.68/9.94 tff(20101,plain,
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% 9.68/9.95 tff(20121,plain,
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% 9.68/9.96 tff(20149,plain,
% 9.68/9.96 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 9.68/9.96 inference(rewrite,[status(thm)],[])).
% 9.68/9.96 tff(20150,plain,
% 9.68/9.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 9.68/9.96 inference(monotonicity,[status(thm)],[20149])).
% 9.68/9.96 tff(20151,plain,
% 9.68/9.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 9.68/9.96 inference(transitivity,[status(thm)],[20150, 20148])).
% 9.68/9.96 tff(20152,plain,
% 9.68/9.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 9.68/9.96 inference(quant_inst,[status(thm)],[])).
% 9.68/9.96 tff(20153,plain,
% 9.68/9.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 9.68/9.96 inference(modus_ponens,[status(thm)],[20152, 20151])).
% 9.68/9.96 tff(20154,plain,
% 9.68/9.96 (~r(z, s(s(s(s(elem!1)))))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[20153, 194, 364, 326, 1177])).
% 9.68/9.96 tff(20155,plain,
% 9.68/9.96 (b(z, s(s(s(s(elem!1)))))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[2767, 20154])).
% 9.68/9.96 tff(20156,plain,
% 9.68/9.96 (~b(elem!1, s(s(s(s(elem!1)))))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[20096, 20155, 665, 20147])).
% 9.68/9.96 tff(20157,plain,
% 9.68/9.96 (r(elem!1, s(s(s(s(elem!1)))))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[1018, 20156, 14203])).
% 9.68/9.96 tff(20158,plain,
% 9.68/9.96 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[20047, 20147, 448, 1374, 1457, 411, 364, 380])).
% 9.68/9.96 tff(20159,plain,
% 9.68/9.96 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[1048, 20158, 1035])).
% 9.68/9.96 tff(20160,plain,
% 9.68/9.96 ($false),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[20086, 20159, 20157, 364, 1177])).
% 9.68/9.96 tff(20161,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.96 tff(20162,plain,
% 9.68/9.96 (~r(z, s(s(elem!1)))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[20161, 20139, 20136, 19140, 18176, 448, 20122, 9651, 411, 380, 665])).
% 9.68/9.96 tff(20163,plain,
% 9.68/9.96 (b(z, s(s(elem!1)))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[324, 20162])).
% 9.68/9.96 tff(20164,plain,
% 9.68/9.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(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(elem!1), z)))),
% 9.68/9.96 inference(rewrite,[status(thm)],[])).
% 9.68/9.96 tff(20165,plain,
% 9.68/9.96 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(z, s(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(elem!1), z)))),
% 9.68/9.96 inference(rewrite,[status(thm)],[])).
% 9.68/9.96 tff(20166,plain,
% 9.68/9.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(elem!1), z))))),
% 9.68/9.96 inference(monotonicity,[status(thm)],[20165])).
% 9.68/9.96 tff(20167,plain,
% 9.68/9.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(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(elem!1), z)))),
% 9.68/9.96 inference(transitivity,[status(thm)],[20166, 20164])).
% 9.68/9.96 tff(20168,plain,
% 9.68/9.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 9.68/9.96 inference(quant_inst,[status(thm)],[])).
% 9.68/9.96 tff(20169,plain,
% 9.68/9.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 9.68/9.96 inference(modus_ponens,[status(thm)],[20168, 20167])).
% 9.68/9.96 tff(20170,plain,
% 9.68/9.96 ($false),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[20169, 391, 19980, 448, 20163, 20111, 19954])).
% 9.68/9.96 tff(20171,plain,(r(elem!1, s(elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.96 tff(20172,plain,
% 9.68/9.96 (r(elem!1, s(elem!1))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[20171, 19917, 8232, 19946, 18965, 19900, 19947, 19688, 59, 19338, 19788])).
% 9.68/9.96 tff(20173,plain,
% 9.68/9.96 (r(s(z), s(s(z)))),
% 9.68/9.96 inference(modus_ponens,[status(thm)],[20172, 19953])).
% 9.68/9.96 tff(20174,plain,
% 9.68/9.96 (elem!1 = s(z)),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[1495, 19947])).
% 9.68/9.96 tff(20175,plain,
% 9.68/9.96 (b(elem!1, s(s(s(s(z)))))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[8539, 19947, 19338])).
% 9.68/9.96 tff(20176,plain,
% 9.68/9.96 (~b(z, s(s(s(s(z)))))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[3234, 20175, 18965, 19917])).
% 9.68/9.96 tff(20177,plain,
% 9.68/9.96 (r(z, s(z))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[11318, 20176, 2, 20174])).
% 9.68/9.96 tff(20178,plain,
% 9.68/9.96 (~b(s(s(elem!1)), s(z))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[19556, 3927, 665, 448, 380])).
% 9.68/9.96 tff(20179,plain,
% 9.68/9.96 (r(s(s(elem!1)), s(z))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[362, 20178])).
% 9.68/9.96 tff(20180,plain,
% 9.68/9.96 (~r(s(s(elem!1)), z)),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[9045, 20179, 722, 1747])).
% 9.68/9.96 tff(20181,plain,
% 9.68/9.96 (b(s(s(elem!1)), z)),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[2629, 20180])).
% 9.68/9.96 tff(20182,plain,
% 9.68/9.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)))),
% 9.68/9.96 inference(rewrite,[status(thm)],[])).
% 9.68/9.96 tff(20183,plain,
% 9.68/9.96 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)))),
% 9.68/9.96 inference(rewrite,[status(thm)],[])).
% 9.68/9.96 tff(20184,plain,
% 9.68/9.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z))))),
% 9.68/9.96 inference(monotonicity,[status(thm)],[20183])).
% 9.68/9.96 tff(20185,plain,
% 9.68/9.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)))),
% 9.68/9.96 inference(transitivity,[status(thm)],[20184, 20182])).
% 9.68/9.96 tff(20186,plain,
% 9.68/9.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 9.68/9.96 inference(quant_inst,[status(thm)],[])).
% 9.68/9.96 tff(20187,plain,
% 9.68/9.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z))),
% 9.68/9.96 inference(modus_ponens,[status(thm)],[20186, 20185])).
% 9.68/9.96 tff(20188,plain,
% 9.68/9.96 ($false),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[20187, 391, 665, 900, 380, 3927, 20181])).
% 9.68/9.96 tff(20189,plain,((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.96 tff(20190,plain,
% 9.68/9.96 (~b(z, s(s(elem!1)))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[20189, 20177, 19688, 19946, 18965, 20173, 19900])).
% 9.68/9.96 tff(20191,plain,
% 9.68/9.96 (r(z, s(s(elem!1)))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[324, 20190])).
% 9.68/9.96 tff(20192,plain,
% 9.68/9.96 (b(s(s(s(s(z)))), elem!1)),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[1563, 20174, 19688])).
% 9.68/9.96 tff(20193,plain,
% 9.68/9.96 (b(s(s(s(s(z)))), s(z))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[9614, 20192, 19947])).
% 9.68/9.96 tff(20194,plain,
% 9.68/9.96 (b(s(s(s(elem!1))), s(z))),
% 9.68/9.96 inference(unit_resolution,[status(thm)],[11177, 20193, 20174])).
% 9.68/9.96 tff(20195,plain,
% 9.68/9.96 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 9.68/9.96 inference(monotonicity,[status(thm)],[19947])).
% 9.68/9.96 tff(20196,plain,
% 9.68/9.97 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 9.68/9.97 inference(symmetry,[status(thm)],[20195])).
% 9.68/9.97 tff(20197,plain,
% 9.68/9.97 (b(s(z), s(s(s(elem!1))))),
% 9.68/9.97 inference(modus_ponens,[status(thm)],[19900, 20196])).
% 9.68/9.97 tff(20198,plain,
% 9.68/9.97 (~(s(s(s(elem!1))) = elem!1)),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[15370, 19900])).
% 9.68/9.97 tff(20199,plain,
% 9.68/9.97 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[8251, 20198])).
% 9.68/9.97 tff(20200,plain,
% 9.68/9.97 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 9.68/9.97 inference(monotonicity,[status(thm)],[19947])).
% 9.68/9.97 tff(20201,plain,
% 9.68/9.97 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 9.68/9.97 inference(monotonicity,[status(thm)],[20200])).
% 9.68/9.97 tff(20202,plain,
% 9.68/9.97 (~(s(s(elem!1)) = elem!1)),
% 9.68/9.97 inference(modus_ponens,[status(thm)],[357, 20201])).
% 9.68/9.97 tff(20203,plain,
% 9.68/9.97 (b(s(s(elem!1)), elem!1)),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[872, 373, 249])).
% 9.68/9.97 tff(20204,plain,
% 9.68/9.97 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[6001, 20203, 900, 448])).
% 9.68/9.97 tff(20205,plain,
% 9.68/9.97 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[1356, 20204, 16095])).
% 9.68/9.97 tff(20206,plain,
% 9.68/9.97 ($false),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[1363, 194, 184, 327, 326, 20205])).
% 9.68/9.97 tff(20207,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.68/9.97 tff(20208,plain,
% 9.68/9.97 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[20207, 20191, 59, 19688, 19900, 20202])).
% 9.68/9.97 tff(20209,plain,
% 9.68/9.97 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[1370, 20208, 20199])).
% 9.68/9.97 tff(20210,plain,
% 9.68/9.97 (~b(s(s(elem!1)), s(z))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[4762, 20209, 20197, 20194])).
% 9.68/9.97 tff(20211,plain,
% 9.68/9.97 (r(s(s(elem!1)), s(z))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[362, 20210])).
% 9.68/9.97 tff(20212,plain,
% 9.68/9.97 (r(s(s(elem!1)), elem!1)),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[2220, 20211, 19947])).
% 9.68/9.97 tff(20213,plain,
% 9.68/9.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 9.68/9.97 inference(rewrite,[status(thm)],[])).
% 9.68/9.97 tff(20214,plain,
% 9.68/9.97 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 9.68/9.97 inference(rewrite,[status(thm)],[])).
% 9.68/9.97 tff(20215,plain,
% 9.68/9.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 9.68/9.97 inference(monotonicity,[status(thm)],[20214])).
% 9.68/9.97 tff(20216,plain,
% 9.68/9.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 9.68/9.97 inference(transitivity,[status(thm)],[20215, 20213])).
% 9.68/9.97 tff(20217,plain,
% 9.68/9.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 9.68/9.97 inference(quant_inst,[status(thm)],[])).
% 9.68/9.97 tff(20218,plain,
% 9.68/9.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 9.68/9.97 inference(modus_ponens,[status(thm)],[20217, 20216])).
% 9.68/9.97 tff(20219,plain,
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% 9.68/9.97 inference(unit_resolution,[status(thm)],[20218, 194, 8232, 20172, 20212, 20191])).
% 9.68/9.97 tff(20220,plain,(b(s(z), elem!1) | (elem!1 = z) | b(elem!1, s(z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.97 tff(20221,plain,
% 9.68/9.97 (b(s(z), elem!1)),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[20220, 31, 2, 10])).
% 9.68/9.97 tff(20222,plain,
% 9.68/9.97 (~(elem!1 = s(z))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[8805, 20221])).
% 9.68/9.97 tff(20223,plain,
% 9.68/9.97 (r(elem!1, s(z))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[837, 20222, 31])).
% 9.68/9.97 tff(20224,plain,
% 9.68/9.97 (~r(s(elem!1), elem!1)),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[19786, 20223, 19688, 18965, 8232, 19946])).
% 9.68/9.97 tff(20225,plain,
% 9.68/9.97 (b(s(elem!1), elem!1)),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[2168, 20224, 18971])).
% 9.68/9.97 tff(20226,plain,
% 9.68/9.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 9.68/9.97 inference(rewrite,[status(thm)],[])).
% 9.68/9.97 tff(20227,plain,
% 9.68/9.97 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 9.68/9.97 inference(rewrite,[status(thm)],[])).
% 9.68/9.97 tff(20228,plain,
% 9.68/9.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))))),
% 9.68/9.97 inference(monotonicity,[status(thm)],[20227])).
% 9.68/9.97 tff(20229,plain,
% 9.68/9.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 9.68/9.97 inference(transitivity,[status(thm)],[20228, 20226])).
% 9.68/9.97 tff(20230,plain,
% 9.68/9.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 9.68/9.97 inference(quant_inst,[status(thm)],[])).
% 9.68/9.97 tff(20231,plain,
% 9.68/9.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 9.68/9.97 inference(modus_ponens,[status(thm)],[20230, 20229])).
% 9.68/9.97 tff(20232,plain,
% 9.68/9.97 (~b(s(elem!1), s(z))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[20231, 391, 19688, 19900, 20221, 20225])).
% 9.68/9.97 tff(20233,plain,
% 9.68/9.97 (r(s(elem!1), s(z))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[13479, 20232, 124])).
% 9.68/9.97 tff(20234,plain,
% 9.68/9.97 (~b(s(s(s(elem!1))), s(z))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[17846, 391, 19688, 19900, 20221])).
% 9.68/9.97 tff(20235,plain,
% 9.68/9.97 (r(s(s(s(elem!1))), s(z))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[223, 20234])).
% 9.68/9.97 tff(20236,plain,
% 9.68/9.97 (~b(s(z), s(s(s(elem!1))))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[16825, 391, 19688, 19900, 20221])).
% 9.68/9.97 tff(20237,plain,
% 9.68/9.97 (r(s(z), s(s(s(elem!1))))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[247, 20236])).
% 9.68/9.97 tff(20238,plain,
% 9.68/9.97 (~b(s(s(s(elem!1))), s(elem!1))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[6869, 20225, 19688, 19900])).
% 9.68/9.97 tff(20239,plain,
% 9.68/9.97 (~(s(z) = elem!1)),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[1495, 20222])).
% 9.68/9.97 tff(20240,plain,
% 9.68/9.97 (b(s(s(s(s(z)))), z)),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[19744, 20223, 10550, 18965, 19688, 19946, 20239, 8232, 19338, 10])).
% 9.68/9.97 tff(20241,plain,
% 9.68/9.97 (~b(z, s(s(s(s(z)))))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[10438, 20223, 19338, 8232, 20240])).
% 9.68/9.97 tff(20242,plain,
% 9.68/9.97 (r(z, s(s(s(s(z)))))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[800, 20241])).
% 9.68/9.97 tff(20243,plain,
% 9.68/9.97 (~r(s(s(s(s(z)))), elem!1)),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[10418, 20242, 20223, 8232])).
% 9.68/9.97 tff(20244,plain,
% 9.68/9.97 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.68/9.97 inference(rewrite,[status(thm)],[])).
% 9.68/9.97 tff(20245,plain,
% 9.68/9.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 9.68/9.97 inference(monotonicity,[status(thm)],[20244])).
% 9.68/9.97 tff(20246,plain,
% 9.68/9.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.68/9.97 inference(transitivity,[status(thm)],[20245, 17851])).
% 9.68/9.97 tff(20247,plain,
% 9.68/9.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 9.68/9.97 inference(quant_inst,[status(thm)],[])).
% 9.68/9.97 tff(20248,plain,
% 9.68/9.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 9.68/9.97 inference(modus_ponens,[status(thm)],[20247, 20246])).
% 9.68/9.97 tff(20249,plain,
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% 9.68/9.97 inference(unit_resolution,[status(thm)],[20248, 194, 59, 20237, 20235])).
% 9.68/9.97 tff(20250,plain,
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% 9.68/9.97 inference(unit_resolution,[status(thm)],[678, 20249])).
% 9.68/9.97 tff(20251,plain,
% 9.68/9.97 (~b(s(s(s(s(z)))), elem!1)),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[14978, 20250, 10550, 18965, 20240])).
% 9.68/9.97 tff(20252,plain,
% 9.68/9.97 (s(s(s(s(z)))) = elem!1),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[762, 20251, 20243])).
% 9.68/9.97 tff(20253,plain,
% 9.68/9.97 (~(s(s(s(elem!1))) = s(elem!1))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[717, 20252])).
% 9.68/9.97 tff(20254,plain,
% 9.68/9.97 (r(s(s(s(elem!1))), s(elem!1))),
% 9.68/9.97 inference(unit_resolution,[status(thm)],[588, 20253, 20238])).
% 9.68/9.97 tff(20255,plain,
% 9.68/9.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.68/9.98 inference(rewrite,[status(thm)],[])).
% 9.68/9.98 tff(20256,plain,
% 9.68/9.98 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.68/9.98 inference(rewrite,[status(thm)],[])).
% 9.68/9.98 tff(20257,plain,
% 9.68/9.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 9.68/9.98 inference(monotonicity,[status(thm)],[20256])).
% 9.68/9.98 tff(20258,plain,
% 9.68/9.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 9.68/9.98 inference(transitivity,[status(thm)],[20257, 20255])).
% 9.68/9.98 tff(20259,plain,
% 9.68/9.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 9.68/9.98 inference(quant_inst,[status(thm)],[])).
% 9.68/9.98 tff(20260,plain,
% 9.68/9.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 9.68/9.98 inference(modus_ponens,[status(thm)],[20259, 20258])).
% 9.68/9.98 tff(20261,plain,
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% 9.68/9.98 inference(unit_resolution,[status(thm)],[20260, 194, 20254, 20237, 20235, 20233])).
% 9.68/9.98 tff(20262,plain,(b(elem!1, s(z)) | b(z, s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 9.68/9.98 tff(20263,plain,
% 9.68/9.98 (b(elem!1, s(z))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[20262, 10, 2])).
% 9.68/9.98 tff(20264,plain,
% 9.68/9.98 (r(s(z), s(s(s(elem!1))))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[247, 14870])).
% 9.68/9.98 tff(20265,plain,
% 9.68/9.98 (~r(s(s(s(elem!1))), elem!1)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[241, 20264, 59, 181])).
% 9.68/9.98 tff(20266,plain,
% 9.68/9.98 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 9.68/9.98 inference(monotonicity,[status(thm)],[812])).
% 9.68/9.98 tff(20267,plain,
% 9.68/9.98 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 9.68/9.98 inference(symmetry,[status(thm)],[20266])).
% 9.68/9.98 tff(20268,plain,
% 9.68/9.98 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 9.68/9.98 inference(monotonicity,[status(thm)],[20267])).
% 9.68/9.98 tff(20269,plain,
% 9.68/9.98 (~b(elem!1, s(z))),
% 9.68/9.98 inference(modus_ponens,[status(thm)],[4741, 20268])).
% 9.68/9.98 tff(20270,plain,
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% 9.68/9.98 inference(unit_resolution,[status(thm)],[721, 20269])).
% 9.68/9.98 tff(20271,plain,((~(s(z) = elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.98 tff(20272,plain,
% 9.68/9.98 (~(s(z) = elem!1)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[20271, 20263])).
% 9.68/9.98 tff(20273,plain,
% 9.68/9.98 (~r(s(s(s(elem!1))), s(elem!1))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[641, 20264, 59, 181])).
% 9.68/9.98 tff(20274,plain,
% 9.68/9.98 (~r(s(elem!1), z)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[2594, 20264, 15899, 181, 1526, 20273, 118])).
% 9.68/9.98 tff(20275,plain,
% 9.68/9.98 (~r(elem!1, s(elem!1))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[2582, 1484, 15899, 181])).
% 9.68/9.98 tff(20276,plain,
% 9.68/9.98 (~r(elem!1, z)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[627, 1484, 15899, 181])).
% 9.68/9.98 tff(20277,plain,
% 9.68/9.98 (b(elem!1, z)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[526, 20276, 2])).
% 9.68/9.98 tff(20278,plain,
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% 9.68/9.98 inference(unit_resolution,[status(thm)],[3924, 15838, 10, 91])).
% 9.68/9.98 tff(20279,plain,
% 9.68/9.98 (~r(s(s(s(elem!1))), z)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[1867, 232, 59, 181])).
% 9.68/9.98 tff(20280,plain,
% 9.68/9.98 (b(s(s(s(elem!1))), z)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[377, 20279])).
% 9.68/9.98 tff(20281,plain,
% 9.68/9.98 (b(s(s(s(elem!1))), elem!1)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[5715, 127, 4028, 1484, 232])).
% 9.68/9.98 tff(20282,plain,
% 9.68/9.98 (b(elem!1, s(elem!1))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[443, 4598, 438])).
% 9.68/9.98 tff(20283,plain,
% 9.68/9.98 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[337, 232, 59, 181])).
% 9.68/9.98 tff(20284,plain,
% 9.68/9.98 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[1370, 15838, 20283])).
% 9.68/9.98 tff(20285,plain,
% 9.68/9.98 (~b(s(s(elem!1)), elem!1)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[8469, 20284, 20280, 20278, 20282])).
% 9.68/9.98 tff(20286,plain,
% 9.68/9.98 (~(s(s(s(elem!1))) = s(elem!1))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[4603, 20282, 4028])).
% 9.68/9.98 tff(20287,plain,
% 9.68/9.98 (~(s(s(elem!1)) = elem!1)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[451, 20286])).
% 9.68/9.98 tff(20288,plain,
% 9.68/9.98 (r(s(s(elem!1)), elem!1)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[872, 20287, 20285])).
% 9.68/9.98 tff(20289,plain,
% 9.68/9.98 (~r(s(s(elem!1)), s(z))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[2379, 20288, 1484, 4030])).
% 9.68/9.98 tff(20290,plain,
% 9.68/9.98 (b(s(s(elem!1)), s(z))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[362, 20289])).
% 9.68/9.98 tff(20291,plain,
% 9.68/9.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 9.68/9.98 inference(rewrite,[status(thm)],[])).
% 9.68/9.98 tff(20292,plain,
% 9.68/9.98 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 9.68/9.98 inference(rewrite,[status(thm)],[])).
% 9.68/9.98 tff(20293,plain,
% 9.68/9.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 9.68/9.98 inference(monotonicity,[status(thm)],[20292])).
% 9.68/9.98 tff(20294,plain,
% 9.68/9.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 9.68/9.98 inference(transitivity,[status(thm)],[20293, 20291])).
% 9.68/9.98 tff(20295,plain,
% 9.68/9.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 9.68/9.98 inference(quant_inst,[status(thm)],[])).
% 9.68/9.98 tff(20296,plain,
% 9.68/9.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 9.68/9.98 inference(modus_ponens,[status(thm)],[20295, 20294])).
% 9.68/9.98 tff(20297,plain,
% 9.68/9.98 ($false),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[20296, 391, 665, 20290, 20281, 20280, 20278])).
% 9.68/9.98 tff(20298,plain,((s(s(s(elem!1))) = elem!1) | (~b(elem!1, z)) | (~r(s(z), elem!1)) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(elem!1)) | b(z, s(s(s(elem!1)))) | b(s(z), z) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.98 tff(20299,plain,
% 9.68/9.98 (s(s(s(elem!1))) = elem!1),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[20298, 20277, 1484, 4028, 20275, 10, 91, 232])).
% 9.68/9.98 tff(20300,plain,
% 9.68/9.98 (s(s(s(s(elem!1)))) = s(elem!1)),
% 9.68/9.98 inference(monotonicity,[status(thm)],[20299])).
% 9.68/9.98 tff(20301,plain,
% 9.68/9.98 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(elem!1), elem!1)),
% 9.68/9.98 inference(monotonicity,[status(thm)],[20300])).
% 9.68/9.98 tff(20302,plain,
% 9.68/9.98 ((~r(s(s(s(s(elem!1)))), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 9.68/9.98 inference(monotonicity,[status(thm)],[20301])).
% 9.68/9.98 tff(20303,plain,
% 9.68/9.98 (elem!1 = s(s(s(elem!1)))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[8, 20299])).
% 9.68/9.98 tff(20304,plain,
% 9.68/9.98 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[2849, 20272])).
% 9.68/9.98 tff(20305,plain,
% 9.68/9.98 (~r(s(s(s(s(z)))), elem!1)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[12394, 20280, 90, 181, 20304, 1216, 232])).
% 9.68/9.98 tff(20306,plain,
% 9.68/9.98 (~(s(s(s(s(z)))) = elem!1)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[1436, 20299])).
% 9.68/9.98 tff(20307,plain,
% 9.68/9.98 (b(s(s(s(s(z)))), elem!1)),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[762, 20306, 20305])).
% 9.68/9.98 tff(20308,plain,
% 9.68/9.98 (~b(z, s(s(s(s(z)))))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[4246, 20307, 90, 20277])).
% 9.68/9.98 tff(20309,plain,
% 9.68/9.98 (r(z, s(s(s(s(z)))))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[800, 20308])).
% 9.68/9.98 tff(20310,plain,
% 9.68/9.98 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[1705, 20309, 1216, 181])).
% 9.68/9.98 tff(20311,plain,
% 9.68/9.98 (b(s(s(s(s(z)))), s(s(z)))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[1714, 20310])).
% 9.68/9.98 tff(20312,plain,
% 9.68/9.98 (~r(elem!1, s(s(s(s(z)))))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[2040, 1484, 15899, 181])).
% 9.68/9.98 tff(20313,plain,
% 9.68/9.98 (~(elem!1 = s(s(s(s(z)))))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[769, 20306])).
% 9.68/9.98 tff(20314,plain,
% 9.68/9.98 (b(elem!1, s(s(s(s(z)))))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[781, 20313, 20312])).
% 9.68/9.98 tff(20315,plain,
% 9.68/9.98 (~r(s(s(s(s(z)))), s(z))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[3236, 20314, 15899, 1216, 181, 20277])).
% 9.68/9.98 tff(20316,plain,
% 9.68/9.98 (b(s(s(s(s(z)))), s(z))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[749, 20315])).
% 9.68/9.98 tff(20317,plain,
% 9.68/9.98 (~r(elem!1, s(s(z)))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[3389, 1484, 15899, 181])).
% 9.68/9.98 tff(20318,plain,
% 9.68/9.98 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[3852, 20311, 90, 59, 20304, 20317, 20303, 20309])).
% 9.68/9.98 tff(20319,plain,
% 9.68/9.98 (r(s(s(z)), s(s(s(s(z)))))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[3652, 20318])).
% 9.68/9.98 tff(20320,plain,
% 9.68/9.98 (~b(z, s(s(z)))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[15053, 1235, 90, 3563])).
% 9.68/9.98 tff(20321,plain,
% 9.68/9.98 (r(z, s(s(z)))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[18613, 20320])).
% 9.68/9.98 tff(20322,plain,
% 9.68/9.98 (~b(s(z), s(s(z)))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[2447, 1235, 721, 1652, 1759])).
% 9.68/9.98 tff(20323,plain,
% 9.68/9.98 (r(s(z), s(s(z)))),
% 9.68/9.98 inference(unit_resolution,[status(thm)],[1788, 20322])).
% 9.68/9.98 tff(20324,plain,
% 9.68/9.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 9.68/9.98 inference(rewrite,[status(thm)],[])).
% 9.68/9.98 tff(20325,plain,
% 9.68/9.98 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 9.68/9.98 inference(rewrite,[status(thm)],[])).
% 9.68/9.99 tff(20326,plain,
% 9.68/9.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 9.68/9.99 inference(monotonicity,[status(thm)],[20325])).
% 9.68/9.99 tff(20327,plain,
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% 9.68/9.99 inference(transitivity,[status(thm)],[20326, 20324])).
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% 9.68/9.99 inference(quant_inst,[status(thm)],[])).
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% 9.68/9.99 inference(modus_ponens,[status(thm)],[20328, 20327])).
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% 9.68/9.99 tff(20331,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.99 tff(20332,plain,
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% 9.68/9.99 inference(unit_resolution,[status(thm)],[20331, 20323, 20321, 182, 1749])).
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% 9.68/9.99 tff(20334,plain,
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% 9.68/9.99 inference(unit_resolution,[status(thm)],[20333, 20319, 181, 20263, 20307, 20316, 90, 20311])).
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% 9.68/9.99 (b(z, s(s(elem!1))) <=> b(z, s(s(s(elem!1))))),
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% 9.68/9.99 tff(20340,plain,
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% 9.68/9.99 inference(symmetry,[status(thm)],[20339])).
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% 9.68/9.99 inference(monotonicity,[status(thm)],[20340])).
% 9.68/9.99 tff(20342,plain,
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% 9.68/9.99 tff(20344,plain,((~(s(s(elem!1)) = elem!1)) | (~b(z, s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.99 tff(20345,plain,
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% 9.68/9.99 tff(20347,plain,
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% 9.68/9.99 tff(20356,plain,
% 9.68/9.99 (r(z, s(elem!1)) <=> r(z, s(s(s(s(elem!1)))))),
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% 9.68/9.99 tff(20360,plain,
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% 9.68/9.99 inference(monotonicity,[status(thm)],[20299])).
% 9.68/9.99 tff(20361,plain,
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% 9.68/9.99 tff(20366,plain,((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.68/9.99 tff(20367,plain,
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% 9.68/9.99 tff(20375,plain,
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% 9.68/9.99 tff(20378,plain,
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% 9.68/9.99 inference(modus_ponens,[status(thm)],[20384, 20383])).
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% 9.68/9.99 tff(20388,plain,
% 9.68/9.99 (~b(s(s(s(elem!1))), elem!1)),
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% 9.68/9.99 tff(20391,plain,
% 9.68/9.99 (b(s(z), s(s(s(elem!1))))),
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% 9.68/9.99 tff(20400,plain,
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% 9.68/10.00 tff(20407,plain,
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% 9.68/10.00 tff(20408,plain,
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% 9.68/10.00 inference(transitivity,[status(thm)],[20407, 20404])).
% 9.68/10.00 tff(20409,plain,
% 9.68/10.00 ((elem!1 = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 9.68/10.00 inference(monotonicity,[status(thm)],[125])).
% 9.68/10.00 tff(20410,plain,
% 9.68/10.00 ((s(s(s(elem!1))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 9.68/10.00 inference(symmetry,[status(thm)],[20409])).
% 9.68/10.00 tff(20411,plain,
% 9.68/10.00 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 9.68/10.00 inference(transitivity,[status(thm)],[20410, 161])).
% 9.68/10.00 tff(20412,plain,
% 9.68/10.00 (s(elem!1) = elem!1),
% 9.68/10.00 inference(modus_ponens,[status(thm)],[20397, 20411])).
% 9.68/10.00 tff(20413,plain,
% 9.68/10.00 ((s(elem!1) = z) <=> (elem!1 = z)),
% 9.68/10.00 inference(monotonicity,[status(thm)],[152])).
% 9.68/10.00 tff(20414,plain,
% 9.68/10.00 ((s(elem!1) = z) <=> (z = elem!1)),
% 9.68/10.00 inference(transitivity,[status(thm)],[20413, 92])).
% 9.68/10.00 tff(20415,plain,
% 9.68/10.00 ((z = elem!1) <=> (s(elem!1) = z)),
% 9.68/10.00 inference(symmetry,[status(thm)],[20414])).
% 9.68/10.00 tff(20416,plain,
% 9.68/10.00 (~r(elem!1, z)),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[533, 18966, 329])).
% 9.68/10.00 tff(20417,plain,
% 9.68/10.00 (elem!1 = z),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[526, 20416, 484])).
% 9.68/10.00 tff(20418,plain,
% 9.68/10.00 (z = elem!1),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[5453, 20417])).
% 9.68/10.00 tff(20419,plain,
% 9.68/10.00 (s(elem!1) = z),
% 9.68/10.00 inference(modus_ponens,[status(thm)],[20418, 20415])).
% 9.68/10.00 tff(20420,plain,
% 9.68/10.00 ($false),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[355, 20419])).
% 9.68/10.00 tff(20421,plain,((~(s(elem!1) = elem!1)) | b(elem!1, z) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 9.68/10.00 tff(20422,plain,
% 9.68/10.00 (r(s(s(s(elem!1))), z)),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[20421, 484, 20412])).
% 9.68/10.00 tff(20423,plain,
% 9.68/10.00 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[1450, 325, 59, 174])).
% 9.68/10.00 tff(20424,plain,
% 9.68/10.00 (~r(s(s(elem!1)), elem!1)),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[867, 325, 411, 530])).
% 9.68/10.00 tff(20425,plain,
% 9.68/10.00 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[15335, 2053, 174, 184])).
% 9.68/10.00 tff(20426,plain,
% 9.68/10.00 (~r(s(s(s(s(z)))), elem!1)),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[2116, 20425, 130])).
% 9.68/10.00 tff(20427,plain,
% 9.68/10.00 (r(z, s(elem!1)) <=> r(z, s(s(s(s(elem!1)))))),
% 9.68/10.00 inference(monotonicity,[status(thm)],[20402])).
% 9.68/10.00 tff(20428,plain,
% 9.68/10.00 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(elem!1))),
% 9.68/10.00 inference(symmetry,[status(thm)],[20427])).
% 9.68/10.00 tff(20429,plain,
% 9.68/10.00 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[6956, 194, 174, 184, 2053])).
% 9.68/10.00 tff(20430,plain,
% 9.68/10.00 (~r(elem!1, s(s(s(s(z)))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[14788, 20429, 125])).
% 9.68/10.00 tff(20431,plain,
% 9.68/10.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.68/10.00 inference(rewrite,[status(thm)],[])).
% 9.68/10.00 tff(20432,plain,
% 9.68/10.00 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.68/10.00 inference(rewrite,[status(thm)],[])).
% 9.68/10.00 tff(20433,plain,
% 9.68/10.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 9.68/10.00 inference(monotonicity,[status(thm)],[20432])).
% 9.68/10.00 tff(20434,plain,
% 9.68/10.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.68/10.00 inference(transitivity,[status(thm)],[20433, 20431])).
% 9.68/10.00 tff(20435,plain,
% 9.68/10.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 9.68/10.00 inference(quant_inst,[status(thm)],[])).
% 9.68/10.00 tff(20436,plain,
% 9.68/10.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 9.68/10.00 inference(modus_ponens,[status(thm)],[20435, 20434])).
% 9.68/10.00 tff(20437,plain,
% 9.68/10.00 ($false),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[20436, 391, 6223, 6222, 1234, 721])).
% 9.68/10.00 tff(20438,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 9.68/10.00 tff(20439,plain,
% 9.68/10.00 (~b(s(z), s(s(s(s(z)))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[20438, 20430, 721, 20426, 2642])).
% 9.68/10.00 tff(20440,plain,
% 9.68/10.00 (b(s(s(s(s(z)))), elem!1)),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[2694, 20425, 130])).
% 9.68/10.00 tff(20441,plain,
% 9.68/10.00 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.68/10.00 inference(modus_ponens,[status(thm)],[20440, 9969])).
% 9.68/10.00 tff(20442,plain,
% 9.68/10.00 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 9.68/10.00 inference(monotonicity,[status(thm)],[125])).
% 9.68/10.00 tff(20443,plain,
% 9.68/10.00 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 9.68/10.00 inference(transitivity,[status(thm)],[20442, 3928])).
% 9.68/10.00 tff(20444,plain,
% 9.68/10.00 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 9.68/10.00 inference(monotonicity,[status(thm)],[20443])).
% 9.68/10.00 tff(20445,plain,
% 9.68/10.00 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 9.68/10.00 inference(modus_ponens,[status(thm)],[3810, 20444])).
% 9.68/10.00 tff(20446,plain,
% 9.68/10.00 (~r(s(z), z)),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[3969, 2053, 174, 184, 20445])).
% 9.68/10.00 tff(20447,plain,
% 9.68/10.00 (b(s(z), z)),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[180, 20446])).
% 9.68/10.00 tff(20448,plain,
% 9.68/10.00 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 9.68/10.00 inference(transitivity,[status(thm)],[20443, 3929])).
% 9.68/10.00 tff(20449,plain,
% 9.68/10.00 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 9.68/10.00 inference(monotonicity,[status(thm)],[20448])).
% 9.68/10.00 tff(20450,plain,
% 9.68/10.00 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 9.68/10.00 inference(modus_ponens,[status(thm)],[3810, 20449])).
% 9.68/10.00 tff(20451,plain,
% 9.68/10.00 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[15351, 20429, 20450])).
% 9.68/10.00 tff(20452,plain,
% 9.68/10.00 (~r(s(z), s(s(s(s(z)))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[16341, 20451, 125, 328, 2053, 20447, 20441, 184])).
% 9.68/10.00 tff(20453,plain,
% 9.68/10.00 ($false),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[1230, 20452, 20439])).
% 9.68/10.00 tff(20454,plain,((~r(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 9.68/10.00 tff(20455,plain,
% 9.68/10.00 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[20454, 2053, 125, 184, 721, 174])).
% 9.68/10.00 tff(20456,plain,
% 9.68/10.00 (s(s(elem!1)) = s(s(s(elem!1)))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[1356, 20455, 1350])).
% 9.68/10.00 tff(20457,plain,
% 9.68/10.00 (s(s(s(elem!1))) = s(elem!1)),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[281, 20456])).
% 9.68/10.00 tff(20458,plain,
% 9.68/10.00 (s(elem!1) = s(s(s(elem!1)))),
% 9.68/10.00 inference(symmetry,[status(thm)],[20457])).
% 9.68/10.00 tff(20459,plain,
% 9.68/10.00 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 9.68/10.00 inference(transitivity,[status(thm)],[16458, 20458])).
% 9.68/10.00 tff(20460,plain,
% 9.68/10.00 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(elem!1))))),
% 9.68/10.00 inference(monotonicity,[status(thm)],[20459])).
% 9.68/10.00 tff(20461,plain,
% 9.68/10.00 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(elem!1)))))),
% 9.68/10.00 inference(symmetry,[status(thm)],[20460])).
% 9.68/10.00 tff(20462,plain,
% 9.68/10.00 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 9.68/10.00 inference(transitivity,[status(thm)],[20461, 20428])).
% 9.68/10.00 tff(20463,plain,
% 9.68/10.00 (r(z, s(elem!1))),
% 9.68/10.00 inference(modus_ponens,[status(thm)],[184, 20462])).
% 9.68/10.00 tff(20464,plain,
% 9.68/10.00 (~r(elem!1, s(s(s(s(z)))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[6444, 20463, 530, 2053])).
% 9.68/10.00 tff(20465,plain,
% 9.68/10.00 (~b(s(z), s(s(s(s(z)))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[20438, 20464, 721, 20426, 2642])).
% 9.68/10.00 tff(20466,plain,
% 9.68/10.00 (r(s(z), s(s(s(s(z)))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[1230, 20465])).
% 9.68/10.00 tff(20467,plain,
% 9.68/10.00 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 9.68/10.00 inference(monotonicity,[status(thm)],[125])).
% 9.68/10.00 tff(20468,plain,
% 9.68/10.00 (b(s(s(s(elem!1))), s(z))),
% 9.68/10.00 inference(modus_ponens,[status(thm)],[721, 20467])).
% 9.68/10.00 tff(20469,plain,
% 9.68/10.00 (s(s(s(elem!1))) = s(s(elem!1))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[314, 20456])).
% 9.68/10.00 tff(20470,plain,
% 9.68/10.00 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[9242, 20469, 20440])).
% 9.68/10.00 tff(20471,plain,
% 9.68/10.00 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[16076, 1686, 1526, 2053, 184, 3843, 590, 10679, 411])).
% 9.68/10.00 tff(20472,plain,
% 9.68/10.00 (r(s(s(z)), s(s(s(s(z)))))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[3652, 20471])).
% 9.68/10.00 tff(20473,plain,
% 9.68/10.00 (~r(s(s(z)), s(z))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[5567, 20472, 2053, 1216])).
% 9.68/10.00 tff(20474,plain,
% 9.68/10.00 (b(s(s(z)), s(z))),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[3778, 20473])).
% 9.68/10.00 tff(20475,plain,
% 9.68/10.00 (~r(s(s(z)), z)),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[14746, 20472, 2053, 184])).
% 9.68/10.00 tff(20476,plain,
% 9.68/10.00 (b(s(s(z)), z)),
% 9.68/10.00 inference(unit_resolution,[status(thm)],[1211, 20475])).
% 9.68/10.00 tff(20477,plain,
% 9.68/10.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 9.68/10.00 inference(rewrite,[status(thm)],[])).
% 9.68/10.00 tff(20478,plain,
% 9.68/10.00 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 9.68/10.00 inference(rewrite,[status(thm)],[])).
% 9.68/10.00 tff(20479,plain,
% 9.68/10.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(z)))))),
% 9.68/10.00 inference(monotonicity,[status(thm)],[20478])).
% 9.68/10.00 tff(20480,plain,
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% 9.68/10.01 inference(transitivity,[status(thm)],[20479, 20477])).
% 9.68/10.01 tff(20481,plain,
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% 9.68/10.01 inference(quant_inst,[status(thm)],[])).
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% 9.68/10.01 inference(modus_ponens,[status(thm)],[20481, 20480])).
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% 9.68/10.01 inference(unit_resolution,[status(thm)],[20482, 391, 1235, 1686, 1233, 590, 1232])).
% 9.68/10.01 tff(20484,plain,((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.68/10.01 tff(20485,plain,
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% 9.68/10.01 tff(20487,plain,
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% 9.68/10.01 tff(20496,plain,
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% 9.68/10.01 inference(monotonicity,[status(thm)],[20501])).
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% 9.68/10.01 tff(20511,plain,
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% 9.68/10.01 tff(20514,plain,
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% 9.68/10.01 tff(20541,plain,
% 9.68/10.01 (b(z, s(s(z)))),
% 9.68/10.01 inference(unit_resolution,[status(thm)],[18613, 20540])).
% 9.68/10.01 tff(20542,plain,
% 9.68/10.01 (r(s(s(z)), s(s(s(elem!1))))),
% 9.68/10.01 inference(unit_resolution,[status(thm)],[11041, 20533])).
% 9.68/10.01 tff(20543,assumption,(r(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 9.68/10.01 tff(20544,plain,
% 9.68/10.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.02 inference(rewrite,[status(thm)],[])).
% 9.68/10.02 tff(20545,plain,
% 9.68/10.02 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.02 inference(rewrite,[status(thm)],[])).
% 9.68/10.02 tff(20546,plain,
% 9.68/10.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 9.68/10.02 inference(monotonicity,[status(thm)],[20545])).
% 9.68/10.02 tff(20547,plain,
% 9.68/10.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.02 inference(transitivity,[status(thm)],[20546, 20544])).
% 9.68/10.02 tff(20548,plain,
% 9.68/10.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 9.68/10.02 inference(quant_inst,[status(thm)],[])).
% 9.68/10.02 tff(20549,plain,
% 9.68/10.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 9.68/10.02 inference(modus_ponens,[status(thm)],[20548, 20547])).
% 9.68/10.02 tff(20550,plain,
% 9.68/10.02 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 9.68/10.02 inference(unit_resolution,[status(thm)],[20549, 194, 174, 9130, 20543])).
% 9.68/10.02 tff(20551,plain,
% 9.68/10.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.02 inference(rewrite,[status(thm)],[])).
% 9.68/10.02 tff(20552,plain,
% 9.68/10.02 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.02 inference(rewrite,[status(thm)],[])).
% 9.68/10.02 tff(20553,plain,
% 9.68/10.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 9.68/10.02 inference(monotonicity,[status(thm)],[20552])).
% 9.68/10.02 tff(20554,plain,
% 9.68/10.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.02 inference(transitivity,[status(thm)],[20553, 20551])).
% 9.68/10.02 tff(20555,plain,
% 9.68/10.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))),
% 9.68/10.02 inference(quant_inst,[status(thm)],[])).
% 9.68/10.02 tff(20556,plain,
% 9.68/10.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 9.68/10.02 inference(modus_ponens,[status(thm)],[20555, 20554])).
% 9.68/10.02 tff(20557,plain,
% 9.68/10.02 ($false),
% 9.68/10.02 inference(unit_resolution,[status(thm)],[20556, 194, 174, 184, 16500, 20543])).
% 9.68/10.02 tff(20558,plain,((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 9.68/10.02 tff(20559,plain,
% 9.68/10.02 (~r(s(s(s(s(s(z))))), z)),
% 9.68/10.02 inference(unit_resolution,[status(thm)],[20558, 20543, 184, 174])).
% 9.68/10.02 tff(20560,plain,
% 9.68/10.02 (b(s(s(s(s(s(z))))), z)),
% 9.68/10.02 inference(unit_resolution,[status(thm)],[16530, 20559])).
% 9.68/10.02 tff(20561,plain,
% 9.68/10.02 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 9.68/10.02 inference(unit_resolution,[status(thm)],[18792, 20560, 664, 15045, 1235])).
% 9.68/10.02 tff(20562,plain,
% 9.68/10.02 ($false),
% 9.68/10.02 inference(unit_resolution,[status(thm)],[16516, 42, 20561, 8678, 20550])).
% 9.68/10.02 tff(20563,plain,((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.68/10.02 tff(20564,plain,
% 9.68/10.02 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 9.68/10.02 inference(unit_resolution,[status(thm)],[20563, 20542, 174, 20526, 20541, 20532, 184])).
% 9.68/10.02 tff(20565,plain,
% 9.68/10.02 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 9.68/10.02 inference(unit_resolution,[status(thm)],[18857, 42, 20564])).
% 9.68/10.02 tff(20566,plain,
% 9.68/10.02 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 9.68/10.02 inference(unit_resolution,[status(thm)],[20565, 20524])).
% 9.68/10.02 tff(20567,assumption,(b(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 9.68/10.02 tff(20568,plain,
% 9.68/10.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.02 inference(rewrite,[status(thm)],[])).
% 9.68/10.02 tff(20569,plain,
% 9.68/10.02 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.02 inference(rewrite,[status(thm)],[])).
% 9.68/10.02 tff(20570,plain,
% 9.68/10.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 9.68/10.03 inference(monotonicity,[status(thm)],[20569])).
% 9.68/10.03 tff(20571,plain,
% 9.68/10.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.03 inference(transitivity,[status(thm)],[20570, 20568])).
% 9.68/10.03 tff(20572,plain,
% 9.68/10.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 9.68/10.03 inference(quant_inst,[status(thm)],[])).
% 9.68/10.03 tff(20573,plain,
% 9.68/10.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 9.68/10.03 inference(modus_ponens,[status(thm)],[20572, 20571])).
% 9.68/10.03 tff(20574,plain,
% 9.68/10.03 ($false),
% 9.68/10.03 inference(unit_resolution,[status(thm)],[20573, 391, 379, 1526, 3325, 15646, 20567])).
% 9.68/10.03 tff(20575,plain,((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 9.68/10.03 tff(20576,plain,
% 9.68/10.03 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 9.68/10.03 inference(unit_resolution,[status(thm)],[20575, 20566, 20468, 20441, 20515])).
% 9.68/10.03 tff(20577,plain,
% 9.68/10.03 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 9.68/10.03 inference(unit_resolution,[status(thm)],[8761, 20576])).
% 9.68/10.03 tff(20578,plain,
% 9.68/10.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.03 inference(rewrite,[status(thm)],[])).
% 9.68/10.03 tff(20579,plain,
% 9.68/10.03 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.68/10.03 inference(rewrite,[status(thm)],[])).
% 9.68/10.03 tff(20580,plain,
% 9.68/10.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 9.68/10.03 inference(monotonicity,[status(thm)],[20579])).
% 9.68/10.03 tff(20581,plain,
% 9.68/10.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.81/10.03 inference(transitivity,[status(thm)],[20580, 20578])).
% 9.81/10.03 tff(20582,plain,
% 9.81/10.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 9.81/10.03 inference(quant_inst,[status(thm)],[])).
% 9.81/10.03 tff(20583,plain,
% 9.81/10.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 9.81/10.03 inference(modus_ponens,[status(thm)],[20582, 20581])).
% 9.81/10.03 tff(20584,plain,
% 9.81/10.03 (~b(s(s(s(s(s(z))))), s(z))),
% 9.81/10.03 inference(unit_resolution,[status(thm)],[20583, 391, 20515, 20468, 20566])).
% 9.81/10.03 tff(20585,plain,
% 9.81/10.03 (r(s(s(s(s(s(z))))), s(z))),
% 9.81/10.03 inference(unit_resolution,[status(thm)],[15766, 42, 15763, 20584])).
% 9.81/10.03 tff(20586,plain,
% 9.81/10.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.81/10.03 inference(rewrite,[status(thm)],[])).
% 9.81/10.03 tff(20587,plain,
% 9.81/10.03 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.81/10.03 inference(rewrite,[status(thm)],[])).
% 9.81/10.03 tff(20588,plain,
% 9.81/10.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 9.81/10.03 inference(monotonicity,[status(thm)],[20587])).
% 9.81/10.03 tff(20589,plain,
% 9.81/10.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 9.81/10.03 inference(transitivity,[status(thm)],[20588, 20586])).
% 9.81/10.03 tff(20590,plain,
% 9.81/10.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 9.81/10.03 inference(quant_inst,[status(thm)],[])).
% 9.81/10.03 tff(20591,plain,
% 9.81/10.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 9.81/10.03 inference(modus_ponens,[status(thm)],[20590, 20589])).
% 9.81/10.03 tff(20592,plain,
% 9.81/10.03 (~b(s(z), s(s(s(s(s(z))))))),
% 9.81/10.03 inference(unit_resolution,[status(thm)],[20591, 391, 20515, 20468, 20566])).
% 9.81/10.03 tff(20593,plain,
% 9.81/10.03 (r(s(z), s(s(s(s(s(z))))))),
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% 9.81/10.03 tff(20594,plain,
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% 9.81/10.03 inference(unit_resolution,[status(thm)],[16571, 20593, 20585, 20466, 20577])).
% 9.81/10.03 tff(20595,plain,((~r(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | r(s(s(elem!1)), elem!1) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.03 tff(20596,plain,
% 9.81/10.03 (~r(s(s(s(s(z)))), z)),
% 9.81/10.03 inference(unit_resolution,[status(thm)],[20595, 125, 174, 59, 530, 411, 721, 20424, 20423])).
% 9.81/10.03 tff(20597,plain,
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% 9.81/10.03 inference(unit_resolution,[status(thm)],[87, 20596])).
% 9.81/10.03 tff(20598,plain,
% 9.81/10.03 ((s(z) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
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% 9.81/10.03 tff(20599,plain,
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% 9.81/10.03 tff(20600,plain,
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% 9.81/10.03 tff(20601,plain,
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% 9.81/10.03 inference(modus_ponens,[status(thm)],[217, 20600])).
% 9.81/10.03 tff(20602,plain,
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% 9.81/10.03 tff(20603,plain,
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% 9.81/10.03 tff(20604,plain,
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% 9.81/10.03 tff(20605,plain,
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% 9.81/10.03 tff(20606,plain,
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% 9.81/10.03 tff(20607,plain,
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% 9.81/10.03 tff(20608,plain,
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% 9.81/10.03 tff(20609,plain,
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% 9.81/10.03 tff(20610,plain,
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% 9.81/10.03 inference(unit_resolution,[status(thm)],[247, 20609])).
% 9.81/10.03 tff(20611,plain,
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% 9.81/10.03 tff(20612,plain,
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% 9.81/10.03 tff(20613,plain,
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% 9.81/10.03 inference(unit_resolution,[status(thm)],[9608, 20612, 266])).
% 9.81/10.03 tff(20614,plain,
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% 9.81/10.03 inference(unit_resolution,[status(thm)],[781, 20613, 3810])).
% 9.81/10.03 tff(20615,plain,
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% 9.81/10.03 inference(unit_resolution,[status(thm)],[3967, 391, 379, 20468, 1759])).
% 9.81/10.03 tff(20616,plain,
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% 9.81/10.03 tff(20617,plain,
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% 9.81/10.03 inference(unit_resolution,[status(thm)],[6337, 20616, 530, 20614])).
% 9.81/10.03 tff(20618,plain,
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% 9.81/10.03 tff(20619,plain,
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% 9.81/10.03 inference(unit_resolution,[status(thm)],[6252, 644, 2881])).
% 9.81/10.03 tff(20620,plain,
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% 9.81/10.03 tff(20621,plain,
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% 9.81/10.03 tff(20622,plain,
% 9.81/10.03 (b(s(s(s(s(z)))), s(z))),
% 9.81/10.03 inference(unit_resolution,[status(thm)],[749, 20621])).
% 9.81/10.03 tff(20623,plain,
% 9.81/10.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 9.81/10.04 inference(rewrite,[status(thm)],[])).
% 9.81/10.04 tff(20624,plain,
% 9.81/10.04 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 9.81/10.04 inference(rewrite,[status(thm)],[])).
% 9.81/10.04 tff(20625,plain,
% 9.81/10.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 9.81/10.04 inference(monotonicity,[status(thm)],[20624])).
% 9.81/10.04 tff(20626,plain,
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% 9.81/10.04 inference(transitivity,[status(thm)],[20625, 20623])).
% 9.81/10.04 tff(20627,plain,
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% 9.81/10.04 inference(quant_inst,[status(thm)],[])).
% 9.81/10.04 tff(20628,plain,
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% 9.81/10.04 inference(modus_ponens,[status(thm)],[20627, 20626])).
% 9.81/10.04 tff(20629,plain,
% 9.81/10.04 ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[20628, 194])).
% 9.81/10.04 tff(20630,plain,
% 9.81/10.04 (~r(s(s(s(s(z)))), elem!1)),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[20629, 14905, 1216, 1747])).
% 9.81/10.04 tff(20631,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[762, 20630, 720])).
% 9.81/10.04 tff(20632,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[3589, 1235, 484])).
% 9.81/10.04 tff(20633,plain,
% 9.81/10.04 (~(s(z) = elem!1)),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[1495, 20620])).
% 9.81/10.04 tff(20634,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[1775, 20622, 20633, 1747, 14905, 20631])).
% 9.81/10.04 tff(20635,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[3394, 20634, 20632])).
% 9.81/10.04 tff(20636,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[18620, 391, 644, 1235, 20635, 20631, 20622])).
% 9.81/10.04 tff(20637,plain,((~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 9.81/10.04 tff(20638,plain,
% 9.81/10.04 (~b(s(s(z)), z)),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[20637, 17107, 644, 720, 1216, 1686, 90, 484])).
% 9.81/10.04 tff(20639,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[1211, 20638])).
% 9.81/10.04 tff(20640,plain,
% 9.81/10.04 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[11508, 20639, 1216, 17107])).
% 9.81/10.04 tff(20641,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[1714, 20640])).
% 9.81/10.04 tff(20642,plain,
% 9.81/10.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
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% 9.81/10.04 tff(20643,plain,
% 9.81/10.04 (((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 9.81/10.04 inference(rewrite,[status(thm)],[])).
% 9.81/10.04 tff(20644,plain,
% 9.81/10.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))))),
% 9.81/10.04 inference(monotonicity,[status(thm)],[20643])).
% 9.81/10.04 tff(20645,plain,
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% 9.81/10.04 inference(transitivity,[status(thm)],[20644, 20642])).
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% 9.81/10.04 inference(quant_inst,[status(thm)],[])).
% 9.81/10.04 tff(20647,plain,
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% 9.81/10.04 inference(modus_ponens,[status(thm)],[20646, 20645])).
% 9.81/10.04 tff(20648,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[20647, 194, 182, 3557, 1747, 8505])).
% 9.81/10.04 tff(20649,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.04 tff(20650,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[20649, 20639, 182, 17107])).
% 9.81/10.04 tff(20651,plain,
% 9.81/10.04 ((z = s(s(z))) | b(z, s(s(z)))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[10164, 42, 20650])).
% 9.81/10.04 tff(20652,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[20651, 11718])).
% 9.81/10.04 tff(20653,plain,
% 9.81/10.04 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[11508, 1747, 1216, 3557])).
% 9.81/10.04 tff(20654,plain,
% 9.81/10.04 (b(s(s(s(s(z)))), s(s(z)))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[1714, 20653])).
% 9.81/10.04 tff(20655,plain,
% 9.81/10.04 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[20629, 1747, 1216, 2112])).
% 9.81/10.04 tff(20656,plain,
% 9.81/10.04 (b(s(s(z)), s(s(s(s(z)))))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[3652, 20655])).
% 9.81/10.04 tff(20657,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[15550, 20656, 20654, 15045, 1686])).
% 9.81/10.04 tff(20658,plain,((~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.04 tff(20659,plain,
% 9.81/10.04 (~r(s(s(s(s(z)))), elem!1)),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[20658, 20652, 1686, 1216, 17107, 20639])).
% 9.81/10.04 tff(20660,plain,
% 9.81/10.04 (b(s(s(s(s(z)))), elem!1)),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[762, 20659, 720])).
% 9.81/10.04 tff(20661,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[11253, 11250, 644])).
% 9.81/10.04 tff(20662,plain,
% 9.81/10.04 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[15550, 20652, 20641, 1686])).
% 9.81/10.04 tff(20663,plain,
% 9.81/10.04 (r(s(s(z)), s(s(s(s(z)))))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[3652, 20662])).
% 9.81/10.04 tff(20664,plain,
% 9.81/10.04 (~r(s(s(s(s(z)))), s(z))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[16396, 20663, 1216, 17107])).
% 9.81/10.04 tff(20665,plain,
% 9.81/10.04 (b(s(s(s(s(z)))), s(z))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[749, 20664])).
% 9.81/10.04 tff(20666,plain,
% 9.81/10.04 (~r(elem!1, s(s(z)))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[1775, 20665, 20633, 17107, 20663, 20660])).
% 9.81/10.04 tff(20667,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[3394, 20666, 20661])).
% 9.81/10.04 tff(20668,plain,
% 9.81/10.04 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.81/10.04 inference(rewrite,[status(thm)],[])).
% 9.81/10.04 tff(20669,plain,
% 9.81/10.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 9.81/10.04 inference(monotonicity,[status(thm)],[20668])).
% 9.81/10.04 tff(20670,plain,
% 9.81/10.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.81/10.04 inference(transitivity,[status(thm)],[20669, 1768])).
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% 9.81/10.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.81/10.04 inference(quant_inst,[status(thm)],[])).
% 9.81/10.04 tff(20672,plain,
% 9.81/10.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 9.81/10.04 inference(modus_ponens,[status(thm)],[20671, 20670])).
% 9.81/10.04 tff(20673,plain,
% 9.81/10.04 (~b(s(s(s(s(z)))), s(z))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[20672, 391, 644, 1652, 721])).
% 9.81/10.04 tff(20674,plain,
% 9.81/10.04 (r(s(s(s(s(z)))), s(z))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[749, 20673])).
% 9.81/10.04 tff(20675,plain,
% 9.81/10.04 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.81/10.04 inference(unit_resolution,[status(thm)],[16396, 20674, 1216, 1747])).
% 9.81/10.04 tff(20676,plain,
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% 9.81/10.04 inference(unit_resolution,[status(thm)],[3652, 20675])).
% 9.81/10.04 tff(20677,plain,
% 9.81/10.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 9.81/10.04 inference(rewrite,[status(thm)],[])).
% 9.81/10.04 tff(20678,plain,
% 9.81/10.04 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 9.81/10.04 inference(rewrite,[status(thm)],[])).
% 9.81/10.04 tff(20679,plain,
% 9.81/10.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 9.81/10.05 inference(monotonicity,[status(thm)],[20678])).
% 9.81/10.05 tff(20680,plain,
% 9.81/10.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 9.81/10.05 inference(transitivity,[status(thm)],[20679, 20677])).
% 9.81/10.05 tff(20681,plain,
% 9.81/10.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 9.81/10.05 inference(quant_inst,[status(thm)],[])).
% 9.81/10.05 tff(20682,plain,
% 9.81/10.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 9.81/10.05 inference(modus_ponens,[status(thm)],[20681, 20680])).
% 9.81/10.05 tff(20683,plain,
% 9.81/10.05 ($false),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[20682, 391, 20676, 90, 3369, 1652, 3563])).
% 9.81/10.05 tff(20684,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.05 tff(20685,plain,
% 9.81/10.05 (~b(elem!1, s(z))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[20684, 20667, 20660, 20641, 1216, 17107, 644, 90])).
% 9.81/10.05 tff(20686,plain,
% 9.81/10.05 (r(elem!1, s(z))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[837, 20685, 20620])).
% 9.81/10.05 tff(20687,plain,
% 9.81/10.05 (~r(z, s(z))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[17266, 20686, 182, 530])).
% 9.81/10.05 tff(20688,plain,
% 9.81/10.05 (b(z, s(z))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[678, 20687])).
% 9.81/10.05 tff(20689,plain,
% 9.81/10.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 9.81/10.05 inference(rewrite,[status(thm)],[])).
% 9.81/10.05 tff(20690,plain,
% 9.81/10.05 (((~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 9.81/10.05 inference(rewrite,[status(thm)],[])).
% 9.81/10.05 tff(20691,plain,
% 9.81/10.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 9.81/10.05 inference(monotonicity,[status(thm)],[20690])).
% 9.81/10.05 tff(20692,plain,
% 9.81/10.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 9.81/10.05 inference(transitivity,[status(thm)],[20691, 20689])).
% 9.81/10.05 tff(20693,plain,
% 9.81/10.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 9.81/10.05 inference(quant_inst,[status(thm)],[])).
% 9.81/10.05 tff(20694,plain,
% 9.81/10.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 9.81/10.05 inference(modus_ponens,[status(thm)],[20693, 20692])).
% 9.81/10.05 tff(20695,plain,
% 9.81/10.05 ($false),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[20694, 391, 644, 20667, 20665, 1686, 20688])).
% 9.81/10.05 tff(20696,plain,(b(s(z), s(s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 9.81/10.05 tff(20697,plain,
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% 9.81/10.05 inference(unit_resolution,[status(thm)],[20696, 20619, 644, 1686, 182, 530, 2913, 90, 11250, 484])).
% 9.81/10.05 tff(20698,plain,((~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(z))) | b(elem!1, z) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.05 tff(20699,plain,
% 9.81/10.05 (b(s(z), s(s(z)))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[20698, 20618, 530, 90, 2881, 182, 484, 644])).
% 9.81/10.05 tff(20700,plain,
% 9.81/10.05 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), elem!1)),
% 9.81/10.05 inference(symmetry,[status(thm)],[9969])).
% 9.81/10.05 tff(20701,plain,
% 9.81/10.05 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 9.81/10.05 inference(monotonicity,[status(thm)],[20700])).
% 9.81/10.05 tff(20702,plain,
% 9.81/10.05 (~b(s(s(s(s(z)))), elem!1)),
% 9.81/10.05 inference(modus_ponens,[status(thm)],[20615, 20701])).
% 9.81/10.05 tff(20703,plain,
% 9.81/10.05 (r(s(s(s(s(z)))), elem!1)),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[762, 20702, 2642])).
% 9.81/10.05 tff(20704,plain,
% 9.81/10.05 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[15351, 20612, 20450])).
% 9.81/10.05 tff(20705,plain,
% 9.81/10.05 (~r(s(s(z)), s(z))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[4702, 1749, 1216, 2112])).
% 9.81/10.05 tff(20706,plain,
% 9.81/10.05 (b(s(s(z)), s(z))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[3778, 20705])).
% 9.81/10.05 tff(20707,plain,
% 9.81/10.05 (~b(elem!1, s(s(z)))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[10150, 20706, 721, 2439])).
% 9.81/10.05 tff(20708,plain,
% 9.81/10.05 (r(elem!1, s(s(z)))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[3394, 20707, 3820])).
% 9.81/10.05 tff(20709,plain,
% 9.81/10.05 (r(s(s(s(elem!1))), s(s(z)))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[10022, 20708, 125])).
% 9.81/10.05 tff(20710,plain,
% 9.81/10.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 9.81/10.05 inference(rewrite,[status(thm)],[])).
% 9.81/10.05 tff(20711,plain,
% 9.81/10.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 9.81/10.05 inference(quant_inst,[status(thm)],[])).
% 9.81/10.05 tff(20712,plain,
% 9.81/10.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 9.81/10.05 inference(modus_ponens,[status(thm)],[20711, 20710])).
% 9.81/10.05 tff(20713,plain,
% 9.81/10.05 ($false),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[20712, 391, 644, 1759, 3563, 1233, 721])).
% 9.81/10.05 tff(20714,plain,((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.05 tff(20715,plain,
% 9.81/10.05 (~b(s(s(s(s(z)))), s(s(z)))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[20714, 20706, 721, 1759, 644])).
% 9.81/10.05 tff(20716,plain,
% 9.81/10.05 (r(s(s(s(s(z)))), s(s(z)))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[1714, 20715])).
% 9.81/10.05 tff(20717,plain,
% 9.81/10.05 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.81/10.05 inference(rewrite,[status(thm)],[])).
% 9.81/10.05 tff(20718,plain,
% 9.81/10.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.81/10.05 inference(monotonicity,[status(thm)],[20717])).
% 9.81/10.05 tff(20719,plain,
% 9.81/10.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.81/10.05 inference(transitivity,[status(thm)],[20718, 17506])).
% 9.81/10.05 tff(20720,plain,
% 9.81/10.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 9.81/10.05 inference(quant_inst,[status(thm)],[])).
% 9.81/10.05 tff(20721,plain,
% 9.81/10.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.81/10.05 inference(modus_ponens,[status(thm)],[20720, 20719])).
% 9.81/10.05 tff(20722,plain,
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% 9.81/10.05 tff(20723,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.05 tff(20724,plain,
% 9.81/10.05 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[20723, 20704, 125, 721, 1759, 644, 20699, 2913, 20703])).
% 9.81/10.05 tff(20725,plain,
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% 9.81/10.05 inference(unit_resolution,[status(thm)],[3652, 20724])).
% 9.81/10.05 tff(20726,plain,
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% 9.81/10.05 tff(20727,plain,
% 9.81/10.05 (r(s(s(z)), z)),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[1211, 20726])).
% 9.81/10.05 tff(20728,plain,
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% 9.81/10.05 inference(unit_resolution,[status(thm)],[18602, 20727, 530, 722])).
% 9.81/10.05 tff(20729,plain,
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% 9.81/10.05 inference(unit_resolution,[status(thm)],[3394, 20728, 3820])).
% 9.81/10.05 tff(20730,plain,
% 9.81/10.05 (~r(s(s(z)), s(z))),
% 9.81/10.05 inference(unit_resolution,[status(thm)],[10610, 20727, 722, 2913])).
% 9.81/10.05 tff(20731,plain,
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% 9.81/10.05 tff(20732,plain,
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% 9.81/10.06 tff(20733,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(z), elem!1)) | b(s(z), s(s(s(s(z))))) | (~r(s(z), z)) | b(elem!1, z) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.06 tff(20734,plain,
% 9.81/10.06 (~b(s(s(s(s(z)))), s(z))),
% 9.81/10.06 inference(unit_resolution,[status(thm)],[20733, 2881, 722, 530, 90, 125, 20611, 721, 182, 484, 266, 20610])).
% 9.81/10.06 tff(20735,plain,
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% 9.81/10.06 tff(20736,plain,
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% 9.81/10.06 tff(20737,plain,
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% 9.81/10.06 inference(unit_resolution,[status(thm)],[800, 20736])).
% 9.81/10.06 tff(20738,plain,
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% 9.81/10.06 inference(unit_resolution,[status(thm)],[20698, 20737, 530, 90, 2881, 182, 484, 20611])).
% 9.81/10.06 tff(20739,plain,
% 9.81/10.06 (~r(s(s(z)), s(z))),
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% 9.81/10.06 tff(20740,plain,
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% 9.81/10.06 tff(20741,plain,
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% 9.81/10.06 tff(20742,plain,((~r(s(s(z)), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (elem!1 = s(s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.06 tff(20743,plain,
% 9.81/10.06 (~r(s(s(z)), z)),
% 9.81/10.06 inference(unit_resolution,[status(thm)],[20742, 20738, 721, 3820, 722, 2913, 530])).
% 9.81/10.06 tff(20744,plain,
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% 9.81/10.06 tff(20745,plain,
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% 9.81/10.06 tff(20746,plain,
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% 9.81/10.06 inference(unit_resolution,[status(thm)],[3652, 20745])).
% 9.81/10.06 tff(20747,plain,
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% 9.81/10.06 tff(20749,plain,
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% 9.81/10.06 tff(20750,plain,
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% 9.81/10.06 tff(20758,assumption,(s(s(s(s(s(z))))) = s(s(s(elem!1)))), introduced(assumption)).
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% 9.81/10.06 tff(20762,plain,
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% 9.81/10.06 tff(20763,plain,
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% 9.81/10.06 tff(20764,plain,
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% 9.81/10.06 tff(20765,plain,
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% 9.81/10.06 tff(20766,plain,
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% 9.81/10.06 inference(unit_resolution,[status(thm)],[11041, 20765])).
% 9.81/10.06 tff(20767,assumption,(~(s(s(s(s(s(z))))) = s(s(s(elem!1))))), introduced(assumption)).
% 9.81/10.06 tff(20768,plain,
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% 9.81/10.06 inference(unit_resolution,[status(thm)],[20575, 18839, 1526, 3325, 379])).
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% 9.81/10.06 tff(20770,plain,((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.06 tff(20771,plain,
% 9.81/10.06 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 9.81/10.06 inference(unit_resolution,[status(thm)],[20770, 18827, 9130, 174])).
% 9.81/10.06 tff(20772,plain,
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% 9.81/10.06 tff(20774,plain,
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% 9.81/10.06 tff(20775,assumption,(~r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 9.81/10.06 tff(20776,assumption,(~b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
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% 9.81/10.06 tff(20778,plain,(b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.06 tff(20779,plain,
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% 9.81/10.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
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% 9.81/10.06 tff(20785,plain,
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% 9.81/10.06 tff(20786,assumption,(~b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 9.81/10.06 tff(20787,assumption,(~r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
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% 9.81/10.06 tff(20789,plain,(b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.06 tff(20790,plain,
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% 9.81/10.06 inference(unit_resolution,[status(thm)],[20789, 20785])).
% 9.81/10.06 tff(20791,plain,
% 9.81/10.06 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
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% 9.81/10.06 tff(20792,plain,
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% 9.81/10.06 tff(20793,plain,
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% 9.81/10.06 inference(unit_resolution,[status(thm)],[20575, 20792, 20468, 20757, 20610])).
% 9.81/10.06 tff(20794,assumption,(~b(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 9.81/10.06 tff(20795,assumption,(~r(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
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% 9.81/10.06 tff(20797,plain,(b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.06 tff(20798,plain,
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% 9.81/10.06 tff(20799,plain,
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% 9.81/10.06 tff(20800,plain,
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% 9.81/10.06 inference(unit_resolution,[status(thm)],[16530, 20799])).
% 9.81/10.06 tff(20801,plain,
% 9.81/10.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 9.81/10.06 inference(rewrite,[status(thm)],[])).
% 9.81/10.06 tff(20802,plain,
% 9.81/10.06 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 9.81/10.06 inference(rewrite,[status(thm)],[])).
% 9.81/10.06 tff(20803,plain,
% 9.81/10.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
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% 9.81/10.06 inference(transitivity,[status(thm)],[20803, 20801])).
% 9.81/10.06 tff(20805,plain,
% 9.81/10.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 9.81/10.06 inference(quant_inst,[status(thm)],[])).
% 9.81/10.06 tff(20806,plain,
% 9.81/10.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 9.81/10.07 inference(modus_ponens,[status(thm)],[20805, 20804])).
% 9.81/10.07 tff(20807,plain,
% 9.81/10.07 ($false),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[20806, 391, 90, 20744, 20737, 20800, 20779])).
% 9.81/10.07 tff(20808,plain,(b(s(z), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)) | b(elem!1, z) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.07 tff(20809,plain,
% 9.81/10.07 (b(s(z), s(s(s(s(z)))))),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[20808, 722, 184, 174, 182, 125, 721, 20608, 530, 484, 266])).
% 9.81/10.07 tff(20810,plain,
% 9.81/10.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.81/10.07 inference(rewrite,[status(thm)],[])).
% 9.81/10.07 tff(20811,plain,
% 9.81/10.07 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.81/10.07 inference(rewrite,[status(thm)],[])).
% 9.81/10.07 tff(20812,plain,
% 9.81/10.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 9.81/10.07 inference(monotonicity,[status(thm)],[20811])).
% 9.81/10.07 tff(20813,plain,
% 9.81/10.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.81/10.07 inference(transitivity,[status(thm)],[20812, 20810])).
% 9.81/10.07 tff(20814,plain,
% 9.81/10.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.81/10.07 inference(quant_inst,[status(thm)],[])).
% 9.81/10.07 tff(20815,plain,
% 9.81/10.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 9.81/10.07 inference(modus_ponens,[status(thm)],[20814, 20813])).
% 9.81/10.07 tff(20816,plain,
% 9.81/10.07 ($false),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[20815, 391, 379, 1526, 1234, 3325])).
% 9.81/10.07 tff(20817,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.07 tff(20818,plain,
% 9.81/10.07 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[20817, 20809, 20468, 20610])).
% 9.81/10.07 tff(20819,plain,
% 9.81/10.07 ($false),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[2863, 9970])).
% 9.81/10.07 tff(20820,plain,((~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.07 tff(20821,plain,
% 9.81/10.07 (~b(s(s(s(s(z)))), elem!1)),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[20820, 20818, 125])).
% 9.81/10.07 tff(20822,plain,
% 9.81/10.07 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[2694, 20821, 130])).
% 9.81/10.07 tff(20823,plain,
% 9.81/10.07 (~r(z, s(s(s(s(z)))))),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[4324, 194, 174, 184, 20822])).
% 9.81/10.07 tff(20824,plain,
% 9.81/10.07 (b(z, s(s(s(s(z)))))),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[800, 20823])).
% 9.81/10.07 tff(20825,plain,
% 9.81/10.07 (r(s(s(s(s(z)))), elem!1)),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[762, 20821, 2642])).
% 9.81/10.07 tff(20826,plain,
% 9.81/10.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.81/10.07 inference(rewrite,[status(thm)],[])).
% 9.81/10.07 tff(20827,plain,
% 9.81/10.07 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.81/10.07 inference(rewrite,[status(thm)],[])).
% 9.81/10.07 tff(20828,plain,
% 9.81/10.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 9.81/10.07 inference(monotonicity,[status(thm)],[20827])).
% 9.81/10.07 tff(20829,plain,
% 9.81/10.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.81/10.07 inference(transitivity,[status(thm)],[20828, 20826])).
% 9.81/10.07 tff(20830,plain,
% 9.81/10.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.81/10.07 inference(quant_inst,[status(thm)],[])).
% 9.81/10.07 tff(20831,plain,
% 9.81/10.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 9.81/10.07 inference(modus_ponens,[status(thm)],[20830, 20829])).
% 9.81/10.07 tff(20832,plain,
% 9.81/10.07 (~b(s(s(s(elem!1))), s(s(z)))),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[20831, 391, 379, 1526, 1233])).
% 9.81/10.07 tff(20833,plain,
% 9.81/10.07 (~b(elem!1, s(s(z)))),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[16425, 20832, 125])).
% 9.81/10.07 tff(20834,plain,
% 9.81/10.07 (r(elem!1, s(s(z)))),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[3394, 20833, 3820])).
% 9.81/10.07 tff(20835,plain,
% 9.81/10.07 (~r(s(s(z)), z)),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[18602, 20834, 530, 722])).
% 9.81/10.07 tff(20836,plain,
% 9.81/10.07 (b(s(s(z)), z)),
% 9.81/10.07 inference(unit_resolution,[status(thm)],[1211, 20835])).
% 9.81/10.07 tff(20837,plain,
% 9.81/10.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.81/10.08 inference(rewrite,[status(thm)],[])).
% 9.81/10.08 tff(20838,plain,
% 9.81/10.08 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.81/10.08 inference(rewrite,[status(thm)],[])).
% 9.81/10.08 tff(20839,plain,
% 9.81/10.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 9.81/10.08 inference(monotonicity,[status(thm)],[20838])).
% 9.81/10.08 tff(20840,plain,
% 9.81/10.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.81/10.08 inference(transitivity,[status(thm)],[20839, 20837])).
% 9.81/10.08 tff(20841,plain,
% 9.81/10.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.81/10.08 inference(quant_inst,[status(thm)],[])).
% 9.81/10.08 tff(20842,plain,
% 9.81/10.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 9.81/10.08 inference(modus_ponens,[status(thm)],[20841, 20840])).
% 9.81/10.08 tff(20843,plain,
% 9.81/10.08 (~b(s(s(z)), s(s(s(elem!1))))),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[20842, 391, 379, 1526, 1233])).
% 9.81/10.08 tff(20844,plain,
% 9.81/10.08 (~b(s(s(z)), elem!1)),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[20537, 20843, 125])).
% 9.81/10.08 tff(20845,plain,
% 9.81/10.08 (r(s(s(z)), elem!1)),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[4730, 20844, 18819])).
% 9.81/10.08 tff(20846,plain,
% 9.81/10.08 (~r(z, s(s(z)))),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[8513, 20845, 530, 411])).
% 9.81/10.08 tff(20847,plain,
% 9.81/10.08 (b(z, s(s(z)))),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[18613, 20846])).
% 9.81/10.08 tff(20848,plain,
% 9.81/10.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 9.81/10.08 inference(rewrite,[status(thm)],[])).
% 9.81/10.08 tff(20849,plain,
% 9.81/10.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 9.81/10.08 inference(quant_inst,[status(thm)],[])).
% 9.81/10.08 tff(20850,plain,
% 9.81/10.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 9.81/10.08 inference(modus_ponens,[status(thm)],[20849, 20848])).
% 9.81/10.08 tff(20851,plain,
% 9.81/10.08 ($false),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[20850, 194, 530, 2112, 1697, 6669])).
% 9.81/10.08 tff(20852,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.08 tff(20853,plain,
% 9.81/10.08 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[20852, 20845, 530, 2112])).
% 9.81/10.08 tff(20854,plain,
% 9.81/10.08 (b(s(s(s(s(z)))), s(s(z)))),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[1714, 20853])).
% 9.81/10.08 tff(20855,plain,
% 9.81/10.08 ($false),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[15053, 20854, 20847, 90, 20836])).
% 9.81/10.08 tff(20856,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.08 tff(20857,plain,
% 9.81/10.08 (~b(s(s(z)), s(z))),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[20856, 722, 530, 20608, 20825, 411, 125, 20610, 20468])).
% 9.81/10.08 tff(20858,plain,
% 9.81/10.08 (r(s(s(z)), s(z))),
% 9.81/10.08 inference(unit_resolution,[status(thm)],[3778, 20857])).
% 9.81/10.08 tff(20859,plain,
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% 9.81/10.08 inference(rewrite,[status(thm)],[])).
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% 9.81/10.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 9.81/10.08 inference(monotonicity,[status(thm)],[20859])).
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% 9.81/10.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
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% 9.81/10.08 inference(modus_ponens,[status(thm)],[20862, 20861])).
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% 9.81/10.08 tff(20867,plain,
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% 9.81/10.08 inference(rewrite,[status(thm)],[])).
% 9.81/10.08 tff(20871,plain,
% 9.81/10.08 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.81/10.08 inference(rewrite,[status(thm)],[])).
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% 9.81/10.08 inference(transitivity,[status(thm)],[20872, 20870])).
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% 9.81/10.08 tff(20878,plain,
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% 9.81/10.08 tff(20882,plain,
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% 9.81/10.09 ($false),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[20806, 391, 20608, 20865, 20824, 20908, 20893])).
% 9.81/10.09 tff(20910,plain,((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~r(elem!1, z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 9.81/10.09 tff(20911,plain,
% 9.81/10.09 (~r(z, s(z))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[20910, 20604, 174, 125, 530, 59, 181, 411, 325, 721, 484])).
% 9.81/10.09 tff(20912,plain,
% 9.81/10.09 (b(z, s(z))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[678, 20911])).
% 9.81/10.09 tff(20913,plain,
% 9.81/10.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.81/10.09 inference(rewrite,[status(thm)],[])).
% 9.81/10.09 tff(20914,plain,
% 9.81/10.09 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.81/10.09 inference(rewrite,[status(thm)],[])).
% 9.81/10.09 tff(20915,plain,
% 9.81/10.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 9.81/10.09 inference(monotonicity,[status(thm)],[20914])).
% 9.81/10.09 tff(20916,plain,
% 9.81/10.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.81/10.09 inference(transitivity,[status(thm)],[20915, 20913])).
% 9.81/10.09 tff(20917,plain,
% 9.81/10.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 9.81/10.09 inference(quant_inst,[status(thm)],[])).
% 9.81/10.09 tff(20918,plain,
% 9.81/10.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 9.81/10.09 inference(modus_ponens,[status(thm)],[20917, 20916])).
% 9.81/10.09 tff(20919,plain,
% 9.81/10.09 ($false),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[20918, 391, 644, 90, 1759, 664, 721])).
% 9.81/10.09 tff(20920,plain,((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.09 tff(20921,plain,
% 9.81/10.09 (~b(s(s(s(s(z)))), s(z))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[20920, 20912, 721, 20603, 20597])).
% 9.81/10.09 tff(20922,plain,
% 9.81/10.09 (r(s(s(s(s(z)))), s(z))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[749, 20921])).
% 9.81/10.09 tff(20923,plain,
% 9.81/10.09 (~r(s(z), s(s(s(elem!1))))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[1867, 181, 59, 174])).
% 9.81/10.09 tff(20924,plain,
% 9.81/10.09 (b(s(z), s(s(s(elem!1))))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[247, 20923])).
% 9.81/10.09 tff(20925,plain,
% 9.81/10.09 (~r(elem!1, s(s(s(s(z)))))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[15063, 719, 411, 723])).
% 9.81/10.09 tff(20926,plain,
% 9.81/10.09 (b(elem!1, s(s(s(s(z)))))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[781, 20925, 8922])).
% 9.81/10.09 tff(20927,plain,
% 9.81/10.09 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[9608, 20926, 266])).
% 9.81/10.09 tff(20928,plain,
% 9.81/10.09 (~r(s(z), s(s(s(s(z)))))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[1224, 719, 182, 723])).
% 9.81/10.09 tff(20929,plain,
% 9.81/10.09 (b(s(z), s(s(s(s(z)))))),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[1230, 20928])).
% 9.81/10.09 tff(20930,plain,
% 9.81/10.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.81/10.09 inference(rewrite,[status(thm)],[])).
% 9.81/10.09 tff(20931,plain,
% 9.81/10.09 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.81/10.09 inference(rewrite,[status(thm)],[])).
% 9.81/10.09 tff(20932,plain,
% 9.81/10.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.81/10.09 inference(monotonicity,[status(thm)],[20931])).
% 9.81/10.09 tff(20933,plain,
% 9.81/10.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.81/10.09 inference(transitivity,[status(thm)],[20932, 20930])).
% 9.81/10.09 tff(20934,plain,
% 9.81/10.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.81/10.09 inference(quant_inst,[status(thm)],[])).
% 9.81/10.09 tff(20935,plain,
% 9.81/10.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.81/10.09 inference(modus_ponens,[status(thm)],[20934, 20933])).
% 9.81/10.09 tff(20936,plain,
% 9.81/10.09 ($false),
% 9.81/10.09 inference(unit_resolution,[status(thm)],[20935, 391, 379, 90, 20929, 664, 20927])).
% 9.81/10.10 tff(20937,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (elem!1 = s(s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.10 tff(20938,plain,
% 9.81/10.10 (~r(z, s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20937, 20924, 20597, 20912, 20604, 3810, 411, 20922, 181])).
% 9.81/10.10 tff(20939,plain,
% 9.81/10.10 (b(z, s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[800, 20938])).
% 9.81/10.10 tff(20940,plain,
% 9.81/10.10 (~b(s(s(z)), z)),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[4472, 1686, 90, 3823])).
% 9.81/10.10 tff(20941,plain,
% 9.81/10.10 (r(s(s(z)), z)),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[1211, 20940])).
% 9.81/10.10 tff(20942,plain,
% 9.81/10.10 (~r(s(s(s(elem!1))), s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[16495, 194, 174, 184, 20941])).
% 9.81/10.10 tff(20943,plain,
% 9.81/10.10 (~r(elem!1, s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[10022, 20942, 125])).
% 9.81/10.10 tff(20944,plain,
% 9.81/10.10 (~b(s(z), s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20877, 1686, 90, 3823, 326, 182])).
% 9.81/10.10 tff(20945,plain,
% 9.81/10.10 (b(s(z), s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20698, 20944, 530, 90, 1686, 182, 484, 20611])).
% 9.81/10.10 tff(20946,plain,
% 9.81/10.10 (~r(s(s(z)), s(z))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[5141, 194, 184, 182, 20941])).
% 9.81/10.10 tff(20947,plain,
% 9.81/10.10 (b(s(s(z)), s(z))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[3778, 20946])).
% 9.81/10.10 tff(20948,plain,
% 9.81/10.10 (~b(elem!1, s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[10150, 20947, 721, 20945])).
% 9.81/10.10 tff(20949,plain,
% 9.81/10.10 ($false),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[3394, 20948, 20943, 3820])).
% 9.81/10.10 tff(20950,plain,((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | b(elem!1, z) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.10 tff(20951,plain,
% 9.81/10.10 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20950, 20939, 125, 174, 59, 181, 530, 20597, 484, 721, 325])).
% 9.81/10.10 tff(20952,plain,
% 9.81/10.10 (r(s(s(z)), s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[3652, 20951])).
% 9.81/10.10 tff(20953,plain,
% 9.81/10.10 (~r(s(s(z)), s(z))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20881, 20952, 181, 20922])).
% 9.81/10.10 tff(20954,plain,
% 9.81/10.10 (b(s(s(z)), s(z))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[3778, 20953])).
% 9.81/10.10 tff(20955,plain,
% 9.81/10.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 9.81/10.10 inference(rewrite,[status(thm)],[])).
% 9.81/10.10 tff(20956,plain,
% 9.81/10.10 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 9.81/10.10 inference(rewrite,[status(thm)],[])).
% 9.81/10.10 tff(20957,plain,
% 9.81/10.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 9.81/10.10 inference(monotonicity,[status(thm)],[20956])).
% 9.81/10.10 tff(20958,plain,
% 9.81/10.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 9.81/10.10 inference(transitivity,[status(thm)],[20957, 20955])).
% 9.81/10.10 tff(20959,plain,
% 9.81/10.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 9.81/10.10 inference(quant_inst,[status(thm)],[])).
% 9.81/10.10 tff(20960,plain,
% 9.81/10.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 9.81/10.10 inference(modus_ponens,[status(thm)],[20959, 20958])).
% 9.81/10.10 tff(20961,plain,
% 9.81/10.10 (~b(z, s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20960, 391, 20924, 20468, 20954, 20912])).
% 9.81/10.10 tff(20962,plain,
% 9.81/10.10 (r(z, s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[18613, 20961])).
% 9.81/10.10 tff(20963,plain,
% 9.81/10.10 (~b(s(s(s(elem!1))), s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20831, 391, 20924, 20468, 20954])).
% 9.81/10.10 tff(20964,plain,
% 9.81/10.10 (~b(elem!1, s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[16425, 20963, 125])).
% 9.81/10.10 tff(20965,plain,
% 9.81/10.10 (r(elem!1, s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[3394, 20964, 3820])).
% 9.81/10.10 tff(20966,plain,
% 9.81/10.10 ($false),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[18632, 20965, 20962, 411, 20952])).
% 9.81/10.10 tff(20967,plain,(b(s(z), z) | (~r(z, elem!1)) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | b(elem!1, z) | (~b(elem!1, s(z))) | b(z, s(s(s(elem!1)))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.10 tff(20968,plain,
% 9.81/10.10 ($false),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20967, 20422, 3618, 15899, 91, 125, 484, 20263, 10, 309])).
% 9.81/10.10 tff(20969,plain,(b(elem!1, z) | b(s(z), z) | (~(elem!1 = s(s(s(elem!1))))) | b(z, s(s(s(elem!1)))) | b(z, s(s(elem!1))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 9.81/10.10 tff(20970,plain,
% 9.81/10.10 (b(elem!1, z)),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20969, 309, 125, 10, 91, 2])).
% 9.81/10.10 tff(20971,plain,
% 9.81/10.10 (b(s(s(s(elem!1))), z)),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[9553, 20970, 125])).
% 9.81/10.10 tff(20972,plain,
% 9.81/10.10 (b(s(elem!1), z)),
% 9.81/10.10 inference(modus_ponens,[status(thm)],[20971, 20408])).
% 9.81/10.10 tff(20973,plain,
% 9.81/10.10 (~r(z, s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[790, 20972, 20263, 20401, 181, 15899, 2642, 722])).
% 9.81/10.10 tff(20974,plain,
% 9.81/10.10 (b(z, s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[800, 20973])).
% 9.81/10.10 tff(20975,plain,
% 9.81/10.10 (~b(s(s(s(s(z)))), elem!1)),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[4246, 20974, 90, 20970])).
% 9.81/10.10 tff(20976,plain,
% 9.81/10.10 (r(s(s(s(s(z)))), elem!1)),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[762, 20975, 2642])).
% 9.81/10.10 tff(20977,plain,
% 9.81/10.10 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 9.81/10.10 inference(monotonicity,[status(thm)],[125])).
% 9.81/10.10 tff(20978,plain,
% 9.81/10.10 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 9.81/10.10 inference(symmetry,[status(thm)],[20977])).
% 9.81/10.10 tff(20979,plain,
% 9.81/10.10 (b(s(z), elem!1)),
% 9.81/10.10 inference(modus_ponens,[status(thm)],[379, 20978])).
% 9.81/10.10 tff(20980,plain,
% 9.81/10.10 (~b(elem!1, s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[15166, 20970, 15899, 130, 181, 20979, 1216])).
% 9.81/10.10 tff(20981,plain,
% 9.81/10.10 (r(elem!1, s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[781, 20980, 3810])).
% 9.81/10.10 tff(20982,plain,
% 9.81/10.10 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[14788, 20981, 125])).
% 9.81/10.10 tff(20983,plain,
% 9.81/10.10 (~r(s(z), s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20629, 1749, 1216, 2112])).
% 9.81/10.10 tff(20984,plain,
% 9.81/10.10 (b(s(z), s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[1788, 20983])).
% 9.81/10.10 tff(20985,plain,
% 9.81/10.10 (~b(elem!1, s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[10150, 20706, 721, 20984])).
% 9.81/10.10 tff(20986,plain,
% 9.81/10.10 (r(elem!1, s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[3394, 20985, 3820])).
% 9.81/10.10 tff(20987,plain,
% 9.81/10.10 (r(s(s(s(elem!1))), s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[10022, 20986, 125])).
% 9.81/10.10 tff(20988,plain,
% 9.81/10.10 (~b(s(s(s(s(z)))), s(z))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20723, 20984, 125, 721, 1216, 644, 1749, 4317, 2112])).
% 9.81/10.10 tff(20989,plain,
% 9.81/10.10 (r(s(s(s(s(z)))), s(z))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[749, 20988])).
% 9.81/10.10 tff(20990,plain,
% 9.81/10.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.81/10.10 inference(rewrite,[status(thm)],[])).
% 9.81/10.10 tff(20991,plain,
% 9.81/10.10 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.81/10.10 inference(rewrite,[status(thm)],[])).
% 9.81/10.10 tff(20992,plain,
% 9.81/10.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.81/10.10 inference(monotonicity,[status(thm)],[20991])).
% 9.81/10.10 tff(20993,plain,
% 9.81/10.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.81/10.10 inference(transitivity,[status(thm)],[20992, 20990])).
% 9.81/10.10 tff(20994,plain,
% 9.81/10.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 9.81/10.10 inference(quant_inst,[status(thm)],[])).
% 9.81/10.10 tff(20995,plain,
% 9.81/10.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.81/10.10 inference(modus_ponens,[status(thm)],[20994, 20993])).
% 9.81/10.10 tff(20996,plain,
% 9.81/10.10 ($false),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20995, 194, 1749, 20989, 20987, 4317])).
% 9.81/10.10 tff(20997,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.10 tff(20998,plain,
% 9.81/10.10 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[20997, 20982, 125, 20263, 1216, 20979, 20976])).
% 9.81/10.10 tff(20999,plain,
% 9.81/10.10 (b(s(s(z)), s(s(s(s(z)))))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[3652, 20998])).
% 9.81/10.10 tff(21000,plain,
% 9.81/10.10 (~b(s(s(z)), z)),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[4472, 20999, 90, 20974])).
% 9.81/10.10 tff(21001,plain,
% 9.81/10.10 (r(s(s(z)), z)),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[1211, 21000])).
% 9.81/10.10 tff(21002,plain,
% 9.81/10.10 (~r(s(z), s(s(z)))),
% 9.81/10.10 inference(unit_resolution,[status(thm)],[3787, 21001, 181, 325])).
% 9.81/10.10 tff(21003,plain,
% 9.81/10.10 (b(s(z), s(s(z)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[1788, 21002])).
% 9.81/10.11 tff(21004,plain,
% 9.81/10.11 (~r(s(s(z)), s(z))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[10610, 21001, 1216, 722])).
% 9.81/10.11 tff(21005,plain,
% 9.81/10.11 (b(s(s(z)), s(z))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[3778, 21004])).
% 9.81/10.11 tff(21006,plain,
% 9.81/10.11 (~b(elem!1, s(s(z)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[10150, 21005, 20263, 21003])).
% 9.81/10.11 tff(21007,plain,
% 9.81/10.11 (r(elem!1, s(s(z)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[3394, 21006, 3820])).
% 9.81/10.11 tff(21008,plain,
% 9.81/10.11 (r(s(s(s(elem!1))), s(s(z)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[10022, 21007, 125])).
% 9.81/10.11 tff(21009,plain,
% 9.81/10.11 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[12538, 20981, 20395])).
% 9.81/10.11 tff(21010,plain,
% 9.81/10.11 (r(s(s(elem!1)), s(s(z)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[11777, 21007, 20395])).
% 9.81/10.11 tff(21011,plain,
% 9.81/10.11 (~r(s(s(s(s(z)))), s(s(z)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[6295, 21010, 21009, 21001])).
% 9.81/10.11 tff(21012,plain,
% 9.81/10.11 (b(s(s(s(s(z)))), s(s(z)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[1714, 21011])).
% 9.81/10.11 tff(21013,plain,
% 9.81/10.11 (~b(z, s(s(z)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[15550, 21012, 20999, 20974])).
% 9.81/10.11 tff(21014,plain,
% 9.81/10.11 (r(z, s(s(z)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[18613, 21013])).
% 9.81/10.11 tff(21015,plain,
% 9.81/10.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 9.81/10.11 inference(rewrite,[status(thm)],[])).
% 9.81/10.11 tff(21016,plain,
% 9.81/10.11 (((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 9.81/10.11 inference(rewrite,[status(thm)],[])).
% 9.81/10.11 tff(21017,plain,
% 9.81/10.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 9.81/10.11 inference(monotonicity,[status(thm)],[21016])).
% 9.81/10.11 tff(21018,plain,
% 9.81/10.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 9.81/10.11 inference(transitivity,[status(thm)],[21017, 21015])).
% 9.81/10.11 tff(21019,plain,
% 9.81/10.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 9.81/10.11 inference(quant_inst,[status(thm)],[])).
% 9.81/10.11 tff(21020,plain,
% 9.81/10.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 9.81/10.11 inference(modus_ponens,[status(thm)],[21019, 21018])).
% 9.81/10.11 tff(21021,plain,
% 9.81/10.11 ($false),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[21020, 194, 59, 21001, 21014, 21008])).
% 9.81/10.11 tff(21022,plain,(b(z, s(s(elem!1))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | b(z, s(s(s(elem!1)))) | b(s(z), z) | (elem!1 = z) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.11 tff(21023,plain,
% 9.81/10.11 (b(z, s(s(elem!1)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[21022, 20393, 1216, 722, 90, 10, 91, 2, 379])).
% 9.81/10.11 tff(21024,plain,
% 9.81/10.11 (r(s(s(s(elem!1))), z)),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[533, 530, 130])).
% 9.81/10.11 tff(21025,plain,
% 9.81/10.11 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 9.81/10.11 inference(symmetry,[status(thm)],[16693])).
% 9.81/10.11 tff(21026,plain,
% 9.81/10.11 (b(z, s(s(s(s(s(elem!1))))))),
% 9.81/10.11 inference(modus_ponens,[status(thm)],[3927, 21025])).
% 9.81/10.11 tff(21027,assumption,(~b(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 9.81/10.11 tff(21028,plain,
% 9.81/10.11 ($false),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[21027, 21026])).
% 9.81/10.11 tff(21029,plain,(b(z, s(s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.11 tff(21030,plain,
% 9.81/10.11 (b(z, s(s(s(s(s(elem!1))))))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[21029, 3927, 125])).
% 9.81/10.11 tff(21031,plain,
% 9.81/10.11 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 9.81/10.11 inference(monotonicity,[status(thm)],[3066])).
% 9.81/10.11 tff(21032,plain,
% 9.81/10.11 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 9.81/10.11 inference(monotonicity,[status(thm)],[125])).
% 9.81/10.11 tff(21033,plain,
% 9.81/10.11 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 9.81/10.11 inference(transitivity,[status(thm)],[21032, 21031])).
% 9.81/10.11 tff(21034,plain,
% 9.81/10.11 (~(s(s(elem!1)) = elem!1)),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[20344, 3927, 10, 125])).
% 9.81/10.11 tff(21035,plain,
% 9.81/10.11 (~(s(s(s(elem!1))) = s(elem!1))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[6159, 21034])).
% 9.81/10.11 tff(21036,plain,
% 9.81/10.11 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[2686, 21035])).
% 9.81/10.11 tff(21037,plain,
% 9.81/10.11 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[2711, 21036])).
% 9.81/10.11 tff(21038,plain,
% 9.81/10.11 (~(s(elem!1) = elem!1)),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[1943, 21034])).
% 9.81/10.11 tff(21039,plain,
% 9.81/10.11 (~(elem!1 = s(elem!1))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[166, 21038])).
% 9.81/10.11 tff(21040,plain,
% 9.81/10.11 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[1887, 973, 125])).
% 9.81/10.11 tff(21041,plain,
% 9.81/10.11 (~r(s(s(s(s(z)))), z)),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[20454, 21040, 125, 184, 721, 174])).
% 9.81/10.11 tff(21042,plain,
% 9.81/10.11 (b(s(s(s(s(z)))), z)),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[87, 21041])).
% 9.81/10.11 tff(21043,assumption,(b(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 9.81/10.11 tff(21044,plain,
% 9.81/10.11 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 9.81/10.11 inference(modus_ponens,[status(thm)],[21040, 16288])).
% 9.81/10.11 tff(21045,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 9.81/10.11 tff(21046,plain,
% 9.81/10.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.81/10.11 inference(rewrite,[status(thm)],[])).
% 9.81/10.11 tff(21047,plain,
% 9.81/10.11 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.81/10.11 inference(rewrite,[status(thm)],[])).
% 9.81/10.11 tff(21048,plain,
% 9.81/10.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 9.81/10.11 inference(monotonicity,[status(thm)],[21047])).
% 9.81/10.11 tff(21049,plain,
% 9.81/10.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.81/10.11 inference(transitivity,[status(thm)],[21048, 21046])).
% 9.81/10.11 tff(21050,plain,
% 9.81/10.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)))),
% 9.81/10.11 inference(quant_inst,[status(thm)],[])).
% 9.81/10.11 tff(21051,plain,
% 9.81/10.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 9.81/10.11 inference(modus_ponens,[status(thm)],[21050, 21049])).
% 9.81/10.11 tff(21052,plain,
% 9.81/10.11 ($false),
% 9.81/10.11 inference(unit_resolution,[status(thm)],[21051, 391, 1526, 90, 9469, 21043, 21045])).
% 9.81/10.11 tff(21053,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(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(elem!1))))) | (~b(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 9.81/10.12 tff(21054,plain,
% 9.81/10.12 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 9.81/10.12 inference(unit_resolution,[status(thm)],[21053, 90, 1526, 9469, 21043])).
% 9.81/10.12 tff(21055,plain,
% 9.81/10.12 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 9.81/10.12 inference(modus_ponens,[status(thm)],[21054, 16715])).
% 9.81/10.12 tff(21056,plain,
% 9.81/10.12 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 9.81/10.12 inference(unit_resolution,[status(thm)],[9445, 21055, 125, 16285])).
% 9.81/10.12 tff(21057,plain,
% 9.81/10.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.81/10.12 inference(rewrite,[status(thm)],[])).
% 9.81/10.12 tff(21058,plain,
% 9.81/10.12 (((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.81/10.12 inference(rewrite,[status(thm)],[])).
% 9.81/10.12 tff(21059,plain,
% 9.81/10.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 9.81/10.12 inference(monotonicity,[status(thm)],[21058])).
% 9.81/10.12 tff(21060,plain,
% 9.81/10.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.81/10.12 inference(transitivity,[status(thm)],[21059, 21057])).
% 9.81/10.12 tff(21061,plain,
% 9.81/10.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 9.81/10.12 inference(quant_inst,[status(thm)],[])).
% 9.81/10.12 tff(21062,plain,
% 9.81/10.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 9.81/10.12 inference(modus_ponens,[status(thm)],[21061, 21060])).
% 9.81/10.12 tff(21063,plain,
% 9.81/10.12 (~b(s(s(s(s(z)))), s(z))),
% 9.81/10.12 inference(unit_resolution,[status(thm)],[21062, 391, 90, 590, 9469, 21043])).
% 9.81/10.12 tff(21064,plain,
% 9.81/10.12 (r(s(s(s(s(z)))), s(z))),
% 9.81/10.12 inference(unit_resolution,[status(thm)],[749, 21063])).
% 9.81/10.12 tff(21065,plain,
% 9.81/10.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.81/10.12 inference(rewrite,[status(thm)],[])).
% 9.81/10.12 tff(21066,plain,
% 9.81/10.12 (((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(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)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.81/10.12 inference(rewrite,[status(thm)],[])).
% 9.81/10.12 tff(21067,plain,
% 9.81/10.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 9.81/10.12 inference(monotonicity,[status(thm)],[21066])).
% 9.81/10.12 tff(21068,plain,
% 9.81/10.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.81/10.12 inference(transitivity,[status(thm)],[21067, 21065])).
% 9.81/10.12 tff(21069,plain,
% 9.81/10.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.81/10.12 inference(quant_inst,[status(thm)],[])).
% 9.81/10.12 tff(21070,plain,
% 9.81/10.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 9.81/10.12 inference(modus_ponens,[status(thm)],[21069, 21068])).
% 9.81/10.12 tff(21071,plain,
% 9.81/10.12 (~b(s(z), s(s(s(s(z)))))),
% 9.81/10.12 inference(unit_resolution,[status(thm)],[21070, 391, 90, 590, 9469, 21043])).
% 9.81/10.12 tff(21072,plain,
% 9.81/10.12 (r(s(z), s(s(s(s(z)))))),
% 9.81/10.12 inference(unit_resolution,[status(thm)],[1230, 21071])).
% 9.81/10.12 tff(21073,plain,
% 9.81/10.12 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 9.81/10.12 inference(monotonicity,[status(thm)],[3067])).
% 9.81/10.12 tff(21074,plain,
% 9.81/10.12 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 9.81/10.12 inference(symmetry,[status(thm)],[21073])).
% 9.81/10.12 tff(21075,plain,
% 9.81/10.12 (r(s(s(s(s(s(elem!1))))), s(z))),
% 9.81/10.12 inference(modus_ponens,[status(thm)],[340, 21074])).
% 9.81/10.12 tff(21076,plain,
% 9.81/10.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.81/10.12 inference(rewrite,[status(thm)],[])).
% 9.81/10.12 tff(21077,plain,
% 9.81/10.12 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.81/10.12 inference(rewrite,[status(thm)],[])).
% 9.81/10.12 tff(21078,plain,
% 9.81/10.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 9.81/10.12 inference(monotonicity,[status(thm)],[21077])).
% 9.81/10.12 tff(21079,plain,
% 9.81/10.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.81/10.12 inference(transitivity,[status(thm)],[21078, 21076])).
% 9.81/10.12 tff(21080,plain,
% 9.81/10.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.81/10.12 inference(quant_inst,[status(thm)],[])).
% 9.81/10.12 tff(21081,plain,
% 9.81/10.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 9.81/10.12 inference(modus_ponens,[status(thm)],[21080, 21079])).
% 9.81/10.12 tff(21082,plain,
% 9.81/10.12 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 9.81/10.12 inference(unit_resolution,[status(thm)],[21081, 194, 1216, 723, 9500])).
% 9.81/10.12 tff(21083,plain,
% 9.81/10.12 ($false),
% 9.81/10.12 inference(unit_resolution,[status(thm)],[21082, 21075])).
% 9.81/10.12 tff(21084,plain,((~r(s(s(elem!1)), s(z))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 9.92/10.13 tff(21085,plain,
% 9.92/10.13 (~r(s(s(elem!1)), s(z))),
% 9.92/10.13 inference(unit_resolution,[status(thm)],[21084, 21072, 125, 21064, 21056])).
% 9.92/10.13 tff(21086,plain,
% 9.92/10.13 (b(s(s(elem!1)), s(z))),
% 9.92/10.13 inference(unit_resolution,[status(thm)],[362, 21085])).
% 9.92/10.13 tff(21087,plain,
% 9.92/10.13 (b(s(s(s(s(s(elem!1))))), s(z))),
% 9.92/10.13 inference(modus_ponens,[status(thm)],[21086, 18695])).
% 9.92/10.13 tff(21088,plain,
% 9.92/10.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.92/10.13 inference(rewrite,[status(thm)],[])).
% 9.92/10.13 tff(21089,plain,
% 9.92/10.13 (((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.92/10.13 inference(rewrite,[status(thm)],[])).
% 9.92/10.13 tff(21090,plain,
% 9.92/10.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 9.92/10.13 inference(monotonicity,[status(thm)],[21089])).
% 9.92/10.13 tff(21091,plain,
% 9.92/10.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.92/10.13 inference(transitivity,[status(thm)],[21090, 21088])).
% 9.92/10.13 tff(21092,plain,
% 9.92/10.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 9.92/10.13 inference(quant_inst,[status(thm)],[])).
% 9.92/10.13 tff(21093,plain,
% 9.92/10.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 9.92/10.13 inference(modus_ponens,[status(thm)],[21092, 21091])).
% 9.92/10.13 tff(21094,plain,
% 9.92/10.13 ($false),
% 9.92/10.13 inference(unit_resolution,[status(thm)],[21093, 391, 1526, 590, 9469, 21087, 21043])).
% 9.92/10.13 tff(21095,plain,((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.92/10.13 tff(21096,plain,
% 9.92/10.13 (~b(s(z), z)),
% 9.92/10.13 inference(unit_resolution,[status(thm)],[21095, 21044, 20468, 21043, 125, 21042])).
% 9.92/10.13 tff(21097,plain,
% 9.92/10.13 (r(s(z), z)),
% 9.92/10.13 inference(unit_resolution,[status(thm)],[180, 21096])).
% 9.92/10.13 tff(21098,plain,
% 9.92/10.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 9.92/10.13 inference(rewrite,[status(thm)],[])).
% 9.92/10.13 tff(21099,plain,
% 9.92/10.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 9.92/10.13 inference(quant_inst,[status(thm)],[])).
% 9.92/10.13 tff(21100,plain,
% 9.92/10.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 9.92/10.13 inference(modus_ponens,[status(thm)],[21099, 21098])).
% 9.92/10.13 tff(21101,plain,
% 9.92/10.13 (~r(s(s(s(elem!1))), s(z))),
% 9.92/10.13 inference(unit_resolution,[status(thm)],[21100, 194, 411, 174, 182])).
% 9.92/10.13 tff(21102,plain,
% 9.92/10.13 (b(s(s(s(elem!1))), s(z))),
% 9.92/10.13 inference(unit_resolution,[status(thm)],[223, 21101])).
% 9.92/10.13 tff(21103,plain,
% 9.92/10.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 9.92/10.13 inference(rewrite,[status(thm)],[])).
% 9.92/10.13 tff(21104,plain,
% 9.92/10.13 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 9.92/10.13 inference(rewrite,[status(thm)],[])).
% 9.92/10.13 tff(21105,plain,
% 9.92/10.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 9.92/10.13 inference(monotonicity,[status(thm)],[21104])).
% 9.92/10.13 tff(21106,plain,
% 9.92/10.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 9.92/10.13 inference(transitivity,[status(thm)],[21105, 21103])).
% 9.92/10.13 tff(21107,plain,
% 9.92/10.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 9.92/10.13 inference(quant_inst,[status(thm)],[])).
% 9.92/10.13 tff(21108,plain,
% 9.92/10.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 9.92/10.13 inference(modus_ponens,[status(thm)],[21107, 21106])).
% 9.92/10.13 tff(21109,plain,
% 9.92/10.13 (~r(s(z), s(s(s(elem!1))))),
% 9.92/10.13 inference(unit_resolution,[status(thm)],[21108, 194, 411, 174, 182])).
% 9.92/10.13 tff(21110,plain,
% 9.92/10.13 (b(s(z), s(s(s(elem!1))))),
% 9.92/10.13 inference(unit_resolution,[status(thm)],[247, 21109])).
% 9.92/10.13 tff(21111,plain,
% 9.92/10.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.92/10.14 inference(rewrite,[status(thm)],[])).
% 9.92/10.14 tff(21112,plain,
% 9.92/10.14 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.92/10.14 inference(rewrite,[status(thm)],[])).
% 9.92/10.14 tff(21113,plain,
% 9.92/10.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 9.92/10.14 inference(monotonicity,[status(thm)],[21112])).
% 9.92/10.14 tff(21114,plain,
% 9.92/10.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.92/10.14 inference(transitivity,[status(thm)],[21113, 21111])).
% 9.92/10.14 tff(21115,plain,
% 9.92/10.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 9.92/10.14 inference(quant_inst,[status(thm)],[])).
% 9.92/10.14 tff(21116,plain,
% 9.92/10.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 9.92/10.14 inference(modus_ponens,[status(thm)],[21115, 21114])).
% 9.92/10.14 tff(21117,plain,
% 9.92/10.14 ($false),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[21116, 391, 381, 973, 21110, 21102, 721])).
% 9.92/10.14 tff(21118,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 9.92/10.14 tff(21119,plain,
% 9.92/10.14 (~b(s(s(elem!1)), s(z))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[21118, 21097, 411, 721, 174, 973])).
% 9.92/10.14 tff(21120,plain,
% 9.92/10.14 (r(s(s(elem!1)), s(z))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[362, 21119])).
% 9.92/10.14 tff(21121,plain,
% 9.92/10.14 (r(s(s(s(s(s(elem!1))))), s(z))),
% 9.92/10.14 inference(modus_ponens,[status(thm)],[21120, 21074])).
% 9.92/10.14 tff(21122,plain,
% 9.92/10.14 (~r(s(z), elem!1)),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[1489, 21097, 184, 530])).
% 9.92/10.14 tff(21123,plain,
% 9.92/10.14 (b(s(z), elem!1)),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[632, 21122, 20601])).
% 9.92/10.14 tff(21124,plain,
% 9.92/10.14 (~r(s(z), s(s(s(elem!1))))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[1867, 21097, 184, 174])).
% 9.92/10.14 tff(21125,plain,
% 9.92/10.14 (b(s(z), s(s(s(elem!1))))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[247, 21124])).
% 9.92/10.14 tff(21126,plain,
% 9.92/10.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 9.92/10.14 inference(rewrite,[status(thm)],[])).
% 9.92/10.14 tff(21127,plain,
% 9.92/10.14 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 9.92/10.14 inference(rewrite,[status(thm)],[])).
% 9.92/10.14 tff(21128,plain,
% 9.92/10.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 9.92/10.14 inference(monotonicity,[status(thm)],[21127])).
% 9.92/10.14 tff(21129,plain,
% 9.92/10.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 9.92/10.14 inference(transitivity,[status(thm)],[21128, 21126])).
% 9.92/10.14 tff(21130,plain,
% 9.92/10.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 9.92/10.14 inference(quant_inst,[status(thm)],[])).
% 9.92/10.14 tff(21131,plain,
% 9.92/10.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 9.92/10.14 inference(modus_ponens,[status(thm)],[21130, 21129])).
% 9.92/10.14 tff(21132,plain,
% 9.92/10.14 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[21131, 391, 21125, 20468, 21044])).
% 9.92/10.14 tff(21133,plain,
% 9.92/10.14 ((s(z) = s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[8448, 42, 21132])).
% 9.92/10.14 tff(21134,plain,
% 9.92/10.14 (r(s(z), s(s(s(s(s(elem!1))))))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[21133, 16280])).
% 9.92/10.14 tff(21135,plain,
% 9.92/10.14 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[21053, 21042, 20468, 21044, 21043])).
% 9.92/10.14 tff(21136,plain,
% 9.92/10.14 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 9.92/10.14 inference(modus_ponens,[status(thm)],[21135, 16715])).
% 9.92/10.14 tff(21137,plain,
% 9.92/10.14 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[9445, 21136, 125, 16285])).
% 9.92/10.14 tff(21138,plain,
% 9.92/10.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.92/10.14 inference(rewrite,[status(thm)],[])).
% 9.92/10.14 tff(21139,plain,
% 9.92/10.14 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.92/10.14 inference(rewrite,[status(thm)],[])).
% 9.92/10.14 tff(21140,plain,
% 9.92/10.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 9.92/10.14 inference(monotonicity,[status(thm)],[21139])).
% 9.92/10.14 tff(21141,plain,
% 9.92/10.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.92/10.14 inference(transitivity,[status(thm)],[21140, 21138])).
% 9.92/10.14 tff(21142,plain,
% 9.92/10.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 9.92/10.14 inference(quant_inst,[status(thm)],[])).
% 9.92/10.14 tff(21143,plain,
% 9.92/10.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 9.92/10.14 inference(modus_ponens,[status(thm)],[21142, 21141])).
% 9.92/10.14 tff(21144,plain,
% 9.92/10.14 (~r(s(s(s(s(z)))), s(z))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[21143, 194, 21137, 21134, 21121])).
% 9.92/10.14 tff(21145,plain,
% 9.92/10.14 (b(s(s(s(s(z)))), s(z))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[749, 21144])).
% 9.92/10.14 tff(21146,plain,
% 9.92/10.14 (~b(z, s(z))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[20920, 21145, 721, 21123, 21042])).
% 9.92/10.14 tff(21147,plain,
% 9.92/10.14 (r(z, s(z))),
% 9.92/10.14 inference(unit_resolution,[status(thm)],[678, 21146])).
% 9.92/10.14 tff(21148,plain,
% 9.92/10.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 9.92/10.14 inference(rewrite,[status(thm)],[])).
% 9.92/10.14 tff(21149,plain,
% 9.92/10.14 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 9.92/10.14 inference(rewrite,[status(thm)],[])).
% 9.92/10.14 tff(21150,plain,
% 9.92/10.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 9.92/10.14 inference(monotonicity,[status(thm)],[21149])).
% 9.92/10.14 tff(21151,plain,
% 9.92/10.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 9.92/10.14 inference(transitivity,[status(thm)],[21150, 21148])).
% 9.92/10.14 tff(21152,plain,
% 9.92/10.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 9.92/10.15 inference(quant_inst,[status(thm)],[])).
% 9.92/10.15 tff(21153,plain,
% 9.92/10.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 9.92/10.15 inference(modus_ponens,[status(thm)],[21152, 21151])).
% 9.92/10.15 tff(21154,plain,
% 9.92/10.15 (~r(s(s(s(s(s(elem!1))))), z)),
% 9.92/10.15 inference(unit_resolution,[status(thm)],[21153, 194, 21147, 21097, 21121])).
% 9.92/10.15 tff(21155,plain,
% 9.92/10.15 (b(s(s(s(s(s(elem!1))))), z)),
% 9.92/10.15 inference(unit_resolution,[status(thm)],[18703, 21154])).
% 9.92/10.15 tff(21156,plain,
% 9.92/10.15 (~(s(elem!1) = s(s(s(s(z)))))),
% 9.92/10.15 inference(unit_resolution,[status(thm)],[1965, 130])).
% 9.92/10.15 tff(21157,plain,
% 9.92/10.15 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 9.92/10.15 inference(modus_ponens,[status(thm)],[21156, 17407])).
% 9.92/10.15 tff(21158,plain,
% 9.92/10.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.15 inference(rewrite,[status(thm)],[])).
% 9.92/10.15 tff(21159,plain,
% 9.92/10.15 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.15 inference(rewrite,[status(thm)],[])).
% 9.92/10.15 tff(21160,plain,
% 9.92/10.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 9.92/10.15 inference(monotonicity,[status(thm)],[21159])).
% 9.92/10.15 tff(21161,plain,
% 9.92/10.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.15 inference(transitivity,[status(thm)],[21160, 21158])).
% 9.92/10.15 tff(21162,plain,
% 9.92/10.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.15 inference(quant_inst,[status(thm)],[])).
% 9.92/10.15 tff(21163,plain,
% 9.92/10.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 9.92/10.15 inference(modus_ponens,[status(thm)],[21162, 21161])).
% 9.92/10.15 tff(21164,plain,
% 9.92/10.15 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 9.92/10.15 inference(unit_resolution,[status(thm)],[21163, 391, 90, 8153, 21043])).
% 9.92/10.15 tff(21165,plain,
% 9.92/10.15 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 9.92/10.15 inference(unit_resolution,[status(thm)],[16299, 42, 21164])).
% 9.92/10.15 tff(21166,plain,
% 9.92/10.15 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 9.92/10.15 inference(unit_resolution,[status(thm)],[21165, 16286])).
% 9.92/10.15 tff(21167,plain,
% 9.92/10.15 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.92/10.15 inference(monotonicity,[status(thm)],[3067])).
% 9.92/10.15 tff(21168,plain,
% 9.92/10.15 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 9.92/10.15 inference(symmetry,[status(thm)],[21167])).
% 9.92/10.15 tff(21169,plain,
% 9.92/10.15 (b(s(elem!1), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.92/10.15 inference(monotonicity,[status(thm)],[3065, 3067])).
% 9.92/10.15 tff(21170,plain,
% 9.92/10.15 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 9.92/10.15 inference(monotonicity,[status(thm)],[17357])).
% 9.92/10.15 tff(21171,plain,
% 9.92/10.15 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.92/10.15 inference(transitivity,[status(thm)],[21170, 21169])).
% 9.92/10.15 tff(21172,plain,
% 9.92/10.15 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 9.92/10.15 inference(monotonicity,[status(thm)],[21171])).
% 9.92/10.15 tff(21173,plain,
% 9.92/10.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.15 inference(rewrite,[status(thm)],[])).
% 9.92/10.15 tff(21174,plain,
% 9.92/10.15 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.15 inference(rewrite,[status(thm)],[])).
% 9.92/10.15 tff(21175,plain,
% 9.92/10.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 9.92/10.15 inference(monotonicity,[status(thm)],[21174])).
% 9.92/10.15 tff(21176,plain,
% 9.92/10.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.15 inference(transitivity,[status(thm)],[21175, 21173])).
% 9.92/10.15 tff(21177,plain,
% 9.92/10.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 9.92/10.15 inference(quant_inst,[status(thm)],[])).
% 9.92/10.15 tff(21178,plain,
% 9.92/10.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 9.92/10.15 inference(modus_ponens,[status(thm)],[21177, 21176])).
% 9.92/10.15 tff(21179,plain,
% 9.92/10.15 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 9.92/10.15 inference(unit_resolution,[status(thm)],[21178, 391, 17911, 8153, 21043])).
% 9.92/10.15 tff(21180,plain,
% 9.92/10.15 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.92/10.15 inference(modus_ponens,[status(thm)],[21179, 21172])).
% 9.92/10.15 tff(21181,plain,
% 9.92/10.15 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 9.92/10.15 inference(unit_resolution,[status(thm)],[1061, 21180, 1050])).
% 9.92/10.15 tff(21182,plain,
% 9.92/10.15 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 9.92/10.15 inference(modus_ponens,[status(thm)],[21181, 21168])).
% 9.92/10.15 tff(21183,plain,
% 9.92/10.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.92/10.15 inference(rewrite,[status(thm)],[])).
% 9.92/10.15 tff(21184,plain,
% 9.92/10.15 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.92/10.15 inference(rewrite,[status(thm)],[])).
% 9.92/10.15 tff(21185,plain,
% 9.92/10.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 9.92/10.15 inference(monotonicity,[status(thm)],[21184])).
% 9.92/10.15 tff(21186,plain,
% 9.92/10.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.92/10.15 inference(transitivity,[status(thm)],[21185, 21183])).
% 9.92/10.15 tff(21187,plain,
% 9.92/10.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 9.92/10.15 inference(quant_inst,[status(thm)],[])).
% 9.92/10.15 tff(21188,plain,
% 9.92/10.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 9.92/10.15 inference(modus_ponens,[status(thm)],[21187, 21186])).
% 9.92/10.15 tff(21189,plain,
% 9.92/10.15 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 9.92/10.15 inference(unit_resolution,[status(thm)],[21188, 194, 21182, 9500, 21166])).
% 9.92/10.15 tff(21190,plain,
% 9.92/10.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.16 inference(rewrite,[status(thm)],[])).
% 9.92/10.16 tff(21191,plain,
% 9.92/10.16 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.16 inference(rewrite,[status(thm)],[])).
% 9.92/10.16 tff(21192,plain,
% 9.92/10.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 9.92/10.16 inference(monotonicity,[status(thm)],[21191])).
% 9.92/10.16 tff(21193,plain,
% 9.92/10.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.16 inference(transitivity,[status(thm)],[21192, 21190])).
% 9.92/10.16 tff(21194,plain,
% 9.92/10.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 9.92/10.16 inference(quant_inst,[status(thm)],[])).
% 9.92/10.16 tff(21195,plain,
% 9.92/10.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 9.92/10.16 inference(modus_ponens,[status(thm)],[21194, 21193])).
% 9.92/10.16 tff(21196,plain,
% 9.92/10.16 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[21195, 391, 17911, 90, 8153, 21043])).
% 9.92/10.16 tff(21197,plain,
% 9.92/10.16 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[17418, 42, 21196])).
% 9.92/10.16 tff(21198,plain,
% 9.92/10.16 ($false),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[21197, 21189, 21157])).
% 9.92/10.16 tff(21199,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.92/10.16 tff(21200,plain,
% 9.92/10.16 (~b(s(s(s(s(elem!1)))), z)),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[21199, 21137, 125, 1050, 21155, 21043, 21042])).
% 9.92/10.16 tff(21201,plain,
% 9.92/10.16 (r(s(s(s(s(elem!1)))), z)),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[1626, 21200])).
% 9.92/10.16 tff(21202,plain,
% 9.92/10.16 (r(s(elem!1), z)),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[12857, 21201, 130])).
% 9.92/10.16 tff(21203,plain,
% 9.92/10.16 (~b(elem!1, s(elem!1))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[1930, 21202, 411, 721, 121, 21097])).
% 9.92/10.16 tff(21204,plain,
% 9.92/10.16 (~r(elem!1, s(elem!1))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[2259, 21202, 184, 530])).
% 9.92/10.16 tff(21205,plain,
% 9.92/10.16 ($false),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[443, 21204, 21203, 437])).
% 9.92/10.16 tff(21206,plain,((~b(s(s(elem!1)), elem!1)) | (elem!1 = s(elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 9.92/10.16 tff(21207,plain,
% 9.92/10.16 (~b(s(s(elem!1)), elem!1)),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[21206, 21039, 59, 530, 411, 721, 121, 125, 21037, 21030, 174])).
% 9.92/10.16 tff(21208,plain,
% 9.92/10.16 (r(s(s(elem!1)), elem!1)),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[872, 21207, 21034])).
% 9.92/10.16 tff(21209,plain,
% 9.92/10.16 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 9.92/10.16 inference(modus_ponens,[status(thm)],[21208, 21033])).
% 9.92/10.16 tff(21210,plain,
% 9.92/10.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 9.92/10.16 inference(rewrite,[status(thm)],[])).
% 9.92/10.16 tff(21211,plain,
% 9.92/10.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 9.92/10.16 inference(quant_inst,[status(thm)],[])).
% 9.92/10.16 tff(21212,plain,
% 9.92/10.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z))),
% 9.92/10.16 inference(modus_ponens,[status(thm)],[21211, 21210])).
% 9.92/10.16 tff(21213,plain,
% 9.92/10.16 (~r(s(s(s(s(s(elem!1))))), z)),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[21212, 194, 174, 59, 21209])).
% 9.92/10.16 tff(21214,plain,
% 9.92/10.16 (b(s(s(s(s(s(elem!1))))), z)),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[18703, 21213])).
% 9.92/10.16 tff(21215,plain,
% 9.92/10.16 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 9.92/10.16 inference(modus_ponens,[status(thm)],[21208, 21032])).
% 9.92/10.16 tff(21216,plain,
% 9.92/10.16 (~r(s(z), s(s(s(elem!1))))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[5792, 21215, 174, 59])).
% 9.92/10.16 tff(21217,plain,
% 9.92/10.16 (b(s(z), s(s(s(elem!1))))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[247, 21216])).
% 9.92/10.16 tff(21218,plain,
% 9.92/10.16 (~(s(s(elem!1)) = s(elem!1))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[264, 21034])).
% 9.92/10.16 tff(21219,plain,
% 9.92/10.16 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[287, 21218])).
% 9.92/10.16 tff(21220,plain,
% 9.92/10.16 (~(s(s(z)) = s(s(s(s(s(elem!1))))))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[16611, 125, 11940])).
% 9.92/10.16 tff(21221,plain,
% 9.92/10.16 (~r(s(s(s(s(s(elem!1))))), z)),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[21212, 194, 174, 184, 9513])).
% 9.92/10.16 tff(21222,plain,
% 9.92/10.16 (b(s(s(s(s(s(elem!1))))), z)),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[18703, 21221])).
% 9.92/10.16 tff(21223,plain,
% 9.92/10.16 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[8418, 391, 20447, 21222, 21043])).
% 9.92/10.16 tff(21224,plain,
% 9.92/10.16 (~b(s(s(elem!1)), s(z))),
% 9.92/10.16 inference(modus_ponens,[status(thm)],[21223, 18697])).
% 9.92/10.16 tff(21225,plain,
% 9.92/10.16 (r(s(s(elem!1)), s(z))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[362, 21224])).
% 9.92/10.16 tff(21226,plain,
% 9.92/10.16 (r(s(s(s(s(s(elem!1))))), s(z))),
% 9.92/10.16 inference(modus_ponens,[status(thm)],[21225, 21074])).
% 9.92/10.16 tff(21227,plain,
% 9.92/10.16 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.92/10.16 inference(rewrite,[status(thm)],[])).
% 9.92/10.16 tff(21228,plain,
% 9.92/10.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 9.92/10.16 inference(monotonicity,[status(thm)],[21227])).
% 9.92/10.16 tff(21229,plain,
% 9.92/10.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.92/10.16 inference(transitivity,[status(thm)],[21228, 3962])).
% 9.92/10.16 tff(21230,plain,
% 9.92/10.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))),
% 9.92/10.16 inference(quant_inst,[status(thm)],[])).
% 9.92/10.16 tff(21231,plain,
% 9.92/10.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 9.92/10.16 inference(modus_ponens,[status(thm)],[21230, 21229])).
% 9.92/10.16 tff(21232,plain,
% 9.92/10.16 (~b(s(s(s(s(z)))), s(z))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[21231, 391, 379, 1526, 20441])).
% 9.92/10.16 tff(21233,plain,
% 9.92/10.16 (r(s(s(s(s(z)))), s(z))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[749, 21232])).
% 9.92/10.16 tff(21234,plain,
% 9.92/10.16 (~b(s(z), s(s(s(s(z)))))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[20815, 391, 379, 1526, 20441])).
% 9.92/10.16 tff(21235,plain,
% 9.92/10.16 (r(s(z), s(s(s(s(z)))))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[1230, 21234])).
% 9.92/10.16 tff(21236,plain,
% 9.92/10.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.16 inference(rewrite,[status(thm)],[])).
% 9.92/10.16 tff(21237,plain,
% 9.92/10.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.16 inference(quant_inst,[status(thm)],[])).
% 9.92/10.16 tff(21238,plain,
% 9.92/10.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 9.92/10.16 inference(modus_ponens,[status(thm)],[21237, 21236])).
% 9.92/10.16 tff(21239,plain,
% 9.92/10.16 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[21238, 194, 21235, 21233, 21226])).
% 9.92/10.16 tff(21240,plain,
% 9.92/10.16 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[16299, 42, 21239])).
% 9.92/10.16 tff(21241,plain,
% 9.92/10.16 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 9.92/10.16 inference(unit_resolution,[status(thm)],[21240, 16286])).
% 9.92/10.16 tff(21242,plain,
% 9.92/10.16 (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 9.92/10.16 inference(modus_ponens,[status(thm)],[16285, 9433])).
% 9.92/10.16 tff(21243,plain,
% 9.92/10.17 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[21084, 21225, 125, 21233, 21235])).
% 9.92/10.17 tff(21244,plain,
% 9.92/10.17 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[9442, 42, 21243])).
% 9.92/10.17 tff(21245,plain,
% 9.92/10.17 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[21244, 21242])).
% 9.92/10.17 tff(21246,plain,
% 9.92/10.17 (~r(z, s(z))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[10620, 21235, 2053])).
% 9.92/10.17 tff(21247,plain,
% 9.92/10.17 (b(z, s(z))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[678, 21246])).
% 9.92/10.17 tff(21248,plain,
% 9.92/10.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.17 inference(rewrite,[status(thm)],[])).
% 9.92/10.17 tff(21249,plain,
% 9.92/10.17 (((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.17 inference(rewrite,[status(thm)],[])).
% 9.92/10.17 tff(21250,plain,
% 9.92/10.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 9.92/10.17 inference(monotonicity,[status(thm)],[21249])).
% 9.92/10.17 tff(21251,plain,
% 9.92/10.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.17 inference(transitivity,[status(thm)],[21250, 21248])).
% 9.92/10.17 tff(21252,plain,
% 9.92/10.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))))),
% 9.92/10.17 inference(quant_inst,[status(thm)],[])).
% 9.92/10.17 tff(21253,plain,
% 9.92/10.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 9.92/10.17 inference(modus_ponens,[status(thm)],[21252, 21251])).
% 9.92/10.17 tff(21254,plain,
% 9.92/10.17 (~b(z, s(s(s(s(z)))))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[21253, 391, 21043, 21245, 21241])).
% 9.92/10.17 tff(21255,plain,
% 9.92/10.17 (r(z, s(s(s(s(z)))))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[800, 21254])).
% 9.92/10.17 tff(21256,plain,
% 9.92/10.17 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[16415, 21255, 21235, 21233, 20447, 21247])).
% 9.92/10.17 tff(21257,plain,
% 9.92/10.17 (b(s(s(z)), s(s(s(s(z)))))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[3652, 21256])).
% 9.92/10.17 tff(21258,plain,
% 9.92/10.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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))))))))),
% 9.92/10.17 inference(rewrite,[status(thm)],[])).
% 9.92/10.17 tff(21259,plain,
% 9.92/10.17 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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(z)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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))))))))),
% 9.92/10.17 inference(rewrite,[status(thm)],[])).
% 9.92/10.17 tff(21260,plain,
% 9.92/10.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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)))))))))),
% 9.92/10.17 inference(monotonicity,[status(thm)],[21259])).
% 9.92/10.17 tff(21261,plain,
% 9.92/10.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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))))))))),
% 9.92/10.17 inference(transitivity,[status(thm)],[21260, 21258])).
% 9.92/10.17 tff(21262,plain,
% 9.92/10.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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(z)), s(s(s(s(s(elem!1))))))))),
% 9.92/10.17 inference(quant_inst,[status(thm)],[])).
% 9.92/10.17 tff(21263,plain,
% 9.92/10.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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)))))))),
% 9.92/10.17 inference(modus_ponens,[status(thm)],[21262, 21261])).
% 9.92/10.17 tff(21264,plain,
% 9.92/10.17 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[21263, 391, 21257, 21222, 21245, 21241])).
% 9.92/10.17 tff(21265,plain,
% 9.92/10.17 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 9.92/10.17 inference(unit_resolution,[status(thm)],[9497, 42, 16662, 21264])).
% 9.92/10.17 tff(21266,plain,
% 9.92/10.17 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.92/10.17 inference(monotonicity,[status(thm)],[3067])).
% 9.92/10.17 tff(21267,plain,
% 9.92/10.17 ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 9.92/10.17 inference(monotonicity,[status(thm)],[21266])).
% 9.92/10.18 tff(21268,plain,
% 9.92/10.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.18 inference(rewrite,[status(thm)],[])).
% 9.92/10.18 tff(21269,plain,
% 9.92/10.18 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.18 inference(rewrite,[status(thm)],[])).
% 9.92/10.18 tff(21270,plain,
% 9.92/10.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 9.92/10.18 inference(monotonicity,[status(thm)],[21269])).
% 9.92/10.18 tff(21271,plain,
% 9.92/10.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 9.92/10.18 inference(transitivity,[status(thm)],[21270, 21268])).
% 9.92/10.18 tff(21272,plain,
% 9.92/10.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 9.92/10.18 inference(quant_inst,[status(thm)],[])).
% 9.92/10.18 tff(21273,plain,
% 9.92/10.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 9.92/10.18 inference(modus_ponens,[status(thm)],[21272, 21271])).
% 9.92/10.18 tff(21274,plain,
% 9.92/10.18 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 9.92/10.18 inference(unit_resolution,[status(thm)],[21273, 391, 20451, 21222, 21245, 21241])).
% 9.92/10.18 tff(21275,plain,
% 9.92/10.18 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.92/10.18 inference(modus_ponens,[status(thm)],[21274, 21267])).
% 9.92/10.18 tff(21276,plain,
% 9.92/10.18 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.92/10.18 inference(unit_resolution,[status(thm)],[1370, 21275, 297])).
% 9.92/10.18 tff(21277,plain,
% 9.92/10.18 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 9.92/10.18 inference(modus_ponens,[status(thm)],[21276, 9531])).
% 9.92/10.18 tff(21278,plain,
% 9.92/10.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 9.92/10.18 inference(rewrite,[status(thm)],[])).
% 9.92/10.18 tff(21279,plain,
% 9.92/10.18 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 9.92/10.18 inference(rewrite,[status(thm)],[])).
% 9.92/10.18 tff(21280,plain,
% 9.92/10.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 9.92/10.18 inference(monotonicity,[status(thm)],[21279])).
% 9.92/10.18 tff(21281,plain,
% 9.92/10.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 9.92/10.18 inference(transitivity,[status(thm)],[21280, 21278])).
% 9.92/10.18 tff(21282,plain,
% 9.92/10.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.92/10.18 inference(quant_inst,[status(thm)],[])).
% 9.92/10.18 tff(21283,plain,
% 9.92/10.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 9.92/10.18 inference(modus_ponens,[status(thm)],[21282, 21281])).
% 9.92/10.18 tff(21284,plain,
% 9.92/10.18 (~b(s(s(z)), s(s(s(elem!1))))),
% 9.92/10.18 inference(unit_resolution,[status(thm)],[21283, 391, 21257, 20451, 21222, 21245])).
% 9.92/10.18 tff(21285,plain,
% 9.92/10.18 (r(s(s(z)), s(s(s(elem!1))))),
% 9.92/10.18 inference(unit_resolution,[status(thm)],[11041, 21284])).
% 9.92/10.18 tff(21286,plain,
% 9.92/10.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 9.92/10.18 inference(rewrite,[status(thm)],[])).
% 9.92/10.18 tff(21287,plain,
% 9.92/10.18 (((~r(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))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 9.92/10.18 inference(rewrite,[status(thm)],[])).
% 9.92/10.18 tff(21288,plain,
% 9.92/10.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 9.92/10.18 inference(monotonicity,[status(thm)],[21287])).
% 9.92/10.18 tff(21289,plain,
% 9.92/10.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 9.92/10.18 inference(transitivity,[status(thm)],[21288, 21286])).
% 9.92/10.18 tff(21290,plain,
% 9.92/10.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 9.92/10.18 inference(quant_inst,[status(thm)],[])).
% 9.92/10.18 tff(21291,plain,
% 9.92/10.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 9.92/10.18 inference(modus_ponens,[status(thm)],[21290, 21289])).
% 9.92/10.18 tff(21292,plain,
% 9.92/10.18 ($false),
% 9.92/10.18 inference(unit_resolution,[status(thm)],[21291, 194, 21285, 9513, 21277, 21265])).
% 9.92/10.18 tff(21293,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (s(s(z)) = s(s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.92/10.18 tff(21294,plain,
% 9.92/10.18 (~r(s(s(s(s(z)))), z)),
% 9.92/10.18 inference(unit_resolution,[status(thm)],[21293, 21209, 21220, 125, 21219, 21030, 21217, 20468, 174, 59])).
% 9.92/10.18 tff(21295,plain,
% 9.92/10.18 (b(s(s(s(s(z)))), z)),
% 9.92/10.18 inference(unit_resolution,[status(thm)],[87, 21294])).
% 9.92/10.18 tff(21296,plain,
% 9.92/10.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.18 inference(rewrite,[status(thm)],[])).
% 9.92/10.18 tff(21297,plain,
% 9.92/10.18 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.18 inference(rewrite,[status(thm)],[])).
% 9.92/10.18 tff(21298,plain,
% 9.92/10.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 9.92/10.19 inference(monotonicity,[status(thm)],[21297])).
% 9.92/10.19 tff(21299,plain,
% 9.92/10.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.19 inference(transitivity,[status(thm)],[21298, 21296])).
% 9.92/10.19 tff(21300,plain,
% 9.92/10.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 9.92/10.19 inference(quant_inst,[status(thm)],[])).
% 9.92/10.19 tff(21301,plain,
% 9.92/10.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 9.92/10.19 inference(modus_ponens,[status(thm)],[21300, 21299])).
% 9.92/10.19 tff(21302,plain,
% 9.92/10.19 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 9.92/10.19 inference(unit_resolution,[status(thm)],[21301, 391, 21295, 21214, 21030])).
% 9.92/10.19 tff(21303,plain,
% 9.92/10.19 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 9.92/10.19 inference(modus_ponens,[status(thm)],[21302, 16715])).
% 9.92/10.19 tff(21304,plain,
% 9.92/10.19 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 9.92/10.19 inference(unit_resolution,[status(thm)],[9445, 21303, 125, 16285])).
% 9.92/10.19 tff(21305,plain,
% 9.92/10.19 (~b(s(s(s(s(elem!1)))), z)),
% 9.92/10.19 inference(unit_resolution,[status(thm)],[21199, 21304, 125, 21037, 21214, 21030, 21295])).
% 9.92/10.19 tff(21306,plain,
% 9.92/10.19 (r(s(s(s(s(elem!1)))), z)),
% 9.92/10.19 inference(unit_resolution,[status(thm)],[1626, 21305])).
% 9.92/10.19 tff(21307,plain,
% 9.92/10.19 (r(s(elem!1), z)),
% 9.92/10.19 inference(unit_resolution,[status(thm)],[12857, 21306, 130])).
% 9.92/10.19 tff(21308,plain,
% 9.92/10.19 (~r(elem!1, s(elem!1))),
% 9.92/10.19 inference(unit_resolution,[status(thm)],[2259, 21307, 59, 530])).
% 9.92/10.19 tff(21309,plain,
% 9.92/10.19 (b(elem!1, s(elem!1))),
% 9.92/10.19 inference(unit_resolution,[status(thm)],[443, 21308, 21039])).
% 9.92/10.19 tff(21310,plain,
% 9.92/10.19 (~r(s(z), z)),
% 9.92/10.19 inference(unit_resolution,[status(thm)],[1930, 21309, 411, 721, 121, 21307])).
% 9.92/10.19 tff(21311,plain,
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% 9.92/10.19 inference(unit_resolution,[status(thm)],[180, 21310])).
% 9.92/10.19 tff(21312,plain,
% 9.92/10.19 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 9.92/10.19 inference(unit_resolution,[status(thm)],[8418, 391, 21311, 21214, 21030])).
% 9.92/10.19 tff(21313,plain,
% 9.92/10.19 (~b(s(s(elem!1)), s(z))),
% 9.92/10.19 inference(modus_ponens,[status(thm)],[21312, 18697])).
% 9.92/10.19 tff(21314,plain,
% 9.92/10.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.19 inference(rewrite,[status(thm)],[])).
% 9.92/10.19 tff(21315,plain,
% 9.92/10.19 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(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)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.19 inference(rewrite,[status(thm)],[])).
% 9.92/10.19 tff(21316,plain,
% 9.92/10.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 9.92/10.19 inference(monotonicity,[status(thm)],[21315])).
% 9.92/10.19 tff(21317,plain,
% 9.92/10.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.19 inference(transitivity,[status(thm)],[21316, 21314])).
% 9.92/10.19 tff(21318,plain,
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% 9.92/10.19 inference(quant_inst,[status(thm)],[])).
% 9.92/10.19 tff(21319,plain,
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% 9.92/10.19 inference(modus_ponens,[status(thm)],[21318, 21317])).
% 9.92/10.19 tff(21320,plain,
% 9.92/10.19 (~b(s(z), s(s(s(s(z)))))),
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% 9.92/10.19 tff(21321,plain,
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% 9.92/10.19 inference(unit_resolution,[status(thm)],[1230, 21320])).
% 9.92/10.19 tff(21322,plain,
% 9.92/10.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.19 inference(rewrite,[status(thm)],[])).
% 9.92/10.19 tff(21323,plain,
% 9.92/10.19 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.19 inference(rewrite,[status(thm)],[])).
% 9.92/10.19 tff(21324,plain,
% 9.92/10.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 9.92/10.19 inference(monotonicity,[status(thm)],[21323])).
% 9.92/10.19 tff(21325,plain,
% 9.92/10.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.92/10.20 inference(transitivity,[status(thm)],[21324, 21322])).
% 9.92/10.20 tff(21326,plain,
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% 9.92/10.20 inference(quant_inst,[status(thm)],[])).
% 9.92/10.20 tff(21327,plain,
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% 9.92/10.20 inference(modus_ponens,[status(thm)],[21326, 21325])).
% 9.92/10.20 tff(21328,plain,
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% 9.92/10.20 tff(21329,plain,
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% 9.92/10.20 tff(21330,plain,
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% 9.92/10.20 tff(21331,plain,
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% 9.92/10.20 tff(21332,plain,
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% 9.92/10.20 inference(unit_resolution,[status(thm)],[21331, 21313])).
% 9.92/10.20 tff(21333,plain,((~b(z, s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.92/10.20 tff(21334,plain,
% 9.92/10.20 ($false),
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% 9.92/10.20 tff(21335,plain,((~r(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.92/10.20 tff(21336,plain,
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% 9.92/10.20 tff(21337,plain,
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% 9.92/10.20 tff(21338,plain,
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% 9.92/10.20 tff(21339,plain,
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% 9.92/10.20 tff(21340,plain,
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% 9.92/10.20 tff(21341,plain,
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% 9.92/10.20 tff(21342,plain,
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% 9.92/10.20 tff(21344,plain,
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% 9.92/10.20 tff(21348,plain,
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% 9.99/10.20 tff(21355,plain,
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% 9.99/10.20 inference(unit_resolution,[status(thm)],[9720, 21354, 21352, 722, 21348])).
% 9.99/10.20 tff(21356,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.20 tff(21357,plain,
% 9.99/10.20 (~b(s(s(s(s(z)))), elem!1)),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[21356, 21340, 20263, 90, 1216, 722, 181, 21337])).
% 9.99/10.20 tff(21358,plain,
% 9.99/10.20 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[2694, 21357, 20394])).
% 9.99/10.20 tff(21359,plain,
% 9.99/10.20 (~r(z, s(s(s(s(z)))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[2108, 21358, 181, 1216])).
% 9.99/10.20 tff(21360,plain,
% 9.99/10.20 (b(z, s(s(s(s(z)))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[800, 21359])).
% 9.99/10.20 tff(21361,plain,
% 9.99/10.20 (~(s(s(s(s(z)))) = elem!1)),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[1436, 20394])).
% 9.99/10.20 tff(21362,plain,
% 9.99/10.20 (~(elem!1 = s(s(s(s(z)))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[769, 21361])).
% 9.99/10.20 tff(21363,plain,
% 9.99/10.20 (~b(elem!1, s(s(s(s(z)))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[15166, 21337, 15899, 20394, 181, 21340, 1216])).
% 9.99/10.20 tff(21364,plain,
% 9.99/10.20 (r(elem!1, s(s(s(s(z)))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[781, 21363, 21362])).
% 9.99/10.20 tff(21365,plain,
% 9.99/10.20 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[14788, 21364, 20393])).
% 9.99/10.20 tff(21366,plain,
% 9.99/10.20 (r(s(s(s(s(z)))), elem!1)),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[762, 21357, 21361])).
% 9.99/10.20 tff(21367,plain,
% 9.99/10.20 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[20997, 21366, 20393, 20263, 1216, 21340, 21365])).
% 9.99/10.20 tff(21368,plain,
% 9.99/10.20 (b(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[3652, 21367])).
% 9.99/10.20 tff(21369,plain,
% 9.99/10.20 (~b(s(s(z)), z)),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[4472, 21368, 90, 21360])).
% 9.99/10.20 tff(21370,plain,
% 9.99/10.20 (r(s(s(z)), z)),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[1211, 21369])).
% 9.99/10.20 tff(21371,plain,
% 9.99/10.20 (~r(s(s(z)), s(z))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[10610, 21370, 1216, 722])).
% 9.99/10.20 tff(21372,plain,
% 9.99/10.20 (b(s(s(z)), s(z))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[3778, 21371])).
% 9.99/10.20 tff(21373,plain,
% 9.99/10.20 (b(s(s(s(elem!1))), z)),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[9553, 21337, 20393])).
% 9.99/10.20 tff(21374,plain,
% 9.99/10.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.99/10.20 inference(rewrite,[status(thm)],[])).
% 9.99/10.20 tff(21375,plain,
% 9.99/10.20 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.99/10.20 inference(rewrite,[status(thm)],[])).
% 9.99/10.20 tff(21376,plain,
% 9.99/10.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 9.99/10.20 inference(monotonicity,[status(thm)],[21375])).
% 9.99/10.20 tff(21377,plain,
% 9.99/10.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.99/10.20 inference(transitivity,[status(thm)],[21376, 21374])).
% 9.99/10.20 tff(21378,plain,
% 9.99/10.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.99/10.20 inference(quant_inst,[status(thm)],[])).
% 9.99/10.20 tff(21379,plain,
% 9.99/10.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 9.99/10.20 inference(modus_ponens,[status(thm)],[21378, 21377])).
% 9.99/10.20 tff(21380,plain,
% 9.99/10.20 (~b(s(s(z)), s(s(s(elem!1))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[21379, 391, 21373, 379, 1526, 21372])).
% 9.99/10.20 tff(21381,plain,
% 9.99/10.20 (r(s(s(z)), s(s(s(elem!1))))),
% 9.99/10.20 inference(unit_resolution,[status(thm)],[11041, 21380])).
% 9.99/10.20 tff(21382,plain,
% 9.99/10.20 (s(s(s(elem!1))) = elem!1),
% 9.99/10.20 inference(symmetry,[status(thm)],[20393])).
% 9.99/10.20 tff(21383,plain,
% 9.99/10.20 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 9.99/10.20 inference(monotonicity,[status(thm)],[21382])).
% 9.99/10.20 tff(21384,plain,
% 9.99/10.20 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 9.99/10.20 inference(transitivity,[status(thm)],[21383, 698])).
% 9.99/10.20 tff(21385,plain,
% 9.99/10.20 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 9.99/10.20 inference(monotonicity,[status(thm)],[21384])).
% 9.99/10.20 tff(21386,plain,
% 9.99/10.20 (~(elem!1 = s(s(z)))),
% 9.99/10.20 inference(modus_ponens,[status(thm)],[1397, 21385])).
% 9.99/10.20 tff(21387,plain,
% 9.99/10.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.99/10.20 inference(rewrite,[status(thm)],[])).
% 9.99/10.20 tff(21388,plain,
% 9.99/10.20 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.99/10.20 inference(rewrite,[status(thm)],[])).
% 9.99/10.20 tff(21389,plain,
% 9.99/10.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 9.99/10.20 inference(monotonicity,[status(thm)],[21388])).
% 9.99/10.20 tff(21390,plain,
% 9.99/10.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.99/10.21 inference(transitivity,[status(thm)],[21389, 21387])).
% 9.99/10.21 tff(21391,plain,
% 9.99/10.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 9.99/10.21 inference(quant_inst,[status(thm)],[])).
% 9.99/10.21 tff(21392,plain,
% 9.99/10.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 9.99/10.21 inference(modus_ponens,[status(thm)],[21391, 21390])).
% 9.99/10.21 tff(21393,plain,
% 9.99/10.21 ($false),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[21392, 391, 380, 379, 1526, 1233, 17493])).
% 9.99/10.21 tff(21394,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.21 tff(21395,plain,
% 9.99/10.21 (~b(s(s(s(elem!1))), s(s(z)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[21394, 21372, 1526, 21373, 379])).
% 9.99/10.21 tff(21396,plain,
% 9.99/10.21 (~b(elem!1, s(s(z)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[16425, 21395, 20393])).
% 9.99/10.21 tff(21397,plain,
% 9.99/10.21 (r(elem!1, s(s(z)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[3394, 21396, 21386])).
% 9.99/10.21 tff(21398,plain,
% 9.99/10.21 (r(s(s(s(elem!1))), s(s(z)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[10022, 21397, 20393])).
% 9.99/10.21 tff(21399,plain,
% 9.99/10.21 ($false),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[16895, 194, 59, 21370, 21398, 21381])).
% 9.99/10.21 tff(21400,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | b(z, s(s(s(elem!1)))) | b(s(z), z) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.21 tff(21401,plain,
% 9.99/10.21 (~r(z, s(z))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[21400, 20391, 1216, 1526, 90, 2, 10, 91, 4028])).
% 9.99/10.21 tff(21402,plain,
% 9.99/10.21 (b(z, s(z))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[678, 21401])).
% 9.99/10.21 tff(21403,plain,
% 9.99/10.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.99/10.21 inference(rewrite,[status(thm)],[])).
% 9.99/10.21 tff(21404,plain,
% 9.99/10.21 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), 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))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.99/10.21 inference(rewrite,[status(thm)],[])).
% 9.99/10.21 tff(21405,plain,
% 9.99/10.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 9.99/10.21 inference(monotonicity,[status(thm)],[21404])).
% 9.99/10.21 tff(21406,plain,
% 9.99/10.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.99/10.21 inference(transitivity,[status(thm)],[21405, 21403])).
% 9.99/10.21 tff(21407,plain,
% 9.99/10.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 9.99/10.21 inference(quant_inst,[status(thm)],[])).
% 9.99/10.21 tff(21408,plain,
% 9.99/10.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 9.99/10.21 inference(modus_ponens,[status(thm)],[21407, 21406])).
% 9.99/10.21 tff(21409,plain,
% 9.99/10.21 (~b(s(s(s(elem!1))), z)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[21408, 391, 20391, 1526, 21402])).
% 9.99/10.21 tff(21410,plain,
% 9.99/10.21 (r(s(s(s(elem!1))), z)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[377, 21409])).
% 9.99/10.21 tff(21411,plain,
% 9.99/10.21 (~b(s(s(s(elem!1))), elem!1)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[2907, 20391, 20263, 1526])).
% 9.99/10.21 tff(21412,plain,
% 9.99/10.21 (elem!1 = s(s(s(elem!1)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[10519, 21411, 15899, 59, 4028])).
% 9.99/10.21 tff(21413,plain,
% 9.99/10.21 (~b(elem!1, z)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[19694, 21409, 59, 15899, 4028])).
% 9.99/10.21 tff(21414,plain,
% 9.99/10.21 (r(elem!1, z)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[526, 21413, 2])).
% 9.99/10.21 tff(21415,plain,
% 9.99/10.21 (b(z, s(s(elem!1)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[20969, 21413, 21412, 10, 91, 2])).
% 9.99/10.21 tff(21416,plain,
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% 9.99/10.21 inference(unit_resolution,[status(thm)],[21333, 21415, 21414, 15899, 20263, 118, 21412, 21410, 10])).
% 9.99/10.21 tff(21417,plain,((~r(s(z), s(s(s(s(z)))))) | b(z, s(s(s(elem!1)))) | b(s(z), z) | (elem!1 = z) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.21 tff(21418,plain,
% 9.99/10.21 (~r(s(z), s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[21417, 4028, 91, 2, 10, 8815, 90])).
% 9.99/10.21 tff(21419,plain,
% 9.99/10.21 (b(s(z), s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[1230, 21418])).
% 9.99/10.21 tff(21420,plain,
% 9.99/10.21 (s(s(s(elem!1))) = elem!1),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[8251, 20395])).
% 9.99/10.21 tff(21421,plain,
% 9.99/10.21 (elem!1 = s(s(s(elem!1)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[8, 21420])).
% 9.99/10.21 tff(21422,plain,
% 9.99/10.21 (b(elem!1, z)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[20969, 21421, 309, 10, 91, 2])).
% 9.99/10.21 tff(21423,plain,
% 9.99/10.21 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 9.99/10.21 inference(monotonicity,[status(thm)],[283])).
% 9.99/10.21 tff(21424,plain,
% 9.99/10.21 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(elem!1)))),
% 9.99/10.21 inference(symmetry,[status(thm)],[21423])).
% 9.99/10.21 tff(21425,plain,
% 9.99/10.21 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 9.99/10.21 inference(monotonicity,[status(thm)],[283])).
% 9.99/10.21 tff(21426,plain,
% 9.99/10.21 ((~r(s(s(z)), s(s(elem!1)))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 9.99/10.21 inference(monotonicity,[status(thm)],[21425])).
% 9.99/10.21 tff(21427,plain,
% 9.99/10.21 (s(s(s(elem!1))) = elem!1),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[8251, 266])).
% 9.99/10.21 tff(21428,plain,
% 9.99/10.21 (~(s(s(s(s(z)))) = elem!1)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[1436, 21427])).
% 9.99/10.21 tff(21429,plain,
% 9.99/10.21 (~(elem!1 = s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[769, 21428])).
% 9.99/10.21 tff(21430,plain,
% 9.99/10.21 (b(s(z), s(elem!1)) <=> b(s(z), s(s(elem!1)))),
% 9.99/10.21 inference(monotonicity,[status(thm)],[8338])).
% 9.99/10.21 tff(21431,plain,
% 9.99/10.21 (b(s(z), s(s(elem!1))) <=> b(s(z), s(elem!1))),
% 9.99/10.21 inference(symmetry,[status(thm)],[21430])).
% 9.99/10.21 tff(21432,plain,
% 9.99/10.21 (elem!1 = s(s(elem!1))),
% 9.99/10.21 inference(symmetry,[status(thm)],[8248])).
% 9.99/10.21 tff(21433,plain,
% 9.99/10.21 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 9.99/10.21 inference(monotonicity,[status(thm)],[21432])).
% 9.99/10.21 tff(21434,plain,
% 9.99/10.21 (b(s(z), elem!1) <=> b(s(z), s(elem!1))),
% 9.99/10.21 inference(transitivity,[status(thm)],[21433, 21431])).
% 9.99/10.21 tff(21435,plain,
% 9.99/10.21 (~(s(z) = elem!1)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[20271, 721])).
% 9.99/10.21 tff(21436,plain,
% 9.99/10.21 (r(elem!1, s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 9.99/10.21 inference(monotonicity,[status(thm)],[21432])).
% 9.99/10.21 tff(21437,plain,
% 9.99/10.21 ((~r(elem!1, s(s(z)))) <=> (~r(s(s(elem!1)), s(s(z))))),
% 9.99/10.21 inference(monotonicity,[status(thm)],[21436])).
% 9.99/10.21 tff(21438,plain,
% 9.99/10.21 (~r(elem!1, s(s(z)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[3389, 1484, 411, 182])).
% 9.99/10.21 tff(21439,plain,
% 9.99/10.21 (~r(s(s(elem!1)), s(s(z)))),
% 9.99/10.21 inference(modus_ponens,[status(thm)],[21438, 21437])).
% 9.99/10.21 tff(21440,plain,
% 9.99/10.21 (b(elem!1, s(s(z)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[3394, 21438, 9254])).
% 9.99/10.21 tff(21441,plain,
% 9.99/10.21 (~r(elem!1, s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[2040, 1484, 411, 182])).
% 9.99/10.21 tff(21442,plain,
% 9.99/10.21 (b(elem!1, s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[781, 21441, 21429])).
% 9.99/10.21 tff(21443,plain,
% 9.99/10.21 (~b(z, s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[3234, 21442, 90, 665])).
% 9.99/10.21 tff(21444,plain,
% 9.99/10.21 (r(z, s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[800, 21443])).
% 9.99/10.21 tff(21445,plain,
% 9.99/10.21 (~b(s(s(s(s(z)))), s(z))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[2097, 21444, 411, 721, 1234, 21428])).
% 9.99/10.21 tff(21446,plain,
% 9.99/10.21 (r(s(s(s(s(z)))), s(z))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[749, 21445])).
% 9.99/10.21 tff(21447,plain,
% 9.99/10.21 (~r(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[9171, 21446, 721, 1234, 1484, 21442, 21440])).
% 9.99/10.21 tff(21448,plain,
% 9.99/10.21 (b(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[3652, 21447])).
% 9.99/10.21 tff(21449,plain,
% 9.99/10.21 (~r(z, s(z))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[731, 21446, 21444, 182])).
% 9.99/10.21 tff(21450,plain,
% 9.99/10.21 (b(z, s(z))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[678, 21449])).
% 9.99/10.21 tff(21451,plain,
% 9.99/10.21 (r(s(s(elem!1)), s(s(z)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[16598, 21450, 90, 21441, 266, 21448])).
% 9.99/10.21 tff(21452,plain,
% 9.99/10.21 ($false),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[21451, 21439])).
% 9.99/10.21 tff(21453,plain,((~r(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.21 tff(21454,plain,
% 9.99/10.21 (~r(s(z), elem!1)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[21453, 266, 90, 721, 1234, 182, 411, 665])).
% 9.99/10.21 tff(21455,plain,
% 9.99/10.21 (b(s(z), elem!1)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[632, 21454, 21435])).
% 9.99/10.21 tff(21456,plain,
% 9.99/10.21 (b(s(z), s(elem!1))),
% 9.99/10.21 inference(modus_ponens,[status(thm)],[21455, 21434])).
% 9.99/10.21 tff(21457,plain,
% 9.99/10.21 (b(s(elem!1), z) <=> b(s(s(elem!1)), z)),
% 9.99/10.21 inference(monotonicity,[status(thm)],[8338])).
% 9.99/10.21 tff(21458,plain,
% 9.99/10.21 (b(s(s(elem!1)), z) <=> b(s(elem!1), z)),
% 9.99/10.21 inference(symmetry,[status(thm)],[21457])).
% 9.99/10.21 tff(21459,plain,
% 9.99/10.21 (elem!1 = s(s(s(elem!1)))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[8, 21427])).
% 9.99/10.21 tff(21460,plain,
% 9.99/10.21 (b(s(s(s(elem!1))), z)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[9553, 665, 21459])).
% 9.99/10.21 tff(21461,plain,
% 9.99/10.21 (b(s(s(elem!1)), z)),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[9291, 21460, 266])).
% 9.99/10.21 tff(21462,plain,
% 9.99/10.21 (b(s(elem!1), z)),
% 9.99/10.21 inference(modus_ponens,[status(thm)],[21461, 21458])).
% 9.99/10.21 tff(21463,plain,
% 9.99/10.21 (~r(z, s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[790, 722, 721, 21462, 182, 411, 21428, 21456])).
% 9.99/10.21 tff(21464,plain,
% 9.99/10.21 (b(z, s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[800, 21463])).
% 9.99/10.21 tff(21465,plain,
% 9.99/10.21 (~b(elem!1, s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[3234, 21464, 90, 665])).
% 9.99/10.21 tff(21466,plain,
% 9.99/10.21 (r(elem!1, s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[781, 21465, 21429])).
% 9.99/10.21 tff(21467,plain,
% 9.99/10.21 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[12538, 21466, 266])).
% 9.99/10.21 tff(21468,plain,
% 9.99/10.21 (b(s(z), s(s(s(elem!1))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[14872, 21455, 21427])).
% 9.99/10.21 tff(21469,plain,
% 9.99/10.21 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.99/10.21 inference(unit_resolution,[status(thm)],[20817, 21468, 1526, 1234])).
% 9.99/10.22 tff(21470,plain,
% 9.99/10.22 (~b(s(s(s(s(z)))), elem!1)),
% 9.99/10.22 inference(unit_resolution,[status(thm)],[20820, 21469, 21459])).
% 9.99/10.22 tff(21471,plain,
% 9.99/10.22 (r(s(s(s(s(z)))), elem!1)),
% 9.99/10.22 inference(unit_resolution,[status(thm)],[762, 21470, 21428])).
% 9.99/10.22 tff(21472,plain,
% 9.99/10.22 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 9.99/10.22 inference(unit_resolution,[status(thm)],[9262, 21471, 266])).
% 9.99/10.22 tff(21473,plain,
% 9.99/10.22 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.22 inference(unit_resolution,[status(thm)],[20877, 21464, 90, 182, 1234, 326])).
% 9.99/10.22 tff(21474,plain,
% 9.99/10.22 (r(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.22 inference(unit_resolution,[status(thm)],[3652, 21473])).
% 9.99/10.22 tff(21475,plain,
% 9.99/10.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 9.99/10.22 inference(rewrite,[status(thm)],[])).
% 9.99/10.22 tff(21476,plain,
% 9.99/10.22 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 9.99/10.22 inference(rewrite,[status(thm)],[])).
% 9.99/10.22 tff(21477,plain,
% 9.99/10.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1))))))),
% 9.99/10.22 inference(monotonicity,[status(thm)],[21476])).
% 9.99/10.22 tff(21478,plain,
% 9.99/10.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 9.99/10.22 inference(transitivity,[status(thm)],[21477, 21475])).
% 9.99/10.22 tff(21479,plain,
% 9.99/10.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 9.99/10.22 inference(quant_inst,[status(thm)],[])).
% 9.99/10.22 tff(21480,plain,
% 9.99/10.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1))))),
% 9.99/10.22 inference(modus_ponens,[status(thm)],[21479, 21478])).
% 9.99/10.22 tff(21481,plain,
% 9.99/10.22 (~r(s(s(z)), s(s(elem!1)))),
% 9.99/10.22 inference(unit_resolution,[status(thm)],[21480, 194, 21474, 21472, 21467])).
% 9.99/10.22 tff(21482,plain,
% 9.99/10.22 (~r(s(s(z)), s(s(s(elem!1))))),
% 9.99/10.22 inference(modus_ponens,[status(thm)],[21481, 21426])).
% 9.99/10.22 tff(21483,plain,
% 9.99/10.22 (b(s(s(z)), s(s(s(elem!1))))),
% 9.99/10.22 inference(unit_resolution,[status(thm)],[11041, 21482])).
% 9.99/10.22 tff(21484,plain,
% 9.99/10.22 (b(s(s(z)), s(s(elem!1)))),
% 9.99/10.22 inference(modus_ponens,[status(thm)],[21483, 21424])).
% 9.99/10.22 tff(21485,plain,
% 9.99/10.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 9.99/10.22 inference(rewrite,[status(thm)],[])).
% 9.99/10.22 tff(21486,plain,
% 9.99/10.22 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 9.99/10.22 inference(rewrite,[status(thm)],[])).
% 9.99/10.22 tff(21487,plain,
% 9.99/10.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 9.99/10.22 inference(monotonicity,[status(thm)],[21486])).
% 9.99/10.22 tff(21488,plain,
% 9.99/10.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 9.99/10.22 inference(transitivity,[status(thm)],[21487, 21485])).
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% 9.99/10.22 inference(quant_inst,[status(thm)],[])).
% 9.99/10.22 tff(21490,plain,
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% 9.99/10.22 inference(modus_ponens,[status(thm)],[21489, 21488])).
% 9.99/10.22 tff(21491,plain,
% 9.99/10.22 (~r(s(s(elem!1)), s(s(z)))),
% 9.99/10.22 inference(unit_resolution,[status(thm)],[21490, 194, 21474, 21472, 21467])).
% 9.99/10.22 tff(21492,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[11777, 21491, 266])).
% 9.99/10.22 tff(21493,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[3394, 21492, 9254])).
% 9.99/10.22 tff(21494,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[16425, 21493, 21459])).
% 9.99/10.22 tff(21495,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[21394, 21494, 1526, 21460, 21468])).
% 9.99/10.22 tff(21496,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[3778, 21495])).
% 9.99/10.22 tff(21497,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[20863, 194, 722, 182, 21496])).
% 9.99/10.22 tff(21498,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[1211, 21497])).
% 9.99/10.22 tff(21499,plain,
% 9.99/10.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 9.99/10.22 inference(rewrite,[status(thm)],[])).
% 9.99/10.22 tff(21500,plain,
% 9.99/10.22 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 9.99/10.22 inference(rewrite,[status(thm)],[])).
% 9.99/10.22 tff(21501,plain,
% 9.99/10.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))))),
% 9.99/10.22 inference(monotonicity,[status(thm)],[21500])).
% 9.99/10.22 tff(21502,plain,
% 9.99/10.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 9.99/10.22 inference(transitivity,[status(thm)],[21501, 21499])).
% 9.99/10.22 tff(21503,plain,
% 9.99/10.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 9.99/10.22 inference(quant_inst,[status(thm)],[])).
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% 9.99/10.22 inference(modus_ponens,[status(thm)],[21503, 21502])).
% 9.99/10.22 tff(21505,plain,
% 9.99/10.22 ($false),
% 9.99/10.22 inference(unit_resolution,[status(thm)],[21504, 391, 21461, 90, 21498, 21464, 21484])).
% 9.99/10.22 tff(21506,plain,((~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.22 tff(21507,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[21506, 20395, 181, 90, 1526, 21422, 1234, 325, 20263, 15899])).
% 9.99/10.22 tff(21508,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[21453, 20395, 90, 20263, 1234, 181, 15899, 21422])).
% 9.99/10.22 tff(21512,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[632, 21511, 20272])).
% 9.99/10.22 tff(21513,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[14872, 21512, 21420])).
% 9.99/10.22 tff(21514,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[20920, 21508, 90, 20263, 21512])).
% 9.99/10.22 tff(21515,plain,
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% 9.99/10.22 tff(21516,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[20937, 21515, 90, 20395, 21513, 21510, 15899, 21508, 181])).
% 9.99/10.22 tff(21517,plain,
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% 9.99/10.22 tff(21518,plain,
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% 9.99/10.22 inference(unit_resolution,[status(thm)],[20877, 21517, 90, 181, 1234, 325])).
% 9.99/10.22 tff(21519,plain,
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% 9.99/10.22 tff(21520,plain,
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% 9.99/10.22 tff(21521,plain,
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% 9.99/10.22 tff(21522,plain,
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% 9.99/10.22 tff(21523,plain,
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% 9.99/10.23 tff(21524,plain,
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% 9.99/10.23 tff(21525,plain,
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% 9.99/10.23 tff(21526,plain,
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% 9.99/10.23 tff(21527,plain,
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% 9.99/10.23 tff(21528,plain,
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% 9.99/10.23 inference(unit_resolution,[status(thm)],[18613, 21527])).
% 9.99/10.23 tff(21529,plain,
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% 9.99/10.23 tff(21530,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.23 tff(21531,plain,
% 9.99/10.23 (~b(s(z), s(s(z)))),
% 9.99/10.23 inference(unit_resolution,[status(thm)],[21530, 21528, 21508, 21521])).
% 9.99/10.23 tff(21532,plain,
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% 9.99/10.23 tff(21533,plain,
% 9.99/10.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.99/10.23 inference(rewrite,[status(thm)],[])).
% 9.99/10.23 tff(21534,plain,
% 9.99/10.23 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.99/10.23 inference(rewrite,[status(thm)],[])).
% 9.99/10.23 tff(21535,plain,
% 9.99/10.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 9.99/10.23 inference(monotonicity,[status(thm)],[21534])).
% 9.99/10.23 tff(21536,plain,
% 9.99/10.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.99/10.23 inference(transitivity,[status(thm)],[21535, 21533])).
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% 9.99/10.23 tff(21594,plain,
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% 9.99/10.23 tff(21596,plain,
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% 9.99/10.23 inference(unit_resolution,[status(thm)],[13062, 21575, 130])).
% 9.99/10.23 tff(21597,plain,
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% 9.99/10.23 inference(unit_resolution,[status(thm)],[2614, 21578, 21596, 17432, 184])).
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% 9.99/10.23 inference(unit_resolution,[status(thm)],[3253, 21592, 182, 665, 411, 1526, 21582, 21441, 832])).
% 9.99/10.23 tff(21599,plain,
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% 9.99/10.23 inference(unit_resolution,[status(thm)],[2621, 21599, 182, 21597])).
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% 9.99/10.23 inference(unit_resolution,[status(thm)],[2629, 21600, 21595])).
% 9.99/10.23 tff(21602,plain,((~r(s(z), elem!1)) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | r(elem!1, s(z)) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(elem!1))))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.23 tff(21603,plain,
% 9.99/10.23 (~r(s(z), elem!1)),
% 9.99/10.23 inference(unit_resolution,[status(thm)],[21602, 21563, 181, 21545, 21568, 15899, 8815, 21567, 59, 20263, 21419, 90, 21556, 118])).
% 9.99/10.23 tff(21604,plain,
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% 9.99/10.23 inference(unit_resolution,[status(thm)],[3234, 1686, 90, 665])).
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% 9.99/10.23 inference(unit_resolution,[status(thm)],[781, 21606, 3810])).
% 9.99/10.23 tff(21608,plain,
% 9.99/10.23 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.99/10.23 inference(unit_resolution,[status(thm)],[14788, 21607, 125])).
% 9.99/10.23 tff(21609,plain,
% 9.99/10.23 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.99/10.23 inference(unit_resolution,[status(thm)],[20817, 379, 1526, 1234])).
% 9.99/10.23 tff(21610,plain,
% 9.99/10.23 (~b(s(s(s(s(z)))), elem!1)),
% 9.99/10.23 inference(unit_resolution,[status(thm)],[20820, 21609, 125])).
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% 9.99/10.23 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.99/10.23 inference(unit_resolution,[status(thm)],[2694, 21610, 130])).
% 9.99/10.23 tff(21612,plain,
% 9.99/10.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.99/10.23 inference(rewrite,[status(thm)],[])).
% 9.99/10.23 tff(21613,plain,
% 9.99/10.23 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.99/10.23 inference(rewrite,[status(thm)],[])).
% 9.99/10.23 tff(21614,plain,
% 9.99/10.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 9.99/10.23 inference(monotonicity,[status(thm)],[21613])).
% 9.99/10.23 tff(21615,plain,
% 9.99/10.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 9.99/10.23 inference(transitivity,[status(thm)],[21614, 21612])).
% 9.99/10.23 tff(21616,plain,
% 9.99/10.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 9.99/10.23 inference(quant_inst,[status(thm)],[])).
% 9.99/10.23 tff(21617,plain,
% 9.99/10.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 9.99/10.23 inference(modus_ponens,[status(thm)],[21616, 21615])).
% 9.99/10.23 tff(21618,plain,
% 9.99/10.23 (~b(s(s(z)), s(z))),
% 9.99/10.23 inference(unit_resolution,[status(thm)],[21617, 391, 3823, 90, 1234, 1686])).
% 9.99/10.23 tff(21619,plain,
% 9.99/10.23 (~r(s(s(z)), s(z))),
% 9.99/10.23 inference(unit_resolution,[status(thm)],[5141, 194, 184, 182, 6918])).
% 9.99/10.23 tff(21620,plain,
% 9.99/10.23 ($false),
% 9.99/10.23 inference(unit_resolution,[status(thm)],[3778, 21619, 21618])).
% 9.99/10.23 tff(21621,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.23 tff(21622,plain,
% 9.99/10.23 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.23 inference(unit_resolution,[status(thm)],[21621, 1686, 182, 90, 1234, 184])).
% 9.99/10.23 tff(21623,plain,
% 9.99/10.23 (r(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[3652, 21622])).
% 9.99/10.24 tff(21624,plain,
% 9.99/10.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.99/10.24 inference(rewrite,[status(thm)],[])).
% 9.99/10.24 tff(21625,plain,
% 9.99/10.24 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.99/10.24 inference(rewrite,[status(thm)],[])).
% 9.99/10.24 tff(21626,plain,
% 9.99/10.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.99/10.24 inference(monotonicity,[status(thm)],[21625])).
% 9.99/10.24 tff(21627,plain,
% 9.99/10.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.99/10.24 inference(transitivity,[status(thm)],[21626, 21624])).
% 9.99/10.24 tff(21628,plain,
% 9.99/10.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 9.99/10.24 inference(quant_inst,[status(thm)],[])).
% 9.99/10.24 tff(21629,plain,
% 9.99/10.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.99/10.24 inference(modus_ponens,[status(thm)],[21628, 21627])).
% 9.99/10.24 tff(21630,plain,
% 9.99/10.24 (~r(s(s(z)), s(s(s(elem!1))))),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[21629, 194, 21623, 21611, 21608])).
% 9.99/10.24 tff(21631,plain,
% 9.99/10.24 (b(s(s(z)), s(s(s(elem!1))))),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[11041, 21630])).
% 9.99/10.24 tff(21632,plain,
% 9.99/10.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.99/10.24 inference(rewrite,[status(thm)],[])).
% 9.99/10.24 tff(21633,plain,
% 9.99/10.24 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.99/10.24 inference(rewrite,[status(thm)],[])).
% 9.99/10.24 tff(21634,plain,
% 9.99/10.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.99/10.24 inference(monotonicity,[status(thm)],[21633])).
% 9.99/10.24 tff(21635,plain,
% 9.99/10.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.99/10.24 inference(transitivity,[status(thm)],[21634, 21632])).
% 9.99/10.24 tff(21636,plain,
% 9.99/10.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 9.99/10.24 inference(quant_inst,[status(thm)],[])).
% 9.99/10.24 tff(21637,plain,
% 9.99/10.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.99/10.24 inference(modus_ponens,[status(thm)],[21636, 21635])).
% 9.99/10.24 tff(21638,plain,
% 9.99/10.24 (~r(s(s(s(elem!1))), s(s(z)))),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[21637, 194, 21623, 21611, 21608])).
% 9.99/10.24 tff(21639,plain,
% 9.99/10.24 (~r(elem!1, s(s(z)))),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[10022, 21638, 125])).
% 9.99/10.24 tff(21640,plain,
% 9.99/10.24 (b(elem!1, s(s(z)))),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[3394, 21639, 3820])).
% 9.99/10.24 tff(21641,plain,
% 9.99/10.24 (b(s(s(s(elem!1))), s(s(z)))),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[16425, 21640, 125])).
% 9.99/10.24 tff(21642,plain,
% 9.99/10.24 (~b(s(s(z)), s(z))),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[21394, 21641, 1526, 17432, 379])).
% 9.99/10.24 tff(21643,plain,
% 9.99/10.24 (r(s(s(z)), s(z))),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[3778, 21642])).
% 9.99/10.24 tff(21644,plain,
% 9.99/10.24 (~r(s(s(z)), z)),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[20863, 194, 10428, 182, 21643])).
% 9.99/10.24 tff(21645,plain,
% 9.99/10.24 (b(s(s(z)), z)),
% 9.99/10.24 inference(unit_resolution,[status(thm)],[1211, 21644])).
% 9.99/10.24 tff(21646,plain,
% 9.99/10.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.99/10.24 inference(rewrite,[status(thm)],[])).
% 9.99/10.24 tff(21647,plain,
% 9.99/10.24 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.99/10.24 inference(rewrite,[status(thm)],[])).
% 9.99/10.24 tff(21648,plain,
% 9.99/10.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 9.99/10.24 inference(monotonicity,[status(thm)],[21647])).
% 9.99/10.24 tff(21649,plain,
% 9.99/10.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.99/10.25 inference(transitivity,[status(thm)],[21648, 21646])).
% 9.99/10.25 tff(21650,plain,
% 9.99/10.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 9.99/10.25 inference(quant_inst,[status(thm)],[])).
% 9.99/10.25 tff(21651,plain,
% 9.99/10.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 9.99/10.25 inference(modus_ponens,[status(thm)],[21650, 21649])).
% 9.99/10.25 tff(21652,plain,
% 9.99/10.25 ($false),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[21651, 391, 17432, 90, 21645, 1686, 21631])).
% 9.99/10.25 tff(21653,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.25 tff(21654,plain,
% 9.99/10.25 (~b(z, s(s(s(s(z)))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[21653, 21605, 181, 8815, 90, 21556, 21419, 59, 21563])).
% 9.99/10.25 tff(21655,plain,
% 9.99/10.25 (r(z, s(s(s(s(z)))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[800, 21654])).
% 9.99/10.25 tff(21656,plain,
% 9.99/10.25 (~b(s(s(s(s(z)))), s(z))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[2097, 21655, 15899, 20263, 21419, 21560])).
% 9.99/10.25 tff(21657,plain,
% 9.99/10.25 (r(s(s(s(s(z)))), s(z))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[749, 21656])).
% 9.99/10.25 tff(21658,plain,
% 9.99/10.25 (~r(elem!1, s(s(s(s(z)))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[15063, 21657, 15899, 21655])).
% 9.99/10.25 tff(21659,plain,
% 9.99/10.25 (b(elem!1, s(s(s(s(z)))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[781, 21658, 21561])).
% 9.99/10.25 tff(21660,plain,
% 9.99/10.25 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.99/10.25 inference(modus_ponens,[status(thm)],[21659, 21558])).
% 9.99/10.25 tff(21661,plain,
% 9.99/10.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.99/10.25 inference(rewrite,[status(thm)],[])).
% 9.99/10.25 tff(21662,plain,
% 9.99/10.25 (((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.99/10.25 inference(rewrite,[status(thm)],[])).
% 9.99/10.25 tff(21663,plain,
% 9.99/10.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 9.99/10.25 inference(monotonicity,[status(thm)],[21662])).
% 9.99/10.25 tff(21664,plain,
% 9.99/10.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 9.99/10.25 inference(transitivity,[status(thm)],[21663, 21661])).
% 9.99/10.25 tff(21665,plain,
% 9.99/10.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 9.99/10.25 inference(quant_inst,[status(thm)],[])).
% 9.99/10.25 tff(21666,plain,
% 9.99/10.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 9.99/10.25 inference(modus_ponens,[status(thm)],[21665, 21664])).
% 9.99/10.25 tff(21667,plain,
% 9.99/10.25 ($false),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[21666, 391, 8815, 90, 21419, 21660, 21557])).
% 9.99/10.25 tff(21668,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | r(s(s(s(elem!1))), s(z)) | (elem!1 = z) | b(z, s(s(s(elem!1)))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 9.99/10.25 tff(21669,plain,
% 9.99/10.25 (b(elem!1, s(s(s(elem!1))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[21668, 8814, 90, 2, 10, 91])).
% 9.99/10.25 tff(21670,plain,
% 9.99/10.25 (~(s(s(s(elem!1))) = elem!1)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[15370, 21669])).
% 9.99/10.25 tff(21671,plain,
% 9.99/10.25 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[8251, 21670])).
% 9.99/10.25 tff(21672,plain,
% 9.99/10.25 (b(z, s(s(elem!1)))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[3924, 21671, 10, 91])).
% 9.99/10.25 tff(21673,plain,
% 9.99/10.25 (b(s(z), elem!1)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[632, 2500, 21435])).
% 9.99/10.25 tff(21674,plain,
% 9.99/10.25 (b(s(s(s(elem!1))), elem!1)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[230, 16963, 127])).
% 9.99/10.25 tff(21675,plain,
% 9.99/10.25 ($false),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[20387, 21674, 21673, 721, 1526])).
% 9.99/10.25 tff(21676,plain,((~r(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.25 tff(21677,plain,
% 9.99/10.25 (~r(elem!1, z)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[21676, 8815, 20263, 21670, 59, 15899, 181])).
% 9.99/10.25 tff(21678,plain,
% 9.99/10.25 (b(elem!1, z)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[526, 21677, 2])).
% 9.99/10.25 tff(21679,plain,
% 9.99/10.25 (~r(s(s(s(elem!1))), elem!1)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[241, 232, 184, 182])).
% 9.99/10.25 tff(21680,plain,
% 9.99/10.25 (b(s(s(s(elem!1))), elem!1)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[230, 21679, 15376])).
% 9.99/10.25 tff(21681,plain,
% 9.99/10.25 (~b(s(z), elem!1)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[20387, 21680, 721, 1526])).
% 9.99/10.25 tff(21682,plain,
% 9.99/10.25 (r(s(z), elem!1)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[632, 21681, 21435])).
% 9.99/10.25 tff(21683,plain,
% 9.99/10.25 (~r(elem!1, s(z))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[2475, 21682, 411, 182])).
% 9.99/10.25 tff(21684,plain,
% 9.99/10.25 (~b(s(s(elem!1)), s(z))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[19556, 2208, 448, 3927, 665])).
% 9.99/10.25 tff(21685,plain,
% 9.99/10.25 (r(s(s(elem!1)), s(z))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[362, 21684])).
% 9.99/10.25 tff(21686,plain,
% 9.99/10.25 (~(s(s(elem!1)) = elem!1)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[4206, 21685, 21683])).
% 9.99/10.25 tff(21687,plain,
% 9.99/10.25 (~(s(s(elem!1)) = s(elem!1))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[264, 21686])).
% 9.99/10.25 tff(21688,plain,
% 9.99/10.25 (~(s(elem!1) = s(s(elem!1)))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[9802, 21687])).
% 9.99/10.25 tff(21689,plain,
% 9.99/10.25 (~r(s(elem!1), z)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[2594, 232, 411, 182, 1526, 2234, 121])).
% 9.99/10.25 tff(21690,plain,
% 9.99/10.25 (b(s(elem!1), z)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[549, 21689])).
% 9.99/10.25 tff(21691,plain,
% 9.99/10.25 (r(z, s(elem!1))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[2614, 21690, 2234, 2208, 184])).
% 9.99/10.25 tff(21692,plain,
% 9.99/10.25 (~r(s(s(elem!1)), z)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[2621, 21685, 182, 21691])).
% 9.99/10.25 tff(21693,plain,
% 9.99/10.25 (b(s(s(elem!1)), z)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[2629, 21692])).
% 9.99/10.25 tff(21694,plain,
% 9.99/10.25 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[337, 232, 184, 182])).
% 9.99/10.25 tff(21695,plain,
% 9.99/10.25 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[1370, 21694, 16094])).
% 9.99/10.25 tff(21696,plain,
% 9.99/10.25 (~r(elem!1, s(elem!1))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[2582, 21682, 411, 182])).
% 9.99/10.25 tff(21697,plain,
% 9.99/10.25 (b(elem!1, s(elem!1))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[443, 21696, 17526])).
% 9.99/10.25 tff(21698,plain,
% 9.99/10.25 (~b(s(s(elem!1)), elem!1)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[8469, 21697, 2208, 3927, 21695])).
% 9.99/10.25 tff(21699,plain,
% 9.99/10.25 (r(s(s(elem!1)), elem!1)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[872, 21698, 21686])).
% 9.99/10.25 tff(21700,plain,
% 9.99/10.25 (~(elem!1 = s(s(elem!1)))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[1292, 21686])).
% 9.99/10.25 tff(21701,plain,
% 9.99/10.25 (~b(elem!1, s(s(elem!1)))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[20366, 21693, 3927, 665])).
% 9.99/10.25 tff(21702,plain,
% 9.99/10.25 (r(elem!1, s(s(elem!1)))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[1307, 21701, 21700])).
% 9.99/10.25 tff(21703,plain,
% 9.99/10.25 ($false),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[15211, 21702, 21699, 21690, 665, 16989, 21693, 3927, 21688])).
% 9.99/10.25 tff(21704,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.25 tff(21705,plain,
% 9.99/10.25 (~r(s(z), s(s(s(elem!1))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[21704, 21678, 21672, 181, 15899, 21669, 59, 20263, 8815, 118])).
% 9.99/10.25 tff(21706,plain,
% 9.99/10.25 (b(s(z), s(s(s(elem!1))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[247, 21705])).
% 9.99/10.25 tff(21707,plain,
% 9.99/10.25 ($false),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[4956, 391, 21669, 21706, 8815, 20263])).
% 9.99/10.25 tff(21708,plain,(r(s(s(s(elem!1))), s(z)) | (elem!1 = z) | b(z, s(s(s(elem!1)))) | b(s(z), z) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.25 tff(21709,plain,
% 9.99/10.25 (r(s(s(s(elem!1))), s(z))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[21708, 91, 10, 2, 90])).
% 9.99/10.25 tff(21710,plain,
% 9.99/10.25 (~r(elem!1, s(s(s(elem!1))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[19887, 21709, 15899, 59])).
% 9.99/10.25 tff(21711,plain,
% 9.99/10.25 (~r(s(z), s(s(s(elem!1))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[3499, 21709, 59, 181])).
% 9.99/10.25 tff(21712,plain,
% 9.99/10.25 (b(s(z), s(s(s(elem!1))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[247, 21711])).
% 9.99/10.25 tff(21713,plain,
% 9.99/10.25 (~r(s(s(s(elem!1))), z)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[202, 21709, 59, 181])).
% 9.99/10.25 tff(21714,plain,
% 9.99/10.25 (b(s(s(s(elem!1))), z)),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[377, 21713])).
% 9.99/10.25 tff(21715,plain,
% 9.99/10.25 (b(elem!1, s(s(s(elem!1))))),
% 9.99/10.25 inference(unit_resolution,[status(thm)],[424, 4029, 2567])).
% 9.99/10.25 tff(21716,plain,
% 9.99/10.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.99/10.25 inference(rewrite,[status(thm)],[])).
% 9.99/10.25 tff(21717,plain,
% 9.99/10.25 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.99/10.26 inference(rewrite,[status(thm)],[])).
% 9.99/10.26 tff(21718,plain,
% 9.99/10.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 9.99/10.26 inference(monotonicity,[status(thm)],[21717])).
% 9.99/10.26 tff(21719,plain,
% 9.99/10.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 9.99/10.26 inference(transitivity,[status(thm)],[21718, 21716])).
% 9.99/10.26 tff(21720,plain,
% 9.99/10.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 9.99/10.26 inference(quant_inst,[status(thm)],[])).
% 9.99/10.26 tff(21721,plain,
% 9.99/10.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 9.99/10.26 inference(modus_ponens,[status(thm)],[21720, 21719])).
% 9.99/10.26 tff(21722,plain,
% 9.99/10.26 ($false),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[21721, 391, 380, 21715, 20278, 379, 721])).
% 9.99/10.26 tff(21723,plain,((s(s(s(elem!1))) = elem!1) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | b(z, s(s(s(elem!1)))) | b(s(z), z) | r(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.26 tff(21724,plain,
% 9.99/10.26 (s(s(s(elem!1))) = elem!1),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[21723, 21714, 21712, 20263, 10, 91, 21710])).
% 9.99/10.26 tff(21725,plain,
% 9.99/10.26 (~r(elem!1, z)),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[533, 21724, 21713])).
% 9.99/10.26 tff(21726,plain,
% 9.99/10.26 ($false),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[15970, 21725, 21724, 10, 21709])).
% 9.99/10.26 tff(21727,plain,(b(s(z), z) | b(z, s(s(s(elem!1)))) | (elem!1 = z) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.26 tff(21728,plain,
% 9.99/10.26 (b(s(z), z)),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[21727, 10, 2, 90])).
% 9.99/10.26 tff(21729,plain,
% 9.99/10.26 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[314, 15838])).
% 9.99/10.26 tff(21730,plain,
% 9.99/10.26 (b(s(s(s(elem!1))), elem!1)),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[230, 18877, 127])).
% 9.99/10.26 tff(21731,plain,
% 9.99/10.26 (~r(s(s(s(elem!1))), s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[19887, 410, 411, 184])).
% 9.99/10.26 tff(21732,plain,
% 9.99/10.26 (b(s(s(s(elem!1))), s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[223, 21731])).
% 9.99/10.26 tff(21733,plain,
% 9.99/10.26 (~b(s(z), elem!1)),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[20387, 21732, 721, 900])).
% 9.99/10.26 tff(21734,plain,
% 9.99/10.26 (r(s(z), elem!1)),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[632, 21733, 21435])).
% 9.99/10.26 tff(21735,plain,
% 9.99/10.26 (~r(z, s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[16803, 21734, 411, 530])).
% 9.99/10.26 tff(21736,plain,
% 9.99/10.26 (b(z, s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[678, 21735])).
% 9.99/10.26 tff(21737,plain,
% 9.99/10.26 (~r(s(s(s(elem!1))), z)),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[8380, 410, 184, 411])).
% 9.99/10.26 tff(21738,plain,
% 9.99/10.26 (b(s(s(s(elem!1))), z)),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[377, 21737])).
% 9.99/10.26 tff(21739,plain,
% 9.99/10.26 ($false),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[10633, 391, 21738, 21732, 21736, 590])).
% 9.99/10.26 tff(21740,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.26 tff(21741,plain,
% 9.99/10.26 (~r(elem!1, s(s(s(elem!1))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[21740, 3618, 411, 590, 721, 21730, 184])).
% 9.99/10.26 tff(21742,plain,
% 9.99/10.26 (b(elem!1, s(s(s(elem!1))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[424, 21741, 4029])).
% 9.99/10.26 tff(21743,plain,
% 9.99/10.26 (~b(s(z), elem!1)),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[20387, 1526, 721, 900])).
% 9.99/10.26 tff(21744,plain,
% 9.99/10.26 (r(s(z), elem!1)),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[632, 21743, 21435])).
% 9.99/10.26 tff(21745,plain,
% 9.99/10.26 (~r(z, s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[16803, 21744, 411, 530])).
% 9.99/10.26 tff(21746,plain,
% 9.99/10.26 (b(z, s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[678, 21745])).
% 9.99/10.26 tff(21747,plain,
% 9.99/10.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.99/10.26 inference(rewrite,[status(thm)],[])).
% 9.99/10.26 tff(21748,plain,
% 9.99/10.26 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.99/10.26 inference(rewrite,[status(thm)],[])).
% 9.99/10.26 tff(21749,plain,
% 9.99/10.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 9.99/10.26 inference(monotonicity,[status(thm)],[21748])).
% 9.99/10.26 tff(21750,plain,
% 9.99/10.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 9.99/10.26 inference(transitivity,[status(thm)],[21749, 21747])).
% 9.99/10.26 tff(21751,plain,
% 9.99/10.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 9.99/10.26 inference(quant_inst,[status(thm)],[])).
% 9.99/10.26 tff(21752,plain,
% 9.99/10.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 9.99/10.26 inference(modus_ponens,[status(thm)],[21751, 21750])).
% 9.99/10.26 tff(21753,plain,
% 9.99/10.26 ($false),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[21752, 391, 448, 1526, 21746, 590, 721])).
% 9.99/10.26 tff(21754,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.26 tff(21755,plain,
% 9.99/10.26 (~b(s(s(s(elem!1))), s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[21754, 21742, 590, 721, 411, 3618, 21730])).
% 9.99/10.26 tff(21756,plain,
% 9.99/10.26 (r(s(s(s(elem!1))), s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[223, 21755])).
% 9.99/10.26 tff(21757,plain,
% 9.99/10.26 (~r(z, s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[20248, 194, 184, 232, 21756])).
% 9.99/10.26 tff(21758,plain,
% 9.99/10.26 (b(z, s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[678, 21757])).
% 9.99/10.26 tff(21759,plain,
% 9.99/10.26 (~b(s(s(s(s(z)))), s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[5575, 391, 90, 21758, 590])).
% 9.99/10.26 tff(21760,plain,
% 9.99/10.26 (r(s(s(s(s(z)))), s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[749, 21759])).
% 9.99/10.26 tff(21761,plain,
% 9.99/10.26 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.99/10.26 inference(rewrite,[status(thm)],[])).
% 9.99/10.26 tff(21762,plain,
% 9.99/10.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 9.99/10.26 inference(monotonicity,[status(thm)],[21761])).
% 9.99/10.26 tff(21763,plain,
% 9.99/10.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.99/10.26 inference(transitivity,[status(thm)],[21762, 18950])).
% 9.99/10.26 tff(21764,plain,
% 9.99/10.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 9.99/10.26 inference(quant_inst,[status(thm)],[])).
% 9.99/10.26 tff(21765,plain,
% 9.99/10.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 9.99/10.26 inference(modus_ponens,[status(thm)],[21764, 21763])).
% 9.99/10.26 tff(21766,plain,
% 9.99/10.26 (~b(s(z), s(s(s(s(z)))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[21765, 391, 90, 21758, 590])).
% 9.99/10.26 tff(21767,plain,
% 9.99/10.26 (r(s(z), s(s(s(s(z)))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[1230, 21766])).
% 9.99/10.26 tff(21768,plain,
% 9.99/10.26 (~(elem!1 = s(s(s(s(z)))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[16358, 484, 90])).
% 9.99/10.26 tff(21769,plain,
% 9.99/10.26 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[2849, 21435])).
% 9.99/10.26 tff(21770,plain,
% 9.99/10.26 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[10940, 21769])).
% 9.99/10.26 tff(21771,plain,
% 9.99/10.26 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[10947, 194, 21756, 21767, 21760])).
% 9.99/10.26 tff(21772,plain,
% 9.99/10.26 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[15351, 21771, 21770])).
% 9.99/10.26 tff(21773,plain,
% 9.99/10.26 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[10698, 194, 21756, 21767, 21760])).
% 9.99/10.26 tff(21774,plain,
% 9.99/10.26 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[2853, 42, 21769, 21773])).
% 9.99/10.26 tff(21775,plain,
% 9.99/10.26 (~b(elem!1, s(s(s(s(z)))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[10959, 21774, 21730, 21772])).
% 9.99/10.26 tff(21776,plain,
% 9.99/10.26 (r(elem!1, s(s(s(s(z)))))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[781, 21775, 21768])).
% 9.99/10.26 tff(21777,plain,
% 9.99/10.26 (~r(elem!1, s(z))),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[6347, 21776, 21767, 21760])).
% 9.99/10.26 tff(21778,plain,
% 9.99/10.26 (~(s(s(s(s(z)))) = elem!1)),
% 9.99/10.26 inference(unit_resolution,[status(thm)],[16908, 21768])).
% 9.99/10.26 tff(21779,plain,
% 9.99/10.26 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.99/10.27 inference(rewrite,[status(thm)],[])).
% 9.99/10.27 tff(21780,plain,
% 9.99/10.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21779])).
% 9.99/10.27 tff(21781,plain,
% 9.99/10.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 9.99/10.27 inference(transitivity,[status(thm)],[21780, 16853])).
% 9.99/10.27 tff(21782,plain,
% 9.99/10.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 9.99/10.27 inference(quant_inst,[status(thm)],[])).
% 9.99/10.27 tff(21783,plain,
% 9.99/10.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 9.99/10.27 inference(modus_ponens,[status(thm)],[21782, 21781])).
% 9.99/10.27 tff(21784,plain,
% 9.99/10.27 (~b(s(s(s(s(z)))), elem!1)),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[21783, 391, 21730, 21742, 21774])).
% 9.99/10.27 tff(21785,plain,
% 9.99/10.27 (r(s(s(s(s(z)))), elem!1)),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[762, 21784, 21778])).
% 9.99/10.27 tff(21786,plain,
% 9.99/10.27 (~r(z, s(s(s(s(z)))))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[15063, 21776, 411, 21760])).
% 9.99/10.27 tff(21787,plain,
% 9.99/10.27 (b(z, s(s(s(s(z)))))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[800, 21786])).
% 9.99/10.27 tff(21788,plain,
% 9.99/10.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.99/10.27 inference(rewrite,[status(thm)],[])).
% 9.99/10.27 tff(21789,plain,
% 9.99/10.27 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.99/10.27 inference(rewrite,[status(thm)],[])).
% 9.99/10.27 tff(21790,plain,
% 9.99/10.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21789])).
% 9.99/10.27 tff(21791,plain,
% 9.99/10.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 9.99/10.27 inference(transitivity,[status(thm)],[21790, 21788])).
% 9.99/10.27 tff(21792,plain,
% 9.99/10.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)))),
% 9.99/10.27 inference(quant_inst,[status(thm)],[])).
% 9.99/10.27 tff(21793,plain,
% 9.99/10.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 9.99/10.27 inference(modus_ponens,[status(thm)],[21792, 21791])).
% 9.99/10.27 tff(21794,plain,
% 9.99/10.27 (~b(s(s(s(elem!1))), z)),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[21793, 391, 21730, 21787, 21774, 21772])).
% 9.99/10.27 tff(21795,plain,
% 9.99/10.27 (r(s(s(s(elem!1))), z)),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[377, 21794])).
% 9.99/10.27 tff(21796,plain,
% 9.99/10.27 (~b(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[16453, 21795, 90, 184, 590, 21758, 21772, 21787])).
% 9.99/10.27 tff(21797,plain,
% 9.99/10.27 (r(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[3652, 21796])).
% 9.99/10.27 tff(21798,plain,
% 9.99/10.27 (~r(s(s(z)), s(z))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[4702, 21797, 21767, 21785])).
% 9.99/10.27 tff(21799,plain,
% 9.99/10.27 (b(s(s(z)), s(z))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[3778, 21798])).
% 9.99/10.27 tff(21800,plain,
% 9.99/10.27 (~r(s(z), s(s(z)))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[16396, 21797, 21767, 21760])).
% 9.99/10.27 tff(21801,plain,
% 9.99/10.27 (b(s(z), s(s(z)))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[1788, 21800])).
% 9.99/10.27 tff(21802,plain,
% 9.99/10.27 (~b(elem!1, s(s(z)))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[10150, 21801, 721, 21799])).
% 9.99/10.27 tff(21803,plain,
% 9.99/10.27 (~b(z, s(s(z)))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[21530, 21801, 21758, 21799])).
% 9.99/10.27 tff(21804,plain,
% 9.99/10.27 (r(z, s(s(z)))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[18613, 21803])).
% 9.99/10.27 tff(21805,plain,
% 9.99/10.27 (~r(elem!1, s(s(z)))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[18632, 21804, 411, 21797])).
% 9.99/10.27 tff(21806,plain,
% 9.99/10.27 (elem!1 = s(s(z))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[3394, 21805, 21802])).
% 9.99/10.27 tff(21807,plain,
% 9.99/10.27 (~b(s(s(elem!1)), s(z))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[9032, 21806, 21759])).
% 9.99/10.27 tff(21808,plain,
% 9.99/10.27 (r(s(s(elem!1)), s(z))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[362, 21807])).
% 9.99/10.27 tff(21809,plain,
% 9.99/10.27 (~(s(s(elem!1)) = elem!1)),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[4206, 21808, 21777])).
% 9.99/10.27 tff(21810,plain,
% 9.99/10.27 (~(s(s(s(elem!1))) = s(elem!1))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[6159, 21809])).
% 9.99/10.27 tff(21811,plain,
% 9.99/10.27 (s(elem!1) = s(s(s(z)))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21806])).
% 9.99/10.27 tff(21812,plain,
% 9.99/10.27 (b(s(elem!1), z) <=> b(s(s(s(z))), z)),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21811])).
% 9.99/10.27 tff(21813,plain,
% 9.99/10.27 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 9.99/10.27 inference(symmetry,[status(thm)],[21812])).
% 9.99/10.27 tff(21814,plain,
% 9.99/10.27 ((~b(s(s(s(z))), z)) <=> (~b(s(elem!1), z))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21813])).
% 9.99/10.27 tff(21815,plain,
% 9.99/10.27 (s(s(elem!1)) = s(s(s(s(z))))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21811])).
% 9.99/10.27 tff(21816,plain,
% 9.99/10.27 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21815, 21811])).
% 9.99/10.27 tff(21817,plain,
% 9.99/10.27 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21816])).
% 9.99/10.27 tff(21818,plain,
% 9.99/10.27 (~(s(s(elem!1)) = s(elem!1))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[264, 21809])).
% 9.99/10.27 tff(21819,plain,
% 9.99/10.27 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 9.99/10.27 inference(modus_ponens,[status(thm)],[21818, 21817])).
% 9.99/10.27 tff(21820,plain,
% 9.99/10.27 (~(s(elem!1) = s(s(elem!1)))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[9802, 21818])).
% 9.99/10.27 tff(21821,plain,
% 9.99/10.27 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[5792, 21795, 184, 232])).
% 9.99/10.27 tff(21822,plain,
% 9.99/10.27 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[1356, 21821, 21729])).
% 9.99/10.27 tff(21823,plain,
% 9.99/10.27 (~b(s(s(elem!1)), elem!1)),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[6001, 21822, 21730, 21742])).
% 9.99/10.27 tff(21824,plain,
% 9.99/10.27 (r(s(s(elem!1)), elem!1)),
% 9.99/10.27 inference(unit_resolution,[status(thm)],[872, 21809, 21823])).
% 9.99/10.27 tff(21825,plain,
% 9.99/10.27 (r(elem!1, s(s(elem!1))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21806, 21815])).
% 9.99/10.27 tff(21826,plain,
% 9.99/10.27 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 9.99/10.27 inference(symmetry,[status(thm)],[21825])).
% 9.99/10.27 tff(21827,plain,
% 9.99/10.27 (r(elem!1, s(s(elem!1)))),
% 9.99/10.27 inference(modus_ponens,[status(thm)],[21797, 21826])).
% 9.99/10.27 tff(21828,plain,
% 9.99/10.27 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 9.99/10.27 inference(commutativity,[status(thm)],[])).
% 9.99/10.27 tff(21829,plain,
% 9.99/10.27 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 9.99/10.27 inference(symmetry,[status(thm)],[21828])).
% 9.99/10.27 tff(21830,plain,
% 9.99/10.27 (s(s(s(z))) = s(elem!1)),
% 9.99/10.27 inference(symmetry,[status(thm)],[21811])).
% 9.99/10.27 tff(21831,plain,
% 9.99/10.27 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(elem!1))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21830])).
% 9.99/10.27 tff(21832,plain,
% 9.99/10.27 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = s(s(s(z))))),
% 9.99/10.27 inference(symmetry,[status(thm)],[21831])).
% 9.99/10.27 tff(21833,plain,
% 9.99/10.27 ((s(s(z)) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 9.99/10.27 inference(transitivity,[status(thm)],[21832, 21829])).
% 9.99/10.27 tff(21834,plain,
% 9.99/10.27 ((~(s(s(z)) = s(elem!1))) <=> (~(s(s(s(z))) = s(s(z))))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21833])).
% 9.99/10.27 tff(21835,plain,
% 9.99/10.27 (s(s(z)) = elem!1),
% 9.99/10.27 inference(symmetry,[status(thm)],[21806])).
% 9.99/10.27 tff(21836,plain,
% 9.99/10.27 ((s(s(z)) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21835])).
% 9.99/10.27 tff(21837,plain,
% 9.99/10.27 ((elem!1 = s(elem!1)) <=> (s(s(z)) = s(elem!1))),
% 9.99/10.27 inference(symmetry,[status(thm)],[21836])).
% 9.99/10.27 tff(21838,plain,
% 9.99/10.27 ((~(elem!1 = s(elem!1))) <=> (~(s(s(z)) = s(elem!1)))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21837])).
% 9.99/10.27 tff(21839,plain,
% 9.99/10.27 (~(s(s(z)) = s(elem!1))),
% 9.99/10.27 inference(modus_ponens,[status(thm)],[4598, 21838])).
% 9.99/10.27 tff(21840,plain,
% 9.99/10.27 (~(s(s(s(z))) = s(s(z)))),
% 9.99/10.27 inference(modus_ponens,[status(thm)],[21839, 21834])).
% 9.99/10.27 tff(21841,plain,
% 9.99/10.27 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21815])).
% 9.99/10.27 tff(21842,plain,
% 9.99/10.27 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21841])).
% 9.99/10.27 tff(21843,plain,
% 9.99/10.27 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(z)))),
% 9.99/10.27 inference(monotonicity,[status(thm)],[21806])).
% 9.99/10.27 tff(21844,plain,
% 9.99/10.27 (b(s(s(s(elem!1))), s(s(z)))),
% 9.99/10.27 inference(modus_ponens,[status(thm)],[21730, 21843])).
% 9.99/10.27 tff(21845,plain,
% 9.99/10.27 (b(s(s(s(s(s(z))))), s(s(z)))),
% 9.99/10.27 inference(modus_ponens,[status(thm)],[21844, 21842])).
% 9.99/10.27 tff(21846,plain,
% 9.99/10.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 9.99/10.28 inference(rewrite,[status(thm)],[])).
% 9.99/10.28 tff(21847,plain,
% 9.99/10.28 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 9.99/10.28 inference(rewrite,[status(thm)],[])).
% 9.99/10.28 tff(21848,plain,
% 9.99/10.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 9.99/10.28 inference(monotonicity,[status(thm)],[21847])).
% 9.99/10.28 tff(21849,plain,
% 9.99/10.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 9.99/10.28 inference(transitivity,[status(thm)],[21848, 21846])).
% 9.99/10.28 tff(21850,plain,
% 9.99/10.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 9.99/10.28 inference(quant_inst,[status(thm)],[])).
% 9.99/10.28 tff(21851,plain,
% 9.99/10.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 9.99/10.28 inference(modus_ponens,[status(thm)],[21850, 21849])).
% 9.99/10.28 tff(21852,plain,
% 9.99/10.28 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[21851, 391, 90, 1686, 1685])).
% 9.99/10.28 tff(21853,plain,
% 9.99/10.28 (r(s(s(s(s(z)))), s(s(s(z))))),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[4426, 42, 21852, 4414])).
% 9.99/10.28 tff(21854,plain,
% 9.99/10.28 ((s(z) = s(s(s(z)))) <=> (s(z) = s(elem!1))),
% 9.99/10.28 inference(monotonicity,[status(thm)],[13915])).
% 9.99/10.28 tff(21855,plain,
% 9.99/10.28 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(z))))),
% 9.99/10.28 inference(symmetry,[status(thm)],[21854])).
% 9.99/10.28 tff(21856,plain,
% 9.99/10.28 ((~(s(z) = s(elem!1))) <=> (~(s(z) = s(s(s(z)))))),
% 9.99/10.28 inference(monotonicity,[status(thm)],[21855])).
% 9.99/10.28 tff(21857,plain,
% 9.99/10.28 (~(s(z) = s(s(s(z))))),
% 9.99/10.28 inference(modus_ponens,[status(thm)],[121, 21856])).
% 9.99/10.28 tff(21858,plain,
% 9.99/10.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 9.99/10.28 inference(rewrite,[status(thm)],[])).
% 9.99/10.28 tff(21859,plain,
% 9.99/10.28 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 9.99/10.28 inference(rewrite,[status(thm)],[])).
% 9.99/10.28 tff(21860,plain,
% 9.99/10.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))))),
% 9.99/10.28 inference(monotonicity,[status(thm)],[21859])).
% 9.99/10.28 tff(21861,plain,
% 9.99/10.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 9.99/10.28 inference(transitivity,[status(thm)],[21860, 21858])).
% 9.99/10.28 tff(21862,plain,
% 9.99/10.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 9.99/10.28 inference(quant_inst,[status(thm)],[])).
% 9.99/10.28 tff(21863,plain,
% 9.99/10.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 9.99/10.28 inference(modus_ponens,[status(thm)],[21862, 21861])).
% 9.99/10.28 tff(21864,plain,
% 9.99/10.28 (~b(s(z), s(s(s(z))))),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[21863, 391, 90, 1686, 590, 1685])).
% 9.99/10.28 tff(21865,plain,
% 9.99/10.28 (((~![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)))))),
% 9.99/10.28 inference(rewrite,[status(thm)],[])).
% 9.99/10.28 tff(21866,plain,
% 9.99/10.28 ((~![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)))))),
% 9.99/10.28 inference(quant_inst,[status(thm)],[])).
% 9.99/10.28 tff(21867,plain,
% 9.99/10.28 ((~![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))))),
% 9.99/10.28 inference(modus_ponens,[status(thm)],[21866, 21865])).
% 9.99/10.28 tff(21868,plain,
% 9.99/10.28 ((s(z) = s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[21867, 42, 21864])).
% 9.99/10.28 tff(21869,plain,
% 9.99/10.28 (r(s(z), s(s(s(z))))),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[21868, 21857])).
% 9.99/10.28 tff(21870,plain,
% 9.99/10.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 9.99/10.28 inference(rewrite,[status(thm)],[])).
% 9.99/10.28 tff(21871,plain,
% 9.99/10.28 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 9.99/10.28 inference(rewrite,[status(thm)],[])).
% 9.99/10.28 tff(21872,plain,
% 9.99/10.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 9.99/10.28 inference(monotonicity,[status(thm)],[21871])).
% 9.99/10.28 tff(21873,plain,
% 9.99/10.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 9.99/10.28 inference(transitivity,[status(thm)],[21872, 21870])).
% 9.99/10.28 tff(21874,plain,
% 9.99/10.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 9.99/10.28 inference(quant_inst,[status(thm)],[])).
% 9.99/10.28 tff(21875,plain,
% 9.99/10.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 9.99/10.28 inference(modus_ponens,[status(thm)],[21874, 21873])).
% 9.99/10.28 tff(21876,plain,
% 9.99/10.28 ($false),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[21875, 194, 723, 15705, 15704, 15703])).
% 9.99/10.28 tff(21877,plain,((~r(s(s(s(z))), s(s(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(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.28 tff(21878,plain,
% 9.99/10.28 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[21877, 21869, 21853, 723])).
% 9.99/10.28 tff(21879,plain,
% 9.99/10.28 (b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[17001, 8593])).
% 9.99/10.28 tff(21880,plain,
% 9.99/10.28 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[21879, 21878])).
% 9.99/10.28 tff(21881,assumption,(~(s(s(s(z))) = s(s(z)))), introduced(assumption)).
% 9.99/10.28 tff(21882,plain,
% 9.99/10.28 (r(s(s(s(z))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 9.99/10.28 inference(monotonicity,[status(thm)],[13915])).
% 9.99/10.28 tff(21883,plain,
% 9.99/10.28 (r(s(elem!1), s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 9.99/10.28 inference(symmetry,[status(thm)],[21882])).
% 9.99/10.28 tff(21884,plain,
% 9.99/10.28 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(z)))),
% 9.99/10.28 inference(monotonicity,[status(thm)],[3584])).
% 9.99/10.28 tff(21885,plain,
% 9.99/10.28 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), s(s(z)))),
% 9.99/10.28 inference(transitivity,[status(thm)],[21884, 21883])).
% 9.99/10.28 tff(21886,plain,
% 9.99/10.28 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(z))), s(s(z))))),
% 9.99/10.28 inference(monotonicity,[status(thm)],[21885])).
% 9.99/10.28 tff(21887,plain,
% 9.99/10.28 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 9.99/10.28 inference(monotonicity,[status(thm)],[9025, 9026])).
% 9.99/10.28 tff(21888,plain,
% 9.99/10.28 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 9.99/10.28 inference(symmetry,[status(thm)],[21887])).
% 9.99/10.28 tff(21889,plain,
% 9.99/10.28 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 9.99/10.28 inference(monotonicity,[status(thm)],[21888])).
% 9.99/10.28 tff(21890,plain,
% 9.99/10.28 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[1694, 1685, 90, 1686])).
% 9.99/10.28 tff(21891,plain,
% 9.99/10.28 (~b(s(elem!1), s(s(elem!1)))),
% 9.99/10.28 inference(modus_ponens,[status(thm)],[21890, 21889])).
% 9.99/10.28 tff(21892,plain,
% 9.99/10.28 (r(s(elem!1), s(s(elem!1)))),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[8644, 21891, 8611])).
% 9.99/10.28 tff(21893,plain,
% 9.99/10.28 (~r(s(elem!1), elem!1)),
% 9.99/10.28 inference(unit_resolution,[status(thm)],[14324, 21892, 1064, 364])).
% 9.99/10.28 tff(21894,plain,
% 9.99/10.28 (~r(s(s(s(z))), s(s(z)))),
% 9.99/10.28 inference(modus_ponens,[status(thm)],[21893, 21886])).
% 9.99/10.28 tff(21895,plain,
% 9.99/10.28 (((~![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))))),
% 9.99/10.28 inference(rewrite,[status(thm)],[])).
% 9.99/10.28 tff(21896,plain,
% 9.99/10.28 ((~![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))))),
% 9.99/10.28 inference(quant_inst,[status(thm)],[])).
% 9.99/10.28 tff(21897,plain,
% 9.99/10.28 ((~![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)))),
% 9.99/10.28 inference(modus_ponens,[status(thm)],[21896, 21895])).
% 9.99/10.29 tff(21898,plain,
% 9.99/10.29 (b(s(s(s(z))), s(s(z)))),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[21897, 42, 21894, 21881])).
% 9.99/10.29 tff(21899,plain,
% 9.99/10.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 9.99/10.29 inference(rewrite,[status(thm)],[])).
% 9.99/10.29 tff(21900,plain,
% 9.99/10.29 (((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 9.99/10.29 inference(rewrite,[status(thm)],[])).
% 9.99/10.29 tff(21901,plain,
% 9.99/10.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 9.99/10.29 inference(monotonicity,[status(thm)],[21900])).
% 9.99/10.29 tff(21902,plain,
% 9.99/10.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 9.99/10.29 inference(transitivity,[status(thm)],[21901, 21899])).
% 9.99/10.29 tff(21903,plain,
% 9.99/10.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 9.99/10.29 inference(quant_inst,[status(thm)],[])).
% 9.99/10.29 tff(21904,plain,
% 9.99/10.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 9.99/10.29 inference(modus_ponens,[status(thm)],[21903, 21902])).
% 9.99/10.29 tff(21905,plain,
% 9.99/10.29 ($false),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[21904, 391, 2439, 1233, 21898, 21880, 18784])).
% 9.99/10.29 tff(21906,plain,((~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(z))) = s(s(z))) | (s(z) = s(elem!1)) | (~(elem!1 = s(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(elem!1))) | (s(s(s(s(z)))) = s(s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.29 tff(21907,plain,
% 9.99/10.29 (~b(s(s(s(z))), z)),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[21906, 21801, 21799, 21845, 21760, 21840, 118, 21806, 21827, 21824, 21820, 21819, 90, 21787, 590])).
% 9.99/10.29 tff(21908,plain,
% 9.99/10.29 (~b(s(elem!1), z)),
% 9.99/10.29 inference(modus_ponens,[status(thm)],[21907, 21814])).
% 9.99/10.29 tff(21909,plain,
% 9.99/10.29 (r(s(elem!1), z)),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[549, 21908])).
% 9.99/10.29 tff(21910,plain,
% 9.99/10.29 (~r(s(s(s(elem!1))), s(elem!1))),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[18120, 21909, 411, 21795])).
% 9.99/10.29 tff(21911,plain,
% 9.99/10.29 (~b(s(s(s(elem!1))), s(elem!1))),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[3554, 21909, 184, 3618, 4598, 21730])).
% 9.99/10.29 tff(21912,plain,
% 9.99/10.29 ($false),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[588, 21911, 21910, 21810])).
% 9.99/10.29 tff(21913,plain,(b(elem!1, z) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 9.99/10.29 tff(21914,plain,
% 9.99/10.29 (b(elem!1, z)),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[21913, 232, 15899, 90, 21728, 20263, 59, 127, 2])).
% 9.99/10.29 tff(21915,plain,
% 9.99/10.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 9.99/10.29 inference(rewrite,[status(thm)],[])).
% 9.99/10.29 tff(21916,plain,
% 9.99/10.29 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 9.99/10.29 inference(rewrite,[status(thm)],[])).
% 9.99/10.29 tff(21917,plain,
% 9.99/10.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 9.99/10.29 inference(monotonicity,[status(thm)],[21916])).
% 9.99/10.29 tff(21918,plain,
% 9.99/10.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 9.99/10.29 inference(transitivity,[status(thm)],[21917, 21915])).
% 9.99/10.29 tff(21919,plain,
% 9.99/10.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 9.99/10.29 inference(quant_inst,[status(thm)],[])).
% 9.99/10.29 tff(21920,plain,
% 9.99/10.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 9.99/10.29 inference(modus_ponens,[status(thm)],[21919, 21918])).
% 9.99/10.29 tff(21921,plain,
% 9.99/10.29 ($false),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[21920, 391, 665, 664, 590, 721])).
% 9.99/10.29 tff(21922,plain,((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 9.99/10.29 tff(21923,plain,
% 9.99/10.29 (~b(z, s(z))),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[21922, 21914, 21728, 20263])).
% 9.99/10.29 tff(21924,plain,
% 9.99/10.29 (r(z, s(z))),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[678, 21923])).
% 9.99/10.29 tff(21925,plain,
% 9.99/10.29 (~r(s(s(s(elem!1))), elem!1)),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[18997, 21924, 59, 232])).
% 9.99/10.29 tff(21926,plain,
% 9.99/10.29 (b(s(s(s(elem!1))), elem!1)),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[230, 21925, 127])).
% 9.99/10.29 tff(21927,plain,
% 9.99/10.29 (~r(s(s(s(elem!1))), z)),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[5980, 21924, 59, 232])).
% 9.99/10.29 tff(21928,plain,
% 9.99/10.29 (b(s(s(s(elem!1))), z)),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[377, 21927])).
% 9.99/10.29 tff(21929,plain,
% 9.99/10.29 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[17255, 6124, 2, 10])).
% 9.99/10.29 tff(21930,plain,
% 9.99/10.29 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[1370, 21929, 297])).
% 9.99/10.29 tff(21931,plain,
% 9.99/10.29 (b(s(s(s(elem!1))), elem!1)),
% 9.99/10.29 inference(unit_resolution,[status(thm)],[10519, 4028, 15899, 59, 1])).
% 10.09/10.30 tff(21932,plain,
% 10.09/10.30 (~r(s(s(s(elem!1))), s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[19887, 6124, 15899, 59])).
% 10.09/10.30 tff(21933,plain,
% 10.09/10.30 (b(s(s(s(elem!1))), s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[223, 21932])).
% 10.09/10.30 tff(21934,plain,
% 10.09/10.30 (~b(s(z), elem!1)),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[20387, 21933, 20263, 21931])).
% 10.09/10.30 tff(21935,plain,
% 10.09/10.30 (r(s(z), elem!1)),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[632, 21934, 20272])).
% 10.09/10.30 tff(21936,plain,
% 10.09/10.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 10.09/10.30 inference(rewrite,[status(thm)],[])).
% 10.09/10.30 tff(21937,plain,
% 10.09/10.30 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 10.09/10.30 inference(rewrite,[status(thm)],[])).
% 10.09/10.30 tff(21938,plain,
% 10.09/10.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), elem!1))))),
% 10.09/10.30 inference(monotonicity,[status(thm)],[21937])).
% 10.09/10.30 tff(21939,plain,
% 10.09/10.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 10.09/10.30 inference(transitivity,[status(thm)],[21938, 21936])).
% 10.09/10.30 tff(21940,plain,
% 10.09/10.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 10.09/10.30 inference(quant_inst,[status(thm)],[])).
% 10.09/10.30 tff(21941,plain,
% 10.09/10.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), elem!1))),
% 10.09/10.30 inference(modus_ponens,[status(thm)],[21940, 21939])).
% 10.09/10.30 tff(21942,plain,
% 10.09/10.30 (~r(z, s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[21941, 194, 15899, 6124, 21935])).
% 10.09/10.30 tff(21943,plain,
% 10.09/10.30 (b(z, s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[678, 21942])).
% 10.09/10.30 tff(21944,plain,
% 10.09/10.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 10.09/10.30 inference(rewrite,[status(thm)],[])).
% 10.09/10.30 tff(21945,plain,
% 10.09/10.30 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 10.09/10.30 inference(rewrite,[status(thm)],[])).
% 10.09/10.30 tff(21946,plain,
% 10.09/10.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 10.09/10.30 inference(monotonicity,[status(thm)],[21945])).
% 10.09/10.30 tff(21947,plain,
% 10.09/10.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 10.09/10.30 inference(transitivity,[status(thm)],[21946, 21944])).
% 10.09/10.30 tff(21948,plain,
% 10.09/10.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 10.09/10.30 inference(quant_inst,[status(thm)],[])).
% 10.09/10.30 tff(21949,plain,
% 10.09/10.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 10.09/10.30 inference(modus_ponens,[status(thm)],[21948, 21947])).
% 10.09/10.30 tff(21950,plain,
% 10.09/10.30 ($false),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[21949, 391, 665, 3927, 664, 590, 721])).
% 10.09/10.30 tff(21951,plain,((~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.30 tff(21952,plain,
% 10.09/10.30 (~b(z, s(s(elem!1)))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[21951, 21943, 20263, 21728, 665])).
% 10.09/10.30 tff(21953,plain,
% 10.09/10.30 (r(z, s(s(elem!1)))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[324, 21952])).
% 10.09/10.30 tff(21954,plain,
% 10.09/10.30 (~r(s(s(elem!1)), elem!1)),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[2562, 21953, 15899, 6124])).
% 10.09/10.30 tff(21955,plain,
% 10.09/10.30 (b(s(s(s(elem!1))), z)),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[19694, 4028, 59, 15899, 665])).
% 10.09/10.30 tff(21956,plain,
% 10.09/10.30 (~b(z, s(s(s(s(z)))))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[6325, 21933, 21728, 21955, 90])).
% 10.09/10.30 tff(21957,plain,
% 10.09/10.30 (r(z, s(s(s(s(z)))))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[800, 21956])).
% 10.09/10.30 tff(21958,plain,
% 10.09/10.30 (~r(s(s(s(s(z)))), elem!1)),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[8972, 21957, 15899, 6124])).
% 10.09/10.30 tff(21959,plain,
% 10.09/10.30 (~b(s(s(s(s(z)))), elem!1)),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[14978, 21943, 90, 21728, 665])).
% 10.09/10.30 tff(21960,plain,
% 10.09/10.30 (s(s(s(s(z)))) = elem!1),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[762, 21959, 21958])).
% 10.09/10.30 tff(21961,plain,
% 10.09/10.30 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[717, 21960])).
% 10.09/10.30 tff(21962,plain,
% 10.09/10.30 (~(s(s(elem!1)) = elem!1)),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[451, 21961])).
% 10.09/10.30 tff(21963,plain,
% 10.09/10.30 (b(s(s(elem!1)), elem!1)),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[872, 21962, 21954])).
% 10.09/10.30 tff(21964,plain,
% 10.09/10.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.30 inference(rewrite,[status(thm)],[])).
% 10.09/10.30 tff(21965,plain,
% 10.09/10.30 (((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(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(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.30 inference(rewrite,[status(thm)],[])).
% 10.09/10.30 tff(21966,plain,
% 10.09/10.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 10.09/10.30 inference(monotonicity,[status(thm)],[21965])).
% 10.09/10.30 tff(21967,plain,
% 10.09/10.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.30 inference(transitivity,[status(thm)],[21966, 21964])).
% 10.09/10.30 tff(21968,plain,
% 10.09/10.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.30 inference(quant_inst,[status(thm)],[])).
% 10.09/10.30 tff(21969,plain,
% 10.09/10.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 10.09/10.30 inference(modus_ponens,[status(thm)],[21968, 21967])).
% 10.09/10.30 tff(21970,plain,
% 10.09/10.30 ($false),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[21969, 391, 21931, 21963, 21930, 21728, 20263])).
% 10.09/10.30 tff(21971,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (elem!1 = z) | b(z, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.30 tff(21972,plain,
% 10.09/10.30 (b(elem!1, s(s(s(elem!1))))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[21971, 21914, 90, 15838, 2, 10, 4029])).
% 10.09/10.30 tff(21973,plain,
% 10.09/10.30 ($false),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[17856, 194, 184, 232, 183, 722])).
% 10.09/10.30 tff(21974,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.30 tff(21975,plain,
% 10.09/10.30 (~r(s(s(s(elem!1))), s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[21974, 232, 59, 21924])).
% 10.09/10.30 tff(21976,plain,
% 10.09/10.30 (b(s(s(s(elem!1))), s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[223, 21975])).
% 10.09/10.30 tff(21977,plain,
% 10.09/10.30 (~b(z, s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[21922, 665, 590, 721])).
% 10.09/10.30 tff(21978,plain,
% 10.09/10.30 (r(z, s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[678, 21977])).
% 10.09/10.30 tff(21979,plain,
% 10.09/10.30 (~r(elem!1, s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[14725, 21744, 411, 21978])).
% 10.09/10.30 tff(21980,plain,
% 10.09/10.30 (~r(s(s(elem!1)), s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[4206, 445, 21979])).
% 10.09/10.30 tff(21981,plain,
% 10.09/10.30 (b(s(s(elem!1)), s(z))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[362, 21980])).
% 10.09/10.30 tff(21982,plain,
% 10.09/10.30 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.30 inference(modus_ponens,[status(thm)],[900, 1841])).
% 10.09/10.30 tff(21983,plain,
% 10.09/10.30 (~b(z, s(s(s(s(z)))))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[6325, 1526, 590, 380, 90])).
% 10.09/10.30 tff(21984,plain,
% 10.09/10.30 (r(z, s(s(s(s(z)))))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[800, 21983])).
% 10.09/10.30 tff(21985,plain,
% 10.09/10.30 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 10.09/10.30 inference(monotonicity,[status(thm)],[452])).
% 10.09/10.30 tff(21986,plain,
% 10.09/10.30 (b(s(elem!1), elem!1)),
% 10.09/10.30 inference(modus_ponens,[status(thm)],[900, 21985])).
% 10.09/10.30 tff(21987,plain,
% 10.09/10.30 (~(s(elem!1) = s(s(s(s(z)))))),
% 10.09/10.30 inference(unit_resolution,[status(thm)],[5377, 452, 21769])).
% 10.09/10.30 tff(21988,plain,
% 10.09/10.30 (b(s(elem!1), z)),
% 10.09/10.30 inference(modus_ponens,[status(thm)],[380, 682])).
% 10.09/10.30 tff(21989,plain,
% 10.09/10.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.09/10.31 inference(rewrite,[status(thm)],[])).
% 10.09/10.31 tff(21990,plain,
% 10.09/10.31 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.09/10.31 inference(rewrite,[status(thm)],[])).
% 10.09/10.31 tff(21991,plain,
% 10.09/10.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z))))))))),
% 10.09/10.31 inference(monotonicity,[status(thm)],[21990])).
% 10.09/10.31 tff(21992,plain,
% 10.09/10.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.09/10.31 inference(transitivity,[status(thm)],[21991, 21989])).
% 10.09/10.31 tff(21993,plain,
% 10.09/10.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 10.09/10.31 inference(quant_inst,[status(thm)],[])).
% 10.09/10.31 tff(21994,plain,
% 10.09/10.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 10.09/10.31 inference(modus_ponens,[status(thm)],[21993, 21992])).
% 10.09/10.31 tff(21995,plain,
% 10.09/10.31 ($false),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[21994, 194, 411, 1484, 722, 2032])).
% 10.09/10.31 tff(21996,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.31 tff(21997,plain,
% 10.09/10.31 (~r(elem!1, s(s(s(s(z)))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[21996, 21744, 411, 21978])).
% 10.09/10.31 tff(21998,plain,
% 10.09/10.31 (b(elem!1, s(s(s(s(z)))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[781, 12003, 21997])).
% 10.09/10.31 tff(21999,plain,
% 10.09/10.31 (~b(s(s(s(s(z)))), elem!1)),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[2161, 4805, 665, 21998, 21988, 21987, 21986, 21984])).
% 10.09/10.31 tff(22000,plain,
% 10.09/10.31 (r(s(s(s(s(z)))), elem!1)),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[762, 21999, 718])).
% 10.09/10.31 tff(22001,plain,
% 10.09/10.31 (~(elem!1 = s(s(z)))),
% 10.09/10.31 inference(modus_ponens,[status(thm)],[2689, 11939])).
% 10.09/10.31 tff(22002,plain,
% 10.09/10.31 ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[11439, 194])).
% 10.09/10.31 tff(22003,plain,
% 10.09/10.31 (~r(s(s(z)), z)),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[22002, 1749, 719, 2112])).
% 10.09/10.31 tff(22004,plain,
% 10.09/10.31 (b(s(s(z)), z)),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[1211, 22003])).
% 10.09/10.31 tff(22005,plain,
% 10.09/10.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 10.09/10.31 inference(rewrite,[status(thm)],[])).
% 10.09/10.31 tff(22006,plain,
% 10.09/10.31 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~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))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 10.09/10.31 inference(rewrite,[status(thm)],[])).
% 10.09/10.31 tff(22007,plain,
% 10.09/10.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 10.09/10.31 inference(monotonicity,[status(thm)],[22006])).
% 10.09/10.31 tff(22008,plain,
% 10.09/10.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 10.09/10.31 inference(transitivity,[status(thm)],[22007, 22005])).
% 10.09/10.31 tff(22009,plain,
% 10.09/10.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~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)))))),
% 10.09/10.31 inference(quant_inst,[status(thm)],[])).
% 10.09/10.31 tff(22010,plain,
% 10.09/10.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 10.09/10.31 inference(modus_ponens,[status(thm)],[22009, 22008])).
% 10.09/10.31 tff(22011,plain,
% 10.09/10.31 ($false),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[22010, 391, 381, 1374, 1526, 1235, 2439])).
% 10.09/10.31 tff(22012,plain,((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.31 tff(22013,plain,
% 10.09/10.31 (~b(s(z), s(s(z)))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[22012, 22004, 1526, 1374, 381])).
% 10.09/10.31 tff(22014,plain,
% 10.09/10.31 (r(s(z), s(s(z)))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[1788, 22013])).
% 10.09/10.31 tff(22015,plain,
% 10.09/10.31 (~r(s(z), s(s(s(s(z)))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[20629, 22014, 2112, 1749])).
% 10.09/10.31 tff(22016,plain,
% 10.09/10.31 (b(s(z), s(s(s(s(z)))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[1230, 22015])).
% 10.09/10.31 tff(22017,plain,
% 10.09/10.31 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[9010, 22016, 721, 1526, 448])).
% 10.09/10.31 tff(22018,plain,
% 10.09/10.31 (r(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[1714, 22017])).
% 10.09/10.31 tff(22019,plain,
% 10.09/10.31 (~b(s(s(s(s(z)))), s(z))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[3263, 22016, 1526, 381, 1374])).
% 10.09/10.31 tff(22020,plain,
% 10.09/10.31 (r(s(s(s(s(z)))), s(z))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[749, 22019])).
% 10.09/10.31 tff(22021,plain,
% 10.09/10.31 ($false),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[9076, 22020, 22018, 22014, 1749])).
% 10.09/10.31 tff(22022,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.31 tff(22023,plain,
% 10.09/10.31 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[22022, 21981, 1526, 21982, 721, 448, 22000, 21984])).
% 10.09/10.31 tff(22024,plain,
% 10.09/10.31 (b(s(s(z)), s(s(s(s(z)))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[3652, 22023])).
% 10.09/10.31 tff(22025,plain,
% 10.09/10.31 (~r(elem!1, s(s(s(s(z)))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[21996, 1484, 411, 722])).
% 10.09/10.31 tff(22026,plain,
% 10.09/10.31 (b(elem!1, s(s(s(s(z)))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[781, 770, 22025])).
% 10.09/10.31 tff(22027,plain,
% 10.09/10.31 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[9127, 12408, 3823, 22026])).
% 10.09/10.31 tff(22028,plain,
% 10.09/10.31 (r(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[1714, 22027])).
% 10.09/10.31 tff(22029,plain,
% 10.09/10.31 (~b(z, s(s(s(s(z)))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[4472, 3823, 90, 1235])).
% 10.09/10.31 tff(22030,plain,
% 10.09/10.31 (r(z, s(s(s(s(z)))))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[800, 22029])).
% 10.09/10.31 tff(22031,plain,
% 10.09/10.31 (~b(s(z), z)),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[7203, 3823, 90, 664, 1235])).
% 10.09/10.31 tff(22032,plain,
% 10.09/10.31 (r(s(z), z)),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[180, 22031])).
% 10.09/10.31 tff(22033,plain,
% 10.09/10.31 ($false),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[1705, 22032, 22030, 1216, 1697])).
% 10.09/10.31 tff(22034,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.31 tff(22035,plain,
% 10.09/10.31 (~b(z, s(z))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[22034, 3823, 1216, 1697, 90, 1235])).
% 10.09/10.31 tff(22036,plain,
% 10.09/10.31 (r(z, s(z))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[678, 22035])).
% 10.09/10.31 tff(22037,plain,
% 10.09/10.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 10.09/10.31 inference(rewrite,[status(thm)],[])).
% 10.09/10.31 tff(22038,plain,
% 10.09/10.31 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 10.09/10.31 inference(rewrite,[status(thm)],[])).
% 10.09/10.31 tff(22039,plain,
% 10.09/10.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 10.09/10.31 inference(monotonicity,[status(thm)],[22038])).
% 10.09/10.31 tff(22040,plain,
% 10.09/10.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 10.09/10.31 inference(transitivity,[status(thm)],[22039, 22037])).
% 10.09/10.31 tff(22041,plain,
% 10.09/10.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 10.09/10.31 inference(quant_inst,[status(thm)],[])).
% 10.09/10.31 tff(22042,plain,
% 10.09/10.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 10.09/10.31 inference(modus_ponens,[status(thm)],[22041, 22040])).
% 10.09/10.31 tff(22043,plain,
% 10.09/10.31 ($false),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[22042, 194, 22036, 1216, 1697, 22030])).
% 10.09/10.31 tff(22044,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.31 tff(22045,plain,
% 10.09/10.31 (~b(s(s(z)), z)),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[22044, 22028, 90, 3823, 1216])).
% 10.09/10.31 tff(22046,plain,
% 10.09/10.31 (~r(s(s(z)), z)),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[10610, 2405, 1216, 722])).
% 10.09/10.31 tff(22047,plain,
% 10.09/10.31 (b(s(s(z)), z)),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[1211, 22046])).
% 10.09/10.31 tff(22048,plain,
% 10.09/10.31 (~b(s(z), s(s(z)))),
% 10.09/10.31 inference(unit_resolution,[status(thm)],[22012, 22047, 1526, 1374, 381])).
% 10.09/10.32 tff(22049,plain,
% 10.09/10.32 (r(s(z), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1788, 22048])).
% 10.09/10.32 tff(22050,plain,
% 10.09/10.32 (~r(z, s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[9720, 22049, 722, 2405])).
% 10.09/10.32 tff(22051,plain,
% 10.09/10.32 (b(z, s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[18613, 22050])).
% 10.09/10.32 tff(22052,plain,
% 10.09/10.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[15053, 22051, 90, 22047])).
% 10.09/10.32 tff(22053,plain,
% 10.09/10.32 (~b(z, s(s(s(s(z)))))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[4472, 1235, 90, 3823])).
% 10.09/10.32 tff(22054,plain,
% 10.09/10.32 (r(z, s(s(s(s(z)))))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[800, 22053])).
% 10.09/10.32 tff(22055,plain,
% 10.09/10.32 (~b(z, s(z))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[7203, 1235, 90, 590, 3823])).
% 10.09/10.32 tff(22056,plain,
% 10.09/10.32 (r(z, s(z))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[678, 22055])).
% 10.09/10.32 tff(22057,plain,
% 10.09/10.32 (~r(z, s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[9720, 22056, 1747, 2405])).
% 10.09/10.32 tff(22058,plain,
% 10.09/10.32 (b(z, s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[18613, 22057])).
% 10.09/10.32 tff(22059,plain,
% 10.09/10.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[15053, 22058, 90, 1235])).
% 10.09/10.32 tff(22060,plain,
% 10.09/10.32 (r(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1714, 22059])).
% 10.09/10.32 tff(22061,plain,
% 10.09/10.32 (~r(s(s(s(s(z)))), s(z))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[10673, 22060, 1747, 2405])).
% 10.09/10.32 tff(22062,plain,
% 10.09/10.32 (b(s(s(s(s(z)))), s(z))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[749, 22061])).
% 10.09/10.32 tff(22063,plain,
% 10.09/10.32 (~r(s(z), s(s(s(s(z)))))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[22044, 22060, 90, 3823, 1235])).
% 10.09/10.32 tff(22064,plain,
% 10.09/10.32 (b(s(z), s(s(s(s(z)))))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1230, 22063])).
% 10.09/10.32 tff(22065,plain,
% 10.09/10.32 ($false),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[2097, 22064, 22062, 411, 721, 720, 22054])).
% 10.09/10.32 tff(22066,plain,((~b(s(s(z)), z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.32 tff(22067,plain,
% 10.09/10.32 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[22066, 22049, 90, 721, 590, 411, 720, 2405, 22047])).
% 10.09/10.32 tff(22068,plain,
% 10.09/10.32 (r(s(s(z)), s(s(s(s(z)))))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[3652, 22067])).
% 10.09/10.32 tff(22069,plain,
% 10.09/10.32 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[14395, 22068, 1216, 2405])).
% 10.09/10.32 tff(22070,plain,
% 10.09/10.32 ($false),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1714, 22069, 22052])).
% 10.09/10.32 tff(22071,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.32 tff(22072,plain,
% 10.09/10.32 (~r(s(s(z)), s(z))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[22071, 1216, 90, 721, 590, 411, 720, 722, 1526, 1374, 381])).
% 10.09/10.32 tff(22073,plain,
% 10.09/10.32 (b(s(s(z)), s(z))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[3778, 22072])).
% 10.09/10.32 tff(22074,plain,
% 10.09/10.32 (~b(s(z), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[9961, 22073, 721, 1526, 448])).
% 10.09/10.32 tff(22075,plain,
% 10.09/10.32 (r(s(z), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1788, 22074])).
% 10.09/10.32 tff(22076,plain,
% 10.09/10.32 (~r(s(s(z)), z)),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[11508, 22028, 1216, 22075])).
% 10.09/10.32 tff(22077,plain,
% 10.09/10.32 ($false),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1211, 22076, 22045])).
% 10.09/10.32 tff(22078,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = s(s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), z)) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.32 tff(22079,plain,
% 10.09/10.32 (~r(s(z), s(s(s(s(z)))))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[22078, 22024, 90, 721, 1526, 448, 22001, 21744, 22000, 590, 411, 718, 21978, 21982, 21981])).
% 10.09/10.32 tff(22080,plain,
% 10.09/10.32 (b(s(z), s(s(s(s(z)))))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1230, 22079])).
% 10.09/10.32 tff(22081,plain,
% 10.09/10.32 (~b(s(s(s(s(z)))), s(z))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[3263, 22080, 1526, 21981, 21982])).
% 10.09/10.32 tff(22082,plain,
% 10.09/10.32 (r(s(s(s(s(z)))), s(z))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[749, 22081])).
% 10.09/10.32 tff(22083,plain,
% 10.09/10.32 (~r(elem!1, s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[9117, 22082, 21744, 22000])).
% 10.09/10.32 tff(22084,plain,
% 10.09/10.32 (b(elem!1, s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[3394, 22083, 22001])).
% 10.09/10.32 tff(22085,plain,
% 10.09/10.32 (~b(s(s(z)), s(s(s(elem!1))))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[8561, 22084, 1526, 448, 22080])).
% 10.09/10.32 tff(22086,plain,
% 10.09/10.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[9010, 22080, 721, 1526, 448])).
% 10.09/10.32 tff(22087,plain,
% 10.09/10.32 (r(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1714, 22086])).
% 10.09/10.32 tff(22088,plain,
% 10.09/10.32 (~b(s(z), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[10152, 22082, 21743, 22001, 21435, 21979, 22024, 22080])).
% 10.09/10.32 tff(22089,plain,
% 10.09/10.32 (r(s(z), s(s(z)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1788, 22088])).
% 10.09/10.32 tff(22090,plain,
% 10.09/10.32 (~r(s(s(z)), s(s(s(elem!1))))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[9138, 22089, 22087, 22082])).
% 10.09/10.32 tff(22091,plain,
% 10.09/10.32 ($false),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[11041, 22090, 22085])).
% 10.09/10.32 tff(22092,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.32 tff(22093,plain,
% 10.09/10.32 (~(s(s(elem!1)) = elem!1)),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[22092, 21976, 21972, 20263, 90, 21728, 15899, 21914, 21928, 21926, 2680])).
% 10.09/10.32 tff(22094,plain,
% 10.09/10.32 (~(elem!1 = s(s(elem!1)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1292, 22093])).
% 10.09/10.32 tff(22095,plain,
% 10.09/10.32 (~b(z, s(s(elem!1)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[9087, 21976, 20263, 21728, 21972])).
% 10.09/10.32 tff(22096,plain,
% 10.09/10.32 (r(z, s(s(elem!1)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[324, 22095])).
% 10.09/10.32 tff(22097,plain,
% 10.09/10.32 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[20207, 249, 184, 448, 900, 326])).
% 10.09/10.32 tff(22098,plain,
% 10.09/10.32 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1370, 22097, 297])).
% 10.09/10.32 tff(22099,plain,
% 10.09/10.32 (b(s(s(elem!1)), elem!1)),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[872, 249, 888])).
% 10.09/10.32 tff(22100,plain,
% 10.09/10.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.32 inference(rewrite,[status(thm)],[])).
% 10.09/10.32 tff(22101,plain,
% 10.09/10.32 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(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(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.32 inference(rewrite,[status(thm)],[])).
% 10.09/10.32 tff(22102,plain,
% 10.09/10.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(elem!1))), s(s(elem!1))))))),
% 10.09/10.32 inference(monotonicity,[status(thm)],[22101])).
% 10.09/10.32 tff(22103,plain,
% 10.09/10.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.32 inference(transitivity,[status(thm)],[22102, 22100])).
% 10.09/10.32 tff(22104,plain,
% 10.09/10.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.32 inference(quant_inst,[status(thm)],[])).
% 10.09/10.32 tff(22105,plain,
% 10.09/10.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 10.09/10.32 inference(modus_ponens,[status(thm)],[22104, 22103])).
% 10.09/10.32 tff(22106,plain,
% 10.09/10.32 ($false),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[22105, 391, 900, 22099, 448, 22098])).
% 10.09/10.32 tff(22107,plain,((s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.09/10.32 tff(22108,plain,
% 10.09/10.32 (r(s(s(elem!1)), elem!1)),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[22107, 22093, 21972, 15838, 59, 22096, 21926])).
% 10.09/10.32 tff(22109,plain,
% 10.09/10.32 (~r(elem!1, s(s(elem!1)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1979, 22108, 15899, 22096])).
% 10.09/10.32 tff(22110,plain,
% 10.09/10.32 (b(elem!1, s(s(elem!1)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1307, 22109, 22094])).
% 10.09/10.32 tff(22111,plain,
% 10.09/10.32 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[20207, 22093, 59, 21972, 21926, 22096])).
% 10.09/10.32 tff(22112,plain,
% 10.09/10.32 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[1370, 22111, 15838])).
% 10.09/10.32 tff(22113,plain,
% 10.09/10.32 (~b(s(z), elem!1)),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[20387, 21976, 20263, 21926])).
% 10.09/10.32 tff(22114,plain,
% 10.09/10.32 (r(s(z), elem!1)),
% 10.09/10.32 inference(unit_resolution,[status(thm)],[632, 22113, 20272])).
% 10.09/10.32 tff(22115,plain,
% 10.09/10.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(elem!1)))))),
% 10.09/10.32 inference(rewrite,[status(thm)],[])).
% 10.09/10.32 tff(22116,plain,
% 10.09/10.32 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(elem!1)))))),
% 10.09/10.32 inference(rewrite,[status(thm)],[])).
% 10.09/10.32 tff(22117,plain,
% 10.09/10.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(elem!1))))))),
% 10.09/10.32 inference(monotonicity,[status(thm)],[22116])).
% 10.09/10.32 tff(22118,plain,
% 10.09/10.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(elem!1)))))),
% 10.09/10.33 inference(transitivity,[status(thm)],[22117, 22115])).
% 10.09/10.33 tff(22119,plain,
% 10.09/10.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 10.09/10.33 inference(quant_inst,[status(thm)],[])).
% 10.09/10.33 tff(22120,plain,
% 10.09/10.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(elem!1))))),
% 10.09/10.33 inference(modus_ponens,[status(thm)],[22119, 22118])).
% 10.09/10.33 tff(22121,plain,
% 10.09/10.33 ($false),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[22120, 194, 340, 326, 1484, 722])).
% 10.09/10.33 tff(22122,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.33 tff(22123,plain,
% 10.09/10.33 (~r(s(s(elem!1)), s(z))),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[22122, 22096, 22114, 21924])).
% 10.09/10.33 tff(22124,plain,
% 10.09/10.33 (b(s(s(elem!1)), s(z))),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[362, 22123])).
% 10.09/10.33 tff(22125,plain,
% 10.09/10.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.33 inference(rewrite,[status(thm)],[])).
% 10.09/10.33 tff(22126,plain,
% 10.09/10.33 (((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.33 inference(rewrite,[status(thm)],[])).
% 10.09/10.33 tff(22127,plain,
% 10.09/10.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 10.09/10.33 inference(monotonicity,[status(thm)],[22126])).
% 10.09/10.33 tff(22128,plain,
% 10.09/10.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.33 inference(transitivity,[status(thm)],[22127, 22125])).
% 10.09/10.33 tff(22129,plain,
% 10.09/10.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 10.09/10.33 inference(quant_inst,[status(thm)],[])).
% 10.09/10.33 tff(22130,plain,
% 10.09/10.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 10.09/10.33 inference(modus_ponens,[status(thm)],[22129, 22128])).
% 10.09/10.33 tff(22131,plain,
% 10.09/10.33 ($false),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[22130, 391, 22124, 21972, 22112, 22110, 21728])).
% 10.09/10.33 tff(22132,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = elem!1) | (elem!1 = z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.33 tff(22133,plain,
% 10.09/10.33 (~r(s(z), s(s(s(elem!1))))),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[22132, 127, 90, 2, 10])).
% 10.09/10.33 tff(22134,plain,
% 10.09/10.33 (b(s(z), s(s(s(elem!1))))),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[247, 22133])).
% 10.09/10.33 tff(22135,plain,
% 10.09/10.33 (~r(elem!1, s(s(s(elem!1))))),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[21740, 21674, 411, 590, 721, 530, 184])).
% 10.09/10.33 tff(22136,plain,
% 10.09/10.33 (b(elem!1, s(s(s(elem!1))))),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[424, 22135, 4029])).
% 10.09/10.33 tff(22137,plain,
% 10.09/10.33 ($false),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[906, 391, 21674, 22136, 379, 721])).
% 10.09/10.33 tff(22138,plain,((~r(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.09/10.33 tff(22139,plain,
% 10.09/10.33 (~r(elem!1, z)),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[22138, 22134, 20263, 15899, 21728, 59, 127])).
% 10.09/10.33 tff(22140,plain,
% 10.09/10.33 (b(elem!1, z)),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[526, 22139, 2])).
% 10.09/10.33 tff(22141,plain,
% 10.09/10.33 (b(elem!1, s(s(s(elem!1))))),
% 10.09/10.33 inference(unit_resolution,[status(thm)],[21971, 22140, 90, 15838, 2, 10, 4029])).
% 10.09/10.33 tff(22142,plain,
% 10.09/10.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.33 inference(rewrite,[status(thm)],[])).
% 10.09/10.33 tff(22143,plain,
% 10.09/10.33 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.33 inference(rewrite,[status(thm)],[])).
% 10.09/10.33 tff(22144,plain,
% 10.09/10.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 10.09/10.33 inference(monotonicity,[status(thm)],[22143])).
% 10.09/10.33 tff(22145,plain,
% 10.09/10.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.33 inference(transitivity,[status(thm)],[22144, 22142])).
% 10.09/10.33 tff(22146,plain,
% 10.09/10.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 10.09/10.34 inference(quant_inst,[status(thm)],[])).
% 10.09/10.34 tff(22147,plain,
% 10.09/10.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 10.09/10.34 inference(modus_ponens,[status(thm)],[22146, 22145])).
% 10.09/10.34 tff(22148,plain,
% 10.09/10.34 ($false),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[22147, 391, 665, 900, 448, 379, 721])).
% 10.09/10.34 tff(22149,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.34 tff(22150,plain,
% 10.09/10.34 (~b(s(s(s(elem!1))), elem!1)),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[22149, 22140, 20263, 22134, 22141])).
% 10.09/10.34 tff(22151,plain,
% 10.09/10.34 (r(s(s(s(elem!1))), elem!1)),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[230, 22150, 127])).
% 10.09/10.34 tff(22152,plain,
% 10.09/10.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))))),
% 10.09/10.34 inference(rewrite,[status(thm)],[])).
% 10.09/10.34 tff(22153,plain,
% 10.09/10.34 (((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))))),
% 10.09/10.34 inference(rewrite,[status(thm)],[])).
% 10.09/10.34 tff(22154,plain,
% 10.09/10.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z))))))),
% 10.09/10.34 inference(monotonicity,[status(thm)],[22153])).
% 10.09/10.34 tff(22155,plain,
% 10.09/10.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))))),
% 10.09/10.34 inference(transitivity,[status(thm)],[22154, 22152])).
% 10.09/10.34 tff(22156,plain,
% 10.09/10.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 10.09/10.34 inference(quant_inst,[status(thm)],[])).
% 10.09/10.34 tff(22157,plain,
% 10.09/10.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z))))),
% 10.09/10.34 inference(modus_ponens,[status(thm)],[22156, 22155])).
% 10.09/10.34 tff(22158,plain,
% 10.09/10.34 ($false),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[22157, 194, 184, 183, 722, 1747])).
% 10.09/10.34 tff(22159,plain,((~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.34 tff(22160,plain,
% 10.09/10.34 (~r(s(z), s(s(z)))),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[22159, 183, 184, 21978])).
% 10.09/10.34 tff(22161,plain,
% 10.09/10.34 (b(s(z), s(s(z)))),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[1788, 22160])).
% 10.09/10.34 tff(22162,plain,
% 10.09/10.34 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[16185, 194, 411, 174, 2616])).
% 10.09/10.34 tff(22163,plain,
% 10.09/10.34 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[1354, 42, 270, 22162])).
% 10.09/10.34 tff(22164,plain,
% 10.09/10.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.34 inference(rewrite,[status(thm)],[])).
% 10.09/10.34 tff(22165,plain,
% 10.09/10.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.09/10.34 inference(quant_inst,[status(thm)],[])).
% 10.09/10.34 tff(22166,plain,
% 10.09/10.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 10.09/10.34 inference(modus_ponens,[status(thm)],[22165, 22164])).
% 10.09/10.34 tff(22167,plain,
% 10.09/10.34 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[22166, 194, 411, 174, 2616])).
% 10.09/10.34 tff(22168,plain,
% 10.09/10.34 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[1370, 22167, 7463])).
% 10.09/10.34 tff(22169,plain,
% 10.09/10.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.34 inference(rewrite,[status(thm)],[])).
% 10.09/10.34 tff(22170,plain,
% 10.09/10.34 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.34 inference(rewrite,[status(thm)],[])).
% 10.09/10.34 tff(22171,plain,
% 10.09/10.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 10.09/10.34 inference(monotonicity,[status(thm)],[22170])).
% 10.09/10.34 tff(22172,plain,
% 10.09/10.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.34 inference(transitivity,[status(thm)],[22171, 22169])).
% 10.09/10.34 tff(22173,plain,
% 10.09/10.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 10.09/10.34 inference(quant_inst,[status(thm)],[])).
% 10.09/10.34 tff(22174,plain,
% 10.09/10.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 10.09/10.34 inference(modus_ponens,[status(thm)],[22173, 22172])).
% 10.09/10.34 tff(22175,plain,
% 10.09/10.34 ($false),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[22174, 391, 448, 22168, 644, 379, 22163])).
% 10.09/10.34 tff(22176,plain,((~r(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.34 tff(22177,plain,
% 10.09/10.34 (~r(s(s(elem!1)), z)),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[22176, 174, 411, 379, 315, 448, 644])).
% 10.09/10.34 tff(22178,plain,
% 10.09/10.34 (b(s(s(elem!1)), z)),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[2629, 22177])).
% 10.09/10.34 tff(22179,plain,
% 10.09/10.34 (~b(z, s(s(elem!1)))),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[19801, 22178, 590, 665, 644])).
% 10.09/10.34 tff(22180,plain,
% 10.09/10.34 (r(z, s(s(elem!1)))),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[324, 22179])).
% 10.09/10.34 tff(22181,plain,
% 10.09/10.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.34 inference(rewrite,[status(thm)],[])).
% 10.09/10.34 tff(22182,plain,
% 10.09/10.34 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.34 inference(rewrite,[status(thm)],[])).
% 10.09/10.34 tff(22183,plain,
% 10.09/10.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 10.09/10.34 inference(monotonicity,[status(thm)],[22182])).
% 10.09/10.34 tff(22184,plain,
% 10.09/10.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.34 inference(transitivity,[status(thm)],[22183, 22181])).
% 10.09/10.34 tff(22185,plain,
% 10.09/10.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 10.09/10.34 inference(quant_inst,[status(thm)],[])).
% 10.09/10.34 tff(22186,plain,
% 10.09/10.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 10.09/10.34 inference(modus_ponens,[status(thm)],[22185, 22184])).
% 10.09/10.34 tff(22187,plain,
% 10.09/10.34 ($false),
% 10.09/10.34 inference(unit_resolution,[status(thm)],[22186, 391, 448, 1374, 379, 328, 721])).
% 10.09/10.34 tff(22188,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.35 tff(22189,plain,
% 10.09/10.35 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[22188, 1374, 448, 379, 721])).
% 10.09/10.35 tff(22190,plain,
% 10.09/10.35 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[1354, 42, 22189, 270])).
% 10.09/10.35 tff(22191,plain,
% 10.09/10.35 (~r(s(s(elem!1)), z)),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[16187, 22190, 174, 411])).
% 10.09/10.35 tff(22192,plain,
% 10.09/10.35 (b(s(s(elem!1)), z)),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[2629, 22191])).
% 10.09/10.35 tff(22193,plain,
% 10.09/10.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.35 inference(rewrite,[status(thm)],[])).
% 10.09/10.35 tff(22194,plain,
% 10.09/10.35 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.35 inference(rewrite,[status(thm)],[])).
% 10.09/10.35 tff(22195,plain,
% 10.09/10.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 10.09/10.35 inference(monotonicity,[status(thm)],[22194])).
% 10.09/10.35 tff(22196,plain,
% 10.09/10.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.35 inference(transitivity,[status(thm)],[22195, 22193])).
% 10.09/10.35 tff(22197,plain,
% 10.09/10.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 10.09/10.35 inference(quant_inst,[status(thm)],[])).
% 10.09/10.35 tff(22198,plain,
% 10.09/10.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 10.09/10.35 inference(modus_ponens,[status(thm)],[22197, 22196])).
% 10.09/10.35 tff(22199,plain,
% 10.09/10.35 ($false),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[22198, 391, 448, 1374, 379, 22192, 721])).
% 10.09/10.35 tff(22200,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.35 tff(22201,plain,
% 10.09/10.35 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[22200, 174, 411, 721, 379, 448, 315])).
% 10.09/10.35 tff(22202,plain,
% 10.09/10.35 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[1370, 22201, 297])).
% 10.09/10.35 tff(22203,plain,
% 10.09/10.35 (~r(s(s(elem!1)), s(z))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[7327, 22180, 174, 22202])).
% 10.09/10.35 tff(22204,plain,
% 10.09/10.35 (b(s(s(elem!1)), s(z))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[362, 22203])).
% 10.09/10.35 tff(22205,plain,
% 10.09/10.35 (s(s(elem!1)) = elem!1),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[1324, 22204, 411, 721, 644, 22180, 665])).
% 10.09/10.35 tff(22206,plain,
% 10.09/10.35 (s(s(s(elem!1))) = s(elem!1)),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[451, 22205])).
% 10.09/10.35 tff(22207,plain,
% 10.09/10.35 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 10.09/10.35 inference(monotonicity,[status(thm)],[22206])).
% 10.09/10.35 tff(22208,plain,
% 10.09/10.35 (r(s(elem!1), s(z))),
% 10.09/10.35 inference(modus_ponens,[status(thm)],[183, 22207])).
% 10.09/10.35 tff(22209,plain,
% 10.09/10.35 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 10.09/10.35 inference(monotonicity,[status(thm)],[22206])).
% 10.09/10.35 tff(22210,plain,
% 10.09/10.35 (r(s(elem!1), z)),
% 10.09/10.35 inference(modus_ponens,[status(thm)],[174, 22209])).
% 10.09/10.35 tff(22211,plain,
% 10.09/10.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))),
% 10.09/10.35 inference(rewrite,[status(thm)],[])).
% 10.09/10.35 tff(22212,plain,
% 10.09/10.35 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))),
% 10.09/10.35 inference(rewrite,[status(thm)],[])).
% 10.09/10.35 tff(22213,plain,
% 10.09/10.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z))))))),
% 10.09/10.35 inference(monotonicity,[status(thm)],[22212])).
% 10.09/10.35 tff(22214,plain,
% 10.09/10.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))),
% 10.09/10.35 inference(transitivity,[status(thm)],[22213, 22211])).
% 10.09/10.35 tff(22215,plain,
% 10.09/10.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 10.09/10.35 inference(quant_inst,[status(thm)],[])).
% 10.09/10.35 tff(22216,plain,
% 10.09/10.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z))))),
% 10.09/10.35 inference(modus_ponens,[status(thm)],[22215, 22214])).
% 10.09/10.35 tff(22217,plain,
% 10.09/10.35 ($false),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[22216, 194, 1628, 722, 1747, 13481])).
% 10.09/10.35 tff(22218,plain,((~r(s(z), s(s(z)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.35 tff(22219,plain,
% 10.09/10.35 (~r(s(z), s(s(z)))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[22218, 22210, 21978, 22208])).
% 10.09/10.35 tff(22220,plain,
% 10.09/10.35 (b(s(z), s(s(z)))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[1788, 22219])).
% 10.09/10.35 tff(22221,plain,
% 10.09/10.35 (~r(s(z), s(s(s(s(z)))))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[16377, 174, 21978, 183])).
% 10.09/10.35 tff(22222,plain,
% 10.09/10.35 (b(s(z), s(s(s(s(z)))))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[1230, 22221])).
% 10.09/10.35 tff(22223,plain,
% 10.09/10.35 (~b(z, s(s(s(s(z)))))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[14881, 644, 90, 590, 665])).
% 10.09/10.35 tff(22224,plain,
% 10.09/10.35 (r(z, s(s(s(s(z)))))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[800, 22223])).
% 10.09/10.35 tff(22225,plain,
% 10.09/10.35 (~(s(s(s(s(z)))) = elem!1)),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[717, 22206])).
% 10.09/10.35 tff(22226,plain,
% 10.09/10.35 (~b(s(s(s(s(z)))), s(z))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[2097, 22225, 411, 721, 22224, 22222])).
% 10.09/10.35 tff(22227,plain,
% 10.09/10.35 (~(elem!1 = s(s(z)))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[9032, 22226, 22204])).
% 10.09/10.35 tff(22228,plain,
% 10.09/10.35 (r(s(elem!1), elem!1)),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[472, 22206, 233])).
% 10.09/10.35 tff(22229,plain,
% 10.09/10.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))))),
% 10.09/10.35 inference(rewrite,[status(thm)],[])).
% 10.09/10.35 tff(22230,plain,
% 10.09/10.35 (((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))))),
% 10.09/10.35 inference(rewrite,[status(thm)],[])).
% 10.09/10.35 tff(22231,plain,
% 10.09/10.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z))))))),
% 10.09/10.35 inference(monotonicity,[status(thm)],[22230])).
% 10.09/10.35 tff(22232,plain,
% 10.09/10.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))))),
% 10.09/10.35 inference(transitivity,[status(thm)],[22231, 22229])).
% 10.09/10.35 tff(22233,plain,
% 10.09/10.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 10.09/10.35 inference(quant_inst,[status(thm)],[])).
% 10.09/10.35 tff(22234,plain,
% 10.09/10.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z))))),
% 10.09/10.35 inference(modus_ponens,[status(thm)],[22233, 22232])).
% 10.09/10.35 tff(22235,plain,
% 10.09/10.35 ($false),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[22234, 194, 411, 485, 1628, 1748])).
% 10.09/10.35 tff(22236,plain,((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.35 tff(22237,plain,
% 10.09/10.35 (~r(elem!1, s(s(z)))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[22236, 22228, 411, 22210])).
% 10.09/10.35 tff(22238,plain,
% 10.09/10.35 (b(elem!1, s(s(z)))),
% 10.09/10.35 inference(unit_resolution,[status(thm)],[3394, 22237, 22227])).
% 10.09/10.35 tff(22239,plain,
% 10.09/10.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.09/10.35 inference(rewrite,[status(thm)],[])).
% 10.09/10.35 tff(22240,plain,
% 10.09/10.35 (((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.09/10.35 inference(rewrite,[status(thm)],[])).
% 10.09/10.35 tff(22241,plain,
% 10.09/10.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z))))))))),
% 10.09/10.36 inference(monotonicity,[status(thm)],[22240])).
% 10.09/10.36 tff(22242,plain,
% 10.09/10.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.09/10.36 inference(transitivity,[status(thm)],[22241, 22239])).
% 10.09/10.36 tff(22243,plain,
% 10.09/10.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 10.09/10.36 inference(quant_inst,[status(thm)],[])).
% 10.09/10.36 tff(22244,plain,
% 10.09/10.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 10.09/10.36 inference(modus_ponens,[status(thm)],[22243, 22242])).
% 10.09/10.36 tff(22245,plain,
% 10.09/10.36 ($false),
% 10.09/10.36 inference(unit_resolution,[status(thm)],[22244, 194, 411, 174, 233, 2032])).
% 10.09/10.36 tff(22246,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.36 tff(22247,plain,
% 10.09/10.36 (~r(elem!1, s(s(s(s(z)))))),
% 10.09/10.36 inference(unit_resolution,[status(thm)],[22246, 174, 411, 233])).
% 10.09/10.36 tff(22248,plain,
% 10.09/10.36 (r(s(s(s(s(z)))), elem!1)),
% 10.09/10.36 inference(unit_resolution,[status(thm)],[20438, 22225, 721, 22247, 22222])).
% 10.09/10.36 tff(22249,plain,
% 10.09/10.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 10.09/10.36 inference(rewrite,[status(thm)],[])).
% 10.09/10.36 tff(22250,plain,
% 10.09/10.36 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 10.09/10.36 inference(rewrite,[status(thm)],[])).
% 10.09/10.36 tff(22251,plain,
% 10.09/10.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 10.09/10.36 inference(monotonicity,[status(thm)],[22250])).
% 10.09/10.36 tff(22252,plain,
% 10.09/10.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 10.09/10.36 inference(transitivity,[status(thm)],[22251, 22249])).
% 10.09/10.36 tff(22253,plain,
% 10.09/10.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 10.09/10.36 inference(quant_inst,[status(thm)],[])).
% 10.09/10.36 tff(22254,plain,
% 10.09/10.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 10.09/10.36 inference(modus_ponens,[status(thm)],[22253, 22252])).
% 10.09/10.36 tff(22255,plain,
% 10.09/10.36 (~r(z, s(s(z)))),
% 10.09/10.36 inference(unit_resolution,[status(thm)],[22254, 194, 1749, 2112, 719])).
% 10.09/10.36 tff(22256,plain,
% 10.09/10.36 (b(z, s(s(z)))),
% 10.09/10.36 inference(unit_resolution,[status(thm)],[18613, 22255])).
% 10.09/10.36 tff(22257,plain,
% 10.09/10.36 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 10.09/10.36 inference(rewrite,[status(thm)],[])).
% 10.09/10.36 tff(22258,plain,
% 10.09/10.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 10.09/10.36 inference(monotonicity,[status(thm)],[22257])).
% 10.09/10.36 tff(22259,plain,
% 10.09/10.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 10.09/10.36 inference(transitivity,[status(thm)],[22258, 17084])).
% 10.09/10.36 tff(22260,plain,
% 10.09/10.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 10.09/10.36 inference(quant_inst,[status(thm)],[])).
% 10.09/10.36 tff(22261,plain,
% 10.09/10.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 10.09/10.36 inference(modus_ponens,[status(thm)],[22260, 22259])).
% 10.09/10.36 tff(22262,plain,
% 10.09/10.36 ($false),
% 10.09/10.36 inference(unit_resolution,[status(thm)],[22261, 391, 22004, 2439, 590, 22256])).
% 10.09/10.36 tff(22263,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.36 tff(22264,plain,
% 10.09/10.36 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.09/10.36 inference(unit_resolution,[status(thm)],[22263, 22220, 590, 22248, 22224])).
% 10.09/10.36 tff(22265,plain,
% 10.09/10.36 (b(s(s(z)), s(s(s(s(z)))))),
% 10.09/10.36 inference(unit_resolution,[status(thm)],[3652, 22264])).
% 10.09/10.36 tff(22266,plain,
% 10.09/10.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 10.09/10.36 inference(rewrite,[status(thm)],[])).
% 10.09/10.36 tff(22267,plain,
% 10.09/10.36 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 10.09/10.36 inference(rewrite,[status(thm)],[])).
% 10.09/10.36 tff(22268,plain,
% 10.09/10.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z))))))),
% 10.09/10.36 inference(monotonicity,[status(thm)],[22267])).
% 10.09/10.37 tff(22269,plain,
% 10.09/10.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 10.09/10.37 inference(transitivity,[status(thm)],[22268, 22266])).
% 10.09/10.37 tff(22270,plain,
% 10.09/10.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))),
% 10.09/10.37 inference(quant_inst,[status(thm)],[])).
% 10.09/10.37 tff(22271,plain,
% 10.09/10.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z))))),
% 10.09/10.37 inference(modus_ponens,[status(thm)],[22270, 22269])).
% 10.09/10.37 tff(22272,plain,
% 10.09/10.37 ($false),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[22271, 391, 22265, 90, 22238, 22220, 721])).
% 10.09/10.37 tff(22273,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.37 tff(22274,plain,
% 10.09/10.37 (~r(s(s(s(elem!1))), z)),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[22273, 644, 721, 411, 590, 183, 233, 90, 665, 297, 379, 448])).
% 10.09/10.37 tff(22275,plain,
% 10.09/10.37 (b(s(s(s(elem!1))), z)),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[377, 22274])).
% 10.09/10.37 tff(22276,plain,
% 10.09/10.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.37 inference(rewrite,[status(thm)],[])).
% 10.09/10.37 tff(22277,plain,
% 10.09/10.37 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.37 inference(rewrite,[status(thm)],[])).
% 10.09/10.37 tff(22278,plain,
% 10.09/10.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 10.09/10.37 inference(monotonicity,[status(thm)],[22277])).
% 10.09/10.37 tff(22279,plain,
% 10.09/10.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 10.09/10.37 inference(transitivity,[status(thm)],[22278, 22276])).
% 10.09/10.37 tff(22280,plain,
% 10.09/10.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 10.09/10.37 inference(quant_inst,[status(thm)],[])).
% 10.09/10.37 tff(22281,plain,
% 10.09/10.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 10.09/10.37 inference(modus_ponens,[status(thm)],[22280, 22279])).
% 10.09/10.37 tff(22282,plain,
% 10.09/10.37 ($false),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[22281, 391, 380, 448, 3927, 644, 379])).
% 10.09/10.37 tff(22283,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.37 tff(22284,plain,
% 10.09/10.37 (~b(z, s(s(elem!1)))),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[22283, 22275, 448, 644, 379])).
% 10.09/10.37 tff(22285,plain,
% 10.09/10.37 (r(z, s(s(elem!1)))),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[324, 22284])).
% 10.09/10.37 tff(22286,plain,
% 10.09/10.37 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[1418, 22285, 184, 183])).
% 10.09/10.37 tff(22287,plain,
% 10.09/10.37 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[1356, 22286, 315])).
% 10.09/10.37 tff(22288,plain,
% 10.09/10.37 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[22188, 22287, 721, 379, 448])).
% 10.09/10.37 tff(22289,plain,
% 10.09/10.37 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[1370, 22288, 297])).
% 10.09/10.37 tff(22290,plain,
% 10.09/10.37 (~r(s(s(elem!1)), s(z))),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[348, 22289, 184, 22285])).
% 10.09/10.37 tff(22291,plain,
% 10.09/10.37 (b(s(s(elem!1)), s(z))),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[362, 22290])).
% 10.09/10.37 tff(22292,plain,
% 10.09/10.37 (s(s(elem!1)) = elem!1),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[1324, 22291, 411, 721, 644, 22285, 665])).
% 10.09/10.37 tff(22293,plain,
% 10.09/10.37 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 10.09/10.37 inference(monotonicity,[status(thm)],[22292])).
% 10.09/10.37 tff(22294,plain,
% 10.09/10.37 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 10.09/10.37 inference(monotonicity,[status(thm)],[22293])).
% 10.09/10.37 tff(22295,plain,
% 10.09/10.37 (~(elem!1 = s(s(z)))),
% 10.09/10.37 inference(modus_ponens,[status(thm)],[2689, 22294])).
% 10.09/10.37 tff(22296,plain,
% 10.09/10.37 (s(s(s(elem!1))) = s(elem!1)),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[451, 22292])).
% 10.09/10.37 tff(22297,plain,
% 10.09/10.37 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 10.09/10.37 inference(monotonicity,[status(thm)],[22296])).
% 10.09/10.37 tff(22298,plain,
% 10.09/10.37 (r(s(elem!1), s(z))),
% 10.09/10.37 inference(modus_ponens,[status(thm)],[183, 22297])).
% 10.09/10.37 tff(22299,plain,
% 10.09/10.37 (~b(z, s(elem!1))),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[652, 22275, 379, 448, 644])).
% 10.09/10.37 tff(22300,plain,
% 10.09/10.37 (r(z, s(elem!1))),
% 10.09/10.37 inference(unit_resolution,[status(thm)],[566, 22299])).
% 10.09/10.37 tff(22301,plain,
% 10.09/10.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 10.09/10.37 inference(rewrite,[status(thm)],[])).
% 10.09/10.37 tff(22302,plain,
% 10.09/10.37 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 10.09/10.37 inference(rewrite,[status(thm)],[])).
% 10.09/10.37 tff(22303,plain,
% 10.09/10.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 10.09/10.37 inference(monotonicity,[status(thm)],[22302])).
% 10.09/10.37 tff(22304,plain,
% 10.09/10.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 10.09/10.37 inference(transitivity,[status(thm)],[22303, 22301])).
% 10.09/10.37 tff(22305,plain,
% 10.09/10.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 10.09/10.37 inference(quant_inst,[status(thm)],[])).
% 10.09/10.37 tff(22306,plain,
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% 10.09/10.38 tff(22391,plain,
% 10.09/10.38 (~r(z, s(s(s(s(z)))))),
% 10.09/10.38 inference(unit_resolution,[status(thm)],[3852, 22390, 20445, 184, 90, 125, 22382, 22386])).
% 10.09/10.38 tff(22392,plain,
% 10.09/10.38 (b(z, s(s(s(s(z)))))),
% 10.09/10.38 inference(unit_resolution,[status(thm)],[800, 22391])).
% 10.09/10.38 tff(22393,plain,
% 10.09/10.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 10.09/10.38 inference(rewrite,[status(thm)],[])).
% 10.09/10.38 tff(22394,plain,
% 10.09/10.38 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 10.09/10.38 inference(rewrite,[status(thm)],[])).
% 10.09/10.38 tff(22395,plain,
% 10.09/10.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))))),
% 10.09/10.38 inference(monotonicity,[status(thm)],[22394])).
% 10.09/10.38 tff(22396,plain,
% 10.09/10.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 10.09/10.38 inference(transitivity,[status(thm)],[22395, 22393])).
% 10.09/10.38 tff(22397,plain,
% 10.09/10.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 10.09/10.38 inference(quant_inst,[status(thm)],[])).
% 10.09/10.38 tff(22398,plain,
% 10.09/10.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))),
% 10.09/10.38 inference(modus_ponens,[status(thm)],[22397, 22396])).
% 10.09/10.38 tff(22399,plain,
% 10.09/10.38 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))),
% 10.09/10.38 inference(unit_resolution,[status(thm)],[22398, 391])).
% 10.09/10.38 tff(22400,plain,
% 10.09/10.38 (~b(z, s(s(z)))),
% 10.09/10.38 inference(unit_resolution,[status(thm)],[22399, 22392, 721, 22384, 22382])).
% 10.09/10.39 tff(22401,plain,
% 10.09/10.39 (b(elem!1, s(s(z)))),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[3394, 22390, 3820])).
% 10.09/10.39 tff(22402,plain,
% 10.09/10.39 (~b(s(s(z)), elem!1)),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[11012, 22401, 22384, 22386])).
% 10.09/10.39 tff(22403,plain,
% 10.09/10.39 (r(s(s(z)), elem!1)),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[4730, 22402, 18819])).
% 10.09/10.39 tff(22404,plain,
% 10.09/10.39 (~r(z, s(s(z)))),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[8513, 22403, 530, 411])).
% 10.09/10.39 tff(22405,plain,
% 10.09/10.39 ($false),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[18613, 22404, 22400])).
% 10.09/10.39 tff(22406,plain,((~r(s(s(z)), s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.39 tff(22407,plain,
% 10.09/10.39 (~r(s(s(z)), s(z))),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[22406, 22376, 411, 721, 184, 90, 125, 174, 590, 530, 22378])).
% 10.09/10.39 tff(22408,plain,
% 10.09/10.39 (b(s(s(z)), s(z))),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[3778, 22407])).
% 10.09/10.39 tff(22409,plain,
% 10.09/10.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 10.09/10.39 inference(rewrite,[status(thm)],[])).
% 10.09/10.39 tff(22410,plain,
% 10.09/10.39 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 10.09/10.39 inference(rewrite,[status(thm)],[])).
% 10.09/10.39 tff(22411,plain,
% 10.09/10.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 10.09/10.39 inference(monotonicity,[status(thm)],[22410])).
% 10.09/10.39 tff(22412,plain,
% 10.09/10.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 10.09/10.39 inference(transitivity,[status(thm)],[22411, 22409])).
% 10.09/10.39 tff(22413,plain,
% 10.09/10.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 10.09/10.39 inference(quant_inst,[status(thm)],[])).
% 10.09/10.39 tff(22414,plain,
% 10.09/10.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 10.09/10.39 inference(modus_ponens,[status(thm)],[22413, 22412])).
% 10.09/10.39 tff(22415,plain,
% 10.09/10.39 (~b(z, s(s(z)))),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[22414, 391, 22408, 22376, 590])).
% 10.09/10.39 tff(22416,plain,
% 10.09/10.39 (r(z, s(s(z)))),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[18613, 22415])).
% 10.09/10.39 tff(22417,plain,
% 10.09/10.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.09/10.39 inference(rewrite,[status(thm)],[])).
% 10.09/10.39 tff(22418,plain,
% 10.09/10.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.09/10.39 inference(quant_inst,[status(thm)],[])).
% 10.09/10.39 tff(22419,plain,
% 10.09/10.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 10.09/10.39 inference(modus_ponens,[status(thm)],[22418, 22417])).
% 10.09/10.39 tff(22420,plain,
% 10.09/10.39 (~b(s(s(z)), s(s(s(elem!1))))),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[22419, 391, 20468, 22408, 22376, 590])).
% 10.09/10.39 tff(22421,plain,
% 10.09/10.39 (~b(s(s(z)), elem!1)),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[20537, 22420, 125])).
% 10.09/10.39 tff(22422,plain,
% 10.09/10.39 (r(s(s(z)), elem!1)),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[4730, 22421, 18819])).
% 10.09/10.39 tff(22423,plain,
% 10.09/10.39 ($false),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[8513, 22422, 22416, 530, 411])).
% 10.09/10.39 tff(22424,plain,(b(s(z), s(s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 10.09/10.39 tff(22425,plain,
% 10.09/10.39 (b(s(z), s(s(s(elem!1))))),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[22424, 530, 411, 3807, 590, 721, 184, 90, 22374])).
% 10.09/10.39 tff(22426,plain,
% 10.09/10.39 (b(s(z), elem!1)),
% 10.09/10.39 inference(modus_ponens,[status(thm)],[22425, 14867])).
% 10.09/10.39 tff(22427,plain,
% 10.09/10.39 (~b(s(s(s(s(z)))), s(z))),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[20920, 22426, 90, 721, 664])).
% 10.09/10.39 tff(22428,plain,
% 10.09/10.39 (r(s(s(s(s(z)))), s(z))),
% 10.09/10.39 inference(unit_resolution,[status(thm)],[749, 22427])).
% 10.09/10.39 tff(22429,plain,
% 10.09/10.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.09/10.39 inference(rewrite,[status(thm)],[])).
% 10.09/10.39 tff(22430,plain,
% 10.09/10.39 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.09/10.39 inference(rewrite,[status(thm)],[])).
% 10.09/10.39 tff(22431,plain,
% 10.09/10.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 10.09/10.39 inference(monotonicity,[status(thm)],[22430])).
% 10.09/10.39 tff(22432,plain,
% 10.09/10.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.09/10.39 inference(transitivity,[status(thm)],[22431, 22429])).
% 10.09/10.39 tff(22433,plain,
% 10.09/10.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.09/10.39 inference(quant_inst,[status(thm)],[])).
% 10.09/10.40 tff(22434,plain,
% 10.09/10.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 10.09/10.40 inference(modus_ponens,[status(thm)],[22433, 22432])).
% 10.09/10.40 tff(22435,plain,
% 10.09/10.40 (~b(s(z), s(s(s(s(z)))))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[22434, 391, 22426, 90, 664, 590])).
% 10.09/10.40 tff(22436,plain,
% 10.09/10.40 (r(s(z), s(s(s(s(z)))))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[1230, 22435])).
% 10.09/10.40 tff(22437,plain,
% 10.09/10.40 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[16396, 22436, 22428, 1747])).
% 10.09/10.40 tff(22438,plain,
% 10.09/10.40 (b(s(s(z)), s(s(s(s(z)))))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[3652, 22437])).
% 10.09/10.40 tff(22439,plain,
% 10.09/10.40 (~b(s(s(z)), z)),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[7203, 22438, 90, 590, 664])).
% 10.09/10.40 tff(22440,plain,
% 10.09/10.40 (r(s(s(z)), z)),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[1211, 22439])).
% 10.09/10.40 tff(22441,plain,
% 10.09/10.40 (~r(elem!1, s(s(z)))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[16978, 194, 411, 530, 22440])).
% 10.09/10.40 tff(22442,plain,
% 10.09/10.40 (b(elem!1, s(s(z)))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[3394, 22441, 3694])).
% 10.09/10.40 tff(22443,plain,
% 10.09/10.40 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[11508, 22440, 22436, 1747])).
% 10.09/10.40 tff(22444,plain,
% 10.09/10.40 (b(s(s(s(s(z)))), s(s(z)))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[1714, 22443])).
% 10.09/10.40 tff(22445,plain,
% 10.09/10.40 (~r(s(s(z)), elem!1)),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[15383, 194, 411, 530, 22440])).
% 10.09/10.40 tff(22446,plain,
% 10.09/10.40 (b(s(s(z)), elem!1)),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[4730, 22445, 14710])).
% 10.09/10.40 tff(22447,plain,
% 10.09/10.40 (~b(s(s(s(s(z)))), elem!1)),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[11012, 22446, 22444, 22442])).
% 10.09/10.40 tff(22448,plain,
% 10.09/10.40 (r(s(s(s(s(z)))), elem!1)),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[762, 22447, 2691])).
% 10.09/10.40 tff(22449,plain,
% 10.09/10.40 (~r(z, s(s(s(s(z)))))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[3852, 22441, 90, 184, 21769, 3807, 22438, 22444])).
% 10.09/10.40 tff(22450,plain,
% 10.09/10.40 (b(z, s(s(s(s(z)))))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[800, 22449])).
% 10.09/10.40 tff(22451,plain,
% 10.09/10.40 (~b(z, s(s(z)))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[20658, 22450, 22436, 22440, 1747, 22448])).
% 10.09/10.40 tff(22452,plain,
% 10.09/10.40 (r(z, s(s(z)))),
% 10.09/10.40 inference(unit_resolution,[status(thm)],[18613, 22451])).
% 10.09/10.40 tff(22453,plain,
% 10.09/10.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.09/10.40 inference(rewrite,[status(thm)],[])).
% 10.09/10.40 tff(22454,plain,
% 10.09/10.40 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.09/10.40 inference(rewrite,[status(thm)],[])).
% 10.09/10.40 tff(22455,plain,
% 10.09/10.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 10.09/10.40 inference(monotonicity,[status(thm)],[22454])).
% 10.09/10.40 tff(22456,plain,
% 10.09/10.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.40 inference(transitivity,[status(thm)],[22455, 22453])).
% 10.19/10.40 tff(22457,plain,
% 10.19/10.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 10.19/10.40 inference(quant_inst,[status(thm)],[])).
% 10.19/10.40 tff(22458,plain,
% 10.19/10.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 10.19/10.40 inference(modus_ponens,[status(thm)],[22457, 22456])).
% 10.19/10.40 tff(22459,plain,
% 10.19/10.40 (~r(s(s(s(s(s(z))))), s(z))),
% 10.19/10.40 inference(unit_resolution,[status(thm)],[22458, 194, 3557, 1747, 18827])).
% 10.19/10.40 tff(22460,plain,
% 10.19/10.40 (b(s(s(s(s(s(z))))), s(z))),
% 10.19/10.40 inference(unit_resolution,[status(thm)],[20789, 22459])).
% 10.19/10.40 tff(22461,plain,
% 10.19/10.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.40 inference(rewrite,[status(thm)],[])).
% 10.19/10.40 tff(22462,plain,
% 10.19/10.40 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.40 inference(rewrite,[status(thm)],[])).
% 10.19/10.40 tff(22463,plain,
% 10.19/10.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 10.19/10.40 inference(monotonicity,[status(thm)],[22462])).
% 10.19/10.40 tff(22464,plain,
% 10.19/10.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.40 inference(transitivity,[status(thm)],[22463, 22461])).
% 10.19/10.40 tff(22465,plain,
% 10.19/10.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 10.19/10.40 inference(quant_inst,[status(thm)],[])).
% 10.19/10.40 tff(22466,plain,
% 10.19/10.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 10.19/10.40 inference(modus_ponens,[status(thm)],[22465, 22464])).
% 10.19/10.40 tff(22467,plain,
% 10.19/10.40 (~r(s(z), s(s(s(s(s(z))))))),
% 10.19/10.40 inference(unit_resolution,[status(thm)],[22466, 194, 3557, 1747, 18827])).
% 10.19/10.40 tff(22468,plain,
% 10.19/10.40 (b(s(z), s(s(s(s(s(z))))))),
% 10.19/10.40 inference(unit_resolution,[status(thm)],[16561, 42, 22467, 16551])).
% 10.19/10.40 tff(22469,plain,
% 10.19/10.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.40 inference(rewrite,[status(thm)],[])).
% 10.19/10.40 tff(22470,plain,
% 10.19/10.40 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.40 inference(rewrite,[status(thm)],[])).
% 10.19/10.40 tff(22471,plain,
% 10.19/10.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 10.19/10.40 inference(monotonicity,[status(thm)],[22470])).
% 10.19/10.40 tff(22472,plain,
% 10.19/10.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.40 inference(transitivity,[status(thm)],[22471, 22469])).
% 10.19/10.40 tff(22473,plain,
% 10.19/10.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 10.19/10.40 inference(quant_inst,[status(thm)],[])).
% 10.19/10.40 tff(22474,plain,
% 10.19/10.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 10.19/10.40 inference(modus_ponens,[status(thm)],[22473, 22472])).
% 10.19/10.40 tff(22475,plain,
% 10.19/10.40 (~r(z, s(s(s(s(s(z))))))),
% 10.19/10.40 inference(unit_resolution,[status(thm)],[22474, 194, 3557, 8505, 18827])).
% 10.19/10.40 tff(22476,assumption,(z = s(s(s(s(s(z)))))), introduced(assumption)).
% 10.19/10.40 tff(22477,plain,
% 10.19/10.40 (s(s(s(s(s(z))))) = z),
% 10.19/10.40 inference(symmetry,[status(thm)],[22476])).
% 10.19/10.40 tff(22478,plain,
% 10.19/10.40 ($false),
% 10.19/10.40 inference(unit_resolution,[status(thm)],[5063, 22477])).
% 10.19/10.40 tff(22479,plain,(~(z = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.40 tff(22480,plain,
% 10.19/10.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 10.19/10.40 inference(rewrite,[status(thm)],[])).
% 10.19/10.40 tff(22481,plain,
% 10.19/10.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 10.19/10.40 inference(quant_inst,[status(thm)],[])).
% 10.19/10.40 tff(22482,plain,
% 10.19/10.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 10.19/10.40 inference(modus_ponens,[status(thm)],[22481, 22480])).
% 10.19/10.40 tff(22483,plain,
% 10.19/10.40 (b(z, s(s(s(s(s(z))))))),
% 10.19/10.40 inference(unit_resolution,[status(thm)],[22482, 42, 22479, 22475])).
% 10.19/10.40 tff(22484,plain,
% 10.19/10.40 ($false),
% 10.19/10.40 inference(unit_resolution,[status(thm)],[15777, 22483, 22468, 664, 22460])).
% 10.19/10.40 tff(22485,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.40 tff(22486,plain,
% 10.19/10.40 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 10.19/10.40 inference(unit_resolution,[status(thm)],[22485, 22440, 664, 22452, 1747])).
% 10.19/10.40 tff(22487,plain,
% 10.19/10.40 (b(s(s(s(s(s(z))))), s(s(z)))),
% 10.19/10.40 inference(unit_resolution,[status(thm)],[20778, 22486])).
% 10.19/10.40 tff(22488,plain,
% 10.19/10.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.41 inference(rewrite,[status(thm)],[])).
% 10.19/10.41 tff(22489,plain,
% 10.19/10.41 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.41 inference(rewrite,[status(thm)],[])).
% 10.19/10.41 tff(22490,plain,
% 10.19/10.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 10.19/10.41 inference(monotonicity,[status(thm)],[22489])).
% 10.19/10.41 tff(22491,plain,
% 10.19/10.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.41 inference(transitivity,[status(thm)],[22490, 22488])).
% 10.19/10.41 tff(22492,plain,
% 10.19/10.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 10.19/10.41 inference(quant_inst,[status(thm)],[])).
% 10.19/10.41 tff(22493,plain,
% 10.19/10.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 10.19/10.41 inference(modus_ponens,[status(thm)],[22492, 22491])).
% 10.19/10.41 tff(22494,plain,
% 10.19/10.41 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[22493, 391, 22438, 90, 22444, 22487])).
% 10.19/10.41 tff(22495,plain,
% 10.19/10.41 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[6561, 42, 22494])).
% 10.19/10.41 tff(22496,plain,
% 10.19/10.41 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[22495, 22373])).
% 10.19/10.41 tff(22497,plain,
% 10.19/10.41 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 10.19/10.41 inference(monotonicity,[status(thm)],[1422])).
% 10.19/10.41 tff(22498,plain,
% 10.19/10.41 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 10.19/10.41 inference(symmetry,[status(thm)],[22497])).
% 10.19/10.41 tff(22499,plain,
% 10.19/10.41 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 10.19/10.41 inference(monotonicity,[status(thm)],[22498])).
% 10.19/10.41 tff(22500,plain,
% 10.19/10.41 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 10.19/10.41 inference(transitivity,[status(thm)],[14706, 268])).
% 10.19/10.41 tff(22501,plain,
% 10.19/10.41 (b(s(s(s(elem!1))), elem!1) <=> b(elem!1, elem!1)),
% 10.19/10.41 inference(monotonicity,[status(thm)],[5])).
% 10.19/10.41 tff(22502,plain,
% 10.19/10.41 (b(elem!1, elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 10.19/10.41 inference(symmetry,[status(thm)],[22501])).
% 10.19/10.41 tff(22503,plain,
% 10.19/10.41 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 10.19/10.41 inference(monotonicity,[status(thm)],[22502])).
% 10.19/10.41 tff(22504,plain,
% 10.19/10.41 (~b(s(s(s(elem!1))), elem!1)),
% 10.19/10.41 inference(modus_ponens,[status(thm)],[4741, 22503])).
% 10.19/10.41 tff(22505,plain,
% 10.19/10.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)))))) | (~r(s(z), s(s(z)))))),
% 10.19/10.41 inference(rewrite,[status(thm)],[])).
% 10.19/10.41 tff(22506,plain,
% 10.19/10.41 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), 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)))))) | (~r(s(z), s(s(z)))))),
% 10.19/10.41 inference(rewrite,[status(thm)],[])).
% 10.19/10.41 tff(22507,plain,
% 10.19/10.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)))))) | (~r(s(z), s(s(z))))))),
% 10.19/10.41 inference(monotonicity,[status(thm)],[22506])).
% 10.19/10.41 tff(22508,plain,
% 10.19/10.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)))))) | (~r(s(z), s(s(z)))))),
% 10.19/10.41 inference(transitivity,[status(thm)],[22507, 22505])).
% 10.19/10.41 tff(22509,plain,
% 10.19/10.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 10.19/10.41 inference(quant_inst,[status(thm)],[])).
% 10.19/10.41 tff(22510,plain,
% 10.19/10.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))),
% 10.19/10.41 inference(modus_ponens,[status(thm)],[22509, 22508])).
% 10.19/10.41 tff(22511,plain,
% 10.19/10.41 ($false),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[22510, 194, 340, 723, 1747, 6257])).
% 10.19/10.41 tff(22512,plain,((~r(s(z), 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))))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.41 tff(22513,plain,
% 10.19/10.41 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[22512, 340, 723, 1747])).
% 10.19/10.41 tff(22514,plain,
% 10.19/10.41 ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[1994, 42, 22513])).
% 10.19/10.41 tff(22515,plain,
% 10.19/10.41 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[22514, 1984])).
% 10.19/10.41 tff(22516,plain,
% 10.19/10.41 (~b(s(z), s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[22434, 391, 644, 90, 664, 590])).
% 10.19/10.41 tff(22517,plain,
% 10.19/10.41 (r(s(z), s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[1230, 22516])).
% 10.19/10.41 tff(22518,plain,
% 10.19/10.41 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[16396, 22517, 723, 1747])).
% 10.19/10.41 tff(22519,plain,
% 10.19/10.41 (b(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[3652, 22518])).
% 10.19/10.41 tff(22520,plain,
% 10.19/10.41 (~b(s(s(z)), z)),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[7203, 22519, 90, 590, 664])).
% 10.19/10.41 tff(22521,plain,
% 10.19/10.41 (r(s(s(z)), z)),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[1211, 22520])).
% 10.19/10.41 tff(22522,plain,
% 10.19/10.41 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[11508, 22521, 22517, 1747])).
% 10.19/10.41 tff(22523,plain,
% 10.19/10.41 (b(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[1714, 22522])).
% 10.19/10.41 tff(22524,plain,
% 10.19/10.41 (~r(elem!1, s(s(z)))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[16978, 194, 411, 530, 22521])).
% 10.19/10.41 tff(22525,plain,
% 10.19/10.41 (~r(z, s(s(s(s(z)))))),
% 10.19/10.41 inference(unit_resolution,[status(thm)],[3852, 22524, 90, 184, 3843, 125, 22519, 22523])).
% 10.19/10.42 tff(22526,plain,
% 10.19/10.42 (b(z, s(s(s(s(z)))))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[800, 22525])).
% 10.19/10.42 tff(22527,plain,
% 10.19/10.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 10.19/10.42 inference(rewrite,[status(thm)],[])).
% 10.19/10.42 tff(22528,plain,
% 10.19/10.42 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 10.19/10.42 inference(rewrite,[status(thm)],[])).
% 10.19/10.42 tff(22529,plain,
% 10.19/10.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 10.19/10.42 inference(monotonicity,[status(thm)],[22528])).
% 10.19/10.42 tff(22530,plain,
% 10.19/10.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 10.19/10.42 inference(transitivity,[status(thm)],[22529, 22527])).
% 10.19/10.42 tff(22531,plain,
% 10.19/10.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 10.19/10.42 inference(quant_inst,[status(thm)],[])).
% 10.19/10.42 tff(22532,plain,
% 10.19/10.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 10.19/10.42 inference(modus_ponens,[status(thm)],[22531, 22530])).
% 10.19/10.42 tff(22533,plain,
% 10.19/10.42 (~b(s(s(elem!1)), s(s(z)))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[22532, 391, 22519, 90, 22526, 22515])).
% 10.19/10.42 tff(22534,plain,
% 10.19/10.42 (r(s(s(elem!1)), s(s(z)))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[5174, 42, 22533, 2689])).
% 10.19/10.42 tff(22535,plain,
% 10.19/10.42 (~r(s(s(z)), elem!1)),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[15383, 194, 411, 530, 22521])).
% 10.19/10.42 tff(22536,plain,
% 10.19/10.42 (b(s(s(z)), elem!1)),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[4730, 22535, 5547])).
% 10.19/10.42 tff(22537,plain,
% 10.19/10.42 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[348, 340, 184, 326])).
% 10.19/10.42 tff(22538,plain,
% 10.19/10.42 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[1370, 22537, 297])).
% 10.19/10.42 tff(22539,plain,
% 10.19/10.42 (~(s(s(elem!1)) = elem!1)),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[1845, 22538, 168])).
% 10.19/10.42 tff(22540,plain,
% 10.19/10.42 (~(elem!1 = s(s(elem!1)))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[1292, 22539])).
% 10.19/10.42 tff(22541,plain,
% 10.19/10.42 (b(elem!1, s(s(elem!1)))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[1307, 22540, 9093])).
% 10.19/10.42 tff(22542,plain,
% 10.19/10.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 10.19/10.42 inference(rewrite,[status(thm)],[])).
% 10.19/10.42 tff(22543,plain,
% 10.19/10.42 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 10.19/10.42 inference(rewrite,[status(thm)],[])).
% 10.19/10.42 tff(22544,plain,
% 10.19/10.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 10.19/10.42 inference(monotonicity,[status(thm)],[22543])).
% 10.19/10.42 tff(22545,plain,
% 10.19/10.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 10.19/10.42 inference(transitivity,[status(thm)],[22544, 22542])).
% 10.19/10.42 tff(22546,plain,
% 10.19/10.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 10.19/10.42 inference(quant_inst,[status(thm)],[])).
% 10.19/10.42 tff(22547,plain,
% 10.19/10.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 10.19/10.42 inference(modus_ponens,[status(thm)],[22546, 22545])).
% 10.19/10.42 tff(22548,plain,
% 10.19/10.42 (~b(s(s(z)), s(z))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[22547, 391, 644, 22541, 22536, 22515])).
% 10.19/10.42 tff(22549,plain,
% 10.19/10.42 (r(s(s(z)), s(z))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[3778, 22548])).
% 10.19/10.42 tff(22550,plain,
% 10.19/10.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 10.19/10.42 inference(rewrite,[status(thm)],[])).
% 10.19/10.42 tff(22551,plain,
% 10.19/10.42 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 10.19/10.42 inference(rewrite,[status(thm)],[])).
% 10.19/10.42 tff(22552,plain,
% 10.19/10.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 10.19/10.42 inference(monotonicity,[status(thm)],[22551])).
% 10.19/10.42 tff(22553,plain,
% 10.19/10.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 10.19/10.42 inference(transitivity,[status(thm)],[22552, 22550])).
% 10.19/10.42 tff(22554,plain,
% 10.19/10.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 10.19/10.42 inference(quant_inst,[status(thm)],[])).
% 10.19/10.42 tff(22555,plain,
% 10.19/10.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 10.19/10.42 inference(modus_ponens,[status(thm)],[22554, 22553])).
% 10.19/10.42 tff(22556,plain,
% 10.19/10.42 ($false),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[22555, 194, 340, 22517, 22549, 22534])).
% 10.19/10.42 tff(22557,plain,((~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(z)) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.42 tff(22558,plain,
% 10.19/10.42 (~r(s(s(elem!1)), s(z))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[22557, 297, 22426, 90, 184, 21769, 3807, 14710, 411, 530, 3695, 1747, 590, 664, 22428, 22504, 2689, 326])).
% 10.19/10.42 tff(22559,plain,
% 10.19/10.42 (b(s(s(elem!1)), s(z))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[362, 22558])).
% 10.19/10.42 tff(22560,plain,
% 10.19/10.42 ($false),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[879, 391, 381, 973, 644, 721])).
% 10.19/10.42 tff(22561,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.42 tff(22562,plain,
% 10.19/10.42 (~b(s(s(elem!1)), elem!1)),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[22561, 22559, 721, 22426])).
% 10.19/10.42 tff(22563,plain,
% 10.19/10.42 (s(s(elem!1)) = elem!1),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[872, 22562, 20606])).
% 10.19/10.42 tff(22564,plain,
% 10.19/10.42 (s(s(elem!1)) = s(s(s(elem!1)))),
% 10.19/10.42 inference(modus_ponens,[status(thm)],[22563, 22500])).
% 10.19/10.42 tff(22565,plain,
% 10.19/10.42 ($false),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[315, 22564])).
% 10.19/10.42 tff(22566,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.42 tff(22567,plain,
% 10.19/10.42 (s(s(s(elem!1))) = s(s(elem!1))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[22566, 1747, 721, 90, 184, 411, 530, 5, 590, 664, 2689, 326])).
% 10.19/10.42 tff(22568,plain,
% 10.19/10.42 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 10.19/10.42 inference(unit_resolution,[status(thm)],[20761, 22567])).
% 10.19/10.42 tff(22569,plain,
% 10.19/10.42 (~(s(s(s(s(s(z))))) = elem!1)),
% 10.19/10.42 inference(modus_ponens,[status(thm)],[22568, 22499])).
% 10.19/10.42 tff(22570,plain,
% 10.19/10.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.43 inference(rewrite,[status(thm)],[])).
% 10.19/10.43 tff(22571,plain,
% 10.19/10.43 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.43 inference(rewrite,[status(thm)],[])).
% 10.19/10.43 tff(22572,plain,
% 10.19/10.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 10.19/10.43 inference(monotonicity,[status(thm)],[22571])).
% 10.19/10.43 tff(22573,plain,
% 10.19/10.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 10.19/10.43 inference(transitivity,[status(thm)],[22572, 22570])).
% 10.19/10.43 tff(22574,plain,
% 10.19/10.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 10.19/10.43 inference(quant_inst,[status(thm)],[])).
% 10.19/10.43 tff(22575,plain,
% 10.19/10.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 10.19/10.43 inference(modus_ponens,[status(thm)],[22574, 22573])).
% 10.19/10.43 tff(22576,plain,
% 10.19/10.43 (~b(s(s(s(s(s(z))))), elem!1)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22575, 391, 22438, 90, 22442, 22487])).
% 10.19/10.43 tff(22577,plain,
% 10.19/10.43 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 10.19/10.43 inference(rewrite,[status(thm)],[])).
% 10.19/10.43 tff(22578,plain,
% 10.19/10.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 10.19/10.43 inference(quant_inst,[status(thm)],[])).
% 10.19/10.43 tff(22579,plain,
% 10.19/10.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 10.19/10.43 inference(modus_ponens,[status(thm)],[22578, 22577])).
% 10.19/10.43 tff(22580,plain,
% 10.19/10.43 ((s(s(s(s(s(z))))) = elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22579, 42, 22576])).
% 10.19/10.43 tff(22581,plain,
% 10.19/10.43 (r(s(s(s(s(s(z))))), elem!1)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22580, 22569])).
% 10.19/10.43 tff(22582,plain,
% 10.19/10.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 10.19/10.43 inference(rewrite,[status(thm)],[])).
% 10.19/10.43 tff(22583,plain,
% 10.19/10.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 10.19/10.43 inference(quant_inst,[status(thm)],[])).
% 10.19/10.43 tff(22584,plain,
% 10.19/10.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 10.19/10.43 inference(modus_ponens,[status(thm)],[22583, 22582])).
% 10.19/10.43 tff(22585,plain,
% 10.19/10.43 ($false),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22584, 194, 530, 22448, 22581, 22496])).
% 10.19/10.43 tff(22586,plain,((~r(s(z), s(s(z)))) | (~r(elem!1, z)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.43 tff(22587,plain,
% 10.19/10.43 (~r(s(z), s(s(z)))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22586, 22365, 22359, 90, 664, 59, 15899, 21728, 20263, 2680, 22369])).
% 10.19/10.43 tff(22588,plain,
% 10.19/10.43 (b(s(z), s(s(z)))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[1788, 22587])).
% 10.19/10.43 tff(22589,plain,
% 10.19/10.43 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 10.19/10.43 inference(monotonicity,[status(thm)],[22359])).
% 10.19/10.43 tff(22590,plain,
% 10.19/10.43 (b(s(z), s(s(s(elem!1))))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22424, 22365, 15899, 22367, 21728, 20263, 59, 90, 22366])).
% 10.19/10.43 tff(22591,plain,
% 10.19/10.43 (b(s(z), elem!1)),
% 10.19/10.43 inference(modus_ponens,[status(thm)],[22590, 22589])).
% 10.19/10.43 tff(22592,plain,
% 10.19/10.43 (~b(s(z), s(s(s(s(z)))))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22434, 391, 22591, 90, 664, 21728])).
% 10.19/10.43 tff(22593,plain,
% 10.19/10.43 (r(s(z), s(s(s(s(z)))))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[1230, 22592])).
% 10.19/10.43 tff(22594,plain,
% 10.19/10.43 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22319, 3369, 90, 2439, 721])).
% 10.19/10.43 tff(22595,plain,
% 10.19/10.43 (r(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[3652, 22594])).
% 10.19/10.43 tff(22596,plain,
% 10.19/10.43 (~b(s(s(z)), s(z))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[10150, 3369, 721, 2439])).
% 10.19/10.43 tff(22597,plain,
% 10.19/10.43 (r(s(s(z)), s(z))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[3778, 22596])).
% 10.19/10.43 tff(22598,plain,
% 10.19/10.43 ($false),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[5585, 22597, 22595, 590, 664, 1216])).
% 10.19/10.43 tff(22599,plain,((~b(elem!1, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.43 tff(22600,plain,
% 10.19/10.43 (~b(elem!1, s(s(z)))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22599, 664, 21728, 22593, 20263, 22588, 90])).
% 10.19/10.43 tff(22601,plain,
% 10.19/10.43 (r(elem!1, s(s(z)))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[3394, 22600, 22363])).
% 10.19/10.43 tff(22602,plain,
% 10.19/10.43 (~r(z, s(s(z)))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[18632, 1749, 411, 1748])).
% 10.19/10.43 tff(22603,plain,
% 10.19/10.43 (b(z, s(s(z)))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[18613, 22602])).
% 10.19/10.43 tff(22604,plain,
% 10.19/10.43 ($false),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[21530, 22603, 16388, 664, 2439])).
% 10.19/10.43 tff(22605,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(z)))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.43 tff(22606,plain,
% 10.19/10.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22605, 664, 22588, 15899, 22601, 21728, 22593])).
% 10.19/10.43 tff(22607,plain,
% 10.19/10.43 (b(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[3652, 22606])).
% 10.19/10.43 tff(22608,plain,
% 10.19/10.43 (~b(s(s(z)), z)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[7203, 22607, 90, 21728, 664])).
% 10.19/10.43 tff(22609,plain,
% 10.19/10.43 (r(s(s(z)), z)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[1211, 22608])).
% 10.19/10.43 tff(22610,plain,
% 10.19/10.43 ($false),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[16978, 194, 15899, 22365, 22609, 22601])).
% 10.19/10.43 tff(22611,plain,((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | b(z, s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 10.19/10.43 tff(22612,plain,
% 10.19/10.43 (~b(z, s(z))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22611, 10, 90, 2])).
% 10.19/10.43 tff(22613,plain,
% 10.19/10.43 (r(z, s(z))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[678, 22612])).
% 10.19/10.43 tff(22614,plain,
% 10.19/10.43 (~b(elem!1, s(s(s(elem!1))))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[15370, 5])).
% 10.19/10.43 tff(22615,plain,
% 10.19/10.43 (b(s(s(s(elem!1))), s(z))),
% 10.19/10.43 inference(modus_ponens,[status(thm)],[721, 8396])).
% 10.19/10.43 tff(22616,plain,
% 10.19/10.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))))),
% 10.19/10.43 inference(rewrite,[status(thm)],[])).
% 10.19/10.43 tff(22617,plain,
% 10.19/10.43 (((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))))),
% 10.19/10.43 inference(rewrite,[status(thm)],[])).
% 10.19/10.43 tff(22618,plain,
% 10.19/10.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z))))))),
% 10.19/10.43 inference(monotonicity,[status(thm)],[22617])).
% 10.19/10.43 tff(22619,plain,
% 10.19/10.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))))),
% 10.19/10.43 inference(transitivity,[status(thm)],[22618, 22616])).
% 10.19/10.43 tff(22620,plain,
% 10.19/10.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 10.19/10.43 inference(quant_inst,[status(thm)],[])).
% 10.19/10.43 tff(22621,plain,
% 10.19/10.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z))))),
% 10.19/10.43 inference(modus_ponens,[status(thm)],[22620, 22619])).
% 10.19/10.43 tff(22622,plain,
% 10.19/10.43 ($false),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22621, 194, 411, 1484, 722, 1748])).
% 10.19/10.43 tff(22623,plain,((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.43 tff(22624,plain,
% 10.19/10.43 (~r(s(z), elem!1)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22623, 1748, 411, 722])).
% 10.19/10.43 tff(22625,plain,
% 10.19/10.43 (b(s(z), elem!1)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[632, 22624, 21435])).
% 10.19/10.43 tff(22626,plain,
% 10.19/10.43 (~b(elem!1, z)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[14881, 1686, 90, 590, 644])).
% 10.19/10.43 tff(22627,plain,
% 10.19/10.43 (r(elem!1, z)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[526, 22626, 2])).
% 10.19/10.43 tff(22628,plain,
% 10.19/10.43 (~b(s(s(z)), z)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[16487, 1686, 90, 590, 2439])).
% 10.19/10.43 tff(22629,plain,
% 10.19/10.43 (r(s(s(z)), z)),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[1211, 22628])).
% 10.19/10.43 tff(22630,plain,
% 10.19/10.43 ($false),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[18602, 22629, 22627, 722, 1748])).
% 10.19/10.43 tff(22631,plain,((~b(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (elem!1 = z) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.43 tff(22632,plain,
% 10.19/10.43 (~b(z, s(s(s(s(z)))))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[22631, 1748, 722, 2, 90, 590, 2439, 22625])).
% 10.19/10.43 tff(22633,plain,
% 10.19/10.43 (r(z, s(s(s(s(z)))))),
% 10.19/10.43 inference(unit_resolution,[status(thm)],[800, 22632])).
% 10.19/10.44 tff(22634,plain,
% 10.19/10.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 10.19/10.44 inference(rewrite,[status(thm)],[])).
% 10.19/10.44 tff(22635,plain,
% 10.19/10.44 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 10.19/10.44 inference(rewrite,[status(thm)],[])).
% 10.19/10.44 tff(22636,plain,
% 10.19/10.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))))),
% 10.19/10.44 inference(monotonicity,[status(thm)],[22635])).
% 10.19/10.44 tff(22637,plain,
% 10.19/10.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 10.19/10.44 inference(transitivity,[status(thm)],[22636, 22634])).
% 10.19/10.44 tff(22638,plain,
% 10.19/10.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 10.19/10.44 inference(quant_inst,[status(thm)],[])).
% 10.19/10.44 tff(22639,plain,
% 10.19/10.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))),
% 10.19/10.44 inference(modus_ponens,[status(thm)],[22638, 22637])).
% 10.19/10.44 tff(22640,plain,
% 10.19/10.44 ($false),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[22639, 194, 411, 1748, 2112, 719])).
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% 10.19/10.44 tff(22642,plain,
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% 10.19/10.44 inference(unit_resolution,[status(thm)],[762, 22642, 2691])).
% 10.19/10.44 tff(22644,plain,
% 10.19/10.44 (~b(s(s(s(s(z)))), s(z))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[20672, 391, 22625, 22643, 721])).
% 10.19/10.44 tff(22645,plain,
% 10.19/10.44 (r(s(s(s(s(z)))), s(z))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[749, 22644])).
% 10.19/10.44 tff(22646,plain,
% 10.19/10.44 (b(s(z), s(s(s(elem!1))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[14872, 22625, 5])).
% 10.19/10.44 tff(22647,plain,
% 10.19/10.44 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[20820, 22643, 3807])).
% 10.19/10.44 tff(22648,plain,
% 10.19/10.44 (~b(s(z), s(s(s(s(z)))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[20817, 22647, 22646, 22615])).
% 10.19/10.44 tff(22649,plain,
% 10.19/10.44 (r(s(z), s(s(s(s(z)))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[1230, 22648])).
% 10.19/10.44 tff(22650,plain,
% 10.19/10.44 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
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% 10.19/10.44 inference(transitivity,[status(thm)],[22651, 14961])).
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% 10.19/10.44 inference(modus_ponens,[status(thm)],[22653, 22652])).
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% 10.19/10.44 inference(unit_resolution,[status(thm)],[22654, 194, 722, 22649, 22645, 22633])).
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% 10.19/10.44 tff(22657,plain,
% 10.19/10.44 (~r(elem!1, s(s(z)))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[22656, 2439, 721, 411, 2, 90, 590, 722, 5])).
% 10.19/10.44 tff(22658,plain,
% 10.19/10.44 (b(elem!1, s(s(z)))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[3394, 22657, 3694])).
% 10.19/10.44 tff(22659,plain,
% 10.19/10.44 (~b(s(s(z)), s(z))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[10150, 22658, 721, 2439])).
% 10.19/10.44 tff(22660,plain,
% 10.19/10.44 (r(s(s(z)), s(z))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[3778, 22659])).
% 10.19/10.44 tff(22661,plain,
% 10.19/10.44 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[22319, 22658, 90, 2439, 721])).
% 10.19/10.44 tff(22662,plain,
% 10.19/10.44 (r(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[3652, 22661])).
% 10.19/10.44 tff(22663,plain,
% 10.19/10.44 ($false),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[10434, 391, 90, 1234, 1686, 590])).
% 10.19/10.44 tff(22664,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.44 tff(22665,plain,
% 10.19/10.44 (~b(z, s(s(s(s(z)))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[22664, 1234, 90, 590])).
% 10.19/10.44 tff(22666,plain,
% 10.19/10.44 (r(z, s(s(s(s(z)))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[800, 22665])).
% 10.19/10.44 tff(22667,plain,
% 10.19/10.44 (~r(s(s(s(s(z)))), elem!1)),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[22263, 22666, 590, 2439, 1749])).
% 10.19/10.44 tff(22668,plain,
% 10.19/10.44 (r(elem!1, s(s(s(s(z)))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[20438, 22667, 721, 720, 1234])).
% 10.19/10.44 tff(22669,plain,
% 10.19/10.44 (~b(s(s(s(s(z)))), s(z))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[2097, 22666, 411, 721, 1234, 720])).
% 10.19/10.44 tff(22670,plain,
% 10.19/10.44 (r(s(s(s(s(z)))), s(z))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[749, 22669])).
% 10.19/10.44 tff(22671,plain,
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% 10.19/10.44 inference(unit_resolution,[status(thm)],[15063, 22670, 22668, 411, 22666])).
% 10.19/10.44 tff(22672,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.44 tff(22673,plain,
% 10.19/10.44 (~b(s(z), s(s(s(s(z)))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[22672, 2439, 721, 2691, 590, 411, 22662, 90])).
% 10.19/10.44 tff(22674,plain,
% 10.19/10.44 (r(s(z), s(s(s(s(z)))))),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[1230, 22673])).
% 10.19/10.44 tff(22675,plain,
% 10.19/10.44 (~r(s(s(s(s(z)))), elem!1)),
% 10.19/10.44 inference(unit_resolution,[status(thm)],[4702, 22674, 22660, 22662])).
% 10.19/10.44 tff(22676,plain,
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% 10.19/10.44 inference(unit_resolution,[status(thm)],[762, 22675, 2691])).
% 10.19/10.44 tff(22677,plain,
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[10610, 22674, 722, 22660])).
% 10.19/10.45 tff(22678,plain,
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[1211, 22677])).
% 10.19/10.45 tff(22679,plain,
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[2447, 22678, 721, 2439, 22676])).
% 10.19/10.45 tff(22680,plain,
% 10.19/10.45 (r(s(s(s(s(z)))), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[749, 22679])).
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% 10.19/10.45 inference(modus_ponens,[status(thm)],[22681, 5578])).
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[22682, 194, 22662, 22674, 22680, 22660])).
% 10.19/10.45 tff(22684,plain,((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.45 tff(22685,plain,
% 10.19/10.45 (~b(s(z), s(s(z)))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22684, 721, 722, 590, 411, 90, 2, 5])).
% 10.19/10.45 tff(22686,plain,
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[1788, 22685])).
% 10.19/10.45 tff(22687,plain,
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[11508, 12413, 1747, 1216])).
% 10.19/10.45 tff(22688,plain,
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[22044, 12413, 90, 1216, 3823])).
% 10.19/10.45 tff(22689,plain,
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[1211, 22688, 22687])).
% 10.19/10.45 tff(22690,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.45 tff(22691,plain,
% 10.19/10.45 (~b(elem!1, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22690, 3369, 90, 22686, 3823, 1216])).
% 10.19/10.45 tff(22692,plain,
% 10.19/10.45 (r(elem!1, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[781, 22691, 3696])).
% 10.19/10.45 tff(22693,plain,
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[21996, 22692, 411, 722])).
% 10.19/10.45 tff(22694,plain,
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[632, 22693, 21435])).
% 10.19/10.45 tff(22695,plain,
% 10.19/10.45 (b(s(z), s(s(s(elem!1))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[14872, 22694, 5])).
% 10.19/10.45 tff(22696,plain,
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[21996, 2032, 411, 722])).
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% 10.19/10.45 inference(unit_resolution,[status(thm)],[632, 22696, 21435])).
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% 10.19/10.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
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% 10.19/10.45 (((~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
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% 10.19/10.45 inference(modus_ponens,[status(thm)],[22702, 22701])).
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% 10.19/10.45 tff(22710,plain,
% 10.19/10.45 (~b(z, s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[20920, 1759, 721, 644, 90])).
% 10.19/10.45 tff(22711,plain,
% 10.19/10.45 (r(z, s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[678, 22710])).
% 10.19/10.45 tff(22712,plain,
% 10.19/10.45 (~r(s(z), s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[10610, 22711, 3557, 2405])).
% 10.19/10.45 tff(22713,plain,
% 10.19/10.45 (b(s(z), s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[1230, 22712])).
% 10.19/10.45 tff(22714,plain,
% 10.19/10.45 (~b(z, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[17292, 22713, 590, 1759])).
% 10.19/10.45 tff(22715,plain,
% 10.19/10.45 (~r(z, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[2097, 22713, 411, 721, 720, 1759])).
% 10.19/10.45 tff(22716,plain,
% 10.19/10.45 ($false),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[800, 22715, 22714])).
% 10.19/10.45 tff(22717,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.45 tff(22718,plain,
% 10.19/10.45 (~r(s(s(z)), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22717, 22709, 721, 411, 590, 720, 1759, 22697, 90])).
% 10.19/10.45 tff(22719,plain,
% 10.19/10.45 (~b(elem!1, z)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[14881, 22707, 90, 590, 22697])).
% 10.19/10.45 tff(22720,plain,
% 10.19/10.45 (r(elem!1, z)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[526, 22719, 2])).
% 10.19/10.45 tff(22721,plain,
% 10.19/10.45 (~b(s(s(z)), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[20856, 22720, 90, 722, 22705, 411, 125, 379, 1526])).
% 10.19/10.45 tff(22722,plain,
% 10.19/10.45 ($false),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[3778, 22721, 22718])).
% 10.19/10.45 tff(22723,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (s(s(s(s(z)))) = elem!1) | (elem!1 = z) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.45 tff(22724,plain,
% 10.19/10.45 (~b(s(s(s(s(z)))), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22723, 22695, 722, 411, 3807, 90, 22615, 721, 590, 2691, 2, 3823, 22692, 3369])).
% 10.19/10.45 tff(22725,plain,
% 10.19/10.45 (r(s(s(s(s(z)))), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[749, 22724])).
% 10.19/10.45 tff(22726,plain,
% 10.19/10.45 (~r(z, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[15063, 22725, 411, 22692])).
% 10.19/10.45 tff(22727,plain,
% 10.19/10.45 (b(z, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[800, 22726])).
% 10.19/10.45 tff(22728,plain,
% 10.19/10.45 (~b(elem!1, z)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[14881, 22727, 90, 590, 22694])).
% 10.19/10.45 tff(22729,plain,
% 10.19/10.45 (r(elem!1, z)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[526, 22728, 2])).
% 10.19/10.45 tff(22730,plain,
% 10.19/10.45 (~b(s(s(z)), z)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[4472, 22727, 90, 3823])).
% 10.19/10.45 tff(22731,plain,
% 10.19/10.45 (r(s(s(z)), z)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[1211, 22730])).
% 10.19/10.45 tff(22732,plain,
% 10.19/10.45 (~r(s(s(z)), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[10610, 22731, 722, 1216])).
% 10.19/10.45 tff(22733,plain,
% 10.19/10.45 (b(s(s(z)), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[3778, 22732])).
% 10.19/10.45 tff(22734,plain,
% 10.19/10.45 (~r(s(s(s(s(z)))), elem!1)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[20856, 22733, 90, 722, 22729, 411, 3807, 22695, 22615])).
% 10.19/10.45 tff(22735,plain,
% 10.19/10.45 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[11508, 22731, 22686, 1216])).
% 10.19/10.45 tff(22736,plain,
% 10.19/10.45 (b(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[1714, 22735])).
% 10.19/10.45 tff(22737,plain,
% 10.19/10.45 (~b(s(s(s(s(z)))), elem!1)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[18608, 22736, 411, 722, 22731, 14710, 3694, 22729])).
% 10.19/10.45 tff(22738,plain,
% 10.19/10.45 ($false),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[762, 22737, 22734, 2691])).
% 10.19/10.45 tff(22739,plain,((~b(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (elem!1 = z) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.45 tff(22740,plain,
% 10.19/10.45 (~b(elem!1, s(s(z)))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22739, 1216, 722, 90, 411, 2, 590, 3823, 721, 5])).
% 10.19/10.45 tff(22741,plain,
% 10.19/10.45 (r(elem!1, s(s(z)))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[3394, 22740, 3694])).
% 10.19/10.45 tff(22742,plain,
% 10.19/10.45 (~r(s(z), elem!1)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22623, 22741, 411, 722])).
% 10.19/10.45 tff(22743,plain,
% 10.19/10.45 (b(s(z), elem!1)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[632, 22742, 21435])).
% 10.19/10.45 tff(22744,plain,
% 10.19/10.45 ($false),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[18602, 22627, 20941, 722, 1748])).
% 10.19/10.45 tff(22745,plain,((~b(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (elem!1 = z) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.45 tff(22746,plain,
% 10.19/10.45 (~b(z, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22745, 22741, 722, 2, 90, 590, 22743, 3823])).
% 10.19/10.45 tff(22747,plain,
% 10.19/10.45 (r(z, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[800, 22746])).
% 10.19/10.45 tff(22748,plain,
% 10.19/10.45 (~r(s(s(s(s(z)))), elem!1)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22641, 22747, 411, 22741])).
% 10.19/10.45 tff(22749,plain,
% 10.19/10.45 (b(s(s(s(s(z)))), elem!1)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[762, 22748, 2691])).
% 10.19/10.45 tff(22750,plain,
% 10.19/10.45 (~b(s(s(s(s(z)))), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[20672, 391, 22743, 22749, 721])).
% 10.19/10.45 tff(22751,plain,
% 10.19/10.45 (r(s(s(s(s(z)))), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[749, 22750])).
% 10.19/10.45 tff(22752,plain,
% 10.19/10.45 ($false),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22654, 194, 722, 1216, 22751, 22747])).
% 10.19/10.45 tff(22753,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (elem!1 = z) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.45 tff(22754,plain,
% 10.19/10.45 (~r(s(z), s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22753, 3823, 721, 411, 2, 90, 590, 722, 5])).
% 10.19/10.45 tff(22755,plain,
% 10.19/10.45 (b(s(z), s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[1230, 22754])).
% 10.19/10.45 tff(22756,plain,
% 10.19/10.45 (~b(z, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22664, 22755, 90, 590])).
% 10.19/10.45 tff(22757,plain,
% 10.19/10.45 (r(z, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[800, 22756])).
% 10.19/10.45 tff(22758,plain,
% 10.19/10.45 (~b(s(s(s(s(z)))), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[2097, 22757, 411, 721, 22755, 2691])).
% 10.19/10.45 tff(22759,plain,
% 10.19/10.45 (r(s(s(s(s(z)))), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[749, 22758])).
% 10.19/10.45 tff(22760,plain,
% 10.19/10.45 (~r(elem!1, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[15063, 22759, 411, 22757])).
% 10.19/10.45 tff(22761,plain,
% 10.19/10.45 (b(elem!1, s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[781, 22760, 3696])).
% 10.19/10.45 tff(22762,plain,
% 10.19/10.45 (r(s(s(s(s(z)))), elem!1)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[20438, 22760, 721, 2691, 22755])).
% 10.19/10.45 tff(22763,plain,
% 10.19/10.45 (~r(elem!1, s(s(z)))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22641, 22762, 411, 22757])).
% 10.19/10.45 tff(22764,plain,
% 10.19/10.45 (b(elem!1, s(s(z)))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[3394, 22763, 3694])).
% 10.19/10.45 tff(22765,plain,
% 10.19/10.45 (~b(s(s(s(s(z)))), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[2097, 1234, 411, 721, 719, 720])).
% 10.19/10.45 tff(22766,plain,
% 10.19/10.45 (r(s(s(s(s(z)))), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[749, 22765])).
% 10.19/10.45 tff(22767,plain,
% 10.19/10.45 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[9171, 22766, 721, 1484, 3369, 2064, 1234])).
% 10.19/10.45 tff(22768,plain,
% 10.19/10.45 (b(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[3652, 22767])).
% 10.19/10.45 tff(22769,plain,
% 10.19/10.45 (~r(s(s(z)), z)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[9187, 22766, 721, 1484, 3369, 1234, 2064])).
% 10.19/10.45 tff(22770,plain,
% 10.19/10.45 (b(s(s(z)), z)),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[1211, 22769])).
% 10.19/10.45 tff(22771,plain,
% 10.19/10.45 (~r(s(s(z)), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[22066, 22770, 90, 721, 590, 411, 720, 1747, 22768])).
% 10.19/10.45 tff(22772,plain,
% 10.19/10.45 (b(s(s(z)), s(z))),
% 10.19/10.45 inference(unit_resolution,[status(thm)],[3778, 22771])).
% 10.19/10.45 tff(22773,plain,
% 10.19/10.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 10.19/10.45 inference(rewrite,[status(thm)],[])).
% 10.19/10.45 tff(22774,plain,
% 10.19/10.45 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 10.19/10.45 inference(rewrite,[status(thm)],[])).
% 10.19/10.45 tff(22775,plain,
% 10.19/10.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 10.19/10.45 inference(monotonicity,[status(thm)],[22774])).
% 10.19/10.45 tff(22776,plain,
% 10.19/10.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 10.19/10.46 inference(transitivity,[status(thm)],[22775, 22773])).
% 10.19/10.46 tff(22777,plain,
% 10.19/10.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 10.19/10.46 inference(quant_inst,[status(thm)],[])).
% 10.19/10.46 tff(22778,plain,
% 10.19/10.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 10.19/10.46 inference(modus_ponens,[status(thm)],[22777, 22776])).
% 10.19/10.46 tff(22779,plain,
% 10.19/10.46 ($false),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[22778, 391, 90, 3369, 1234, 22772, 721])).
% 10.19/10.46 tff(22780,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.46 tff(22781,plain,
% 10.19/10.46 (~r(s(z), elem!1)),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[22780, 22764, 22686, 721, 590, 411, 2691, 90, 22755, 22761, 22757])).
% 10.19/10.46 tff(22782,plain,
% 10.19/10.46 (b(s(z), elem!1)),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[632, 22781, 21435])).
% 10.19/10.46 tff(22783,plain,
% 10.19/10.46 (b(s(z), s(s(s(elem!1))))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[14872, 22782, 5])).
% 10.19/10.46 tff(22784,plain,
% 10.19/10.46 (b(s(s(s(elem!1))), s(s(z)))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[16425, 22764, 3807])).
% 10.19/10.46 tff(22785,plain,
% 10.19/10.46 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[3852, 22763, 90, 184, 21769, 3807, 3823, 22757])).
% 10.19/10.46 tff(22786,plain,
% 10.19/10.46 (r(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[1714, 22785])).
% 10.19/10.46 tff(22787,plain,
% 10.19/10.46 (~r(s(s(z)), s(z))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[10673, 22786, 22686, 22759])).
% 10.19/10.46 tff(22788,plain,
% 10.19/10.46 (b(s(s(z)), s(z))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[3778, 22787])).
% 10.19/10.46 tff(22789,plain,
% 10.19/10.46 (~b(s(s(s(elem!1))), z)),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[21394, 22788, 22784, 22615, 22783])).
% 10.19/10.46 tff(22790,plain,
% 10.19/10.46 (~r(elem!1, z)),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[20856, 22788, 90, 722, 22762, 411, 3807, 22783, 22615])).
% 10.19/10.46 tff(22791,plain,
% 10.19/10.46 (b(elem!1, z)),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[526, 22790, 2])).
% 10.19/10.46 tff(22792,plain,
% 10.19/10.46 ($false),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[19694, 22791, 22789, 184, 411, 22614])).
% 10.19/10.46 tff(22793,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (elem!1 = z) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.46 tff(22794,plain,
% 10.19/10.46 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[22793, 59, 15899, 2, 90, 22613, 22359, 20263, 21728])).
% 10.19/10.46 tff(22795,plain,
% 10.19/10.46 (r(s(s(z)), s(s(s(s(z)))))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[3652, 22794])).
% 10.19/10.46 tff(22796,plain,
% 10.19/10.46 (~b(s(z), s(s(z)))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[22684, 20263, 22613, 21728, 15899, 90, 2, 22359])).
% 10.19/10.46 tff(22797,plain,
% 10.19/10.46 (r(s(z), s(s(z)))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[1788, 22796])).
% 10.19/10.46 tff(22798,plain,
% 10.19/10.46 (~(s(s(s(s(z)))) = elem!1)),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[1436, 22359])).
% 10.19/10.46 tff(22799,plain,
% 10.19/10.46 (~r(elem!1, s(s(z)))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[22623, 1484, 411, 722])).
% 10.19/10.46 tff(22800,plain,
% 10.19/10.46 (b(elem!1, s(s(z)))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[3394, 22799, 1405])).
% 10.19/10.46 tff(22801,plain,
% 10.19/10.46 (b(elem!1, s(s(s(s(z)))))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[781, 22025, 770])).
% 10.19/10.46 tff(22802,plain,
% 10.19/10.46 (~r(elem!1, z)),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[16803, 1484, 411, 722])).
% 10.19/10.46 tff(22803,plain,
% 10.19/10.46 (b(elem!1, z)),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[526, 22802, 2])).
% 10.19/10.46 tff(22804,plain,
% 10.19/10.46 (~b(z, s(s(s(s(z)))))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[3234, 22803, 90, 22801])).
% 10.19/10.46 tff(22805,plain,
% 10.19/10.46 (r(z, s(s(s(s(z)))))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[800, 22804])).
% 10.19/10.46 tff(22806,plain,
% 10.19/10.46 (~b(s(z), s(s(s(s(z)))))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[22780, 22805, 1747, 721, 590, 411, 720, 90, 1484, 22801, 22800])).
% 10.19/10.46 tff(22807,plain,
% 10.19/10.46 (r(s(z), s(s(s(s(z)))))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[1230, 22806])).
% 10.19/10.46 tff(22808,plain,
% 10.19/10.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 10.19/10.46 inference(rewrite,[status(thm)],[])).
% 10.19/10.46 tff(22809,plain,
% 10.19/10.46 (((~r(s(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))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 10.19/10.46 inference(rewrite,[status(thm)],[])).
% 10.19/10.46 tff(22810,plain,
% 10.19/10.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 10.19/10.46 inference(monotonicity,[status(thm)],[22809])).
% 10.19/10.46 tff(22811,plain,
% 10.19/10.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 10.19/10.46 inference(transitivity,[status(thm)],[22810, 22808])).
% 10.19/10.46 tff(22812,plain,
% 10.19/10.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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)))))))),
% 10.19/10.46 inference(quant_inst,[status(thm)],[])).
% 10.19/10.46 tff(22813,plain,
% 10.19/10.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 10.19/10.46 inference(modus_ponens,[status(thm)],[22812, 22811])).
% 10.19/10.46 tff(22814,plain,
% 10.19/10.46 ($false),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[22813, 194, 1749, 1216, 1747, 1697])).
% 10.19/10.46 tff(22815,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.46 tff(22816,plain,
% 10.19/10.46 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[22815, 22807, 1747, 1749])).
% 10.19/10.46 tff(22817,plain,
% 10.19/10.46 (b(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[1714, 22816])).
% 10.19/10.46 tff(22818,plain,
% 10.19/10.46 (~r(s(s(s(s(z)))), elem!1)),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[20629, 22807, 1747, 1749])).
% 10.19/10.46 tff(22819,plain,
% 10.19/10.46 (b(s(s(s(s(z)))), elem!1)),
% 10.19/10.46 inference(unit_resolution,[status(thm)],[762, 22818, 720])).
% 10.19/10.46 tff(22820,plain,
% 10.19/10.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 10.19/10.47 inference(rewrite,[status(thm)],[])).
% 10.19/10.47 tff(22821,plain,
% 10.19/10.47 (((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 10.19/10.47 inference(rewrite,[status(thm)],[])).
% 10.19/10.47 tff(22822,plain,
% 10.19/10.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 10.19/10.47 inference(monotonicity,[status(thm)],[22821])).
% 10.19/10.47 tff(22823,plain,
% 10.19/10.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 10.19/10.47 inference(transitivity,[status(thm)],[22822, 22820])).
% 10.19/10.47 tff(22824,plain,
% 10.19/10.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.19/10.47 inference(quant_inst,[status(thm)],[])).
% 10.19/10.47 tff(22825,plain,
% 10.19/10.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 10.19/10.47 inference(modus_ponens,[status(thm)],[22824, 22823])).
% 10.19/10.47 tff(22826,plain,
% 10.19/10.47 ($false),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22825, 391, 3369, 1652, 3563, 1233, 590])).
% 10.19/10.47 tff(22827,plain,((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.47 tff(22828,plain,
% 10.19/10.47 (~b(s(s(z)), s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22827, 22800, 22819, 22817, 590])).
% 10.19/10.47 tff(22829,plain,
% 10.19/10.47 (r(s(s(z)), s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[3778, 22828])).
% 10.19/10.47 tff(22830,plain,
% 10.19/10.47 (~r(z, s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[9720, 22829, 722, 1747])).
% 10.19/10.47 tff(22831,plain,
% 10.19/10.47 (b(z, s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[18613, 22830])).
% 10.19/10.47 tff(22832,plain,
% 10.19/10.47 (~r(s(s(z)), z)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[10610, 22829, 722, 22807])).
% 10.19/10.47 tff(22833,plain,
% 10.19/10.47 (b(s(s(z)), z)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[1211, 22832])).
% 10.19/10.47 tff(22834,plain,
% 10.19/10.47 ($false),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[15053, 22833, 22831, 90, 22817])).
% 10.19/10.47 tff(22835,plain,((~r(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(z), z)) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (elem!1 = s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 10.19/10.47 tff(22836,plain,
% 10.19/10.47 (~r(s(z), elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22835, 22613, 90, 22797, 21728, 22798, 22795, 20263, 15899, 22363, 2])).
% 10.19/10.47 tff(22837,plain,
% 10.19/10.47 (b(s(z), elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[632, 22836, 20272])).
% 10.19/10.47 tff(22838,plain,
% 10.19/10.47 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 10.19/10.47 inference(monotonicity,[status(thm)],[22359])).
% 10.19/10.47 tff(22839,plain,
% 10.19/10.47 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 10.19/10.47 inference(symmetry,[status(thm)],[22838])).
% 10.19/10.47 tff(22840,plain,
% 10.19/10.47 (b(s(s(s(elem!1))), s(z))),
% 10.19/10.47 inference(modus_ponens,[status(thm)],[20263, 22839])).
% 10.19/10.47 tff(22841,plain,
% 10.19/10.47 (b(s(z), s(s(s(elem!1))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[14872, 22837, 22359])).
% 10.19/10.47 tff(22842,plain,
% 10.19/10.47 (~b(elem!1, s(s(s(elem!1))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[15370, 22359])).
% 10.19/10.47 tff(22843,plain,
% 10.19/10.47 (~r(s(s(s(s(z)))), elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22641, 1748, 411, 719])).
% 10.19/10.47 tff(22844,plain,
% 10.19/10.47 (b(s(s(s(s(z)))), elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[762, 22843, 720])).
% 10.19/10.47 tff(22845,plain,
% 10.19/10.47 (~b(s(s(s(s(z)))), s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[1775, 22844, 1747, 150, 1749, 1748])).
% 10.19/10.47 tff(22846,plain,
% 10.19/10.47 (r(s(s(s(s(z)))), s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[749, 22845])).
% 10.19/10.47 tff(22847,plain,
% 10.19/10.47 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[20820, 22844, 125])).
% 10.19/10.47 tff(22848,plain,
% 10.19/10.47 (~b(s(z), s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[20817, 22847, 379, 1526])).
% 10.19/10.47 tff(22849,plain,
% 10.19/10.47 (r(s(z), s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[1230, 22848])).
% 10.19/10.47 tff(22850,plain,
% 10.19/10.47 ($false),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[16396, 22849, 22846, 1747, 1749])).
% 10.19/10.47 tff(22851,plain,((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (s(z) = elem!1) | (~(elem!1 = s(s(s(elem!1))))) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.47 tff(22852,plain,
% 10.19/10.47 (~r(elem!1, s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22851, 719, 1749, 379, 1526, 21435, 125, 720, 411, 1747])).
% 10.19/10.47 tff(22853,plain,
% 10.19/10.47 (b(elem!1, s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[3394, 22852, 1405])).
% 10.19/10.47 tff(22854,plain,
% 10.19/10.47 (b(s(s(s(elem!1))), s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[16425, 22853, 125])).
% 10.19/10.47 tff(22855,plain,
% 10.19/10.47 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[20820, 1652, 125])).
% 10.19/10.47 tff(22856,plain,
% 10.19/10.47 (~b(s(z), s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[20817, 22855, 379, 1526])).
% 10.19/10.47 tff(22857,plain,
% 10.19/10.47 (r(s(z), s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[1230, 22856])).
% 10.19/10.47 tff(22858,plain,
% 10.19/10.47 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22815, 22857, 1747, 1749])).
% 10.19/10.47 tff(22859,plain,
% 10.19/10.47 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[20684, 22857, 721, 1747, 644, 3369, 1652, 90])).
% 10.19/10.47 tff(22860,plain,
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% 10.19/10.47 inference(unit_resolution,[status(thm)],[1714, 22859, 22858])).
% 10.19/10.47 tff(22861,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.47 tff(22862,plain,
% 10.19/10.47 (~b(s(s(s(s(z)))), elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22861, 22853, 1747, 644, 721, 90, 1749, 379, 1526, 125])).
% 10.19/10.47 tff(22863,plain,
% 10.19/10.47 (r(s(s(s(s(z)))), elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[762, 22862, 720])).
% 10.19/10.47 tff(22864,plain,
% 10.19/10.47 (~r(s(s(z)), z)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22002, 22863, 1749, 719])).
% 10.19/10.47 tff(22865,plain,
% 10.19/10.47 (b(s(s(z)), z)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[1211, 22864])).
% 10.19/10.47 tff(22866,plain,
% 10.19/10.47 (~r(s(z), s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[20629, 22863, 1747, 1749])).
% 10.19/10.47 tff(22867,plain,
% 10.19/10.47 (b(s(z), s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[1230, 22866])).
% 10.19/10.47 tff(22868,plain,
% 10.19/10.47 (~b(s(s(s(s(z)))), s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[2097, 22867, 411, 721, 719, 720])).
% 10.19/10.47 tff(22869,plain,
% 10.19/10.47 (r(s(s(s(s(z)))), s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[749, 22868])).
% 10.19/10.47 tff(22870,plain,
% 10.19/10.47 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[9076, 22869, 1747, 1749])).
% 10.19/10.47 tff(22871,plain,
% 10.19/10.47 (b(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[1714, 22870])).
% 10.19/10.47 tff(22872,plain,
% 10.19/10.47 (~b(z, s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[15053, 22871, 90, 22865])).
% 10.19/10.47 tff(22873,plain,
% 10.19/10.47 (r(z, s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[18613, 22872])).
% 10.19/10.47 tff(22874,plain,
% 10.19/10.47 (~r(s(s(z)), s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[9720, 22873, 722, 1747])).
% 10.19/10.47 tff(22875,plain,
% 10.19/10.47 (b(s(s(z)), s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[3778, 22874])).
% 10.19/10.47 tff(22876,plain,
% 10.19/10.47 (~b(s(s(s(elem!1))), z)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[21394, 22875, 379, 1526, 22854])).
% 10.19/10.47 tff(22877,plain,
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% 10.19/10.47 inference(unit_resolution,[status(thm)],[20856, 22875, 90, 722, 22863, 411, 125, 379, 1526])).
% 10.19/10.47 tff(22878,plain,
% 10.19/10.47 (b(elem!1, z)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[526, 22877, 2])).
% 10.19/10.47 tff(22879,plain,
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% 10.19/10.47 inference(unit_resolution,[status(thm)],[19694, 22878, 22876, 184, 411, 4028])).
% 10.19/10.47 tff(22880,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = z) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), elem!1)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.47 tff(22881,plain,
% 10.19/10.47 (~r(z, s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22880, 59, 15899, 22842, 2, 22841, 22840, 90, 22613, 22367, 22797, 22795, 20263, 22798, 22837, 22363])).
% 10.19/10.47 tff(22882,plain,
% 10.19/10.47 (b(z, s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[800, 22881])).
% 10.19/10.47 tff(22883,plain,
% 10.19/10.47 (~b(s(z), s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22664, 22882, 90, 21728])).
% 10.19/10.47 tff(22884,plain,
% 10.19/10.47 (r(s(z), s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[1230, 22883])).
% 10.19/10.47 tff(22885,plain,
% 10.19/10.47 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22815, 22884, 22797, 22795])).
% 10.19/10.47 tff(22886,plain,
% 10.19/10.47 (b(s(s(s(s(z)))), s(s(z)))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[1714, 22885])).
% 10.19/10.47 tff(22887,plain,
% 10.19/10.47 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 10.19/10.47 inference(transitivity,[status(thm)],[22361, 8492])).
% 10.19/10.47 tff(22888,plain,
% 10.19/10.47 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 10.19/10.47 inference(monotonicity,[status(thm)],[22887])).
% 10.19/10.47 tff(22889,plain,
% 10.19/10.47 (~(s(s(z)) = elem!1)),
% 10.19/10.47 inference(modus_ponens,[status(thm)],[1397, 22888])).
% 10.19/10.47 tff(22890,plain,
% 10.19/10.47 (~b(elem!1, z)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[14881, 22882, 90, 21728, 22837])).
% 10.19/10.47 tff(22891,plain,
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% 10.19/10.47 inference(unit_resolution,[status(thm)],[526, 22890, 2])).
% 10.19/10.47 tff(22892,plain,
% 10.19/10.47 (~r(s(s(s(s(z)))), elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[20629, 22884, 22797, 22795])).
% 10.19/10.47 tff(22893,plain,
% 10.19/10.47 (b(s(s(s(s(z)))), elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[762, 22892, 22798])).
% 10.19/10.47 tff(22894,plain,
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% 10.19/10.47 inference(unit_resolution,[status(thm)],[20637, 22884, 90, 22837, 22797, 22798, 22890, 22882])).
% 10.19/10.47 tff(22895,plain,
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% 10.19/10.47 inference(unit_resolution,[status(thm)],[1211, 22894])).
% 10.19/10.47 tff(22896,plain,
% 10.19/10.47 ($false),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[18608, 22895, 22893, 15899, 22613, 22891, 22889, 22363, 22886])).
% 10.19/10.47 tff(22897,plain,(b(z, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 10.19/10.47 tff(22898,plain,
% 10.19/10.47 (b(z, s(s(s(elem!1))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22897, 88, 2])).
% 10.19/10.47 tff(22899,plain,
% 10.19/10.47 ($false),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[89, 17362])).
% 10.19/10.47 tff(22900,plain,((~(elem!1 = s(s(s(elem!1))))) | b(z, elem!1) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.47 tff(22901,plain,
% 10.19/10.47 (~(elem!1 = s(s(s(elem!1))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22900, 89, 22898])).
% 10.19/10.47 tff(22902,plain,
% 10.19/10.47 (b(z, elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[141, 80, 98])).
% 10.19/10.47 tff(22903,plain,
% 10.19/10.47 (b(z, s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[678, 676])).
% 10.19/10.47 tff(22904,plain,
% 10.19/10.47 (~b(z, s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[6914, 1234, 90, 133, 22903])).
% 10.19/10.47 tff(22905,plain,
% 10.19/10.47 (r(z, s(s(s(s(z)))))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[800, 22904])).
% 10.19/10.47 tff(22906,plain,
% 10.19/10.47 (~(elem!1 = s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[11318, 22904, 2, 676])).
% 10.19/10.47 tff(22907,plain,
% 10.19/10.47 (r(elem!1, s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[837, 22906, 31])).
% 10.19/10.47 tff(22908,plain,
% 10.19/10.47 (~r(elem!1, z)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[17062, 22907, 182, 22905])).
% 10.19/10.47 tff(22909,plain,
% 10.19/10.47 (b(elem!1, z)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[526, 22908, 2])).
% 10.19/10.47 tff(22910,plain,
% 10.19/10.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.19/10.47 inference(rewrite,[status(thm)],[])).
% 10.19/10.47 tff(22911,plain,
% 10.19/10.47 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.19/10.47 inference(rewrite,[status(thm)],[])).
% 10.19/10.47 tff(22912,plain,
% 10.19/10.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 10.19/10.47 inference(monotonicity,[status(thm)],[22911])).
% 10.19/10.47 tff(22913,plain,
% 10.19/10.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.19/10.47 inference(transitivity,[status(thm)],[22912, 22910])).
% 10.19/10.47 tff(22914,plain,
% 10.19/10.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.19/10.47 inference(quant_inst,[status(thm)],[])).
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% 10.19/10.47 inference(modus_ponens,[status(thm)],[22914, 22913])).
% 10.19/10.47 tff(22916,plain,
% 10.19/10.47 (~b(s(s(s(s(z)))), elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22915, 391, 22909, 90, 1234, 22903])).
% 10.19/10.47 tff(22917,plain,
% 10.19/10.47 ($false),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[2896, 391, 90, 1234, 1759, 664])).
% 10.19/10.47 tff(22918,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.47 tff(22919,plain,
% 10.19/10.47 (~b(s(s(s(s(z)))), s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[22918, 1234, 90, 22903])).
% 10.19/10.47 tff(22920,plain,
% 10.19/10.47 (r(s(s(s(s(z)))), s(z))),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[749, 22919])).
% 10.19/10.47 tff(22921,plain,
% 10.19/10.47 (~r(s(s(s(s(z)))), elem!1)),
% 10.19/10.47 inference(unit_resolution,[status(thm)],[15864, 22920, 182, 22907])).
% 10.19/10.48 tff(22922,plain,
% 10.19/10.48 (s(s(s(s(z)))) = elem!1),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[762, 22921, 22916])).
% 10.19/10.48 tff(22923,plain,
% 10.19/10.48 (~(s(s(s(elem!1))) = elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[1436, 22922])).
% 10.19/10.48 tff(22924,plain,
% 10.19/10.48 (b(z, s(s(s(elem!1))))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[22897, 90, 2])).
% 10.19/10.48 tff(22925,plain,
% 10.19/10.48 (~b(s(s(s(elem!1))), elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[10743, 22909, 22924, 133])).
% 10.19/10.48 tff(22926,plain,
% 10.19/10.48 (~(s(z) = elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[1495, 22906])).
% 10.19/10.48 tff(22927,plain,
% 10.19/10.48 (b(s(elem!1), elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[14657, 22925, 133, 22924, 22926, 22908, 2])).
% 10.19/10.48 tff(22928,plain,
% 10.19/10.48 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[14662, 22927, 22925])).
% 10.19/10.48 tff(22929,plain,
% 10.19/10.48 (~(s(s(elem!1)) = s(elem!1))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[2279, 22928])).
% 10.19/10.48 tff(22930,plain,
% 10.19/10.48 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[287, 22929])).
% 10.19/10.48 tff(22931,plain,
% 10.19/10.48 (b(s(z), elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[8916, 22922, 1234])).
% 10.19/10.48 tff(22932,plain,
% 10.19/10.48 (~(s(s(elem!1)) = elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[451, 22928])).
% 10.19/10.48 tff(22933,plain,
% 10.19/10.48 (~b(s(s(elem!1)), elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[5286, 22929, 133, 22909, 22927])).
% 10.19/10.48 tff(22934,plain,
% 10.19/10.48 (r(s(s(elem!1)), elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[872, 22933, 22932])).
% 10.19/10.48 tff(22935,plain,
% 10.19/10.48 (~(elem!1 = s(s(s(elem!1))))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[129, 22923])).
% 10.19/10.48 tff(22936,plain,
% 10.19/10.48 (~r(s(s(s(elem!1))), z)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[12936, 22935, 22924, 133, 22925, 22934, 22931, 22930, 22909])).
% 10.19/10.48 tff(22937,plain,
% 10.19/10.48 (b(s(s(s(elem!1))), z)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[377, 22936])).
% 10.19/10.48 tff(22938,plain,
% 10.19/10.48 (~b(elem!1, s(s(s(elem!1))))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[10876, 22937, 133, 22909])).
% 10.19/10.48 tff(22939,plain,
% 10.19/10.48 (r(elem!1, s(s(s(elem!1))))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[424, 22938, 22935])).
% 10.19/10.48 tff(22940,plain,
% 10.19/10.48 (~b(s(s(s(elem!1))), s(z))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[15581, 22939, 22924, 22903, 22925, 22938, 22923])).
% 10.19/10.48 tff(22941,plain,
% 10.19/10.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.19/10.48 inference(rewrite,[status(thm)],[])).
% 10.19/10.48 tff(22942,plain,
% 10.19/10.48 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.19/10.48 inference(rewrite,[status(thm)],[])).
% 10.19/10.48 tff(22943,plain,
% 10.19/10.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 10.19/10.48 inference(monotonicity,[status(thm)],[22942])).
% 10.19/10.48 tff(22944,plain,
% 10.19/10.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.19/10.48 inference(transitivity,[status(thm)],[22943, 22941])).
% 10.19/10.48 tff(22945,plain,
% 10.19/10.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 10.19/10.48 inference(quant_inst,[status(thm)],[])).
% 10.19/10.48 tff(22946,plain,
% 10.19/10.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 10.19/10.48 inference(modus_ponens,[status(thm)],[22945, 22944])).
% 10.19/10.48 tff(22947,plain,
% 10.19/10.48 ($false),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[22946, 391, 133, 380, 10682, 379, 664])).
% 10.19/10.48 tff(22948,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.48 tff(22949,plain,
% 10.19/10.48 (~b(s(z), s(s(s(elem!1))))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[22948, 22937, 22924, 133, 22903])).
% 10.19/10.48 tff(22950,plain,
% 10.19/10.48 (r(s(z), s(s(s(elem!1))))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[247, 22949])).
% 10.19/10.48 tff(22951,plain,
% 10.19/10.48 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 10.19/10.48 inference(rewrite,[status(thm)],[])).
% 10.19/10.48 tff(22952,plain,
% 10.19/10.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))))),
% 10.19/10.48 inference(monotonicity,[status(thm)],[22951])).
% 10.19/10.48 tff(22953,plain,
% 10.19/10.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 10.19/10.48 inference(transitivity,[status(thm)],[22952, 17149])).
% 10.19/10.48 tff(22954,plain,
% 10.19/10.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 10.19/10.48 inference(quant_inst,[status(thm)],[])).
% 10.19/10.48 tff(22955,plain,
% 10.19/10.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))),
% 10.19/10.48 inference(modus_ponens,[status(thm)],[22954, 22953])).
% 10.19/10.48 tff(22956,plain,
% 10.19/10.48 (~r(elem!1, s(s(s(elem!1))))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[22955, 194, 232, 183, 847])).
% 10.19/10.48 tff(22957,plain,
% 10.19/10.48 (b(elem!1, s(s(s(elem!1))))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[424, 22956, 1])).
% 10.19/10.48 tff(22958,plain,
% 10.19/10.48 (~r(s(s(s(elem!1))), elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[5762, 194, 232, 183, 847])).
% 10.19/10.48 tff(22959,plain,
% 10.19/10.48 (b(s(s(s(elem!1))), elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[230, 22958, 9])).
% 10.19/10.48 tff(22960,plain,
% 10.19/10.48 ($false),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[10845, 22959, 22957, 10682, 133])).
% 10.19/10.48 tff(22961,plain,((~r(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.48 tff(22962,plain,
% 10.19/10.48 (~r(s(s(s(elem!1))), s(z))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[22961, 22950, 22924, 133, 22907, 22935])).
% 10.19/10.48 tff(22963,plain,
% 10.19/10.48 ($false),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[223, 22962, 22940])).
% 10.19/10.48 tff(22964,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | b(elem!1, s(z)) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.48 tff(22965,plain,
% 10.19/10.48 (~b(s(z), s(s(s(s(z)))))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[22964, 676, 181, 88, 2, 31, 133])).
% 10.19/10.48 tff(22966,plain,
% 10.19/10.48 (~r(s(s(s(s(z)))), elem!1)),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[2720, 182, 1216, 719])).
% 10.19/10.48 tff(22967,plain,
% 10.19/10.48 (s(s(s(s(z)))) = elem!1),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[762, 22966, 1549])).
% 10.19/10.48 tff(22968,plain,
% 10.19/10.48 (~r(s(s(s(s(z)))), s(z))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[1224, 182, 1216, 719])).
% 10.19/10.48 tff(22969,plain,
% 10.19/10.48 (b(s(s(s(s(z)))), s(z))),
% 10.19/10.48 inference(unit_resolution,[status(thm)],[749, 22968])).
% 10.19/10.48 tff(22970,plain,
% 10.19/10.49 ($false),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[11186, 22969, 22967, 31])).
% 10.19/10.49 tff(22971,plain,((~r(s(z), z)) | b(elem!1, s(z)) | b(s(s(s(s(z)))), elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.49 tff(22972,plain,
% 10.19/10.49 (~r(z, s(s(s(s(z)))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[22971, 1549, 31, 181, 2913])).
% 10.19/10.49 tff(22973,plain,
% 10.19/10.49 (b(z, s(s(s(s(z)))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[800, 22972])).
% 10.19/10.49 tff(22974,plain,
% 10.19/10.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 10.19/10.49 inference(rewrite,[status(thm)],[])).
% 10.19/10.49 tff(22975,plain,
% 10.19/10.49 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 10.19/10.49 inference(rewrite,[status(thm)],[])).
% 10.19/10.49 tff(22976,plain,
% 10.19/10.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 10.19/10.49 inference(monotonicity,[status(thm)],[22975])).
% 10.19/10.49 tff(22977,plain,
% 10.19/10.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 10.19/10.49 inference(transitivity,[status(thm)],[22976, 22974])).
% 10.19/10.49 tff(22978,plain,
% 10.19/10.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 10.19/10.49 inference(quant_inst,[status(thm)],[])).
% 10.19/10.49 tff(22979,plain,
% 10.19/10.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 10.19/10.49 inference(modus_ponens,[status(thm)],[22978, 22977])).
% 10.19/10.49 tff(22980,plain,
% 10.19/10.49 ($false),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[22979, 391, 133, 90, 2064, 1686])).
% 10.19/10.49 tff(22981,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.49 tff(22982,plain,
% 10.19/10.49 (~b(elem!1, s(s(s(s(z)))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[22981, 22973, 90, 133])).
% 10.19/10.49 tff(22983,plain,
% 10.19/10.49 (elem!1 = s(z)),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[837, 832, 31])).
% 10.19/10.49 tff(22984,plain,
% 10.19/10.49 (~b(s(s(s(elem!1))), elem!1)),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[1563, 22983, 1549])).
% 10.19/10.49 tff(22985,plain,
% 10.19/10.49 (s(z) = elem!1),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[172, 22983])).
% 10.19/10.49 tff(22986,plain,
% 10.19/10.49 (~b(s(s(s(elem!1))), s(z))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[3938, 22985, 22984])).
% 10.19/10.49 tff(22987,plain,
% 10.19/10.49 (r(s(s(s(elem!1))), s(z))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[223, 22986])).
% 10.19/10.49 tff(22988,plain,
% 10.19/10.49 (~(s(s(s(elem!1))) = elem!1)),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[8406, 22987, 832])).
% 10.19/10.49 tff(22989,plain,
% 10.19/10.49 (~b(s(z), s(s(s(elem!1))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[2884, 22983, 2881])).
% 10.19/10.49 tff(22990,plain,
% 10.19/10.49 (r(s(z), s(s(s(elem!1))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[247, 22989])).
% 10.19/10.49 tff(22991,plain,
% 10.19/10.49 (~r(z, s(s(s(elem!1))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[3499, 22987, 182, 22990])).
% 10.19/10.49 tff(22992,plain,
% 10.19/10.49 (~(elem!1 = s(z))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[11177, 1759, 11173])).
% 10.19/10.49 tff(22993,plain,
% 10.19/10.49 (~(s(z) = elem!1)),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[1495, 22992])).
% 10.19/10.49 tff(22994,plain,
% 10.19/10.49 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[2849, 22993])).
% 10.19/10.49 tff(22995,plain,
% 10.19/10.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.19/10.49 inference(rewrite,[status(thm)],[])).
% 10.19/10.49 tff(22996,plain,
% 10.19/10.49 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.19/10.49 inference(rewrite,[status(thm)],[])).
% 10.19/10.49 tff(22997,plain,
% 10.19/10.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 10.19/10.49 inference(monotonicity,[status(thm)],[22996])).
% 10.19/10.49 tff(22998,plain,
% 10.19/10.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.19/10.49 inference(transitivity,[status(thm)],[22997, 22995])).
% 10.19/10.49 tff(22999,plain,
% 10.19/10.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.19/10.49 inference(quant_inst,[status(thm)],[])).
% 10.19/10.49 tff(23000,plain,
% 10.19/10.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 10.19/10.49 inference(modus_ponens,[status(thm)],[22999, 22998])).
% 10.19/10.49 tff(23001,plain,
% 10.19/10.49 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[23000, 391, 380, 10682, 90])).
% 10.19/10.49 tff(23002,plain,
% 10.19/10.49 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[4313, 42, 23001])).
% 10.19/10.49 tff(23003,plain,
% 10.19/10.49 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[23002, 6950])).
% 10.19/10.49 tff(23004,plain,
% 10.19/10.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.19/10.49 inference(rewrite,[status(thm)],[])).
% 10.19/10.49 tff(23005,plain,
% 10.19/10.49 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.19/10.49 inference(rewrite,[status(thm)],[])).
% 10.19/10.49 tff(23006,plain,
% 10.19/10.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 10.19/10.49 inference(monotonicity,[status(thm)],[23005])).
% 10.19/10.49 tff(23007,plain,
% 10.19/10.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.19/10.49 inference(transitivity,[status(thm)],[23006, 23004])).
% 10.19/10.49 tff(23008,plain,
% 10.19/10.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.19/10.49 inference(quant_inst,[status(thm)],[])).
% 10.19/10.49 tff(23009,plain,
% 10.19/10.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.19/10.49 inference(modus_ponens,[status(thm)],[23008, 23007])).
% 10.19/10.49 tff(23010,plain,
% 10.19/10.49 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[23009, 391, 380, 10682, 90])).
% 10.19/10.49 tff(23011,plain,
% 10.19/10.49 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 23010])).
% 10.19/10.49 tff(23012,plain,
% 10.19/10.49 ($false),
% 10.19/10.49 inference(unit_resolution,[status(thm)],[16936, 194, 183, 1216, 23011, 23003])).
% 10.19/10.49 tff(23013,plain,((~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 10.19/10.49 tff(23014,plain,
% 10.19/10.49 (~b(s(s(s(elem!1))), z)),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[23013, 22994, 1216, 11174, 10782, 90])).
% 10.19/10.50 tff(23015,plain,
% 10.19/10.50 (r(s(s(s(elem!1))), z)),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[377, 23014])).
% 10.19/10.50 tff(23016,plain,
% 10.19/10.50 (~r(z, s(z))),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[16377, 23015, 11174, 1216])).
% 10.19/10.50 tff(23017,plain,
% 10.19/10.50 (b(z, s(z))),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[678, 23016])).
% 10.19/10.50 tff(23018,plain,
% 10.19/10.50 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[2849, 1496])).
% 10.19/10.50 tff(23019,plain,
% 10.19/10.50 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[10940, 23018])).
% 10.19/10.50 tff(23020,plain,
% 10.19/10.50 (~b(s(s(s(elem!1))), z)),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[23013, 23018, 1216, 183, 10682, 90])).
% 10.19/10.50 tff(23021,plain,
% 10.19/10.50 (r(s(s(s(elem!1))), z)),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[377, 23020])).
% 10.19/10.50 tff(23022,plain,
% 10.19/10.50 (~r(z, s(z))),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[16377, 23021, 183, 1216])).
% 10.19/10.50 tff(23023,plain,
% 10.19/10.50 (b(z, s(z))),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[678, 23022])).
% 10.19/10.50 tff(23024,plain,
% 10.19/10.50 (r(elem!1, s(z))),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[837, 31, 831])).
% 10.19/10.50 tff(23025,plain,
% 10.19/10.50 (~r(s(s(s(elem!1))), elem!1)),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[10854, 194, 183, 23024, 1216])).
% 10.19/10.50 tff(23026,plain,
% 10.19/10.50 (~(z = elem!1)),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[9853, 23025, 23021])).
% 10.19/10.50 tff(23027,plain,
% 10.19/10.50 (~(elem!1 = z)),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[5453, 23026])).
% 10.19/10.50 tff(23028,plain,
% 10.19/10.50 (~r(elem!1, s(s(s(elem!1))))),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[10776, 23024, 183, 1216])).
% 10.19/10.50 tff(23029,plain,
% 10.19/10.50 (b(elem!1, s(s(s(elem!1))))),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[424, 23028, 1])).
% 10.19/10.50 tff(23030,plain,
% 10.19/10.50 (b(s(s(s(elem!1))), elem!1)),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[230, 23025, 9])).
% 10.19/10.50 tff(23031,plain,
% 10.19/10.50 (~b(elem!1, z)),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[10911, 391, 23030, 10682, 23029])).
% 10.19/10.50 tff(23032,plain,
% 10.19/10.50 (r(elem!1, z)),
% 10.19/10.50 inference(unit_resolution,[status(thm)],[526, 23031, 23027])).
% 10.19/10.50 tff(23033,plain,
% 10.19/10.50 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 10.19/10.50 inference(rewrite,[status(thm)],[])).
% 10.19/10.50 tff(23034,plain,
% 10.19/10.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1))))),
% 10.19/10.50 inference(monotonicity,[status(thm)],[23033])).
% 10.19/10.50 tff(23035,plain,
% 10.19/10.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 10.19/10.50 inference(transitivity,[status(thm)],[23034, 10838])).
% 10.19/10.50 tff(23036,plain,
% 10.19/10.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 10.19/10.50 inference(quant_inst,[status(thm)],[])).
% 10.19/10.50 tff(23037,plain,
% 10.19/10.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1))),
% 10.29/10.50 inference(modus_ponens,[status(thm)],[23036, 23035])).
% 10.29/10.50 tff(23038,plain,
% 10.29/10.50 (~b(z, elem!1)),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[23037, 391, 23030, 10682, 23029])).
% 10.29/10.50 tff(23039,plain,
% 10.29/10.50 (r(z, elem!1)),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[141, 23038, 23026])).
% 10.29/10.50 tff(23040,plain,
% 10.29/10.50 (~r(s(s(z)), elem!1)),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[15383, 194, 23039, 23032, 3557])).
% 10.29/10.50 tff(23041,plain,
% 10.29/10.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.50 inference(rewrite,[status(thm)],[])).
% 10.29/10.50 tff(23042,plain,
% 10.29/10.50 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.50 inference(rewrite,[status(thm)],[])).
% 10.29/10.50 tff(23043,plain,
% 10.29/10.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 10.29/10.50 inference(monotonicity,[status(thm)],[23042])).
% 10.29/10.50 tff(23044,plain,
% 10.29/10.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.50 inference(transitivity,[status(thm)],[23043, 23041])).
% 10.29/10.50 tff(23045,plain,
% 10.29/10.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.50 inference(quant_inst,[status(thm)],[])).
% 10.29/10.50 tff(23046,plain,
% 10.29/10.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 10.29/10.50 inference(modus_ponens,[status(thm)],[23045, 23044])).
% 10.29/10.50 tff(23047,plain,
% 10.29/10.50 (~r(s(s(z)), s(s(s(elem!1))))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[23046, 194, 23039, 23021, 3557])).
% 10.29/10.50 tff(23048,plain,
% 10.29/10.50 (b(s(s(z)), s(s(s(elem!1))))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 23047])).
% 10.29/10.50 tff(23049,plain,
% 10.29/10.50 (~b(s(s(z)), elem!1)),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[15437, 391, 23030, 23029, 23048])).
% 10.29/10.50 tff(23050,plain,
% 10.29/10.50 (s(s(z)) = elem!1),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[4730, 23049, 23040])).
% 10.29/10.50 tff(23051,plain,
% 10.29/10.50 (r(s(z), s(s(elem!1)))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[11275, 23050, 1216])).
% 10.29/10.50 tff(23052,plain,
% 10.29/10.50 (~(s(z) = s(elem!1))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[117, 23026])).
% 10.29/10.50 tff(23053,plain,
% 10.29/10.50 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[4584, 23050, 23052])).
% 10.29/10.50 tff(23054,plain,
% 10.29/10.50 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[281, 23053])).
% 10.29/10.50 tff(23055,plain,
% 10.29/10.50 (s(s(s(z))) = s(elem!1)),
% 10.29/10.50 inference(monotonicity,[status(thm)],[23050])).
% 10.29/10.50 tff(23056,plain,
% 10.29/10.50 (s(s(s(s(z)))) = s(s(elem!1))),
% 10.29/10.50 inference(monotonicity,[status(thm)],[23055])).
% 10.29/10.50 tff(23057,plain,
% 10.29/10.50 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 10.29/10.50 inference(monotonicity,[status(thm)],[23056])).
% 10.29/10.50 tff(23058,plain,
% 10.29/10.50 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 10.29/10.50 inference(monotonicity,[status(thm)],[23050])).
% 10.29/10.50 tff(23059,plain,
% 10.29/10.50 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 10.29/10.50 inference(transitivity,[status(thm)],[23058, 23057])).
% 10.29/10.50 tff(23060,plain,
% 10.29/10.50 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 10.29/10.50 inference(monotonicity,[status(thm)],[23056])).
% 10.29/10.50 tff(23061,plain,
% 10.29/10.50 (b(s(s(elem!1)), z)),
% 10.29/10.50 inference(modus_ponens,[status(thm)],[90, 23060])).
% 10.29/10.50 tff(23062,plain,
% 10.29/10.50 (s(s(elem!1)) = s(s(s(s(z))))),
% 10.29/10.50 inference(symmetry,[status(thm)],[11271])).
% 10.29/10.50 tff(23063,plain,
% 10.29/10.50 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 10.29/10.50 inference(monotonicity,[status(thm)],[23062])).
% 10.29/10.50 tff(23064,plain,
% 10.29/10.50 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 10.29/10.50 inference(symmetry,[status(thm)],[23063])).
% 10.29/10.50 tff(23065,plain,
% 10.29/10.50 (~r(elem!1, s(s(s(s(z)))))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[14900, 23024, 1216, 1697])).
% 10.29/10.50 tff(23066,plain,
% 10.29/10.50 (~(s(s(s(s(z)))) = elem!1)),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[11186, 31, 1759])).
% 10.29/10.50 tff(23067,plain,
% 10.29/10.50 (~(elem!1 = s(s(s(s(z)))))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[769, 23066])).
% 10.29/10.50 tff(23068,plain,
% 10.29/10.50 ($false),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[781, 23067, 23065, 8536])).
% 10.29/10.50 tff(23069,plain,(b(elem!1, s(z)) | b(elem!1, s(s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.50 tff(23070,plain,
% 10.29/10.50 (b(elem!1, s(s(s(s(z)))))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[23069, 1697, 1216, 31, 1759, 831])).
% 10.29/10.50 tff(23071,plain,
% 10.29/10.50 (b(elem!1, s(s(elem!1)))),
% 10.29/10.50 inference(modus_ponens,[status(thm)],[23070, 23064])).
% 10.29/10.50 tff(23072,plain,
% 10.29/10.50 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 10.29/10.50 inference(monotonicity,[status(thm)],[4579])).
% 10.29/10.50 tff(23073,plain,
% 10.29/10.50 (~r(s(z), s(s(z)))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[11508, 1697, 1216, 3557])).
% 10.29/10.50 tff(23074,plain,
% 10.29/10.50 (b(s(z), s(s(z)))),
% 10.29/10.50 inference(unit_resolution,[status(thm)],[1788, 23073])).
% 10.29/10.50 tff(23075,plain,
% 10.29/10.50 (b(s(z), elem!1)),
% 10.29/10.50 inference(modus_ponens,[status(thm)],[23074, 23072])).
% 10.29/10.50 tff(23076,plain,
% 10.29/10.50 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 10.29/10.50 inference(monotonicity,[status(thm)],[11271])).
% 10.29/10.50 tff(23077,plain,
% 10.29/10.50 (b(s(s(elem!1)), s(z))),
% 10.29/10.50 inference(modus_ponens,[status(thm)],[1759, 23076])).
% 10.29/10.50 tff(23078,plain,
% 10.29/10.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 10.29/10.50 inference(rewrite,[status(thm)],[])).
% 10.29/10.50 tff(23079,plain,
% 10.29/10.50 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 10.29/10.50 inference(rewrite,[status(thm)],[])).
% 10.29/10.50 tff(23080,plain,
% 10.29/10.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 10.29/10.50 inference(monotonicity,[status(thm)],[23079])).
% 10.29/10.50 tff(23081,plain,
% 10.29/10.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 10.29/10.51 inference(transitivity,[status(thm)],[23080, 23078])).
% 10.29/10.51 tff(23082,plain,
% 10.29/10.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 10.29/10.51 inference(quant_inst,[status(thm)],[])).
% 10.29/10.51 tff(23083,plain,
% 10.29/10.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))),
% 10.29/10.51 inference(modus_ponens,[status(thm)],[23082, 23081])).
% 10.29/10.51 tff(23084,plain,
% 10.29/10.51 ($false),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[23083, 391, 23077, 23075, 23071, 2641, 664])).
% 10.29/10.51 tff(23085,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~(s(s(z)) = elem!1)) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(z)) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = s(z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.51 tff(23086,plain,
% 10.29/10.51 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[23085, 23061, 23023, 23050, 1216, 31, 1759, 831, 3557])).
% 10.29/10.51 tff(23087,plain,
% 10.29/10.51 (b(s(s(s(s(z)))), s(s(z)))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[1714, 23086])).
% 10.29/10.51 tff(23088,plain,
% 10.29/10.51 (b(s(s(elem!1)), elem!1)),
% 10.29/10.51 inference(modus_ponens,[status(thm)],[23087, 23059])).
% 10.29/10.51 tff(23089,plain,
% 10.29/10.51 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[920, 391, 23030, 23088, 23029])).
% 10.29/10.51 tff(23090,plain,
% 10.29/10.51 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[1356, 23089, 23054])).
% 10.29/10.51 tff(23091,plain,
% 10.29/10.51 (~r(elem!1, s(s(z)))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[16978, 194, 23039, 23032, 3557])).
% 10.29/10.51 tff(23092,plain,
% 10.29/10.51 (~b(elem!1, s(s(z)))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[15450, 391, 23030, 23029, 23048])).
% 10.29/10.51 tff(23093,plain,
% 10.29/10.51 (elem!1 = s(s(z))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[3394, 23092, 23091])).
% 10.29/10.51 tff(23094,plain,
% 10.29/10.51 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[9253, 23093])).
% 10.29/10.51 tff(23095,plain,
% 10.29/10.51 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[22105, 391, 23030, 23088, 23029])).
% 10.29/10.51 tff(23096,plain,
% 10.29/10.51 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[1370, 23095, 23094])).
% 10.29/10.51 tff(23097,plain,
% 10.29/10.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.29/10.51 inference(rewrite,[status(thm)],[])).
% 10.29/10.51 tff(23098,plain,
% 10.29/10.51 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.29/10.51 inference(rewrite,[status(thm)],[])).
% 10.29/10.51 tff(23099,plain,
% 10.29/10.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 10.29/10.51 inference(monotonicity,[status(thm)],[23098])).
% 10.29/10.51 tff(23100,plain,
% 10.29/10.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.29/10.51 inference(transitivity,[status(thm)],[23099, 23097])).
% 10.29/10.51 tff(23101,plain,
% 10.29/10.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 10.29/10.51 inference(quant_inst,[status(thm)],[])).
% 10.29/10.51 tff(23102,plain,
% 10.29/10.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 10.29/10.51 inference(modus_ponens,[status(thm)],[23101, 23100])).
% 10.29/10.51 tff(23103,plain,
% 10.29/10.51 ($false),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[23102, 194, 23096, 183, 23090, 23051])).
% 10.29/10.51 tff(23104,plain,(b(elem!1, s(z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = s(z)) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.51 tff(23105,plain,
% 10.29/10.51 (b(elem!1, s(z))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[23104, 3557, 1216, 1759, 831, 183, 90, 10682, 1])).
% 10.29/10.51 tff(23106,plain,
% 10.29/10.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 10.29/10.51 inference(rewrite,[status(thm)],[])).
% 10.29/10.51 tff(23107,plain,
% 10.29/10.51 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 10.29/10.51 inference(rewrite,[status(thm)],[])).
% 10.29/10.51 tff(23108,plain,
% 10.29/10.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1))))),
% 10.29/10.51 inference(monotonicity,[status(thm)],[23107])).
% 10.29/10.51 tff(23109,plain,
% 10.29/10.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 10.29/10.51 inference(transitivity,[status(thm)],[23108, 23106])).
% 10.29/10.51 tff(23110,plain,
% 10.29/10.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 10.29/10.51 inference(quant_inst,[status(thm)],[])).
% 10.29/10.51 tff(23111,plain,
% 10.29/10.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1))),
% 10.29/10.51 inference(modus_ponens,[status(thm)],[23110, 23109])).
% 10.29/10.51 tff(23112,plain,
% 10.29/10.51 ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1))),
% 10.29/10.51 inference(unit_resolution,[status(thm)],[23111, 391])).
% 10.29/10.52 tff(23113,plain,
% 10.29/10.52 (~b(s(z), elem!1)),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[23112, 133, 664, 721])).
% 10.29/10.52 tff(23114,plain,
% 10.29/10.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 10.29/10.52 inference(rewrite,[status(thm)],[])).
% 10.29/10.52 tff(23115,plain,
% 10.29/10.52 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 10.29/10.52 inference(rewrite,[status(thm)],[])).
% 10.29/10.52 tff(23116,plain,
% 10.29/10.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 10.29/10.52 inference(monotonicity,[status(thm)],[23115])).
% 10.29/10.52 tff(23117,plain,
% 10.29/10.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 10.29/10.52 inference(transitivity,[status(thm)],[23116, 23114])).
% 10.29/10.52 tff(23118,plain,
% 10.29/10.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 10.29/10.52 inference(quant_inst,[status(thm)],[])).
% 10.29/10.52 tff(23119,plain,
% 10.29/10.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 10.29/10.52 inference(modus_ponens,[status(thm)],[23118, 23117])).
% 10.29/10.52 tff(23120,plain,
% 10.29/10.52 ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[23119, 391])).
% 10.29/10.52 tff(23121,plain,
% 10.29/10.52 (~b(s(s(z)), s(z))),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[23120, 2439, 721, 664, 133])).
% 10.29/10.52 tff(23122,plain,
% 10.29/10.52 (r(s(s(z)), s(z))),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[3778, 23121])).
% 10.29/10.52 tff(23123,plain,
% 10.29/10.52 (~r(s(s(z)), s(s(s(elem!1))))),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[10923, 194, 1484, 183, 23122])).
% 10.29/10.52 tff(23124,plain,
% 10.29/10.52 (b(s(s(z)), s(s(s(elem!1))))),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 23123])).
% 10.29/10.52 tff(23125,plain,
% 10.29/10.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.52 inference(rewrite,[status(thm)],[])).
% 10.29/10.52 tff(23126,plain,
% 10.29/10.52 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.52 inference(rewrite,[status(thm)],[])).
% 10.29/10.52 tff(23127,plain,
% 10.29/10.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 10.29/10.52 inference(monotonicity,[status(thm)],[23126])).
% 10.29/10.52 tff(23128,plain,
% 10.29/10.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.52 inference(transitivity,[status(thm)],[23127, 23125])).
% 10.29/10.52 tff(23129,plain,
% 10.29/10.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 10.29/10.52 inference(quant_inst,[status(thm)],[])).
% 10.29/10.52 tff(23130,plain,
% 10.29/10.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 10.29/10.52 inference(modus_ponens,[status(thm)],[23129, 23128])).
% 10.29/10.52 tff(23131,plain,
% 10.29/10.52 ($false),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[23130, 391, 90, 1759, 2439, 664, 23124])).
% 10.29/10.52 tff(23132,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.52 tff(23133,plain,
% 10.29/10.52 (~r(s(z), elem!1)),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[23132, 133, 90, 664, 1759, 183, 2439, 721])).
% 10.29/10.52 tff(23134,plain,
% 10.29/10.52 ($false),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[632, 23133, 23113, 150])).
% 10.29/10.52 tff(23135,plain,((~b(z, elem!1)) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.52 tff(23136,plain,
% 10.29/10.52 (~b(z, elem!1)),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[23135, 2439, 90, 664, 1759, 183, 150, 721])).
% 10.29/10.52 tff(23137,plain,
% 10.29/10.52 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 10.29/10.52 inference(monotonicity,[status(thm)],[935])).
% 10.29/10.52 tff(23138,plain,
% 10.29/10.52 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 10.29/10.52 inference(symmetry,[status(thm)],[23137])).
% 10.29/10.52 tff(23139,plain,
% 10.29/10.52 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 10.29/10.52 inference(monotonicity,[status(thm)],[931])).
% 10.29/10.52 tff(23140,plain,
% 10.29/10.52 (b(s(s(s(s(z)))), s(elem!1))),
% 10.29/10.52 inference(modus_ponens,[status(thm)],[1759, 23139])).
% 10.29/10.52 tff(23141,plain,
% 10.29/10.52 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 10.29/10.52 inference(modus_ponens,[status(thm)],[23140, 23138])).
% 10.29/10.52 tff(23142,plain,
% 10.29/10.52 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 10.29/10.52 inference(monotonicity,[status(thm)],[934])).
% 10.29/10.52 tff(23143,plain,
% 10.29/10.52 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 10.29/10.52 inference(monotonicity,[status(thm)],[94])).
% 10.29/10.52 tff(23144,plain,
% 10.29/10.52 (b(s(s(s(s(z)))), elem!1)),
% 10.29/10.52 inference(modus_ponens,[status(thm)],[90, 23143])).
% 10.29/10.52 tff(23145,plain,
% 10.29/10.52 (b(s(s(s(s(elem!1)))), elem!1)),
% 10.29/10.52 inference(modus_ponens,[status(thm)],[23144, 23142])).
% 10.29/10.52 tff(23146,plain,
% 10.29/10.52 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 10.29/10.52 inference(monotonicity,[status(thm)],[931])).
% 10.29/10.52 tff(23147,plain,
% 10.29/10.52 (r(s(s(s(elem!1))), elem!1)),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[9853, 94, 174])).
% 10.29/10.52 tff(23148,plain,
% 10.29/10.52 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 10.29/10.52 inference(monotonicity,[status(thm)],[94])).
% 10.29/10.52 tff(23149,plain,
% 10.29/10.52 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 10.29/10.52 inference(transitivity,[status(thm)],[23148, 698])).
% 10.29/10.52 tff(23150,plain,
% 10.29/10.52 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 10.29/10.52 inference(monotonicity,[status(thm)],[23149])).
% 10.29/10.52 tff(23151,plain,
% 10.29/10.52 (~(elem!1 = s(s(z)))),
% 10.29/10.52 inference(modus_ponens,[status(thm)],[1207, 23150])).
% 10.29/10.52 tff(23152,plain,
% 10.29/10.52 (b(elem!1, s(s(s(elem!1))))),
% 10.29/10.52 inference(modus_ponens,[status(thm)],[10682, 8842])).
% 10.29/10.52 tff(23153,plain,
% 10.29/10.52 ($false),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[4028, 23152])).
% 10.29/10.52 tff(23154,plain,((~(elem!1 = z)) | b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.52 tff(23155,plain,
% 10.29/10.52 (b(elem!1, s(s(s(elem!1))))),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[23154, 1027, 10682])).
% 10.29/10.52 tff(23156,plain,
% 10.29/10.52 (~r(s(z), elem!1)),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[22338, 23155, 183, 2439, 721, 23151, 23147])).
% 10.29/10.52 tff(23157,plain,
% 10.29/10.52 (b(s(z), elem!1)),
% 10.29/10.52 inference(unit_resolution,[status(thm)],[632, 23156, 150])).
% 10.29/10.52 tff(23158,plain,
% 10.29/10.52 (b(s(elem!1), elem!1)),
% 10.29/10.52 inference(modus_ponens,[status(thm)],[23157, 23146])).
% 10.29/10.52 tff(23159,plain,
% 10.29/10.52 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 10.29/10.52 inference(monotonicity,[status(thm)],[931])).
% 10.29/10.52 tff(23160,plain,
% 10.29/10.52 (b(elem!1, s(elem!1))),
% 10.29/10.52 inference(modus_ponens,[status(thm)],[721, 23159])).
% 10.29/10.52 tff(23161,plain,
% 10.29/10.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.29/10.52 inference(rewrite,[status(thm)],[])).
% 10.29/10.52 tff(23162,plain,
% 10.29/10.52 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.29/10.52 inference(rewrite,[status(thm)],[])).
% 10.29/10.52 tff(23163,plain,
% 10.29/10.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 10.29/10.52 inference(monotonicity,[status(thm)],[23162])).
% 10.29/10.52 tff(23164,plain,
% 10.29/10.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.29/10.52 inference(transitivity,[status(thm)],[23163, 23161])).
% 10.29/10.52 tff(23165,plain,
% 10.29/10.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 10.29/10.52 inference(quant_inst,[status(thm)],[])).
% 10.29/10.52 tff(23166,plain,
% 10.29/10.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[23165, 23164])).
% 10.29/10.53 tff(23167,plain,
% 10.29/10.53 ($false),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23166, 391, 23160, 23158, 23145, 23141])).
% 10.29/10.53 tff(23168,plain,((~(z = elem!1)) | (s(z) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.53 tff(23169,plain,
% 10.29/10.53 (~(z = elem!1)),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23168, 2439, 183, 150, 721, 1759, 90, 10682, 174])).
% 10.29/10.53 tff(23170,plain,
% 10.29/10.53 (r(z, elem!1)),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[141, 23169, 23136])).
% 10.29/10.53 tff(23171,plain,
% 10.29/10.53 (~r(s(s(z)), s(s(s(elem!1))))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23046, 194, 23170, 174, 3557])).
% 10.29/10.53 tff(23172,plain,
% 10.29/10.53 (b(s(s(z)), s(s(s(elem!1))))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 23171])).
% 10.29/10.53 tff(23173,plain,
% 10.29/10.53 ($false),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23130, 391, 90, 1759, 2439, 664, 23172])).
% 10.29/10.53 tff(23174,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(z))) | (s(z) = elem!1) | (~b(elem!1, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.53 tff(23175,plain,
% 10.29/10.53 (~b(s(z), s(s(z)))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23174, 3557, 1759, 23023, 23021, 90, 183, 1496, 23105, 10682])).
% 10.29/10.53 tff(23176,plain,
% 10.29/10.53 (r(s(z), s(s(z)))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[1788, 23175])).
% 10.29/10.53 tff(23177,plain,
% 10.29/10.53 (~b(s(z), elem!1)),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[20920, 23105, 1759, 23023, 90])).
% 10.29/10.53 tff(23178,plain,
% 10.29/10.53 (r(s(z), elem!1)),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[632, 23177, 1496])).
% 10.29/10.53 tff(23179,plain,
% 10.29/10.53 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 10.29/10.53 inference(monotonicity,[status(thm)],[489])).
% 10.29/10.53 tff(23180,plain,
% 10.29/10.53 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 10.29/10.53 inference(symmetry,[status(thm)],[23179])).
% 10.29/10.53 tff(23181,plain,
% 10.29/10.53 (r(s(s(elem!1)), z)),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[3557, 23180])).
% 10.29/10.53 tff(23182,plain,
% 10.29/10.53 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[489])).
% 10.29/10.53 tff(23183,plain,
% 10.29/10.53 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 10.29/10.53 inference(symmetry,[status(thm)],[23182])).
% 10.29/10.53 tff(23184,plain,
% 10.29/10.53 (r(s(z), s(s(elem!1)))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[1747, 23183])).
% 10.29/10.53 tff(23185,plain,
% 10.29/10.53 ($false),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[4845, 23184])).
% 10.29/10.53 tff(23186,plain,((~r(s(z), s(s(z)))) | r(s(z), s(s(elem!1))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.53 tff(23187,plain,
% 10.29/10.53 (r(s(z), s(s(elem!1)))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23186, 11, 1747])).
% 10.29/10.53 tff(23188,plain,
% 10.29/10.53 (r(s(s(s(z))), z)),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[4409, 11, 174])).
% 10.29/10.53 tff(23189,plain,
% 10.29/10.53 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[490])).
% 10.29/10.53 tff(23190,plain,
% 10.29/10.53 (b(z, s(s(s(z))))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[10682, 23189])).
% 10.29/10.53 tff(23191,plain,
% 10.29/10.53 (b(elem!1, s(s(s(elem!1))))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23154, 11, 10682])).
% 10.29/10.53 tff(23192,plain,
% 10.29/10.53 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[11])).
% 10.29/10.53 tff(23193,plain,
% 10.29/10.53 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 10.29/10.53 inference(symmetry,[status(thm)],[23192])).
% 10.29/10.53 tff(23194,plain,
% 10.29/10.53 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 10.29/10.53 inference(transitivity,[status(thm)],[3367, 23193])).
% 10.29/10.53 tff(23195,plain,
% 10.29/10.53 (~r(z, s(s(elem!1)))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[3787, 17619, 3557, 1747])).
% 10.29/10.53 tff(23196,plain,
% 10.29/10.53 (b(z, s(s(elem!1)))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[324, 23195])).
% 10.29/10.53 tff(23197,plain,
% 10.29/10.53 (b(elem!1, s(s(z)))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[23196, 23194])).
% 10.29/10.53 tff(23198,plain,
% 10.29/10.53 (~r(s(s(z)), s(z))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[10933, 23197, 183, 23191, 1484])).
% 10.29/10.53 tff(23199,plain,
% 10.29/10.53 (b(s(s(z)), s(z))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[3778, 23198])).
% 10.29/10.53 tff(23200,plain,
% 10.29/10.53 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[488])).
% 10.29/10.53 tff(23201,plain,
% 10.29/10.53 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 10.29/10.53 inference(symmetry,[status(thm)],[23200])).
% 10.29/10.53 tff(23202,plain,
% 10.29/10.53 (r(s(s(s(elem!1))), s(elem!1))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[183, 23201])).
% 10.29/10.53 tff(23203,plain,
% 10.29/10.53 (r(s(s(s(elem!1))), elem!1)),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[9853, 17618, 174])).
% 10.29/10.53 tff(23204,plain,
% 10.29/10.53 (~r(elem!1, s(s(s(s(elem!1)))))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[19658, 17628, 23203, 23202])).
% 10.29/10.53 tff(23205,plain,
% 10.29/10.53 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(elem!1)))))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[11])).
% 10.29/10.53 tff(23206,plain,
% 10.29/10.53 ((~r(elem!1, s(s(s(s(elem!1)))))) <=> (~r(z, s(s(s(s(elem!1))))))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[23205])).
% 10.29/10.53 tff(23207,assumption,(~r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 10.29/10.53 tff(23208,plain,
% 10.29/10.53 (~r(z, s(s(s(s(elem!1)))))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[23207, 23206])).
% 10.29/10.53 tff(23209,plain,
% 10.29/10.53 ($false),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23208, 18459])).
% 10.29/10.53 tff(23210,plain,((~(elem!1 = z)) | (~r(z, s(s(s(s(z)))))) | r(elem!1, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.53 tff(23211,plain,
% 10.29/10.53 (~r(z, s(s(s(s(z)))))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23210, 23204, 11])).
% 10.29/10.53 tff(23212,plain,
% 10.29/10.53 (b(z, s(s(s(s(z)))))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[800, 23211])).
% 10.29/10.53 tff(23213,plain,
% 10.29/10.53 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[2980])).
% 10.29/10.53 tff(23214,plain,
% 10.29/10.53 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 10.29/10.53 inference(transitivity,[status(thm)],[23213, 267])).
% 10.29/10.53 tff(23215,plain,
% 10.29/10.53 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[23214])).
% 10.29/10.53 tff(23216,plain,
% 10.29/10.53 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[1397, 23215])).
% 10.29/10.53 tff(23217,plain,
% 10.29/10.53 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[4840, 232, 4832, 2616])).
% 10.29/10.53 tff(23218,plain,
% 10.29/10.53 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[1370, 23217, 23216])).
% 10.29/10.53 tff(23219,plain,
% 10.29/10.53 (b(s(s(s(z))), s(s(z)))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[2986, 23218, 11])).
% 10.29/10.53 tff(23220,plain,
% 10.29/10.53 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[2401, 490])).
% 10.29/10.53 tff(23221,plain,
% 10.29/10.53 (r(s(z), s(s(s(z))))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[232, 503])).
% 10.29/10.53 tff(23222,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 10.29/10.53 tff(23223,plain,
% 10.29/10.53 ($false),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23222, 23221])).
% 10.29/10.53 tff(23224,plain,((~r(s(z), s(s(s(elem!1))))) | r(s(z), s(s(s(z)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.53 tff(23225,plain,
% 10.29/10.53 (r(s(z), s(s(s(z))))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23224, 232, 11])).
% 10.29/10.53 tff(23226,plain,
% 10.29/10.53 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 10.29/10.53 inference(symmetry,[status(thm)],[2401])).
% 10.29/10.53 tff(23227,plain,
% 10.29/10.53 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[23226, 491])).
% 10.29/10.53 tff(23228,plain,
% 10.29/10.53 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 10.29/10.53 inference(symmetry,[status(thm)],[23227])).
% 10.29/10.53 tff(23229,plain,
% 10.29/10.53 (r(s(s(s(s(z)))), s(s(s(z))))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[1082, 23228])).
% 10.29/10.53 tff(23230,plain,
% 10.29/10.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 10.29/10.53 inference(rewrite,[status(thm)],[])).
% 10.29/10.53 tff(23231,plain,
% 10.29/10.53 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 10.29/10.53 inference(rewrite,[status(thm)],[])).
% 10.29/10.53 tff(23232,plain,
% 10.29/10.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 10.29/10.53 inference(monotonicity,[status(thm)],[23231])).
% 10.29/10.53 tff(23233,plain,
% 10.29/10.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 10.29/10.53 inference(transitivity,[status(thm)],[23232, 23230])).
% 10.29/10.53 tff(23234,plain,
% 10.29/10.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 10.29/10.53 inference(quant_inst,[status(thm)],[])).
% 10.29/10.53 tff(23235,plain,
% 10.29/10.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[23234, 23233])).
% 10.29/10.53 tff(23236,plain,
% 10.29/10.53 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23235, 194, 1216, 4428, 15705])).
% 10.29/10.53 tff(23237,plain,
% 10.29/10.53 ($false),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23236, 23229])).
% 10.29/10.53 tff(23238,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(elem!1 = z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.53 tff(23239,plain,
% 10.29/10.53 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[23238, 23225, 1216, 4428, 11])).
% 10.29/10.53 tff(23240,plain,
% 10.29/10.53 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.29/10.53 inference(unit_resolution,[status(thm)],[1095, 23239, 17615])).
% 10.29/10.53 tff(23241,plain,
% 10.29/10.53 (b(s(s(s(s(z)))), s(s(s(z))))),
% 10.29/10.53 inference(modus_ponens,[status(thm)],[23240, 23220])).
% 10.29/10.53 tff(23242,plain,
% 10.29/10.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 10.29/10.53 inference(rewrite,[status(thm)],[])).
% 10.29/10.53 tff(23243,plain,
% 10.29/10.53 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 10.29/10.53 inference(rewrite,[status(thm)],[])).
% 10.29/10.53 tff(23244,plain,
% 10.29/10.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 10.29/10.54 inference(monotonicity,[status(thm)],[23243])).
% 10.29/10.54 tff(23245,plain,
% 10.29/10.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 10.29/10.54 inference(transitivity,[status(thm)],[23244, 23242])).
% 10.29/10.54 tff(23246,plain,
% 10.29/10.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 10.29/10.54 inference(quant_inst,[status(thm)],[])).
% 10.29/10.54 tff(23247,plain,
% 10.29/10.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 10.29/10.54 inference(modus_ponens,[status(thm)],[23246, 23245])).
% 10.29/10.54 tff(23248,plain,
% 10.29/10.54 ($false),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[23247, 391, 1686, 1233, 23241, 7871, 23219])).
% 10.29/10.54 tff(23249,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~(elem!1 = z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.54 tff(23250,plain,
% 10.29/10.54 (~r(s(z), s(s(s(elem!1))))),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[23249, 23212, 23199, 23190, 11, 1216, 23188, 23187, 23181])).
% 10.29/10.54 tff(23251,plain,
% 10.29/10.54 (b(s(z), s(s(s(elem!1))))),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[247, 23250])).
% 10.29/10.54 tff(23252,plain,
% 10.29/10.54 (b(s(z), s(s(s(z))))),
% 10.29/10.54 inference(modus_ponens,[status(thm)],[23251, 18545])).
% 10.29/10.54 tff(23253,plain,
% 10.29/10.54 (b(z, s(s(z)))),
% 10.29/10.54 inference(modus_ponens,[status(thm)],[23196, 3367])).
% 10.29/10.54 tff(23254,plain,
% 10.29/10.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 10.29/10.54 inference(rewrite,[status(thm)],[])).
% 10.29/10.54 tff(23255,plain,
% 10.29/10.54 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 10.29/10.54 inference(rewrite,[status(thm)],[])).
% 10.29/10.54 tff(23256,plain,
% 10.29/10.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 10.29/10.54 inference(monotonicity,[status(thm)],[23255])).
% 10.29/10.54 tff(23257,plain,
% 10.29/10.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 10.29/10.54 inference(transitivity,[status(thm)],[23256, 23254])).
% 10.29/10.54 tff(23258,plain,
% 10.29/10.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 10.29/10.54 inference(quant_inst,[status(thm)],[])).
% 10.29/10.54 tff(23259,plain,
% 10.29/10.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 10.29/10.54 inference(modus_ponens,[status(thm)],[23258, 23257])).
% 10.29/10.54 tff(23260,plain,
% 10.29/10.54 ($false),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[23259, 391, 20654, 23212, 23199, 23253, 23252])).
% 10.29/10.54 tff(23261,plain,((~(elem!1 = z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.54 tff(23262,plain,
% 10.29/10.54 (~(elem!1 = z)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[23261, 23178, 183, 1216, 10682, 3557, 23176, 23021])).
% 10.29/10.54 tff(23263,plain,
% 10.29/10.54 (~b(s(z), z)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[5970, 149, 664, 721])).
% 10.29/10.54 tff(23264,plain,
% 10.29/10.54 (r(s(z), z)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[180, 23263])).
% 10.29/10.54 tff(23265,plain,
% 10.29/10.54 (~r(z, s(s(elem!1)))),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[3787, 23264, 3557, 1747])).
% 10.29/10.54 tff(23266,plain,
% 10.29/10.54 (b(z, s(s(elem!1)))),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[324, 23265])).
% 10.29/10.54 tff(23267,plain,
% 10.29/10.54 (~r(s(z), s(s(s(elem!1))))),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[5645, 6124, 174, 1484])).
% 10.29/10.54 tff(23268,plain,
% 10.29/10.54 (b(s(z), s(s(s(elem!1))))),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[247, 23267])).
% 10.29/10.54 tff(23269,plain,
% 10.29/10.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.29/10.54 inference(rewrite,[status(thm)],[])).
% 10.29/10.54 tff(23270,plain,
% 10.29/10.54 (((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.29/10.54 inference(rewrite,[status(thm)],[])).
% 10.29/10.54 tff(23271,plain,
% 10.29/10.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 10.29/10.54 inference(monotonicity,[status(thm)],[23270])).
% 10.29/10.54 tff(23272,plain,
% 10.29/10.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 10.29/10.54 inference(transitivity,[status(thm)],[23271, 23269])).
% 10.29/10.54 tff(23273,plain,
% 10.29/10.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 10.29/10.54 inference(quant_inst,[status(thm)],[])).
% 10.29/10.54 tff(23274,plain,
% 10.29/10.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 10.29/10.54 inference(modus_ponens,[status(thm)],[23273, 23272])).
% 10.29/10.54 tff(23275,plain,
% 10.29/10.54 ($false),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[23274, 391, 133, 900, 10682, 379, 721])).
% 10.29/10.54 tff(23276,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.54 tff(23277,plain,
% 10.29/10.54 (~b(s(s(s(elem!1))), elem!1)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[23276, 23268, 10682, 133, 721])).
% 10.29/10.54 tff(23278,plain,
% 10.29/10.54 (r(s(s(s(elem!1))), elem!1)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[230, 23277, 9])).
% 10.29/10.54 tff(23279,plain,
% 10.29/10.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 10.29/10.54 inference(rewrite,[status(thm)],[])).
% 10.29/10.54 tff(23280,plain,
% 10.29/10.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 10.29/10.54 inference(quant_inst,[status(thm)],[])).
% 10.29/10.54 tff(23281,plain,
% 10.29/10.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 10.29/10.54 inference(modus_ponens,[status(thm)],[23280, 23279])).
% 10.29/10.54 tff(23282,plain,
% 10.29/10.54 ($false),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[23281, 194, 530, 233, 1484, 183])).
% 10.29/10.54 tff(23283,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.54 tff(23284,plain,
% 10.29/10.54 (~r(elem!1, z)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[23283, 23278, 183, 1484])).
% 10.29/10.54 tff(23285,plain,
% 10.29/10.54 (b(elem!1, z)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[526, 23284, 2])).
% 10.29/10.54 tff(23286,plain,
% 10.29/10.54 (~b(s(s(elem!1)), elem!1)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[4944, 23285, 3927, 133])).
% 10.29/10.54 tff(23287,plain,
% 10.29/10.54 (b(s(elem!1), elem!1)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[13690, 23284, 10682, 4028, 150, 23285, 23277, 118, 133])).
% 10.29/10.54 tff(23288,plain,
% 10.29/10.54 (~b(s(elem!1), z)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[7777, 23287, 23285, 133])).
% 10.29/10.54 tff(23289,plain,
% 10.29/10.54 (r(s(elem!1), z)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[549, 23288])).
% 10.29/10.54 tff(23290,plain,
% 10.29/10.54 (~r(s(elem!1), elem!1)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[13427, 23289, 133, 182, 3363, 1484, 4028, 10682, 118, 23285, 9, 23277])).
% 10.29/10.54 tff(23291,plain,
% 10.29/10.54 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[472, 23290, 23278])).
% 10.29/10.54 tff(23292,plain,
% 10.29/10.54 (~(s(s(elem!1)) = elem!1)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[451, 23291])).
% 10.29/10.54 tff(23293,plain,
% 10.29/10.54 (r(s(s(elem!1)), elem!1)),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[872, 23292, 23286])).
% 10.29/10.54 tff(23294,plain,
% 10.29/10.54 (~(s(s(elem!1)) = s(elem!1))),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[2279, 23291])).
% 10.29/10.54 tff(23295,plain,
% 10.29/10.54 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[287, 23294])).
% 10.29/10.54 tff(23296,plain,
% 10.29/10.54 ($false),
% 10.29/10.54 inference(unit_resolution,[status(thm)],[12954, 23295, 23293, 10682, 1484, 1, 4028, 23277, 182])).
% 10.29/10.55 tff(23297,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (s(z) = elem!1) | (elem!1 = z) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.55 tff(23298,plain,
% 10.29/10.55 (b(elem!1, s(s(s(elem!1))))),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[23297, 23264, 1484, 1, 10682, 149, 23266, 150, 2, 183, 721, 174])).
% 10.29/10.55 tff(23299,plain,
% 10.29/10.55 (~b(s(s(s(elem!1))), elem!1)),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[10845, 149, 10682, 23298])).
% 10.29/10.55 tff(23300,plain,
% 10.29/10.55 (r(s(s(s(elem!1))), elem!1)),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[230, 23299, 9])).
% 10.29/10.55 tff(23301,plain,
% 10.29/10.55 (~r(elem!1, z)),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[23283, 23300, 183, 1484])).
% 10.29/10.55 tff(23302,plain,
% 10.29/10.55 (b(elem!1, z)),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[526, 23301, 2])).
% 10.29/10.55 tff(23303,plain,
% 10.29/10.55 (b(s(elem!1), elem!1)),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[14657, 23301, 10682, 150, 149, 23299, 2])).
% 10.29/10.55 tff(23304,plain,
% 10.29/10.55 (~b(z, s(elem!1))),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[6555, 23303, 23302, 149])).
% 10.29/10.55 tff(23305,plain,
% 10.29/10.55 (r(z, s(elem!1))),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[566, 23304])).
% 10.29/10.55 tff(23306,plain,
% 10.29/10.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.55 inference(rewrite,[status(thm)],[])).
% 10.29/10.55 tff(23307,plain,
% 10.29/10.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.55 inference(quant_inst,[status(thm)],[])).
% 10.29/10.55 tff(23308,plain,
% 10.29/10.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 10.29/10.55 inference(modus_ponens,[status(thm)],[23307, 23306])).
% 10.29/10.55 tff(23309,plain,
% 10.29/10.55 (~r(s(s(s(elem!1))), s(s(z)))),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[23308, 194, 174, 23305, 3557])).
% 10.29/10.55 tff(23310,plain,
% 10.29/10.55 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[10713, 42, 23309])).
% 10.29/10.55 tff(23311,plain,
% 10.29/10.55 (b(s(s(s(elem!1))), s(s(z)))),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[23310, 10703])).
% 10.29/10.55 tff(23312,plain,
% 10.29/10.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.55 inference(rewrite,[status(thm)],[])).
% 10.29/10.55 tff(23313,plain,
% 10.29/10.55 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.55 inference(rewrite,[status(thm)],[])).
% 10.29/10.55 tff(23314,plain,
% 10.29/10.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 10.29/10.55 inference(monotonicity,[status(thm)],[23313])).
% 10.29/10.55 tff(23315,plain,
% 10.29/10.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.55 inference(transitivity,[status(thm)],[23314, 23312])).
% 10.29/10.55 tff(23316,plain,
% 10.29/10.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.29/10.55 inference(quant_inst,[status(thm)],[])).
% 10.29/10.55 tff(23317,plain,
% 10.29/10.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 10.29/10.55 inference(modus_ponens,[status(thm)],[23316, 23315])).
% 10.29/10.55 tff(23318,plain,
% 10.29/10.55 (~r(s(s(z)), s(s(s(elem!1))))),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[23317, 194, 174, 23305, 3557])).
% 10.29/10.55 tff(23319,plain,
% 10.29/10.55 (b(s(s(z)), s(s(s(elem!1))))),
% 10.29/10.55 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 23318])).
% 10.29/10.55 tff(23320,plain,
% 10.29/10.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.55 inference(rewrite,[status(thm)],[])).
% 10.29/10.55 tff(23321,plain,
% 10.29/10.55 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.55 inference(rewrite,[status(thm)],[])).
% 10.29/10.55 tff(23322,plain,
% 10.29/10.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 10.29/10.55 inference(monotonicity,[status(thm)],[23321])).
% 10.29/10.55 tff(23323,plain,
% 10.29/10.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.55 inference(transitivity,[status(thm)],[23322, 23320])).
% 10.29/10.55 tff(23324,plain,
% 10.29/10.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 10.29/10.55 inference(quant_inst,[status(thm)],[])).
% 10.29/10.55 tff(23325,plain,
% 10.29/10.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 10.29/10.55 inference(modus_ponens,[status(thm)],[23324, 23323])).
% 10.29/10.56 tff(23326,plain,
% 10.29/10.56 ($false),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[23325, 391, 23302, 10682, 23298, 23319, 23311])).
% 10.29/10.56 tff(23327,plain,((elem!1 = z) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (s(z) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.29/10.56 tff(23328,plain,
% 10.29/10.56 (r(z, elem!1)),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[23327, 23262, 23021, 3557, 1496, 183, 23178, 1, 23105, 23176, 23023, 10682])).
% 10.29/10.56 tff(23329,plain,
% 10.29/10.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.56 inference(rewrite,[status(thm)],[])).
% 10.29/10.56 tff(23330,plain,
% 10.29/10.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.56 inference(quant_inst,[status(thm)],[])).
% 10.29/10.56 tff(23331,plain,
% 10.29/10.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 10.29/10.56 inference(modus_ponens,[status(thm)],[23330, 23329])).
% 10.29/10.56 tff(23332,plain,
% 10.29/10.56 (~r(s(s(s(elem!1))), s(s(z)))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[23331, 194, 23328, 23021, 3557])).
% 10.29/10.56 tff(23333,plain,
% 10.29/10.56 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[10713, 42, 23332])).
% 10.29/10.56 tff(23334,plain,
% 10.29/10.56 (b(s(s(s(elem!1))), s(s(z)))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[23333, 10703])).
% 10.29/10.56 tff(23335,plain,
% 10.29/10.56 (~r(s(s(z)), s(s(s(elem!1))))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[23046, 194, 23328, 23021, 3557])).
% 10.29/10.56 tff(23336,plain,
% 10.29/10.56 (b(s(s(z)), s(s(s(elem!1))))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 23335])).
% 10.29/10.56 tff(23337,plain,
% 10.29/10.56 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[11508, 23176, 1216, 3557])).
% 10.29/10.56 tff(23338,plain,
% 10.29/10.56 (b(s(s(s(s(z)))), s(s(z)))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[1714, 23337])).
% 10.29/10.56 tff(23339,plain,
% 10.29/10.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.56 inference(rewrite,[status(thm)],[])).
% 10.29/10.56 tff(23340,plain,
% 10.29/10.56 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.56 inference(rewrite,[status(thm)],[])).
% 10.29/10.56 tff(23341,plain,
% 10.29/10.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 10.29/10.56 inference(monotonicity,[status(thm)],[23340])).
% 10.29/10.56 tff(23342,plain,
% 10.29/10.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.56 inference(transitivity,[status(thm)],[23341, 23339])).
% 10.29/10.56 tff(23343,plain,
% 10.29/10.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.29/10.56 inference(quant_inst,[status(thm)],[])).
% 10.29/10.56 tff(23344,plain,
% 10.29/10.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 10.29/10.56 inference(modus_ponens,[status(thm)],[23343, 23342])).
% 10.29/10.56 tff(23345,plain,
% 10.29/10.56 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[23344, 391, 23338, 23336, 23334])).
% 10.29/10.56 tff(23346,plain,
% 10.29/10.56 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[4313, 42, 23345, 23019])).
% 10.29/10.56 tff(23347,plain,
% 10.29/10.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.56 inference(rewrite,[status(thm)],[])).
% 10.29/10.56 tff(23348,plain,
% 10.29/10.56 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.56 inference(rewrite,[status(thm)],[])).
% 10.29/10.56 tff(23349,plain,
% 10.29/10.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 10.29/10.56 inference(monotonicity,[status(thm)],[23348])).
% 10.29/10.56 tff(23350,plain,
% 10.29/10.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.29/10.56 inference(transitivity,[status(thm)],[23349, 23347])).
% 10.29/10.56 tff(23351,plain,
% 10.29/10.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.29/10.56 inference(quant_inst,[status(thm)],[])).
% 10.29/10.56 tff(23352,plain,
% 10.29/10.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 10.29/10.56 inference(modus_ponens,[status(thm)],[23351, 23350])).
% 10.29/10.56 tff(23353,plain,
% 10.29/10.56 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[23352, 391, 23338, 23336, 23334])).
% 10.29/10.56 tff(23354,plain,
% 10.29/10.56 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[2853, 42, 23018, 23353])).
% 10.29/10.56 tff(23355,plain,
% 10.29/10.56 ($false),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[16936, 194, 183, 1216, 23354, 23346])).
% 10.29/10.56 tff(23356,plain,((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.56 tff(23357,plain,
% 10.29/10.56 (~r(s(s(z)), z)),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[23356, 1759, 1216, 1, 10782, 11174, 90, 22992])).
% 10.29/10.56 tff(23358,plain,
% 10.29/10.56 (b(s(s(z)), z)),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[1211, 23357])).
% 10.29/10.56 tff(23359,plain,
% 10.29/10.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 10.29/10.56 inference(rewrite,[status(thm)],[])).
% 10.29/10.56 tff(23360,plain,
% 10.29/10.56 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 10.29/10.56 inference(rewrite,[status(thm)],[])).
% 10.29/10.56 tff(23361,plain,
% 10.29/10.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 10.29/10.56 inference(monotonicity,[status(thm)],[23360])).
% 10.29/10.56 tff(23362,plain,
% 10.29/10.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 10.29/10.56 inference(transitivity,[status(thm)],[23361, 23359])).
% 10.29/10.56 tff(23363,plain,
% 10.29/10.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 10.29/10.56 inference(quant_inst,[status(thm)],[])).
% 10.29/10.56 tff(23364,plain,
% 10.29/10.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 10.29/10.56 inference(modus_ponens,[status(thm)],[23363, 23362])).
% 10.29/10.56 tff(23365,plain,
% 10.29/10.56 ($false),
% 10.29/10.56 inference(unit_resolution,[status(thm)],[23364, 391, 90, 1235, 1759, 2439, 664])).
% 10.29/10.56 tff(23366,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.57 tff(23367,plain,
% 10.29/10.57 (~b(s(z), s(s(z)))),
% 10.29/10.57 inference(unit_resolution,[status(thm)],[23366, 23358, 90, 1759, 23017])).
% 10.29/10.57 tff(23368,plain,
% 10.29/10.57 (r(s(z), s(s(z)))),
% 10.29/10.57 inference(unit_resolution,[status(thm)],[1788, 23367])).
% 10.29/10.57 tff(23369,plain,
% 10.29/10.57 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.29/10.57 inference(unit_resolution,[status(thm)],[22034, 1697, 1216, 90, 664, 1235])).
% 10.29/10.57 tff(23370,plain,
% 10.29/10.57 (r(s(s(z)), s(s(s(s(z)))))),
% 10.29/10.57 inference(unit_resolution,[status(thm)],[3652, 23369])).
% 10.29/10.57 tff(23371,plain,
% 10.29/10.57 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.57 inference(rewrite,[status(thm)],[])).
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% 10.29/10.57 inference(monotonicity,[status(thm)],[23371])).
% 10.29/10.57 tff(23373,plain,
% 10.29/10.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.57 inference(transitivity,[status(thm)],[23372, 22808])).
% 10.29/10.57 tff(23374,plain,
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% 10.29/10.57 inference(quant_inst,[status(thm)],[])).
% 10.29/10.57 tff(23375,plain,
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% 10.29/10.57 inference(modus_ponens,[status(thm)],[23374, 23373])).
% 10.29/10.57 tff(23376,plain,
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% 10.29/10.57 inference(unit_resolution,[status(thm)],[23375, 194, 23370, 1216, 1747, 1697])).
% 10.29/10.57 tff(23377,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.57 tff(23378,plain,
% 10.29/10.57 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.29/10.57 inference(unit_resolution,[status(thm)],[23377, 23368, 1216, 90, 23017, 23358])).
% 10.29/10.57 tff(23379,plain,
% 10.29/10.57 (b(s(s(s(s(z)))), s(s(z)))),
% 10.29/10.57 inference(unit_resolution,[status(thm)],[1714, 23378])).
% 10.29/10.57 tff(23380,plain,
% 10.29/10.57 (~b(z, s(s(s(s(z)))))),
% 10.29/10.57 inference(unit_resolution,[status(thm)],[20748, 23379, 90, 23358])).
% 10.29/10.57 tff(23381,plain,
% 10.29/10.57 (r(z, s(s(s(s(z)))))),
% 10.29/10.57 inference(unit_resolution,[status(thm)],[800, 23380])).
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% 10.29/10.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.57 inference(rewrite,[status(thm)],[])).
% 10.29/10.57 tff(23383,plain,
% 10.29/10.57 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
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% 10.29/10.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 10.29/10.57 inference(monotonicity,[status(thm)],[23383])).
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% 10.29/10.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.57 inference(transitivity,[status(thm)],[23384, 23382])).
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% 10.29/10.57 inference(quant_inst,[status(thm)],[])).
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% 10.29/10.57 inference(modus_ponens,[status(thm)],[23386, 23385])).
% 10.29/10.57 tff(23388,plain,
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% 10.29/10.57 inference(unit_resolution,[status(thm)],[23387, 391, 900, 10682, 90, 1235])).
% 10.29/10.57 tff(23389,plain,
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% 10.29/10.57 inference(unit_resolution,[status(thm)],[1714, 23388])).
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% 10.29/10.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 10.29/10.57 inference(rewrite,[status(thm)],[])).
% 10.29/10.57 tff(23391,plain,
% 10.29/10.57 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 10.29/10.57 inference(rewrite,[status(thm)],[])).
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% 10.29/10.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))))),
% 10.29/10.57 inference(monotonicity,[status(thm)],[23391])).
% 10.29/10.57 tff(23393,plain,
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% 10.29/10.58 inference(transitivity,[status(thm)],[23392, 23390])).
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% 10.29/10.58 inference(quant_inst,[status(thm)],[])).
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% 10.29/10.58 inference(modus_ponens,[status(thm)],[23394, 23393])).
% 10.29/10.58 tff(23396,plain,
% 10.29/10.58 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23395, 391, 900, 10682, 90, 1235])).
% 10.29/10.58 tff(23397,plain,
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% 10.29/10.58 inference(unit_resolution,[status(thm)],[23375, 194, 23397, 1216, 1747, 23389])).
% 10.29/10.58 tff(23399,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.58 tff(23400,plain,
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% 10.29/10.58 tff(23401,plain,
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% 10.29/10.58 tff(23402,plain,
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% 10.29/10.58 tff(23403,plain,
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% 10.29/10.58 tff(23405,plain,
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% 10.29/10.58 inference(unit_resolution,[status(thm)],[632, 23404, 22993])).
% 10.29/10.58 tff(23406,plain,
% 10.29/10.58 (~b(s(z), s(s(s(elem!1))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[14992, 23358, 90, 23379, 23017])).
% 10.29/10.58 tff(23407,plain,
% 10.29/10.58 (r(s(z), s(s(s(elem!1))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[247, 23406])).
% 10.29/10.58 tff(23408,plain,
% 10.29/10.58 (~r(elem!1, s(s(s(s(elem!1)))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[14585, 23407, 23401, 23405])).
% 10.29/10.58 tff(23409,plain,
% 10.29/10.58 (~(elem!1 = z)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23210, 23408, 23381])).
% 10.29/10.58 tff(23410,plain,
% 10.29/10.58 ($false),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[5677, 194, 233, 410, 1484, 183])).
% 10.29/10.58 tff(23411,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.58 tff(23412,plain,
% 10.29/10.58 (~r(elem!1, s(s(s(elem!1))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23411, 23401, 23405, 11174])).
% 10.29/10.58 tff(23413,plain,
% 10.29/10.58 (b(elem!1, s(s(s(elem!1))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[424, 23412, 1])).
% 10.29/10.58 tff(23414,plain,
% 10.29/10.58 (~r(elem!1, z)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23283, 23405, 11174, 23401])).
% 10.29/10.58 tff(23415,plain,
% 10.29/10.58 (~r(z, s(z))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[16377, 12778, 183, 1216])).
% 10.29/10.58 tff(23416,plain,
% 10.29/10.58 (b(z, s(z))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[678, 23415])).
% 10.29/10.58 tff(23417,plain,
% 10.29/10.58 (~b(s(z), s(s(z)))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23366, 1235, 90, 1759, 23416])).
% 10.29/10.58 tff(23418,plain,
% 10.29/10.58 (r(s(z), s(s(z)))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[1788, 23417])).
% 10.29/10.58 tff(23419,plain,
% 10.29/10.58 (~b(s(s(s(elem!1))), elem!1)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23399, 23418, 1216, 10682, 90, 1235])).
% 10.29/10.58 tff(23420,plain,
% 10.29/10.58 (r(s(s(s(elem!1))), elem!1)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[230, 23419, 127])).
% 10.29/10.58 tff(23421,plain,
% 10.29/10.58 (~r(elem!1, s(s(s(s(z)))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[22246, 411, 23420, 12778])).
% 10.29/10.58 tff(23422,plain,
% 10.29/10.58 (~b(s(s(s(elem!1))), elem!1)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23399, 1747, 1216, 10682, 90, 1235])).
% 10.29/10.58 tff(23423,plain,
% 10.29/10.58 (r(s(s(s(elem!1))), elem!1)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[230, 23422, 127])).
% 10.29/10.58 tff(23424,plain,
% 10.29/10.58 (~r(elem!1, z)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23283, 1484, 183, 23423])).
% 10.29/10.58 tff(23425,plain,
% 10.29/10.58 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23377, 1747, 1216, 90, 23416, 1235])).
% 10.29/10.58 tff(23426,plain,
% 10.29/10.58 (b(s(s(s(s(z)))), s(s(z)))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[1714, 23425])).
% 10.29/10.58 tff(23427,plain,
% 10.29/10.58 (~b(z, s(s(s(s(z)))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[20748, 23426, 90, 1235])).
% 10.29/10.58 tff(23428,plain,
% 10.29/10.58 (r(z, s(s(s(s(z)))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[800, 23427])).
% 10.29/10.58 tff(23429,plain,
% 10.29/10.58 (~b(s(z), s(s(s(elem!1))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[14992, 1235, 90, 23426, 23416])).
% 10.29/10.58 tff(23430,plain,
% 10.29/10.58 (r(s(z), s(s(s(elem!1))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[247, 23429])).
% 10.29/10.58 tff(23431,plain,
% 10.29/10.58 (~r(elem!1, s(s(s(s(elem!1)))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[14585, 23430, 23423, 1484])).
% 10.29/10.58 tff(23432,plain,
% 10.29/10.58 (~(elem!1 = z)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23210, 23431, 23428])).
% 10.29/10.58 tff(23433,plain,
% 10.29/10.58 (b(elem!1, z)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[526, 23432, 23424])).
% 10.29/10.58 tff(23434,assumption,(~b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 10.29/10.58 tff(23435,plain,
% 10.29/10.58 (r(s(s(z)), s(s(s(s(z)))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[3652, 23434])).
% 10.29/10.58 tff(23436,plain,
% 10.29/10.58 (~r(s(s(s(s(z)))), elem!1)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[20629, 23435, 1216, 1747])).
% 10.29/10.58 tff(23437,plain,
% 10.29/10.58 (~r(elem!1, s(s(z)))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[14358, 1484, 183, 23423])).
% 10.29/10.58 tff(23438,plain,
% 10.29/10.58 (~r(elem!1, s(s(s(s(z)))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[22246, 411, 23423, 12778])).
% 10.29/10.58 tff(23439,plain,
% 10.29/10.58 (elem!1 = s(s(z))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[3394, 3583, 3816])).
% 10.29/10.58 tff(23440,plain,
% 10.29/10.58 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 10.29/10.58 inference(monotonicity,[status(thm)],[23439])).
% 10.29/10.58 tff(23441,plain,
% 10.29/10.58 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 10.29/10.58 inference(symmetry,[status(thm)],[23440])).
% 10.29/10.58 tff(23442,plain,
% 10.29/10.58 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 10.29/10.58 inference(monotonicity,[status(thm)],[23441])).
% 10.29/10.58 tff(23443,plain,
% 10.29/10.58 (~b(elem!1, s(s(s(s(z)))))),
% 10.29/10.58 inference(modus_ponens,[status(thm)],[23434, 23442])).
% 10.29/10.58 tff(23444,plain,
% 10.29/10.58 (~(s(s(s(s(z)))) = elem!1)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[11029, 3583, 3563])).
% 10.29/10.58 tff(23445,plain,
% 10.29/10.58 (~(elem!1 = s(s(s(s(z)))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[769, 23444])).
% 10.29/10.58 tff(23446,plain,
% 10.29/10.58 (b(elem!1, s(s(s(s(z)))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[781, 23445, 3222])).
% 10.29/10.58 tff(23447,plain,
% 10.29/10.58 ($false),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23446, 23443])).
% 10.29/10.58 tff(23448,plain,(b(elem!1, s(s(z))) | b(s(s(z)), s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | r(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.58 tff(23449,plain,
% 10.29/10.58 (b(elem!1, s(s(z)))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23448, 23434, 23438, 23426, 23437])).
% 10.29/10.58 tff(23450,plain,
% 10.29/10.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.58 inference(rewrite,[status(thm)],[])).
% 10.29/10.58 tff(23451,plain,
% 10.29/10.58 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.58 inference(rewrite,[status(thm)],[])).
% 10.29/10.58 tff(23452,plain,
% 10.29/10.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 10.29/10.58 inference(monotonicity,[status(thm)],[23451])).
% 10.29/10.58 tff(23453,plain,
% 10.29/10.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.58 inference(transitivity,[status(thm)],[23452, 23450])).
% 10.29/10.58 tff(23454,plain,
% 10.29/10.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.29/10.58 inference(quant_inst,[status(thm)],[])).
% 10.29/10.58 tff(23455,plain,
% 10.29/10.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 10.29/10.58 inference(modus_ponens,[status(thm)],[23454, 23453])).
% 10.29/10.58 tff(23456,plain,
% 10.29/10.58 (~b(s(s(s(s(z)))), elem!1)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[23455, 391, 10682, 1235, 23449, 23426])).
% 10.29/10.58 tff(23457,plain,
% 10.29/10.58 (s(s(s(s(z)))) = elem!1),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[762, 23456, 23436])).
% 10.29/10.58 tff(23458,plain,
% 10.29/10.58 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[717, 23457])).
% 10.29/10.58 tff(23459,plain,
% 10.29/10.58 (~(s(s(elem!1)) = elem!1)),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[451, 23458])).
% 10.29/10.58 tff(23460,plain,
% 10.29/10.58 (~(s(s(elem!1)) = s(elem!1))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[2279, 23458])).
% 10.29/10.58 tff(23461,plain,
% 10.29/10.58 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[287, 23460])).
% 10.29/10.58 tff(23462,plain,
% 10.29/10.58 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.29/10.58 inference(unit_resolution,[status(thm)],[281, 23458])).
% 10.29/10.58 tff(23463,plain,
% 10.29/10.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.58 inference(rewrite,[status(thm)],[])).
% 10.29/10.58 tff(23464,plain,
% 10.29/10.58 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.58 inference(rewrite,[status(thm)],[])).
% 10.29/10.58 tff(23465,plain,
% 10.29/10.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 10.29/10.59 inference(monotonicity,[status(thm)],[23464])).
% 10.29/10.59 tff(23466,plain,
% 10.29/10.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.59 inference(transitivity,[status(thm)],[23465, 23463])).
% 10.29/10.59 tff(23467,plain,
% 10.29/10.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.29/10.59 inference(quant_inst,[status(thm)],[])).
% 10.29/10.59 tff(23468,plain,
% 10.29/10.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 10.29/10.59 inference(modus_ponens,[status(thm)],[23467, 23466])).
% 10.29/10.59 tff(23469,plain,
% 10.29/10.59 (~b(elem!1, s(s(s(s(z)))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23468, 391, 10682, 1235, 23449, 23426])).
% 10.29/10.59 tff(23470,plain,
% 10.29/10.59 (elem!1 = s(s(s(s(z))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[781, 23469, 23438])).
% 10.29/10.59 tff(23471,plain,
% 10.29/10.59 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 10.29/10.59 inference(monotonicity,[status(thm)],[2730])).
% 10.29/10.59 tff(23472,plain,
% 10.29/10.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[1370, 6155, 297])).
% 10.29/10.59 tff(23473,plain,
% 10.29/10.59 (~b(s(s(elem!1)), elem!1)),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[12889, 23472, 10682, 665, 448])).
% 10.29/10.59 tff(23474,plain,
% 10.29/10.59 (s(s(s(elem!1))) = s(s(elem!1))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[1370, 11943, 6155])).
% 10.29/10.59 tff(23475,plain,
% 10.29/10.59 (s(s(elem!1)) = s(s(s(elem!1)))),
% 10.29/10.59 inference(symmetry,[status(thm)],[23474])).
% 10.29/10.59 tff(23476,plain,
% 10.29/10.59 (elem!1 = s(s(elem!1))),
% 10.29/10.59 inference(symmetry,[status(thm)],[445])).
% 10.29/10.59 tff(23477,plain,
% 10.29/10.59 (elem!1 = s(elem!1)),
% 10.29/10.59 inference(transitivity,[status(thm)],[23476, 23475, 452])).
% 10.29/10.59 tff(23478,plain,
% 10.29/10.59 ($false),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[437, 23477])).
% 10.29/10.59 tff(23479,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(elem!1)) | r(s(s(s(elem!1))), s(s(elem!1))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.29/10.59 tff(23480,plain,
% 10.29/10.59 (~(s(s(elem!1)) = elem!1)),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23479, 6155, 437, 168])).
% 10.29/10.59 tff(23481,plain,
% 10.29/10.59 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[6159, 23480])).
% 10.29/10.59 tff(23482,plain,
% 10.29/10.59 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[281, 23481])).
% 10.29/10.59 tff(23483,plain,
% 10.29/10.59 (~(s(s(elem!1)) = s(elem!1))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[264, 23480])).
% 10.29/10.59 tff(23484,plain,
% 10.29/10.59 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[287, 23483])).
% 10.29/10.59 tff(23485,plain,
% 10.29/10.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[1370, 23484, 6155])).
% 10.29/10.59 tff(23486,plain,
% 10.29/10.59 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[12932, 23485, 10682, 3927])).
% 10.29/10.59 tff(23487,plain,
% 10.29/10.59 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[1356, 23486, 23482])).
% 10.29/10.59 tff(23488,plain,
% 10.29/10.59 (~b(s(s(elem!1)), s(z))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[14197, 23485, 10682, 448, 665])).
% 10.29/10.59 tff(23489,plain,
% 10.29/10.59 (r(s(s(elem!1)), s(z))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[362, 23488])).
% 10.29/10.59 tff(23490,plain,
% 10.29/10.59 ($false),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[14489, 194, 23489, 1484, 183, 23487])).
% 10.29/10.59 tff(23491,plain,(r(s(s(s(elem!1))), s(s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (elem!1 = s(elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.29/10.59 tff(23492,plain,
% 10.29/10.59 (~b(z, s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23491, 6155, 183, 10682, 1484, 448, 665, 437, 168])).
% 10.29/10.59 tff(23493,plain,
% 10.29/10.59 (r(z, s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[324, 23492])).
% 10.29/10.59 tff(23494,plain,
% 10.29/10.59 (b(elem!1, s(s(s(elem!1))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[424, 12780, 2688])).
% 10.29/10.59 tff(23495,plain,
% 10.29/10.59 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[13828, 12778, 326, 364])).
% 10.29/10.59 tff(23496,plain,
% 10.29/10.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[1370, 23495, 297])).
% 10.29/10.59 tff(23497,plain,
% 10.29/10.59 (~b(s(z), s(s(s(elem!1))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[22200, 23496, 721, 23494, 12778, 411, 270])).
% 10.29/10.59 tff(23498,plain,
% 10.29/10.59 (r(s(z), s(s(s(elem!1))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[247, 23497])).
% 10.29/10.59 tff(23499,plain,
% 10.29/10.59 ($false),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[21108, 194, 411, 12778, 23498, 182])).
% 10.29/10.59 tff(23500,plain,(b(s(s(s(elem!1))), z) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.59 tff(23501,plain,
% 10.29/10.59 (~r(s(s(elem!1)), elem!1)),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23500, 23493, 721, 9550, 411, 182, 270, 297, 665])).
% 10.29/10.59 tff(23502,plain,
% 10.29/10.59 ($false),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[872, 23501, 23473, 249])).
% 10.29/10.59 tff(23503,plain,(r(s(s(s(elem!1))), s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(z))) | b(s(s(s(elem!1))), z) | (~r(z, elem!1)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (elem!1 = s(elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.29/10.59 tff(23504,plain,
% 10.29/10.59 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23503, 182, 721, 9550, 411, 249, 270, 297, 665, 10682, 448, 183, 1484, 437, 168])).
% 10.29/10.59 tff(23505,plain,
% 10.29/10.59 (~r(s(s(elem!1)), s(z))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[11169, 23504, 1216, 183])).
% 10.29/10.59 tff(23506,plain,
% 10.29/10.59 (b(s(s(elem!1)), s(z))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[362, 23505])).
% 10.29/10.59 tff(23507,plain,
% 10.29/10.59 (~r(s(s(elem!1)), elem!1)),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23500, 9550, 182, 721, 270, 297, 326, 411, 665])).
% 10.29/10.59 tff(23508,plain,
% 10.29/10.59 (~b(s(s(elem!1)), elem!1)),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[21118, 12778, 381, 411, 721, 182])).
% 10.29/10.59 tff(23509,plain,
% 10.29/10.59 ($false),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[872, 23508, 23507, 249])).
% 10.29/10.59 tff(23510,plain,(b(s(s(s(elem!1))), z) | (s(s(elem!1)) = elem!1) | (~b(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.29/10.59 tff(23511,plain,
% 10.29/10.59 (~r(z, s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23510, 23506, 721, 9550, 665, 411, 270, 297, 182, 249])).
% 10.29/10.59 tff(23512,plain,
% 10.29/10.59 (b(z, s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[324, 23511])).
% 10.29/10.59 tff(23513,plain,
% 10.29/10.59 (b(z, s(s(s(s(s(s(z)))))))),
% 10.29/10.59 inference(modus_ponens,[status(thm)],[23512, 23471])).
% 10.29/10.59 tff(23514,plain,
% 10.29/10.59 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 10.29/10.59 inference(monotonicity,[status(thm)],[2730])).
% 10.29/10.59 tff(23515,plain,
% 10.29/10.59 (b(s(s(s(s(s(s(z)))))), s(z))),
% 10.29/10.59 inference(modus_ponens,[status(thm)],[23506, 23514])).
% 10.29/10.59 tff(23516,plain,
% 10.29/10.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 10.29/10.59 inference(rewrite,[status(thm)],[])).
% 10.29/10.59 tff(23517,plain,
% 10.29/10.59 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 10.29/10.59 inference(rewrite,[status(thm)],[])).
% 10.29/10.59 tff(23518,plain,
% 10.29/10.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 10.29/10.59 inference(monotonicity,[status(thm)],[23517])).
% 10.29/10.59 tff(23519,plain,
% 10.29/10.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 10.29/10.59 inference(transitivity,[status(thm)],[23518, 23516])).
% 10.29/10.59 tff(23520,plain,
% 10.29/10.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.29/10.59 inference(quant_inst,[status(thm)],[])).
% 10.29/10.59 tff(23521,plain,
% 10.29/10.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 10.29/10.59 inference(modus_ponens,[status(thm)],[23520, 23519])).
% 10.29/10.59 tff(23522,plain,
% 10.29/10.59 ($false),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23521, 391, 90, 1235, 3563, 23515, 23513])).
% 10.29/10.59 tff(23523,plain,((~r(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = s(s(s(s(z)))))) | (~b(elem!1, s(z))) | b(s(s(s(elem!1))), z) | (~b(elem!1, z)) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (elem!1 = s(elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.29/10.59 tff(23524,plain,
% 10.29/10.59 (~r(s(z), z)),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23523, 23470, 1235, 23426, 90, 721, 9550, 23433, 411, 23462, 23461, 23459, 1216, 183, 10682, 448, 1484, 4598, 23422])).
% 10.29/10.59 tff(23525,plain,
% 10.29/10.59 (b(s(z), z)),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[180, 23524])).
% 10.29/10.59 tff(23526,plain,
% 10.29/10.59 (~b(z, s(s(elem!1)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[21951, 23525, 721, 23416, 23433])).
% 10.29/10.59 tff(23527,plain,
% 10.29/10.59 (~b(s(s(s(s(z)))), elem!1)),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23455, 391, 10682, 1235, 3369, 3563])).
% 10.29/10.59 tff(23528,plain,
% 10.29/10.59 (s(s(s(s(z)))) = elem!1),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[762, 23527, 6221])).
% 10.29/10.59 tff(23529,plain,
% 10.29/10.59 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[2865, 23528, 448])).
% 10.29/10.59 tff(23530,plain,
% 10.29/10.59 (~(elem!1 = z)),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23210, 23207, 719])).
% 10.29/10.59 tff(23531,plain,
% 10.29/10.59 (~(z = elem!1)),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[97, 23530])).
% 10.29/10.59 tff(23532,plain,
% 10.29/10.59 (~(s(z) = s(elem!1))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[117, 23531])).
% 10.29/10.59 tff(23533,plain,
% 10.29/10.59 (~(s(s(elem!1)) = s(s(z)))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[1962, 23532])).
% 10.29/10.59 tff(23534,plain,
% 10.29/10.59 (~(elem!1 = s(s(s(s(elem!1)))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[14423, 23528, 23533])).
% 10.29/10.59 tff(23535,plain,
% 10.29/10.59 (b(elem!1, s(s(s(s(elem!1)))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[1018, 23534, 23207])).
% 10.29/10.59 tff(23536,plain,
% 10.29/10.59 (~r(elem!1, s(s(s(s(z)))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[22246, 411, 4486, 174])).
% 10.29/10.59 tff(23537,plain,
% 10.29/10.59 (~b(elem!1, s(s(s(s(z)))))),
% 10.29/10.59 inference(unit_resolution,[status(thm)],[23468, 391, 10682, 1235, 3369, 3563])).
% 10.29/10.59 tff(23538,plain,
% 10.29/10.60 (elem!1 = s(s(s(s(z))))),
% 10.29/10.60 inference(unit_resolution,[status(thm)],[781, 23537, 23536])).
% 10.29/10.60 tff(23539,plain,
% 10.29/10.60 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.29/10.60 inference(unit_resolution,[status(thm)],[717, 23528])).
% 10.29/10.60 tff(23540,plain,
% 10.29/10.60 (~(s(s(elem!1)) = s(elem!1))),
% 10.29/10.60 inference(unit_resolution,[status(thm)],[2279, 23539])).
% 10.29/10.60 tff(23541,plain,
% 10.29/10.60 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.29/10.60 inference(unit_resolution,[status(thm)],[287, 23540])).
% 10.29/10.60 tff(23542,plain,
% 10.29/10.60 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 10.29/10.60 inference(unit_resolution,[status(thm)],[299, 23541])).
% 10.29/10.60 tff(23543,plain,
% 10.29/10.60 (s(elem!1) = s(s(s(s(s(z)))))),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23538])).
% 10.29/10.60 tff(23544,plain,
% 10.29/10.60 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23543])).
% 10.29/10.60 tff(23545,plain,
% 10.29/10.60 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23544])).
% 10.29/10.60 tff(23546,plain,
% 10.29/10.60 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 10.29/10.60 inference(symmetry,[status(thm)],[23545])).
% 10.29/10.60 tff(23547,plain,
% 10.29/10.60 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(z))))))))),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23545])).
% 10.29/10.60 tff(23548,plain,
% 10.29/10.60 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(elem!1))))),
% 10.29/10.60 inference(symmetry,[status(thm)],[23547])).
% 10.29/10.60 tff(23549,plain,
% 10.29/10.60 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23548, 23546])).
% 10.29/10.60 tff(23550,plain,
% 10.29/10.60 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23549])).
% 10.29/10.60 tff(23551,plain,
% 10.29/10.60 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(elem!1))), z)),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23546])).
% 10.29/10.60 tff(23552,plain,
% 10.29/10.60 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 10.29/10.60 inference(symmetry,[status(thm)],[23551])).
% 10.29/10.60 tff(23553,plain,
% 10.29/10.60 (r(s(s(s(s(s(s(s(z))))))), z)),
% 10.29/10.60 inference(modus_ponens,[status(thm)],[174, 23552])).
% 10.29/10.60 tff(23554,plain,
% 10.29/10.60 (r(s(s(s(s(s(s(s(s(z)))))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23548])).
% 10.29/10.60 tff(23555,plain,
% 10.29/10.60 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 10.29/10.60 inference(symmetry,[status(thm)],[23554])).
% 10.29/10.60 tff(23556,plain,
% 10.29/10.60 (b(s(s(s(s(s(s(s(s(z)))))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23548])).
% 10.29/10.60 tff(23557,plain,
% 10.29/10.60 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23556])).
% 10.29/10.60 tff(23558,plain,
% 10.29/10.60 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23544])).
% 10.29/10.60 tff(23559,plain,
% 10.29/10.60 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 10.29/10.60 inference(monotonicity,[status(thm)],[23538])).
% 10.29/10.60 tff(23560,plain,
% 10.29/10.60 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 10.29/10.60 inference(transitivity,[status(thm)],[23559, 23558])).
% 10.29/10.60 tff(23561,plain,
% 10.29/10.60 (~(s(s(elem!1)) = elem!1)),
% 10.29/10.60 inference(unit_resolution,[status(thm)],[451, 23539])).
% 10.39/10.60 tff(23562,plain,
% 10.39/10.60 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[281, 23539])).
% 10.39/10.60 tff(23563,plain,
% 10.39/10.60 (r(s(s(elem!1)), elem!1)),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[872, 14574, 249])).
% 10.39/10.60 tff(23564,plain,
% 10.39/10.60 (~b(s(s(elem!1)), z)),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[13177, 380, 10682, 1374])).
% 10.39/10.60 tff(23565,plain,
% 10.39/10.60 (r(s(s(elem!1)), z)),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[2629, 23564])).
% 10.39/10.60 tff(23566,plain,
% 10.39/10.60 (~r(elem!1, z)),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[8360, 23565, 411, 364])).
% 10.39/10.60 tff(23567,plain,
% 10.39/10.60 (b(elem!1, z)),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[526, 23566, 2])).
% 10.39/10.60 tff(23568,plain,
% 10.39/10.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 10.39/10.60 inference(rewrite,[status(thm)],[])).
% 10.39/10.60 tff(23569,plain,
% 10.39/10.60 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 10.39/10.60 inference(rewrite,[status(thm)],[])).
% 10.39/10.60 tff(23570,plain,
% 10.39/10.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 10.39/10.60 inference(monotonicity,[status(thm)],[23569])).
% 10.39/10.60 tff(23571,plain,
% 10.39/10.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 10.39/10.60 inference(transitivity,[status(thm)],[23570, 23568])).
% 10.39/10.60 tff(23572,plain,
% 10.39/10.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 10.39/10.60 inference(quant_inst,[status(thm)],[])).
% 10.39/10.60 tff(23573,plain,
% 10.39/10.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1))),
% 10.39/10.60 inference(modus_ponens,[status(thm)],[23572, 23571])).
% 10.39/10.60 tff(23574,plain,
% 10.39/10.60 ($false),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[23573, 391, 665, 10682, 1374, 644, 590])).
% 10.39/10.60 tff(23575,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.60 tff(23576,plain,
% 10.39/10.60 (~b(s(z), elem!1)),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[23575, 23567, 10682, 1374, 590])).
% 10.39/10.60 tff(23577,plain,
% 10.39/10.60 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 10.39/10.60 inference(rewrite,[status(thm)],[])).
% 10.39/10.60 tff(23578,plain,
% 10.39/10.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 10.39/10.60 inference(monotonicity,[status(thm)],[23577])).
% 10.39/10.60 tff(23579,plain,
% 10.39/10.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 10.39/10.60 inference(transitivity,[status(thm)],[23578, 19539])).
% 10.39/10.60 tff(23580,plain,
% 10.39/10.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 10.39/10.60 inference(quant_inst,[status(thm)],[])).
% 10.39/10.60 tff(23581,plain,
% 10.39/10.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 10.39/10.60 inference(modus_ponens,[status(thm)],[23580, 23579])).
% 10.39/10.60 tff(23582,plain,
% 10.39/10.60 (~b(elem!1, s(s(s(elem!1))))),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[23581, 391, 23567, 380, 10682])).
% 10.39/10.60 tff(23583,plain,
% 10.39/10.60 (~r(s(z), elem!1)),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[5715, 23582, 127, 168, 232])).
% 10.39/10.60 tff(23584,plain,
% 10.39/10.60 (s(z) = elem!1),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[632, 23583, 23576])).
% 10.39/10.60 tff(23585,plain,
% 10.39/10.60 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 10.39/10.60 inference(monotonicity,[status(thm)],[23584])).
% 10.39/10.60 tff(23586,plain,
% 10.39/10.60 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 10.39/10.60 inference(symmetry,[status(thm)],[23585])).
% 10.39/10.60 tff(23587,plain,
% 10.39/10.60 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(z)))),
% 10.39/10.60 inference(monotonicity,[status(thm)],[23586])).
% 10.39/10.60 tff(23588,plain,
% 10.39/10.60 (~b(s(s(elem!1)), s(z))),
% 10.39/10.60 inference(modus_ponens,[status(thm)],[4017, 23587])).
% 10.39/10.60 tff(23589,plain,
% 10.39/10.60 (r(elem!1, s(s(s(elem!1))))),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[424, 23582, 4029])).
% 10.39/10.60 tff(23590,plain,
% 10.39/10.60 (~r(z, s(s(elem!1)))),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[2562, 23589, 411, 364])).
% 10.39/10.60 tff(23591,plain,
% 10.39/10.60 (b(z, s(s(elem!1)))),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[324, 23590])).
% 10.39/10.60 tff(23592,plain,
% 10.39/10.60 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[12932, 23591, 10682, 1374])).
% 10.39/10.60 tff(23593,plain,
% 10.39/10.60 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[1356, 23592, 270])).
% 10.39/10.60 tff(23594,plain,
% 10.39/10.60 (~r(s(s(elem!1)), s(z))),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[2201, 23593, 183, 232])).
% 10.39/10.60 tff(23595,plain,
% 10.39/10.60 (b(s(s(elem!1)), s(z))),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[362, 23594])).
% 10.39/10.60 tff(23596,plain,
% 10.39/10.60 ($false),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[23595, 23588])).
% 10.39/10.60 tff(23597,plain,((~b(s(s(s(elem!1))), z)) | b(s(s(elem!1)), elem!1) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~b(s(z), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 10.39/10.60 tff(23598,plain,
% 10.39/10.60 (~b(s(s(s(elem!1))), z)),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[23597, 232, 183, 4017, 270, 10682, 1374, 411, 364, 127, 168, 590, 2])).
% 10.39/10.60 tff(23599,plain,
% 10.39/10.60 (r(s(s(s(elem!1))), z)),
% 10.39/10.60 inference(unit_resolution,[status(thm)],[377, 23598])).
% 10.39/10.61 tff(23600,plain,
% 10.39/10.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 10.39/10.61 inference(rewrite,[status(thm)],[])).
% 10.39/10.61 tff(23601,plain,
% 10.39/10.61 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 10.39/10.61 inference(rewrite,[status(thm)],[])).
% 10.39/10.61 tff(23602,plain,
% 10.39/10.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z))))),
% 10.39/10.61 inference(monotonicity,[status(thm)],[23601])).
% 10.39/10.61 tff(23603,plain,
% 10.39/10.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)))),
% 10.39/10.61 inference(transitivity,[status(thm)],[23602, 23600])).
% 10.39/10.61 tff(23604,plain,
% 10.39/10.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 10.39/10.61 inference(quant_inst,[status(thm)],[])).
% 10.39/10.61 tff(23605,plain,
% 10.39/10.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z))),
% 10.39/10.61 inference(modus_ponens,[status(thm)],[23604, 23603])).
% 10.39/10.61 tff(23606,plain,
% 10.39/10.61 ($false),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[23605, 194, 411, 530, 174, 233])).
% 10.39/10.61 tff(23607,plain,((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.61 tff(23608,plain,
% 10.39/10.61 (~r(elem!1, z)),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[23607, 23599, 411, 4486])).
% 10.39/10.61 tff(23609,plain,
% 10.39/10.61 (b(elem!1, z)),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[526, 23608, 2])).
% 10.39/10.61 tff(23610,plain,
% 10.39/10.61 (~b(s(z), elem!1)),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[23575, 23609, 10682, 1374, 590])).
% 10.39/10.61 tff(23611,plain,
% 10.39/10.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.39/10.61 inference(rewrite,[status(thm)],[])).
% 10.39/10.61 tff(23612,plain,
% 10.39/10.61 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.39/10.61 inference(rewrite,[status(thm)],[])).
% 10.39/10.61 tff(23613,plain,
% 10.39/10.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 10.39/10.61 inference(monotonicity,[status(thm)],[23612])).
% 10.39/10.61 tff(23614,plain,
% 10.39/10.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.39/10.61 inference(transitivity,[status(thm)],[23613, 23611])).
% 10.39/10.61 tff(23615,plain,
% 10.39/10.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 10.39/10.61 inference(quant_inst,[status(thm)],[])).
% 10.39/10.61 tff(23616,plain,
% 10.39/10.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 10.39/10.61 inference(modus_ponens,[status(thm)],[23615, 23614])).
% 10.39/10.61 tff(23617,plain,
% 10.39/10.61 (~b(elem!1, s(z))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[23616, 391, 23609, 10682, 1374, 590])).
% 10.39/10.61 tff(23618,plain,
% 10.39/10.61 (s(z) = elem!1),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[5246, 232, 4486, 23617, 23610])).
% 10.39/10.61 tff(23619,plain,
% 10.39/10.61 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 10.39/10.61 inference(monotonicity,[status(thm)],[23618])).
% 10.39/10.61 tff(23620,plain,
% 10.39/10.61 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 10.39/10.61 inference(symmetry,[status(thm)],[23619])).
% 10.39/10.61 tff(23621,plain,
% 10.39/10.61 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(z)))),
% 10.39/10.61 inference(monotonicity,[status(thm)],[23620])).
% 10.39/10.61 tff(23622,plain,
% 10.39/10.61 (~b(s(s(elem!1)), s(z))),
% 10.39/10.61 inference(modus_ponens,[status(thm)],[4017, 23621])).
% 10.39/10.61 tff(23623,plain,
% 10.39/10.61 (r(elem!1, s(s(s(elem!1))))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[2570, 23618, 232])).
% 10.39/10.61 tff(23624,plain,
% 10.39/10.61 (~r(z, s(s(elem!1)))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[2562, 23623, 411, 364])).
% 10.39/10.61 tff(23625,plain,
% 10.39/10.61 (b(z, s(s(elem!1)))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[324, 23624])).
% 10.39/10.61 tff(23626,plain,
% 10.39/10.61 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[12932, 23625, 10682, 1374])).
% 10.39/10.61 tff(23627,plain,
% 10.39/10.61 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[1356, 23626, 270])).
% 10.39/10.61 tff(23628,plain,
% 10.39/10.61 (~r(s(s(elem!1)), s(z))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[2201, 23627, 183, 232])).
% 10.39/10.61 tff(23629,plain,
% 10.39/10.61 (b(s(s(elem!1)), s(z))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[362, 23628])).
% 10.39/10.61 tff(23630,plain,
% 10.39/10.61 ($false),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[23629, 23622])).
% 10.39/10.61 tff(23631,plain,((~r(s(z), s(s(s(elem!1))))) | b(s(s(elem!1)), elem!1) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (elem!1 = z) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.39/10.61 tff(23632,plain,
% 10.39/10.61 ($false),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[23631, 23563, 14574, 10682, 183, 168, 232, 411, 270, 590, 2, 127, 1374])).
% 10.39/10.61 tff(23633,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), elem!1) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | (elem!1 = z) | (s(s(s(elem!1))) = elem!1) | (s(s(elem!1)) = elem!1) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.61 tff(23634,plain,
% 10.39/10.61 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[23633, 23562, 183, 168, 232, 411, 10682, 590, 23530, 127, 23561, 665, 448])).
% 10.39/10.61 tff(23635,plain,
% 10.39/10.61 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[1370, 23634, 23541])).
% 10.39/10.61 tff(23636,plain,
% 10.39/10.61 (~r(s(s(elem!1)), elem!1)),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[13828, 23635, 174, 326])).
% 10.39/10.61 tff(23637,plain,
% 10.39/10.61 (b(s(s(elem!1)), elem!1)),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[872, 23636, 23561])).
% 10.39/10.61 tff(23638,plain,
% 10.39/10.61 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 10.39/10.61 inference(modus_ponens,[status(thm)],[23637, 23560])).
% 10.39/10.61 tff(23639,plain,
% 10.39/10.61 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 10.39/10.61 inference(unit_resolution,[status(thm)],[2686, 23539])).
% 10.39/10.61 tff(23640,plain,
% 10.39/10.61 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(s(z)))))))),
% 10.39/10.61 inference(monotonicity,[status(thm)],[23544])).
% 10.39/10.61 tff(23641,plain,
% 10.39/10.61 (r(z, s(s(s(s(s(s(z)))))))),
% 10.39/10.61 inference(modus_ponens,[status(thm)],[326, 23640])).
% 10.39/10.61 tff(23642,plain,
% 10.39/10.61 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 10.39/10.61 inference(monotonicity,[status(thm)],[2730])).
% 10.39/10.61 tff(23643,plain,
% 10.39/10.61 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(z))))))))),
% 10.39/10.61 inference(monotonicity,[status(thm)],[23642])).
% 10.39/10.61 tff(23644,plain,
% 10.39/10.61 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(elem!1))))),
% 10.39/10.61 inference(symmetry,[status(thm)],[23643])).
% 10.39/10.61 tff(23645,plain,
% 10.39/10.61 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.39/10.61 inference(monotonicity,[status(thm)],[2731, 23644])).
% 10.39/10.61 tff(23646,plain,
% 10.39/10.61 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))),
% 10.39/10.61 inference(symmetry,[status(thm)],[23645])).
% 10.39/10.61 tff(23647,plain,
% 10.39/10.61 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))),
% 10.39/10.61 inference(modus_ponens,[status(thm)],[1176, 23646])).
% 10.39/10.61 tff(23648,plain,
% 10.39/10.61 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 10.39/10.61 inference(symmetry,[status(thm)],[23642])).
% 10.39/10.61 tff(23649,plain,
% 10.39/10.61 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(elem!1))), z)),
% 10.39/10.61 inference(monotonicity,[status(thm)],[23648])).
% 10.39/10.61 tff(23650,plain,
% 10.39/10.61 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 10.39/10.61 inference(symmetry,[status(thm)],[23649])).
% 10.39/10.61 tff(23651,plain,
% 10.39/10.61 (r(s(s(s(s(s(s(s(z))))))), z)),
% 10.39/10.61 inference(modus_ponens,[status(thm)],[174, 23650])).
% 10.39/10.61 tff(23652,plain,
% 10.39/10.61 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.39/10.61 inference(monotonicity,[status(thm)],[23648, 2731])).
% 10.39/10.61 tff(23653,plain,
% 10.39/10.61 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 10.39/10.61 inference(symmetry,[status(thm)],[23652])).
% 10.39/10.61 tff(23654,plain,
% 10.39/10.61 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 10.39/10.61 inference(modus_ponens,[status(thm)],[327, 23653])).
% 10.39/10.61 tff(23655,plain,
% 10.39/10.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 10.39/10.61 inference(rewrite,[status(thm)],[])).
% 10.39/10.61 tff(23656,plain,
% 10.39/10.61 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 10.39/10.61 inference(rewrite,[status(thm)],[])).
% 10.39/10.61 tff(23657,plain,
% 10.39/10.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 10.39/10.62 inference(monotonicity,[status(thm)],[23656])).
% 10.39/10.62 tff(23658,plain,
% 10.39/10.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 10.39/10.62 inference(transitivity,[status(thm)],[23657, 23655])).
% 10.39/10.62 tff(23659,plain,
% 10.39/10.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 10.39/10.62 inference(quant_inst,[status(thm)],[])).
% 10.39/10.62 tff(23660,plain,
% 10.39/10.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z))))))))))),
% 10.39/10.62 inference(modus_ponens,[status(thm)],[23659, 23658])).
% 10.39/10.62 tff(23661,plain,
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% 10.39/10.62 inference(unit_resolution,[status(thm)],[23660, 194, 14084])).
% 10.39/10.62 tff(23662,plain,
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% 10.39/10.62 inference(unit_resolution,[status(thm)],[23661, 23654, 23651, 23647])).
% 10.39/10.62 tff(23663,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.62 tff(23664,plain,
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% 10.39/10.62 inference(unit_resolution,[status(thm)],[23663, 23641, 23538, 23635, 174])).
% 10.39/10.62 tff(23665,plain,
% 10.39/10.62 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.39/10.62 inference(unit_resolution,[status(thm)],[1048, 23664, 23639])).
% 10.39/10.62 tff(23666,plain,
% 10.39/10.62 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(s(elem!1))))),
% 10.39/10.62 inference(monotonicity,[status(thm)],[23648])).
% 10.39/10.62 tff(23667,plain,
% 10.39/10.62 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 10.39/10.62 inference(symmetry,[status(thm)],[23666])).
% 10.39/10.62 tff(23668,plain,
% 10.39/10.62 (b(z, s(s(s(s(s(s(s(z))))))))),
% 10.39/10.62 inference(modus_ponens,[status(thm)],[10682, 23667])).
% 10.39/10.62 tff(23669,plain,
% 10.39/10.62 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.39/10.62 inference(monotonicity,[status(thm)],[2731, 23644])).
% 10.39/10.62 tff(23670,plain,
% 10.39/10.62 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))),
% 10.39/10.62 inference(symmetry,[status(thm)],[23669])).
% 10.39/10.62 tff(23671,plain,
% 10.39/10.62 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))),
% 10.39/10.62 inference(modus_ponens,[status(thm)],[1152, 23670])).
% 10.39/10.62 tff(23672,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), z)), introduced(assumption)).
% 10.39/10.62 tff(23673,plain,
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% 10.39/10.62 inference(monotonicity,[status(thm)],[2738, 23644])).
% 10.39/10.62 tff(23674,plain,
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% 10.39/10.62 inference(symmetry,[status(thm)],[23673])).
% 10.39/10.62 tff(23675,plain,
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% 10.39/10.62 inference(modus_ponens,[status(thm)],[974, 23674])).
% 10.39/10.62 tff(23676,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 10.39/10.62 tff(23677,plain,
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% 10.39/10.62 tff(23678,plain,
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% 10.39/10.62 inference(monotonicity,[status(thm)],[23678])).
% 10.39/10.62 tff(23680,plain,
% 10.39/10.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 10.39/10.62 inference(transitivity,[status(thm)],[23679, 23677])).
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% 10.39/10.62 inference(quant_inst,[status(thm)],[])).
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% 10.39/10.62 inference(modus_ponens,[status(thm)],[23681, 23680])).
% 10.39/10.62 tff(23683,plain,
% 10.39/10.62 ((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 10.39/10.62 inference(unit_resolution,[status(thm)],[23682, 391, 23676])).
% 10.39/10.62 tff(23684,plain,
% 10.39/10.62 ($false),
% 10.39/10.62 inference(unit_resolution,[status(thm)],[23683, 23675, 23672, 23671, 23668])).
% 10.39/10.62 tff(23685,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.62 tff(23686,plain,
% 10.39/10.62 (~b(s(s(s(s(s(s(s(s(z)))))))), z)),
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% 10.39/10.62 tff(23687,plain,
% 10.39/10.62 (~b(s(s(s(s(elem!1)))), z)),
% 10.39/10.62 inference(modus_ponens,[status(thm)],[23686, 23557])).
% 10.39/10.62 tff(23688,plain,
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% 10.39/10.62 inference(unit_resolution,[status(thm)],[1626, 23687])).
% 10.39/10.62 tff(23689,plain,
% 10.39/10.62 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 10.39/10.62 inference(modus_ponens,[status(thm)],[23688, 23555])).
% 10.39/10.62 tff(23690,plain,
% 10.39/10.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
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% 10.39/10.62 tff(23695,plain,
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% 10.39/10.62 tff(23696,plain,
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% 10.39/10.62 inference(unit_resolution,[status(thm)],[1095, 23695, 23542])).
% 10.39/10.62 tff(23697,plain,
% 10.39/10.62 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
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% 10.39/10.62 tff(23698,plain,
% 10.39/10.62 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
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% 10.39/10.62 tff(23699,plain,
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% 10.39/10.62 inference(monotonicity,[status(thm)],[23698])).
% 10.39/10.62 tff(23700,plain,
% 10.39/10.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
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% 10.39/10.62 tff(23701,plain,
% 10.39/10.62 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 10.39/10.62 inference(rewrite,[status(thm)],[])).
% 10.39/10.62 tff(23702,plain,
% 10.39/10.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))))),
% 10.39/10.63 inference(monotonicity,[status(thm)],[23701])).
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% 10.39/10.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 10.39/10.63 inference(transitivity,[status(thm)],[23702, 23700])).
% 10.39/10.63 tff(23704,plain,
% 10.39/10.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 10.39/10.63 inference(quant_inst,[status(thm)],[])).
% 10.39/10.63 tff(23705,plain,
% 10.39/10.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))),
% 10.39/10.63 inference(modus_ponens,[status(thm)],[23704, 23703])).
% 10.39/10.63 tff(23706,plain,
% 10.39/10.63 ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))),
% 10.39/10.63 inference(unit_resolution,[status(thm)],[23705, 194, 719])).
% 10.39/10.63 tff(23707,plain,
% 10.39/10.63 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 10.39/10.63 inference(unit_resolution,[status(thm)],[23706, 23689, 23553])).
% 10.39/10.63 tff(23708,plain,
% 10.39/10.63 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.39/10.63 inference(modus_ponens,[status(thm)],[23707, 23699])).
% 10.39/10.63 tff(23709,plain,
% 10.39/10.63 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.39/10.63 inference(unit_resolution,[status(thm)],[1164, 23708, 23697])).
% 10.39/10.63 tff(23710,plain,
% 10.39/10.63 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.39/10.63 inference(monotonicity,[status(thm)],[23644, 23648])).
% 10.39/10.63 tff(23711,plain,
% 10.39/10.63 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 10.39/10.63 inference(symmetry,[status(thm)],[23710])).
% 10.39/10.63 tff(23712,plain,
% 10.39/10.63 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 10.39/10.63 inference(modus_ponens,[status(thm)],[1114, 23711])).
% 10.39/10.63 tff(23713,plain,
% 10.39/10.63 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.39/10.63 inference(monotonicity,[status(thm)],[23648])).
% 10.39/10.63 tff(23714,plain,
% 10.39/10.63 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 10.39/10.63 inference(symmetry,[status(thm)],[23713])).
% 10.39/10.63 tff(23715,plain,
% 10.39/10.63 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 10.39/10.63 inference(modus_ponens,[status(thm)],[3325, 23714])).
% 10.39/10.63 tff(23716,plain,
% 10.39/10.63 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.39/10.63 inference(monotonicity,[status(thm)],[23648, 23644])).
% 10.39/10.63 tff(23717,plain,
% 10.39/10.63 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 10.39/10.63 inference(symmetry,[status(thm)],[23716])).
% 10.39/10.63 tff(23718,plain,
% 10.39/10.63 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 10.39/10.63 inference(modus_ponens,[status(thm)],[1573, 23717])).
% 10.39/10.63 tff(23719,plain,
% 10.39/10.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 10.39/10.63 inference(rewrite,[status(thm)],[])).
% 10.39/10.63 tff(23720,plain,
% 10.39/10.63 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 10.39/10.63 inference(rewrite,[status(thm)],[])).
% 10.39/10.63 tff(23721,plain,
% 10.39/10.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))))),
% 10.39/10.63 inference(monotonicity,[status(thm)],[23720])).
% 10.39/10.63 tff(23722,plain,
% 10.39/10.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))))),
% 10.39/10.63 inference(transitivity,[status(thm)],[23721, 23719])).
% 10.39/10.63 tff(23723,plain,
% 10.39/10.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 10.39/10.63 inference(quant_inst,[status(thm)],[])).
% 10.39/10.63 tff(23724,plain,
% 10.39/10.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))),
% 10.39/10.63 inference(modus_ponens,[status(thm)],[23723, 23722])).
% 10.39/10.63 tff(23725,plain,
% 10.39/10.63 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(s(z))))))))))),
% 10.39/10.63 inference(unit_resolution,[status(thm)],[23724, 391])).
% 10.39/10.63 tff(23726,plain,
% 10.39/10.63 ($false),
% 10.39/10.63 inference(unit_resolution,[status(thm)],[23725, 23718, 23715, 23712, 23675])).
% 10.39/10.63 tff(23727,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.63 tff(23728,plain,
% 10.39/10.63 ($false),
% 10.39/10.63 inference(unit_resolution,[status(thm)],[23727, 23709, 23696, 23538, 23535, 23529])).
% 10.39/10.63 tff(23729,plain,((~b(elem!1, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), elem!1) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(s(z), z)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.64 tff(23730,plain,
% 10.39/10.64 (~r(z, s(s(elem!1)))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[23729, 23525, 12778, 10682, 23428, 183, 23422, 23430, 411, 23449, 127, 23433, 448, 23431, 23436, 1235, 23426])).
% 10.39/10.64 tff(23731,plain,
% 10.39/10.64 ($false),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[324, 23730, 23526])).
% 10.39/10.64 tff(23732,plain,(b(s(s(z)), s(s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | b(s(s(s(elem!1))), z) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.64 tff(23733,plain,
% 10.39/10.64 (b(s(s(z)), s(s(s(s(z)))))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[23732, 411, 183, 10682, 127, 448, 1235, 721, 90, 9550, 1216, 1484, 23418])).
% 10.39/10.64 tff(23734,plain,
% 10.39/10.64 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[23377, 23418, 1216, 90, 23416, 1235])).
% 10.39/10.64 tff(23735,plain,
% 10.39/10.64 (b(s(s(s(s(z)))), s(s(z)))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[1714, 23734])).
% 10.39/10.64 tff(23736,plain,
% 10.39/10.64 (~r(elem!1, s(s(z)))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[14358, 1484, 183, 23420])).
% 10.39/10.64 tff(23737,plain,
% 10.39/10.64 (~b(s(z), z)),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[7203, 23733, 90, 23416, 1235])).
% 10.39/10.64 tff(23738,plain,
% 10.39/10.64 (r(s(z), z)),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[180, 23737])).
% 10.39/10.64 tff(23739,plain,
% 10.39/10.64 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 10.39/10.64 inference(monotonicity,[status(thm)],[1399])).
% 10.39/10.64 tff(23740,plain,
% 10.39/10.64 (b(s(s(elem!1)), s(s(z)))),
% 10.39/10.64 inference(modus_ponens,[status(thm)],[3563, 23739])).
% 10.39/10.64 tff(23741,plain,
% 10.39/10.64 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(z)))),
% 10.39/10.64 inference(monotonicity,[status(thm)],[2651])).
% 10.39/10.64 tff(23742,plain,
% 10.39/10.64 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 10.39/10.64 inference(symmetry,[status(thm)],[23741])).
% 10.39/10.64 tff(23743,plain,
% 10.39/10.64 (b(s(s(elem!1)), elem!1)),
% 10.39/10.64 inference(modus_ponens,[status(thm)],[23740, 23742])).
% 10.39/10.64 tff(23744,plain,
% 10.39/10.64 (~r(s(s(s(elem!1))), z)),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[21118, 23743, 381, 411, 721, 182])).
% 10.39/10.64 tff(23745,plain,
% 10.39/10.64 (b(s(s(s(elem!1))), z)),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[377, 23744])).
% 10.39/10.64 tff(23746,plain,
% 10.39/10.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 10.39/10.64 inference(rewrite,[status(thm)],[])).
% 10.39/10.64 tff(23747,plain,
% 10.39/10.64 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 10.39/10.64 inference(rewrite,[status(thm)],[])).
% 10.39/10.64 tff(23748,plain,
% 10.39/10.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 10.39/10.64 inference(monotonicity,[status(thm)],[23747])).
% 10.39/10.64 tff(23749,plain,
% 10.39/10.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 10.39/10.64 inference(transitivity,[status(thm)],[23748, 23746])).
% 10.39/10.64 tff(23750,plain,
% 10.39/10.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 10.39/10.64 inference(quant_inst,[status(thm)],[])).
% 10.39/10.64 tff(23751,plain,
% 10.39/10.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 10.39/10.64 inference(modus_ponens,[status(thm)],[23750, 23749])).
% 10.39/10.64 tff(23752,plain,
% 10.39/10.64 ($false),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[23751, 391, 381, 380, 379, 1233, 6192])).
% 10.39/10.64 tff(23753,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.64 tff(23754,plain,
% 10.39/10.64 (~b(s(z), s(s(s(elem!1))))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[23753, 23745, 381, 2659, 23740])).
% 10.39/10.64 tff(23755,plain,
% 10.39/10.64 (r(s(z), s(s(s(elem!1))))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[247, 23754])).
% 10.39/10.64 tff(23756,plain,
% 10.39/10.64 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 10.39/10.64 inference(monotonicity,[status(thm)],[2652])).
% 10.39/10.64 tff(23757,plain,
% 10.39/10.64 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 10.39/10.64 inference(transitivity,[status(thm)],[23756, 3])).
% 10.39/10.64 tff(23758,plain,
% 10.39/10.64 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 10.39/10.64 inference(monotonicity,[status(thm)],[23757])).
% 10.39/10.64 tff(23759,plain,
% 10.39/10.64 (~(s(s(s(elem!1))) = elem!1)),
% 10.39/10.64 inference(modus_ponens,[status(thm)],[1397, 23758])).
% 10.39/10.64 tff(23760,plain,
% 10.39/10.64 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 10.39/10.64 inference(monotonicity,[status(thm)],[2652])).
% 10.39/10.64 tff(23761,plain,
% 10.39/10.64 ((~b(s(s(s(elem!1))), s(s(z)))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 10.39/10.64 inference(monotonicity,[status(thm)],[23760])).
% 10.39/10.64 tff(23762,plain,
% 10.39/10.64 (s(s(elem!1)) = s(s(s(s(z))))),
% 10.39/10.64 inference(symmetry,[status(thm)],[1399])).
% 10.39/10.64 tff(23763,plain,
% 10.39/10.64 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 10.39/10.64 inference(monotonicity,[status(thm)],[23762])).
% 10.39/10.64 tff(23764,plain,
% 10.39/10.64 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(elem!1)))),
% 10.39/10.64 inference(symmetry,[status(thm)],[23763])).
% 10.39/10.64 tff(23765,plain,
% 10.39/10.64 (b(s(s(z)), s(s(elem!1)))),
% 10.39/10.64 inference(modus_ponens,[status(thm)],[3823, 23764])).
% 10.39/10.64 tff(23766,plain,
% 10.39/10.64 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 10.39/10.64 inference(monotonicity,[status(thm)],[1399])).
% 10.39/10.64 tff(23767,plain,
% 10.39/10.64 (b(s(s(elem!1)), z)),
% 10.39/10.64 inference(modus_ponens,[status(thm)],[90, 23766])).
% 10.39/10.64 tff(23768,plain,
% 10.39/10.64 (~b(z, s(s(s(elem!1))))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[11449, 23745, 23767, 1235, 23740])).
% 10.39/10.64 tff(23769,plain,
% 10.39/10.64 (r(z, s(s(s(elem!1))))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[58, 23768])).
% 10.39/10.64 tff(23770,plain,
% 10.39/10.64 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[337, 23755, 23769, 182])).
% 10.39/10.64 tff(23771,plain,
% 10.39/10.64 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[1370, 23770, 297])).
% 10.39/10.64 tff(23772,plain,
% 10.39/10.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.39/10.64 inference(rewrite,[status(thm)],[])).
% 10.39/10.64 tff(23773,plain,
% 10.39/10.64 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.39/10.64 inference(rewrite,[status(thm)],[])).
% 10.39/10.64 tff(23774,plain,
% 10.39/10.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 10.39/10.64 inference(monotonicity,[status(thm)],[23773])).
% 10.39/10.64 tff(23775,plain,
% 10.39/10.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.39/10.64 inference(transitivity,[status(thm)],[23774, 23772])).
% 10.39/10.64 tff(23776,plain,
% 10.39/10.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.39/10.64 inference(quant_inst,[status(thm)],[])).
% 10.39/10.64 tff(23777,plain,
% 10.39/10.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 10.39/10.64 inference(modus_ponens,[status(thm)],[23776, 23775])).
% 10.39/10.64 tff(23778,plain,
% 10.39/10.64 ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[23777, 391, 23771, 23740])).
% 10.39/10.64 tff(23779,plain,
% 10.39/10.64 (~b(s(s(s(elem!1))), s(s(z)))),
% 10.39/10.64 inference(unit_resolution,[status(thm)],[23778, 23765])).
% 10.39/10.64 tff(23780,plain,
% 10.39/10.64 (~b(s(s(s(elem!1))), elem!1)),
% 10.39/10.64 inference(modus_ponens,[status(thm)],[23779, 23761])).
% 10.39/10.64 tff(23781,plain,
% 10.39/10.64 ((~b(s(s(z)), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 10.39/10.64 inference(monotonicity,[status(thm)],[2653])).
% 10.39/10.64 tff(23782,plain,
% 10.39/10.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.39/10.64 inference(rewrite,[status(thm)],[])).
% 10.39/10.64 tff(23783,plain,
% 10.39/10.64 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.39/10.64 inference(rewrite,[status(thm)],[])).
% 10.39/10.64 tff(23784,plain,
% 10.39/10.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 10.39/10.65 inference(monotonicity,[status(thm)],[23783])).
% 10.39/10.65 tff(23785,plain,
% 10.39/10.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.39/10.65 inference(transitivity,[status(thm)],[23784, 23782])).
% 10.39/10.65 tff(23786,plain,
% 10.39/10.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.39/10.65 inference(quant_inst,[status(thm)],[])).
% 10.39/10.65 tff(23787,plain,
% 10.39/10.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 10.39/10.65 inference(modus_ponens,[status(thm)],[23786, 23785])).
% 10.39/10.65 tff(23788,plain,
% 10.39/10.65 ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23787, 391, 23771, 23740])).
% 10.39/10.65 tff(23789,plain,
% 10.39/10.65 (~b(s(s(z)), s(s(s(elem!1))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23788, 23765])).
% 10.39/10.65 tff(23790,plain,
% 10.39/10.65 (~b(elem!1, s(s(s(elem!1))))),
% 10.39/10.65 inference(modus_ponens,[status(thm)],[23789, 23781])).
% 10.39/10.65 tff(23791,plain,
% 10.39/10.65 ($false),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[5715, 23790, 23780, 1484, 23759, 23755])).
% 10.39/10.65 tff(23792,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (~r(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.65 tff(23793,plain,
% 10.39/10.65 ($false),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23792, 14189, 14183, 90, 1235, 182, 13756, 3823, 411, 721, 3563, 1484])).
% 10.39/10.65 tff(23794,plain,((~(elem!1 = s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.65 tff(23795,plain,
% 10.39/10.65 (~(elem!1 = s(s(z)))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23794, 23738, 1235, 90, 23733, 411, 721, 23735, 1484, 1759])).
% 10.39/10.65 tff(23796,plain,
% 10.39/10.65 (b(elem!1, s(s(z)))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[3394, 23795, 23736])).
% 10.39/10.65 tff(23797,plain,
% 10.39/10.65 (~b(elem!1, s(s(s(s(z)))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[11498, 23796, 1759, 23735, 23733])).
% 10.39/10.65 tff(23798,plain,
% 10.39/10.65 (elem!1 = s(s(s(s(z))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[781, 23797, 23421])).
% 10.39/10.65 tff(23799,plain,
% 10.39/10.65 (s(s(s(s(z)))) = elem!1),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[769, 23798])).
% 10.39/10.65 tff(23800,plain,
% 10.39/10.65 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[717, 23799])).
% 10.39/10.65 tff(23801,plain,
% 10.39/10.65 (~(s(s(elem!1)) = elem!1)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[451, 23800])).
% 10.39/10.65 tff(23802,plain,
% 10.39/10.65 (~r(elem!1, z)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23283, 1484, 183, 23420])).
% 10.39/10.65 tff(23803,plain,
% 10.39/10.65 (~b(z, s(s(s(s(z)))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[20748, 23735, 90, 1235])).
% 10.39/10.65 tff(23804,plain,
% 10.39/10.65 (r(z, s(s(s(s(z)))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[800, 23803])).
% 10.39/10.65 tff(23805,plain,
% 10.39/10.65 (~b(s(z), s(s(s(elem!1))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[14992, 1235, 90, 23735, 23416])).
% 10.39/10.65 tff(23806,plain,
% 10.39/10.65 (r(s(z), s(s(s(elem!1))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[247, 23805])).
% 10.39/10.65 tff(23807,plain,
% 10.39/10.65 (~r(elem!1, s(s(s(s(elem!1)))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[14585, 23806, 23420, 1484])).
% 10.39/10.65 tff(23808,plain,
% 10.39/10.65 (~(elem!1 = z)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23210, 23807, 23804])).
% 10.39/10.65 tff(23809,plain,
% 10.39/10.65 (b(elem!1, z)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[526, 23808, 23802])).
% 10.39/10.65 tff(23810,plain,
% 10.39/10.65 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[281, 23800])).
% 10.39/10.65 tff(23811,plain,
% 10.39/10.65 (~(s(s(elem!1)) = s(elem!1))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[2279, 23800])).
% 10.39/10.65 tff(23812,plain,
% 10.39/10.65 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[287, 23811])).
% 10.39/10.65 tff(23813,plain,
% 10.39/10.65 ($false),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23523, 23812, 23810, 1235, 23735, 90, 721, 9550, 23809, 411, 23738, 23798, 23801, 1216, 183, 10682, 448, 1484, 4598, 23419])).
% 10.39/10.65 tff(23814,plain,((~r(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(z))) | b(s(s(s(elem!1))), z) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.39/10.65 tff(23815,plain,
% 10.39/10.65 (~r(z, elem!1)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23814, 23358, 90, 23403, 23014, 1216, 11174, 10782, 23413, 23405, 1759, 9])).
% 10.39/10.65 tff(23816,plain,
% 10.39/10.65 (b(elem!1, z)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[526, 2, 2282])).
% 10.39/10.65 tff(23817,plain,
% 10.39/10.65 (~b(elem!1, s(s(z)))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[13448, 149, 23816, 1235])).
% 10.39/10.65 tff(23818,plain,
% 10.39/10.65 (~b(s(s(s(s(z)))), elem!1)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[10895, 23816, 10682, 448, 3843, 149])).
% 10.39/10.65 tff(23819,plain,
% 10.39/10.65 (s(s(s(s(z)))) = elem!1),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[762, 23818, 6221])).
% 10.39/10.65 tff(23820,plain,
% 10.39/10.65 ($false),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[11029, 23819, 23817, 3563])).
% 10.39/10.65 tff(23821,plain,((elem!1 = z) | (~b(s(s(s(s(z)))), s(s(z)))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | r(z, elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 10.39/10.65 tff(23822,plain,
% 10.39/10.65 (r(s(s(s(s(z)))), elem!1)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23821, 23815, 23358, 23414, 10782, 23413, 22994, 23379, 23409])).
% 10.39/10.65 tff(23823,plain,
% 10.39/10.65 (~(s(z) = elem!1)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[10733, 22030, 53])).
% 10.39/10.65 tff(23824,plain,
% 10.39/10.65 (~(elem!1 = s(z))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[172, 23823])).
% 10.39/10.65 tff(23825,plain,
% 10.39/10.65 (b(elem!1, s(z))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[837, 23824, 832])).
% 10.39/10.65 tff(23826,plain,
% 10.39/10.65 (~b(z, elem!1)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[5136, 23825, 90, 3823, 1235])).
% 10.39/10.65 tff(23827,plain,
% 10.39/10.65 (z = elem!1),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[141, 23826, 80])).
% 10.39/10.65 tff(23828,plain,
% 10.39/10.65 (elem!1 = z),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[97, 23827])).
% 10.39/10.65 tff(23829,plain,
% 10.39/10.65 (b(z, s(z)) <=> b(elem!1, s(z))),
% 10.39/10.65 inference(monotonicity,[status(thm)],[23827])).
% 10.39/10.65 tff(23830,plain,
% 10.39/10.65 (b(elem!1, s(z)) <=> b(z, s(z))),
% 10.39/10.65 inference(symmetry,[status(thm)],[23829])).
% 10.39/10.65 tff(23831,plain,
% 10.39/10.65 (b(z, s(z))),
% 10.39/10.65 inference(modus_ponens,[status(thm)],[23825, 23830])).
% 10.39/10.65 tff(23832,plain,
% 10.39/10.65 (~b(s(z), z)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[7203, 23831, 90, 3823, 1235])).
% 10.39/10.65 tff(23833,plain,
% 10.39/10.65 (s(z) = s(elem!1)),
% 10.39/10.65 inference(monotonicity,[status(thm)],[23827])).
% 10.39/10.65 tff(23834,plain,
% 10.39/10.65 (s(s(z)) = s(s(elem!1))),
% 10.39/10.65 inference(monotonicity,[status(thm)],[23833])).
% 10.39/10.65 tff(23835,plain,
% 10.39/10.65 (s(s(s(z))) = s(s(s(elem!1)))),
% 10.39/10.65 inference(monotonicity,[status(thm)],[23834])).
% 10.39/10.65 tff(23836,plain,
% 10.39/10.65 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 10.39/10.65 inference(monotonicity,[status(thm)],[23835])).
% 10.39/10.65 tff(23837,plain,
% 10.39/10.65 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 10.39/10.65 inference(monotonicity,[status(thm)],[23836])).
% 10.39/10.65 tff(23838,plain,
% 10.39/10.65 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 10.39/10.65 inference(monotonicity,[status(thm)],[23827])).
% 10.39/10.65 tff(23839,plain,
% 10.39/10.65 (r(elem!1, s(s(s(s(z)))))),
% 10.39/10.65 inference(modus_ponens,[status(thm)],[22030, 23838])).
% 10.39/10.65 tff(23840,plain,
% 10.39/10.65 (r(elem!1, s(s(s(s(elem!1)))))),
% 10.39/10.65 inference(modus_ponens,[status(thm)],[23839, 23837])).
% 10.39/10.65 tff(23841,plain,
% 10.39/10.65 (~r(s(z), elem!1)),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[14585, 23840, 233, 232])).
% 10.39/10.65 tff(23842,plain,
% 10.39/10.65 ($false),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[3205, 23841, 23832, 23828])).
% 10.39/10.65 tff(23843,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | r(z, elem!1) | r(elem!1, s(z)) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.65 tff(23844,plain,
% 10.39/10.65 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23843, 23815, 23401, 90, 23358, 23407, 23402, 53])).
% 10.39/10.65 tff(23845,plain,
% 10.39/10.65 (r(s(s(z)), s(s(s(s(z)))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[3652, 23844])).
% 10.39/10.65 tff(23846,plain,
% 10.39/10.65 ($false),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[20629, 23845, 23822, 1216, 23368])).
% 10.39/10.65 tff(23847,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | r(z, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.65 tff(23848,plain,
% 10.39/10.65 (~b(s(s(s(s(z)))), s(z))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23847, 11173, 90, 53, 1, 2913])).
% 10.39/10.65 tff(23849,plain,
% 10.39/10.65 (r(s(s(s(s(z)))), s(z))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[749, 23848])).
% 10.39/10.65 tff(23850,plain,
% 10.39/10.65 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[10698, 194, 11174, 2913, 23849])).
% 10.39/10.65 tff(23851,plain,
% 10.39/10.65 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[10947, 194, 11174, 2913, 23849])).
% 10.39/10.65 tff(23852,plain,
% 10.39/10.65 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[4313, 42, 10970])).
% 10.39/10.65 tff(23853,plain,
% 10.39/10.65 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23852, 16058])).
% 10.39/10.65 tff(23854,plain,
% 10.39/10.65 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[2853, 42, 2114])).
% 10.39/10.65 tff(23855,plain,
% 10.39/10.65 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.39/10.65 inference(unit_resolution,[status(thm)],[23854, 3843])).
% 10.39/10.65 tff(23856,plain,
% 10.39/10.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.39/10.65 inference(rewrite,[status(thm)],[])).
% 10.39/10.65 tff(23857,plain,
% 10.39/10.65 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.39/10.65 inference(rewrite,[status(thm)],[])).
% 10.39/10.65 tff(23858,plain,
% 10.39/10.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 10.39/10.65 inference(monotonicity,[status(thm)],[23857])).
% 10.39/10.65 tff(23859,plain,
% 10.39/10.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.39/10.65 inference(transitivity,[status(thm)],[23858, 23856])).
% 10.39/10.65 tff(23860,plain,
% 10.39/10.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 10.39/10.66 inference(quant_inst,[status(thm)],[])).
% 10.39/10.66 tff(23861,plain,
% 10.39/10.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 10.39/10.66 inference(modus_ponens,[status(thm)],[23860, 23859])).
% 10.39/10.66 tff(23862,plain,
% 10.39/10.66 ($false),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[23861, 391, 10682, 90, 23855, 23853])).
% 10.39/10.66 tff(23863,plain,((s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | r(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(s(z)))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.66 tff(23864,plain,
% 10.39/10.66 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[23863, 23851, 90, 10782, 23850])).
% 10.39/10.66 tff(23865,plain,
% 10.39/10.66 (s(z) = elem!1),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[2849, 23864])).
% 10.39/10.66 tff(23866,plain,
% 10.39/10.66 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23865])).
% 10.39/10.66 tff(23867,plain,
% 10.39/10.66 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 10.39/10.66 inference(symmetry,[status(thm)],[23866])).
% 10.39/10.66 tff(23868,plain,
% 10.39/10.66 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23867])).
% 10.39/10.66 tff(23869,plain,
% 10.39/10.66 (~b(elem!1, s(z))),
% 10.39/10.66 inference(modus_ponens,[status(thm)],[4741, 23868])).
% 10.39/10.66 tff(23870,plain,
% 10.39/10.66 (~r(elem!1, s(s(s(s(z)))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[6347, 1810, 1216, 723])).
% 10.39/10.66 tff(23871,plain,
% 10.39/10.66 (~r(s(s(s(elem!1))), elem!1)),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[10856, 1810, 183, 1216])).
% 10.39/10.66 tff(23872,plain,
% 10.39/10.66 (b(s(s(s(elem!1))), elem!1)),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[230, 23871, 127])).
% 10.39/10.66 tff(23873,plain,
% 10.39/10.66 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[10698, 194, 183, 1216, 723])).
% 10.39/10.66 tff(23874,plain,
% 10.39/10.66 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[2853, 42, 23873])).
% 10.39/10.66 tff(23875,plain,
% 10.39/10.66 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[23874, 23018])).
% 10.39/10.66 tff(23876,plain,
% 10.39/10.66 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[10947, 194, 183, 1216, 723])).
% 10.39/10.66 tff(23877,plain,
% 10.39/10.66 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[4313, 42, 23876])).
% 10.39/10.66 tff(23878,plain,
% 10.39/10.66 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[23877, 23019])).
% 10.39/10.66 tff(23879,plain,
% 10.39/10.66 (~b(elem!1, s(s(s(s(z)))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[10959, 23878, 23875, 23872])).
% 10.39/10.66 tff(23880,plain,
% 10.39/10.66 (elem!1 = s(s(s(s(z))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[781, 23879, 23870])).
% 10.39/10.66 tff(23881,plain,
% 10.39/10.66 (s(elem!1) = s(s(s(s(s(z)))))),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23880])).
% 10.39/10.66 tff(23882,plain,
% 10.39/10.66 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23881])).
% 10.39/10.66 tff(23883,plain,
% 10.39/10.66 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23882])).
% 10.39/10.66 tff(23884,plain,
% 10.39/10.66 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 10.39/10.66 inference(symmetry,[status(thm)],[23883])).
% 10.39/10.66 tff(23885,plain,
% 10.39/10.66 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(s(elem!1))))),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23884])).
% 10.39/10.66 tff(23886,plain,
% 10.39/10.66 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 10.39/10.66 inference(symmetry,[status(thm)],[23885])).
% 10.39/10.66 tff(23887,plain,
% 10.39/10.66 (b(z, s(s(s(s(s(s(s(z))))))))),
% 10.39/10.66 inference(modus_ponens,[status(thm)],[10682, 23886])).
% 10.39/10.66 tff(23888,plain,
% 10.39/10.66 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23884])).
% 10.39/10.66 tff(23889,plain,
% 10.39/10.66 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 10.39/10.66 inference(symmetry,[status(thm)],[23888])).
% 10.39/10.66 tff(23890,plain,
% 10.39/10.66 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 10.39/10.66 inference(modus_ponens,[status(thm)],[23875, 23889])).
% 10.39/10.66 tff(23891,plain,
% 10.39/10.66 (s(s(s(s(z)))) = elem!1),
% 10.39/10.66 inference(symmetry,[status(thm)],[23880])).
% 10.39/10.66 tff(23892,plain,
% 10.39/10.66 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23891])).
% 10.39/10.66 tff(23893,plain,
% 10.39/10.66 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 10.39/10.66 inference(symmetry,[status(thm)],[23892])).
% 10.39/10.66 tff(23894,plain,
% 10.39/10.66 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23884, 23880])).
% 10.39/10.66 tff(23895,plain,
% 10.39/10.66 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 10.39/10.66 inference(symmetry,[status(thm)],[23894])).
% 10.39/10.66 tff(23896,plain,
% 10.39/10.66 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 10.39/10.66 inference(modus_ponens,[status(thm)],[23878, 23895])).
% 10.39/10.66 tff(23897,plain,
% 10.39/10.66 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 10.39/10.66 inference(modus_ponens,[status(thm)],[23896, 23893])).
% 10.39/10.66 tff(23898,plain,
% 10.39/10.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 10.39/10.66 inference(rewrite,[status(thm)],[])).
% 10.39/10.66 tff(23899,plain,
% 10.39/10.66 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 10.39/10.66 inference(rewrite,[status(thm)],[])).
% 10.39/10.66 tff(23900,plain,
% 10.39/10.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23899])).
% 10.39/10.66 tff(23901,plain,
% 10.39/10.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 10.39/10.66 inference(transitivity,[status(thm)],[23900, 23898])).
% 10.39/10.66 tff(23902,plain,
% 10.39/10.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), z)))),
% 10.39/10.66 inference(quant_inst,[status(thm)],[])).
% 10.39/10.66 tff(23903,plain,
% 10.39/10.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 10.39/10.66 inference(modus_ponens,[status(thm)],[23902, 23901])).
% 10.39/10.66 tff(23904,plain,
% 10.39/10.66 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[23903, 391, 90])).
% 10.39/10.66 tff(23905,plain,
% 10.39/10.66 ($false),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[23904, 23897, 23890, 23887])).
% 10.39/10.66 tff(23906,plain,((elem!1 = s(z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.66 tff(23907,plain,
% 10.39/10.66 (elem!1 = s(z)),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[23906, 31, 10782, 9, 2913, 23849, 11174, 90])).
% 10.39/10.66 tff(23908,plain,
% 10.39/10.66 (s(z) = elem!1),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[172, 23907])).
% 10.39/10.66 tff(23909,plain,
% 10.39/10.66 (~r(z, s(s(s(s(z)))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[10733, 23908, 53])).
% 10.39/10.66 tff(23910,plain,
% 10.39/10.66 (b(z, s(s(s(s(z)))))),
% 10.39/10.66 inference(unit_resolution,[status(thm)],[800, 23909])).
% 10.39/10.66 tff(23911,plain,
% 10.39/10.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.39/10.66 inference(rewrite,[status(thm)],[])).
% 10.39/10.66 tff(23912,plain,
% 10.39/10.66 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.39/10.66 inference(rewrite,[status(thm)],[])).
% 10.39/10.66 tff(23913,plain,
% 10.39/10.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 10.39/10.66 inference(monotonicity,[status(thm)],[23912])).
% 10.39/10.66 tff(23914,plain,
% 10.39/10.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.39/10.67 inference(transitivity,[status(thm)],[23913, 23911])).
% 10.39/10.67 tff(23915,plain,
% 10.39/10.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))),
% 10.39/10.67 inference(quant_inst,[status(thm)],[])).
% 10.39/10.67 tff(23916,plain,
% 10.39/10.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[23915, 23914])).
% 10.39/10.67 tff(23917,plain,
% 10.39/10.67 ($false),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23916, 391, 10682, 90, 1686, 1669])).
% 10.39/10.67 tff(23918,plain,((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.67 tff(23919,plain,
% 10.39/10.67 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23918, 23910, 90, 10782])).
% 10.39/10.67 tff(23920,plain,
% 10.39/10.67 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[4313, 42, 23851])).
% 10.39/10.67 tff(23921,plain,
% 10.39/10.67 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23920, 23919])).
% 10.39/10.67 tff(23922,plain,
% 10.39/10.67 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23921])).
% 10.39/10.67 tff(23923,plain,
% 10.39/10.67 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 10.39/10.67 inference(symmetry,[status(thm)],[23922])).
% 10.39/10.67 tff(23924,plain,
% 10.39/10.67 (b(s(s(s(elem!1))), z)),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[90, 23923])).
% 10.39/10.67 tff(23925,plain,
% 10.39/10.67 (s(elem!1) = s(s(z))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23907])).
% 10.39/10.67 tff(23926,plain,
% 10.39/10.67 (s(s(z)) = s(elem!1)),
% 10.39/10.67 inference(symmetry,[status(thm)],[23925])).
% 10.39/10.67 tff(23927,plain,
% 10.39/10.67 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23926])).
% 10.39/10.67 tff(23928,plain,
% 10.39/10.67 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23927])).
% 10.39/10.67 tff(23929,plain,
% 10.39/10.67 (~b(elem!1, s(s(s(elem!1))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[8314, 23907, 2881])).
% 10.39/10.67 tff(23930,plain,
% 10.39/10.67 (~(elem!1 = z)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23154, 23929, 10782])).
% 10.39/10.67 tff(23931,plain,
% 10.39/10.67 (~(z = elem!1)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[97, 23930])).
% 10.39/10.67 tff(23932,plain,
% 10.39/10.67 (~(s(z) = s(elem!1))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[117, 23931])).
% 10.39/10.67 tff(23933,plain,
% 10.39/10.67 (~(s(s(elem!1)) = s(s(z)))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[1962, 23932])).
% 10.39/10.67 tff(23934,plain,
% 10.39/10.67 (~(s(s(elem!1)) = s(elem!1))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[23933, 23928])).
% 10.39/10.67 tff(23935,plain,
% 10.39/10.67 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[287, 23934])).
% 10.39/10.67 tff(23936,plain,
% 10.39/10.67 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23921])).
% 10.39/10.67 tff(23937,plain,
% 10.39/10.67 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 10.39/10.67 inference(symmetry,[status(thm)],[23936])).
% 10.39/10.67 tff(23938,plain,
% 10.39/10.67 (s(s(s(z))) = s(s(elem!1))),
% 10.39/10.67 inference(transitivity,[status(thm)],[693, 23937, 211])).
% 10.39/10.67 tff(23939,plain,
% 10.39/10.67 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(s(elem!1)))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23938])).
% 10.39/10.67 tff(23940,plain,
% 10.39/10.67 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(z)))),
% 10.39/10.67 inference(transitivity,[status(thm)],[23939, 9482])).
% 10.39/10.67 tff(23941,plain,
% 10.39/10.67 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 10.39/10.67 inference(symmetry,[status(thm)],[23940])).
% 10.39/10.67 tff(23942,plain,
% 10.39/10.67 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23941])).
% 10.39/10.67 tff(23943,plain,
% 10.39/10.67 (~(s(s(z)) = s(s(s(z))))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[23933, 23942])).
% 10.39/10.67 tff(23944,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 10.39/10.67 tff(23945,plain,
% 10.39/10.67 (s(s(z)) = s(s(s(z)))),
% 10.39/10.67 inference(symmetry,[status(thm)],[23944])).
% 10.39/10.67 tff(23946,assumption,(~(s(s(z)) = s(s(s(z))))), introduced(assumption)).
% 10.39/10.67 tff(23947,plain,
% 10.39/10.67 ($false),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23946, 23945])).
% 10.39/10.67 tff(23948,plain,((~(s(s(s(z))) = s(s(z)))) | (s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.67 tff(23949,plain,
% 10.39/10.67 (~(s(s(s(z))) = s(s(z)))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23948, 23943])).
% 10.39/10.67 tff(23950,plain,
% 10.39/10.67 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 10.39/10.67 inference(transitivity,[status(thm)],[23927, 1098])).
% 10.39/10.67 tff(23951,plain,
% 10.39/10.67 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23950])).
% 10.39/10.67 tff(23952,plain,
% 10.39/10.67 (~(s(elem!1) = s(s(elem!1)))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[23933, 23951])).
% 10.39/10.67 tff(23953,plain,
% 10.39/10.67 (~r(elem!1, s(z))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[10776, 6124, 11174, 2913])).
% 10.39/10.67 tff(23954,plain,
% 10.39/10.67 (elem!1 = s(z)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[837, 23953, 31])).
% 10.39/10.67 tff(23955,plain,
% 10.39/10.67 (b(z, elem!1) <=> b(z, s(z))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23954])).
% 10.39/10.67 tff(23956,plain,
% 10.39/10.67 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23955])).
% 10.39/10.67 tff(23957,plain,
% 10.39/10.67 (s(z) = elem!1),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[172, 23954])).
% 10.39/10.67 tff(23958,plain,
% 10.39/10.67 (~b(s(s(s(s(z)))), elem!1)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[9614, 23957, 23848])).
% 10.39/10.67 tff(23959,plain,
% 10.39/10.67 (~b(s(s(s(elem!1))), elem!1)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[1563, 23958, 23954])).
% 10.39/10.67 tff(23960,plain,
% 10.39/10.67 (~b(s(z), s(s(s(elem!1))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[2884, 23954, 2881])).
% 10.39/10.67 tff(23961,plain,
% 10.39/10.67 (r(s(z), s(s(s(elem!1))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[247, 23960])).
% 10.39/10.67 tff(23962,plain,
% 10.39/10.67 (b(z, elem!1) <=> b(z, s(z))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[169])).
% 10.39/10.67 tff(23963,plain,
% 10.39/10.67 (b(z, s(z))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[133, 23962])).
% 10.39/10.67 tff(23964,plain,
% 10.39/10.67 (~r(z, s(s(s(s(z)))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[10733, 8598, 53])).
% 10.39/10.67 tff(23965,plain,
% 10.39/10.67 (b(z, s(s(s(s(z)))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[800, 23964])).
% 10.39/10.67 tff(23966,plain,
% 10.39/10.67 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23918, 23965, 90, 10782])).
% 10.39/10.67 tff(23967,plain,
% 10.39/10.67 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[10947, 194, 11174, 1216, 723])).
% 10.39/10.67 tff(23968,plain,
% 10.39/10.67 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[4313, 42, 23967])).
% 10.39/10.67 tff(23969,plain,
% 10.39/10.67 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23968, 23966])).
% 10.39/10.67 tff(23970,plain,
% 10.39/10.67 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23969])).
% 10.39/10.67 tff(23971,plain,
% 10.39/10.67 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 10.39/10.67 inference(symmetry,[status(thm)],[23970])).
% 10.39/10.67 tff(23972,plain,
% 10.39/10.67 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[1550])).
% 10.39/10.67 tff(23973,plain,
% 10.39/10.67 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 10.39/10.67 inference(symmetry,[status(thm)],[23972])).
% 10.39/10.67 tff(23974,plain,
% 10.39/10.67 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 10.39/10.67 inference(transitivity,[status(thm)],[23973, 23971])).
% 10.39/10.67 tff(23975,plain,
% 10.39/10.67 (r(s(s(s(elem!1))), s(elem!1))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[1697, 23974])).
% 10.39/10.67 tff(23976,plain,
% 10.39/10.67 (~r(s(elem!1), elem!1)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[13054, 23975, 4028, 127, 168])).
% 10.39/10.67 tff(23977,plain,
% 10.39/10.67 (~r(s(s(z)), s(z))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[9729, 23976, 8598])).
% 10.39/10.67 tff(23978,plain,
% 10.39/10.67 (b(s(s(z)), s(z))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[3778, 23977])).
% 10.39/10.67 tff(23979,plain,
% 10.39/10.67 (~(elem!1 = z)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23154, 4028, 10782])).
% 10.39/10.67 tff(23980,plain,
% 10.39/10.67 (~(z = elem!1)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[97, 23979])).
% 10.39/10.67 tff(23981,plain,
% 10.39/10.67 (~(s(z) = s(elem!1))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[117, 23980])).
% 10.39/10.67 tff(23982,plain,
% 10.39/10.67 (~(s(s(elem!1)) = s(s(z)))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[1962, 23981])).
% 10.39/10.67 tff(23983,plain,
% 10.39/10.67 (~(s(s(elem!1)) = s(elem!1))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[23982, 15487])).
% 10.39/10.67 tff(23984,plain,
% 10.39/10.67 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[169])).
% 10.39/10.67 tff(23985,plain,
% 10.39/10.67 (b(s(z), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 10.39/10.67 inference(symmetry,[status(thm)],[23984])).
% 10.39/10.67 tff(23986,plain,
% 10.39/10.67 (b(s(z), s(elem!1)) <=> b(s(z), s(s(z)))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[1550])).
% 10.39/10.67 tff(23987,plain,
% 10.39/10.67 (b(s(z), s(s(z))) <=> b(s(z), s(elem!1))),
% 10.39/10.67 inference(symmetry,[status(thm)],[23986])).
% 10.39/10.67 tff(23988,plain,
% 10.39/10.67 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 10.39/10.67 inference(transitivity,[status(thm)],[23987, 23985])).
% 10.39/10.67 tff(23989,plain,
% 10.39/10.67 (~r(s(z), s(s(z)))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[11508, 3557, 1216, 1697])).
% 10.39/10.67 tff(23990,plain,
% 10.39/10.67 (b(s(z), s(s(z)))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[1788, 23989])).
% 10.39/10.67 tff(23991,plain,
% 10.39/10.67 (b(elem!1, s(elem!1))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[23990, 23988])).
% 10.39/10.67 tff(23992,plain,
% 10.39/10.67 (b(s(elem!1), elem!1)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[2168, 23976, 4597])).
% 10.39/10.67 tff(23993,plain,
% 10.39/10.67 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23969])).
% 10.39/10.67 tff(23994,plain,
% 10.39/10.67 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 10.39/10.67 inference(transitivity,[status(thm)],[23993, 2123])).
% 10.39/10.67 tff(23995,plain,
% 10.39/10.67 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.39/10.67 inference(symmetry,[status(thm)],[23994])).
% 10.39/10.67 tff(23996,plain,
% 10.39/10.67 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[1550])).
% 10.39/10.67 tff(23997,plain,
% 10.39/10.67 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 10.39/10.67 inference(symmetry,[status(thm)],[23996])).
% 10.39/10.67 tff(23998,plain,
% 10.39/10.67 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.39/10.67 inference(transitivity,[status(thm)],[23997, 23995])).
% 10.39/10.67 tff(23999,plain,
% 10.39/10.67 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[23998])).
% 10.39/10.67 tff(24000,plain,
% 10.39/10.67 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[714, 23999])).
% 10.39/10.67 tff(24001,plain,
% 10.39/10.67 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[281, 24000])).
% 10.39/10.67 tff(24002,plain,
% 10.39/10.67 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23918, 1686, 90, 10682])).
% 10.39/10.67 tff(24003,plain,
% 10.39/10.67 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23877, 24002])).
% 10.39/10.67 tff(24004,plain,
% 10.39/10.67 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[24003])).
% 10.39/10.67 tff(24005,plain,
% 10.39/10.67 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 10.39/10.67 inference(symmetry,[status(thm)],[24004])).
% 10.39/10.67 tff(24006,plain,
% 10.39/10.67 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 10.39/10.67 inference(monotonicity,[status(thm)],[24005, 170])).
% 10.39/10.67 tff(24007,plain,
% 10.39/10.67 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 10.39/10.67 inference(symmetry,[status(thm)],[24006])).
% 10.39/10.67 tff(24008,plain,
% 10.39/10.67 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 10.39/10.67 inference(monotonicity,[status(thm)],[24004])).
% 10.39/10.67 tff(24009,plain,
% 10.39/10.67 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 10.39/10.67 inference(symmetry,[status(thm)],[24008])).
% 10.39/10.67 tff(24010,plain,
% 10.39/10.67 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 10.39/10.67 inference(transitivity,[status(thm)],[15804, 24009])).
% 10.39/10.67 tff(24011,plain,
% 10.39/10.67 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[24010])).
% 10.39/10.67 tff(24012,plain,
% 10.39/10.67 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[24003])).
% 10.39/10.67 tff(24013,plain,
% 10.39/10.67 (s(s(elem!1)) = s(s(s(z)))),
% 10.39/10.67 inference(transitivity,[status(thm)],[212, 24012, 692])).
% 10.39/10.67 tff(24014,plain,
% 10.39/10.67 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[24013])).
% 10.39/10.67 tff(24015,plain,
% 10.39/10.67 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[24003])).
% 10.39/10.67 tff(24016,plain,
% 10.39/10.67 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 10.39/10.67 inference(transitivity,[status(thm)],[24015, 2123])).
% 10.39/10.67 tff(24017,plain,
% 10.39/10.67 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.39/10.67 inference(symmetry,[status(thm)],[24016])).
% 10.39/10.67 tff(24018,plain,
% 10.39/10.67 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.39/10.67 inference(transitivity,[status(thm)],[23997, 24017])).
% 10.39/10.67 tff(24019,plain,
% 10.39/10.67 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 10.39/10.67 inference(monotonicity,[status(thm)],[24018])).
% 10.39/10.67 tff(24020,plain,
% 10.39/10.67 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[714, 24019])).
% 10.39/10.67 tff(24021,plain,
% 10.39/10.67 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[281, 24020])).
% 10.39/10.67 tff(24022,plain,
% 10.39/10.67 (~(elem!1 = z)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[23154, 4028, 10682])).
% 10.39/10.67 tff(24023,plain,
% 10.39/10.67 (~(z = elem!1)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[97, 24022])).
% 10.39/10.67 tff(24024,plain,
% 10.39/10.67 (~(s(z) = s(elem!1))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[117, 24023])).
% 10.39/10.67 tff(24025,plain,
% 10.39/10.67 (~(s(s(elem!1)) = s(s(z)))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[1962, 24024])).
% 10.39/10.67 tff(24026,plain,
% 10.39/10.67 (~(s(s(elem!1)) = s(elem!1))),
% 10.39/10.67 inference(modus_ponens,[status(thm)],[24025, 15487])).
% 10.39/10.67 tff(24027,plain,
% 10.39/10.67 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[287, 24026])).
% 10.39/10.67 tff(24028,plain,
% 10.39/10.67 (b(elem!1, z)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[7485, 175, 8598])).
% 10.39/10.67 tff(24029,plain,
% 10.39/10.67 (~b(s(s(elem!1)), elem!1)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[5286, 24028, 2122, 133, 24026])).
% 10.39/10.67 tff(24030,plain,
% 10.39/10.67 (r(s(s(elem!1)), elem!1)),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[872, 24029, 8597])).
% 10.39/10.67 tff(24031,plain,
% 10.39/10.67 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[4039, 24030, 4028, 168, 127])).
% 10.39/10.67 tff(24032,plain,
% 10.39/10.67 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[1370, 24031, 24027])).
% 10.39/10.67 tff(24033,plain,
% 10.39/10.67 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[12932, 3927, 10682, 1374])).
% 10.39/10.67 tff(24034,plain,
% 10.39/10.67 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[1356, 24033, 270])).
% 10.39/10.67 tff(24035,plain,
% 10.39/10.67 (~r(s(s(elem!1)), s(z))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[2201, 24034, 183, 232])).
% 10.39/10.67 tff(24036,plain,
% 10.39/10.67 (b(s(s(elem!1)), s(z))),
% 10.39/10.67 inference(unit_resolution,[status(thm)],[362, 24035])).
% 10.39/10.67 tff(24037,plain,
% 10.39/10.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.39/10.67 inference(rewrite,[status(thm)],[])).
% 10.39/10.67 tff(24038,plain,
% 10.39/10.67 (((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.39/10.67 inference(rewrite,[status(thm)],[])).
% 10.39/10.67 tff(24039,plain,
% 10.39/10.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24038])).
% 10.39/10.68 tff(24040,plain,
% 10.39/10.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.39/10.68 inference(transitivity,[status(thm)],[24039, 24037])).
% 10.39/10.68 tff(24041,plain,
% 10.39/10.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 10.39/10.68 inference(quant_inst,[status(thm)],[])).
% 10.39/10.68 tff(24042,plain,
% 10.39/10.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[24041, 24040])).
% 10.39/10.68 tff(24043,plain,
% 10.39/10.68 ($false),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[24042, 391, 24036, 10682, 1374, 3927, 590])).
% 10.39/10.68 tff(24044,plain,((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.68 tff(24045,plain,
% 10.39/10.68 (~b(z, s(s(elem!1)))),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[24044, 24032, 10682, 5450, 183, 232, 24021])).
% 10.39/10.68 tff(24046,plain,
% 10.39/10.68 (r(z, s(s(elem!1)))),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[324, 24045])).
% 10.39/10.68 tff(24047,plain,
% 10.39/10.68 (r(z, s(s(s(z))))),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[24046, 24014])).
% 10.39/10.68 tff(24048,plain,
% 10.39/10.68 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24013])).
% 10.39/10.68 tff(24049,plain,
% 10.39/10.68 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(s(z))), z))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24048])).
% 10.39/10.68 tff(24050,plain,
% 10.39/10.68 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24003])).
% 10.39/10.68 tff(24051,plain,
% 10.39/10.68 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 10.39/10.68 inference(symmetry,[status(thm)],[24050])).
% 10.39/10.68 tff(24052,plain,
% 10.39/10.68 (b(s(s(s(elem!1))), z)),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[90, 24051])).
% 10.39/10.68 tff(24053,plain,
% 10.39/10.68 (~b(s(s(elem!1)), z)),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[13177, 24032, 10682, 24052])).
% 10.39/10.68 tff(24054,plain,
% 10.39/10.68 (~b(s(s(s(z))), z)),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[24053, 24049])).
% 10.39/10.68 tff(24055,plain,
% 10.39/10.68 (r(s(s(s(z))), z)),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[8765, 42, 741, 24054])).
% 10.39/10.68 tff(24056,plain,
% 10.39/10.68 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[929, 127])).
% 10.39/10.68 tff(24057,plain,
% 10.39/10.68 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 10.39/10.68 inference(symmetry,[status(thm)],[24012])).
% 10.39/10.68 tff(24058,plain,
% 10.39/10.68 (s(s(s(z))) = s(s(elem!1))),
% 10.39/10.68 inference(transitivity,[status(thm)],[693, 24057, 211])).
% 10.39/10.68 tff(24059,plain,
% 10.39/10.68 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(s(elem!1)))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24058])).
% 10.39/10.68 tff(24060,plain,
% 10.39/10.68 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(z)))),
% 10.39/10.68 inference(transitivity,[status(thm)],[24059, 9482])).
% 10.39/10.68 tff(24061,plain,
% 10.39/10.68 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 10.39/10.68 inference(symmetry,[status(thm)],[24060])).
% 10.39/10.68 tff(24062,plain,
% 10.39/10.68 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24061])).
% 10.39/10.68 tff(24063,plain,
% 10.39/10.68 (~(s(s(z)) = s(s(s(z))))),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[24025, 24062])).
% 10.39/10.68 tff(24064,plain,
% 10.39/10.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 10.39/10.68 inference(rewrite,[status(thm)],[])).
% 10.39/10.68 tff(24065,plain,
% 10.39/10.68 (((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 10.39/10.68 inference(rewrite,[status(thm)],[])).
% 10.39/10.68 tff(24066,plain,
% 10.39/10.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24065])).
% 10.39/10.68 tff(24067,plain,
% 10.39/10.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 10.39/10.68 inference(transitivity,[status(thm)],[24066, 24064])).
% 10.39/10.68 tff(24068,plain,
% 10.39/10.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 10.39/10.68 inference(quant_inst,[status(thm)],[])).
% 10.39/10.68 tff(24069,plain,
% 10.39/10.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[24068, 24067])).
% 10.39/10.68 tff(24070,plain,
% 10.39/10.68 (~r(s(s(z)), s(s(s(z))))),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[24069, 194, 3557, 24055, 24047])).
% 10.39/10.68 tff(24071,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 10.39/10.68 tff(24072,plain,
% 10.39/10.68 (((~![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)))))),
% 10.39/10.68 inference(rewrite,[status(thm)],[])).
% 10.39/10.68 tff(24073,plain,
% 10.39/10.68 ((~![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)))))),
% 10.39/10.68 inference(quant_inst,[status(thm)],[])).
% 10.39/10.68 tff(24074,plain,
% 10.39/10.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[24073, 24072])).
% 10.39/10.68 tff(24075,plain,
% 10.39/10.68 ($false),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[24074, 42, 23946, 8636, 24071])).
% 10.39/10.68 tff(24076,plain,(r(s(s(z)), s(s(s(z)))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.68 tff(24077,plain,
% 10.39/10.68 (b(s(s(z)), s(s(s(z))))),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[24076, 24070, 24063])).
% 10.39/10.68 tff(24078,plain,
% 10.39/10.68 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[10937])).
% 10.39/10.68 tff(24079,plain,
% 10.39/10.68 (s(s(elem!1)) = s(s(s(z)))),
% 10.39/10.68 inference(transitivity,[status(thm)],[212, 24078, 692])).
% 10.39/10.68 tff(24080,plain,
% 10.39/10.68 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[10937])).
% 10.39/10.68 tff(24081,plain,
% 10.39/10.68 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24080, 24079])).
% 10.39/10.68 tff(24082,plain,
% 10.39/10.68 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[10937])).
% 10.39/10.68 tff(24083,plain,
% 10.39/10.68 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 10.39/10.68 inference(transitivity,[status(thm)],[24082, 2123])).
% 10.39/10.68 tff(24084,plain,
% 10.39/10.68 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.39/10.68 inference(symmetry,[status(thm)],[24083])).
% 10.39/10.68 tff(24085,plain,
% 10.39/10.68 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.39/10.68 inference(transitivity,[status(thm)],[23997, 24084])).
% 10.39/10.68 tff(24086,plain,
% 10.39/10.68 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24085])).
% 10.39/10.68 tff(24087,plain,
% 10.39/10.68 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[714, 24086])).
% 10.39/10.68 tff(24088,plain,
% 10.39/10.68 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[2686, 24087])).
% 10.39/10.68 tff(24089,plain,
% 10.39/10.68 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[2711, 24088])).
% 10.39/10.68 tff(24090,plain,
% 10.39/10.68 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 10.39/10.68 inference(symmetry,[status(thm)],[24078])).
% 10.39/10.68 tff(24091,plain,
% 10.39/10.68 (s(s(s(z))) = s(s(elem!1))),
% 10.39/10.68 inference(transitivity,[status(thm)],[693, 24090, 211])).
% 10.39/10.68 tff(24092,plain,
% 10.39/10.68 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 10.39/10.68 inference(symmetry,[status(thm)],[24080])).
% 10.39/10.68 tff(24093,plain,
% 10.39/10.68 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24092, 24091])).
% 10.39/10.68 tff(24094,plain,
% 10.39/10.68 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24093])).
% 10.39/10.68 tff(24095,plain,
% 10.39/10.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 10.39/10.68 inference(rewrite,[status(thm)],[])).
% 10.39/10.68 tff(24096,plain,
% 10.39/10.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 10.39/10.68 inference(quant_inst,[status(thm)],[])).
% 10.39/10.68 tff(24097,plain,
% 10.39/10.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[24096, 24095])).
% 10.39/10.68 tff(24098,plain,
% 10.39/10.68 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[24097, 194, 4428, 15510, 16500])).
% 10.39/10.68 tff(24099,plain,
% 10.39/10.68 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[24098, 24094])).
% 10.39/10.68 tff(24100,plain,
% 10.39/10.68 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 10.39/10.68 inference(unit_resolution,[status(thm)],[1061, 24099, 24089])).
% 10.39/10.68 tff(24101,plain,
% 10.39/10.68 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 10.39/10.68 inference(modus_ponens,[status(thm)],[24100, 24081])).
% 10.39/10.68 tff(24102,plain,
% 10.39/10.68 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24080, 1550])).
% 10.39/10.68 tff(24103,plain,
% 10.39/10.68 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24092, 8667])).
% 10.39/10.68 tff(24104,plain,
% 10.39/10.68 ((~r(s(s(s(s(s(z))))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 10.39/10.68 inference(monotonicity,[status(thm)],[24103])).
% 10.39/10.68 tff(24105,plain,
% 10.39/10.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.39/10.68 inference(rewrite,[status(thm)],[])).
% 10.39/10.69 tff(24106,plain,
% 10.39/10.69 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.39/10.69 inference(rewrite,[status(thm)],[])).
% 10.39/10.69 tff(24107,plain,
% 10.39/10.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 10.39/10.69 inference(monotonicity,[status(thm)],[24106])).
% 10.39/10.69 tff(24108,plain,
% 10.39/10.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.39/10.69 inference(transitivity,[status(thm)],[24107, 24105])).
% 10.39/10.69 tff(24109,plain,
% 10.39/10.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 10.39/10.69 inference(quant_inst,[status(thm)],[])).
% 10.39/10.69 tff(24110,plain,
% 10.39/10.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 10.39/10.69 inference(modus_ponens,[status(thm)],[24109, 24108])).
% 10.39/10.69 tff(24111,plain,
% 10.39/10.69 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 10.39/10.69 inference(unit_resolution,[status(thm)],[24110, 194, 3557, 15510, 16500])).
% 10.39/10.69 tff(24112,plain,
% 10.39/10.69 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 10.39/10.69 inference(modus_ponens,[status(thm)],[24111, 24104])).
% 10.39/10.69 tff(24113,plain,
% 10.39/10.69 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 10.39/10.69 inference(unit_resolution,[status(thm)],[988, 24112, 957])).
% 10.39/10.69 tff(24114,plain,
% 10.39/10.69 (b(s(s(s(s(s(z))))), s(s(z)))),
% 10.39/10.69 inference(modus_ponens,[status(thm)],[24113, 24102])).
% 10.39/10.69 tff(24115,plain,
% 10.39/10.69 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 10.39/10.69 inference(monotonicity,[status(thm)],[24079, 24080])).
% 10.39/10.69 tff(24116,plain,
% 10.39/10.69 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 10.39/10.69 inference(monotonicity,[status(thm)],[24079, 24080])).
% 10.39/10.69 tff(24117,plain,
% 10.39/10.69 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.39/10.69 inference(symmetry,[status(thm)],[24116])).
% 10.39/10.69 tff(24118,plain,
% 10.39/10.69 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 10.39/10.69 inference(monotonicity,[status(thm)],[24117])).
% 10.39/10.69 tff(24119,plain,
% 10.39/10.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 10.39/10.69 inference(rewrite,[status(thm)],[])).
% 10.39/10.69 tff(24120,plain,
% 10.39/10.69 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 10.39/10.69 inference(rewrite,[status(thm)],[])).
% 10.39/10.69 tff(24121,plain,
% 10.39/10.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 10.39/10.69 inference(monotonicity,[status(thm)],[24120])).
% 10.39/10.69 tff(24122,plain,
% 10.39/10.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 10.39/10.69 inference(transitivity,[status(thm)],[24121, 24119])).
% 10.39/10.69 tff(24123,plain,
% 10.39/10.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 10.39/10.69 inference(quant_inst,[status(thm)],[])).
% 10.39/10.69 tff(24124,plain,
% 10.39/10.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 10.39/10.69 inference(modus_ponens,[status(thm)],[24123, 24122])).
% 10.39/10.69 tff(24125,plain,
% 10.39/10.69 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 10.39/10.69 inference(unit_resolution,[status(thm)],[24124, 194, 4428, 15510, 16500])).
% 10.39/10.69 tff(24126,plain,
% 10.39/10.69 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.39/10.69 inference(modus_ponens,[status(thm)],[24125, 24118])).
% 10.39/10.69 tff(24127,plain,
% 10.39/10.69 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.39/10.69 inference(unit_resolution,[status(thm)],[1048, 24126, 24088])).
% 10.39/10.69 tff(24128,plain,
% 10.39/10.69 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 10.39/10.69 inference(modus_ponens,[status(thm)],[24127, 24115])).
% 10.39/10.69 tff(24129,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 10.39/10.69 tff(24130,plain,
% 10.39/10.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 10.39/10.69 inference(rewrite,[status(thm)],[])).
% 10.39/10.69 tff(24131,plain,
% 10.39/10.69 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 10.39/10.69 inference(rewrite,[status(thm)],[])).
% 10.39/10.69 tff(24132,plain,
% 10.39/10.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 10.39/10.69 inference(monotonicity,[status(thm)],[24131])).
% 10.39/10.69 tff(24133,plain,
% 10.39/10.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 10.39/10.69 inference(transitivity,[status(thm)],[24132, 24130])).
% 10.39/10.69 tff(24134,plain,
% 10.39/10.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 10.39/10.69 inference(quant_inst,[status(thm)],[])).
% 10.39/10.69 tff(24135,plain,
% 10.39/10.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 10.39/10.69 inference(modus_ponens,[status(thm)],[24134, 24133])).
% 10.39/10.69 tff(24136,plain,
% 10.39/10.69 ($false),
% 10.39/10.69 inference(unit_resolution,[status(thm)],[24135, 391, 24129, 24128, 24114, 24101])).
% 10.39/10.69 tff(24137,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.69 tff(24138,plain,
% 10.39/10.69 (~r(s(s(s(s(s(z))))), z)),
% 10.39/10.70 inference(unit_resolution,[status(thm)],[24137, 24077, 24003, 169, 24056, 24055, 24047, 3557])).
% 10.39/10.70 tff(24139,plain,
% 10.39/10.70 (b(s(s(s(s(s(z))))), z)),
% 10.39/10.70 inference(unit_resolution,[status(thm)],[16528, 42, 5063, 24138])).
% 10.39/10.70 tff(24140,plain,
% 10.39/10.70 (~b(s(s(s(s(s(z))))), s(z))),
% 10.39/10.70 inference(unit_resolution,[status(thm)],[16545, 391, 90, 1686, 5450, 24139])).
% 10.39/10.70 tff(24141,plain,
% 10.39/10.70 (~b(s(s(s(s(elem!1)))), elem!1)),
% 10.39/10.70 inference(modus_ponens,[status(thm)],[24140, 24011])).
% 10.39/10.70 tff(24142,plain,
% 10.39/10.70 (r(s(s(s(s(elem!1)))), elem!1)),
% 10.39/10.70 inference(unit_resolution,[status(thm)],[1004, 24141, 8664])).
% 10.39/10.70 tff(24143,plain,
% 10.39/10.70 (r(s(s(s(s(s(z))))), s(z))),
% 10.39/10.70 inference(modus_ponens,[status(thm)],[24142, 24007])).
% 10.39/10.70 tff(24144,plain,
% 10.39/10.70 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 10.39/10.70 inference(symmetry,[status(thm)],[24003])).
% 10.39/10.70 tff(24145,plain,
% 10.39/10.70 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.39/10.70 inference(monotonicity,[status(thm)],[24144, 24005])).
% 10.39/10.70 tff(24146,plain,
% 10.39/10.70 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 10.39/10.70 inference(symmetry,[status(thm)],[24145])).
% 10.39/10.70 tff(24147,plain,
% 10.39/10.70 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 10.39/10.70 inference(unit_resolution,[status(thm)],[299, 24027])).
% 10.39/10.70 tff(24148,plain,
% 10.39/10.70 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 10.39/10.70 inference(unit_resolution,[status(thm)],[307, 24147])).
% 10.39/10.70 tff(24149,plain,
% 10.39/10.70 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 10.39/10.70 inference(monotonicity,[status(thm)],[24003, 24004])).
% 10.39/10.70 tff(24150,plain,
% 10.39/10.70 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.39/10.70 inference(symmetry,[status(thm)],[24149])).
% 10.39/10.70 tff(24151,plain,
% 10.39/10.70 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 10.39/10.70 inference(monotonicity,[status(thm)],[24150])).
% 10.39/10.70 tff(24152,plain,
% 10.39/10.70 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 10.39/10.70 inference(unit_resolution,[status(thm)],[16537, 391, 90, 1686, 24139])).
% 10.39/10.70 tff(24153,plain,
% 10.39/10.70 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.39/10.70 inference(modus_ponens,[status(thm)],[24152, 24151])).
% 10.39/10.70 tff(24154,plain,
% 10.39/10.70 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.39/10.70 inference(unit_resolution,[status(thm)],[1164, 24153, 24148])).
% 10.39/10.70 tff(24155,plain,
% 10.39/10.70 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 10.39/10.70 inference(modus_ponens,[status(thm)],[24154, 24146])).
% 10.39/10.70 tff(24156,plain,
% 10.39/10.70 ($false),
% 10.39/10.70 inference(unit_resolution,[status(thm)],[13793, 194, 1216, 723, 24155, 24143])).
% 10.39/10.70 tff(24157,plain,(r(s(z), z) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.39/10.70 tff(24158,plain,
% 10.39/10.70 (r(s(z), z)),
% 10.39/10.70 inference(unit_resolution,[status(thm)],[24157, 3557, 723, 169, 90, 23965, 1216, 10782, 11174, 232, 4028, 168, 127, 23992, 133])).
% 10.49/10.70 tff(24159,plain,
% 10.49/10.70 (r(elem!1, z)),
% 10.49/10.70 inference(modus_ponens,[status(thm)],[24158, 15477])).
% 10.49/10.70 tff(24160,plain,
% 10.49/10.70 (~b(s(z), elem!1)),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[8805, 169])).
% 10.49/10.70 tff(24161,plain,
% 10.49/10.70 (r(s(elem!1), z)),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[3560, 3557, 8598])).
% 10.49/10.70 tff(24162,plain,
% 10.49/10.70 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 10.49/10.70 inference(monotonicity,[status(thm)],[23969])).
% 10.49/10.70 tff(24163,plain,
% 10.49/10.70 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 10.49/10.70 inference(symmetry,[status(thm)],[24162])).
% 10.49/10.70 tff(24164,plain,
% 10.49/10.70 (b(s(s(s(elem!1))), z)),
% 10.49/10.70 inference(modus_ponens,[status(thm)],[90, 24163])).
% 10.49/10.70 tff(24165,plain,
% 10.49/10.70 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[287, 285])).
% 10.49/10.70 tff(24166,plain,
% 10.49/10.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 10.49/10.70 inference(rewrite,[status(thm)],[])).
% 10.49/10.70 tff(24167,plain,
% 10.49/10.70 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 10.49/10.70 inference(rewrite,[status(thm)],[])).
% 10.49/10.70 tff(24168,plain,
% 10.49/10.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))))),
% 10.49/10.70 inference(monotonicity,[status(thm)],[24167])).
% 10.49/10.70 tff(24169,plain,
% 10.49/10.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 10.49/10.70 inference(transitivity,[status(thm)],[24168, 24166])).
% 10.49/10.70 tff(24170,plain,
% 10.49/10.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 10.49/10.70 inference(quant_inst,[status(thm)],[])).
% 10.49/10.70 tff(24171,plain,
% 10.49/10.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))),
% 10.49/10.70 inference(modus_ponens,[status(thm)],[24170, 24169])).
% 10.49/10.70 tff(24172,plain,
% 10.49/10.70 (~r(elem!1, s(elem!1))),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[24171, 194, 530, 1628, 326])).
% 10.49/10.70 tff(24173,plain,
% 10.49/10.70 (b(elem!1, s(elem!1))),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[443, 24172, 7586])).
% 10.49/10.70 tff(24174,plain,
% 10.49/10.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 10.49/10.70 inference(rewrite,[status(thm)],[])).
% 10.49/10.70 tff(24175,plain,
% 10.49/10.70 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 10.49/10.70 inference(rewrite,[status(thm)],[])).
% 10.49/10.70 tff(24176,plain,
% 10.49/10.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 10.49/10.70 inference(monotonicity,[status(thm)],[24175])).
% 10.49/10.70 tff(24177,plain,
% 10.49/10.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 10.49/10.70 inference(transitivity,[status(thm)],[24176, 24174])).
% 10.49/10.70 tff(24178,plain,
% 10.49/10.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 10.49/10.70 inference(quant_inst,[status(thm)],[])).
% 10.49/10.70 tff(24179,plain,
% 10.49/10.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 10.49/10.70 inference(modus_ponens,[status(thm)],[24178, 24177])).
% 10.49/10.70 tff(24180,plain,
% 10.49/10.70 (~b(z, s(elem!1))),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[24179, 391, 133, 24173, 2122])).
% 10.49/10.70 tff(24181,plain,
% 10.49/10.70 (r(z, s(elem!1))),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[566, 24180])).
% 10.49/10.70 tff(24182,plain,
% 10.49/10.70 (~r(s(s(elem!1)), s(elem!1))),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[2309, 24181, 326, 1628])).
% 10.49/10.70 tff(24183,plain,
% 10.49/10.70 (b(s(s(elem!1)), s(elem!1))),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[1135, 24182, 285])).
% 10.49/10.70 tff(24184,plain,
% 10.49/10.70 (~b(s(s(elem!1)), elem!1)),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[19494, 24183, 24173, 2122])).
% 10.49/10.70 tff(24185,plain,
% 10.49/10.70 (r(s(s(elem!1)), elem!1)),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[872, 24184, 249])).
% 10.49/10.70 tff(24186,plain,
% 10.49/10.70 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[4039, 24185, 168, 127, 4028])).
% 10.49/10.70 tff(24187,plain,
% 10.49/10.70 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[1370, 24186, 24165])).
% 10.49/10.70 tff(24188,plain,
% 10.49/10.70 (~b(s(s(elem!1)), z)),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[13177, 24187, 10682, 380])).
% 10.49/10.70 tff(24189,plain,
% 10.49/10.70 (r(s(s(elem!1)), z)),
% 10.49/10.70 inference(unit_resolution,[status(thm)],[2629, 24188])).
% 10.49/10.70 tff(24190,plain,
% 10.49/10.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 10.49/10.70 inference(rewrite,[status(thm)],[])).
% 10.49/10.70 tff(24191,plain,
% 10.49/10.70 (((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 10.49/10.70 inference(rewrite,[status(thm)],[])).
% 10.49/10.70 tff(24192,plain,
% 10.49/10.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 10.49/10.70 inference(monotonicity,[status(thm)],[24191])).
% 10.49/10.70 tff(24193,plain,
% 10.49/10.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 10.49/10.71 inference(transitivity,[status(thm)],[24192, 24190])).
% 10.49/10.71 tff(24194,plain,
% 10.49/10.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 10.49/10.71 inference(quant_inst,[status(thm)],[])).
% 10.49/10.71 tff(24195,plain,
% 10.49/10.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[24194, 24193])).
% 10.49/10.71 tff(24196,plain,
% 10.49/10.71 ($false),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[24195, 194, 530, 24181, 24185, 24189])).
% 10.49/10.71 tff(24197,plain,((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | b(elem!1, s(s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.71 tff(24198,plain,
% 10.49/10.71 (~r(z, s(s(elem!1)))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[24197, 24159, 10782, 24164, 168, 127, 4028, 8597, 23992, 23983, 24161, 133])).
% 10.49/10.71 tff(24199,plain,
% 10.49/10.71 (b(z, s(s(elem!1)))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[324, 24198])).
% 10.49/10.71 tff(24200,plain,
% 10.49/10.71 (~r(s(z), elem!1)),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[17163, 194, 4030, 232, 11174])).
% 10.49/10.71 tff(24201,plain,
% 10.49/10.71 (s(z) = elem!1),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[632, 24200, 2829])).
% 10.49/10.71 tff(24202,plain,
% 10.49/10.71 (s(s(z)) = s(elem!1)),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24201])).
% 10.49/10.71 tff(24203,plain,
% 10.49/10.71 (s(s(s(z))) = s(s(elem!1))),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24202])).
% 10.49/10.71 tff(24204,plain,
% 10.49/10.71 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24203])).
% 10.49/10.71 tff(24205,plain,
% 10.49/10.71 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24204])).
% 10.49/10.71 tff(24206,plain,
% 10.49/10.71 (b(s(s(s(elem!1))), z)),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[90, 24205])).
% 10.49/10.71 tff(24207,plain,
% 10.49/10.71 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24202])).
% 10.49/10.71 tff(24208,plain,
% 10.49/10.71 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24207])).
% 10.49/10.71 tff(24209,plain,
% 10.49/10.71 (~(s(s(elem!1)) = s(elem!1))),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[11335, 24208])).
% 10.49/10.71 tff(24210,plain,
% 10.49/10.71 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[287, 24209])).
% 10.49/10.71 tff(24211,plain,
% 10.49/10.71 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[1370, 24210, 8329])).
% 10.49/10.71 tff(24212,plain,
% 10.49/10.71 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24201])).
% 10.49/10.71 tff(24213,plain,
% 10.49/10.71 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24212])).
% 10.49/10.71 tff(24214,plain,
% 10.49/10.71 (~b(s(s(s(elem!1))), elem!1)),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[11173, 24213])).
% 10.49/10.71 tff(24215,plain,
% 10.49/10.71 (~r(z, s(s(s(s(z)))))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[10733, 24201, 53])).
% 10.49/10.71 tff(24216,plain,
% 10.49/10.71 (b(z, s(s(s(s(z)))))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[800, 24215])).
% 10.49/10.71 tff(24217,plain,
% 10.49/10.71 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24204])).
% 10.49/10.71 tff(24218,plain,
% 10.49/10.71 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 10.49/10.71 inference(symmetry,[status(thm)],[24217])).
% 10.49/10.71 tff(24219,plain,
% 10.49/10.71 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24201])).
% 10.49/10.71 tff(24220,plain,
% 10.49/10.71 (r(s(s(s(elem!1))), elem!1)),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[11174, 24219])).
% 10.49/10.71 tff(24221,plain,
% 10.49/10.71 (r(s(s(s(s(z)))), elem!1)),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[24220, 24218])).
% 10.49/10.71 tff(24222,plain,
% 10.49/10.71 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 10.49/10.71 inference(monotonicity,[status(thm)],[812])).
% 10.49/10.71 tff(24223,plain,
% 10.49/10.71 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 10.49/10.71 inference(transitivity,[status(thm)],[24222, 19416])).
% 10.49/10.71 tff(24224,plain,
% 10.49/10.71 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 10.49/10.71 inference(monotonicity,[status(thm)],[812])).
% 10.49/10.71 tff(24225,plain,
% 10.49/10.71 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 10.49/10.71 inference(symmetry,[status(thm)],[24224])).
% 10.49/10.71 tff(24226,plain,
% 10.49/10.71 (~r(s(s(elem!1)), elem!1)),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[4039, 327, 127, 4028, 168])).
% 10.49/10.71 tff(24227,plain,
% 10.49/10.71 (b(s(s(elem!1)), elem!1)),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[872, 24226, 7422])).
% 10.49/10.71 tff(24228,plain,
% 10.49/10.71 (~b(elem!1, s(s(elem!1)))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[3979, 133, 3927, 24227])).
% 10.49/10.71 tff(24229,plain,
% 10.49/10.71 (r(elem!1, s(s(elem!1)))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[1307, 24228, 9651])).
% 10.49/10.71 tff(24230,plain,
% 10.49/10.71 (r(s(z), s(s(elem!1)))),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[24229, 24225])).
% 10.49/10.71 tff(24231,plain,
% 10.49/10.71 (~r(s(s(elem!1)), z)),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[4840, 24230, 327, 232])).
% 10.49/10.71 tff(24232,plain,
% 10.49/10.71 (b(s(s(elem!1)), z)),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[2629, 24231])).
% 10.49/10.71 tff(24233,plain,
% 10.49/10.71 (b(z, s(s(z)))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[8527, 592, 812])).
% 10.49/10.71 tff(24234,plain,
% 10.49/10.71 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 10.49/10.71 inference(symmetry,[status(thm)],[18984])).
% 10.49/10.71 tff(24235,plain,
% 10.49/10.71 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 10.49/10.71 inference(monotonicity,[status(thm)],[7945])).
% 10.49/10.71 tff(24236,plain,
% 10.49/10.71 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 10.49/10.71 inference(transitivity,[status(thm)],[24235, 24234])).
% 10.49/10.71 tff(24237,plain,
% 10.49/10.71 (~r(s(z), s(s(z)))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[20658, 24233, 1686, 1216, 2112, 3557])).
% 10.49/10.71 tff(24238,plain,
% 10.49/10.71 (b(s(z), s(s(z)))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[1788, 24237])).
% 10.49/10.71 tff(24239,plain,
% 10.49/10.71 (b(elem!1, s(elem!1))),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[24238, 24223])).
% 10.49/10.71 tff(24240,plain,
% 10.49/10.71 (((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 10.49/10.71 inference(rewrite,[status(thm)],[])).
% 10.49/10.71 tff(24241,plain,
% 10.49/10.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24240])).
% 10.49/10.71 tff(24242,plain,
% 10.49/10.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 10.49/10.71 inference(transitivity,[status(thm)],[24241, 24174])).
% 10.49/10.71 tff(24243,plain,
% 10.49/10.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 10.49/10.71 inference(quant_inst,[status(thm)],[])).
% 10.49/10.71 tff(24244,plain,
% 10.49/10.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[24243, 24242])).
% 10.49/10.71 tff(24245,plain,
% 10.49/10.71 ($false),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[24244, 391, 133, 592, 802, 2122])).
% 10.49/10.71 tff(24246,plain,((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.71 tff(24247,plain,
% 10.49/10.71 (~b(s(elem!1), elem!1)),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[24246, 24239, 592, 133])).
% 10.49/10.71 tff(24248,plain,
% 10.49/10.71 (r(s(elem!1), elem!1)),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[2168, 24247, 4597])).
% 10.49/10.71 tff(24249,plain,
% 10.49/10.71 (~r(s(s(s(elem!1))), s(elem!1))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[13054, 24248, 4028, 127, 168])).
% 10.49/10.71 tff(24250,plain,
% 10.49/10.71 (b(s(s(s(elem!1))), s(elem!1))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[588, 24249, 7433])).
% 10.49/10.71 tff(24251,plain,
% 10.49/10.71 (b(s(s(s(s(z)))), s(s(z)))),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[24250, 24236])).
% 10.49/10.71 tff(24252,plain,
% 10.49/10.71 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[15550, 24251, 24233, 1686])).
% 10.49/10.71 tff(24253,plain,
% 10.49/10.71 (r(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[3652, 24252])).
% 10.49/10.71 tff(24254,plain,
% 10.49/10.71 (~r(s(s(z)), s(z))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[4702, 24253, 1216, 2112])).
% 10.49/10.71 tff(24255,plain,
% 10.49/10.71 (b(s(s(z)), s(z))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[3778, 24254])).
% 10.49/10.71 tff(24256,plain,
% 10.49/10.71 (b(s(elem!1), elem!1)),
% 10.49/10.71 inference(modus_ponens,[status(thm)],[24255, 7399])).
% 10.49/10.71 tff(24257,plain,
% 10.49/10.71 ($false),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[24247, 24256])).
% 10.49/10.71 tff(24258,plain,((~b(z, s(elem!1))) | (~(s(z) = elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~b(z, elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.71 tff(24259,plain,
% 10.49/10.71 (~b(z, s(elem!1))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[24258, 3557, 1216, 2112, 1686, 4028, 127, 168, 133, 812])).
% 10.49/10.71 tff(24260,plain,
% 10.49/10.71 (r(z, s(elem!1))),
% 10.49/10.71 inference(unit_resolution,[status(thm)],[566, 24259])).
% 10.49/10.71 tff(24261,plain,
% 10.49/10.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 10.49/10.71 inference(rewrite,[status(thm)],[])).
% 10.49/10.71 tff(24262,plain,
% 10.49/10.71 (((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 10.49/10.71 inference(rewrite,[status(thm)],[])).
% 10.49/10.71 tff(24263,plain,
% 10.49/10.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 10.49/10.71 inference(monotonicity,[status(thm)],[24262])).
% 10.49/10.71 tff(24264,plain,
% 10.49/10.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 10.49/10.71 inference(transitivity,[status(thm)],[24263, 24261])).
% 10.49/10.71 tff(24265,plain,
% 10.49/10.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 10.49/10.71 inference(quant_inst,[status(thm)],[])).
% 10.49/10.71 tff(24266,plain,
% 10.49/10.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[24265, 24264])).
% 10.49/10.72 tff(24267,plain,
% 10.49/10.72 (~r(s(elem!1), elem!1)),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[24266, 194, 530, 19022, 24260])).
% 10.49/10.72 tff(24268,plain,
% 10.49/10.72 (b(s(elem!1), elem!1)),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[2168, 24267, 4597])).
% 10.49/10.72 tff(24269,plain,
% 10.49/10.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 10.49/10.72 inference(rewrite,[status(thm)],[])).
% 10.49/10.72 tff(24270,plain,
% 10.49/10.72 (((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 10.49/10.72 inference(rewrite,[status(thm)],[])).
% 10.49/10.72 tff(24271,plain,
% 10.49/10.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1)))))),
% 10.49/10.72 inference(monotonicity,[status(thm)],[24270])).
% 10.49/10.72 tff(24272,plain,
% 10.49/10.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 10.49/10.72 inference(transitivity,[status(thm)],[24271, 24269])).
% 10.49/10.72 tff(24273,plain,
% 10.49/10.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 10.49/10.72 inference(quant_inst,[status(thm)],[])).
% 10.49/10.72 tff(24274,plain,
% 10.49/10.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1)))),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[24273, 24272])).
% 10.49/10.72 tff(24275,plain,
% 10.49/10.72 (~r(elem!1, s(elem!1))),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[24274, 194, 530, 19022, 24260])).
% 10.49/10.72 tff(24276,plain,
% 10.49/10.72 (b(elem!1, s(elem!1))),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[443, 24275, 4598])).
% 10.49/10.72 tff(24277,plain,
% 10.49/10.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.72 inference(rewrite,[status(thm)],[])).
% 10.49/10.72 tff(24278,plain,
% 10.49/10.72 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.72 inference(rewrite,[status(thm)],[])).
% 10.49/10.72 tff(24279,plain,
% 10.49/10.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 10.49/10.72 inference(monotonicity,[status(thm)],[24278])).
% 10.49/10.72 tff(24280,plain,
% 10.49/10.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.72 inference(transitivity,[status(thm)],[24279, 24277])).
% 10.49/10.72 tff(24281,plain,
% 10.49/10.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 10.49/10.72 inference(quant_inst,[status(thm)],[])).
% 10.49/10.72 tff(24282,plain,
% 10.49/10.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[24281, 24280])).
% 10.49/10.72 tff(24283,plain,
% 10.49/10.72 ($false),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[24282, 391, 133, 973, 2641, 24276, 24268])).
% 10.49/10.72 tff(24284,plain,((~r(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.72 tff(24285,plain,
% 10.49/10.72 (~r(s(s(z)), z)),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[24284, 133, 24227, 24232, 530, 1216, 2112, 1686, 4028, 127, 168, 812])).
% 10.49/10.72 tff(24286,plain,
% 10.49/10.72 (b(s(s(z)), z)),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[1211, 24285])).
% 10.49/10.72 tff(24287,plain,
% 10.49/10.72 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[4472, 24286, 1686, 90])).
% 10.49/10.72 tff(24288,plain,
% 10.49/10.72 (r(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[3652, 24287])).
% 10.49/10.72 tff(24289,plain,
% 10.49/10.72 (~r(s(z), s(s(z)))),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[20629, 24288, 1216, 2112])).
% 10.49/10.72 tff(24290,plain,
% 10.49/10.72 (b(s(z), s(s(z)))),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[1788, 24289])).
% 10.49/10.72 tff(24291,plain,
% 10.49/10.72 (b(elem!1, s(elem!1))),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[24290, 24223])).
% 10.49/10.72 tff(24292,plain,
% 10.49/10.72 (b(s(elem!1), z)),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[24286, 9630])).
% 10.49/10.72 tff(24293,plain,
% 10.49/10.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.72 inference(rewrite,[status(thm)],[])).
% 10.49/10.72 tff(24294,plain,
% 10.49/10.72 (((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.72 inference(rewrite,[status(thm)],[])).
% 10.49/10.72 tff(24295,plain,
% 10.49/10.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 10.49/10.72 inference(monotonicity,[status(thm)],[24294])).
% 10.49/10.72 tff(24296,plain,
% 10.49/10.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.72 inference(transitivity,[status(thm)],[24295, 24293])).
% 10.49/10.72 tff(24297,plain,
% 10.49/10.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 10.49/10.72 inference(quant_inst,[status(thm)],[])).
% 10.49/10.72 tff(24298,plain,
% 10.49/10.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[24297, 24296])).
% 10.49/10.72 tff(24299,plain,
% 10.49/10.72 ($false),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[24298, 391, 133, 24227, 24292, 24232, 24291])).
% 10.49/10.72 tff(24300,plain,((~b(z, elem!1)) | (~(s(z) = elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.72 tff(24301,plain,
% 10.49/10.72 (~b(z, elem!1)),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[24300, 24201, 1216, 24221, 24216, 90, 530, 4028, 127, 24214, 24211, 232, 3927])).
% 10.49/10.72 tff(24302,plain,
% 10.49/10.72 (r(z, elem!1)),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[141, 24301, 115])).
% 10.49/10.72 tff(24303,plain,
% 10.49/10.72 (r(z, s(z)) <=> r(z, elem!1)),
% 10.49/10.72 inference(monotonicity,[status(thm)],[24201])).
% 10.49/10.72 tff(24304,plain,
% 10.49/10.72 (r(z, elem!1) <=> r(z, s(z))),
% 10.49/10.72 inference(symmetry,[status(thm)],[24303])).
% 10.49/10.72 tff(24305,plain,
% 10.49/10.72 (r(z, s(z))),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[24302, 24304])).
% 10.49/10.72 tff(24306,plain,
% 10.49/10.72 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 10.49/10.72 inference(monotonicity,[status(thm)],[7945, 8096])).
% 10.49/10.72 tff(24307,plain,
% 10.49/10.72 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 10.49/10.72 inference(transitivity,[status(thm)],[24306, 940])).
% 10.49/10.72 tff(24308,plain,
% 10.49/10.72 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.49/10.72 inference(symmetry,[status(thm)],[24307])).
% 10.49/10.72 tff(24309,plain,
% 10.49/10.72 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 10.49/10.72 inference(monotonicity,[status(thm)],[24308])).
% 10.49/10.72 tff(24310,plain,
% 10.49/10.72 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[714, 24309])).
% 10.49/10.72 tff(24311,plain,
% 10.49/10.72 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[2686, 24310])).
% 10.49/10.72 tff(24312,plain,
% 10.49/10.72 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[281, 24310])).
% 10.49/10.72 tff(24313,plain,
% 10.49/10.72 (r(s(z), z)),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[7479, 812, 530])).
% 10.49/10.72 tff(24314,plain,
% 10.49/10.72 (r(s(z), s(s(s(s(z)))))),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[4030, 7407])).
% 10.49/10.72 tff(24315,plain,
% 10.49/10.72 (~r(s(s(s(s(z)))), z)),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[10558, 24314, 24313, 722])).
% 10.49/10.72 tff(24316,plain,
% 10.49/10.72 (b(s(s(s(s(z)))), z)),
% 10.49/10.72 inference(unit_resolution,[status(thm)],[87, 24315])).
% 10.49/10.72 tff(24317,plain,
% 10.49/10.72 (b(s(s(s(elem!1))), z)),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[24316, 7494])).
% 10.49/10.72 tff(24318,plain,
% 10.49/10.72 (r(z, elem!1)),
% 10.49/10.72 inference(modus_ponens,[status(thm)],[722, 813])).
% 10.49/10.72 tff(24319,plain,
% 10.49/10.72 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 10.49/10.72 inference(monotonicity,[status(thm)],[8096])).
% 10.49/10.72 tff(24320,plain,
% 10.49/10.72 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 10.49/10.72 inference(symmetry,[status(thm)],[24319])).
% 10.49/10.73 tff(24321,plain,
% 10.49/10.73 (b(s(s(z)), elem!1)),
% 10.49/10.73 inference(modus_ponens,[status(thm)],[1233, 7398])).
% 10.49/10.73 tff(24322,plain,
% 10.49/10.73 (b(s(elem!1), elem!1)),
% 10.49/10.73 inference(modus_ponens,[status(thm)],[24321, 24320])).
% 10.49/10.73 tff(24323,plain,
% 10.49/10.73 (r(s(s(elem!1)), z)),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[2629, 2624])).
% 10.49/10.73 tff(24324,plain,
% 10.49/10.73 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[9291, 2624, 380])).
% 10.49/10.73 tff(24325,plain,
% 10.49/10.73 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[299, 24324])).
% 10.49/10.73 tff(24326,plain,
% 10.49/10.73 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.73 inference(monotonicity,[status(thm)],[8096, 7945])).
% 10.49/10.73 tff(24327,plain,
% 10.49/10.73 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 10.49/10.73 inference(monotonicity,[status(thm)],[24326])).
% 10.49/10.73 tff(24328,plain,
% 10.49/10.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.49/10.73 inference(rewrite,[status(thm)],[])).
% 10.49/10.73 tff(24329,plain,
% 10.49/10.73 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.49/10.73 inference(rewrite,[status(thm)],[])).
% 10.49/10.73 tff(24330,plain,
% 10.49/10.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))))),
% 10.49/10.73 inference(monotonicity,[status(thm)],[24329])).
% 10.49/10.73 tff(24331,plain,
% 10.49/10.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.49/10.73 inference(transitivity,[status(thm)],[24330, 24328])).
% 10.49/10.73 tff(24332,plain,
% 10.49/10.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 10.49/10.73 inference(quant_inst,[status(thm)],[])).
% 10.49/10.73 tff(24333,plain,
% 10.49/10.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 10.49/10.73 inference(modus_ponens,[status(thm)],[24332, 24331])).
% 10.49/10.73 tff(24334,plain,
% 10.49/10.73 (~b(s(elem!1), s(s(s(elem!1))))),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[24333, 391, 380, 10682, 591])).
% 10.49/10.73 tff(24335,plain,
% 10.49/10.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.73 inference(modus_ponens,[status(thm)],[24334, 24327])).
% 10.49/10.73 tff(24336,plain,
% 10.49/10.73 (r(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[3652, 24335])).
% 10.49/10.73 tff(24337,plain,
% 10.49/10.73 (r(s(elem!1), s(s(s(elem!1))))),
% 10.49/10.73 inference(modus_ponens,[status(thm)],[24336, 3610])).
% 10.49/10.73 tff(24338,plain,
% 10.49/10.73 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(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(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.49/10.73 inference(rewrite,[status(thm)],[])).
% 10.49/10.73 tff(24339,plain,
% 10.49/10.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))))),
% 10.49/10.73 inference(monotonicity,[status(thm)],[24338])).
% 10.49/10.73 tff(24340,plain,
% 10.49/10.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.49/10.73 inference(transitivity,[status(thm)],[24339, 12792])).
% 10.49/10.73 tff(24341,plain,
% 10.49/10.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 10.49/10.73 inference(quant_inst,[status(thm)],[])).
% 10.49/10.73 tff(24342,plain,
% 10.49/10.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 10.49/10.73 inference(modus_ponens,[status(thm)],[24341, 24340])).
% 10.49/10.73 tff(24343,plain,
% 10.49/10.73 (~b(s(s(s(elem!1))), s(elem!1))),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[24342, 391, 380, 10682, 591])).
% 10.49/10.73 tff(24344,plain,
% 10.49/10.73 (r(s(s(s(elem!1))), s(elem!1))),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[588, 24343, 24310])).
% 10.49/10.73 tff(24345,plain,
% 10.49/10.73 (~r(s(s(elem!1)), elem!1)),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[8360, 2616, 530, 411])).
% 10.49/10.73 tff(24346,plain,
% 10.49/10.73 (b(s(s(elem!1)), elem!1)),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[872, 24345, 7422])).
% 10.49/10.73 tff(24347,plain,
% 10.49/10.73 (~r(elem!1, s(s(elem!1)))),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[16203, 194, 411, 530, 2616])).
% 10.49/10.73 tff(24348,plain,
% 10.49/10.73 (b(elem!1, s(s(elem!1)))),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[1307, 24347, 9651])).
% 10.49/10.73 tff(24349,plain,
% 10.49/10.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 10.49/10.73 inference(rewrite,[status(thm)],[])).
% 10.49/10.73 tff(24350,plain,
% 10.49/10.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 10.49/10.73 inference(quant_inst,[status(thm)],[])).
% 10.49/10.73 tff(24351,plain,
% 10.49/10.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 10.49/10.73 inference(modus_ponens,[status(thm)],[24350, 24349])).
% 10.49/10.73 tff(24352,plain,
% 10.49/10.73 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[24351, 194, 613, 604, 1082])).
% 10.49/10.73 tff(24353,plain,
% 10.49/10.73 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[988, 24352, 957])).
% 10.49/10.73 tff(24354,plain,
% 10.49/10.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 10.49/10.73 inference(rewrite,[status(thm)],[])).
% 10.49/10.73 tff(24355,plain,
% 10.49/10.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 10.49/10.73 inference(quant_inst,[status(thm)],[])).
% 10.49/10.73 tff(24356,plain,
% 10.49/10.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 10.49/10.73 inference(modus_ponens,[status(thm)],[24355, 24354])).
% 10.49/10.73 tff(24357,plain,
% 10.49/10.73 (~r(s(s(s(s(elem!1)))), elem!1)),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[24356, 194, 613, 410, 1082])).
% 10.49/10.73 tff(24358,plain,
% 10.49/10.73 (b(s(s(s(s(elem!1)))), elem!1)),
% 10.49/10.73 inference(unit_resolution,[status(thm)],[1004, 24357, 972])).
% 10.49/10.73 tff(24359,plain,
% 10.49/10.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.49/10.73 inference(rewrite,[status(thm)],[])).
% 10.49/10.73 tff(24360,plain,
% 10.49/10.73 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.49/10.73 inference(rewrite,[status(thm)],[])).
% 10.49/10.73 tff(24361,plain,
% 10.49/10.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 10.49/10.73 inference(monotonicity,[status(thm)],[24360])).
% 10.49/10.73 tff(24362,plain,
% 10.49/10.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.49/10.73 inference(transitivity,[status(thm)],[24361, 24359])).
% 10.49/10.73 tff(24363,plain,
% 10.49/10.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 10.49/10.74 inference(quant_inst,[status(thm)],[])).
% 10.49/10.74 tff(24364,plain,
% 10.49/10.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 10.49/10.74 inference(modus_ponens,[status(thm)],[24363, 24362])).
% 10.49/10.74 tff(24365,plain,
% 10.49/10.74 ($false),
% 10.49/10.74 inference(unit_resolution,[status(thm)],[24364, 391, 973, 1294, 2122, 24358, 24353])).
% 10.49/10.74 tff(24366,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.74 tff(24367,plain,
% 10.49/10.74 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.49/10.74 inference(unit_resolution,[status(thm)],[24366, 24348, 24346, 2122, 957, 7473, 24344, 24337, 410])).
% 10.49/10.74 tff(24368,plain,
% 10.49/10.74 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.49/10.74 inference(unit_resolution,[status(thm)],[1095, 24367, 305])).
% 10.49/10.74 tff(24369,plain,
% 10.49/10.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 10.49/10.74 inference(rewrite,[status(thm)],[])).
% 10.49/10.74 tff(24370,plain,
% 10.49/10.74 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 10.49/10.74 inference(rewrite,[status(thm)],[])).
% 10.49/10.74 tff(24371,plain,
% 10.49/10.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 10.49/10.74 inference(monotonicity,[status(thm)],[24370])).
% 10.49/10.74 tff(24372,plain,
% 10.49/10.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 10.49/10.74 inference(transitivity,[status(thm)],[24371, 24369])).
% 10.49/10.74 tff(24373,plain,
% 10.49/10.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 10.49/10.74 inference(quant_inst,[status(thm)],[])).
% 10.49/10.74 tff(24374,plain,
% 10.49/10.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 10.49/10.74 inference(modus_ponens,[status(thm)],[24373, 24372])).
% 10.49/10.74 tff(24375,plain,
% 10.49/10.74 (~b(s(s(s(s(elem!1)))), z)),
% 10.49/10.74 inference(unit_resolution,[status(thm)],[24374, 391, 380, 10682, 24368])).
% 10.49/10.74 tff(24376,plain,
% 10.49/10.74 (r(s(s(s(s(elem!1)))), z)),
% 10.49/10.74 inference(unit_resolution,[status(thm)],[1626, 24375])).
% 10.49/10.74 tff(24377,plain,
% 10.49/10.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1), s(s(s(elem!1))))))),
% 10.49/10.74 inference(rewrite,[status(thm)],[])).
% 10.49/10.74 tff(24378,plain,
% 10.49/10.74 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(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(elem!1), s(s(s(elem!1))))))),
% 10.49/10.74 inference(rewrite,[status(thm)],[])).
% 10.49/10.74 tff(24379,plain,
% 10.49/10.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1), s(s(s(elem!1)))))))),
% 10.49/10.74 inference(monotonicity,[status(thm)],[24378])).
% 10.49/10.74 tff(24380,plain,
% 10.49/10.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1), s(s(s(elem!1))))))),
% 10.49/10.74 inference(transitivity,[status(thm)],[24379, 24377])).
% 10.49/10.74 tff(24381,plain,
% 10.49/10.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 10.49/10.74 inference(quant_inst,[status(thm)],[])).
% 10.49/10.74 tff(24382,plain,
% 10.49/10.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1), s(s(s(elem!1)))))),
% 10.49/10.74 inference(modus_ponens,[status(thm)],[24381, 24380])).
% 10.49/10.74 tff(24383,plain,
% 10.49/10.74 (~r(elem!1, s(elem!1))),
% 10.49/10.74 inference(unit_resolution,[status(thm)],[24382, 194, 24344, 410, 24337])).
% 10.49/10.74 tff(24384,plain,
% 10.49/10.74 (b(elem!1, s(elem!1))),
% 10.49/10.74 inference(unit_resolution,[status(thm)],[443, 24383, 437])).
% 10.49/10.74 tff(24385,plain,
% 10.49/10.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.74 inference(rewrite,[status(thm)],[])).
% 10.49/10.74 tff(24386,plain,
% 10.49/10.74 (((~b(s(elem!1), z)) | (~b(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)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.74 inference(rewrite,[status(thm)],[])).
% 10.49/10.74 tff(24387,plain,
% 10.49/10.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1))))),
% 10.49/10.75 inference(monotonicity,[status(thm)],[24386])).
% 10.49/10.75 tff(24388,plain,
% 10.49/10.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.75 inference(transitivity,[status(thm)],[24387, 24385])).
% 10.49/10.75 tff(24389,plain,
% 10.49/10.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(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))))),
% 10.49/10.75 inference(quant_inst,[status(thm)],[])).
% 10.49/10.75 tff(24390,plain,
% 10.49/10.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1))),
% 10.49/10.75 inference(modus_ponens,[status(thm)],[24389, 24388])).
% 10.49/10.75 tff(24391,plain,
% 10.49/10.75 (~b(s(s(elem!1)), s(elem!1))),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[24390, 391, 24346, 591, 24384, 2122])).
% 10.49/10.75 tff(24392,plain,
% 10.49/10.75 (r(s(s(elem!1)), s(elem!1))),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[1135, 24391, 9647])).
% 10.49/10.75 tff(24393,plain,
% 10.49/10.75 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[10292, 194, 24344, 24337, 24392])).
% 10.49/10.75 tff(24394,plain,
% 10.49/10.75 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[1354, 42, 24312, 24393])).
% 10.49/10.75 tff(24395,plain,
% 10.49/10.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.75 inference(rewrite,[status(thm)],[])).
% 10.49/10.75 tff(24396,plain,
% 10.49/10.75 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(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(elem!1))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.75 inference(rewrite,[status(thm)],[])).
% 10.49/10.75 tff(24397,plain,
% 10.49/10.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 10.49/10.75 inference(monotonicity,[status(thm)],[24396])).
% 10.49/10.75 tff(24398,plain,
% 10.49/10.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.75 inference(transitivity,[status(thm)],[24397, 24395])).
% 10.49/10.75 tff(24399,plain,
% 10.49/10.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(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(elem!1)))))))),
% 10.49/10.75 inference(quant_inst,[status(thm)],[])).
% 10.49/10.75 tff(24400,plain,
% 10.49/10.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 10.49/10.75 inference(modus_ponens,[status(thm)],[24399, 24398])).
% 10.49/10.75 tff(24401,plain,
% 10.49/10.75 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[24400, 391, 380, 10682, 24394, 24368])).
% 10.49/10.75 tff(24402,plain,
% 10.49/10.75 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[1048, 24401, 24311])).
% 10.49/10.75 tff(24403,plain,
% 10.49/10.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.75 inference(rewrite,[status(thm)],[])).
% 10.49/10.75 tff(24404,plain,
% 10.49/10.75 (((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.75 inference(rewrite,[status(thm)],[])).
% 10.49/10.75 tff(24405,plain,
% 10.49/10.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 10.49/10.75 inference(monotonicity,[status(thm)],[24404])).
% 10.49/10.75 tff(24406,plain,
% 10.49/10.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.75 inference(transitivity,[status(thm)],[24405, 24403])).
% 10.49/10.75 tff(24407,plain,
% 10.49/10.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.75 inference(quant_inst,[status(thm)],[])).
% 10.49/10.75 tff(24408,plain,
% 10.49/10.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 10.49/10.75 inference(modus_ponens,[status(thm)],[24407, 24406])).
% 10.49/10.75 tff(24409,plain,
% 10.49/10.75 ($false),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[24408, 194, 411, 24402, 24376, 2616])).
% 10.49/10.75 tff(24410,plain,((~b(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)) | (elem!1 = s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.75 tff(24411,plain,
% 10.49/10.75 (~b(s(elem!1), z)),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[24410, 24323, 411, 380, 10682, 24325, 2122, 957, 410, 530, 437, 812])).
% 10.49/10.75 tff(24412,plain,
% 10.49/10.75 (r(s(elem!1), z)),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[549, 24411])).
% 10.49/10.75 tff(24413,plain,
% 10.49/10.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 10.49/10.75 inference(rewrite,[status(thm)],[])).
% 10.49/10.75 tff(24414,plain,
% 10.49/10.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 10.49/10.75 inference(quant_inst,[status(thm)],[])).
% 10.49/10.75 tff(24415,plain,
% 10.49/10.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 10.49/10.75 inference(modus_ponens,[status(thm)],[24414, 24413])).
% 10.49/10.75 tff(24416,plain,
% 10.49/10.75 ($false),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[24415, 194, 411, 1628, 2170, 2616])).
% 10.49/10.75 tff(24417,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.75 tff(24418,plain,
% 10.49/10.75 (~r(s(s(elem!1)), s(elem!1))),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[24417, 24412, 24323, 411])).
% 10.49/10.75 tff(24419,plain,
% 10.49/10.75 (b(s(s(elem!1)), s(elem!1))),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[1135, 24418, 9647])).
% 10.49/10.75 tff(24420,plain,
% 10.49/10.75 (~r(elem!1, s(s(elem!1)))),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[16203, 194, 411, 530, 24323])).
% 10.49/10.75 tff(24421,plain,
% 10.49/10.75 (b(elem!1, s(s(elem!1)))),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[1307, 24420, 9651])).
% 10.49/10.75 tff(24422,plain,
% 10.49/10.75 (~r(s(s(elem!1)), elem!1)),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[8360, 24323, 530, 411])).
% 10.49/10.75 tff(24423,plain,
% 10.49/10.75 (b(s(s(elem!1)), elem!1)),
% 10.49/10.75 inference(unit_resolution,[status(thm)],[872, 24422, 7422])).
% 10.49/10.75 tff(24424,plain,
% 10.49/10.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.75 inference(rewrite,[status(thm)],[])).
% 10.49/10.75 tff(24425,plain,
% 10.49/10.75 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.75 inference(rewrite,[status(thm)],[])).
% 10.49/10.75 tff(24426,plain,
% 10.49/10.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 10.49/10.76 inference(monotonicity,[status(thm)],[24425])).
% 10.49/10.76 tff(24427,plain,
% 10.49/10.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.76 inference(transitivity,[status(thm)],[24426, 24424])).
% 10.49/10.76 tff(24428,plain,
% 10.49/10.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 10.49/10.76 inference(quant_inst,[status(thm)],[])).
% 10.49/10.76 tff(24429,plain,
% 10.49/10.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 10.49/10.76 inference(modus_ponens,[status(thm)],[24428, 24427])).
% 10.49/10.76 tff(24430,plain,
% 10.49/10.76 ($false),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[24429, 391, 24423, 24421, 24419, 2122])).
% 10.49/10.76 tff(24431,plain,(b(s(s(elem!1)), z) | (~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.76 tff(24432,plain,
% 10.49/10.76 (b(s(s(elem!1)), z)),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[24431, 24322, 24318, 530, 24317, 10682, 24056, 4030, 4598, 812])).
% 10.49/10.76 tff(24433,plain,
% 10.49/10.76 (~(s(elem!1) = s(s(elem!1)))),
% 10.49/10.76 inference(modus_ponens,[status(thm)],[9647, 1099])).
% 10.49/10.76 tff(24434,plain,
% 10.49/10.76 (~r(s(elem!1), z)),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[9766, 2251, 530, 411])).
% 10.49/10.76 tff(24435,plain,
% 10.49/10.76 (b(s(elem!1), z)),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[549, 24434])).
% 10.49/10.76 tff(24436,plain,
% 10.49/10.76 (~b(s(elem!1), s(s(s(elem!1))))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[24333, 391, 380, 10682, 24435])).
% 10.49/10.76 tff(24437,plain,
% 10.49/10.76 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.76 inference(modus_ponens,[status(thm)],[24436, 24327])).
% 10.49/10.76 tff(24438,plain,
% 10.49/10.76 (r(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[3652, 24437])).
% 10.49/10.76 tff(24439,plain,
% 10.49/10.76 (r(s(elem!1), s(s(s(elem!1))))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[3614, 24438, 812])).
% 10.49/10.76 tff(24440,plain,
% 10.49/10.76 (~b(s(s(s(elem!1))), s(elem!1))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[24342, 391, 380, 10682, 24435])).
% 10.49/10.76 tff(24441,plain,
% 10.49/10.76 (r(s(s(s(elem!1))), s(elem!1))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[588, 24440, 24310])).
% 10.49/10.76 tff(24442,plain,
% 10.49/10.76 ($false),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[24382, 194, 24441, 2251, 410, 24439])).
% 10.49/10.76 tff(24443,plain,((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.76 tff(24444,plain,
% 10.49/10.76 (~r(elem!1, s(elem!1))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[24443, 812, 4030, 24317, 10682, 530, 24318])).
% 10.49/10.76 tff(24445,plain,
% 10.49/10.76 (b(elem!1, s(elem!1))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[443, 24444, 4598])).
% 10.49/10.76 tff(24446,plain,
% 10.49/10.76 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[13177, 24432, 10682, 24317])).
% 10.49/10.76 tff(24447,plain,
% 10.49/10.76 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[272, 24312])).
% 10.49/10.76 tff(24448,plain,
% 10.49/10.76 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[1370, 24447, 24446])).
% 10.49/10.76 tff(24449,plain,
% 10.49/10.76 (~r(s(s(elem!1)), elem!1)),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[4039, 24448, 127, 4028, 168])).
% 10.49/10.76 tff(24450,plain,
% 10.49/10.76 (b(s(s(elem!1)), elem!1)),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[872, 24449, 7422])).
% 10.49/10.76 tff(24451,plain,
% 10.49/10.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.76 inference(rewrite,[status(thm)],[])).
% 10.49/10.76 tff(24452,plain,
% 10.49/10.76 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.76 inference(rewrite,[status(thm)],[])).
% 10.49/10.76 tff(24453,plain,
% 10.49/10.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 10.49/10.76 inference(monotonicity,[status(thm)],[24452])).
% 10.49/10.76 tff(24454,plain,
% 10.49/10.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.76 inference(transitivity,[status(thm)],[24453, 24451])).
% 10.49/10.76 tff(24455,plain,
% 10.49/10.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 10.49/10.76 inference(quant_inst,[status(thm)],[])).
% 10.49/10.76 tff(24456,plain,
% 10.49/10.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 10.49/10.76 inference(modus_ponens,[status(thm)],[24455, 24454])).
% 10.49/10.76 tff(24457,plain,
% 10.49/10.76 (~b(s(elem!1), s(s(elem!1)))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[24456, 391, 24450, 24445, 24322])).
% 10.49/10.76 tff(24458,plain,
% 10.49/10.76 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[1111, 42, 24457])).
% 10.49/10.76 tff(24459,plain,
% 10.49/10.76 (r(s(elem!1), s(s(elem!1)))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[24458, 24433])).
% 10.49/10.76 tff(24460,plain,
% 10.49/10.76 (~b(s(s(elem!1)), s(elem!1))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[19494, 24445, 24450, 24322])).
% 10.49/10.76 tff(24461,plain,
% 10.49/10.76 (r(s(s(elem!1)), s(elem!1))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[1135, 24460, 9647])).
% 10.49/10.76 tff(24462,plain,
% 10.49/10.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 10.49/10.76 inference(rewrite,[status(thm)],[])).
% 10.49/10.76 tff(24463,plain,
% 10.49/10.76 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(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(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 10.49/10.76 inference(rewrite,[status(thm)],[])).
% 10.49/10.76 tff(24464,plain,
% 10.49/10.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 10.49/10.76 inference(monotonicity,[status(thm)],[24463])).
% 10.49/10.76 tff(24465,plain,
% 10.49/10.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 10.49/10.76 inference(transitivity,[status(thm)],[24464, 24462])).
% 10.49/10.76 tff(24466,plain,
% 10.49/10.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 10.49/10.76 inference(quant_inst,[status(thm)],[])).
% 10.49/10.76 tff(24467,plain,
% 10.49/10.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 10.49/10.76 inference(modus_ponens,[status(thm)],[24466, 24465])).
% 10.49/10.76 tff(24468,plain,
% 10.49/10.76 (~r(s(s(s(elem!1))), s(elem!1))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[24467, 194, 24448, 24461, 24459])).
% 10.49/10.76 tff(24469,plain,
% 10.49/10.76 (b(s(s(s(elem!1))), s(elem!1))),
% 10.49/10.76 inference(unit_resolution,[status(thm)],[588, 24468, 24310])).
% 10.49/10.76 tff(24470,plain,
% 10.49/10.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.49/10.76 inference(rewrite,[status(thm)],[])).
% 10.49/10.76 tff(24471,plain,
% 10.49/10.76 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.49/10.76 inference(rewrite,[status(thm)],[])).
% 10.49/10.76 tff(24472,plain,
% 10.49/10.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))))),
% 10.49/10.76 inference(monotonicity,[status(thm)],[24471])).
% 10.49/10.76 tff(24473,plain,
% 10.49/10.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.49/10.77 inference(transitivity,[status(thm)],[24472, 24470])).
% 10.49/10.77 tff(24474,plain,
% 10.49/10.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.49/10.77 inference(quant_inst,[status(thm)],[])).
% 10.49/10.77 tff(24475,plain,
% 10.49/10.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 10.49/10.77 inference(modus_ponens,[status(thm)],[24474, 24473])).
% 10.49/10.77 tff(24476,plain,
% 10.49/10.77 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[24475, 391, 24469, 24317, 10682, 24432])).
% 10.49/10.77 tff(24477,plain,
% 10.49/10.77 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[1354, 42, 24476, 24312])).
% 10.49/10.77 tff(24478,plain,
% 10.49/10.77 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[299, 24447])).
% 10.49/10.77 tff(24479,plain,
% 10.49/10.77 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 10.49/10.77 inference(symmetry,[status(thm)],[24326])).
% 10.49/10.77 tff(24480,plain,
% 10.49/10.77 (~r(s(elem!1), s(s(s(elem!1))))),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[8653, 24459, 24448, 24461])).
% 10.49/10.77 tff(24481,plain,
% 10.49/10.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[3614, 24480, 812])).
% 10.49/10.77 tff(24482,plain,
% 10.49/10.77 (b(s(s(z)), s(s(s(s(z)))))),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[3652, 24481])).
% 10.49/10.77 tff(24483,plain,
% 10.49/10.77 (b(s(elem!1), s(s(s(elem!1))))),
% 10.49/10.77 inference(modus_ponens,[status(thm)],[24482, 24479])).
% 10.49/10.77 tff(24484,plain,
% 10.49/10.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 10.49/10.77 inference(rewrite,[status(thm)],[])).
% 10.49/10.77 tff(24485,plain,
% 10.49/10.77 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 10.49/10.77 inference(rewrite,[status(thm)],[])).
% 10.49/10.77 tff(24486,plain,
% 10.49/10.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 10.49/10.77 inference(monotonicity,[status(thm)],[24485])).
% 10.49/10.77 tff(24487,plain,
% 10.49/10.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 10.49/10.77 inference(transitivity,[status(thm)],[24486, 24484])).
% 10.49/10.77 tff(24488,plain,
% 10.49/10.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 10.49/10.77 inference(quant_inst,[status(thm)],[])).
% 10.49/10.77 tff(24489,plain,
% 10.49/10.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 10.49/10.77 inference(modus_ponens,[status(thm)],[24488, 24487])).
% 10.49/10.77 tff(24490,plain,
% 10.49/10.77 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[24489, 391, 1101, 2122, 1114, 1036])).
% 10.49/10.77 tff(24491,plain,
% 10.49/10.77 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[988, 24490, 957])).
% 10.49/10.77 tff(24492,plain,
% 10.49/10.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 10.49/10.77 inference(rewrite,[status(thm)],[])).
% 10.49/10.77 tff(24493,plain,
% 10.49/10.77 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 10.49/10.77 inference(rewrite,[status(thm)],[])).
% 10.49/10.77 tff(24494,plain,
% 10.49/10.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 10.49/10.77 inference(monotonicity,[status(thm)],[24493])).
% 10.49/10.77 tff(24495,plain,
% 10.49/10.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 10.49/10.77 inference(transitivity,[status(thm)],[24494, 24492])).
% 10.49/10.77 tff(24496,plain,
% 10.49/10.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 10.49/10.77 inference(quant_inst,[status(thm)],[])).
% 10.49/10.77 tff(24497,plain,
% 10.49/10.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 10.49/10.77 inference(modus_ponens,[status(thm)],[24496, 24495])).
% 10.49/10.77 tff(24498,plain,
% 10.49/10.77 (~b(s(s(s(s(elem!1)))), z)),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[24497, 391, 1101, 10682, 2122, 1114])).
% 10.49/10.77 tff(24499,plain,
% 10.49/10.77 (r(s(s(s(s(elem!1)))), z)),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[1626, 24498])).
% 10.49/10.77 tff(24500,plain,
% 10.49/10.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.49/10.77 inference(rewrite,[status(thm)],[])).
% 10.49/10.77 tff(24501,plain,
% 10.49/10.77 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.49/10.77 inference(rewrite,[status(thm)],[])).
% 10.49/10.77 tff(24502,plain,
% 10.49/10.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))))),
% 10.49/10.77 inference(monotonicity,[status(thm)],[24501])).
% 10.49/10.77 tff(24503,plain,
% 10.49/10.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.49/10.77 inference(transitivity,[status(thm)],[24502, 24500])).
% 10.49/10.77 tff(24504,plain,
% 10.49/10.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.49/10.77 inference(quant_inst,[status(thm)],[])).
% 10.49/10.77 tff(24505,plain,
% 10.49/10.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 10.49/10.77 inference(modus_ponens,[status(thm)],[24504, 24503])).
% 10.49/10.77 tff(24506,plain,
% 10.49/10.77 (~b(s(elem!1), z)),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[24505, 391, 1101, 10682, 2122, 1036])).
% 10.49/10.77 tff(24507,plain,
% 10.49/10.77 (r(s(elem!1), z)),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[549, 24506])).
% 10.49/10.77 tff(24508,plain,
% 10.49/10.77 ($false),
% 10.49/10.77 inference(unit_resolution,[status(thm)],[20007, 194, 411, 24507, 24499, 24491])).
% 10.49/10.77 tff(24509,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.78 tff(24510,plain,
% 10.49/10.78 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.49/10.78 inference(unit_resolution,[status(thm)],[24509, 24318, 24056, 24469, 24322, 24483, 10682])).
% 10.49/10.78 tff(24511,plain,
% 10.49/10.78 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.49/10.78 inference(unit_resolution,[status(thm)],[1095, 24510, 24478])).
% 10.49/10.78 tff(24512,plain,
% 10.49/10.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.78 inference(rewrite,[status(thm)],[])).
% 10.49/10.78 tff(24513,plain,
% 10.49/10.78 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(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(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.78 inference(rewrite,[status(thm)],[])).
% 10.49/10.78 tff(24514,plain,
% 10.49/10.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 10.49/10.78 inference(monotonicity,[status(thm)],[24513])).
% 10.49/10.78 tff(24515,plain,
% 10.49/10.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.78 inference(transitivity,[status(thm)],[24514, 24512])).
% 10.49/10.78 tff(24516,plain,
% 10.49/10.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.78 inference(quant_inst,[status(thm)],[])).
% 10.49/10.78 tff(24517,plain,
% 10.49/10.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 10.49/10.78 inference(modus_ponens,[status(thm)],[24516, 24515])).
% 10.49/10.78 tff(24518,plain,
% 10.49/10.78 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.49/10.78 inference(unit_resolution,[status(thm)],[24517, 194, 4486, 24511, 24477])).
% 10.49/10.78 tff(24519,plain,
% 10.49/10.78 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.49/10.78 inference(unit_resolution,[status(thm)],[1048, 24518, 24311])).
% 10.49/10.78 tff(24520,plain,
% 10.49/10.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 10.49/10.78 inference(rewrite,[status(thm)],[])).
% 10.49/10.78 tff(24521,plain,
% 10.49/10.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 10.49/10.78 inference(quant_inst,[status(thm)],[])).
% 10.49/10.78 tff(24522,plain,
% 10.49/10.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 10.49/10.78 inference(modus_ponens,[status(thm)],[24521, 24520])).
% 10.49/10.78 tff(24523,plain,
% 10.49/10.78 (~r(s(s(s(s(elem!1)))), elem!1)),
% 10.49/10.78 inference(unit_resolution,[status(thm)],[24522, 194, 4486, 4030, 24511])).
% 10.49/10.78 tff(24524,plain,
% 10.49/10.78 (b(s(s(s(s(elem!1)))), elem!1)),
% 10.49/10.78 inference(unit_resolution,[status(thm)],[1004, 24523, 7473])).
% 10.49/10.78 tff(24525,plain,
% 10.49/10.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 10.49/10.78 inference(rewrite,[status(thm)],[])).
% 10.49/10.78 tff(24526,plain,
% 10.49/10.78 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 10.49/10.78 inference(rewrite,[status(thm)],[])).
% 10.49/10.78 tff(24527,plain,
% 10.49/10.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))))),
% 10.49/10.78 inference(monotonicity,[status(thm)],[24526])).
% 10.49/10.78 tff(24528,plain,
% 10.49/10.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 10.49/10.78 inference(transitivity,[status(thm)],[24527, 24525])).
% 10.49/10.78 tff(24529,plain,
% 10.49/10.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 10.49/10.78 inference(quant_inst,[status(thm)],[])).
% 10.49/10.78 tff(24530,plain,
% 10.49/10.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))),
% 10.49/10.78 inference(modus_ponens,[status(thm)],[24529, 24528])).
% 10.49/10.78 tff(24531,plain,
% 10.49/10.78 (~r(elem!1, s(s(elem!1)))),
% 10.49/10.78 inference(unit_resolution,[status(thm)],[24530, 194, 4486, 4030, 24477])).
% 10.49/10.78 tff(24532,plain,
% 10.49/10.78 (b(elem!1, s(s(elem!1)))),
% 10.49/10.78 inference(unit_resolution,[status(thm)],[1307, 24531, 9651])).
% 10.49/10.78 tff(24533,plain,
% 10.49/10.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.49/10.79 inference(rewrite,[status(thm)],[])).
% 10.49/10.79 tff(24534,plain,
% 10.49/10.79 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.49/10.79 inference(rewrite,[status(thm)],[])).
% 10.49/10.79 tff(24535,plain,
% 10.49/10.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 10.49/10.79 inference(monotonicity,[status(thm)],[24534])).
% 10.49/10.79 tff(24536,plain,
% 10.49/10.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.49/10.79 inference(transitivity,[status(thm)],[24535, 24533])).
% 10.49/10.79 tff(24537,plain,
% 10.49/10.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.49/10.79 inference(quant_inst,[status(thm)],[])).
% 10.49/10.79 tff(24538,plain,
% 10.49/10.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 10.49/10.79 inference(modus_ponens,[status(thm)],[24537, 24536])).
% 10.49/10.79 tff(24539,plain,
% 10.49/10.79 ($false),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[24538, 391, 24450, 24532, 24524, 24519])).
% 10.49/10.79 tff(24540,plain,((~(s(z) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (s(s(s(elem!1))) = elem!1) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (~r(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.79 tff(24541,plain,
% 10.49/10.79 (~b(s(s(z)), s(z))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[24540, 24305, 24201, 127, 530, 4028, 10782, 24214])).
% 10.49/10.79 tff(24542,plain,
% 10.49/10.79 (r(s(s(z)), s(z))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[3778, 24541])).
% 10.49/10.79 tff(24543,plain,
% 10.49/10.79 (r(s(elem!1), elem!1)),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[9729, 24542, 24201])).
% 10.49/10.79 tff(24544,plain,
% 10.49/10.79 (~r(s(elem!1), z)),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[541, 24543, 24302, 530])).
% 10.49/10.79 tff(24545,plain,
% 10.49/10.79 (b(s(elem!1), z)),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[549, 24544])).
% 10.49/10.79 tff(24546,plain,
% 10.49/10.79 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 10.49/10.79 inference(monotonicity,[status(thm)],[24202])).
% 10.49/10.79 tff(24547,plain,
% 10.49/10.79 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.49/10.79 inference(transitivity,[status(thm)],[24546, 582])).
% 10.49/10.79 tff(24548,plain,
% 10.49/10.79 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 10.49/10.79 inference(monotonicity,[status(thm)],[24547])).
% 10.49/10.79 tff(24549,plain,
% 10.49/10.79 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.49/10.79 inference(modus_ponens,[status(thm)],[1397, 24548])).
% 10.49/10.79 tff(24550,plain,
% 10.49/10.79 (~r(s(s(s(elem!1))), s(elem!1))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[13054, 24543, 4028, 127, 24214])).
% 10.49/10.79 tff(24551,plain,
% 10.49/10.79 (b(s(s(s(elem!1))), s(elem!1))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[588, 24550, 24549])).
% 10.49/10.79 tff(24552,plain,
% 10.49/10.79 ($false),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[12799, 24551, 24545, 10782, 24206])).
% 10.49/10.79 tff(24553,plain,((~r(s(z), s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, z)) | (z = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.49/10.79 tff(24554,plain,
% 10.49/10.79 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[24553, 24199, 1216, 4028, 24160, 23980, 90, 232, 24159, 11173, 53, 127])).
% 10.49/10.79 tff(24555,plain,
% 10.49/10.79 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[4893, 24199, 24164, 24554])).
% 10.49/10.79 tff(24556,plain,
% 10.49/10.79 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[1356, 24555, 24001])).
% 10.49/10.79 tff(24557,plain,
% 10.49/10.79 (~r(s(s(elem!1)), elem!1)),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[5875, 24556, 410, 4486])).
% 10.49/10.79 tff(24558,plain,
% 10.49/10.79 (b(s(s(elem!1)), elem!1)),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[872, 24557, 8597])).
% 10.49/10.79 tff(24559,plain,
% 10.49/10.79 (~b(s(s(elem!1)), s(elem!1))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[19494, 24558, 23992, 23991])).
% 10.49/10.79 tff(24560,plain,
% 10.49/10.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 10.49/10.79 inference(rewrite,[status(thm)],[])).
% 10.49/10.79 tff(24561,plain,
% 10.49/10.79 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 10.49/10.79 inference(rewrite,[status(thm)],[])).
% 10.49/10.79 tff(24562,plain,
% 10.49/10.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))))),
% 10.49/10.79 inference(monotonicity,[status(thm)],[24561])).
% 10.49/10.79 tff(24563,plain,
% 10.49/10.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 10.49/10.79 inference(transitivity,[status(thm)],[24562, 24560])).
% 10.49/10.79 tff(24564,plain,
% 10.49/10.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 10.49/10.79 inference(quant_inst,[status(thm)],[])).
% 10.49/10.79 tff(24565,plain,
% 10.49/10.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))),
% 10.49/10.79 inference(modus_ponens,[status(thm)],[24564, 24563])).
% 10.49/10.79 tff(24566,plain,
% 10.49/10.79 (~r(elem!1, s(s(elem!1)))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[24565, 194, 613, 410, 1378])).
% 10.49/10.79 tff(24567,plain,
% 10.49/10.79 (b(elem!1, s(s(elem!1)))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[1307, 24566, 1457])).
% 10.49/10.79 tff(24568,plain,
% 10.49/10.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.79 inference(rewrite,[status(thm)],[])).
% 10.49/10.79 tff(24569,plain,
% 10.49/10.79 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.79 inference(rewrite,[status(thm)],[])).
% 10.49/10.79 tff(24570,plain,
% 10.49/10.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 10.49/10.79 inference(monotonicity,[status(thm)],[24569])).
% 10.49/10.79 tff(24571,plain,
% 10.49/10.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.49/10.79 inference(transitivity,[status(thm)],[24570, 24568])).
% 10.49/10.79 tff(24572,plain,
% 10.49/10.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 10.49/10.79 inference(quant_inst,[status(thm)],[])).
% 10.49/10.79 tff(24573,plain,
% 10.49/10.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 10.49/10.79 inference(modus_ponens,[status(thm)],[24572, 24571])).
% 10.49/10.79 tff(24574,plain,
% 10.49/10.79 (~b(s(elem!1), s(s(elem!1)))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[24573, 391, 973, 24567, 2122])).
% 10.49/10.79 tff(24575,plain,
% 10.49/10.79 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[1111, 42, 24574])).
% 10.49/10.79 tff(24576,plain,
% 10.49/10.79 (r(s(elem!1), s(s(elem!1)))),
% 10.49/10.79 inference(unit_resolution,[status(thm)],[24575, 1100])).
% 10.49/10.79 tff(24577,plain,
% 10.49/10.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.49/10.79 inference(rewrite,[status(thm)],[])).
% 10.49/10.79 tff(24578,plain,
% 10.49/10.79 (((~r(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(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(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.49/10.80 inference(rewrite,[status(thm)],[])).
% 10.49/10.80 tff(24579,plain,
% 10.49/10.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 10.49/10.80 inference(monotonicity,[status(thm)],[24578])).
% 10.49/10.80 tff(24580,plain,
% 10.49/10.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.49/10.80 inference(transitivity,[status(thm)],[24579, 24577])).
% 10.49/10.80 tff(24581,plain,
% 10.49/10.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(elem!1)), s(s(s(elem!1))))))),
% 10.49/10.80 inference(quant_inst,[status(thm)],[])).
% 10.49/10.80 tff(24582,plain,
% 10.49/10.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 10.49/10.80 inference(modus_ponens,[status(thm)],[24581, 24580])).
% 10.49/10.80 tff(24583,plain,
% 10.49/10.80 ($false),
% 10.49/10.80 inference(unit_resolution,[status(thm)],[24582, 194, 613, 2170, 1378, 24576])).
% 10.49/10.80 tff(24584,plain,((~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))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.80 tff(24585,plain,
% 10.49/10.80 (~r(s(s(elem!1)), s(elem!1))),
% 10.49/10.80 inference(unit_resolution,[status(thm)],[24584, 24558, 410, 23983, 23975, 24556, 15530, 23992])).
% 10.49/10.80 tff(24586,plain,
% 10.49/10.80 ($false),
% 10.49/10.80 inference(unit_resolution,[status(thm)],[1135, 24585, 24559, 23983])).
% 10.49/10.80 tff(24587,plain,((~r(s(s(z)), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~b(z, elem!1)) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.80 tff(24588,plain,
% 10.49/10.80 (~r(s(s(z)), z)),
% 10.49/10.80 inference(unit_resolution,[status(thm)],[24587, 133, 1216, 4028, 90, 232, 11173, 53, 127, 168, 410, 169, 723, 1697])).
% 10.49/10.80 tff(24589,plain,
% 10.49/10.80 (b(s(s(z)), z)),
% 10.49/10.80 inference(unit_resolution,[status(thm)],[1211, 24588])).
% 10.49/10.80 tff(24590,plain,
% 10.49/10.80 (~r(s(z), s(s(z)))),
% 10.49/10.80 inference(unit_resolution,[status(thm)],[23377, 24589, 1216, 90, 1697, 23963])).
% 10.49/10.80 tff(24591,plain,
% 10.49/10.80 (b(s(z), s(s(z)))),
% 10.49/10.80 inference(unit_resolution,[status(thm)],[1788, 24590])).
% 10.49/10.80 tff(24592,plain,
% 10.49/10.80 ($false),
% 10.49/10.80 inference(unit_resolution,[status(thm)],[16413, 391, 24589, 24591, 23978, 23963])).
% 10.49/10.80 tff(24593,plain,((~b(z, elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.49/10.80 tff(24594,plain,
% 10.49/10.80 (~b(z, elem!1)),
% 10.49/10.80 inference(unit_resolution,[status(thm)],[24593, 4028, 90, 1697, 2913, 23961, 11173, 53, 9, 23959, 6124, 23954, 23849])).
% 10.59/10.80 tff(24595,plain,
% 10.59/10.80 (~b(z, s(z))),
% 10.59/10.80 inference(modus_ponens,[status(thm)],[24594, 23956])).
% 10.59/10.80 tff(24596,plain,
% 10.59/10.80 (~r(z, s(s(s(s(z)))))),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[10733, 23957, 53])).
% 10.59/10.80 tff(24597,plain,
% 10.59/10.80 (b(z, s(s(s(s(z)))))),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[800, 24596])).
% 10.59/10.80 tff(24598,plain,
% 10.59/10.80 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[23918, 24597, 90, 10782])).
% 10.59/10.80 tff(24599,plain,
% 10.59/10.80 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[23920, 24598])).
% 10.59/10.80 tff(24600,plain,
% 10.59/10.80 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24599])).
% 10.59/10.80 tff(24601,plain,
% 10.59/10.80 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 10.59/10.80 inference(symmetry,[status(thm)],[24600])).
% 10.59/10.80 tff(24602,plain,
% 10.59/10.80 (s(elem!1) = s(s(z))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[23954])).
% 10.59/10.80 tff(24603,plain,
% 10.59/10.80 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24602])).
% 10.59/10.80 tff(24604,plain,
% 10.59/10.80 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 10.59/10.80 inference(symmetry,[status(thm)],[24603])).
% 10.59/10.80 tff(24605,plain,
% 10.59/10.80 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 10.59/10.80 inference(transitivity,[status(thm)],[24604, 24601])).
% 10.59/10.80 tff(24606,plain,
% 10.59/10.80 (r(s(s(s(elem!1))), s(elem!1))),
% 10.59/10.80 inference(modus_ponens,[status(thm)],[1697, 24605])).
% 10.59/10.80 tff(24607,plain,
% 10.59/10.80 (~r(s(elem!1), elem!1)),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[13054, 24606, 4028, 9, 23959])).
% 10.59/10.80 tff(24608,plain,
% 10.59/10.80 (~r(s(s(z)), s(z))),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[9729, 24607, 23957])).
% 10.59/10.80 tff(24609,plain,
% 10.59/10.80 (b(s(s(z)), s(z))),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[3778, 24608])).
% 10.59/10.80 tff(24610,plain,
% 10.59/10.80 (b(s(elem!1), elem!1)),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[2168, 24607, 426])).
% 10.59/10.80 tff(24611,plain,
% 10.59/10.80 (s(s(z)) = s(elem!1)),
% 10.59/10.80 inference(symmetry,[status(thm)],[24602])).
% 10.59/10.80 tff(24612,plain,
% 10.59/10.80 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24611])).
% 10.59/10.80 tff(24613,plain,
% 10.59/10.80 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24612])).
% 10.59/10.80 tff(24614,plain,
% 10.59/10.80 (~(s(s(elem!1)) = s(elem!1))),
% 10.59/10.80 inference(modus_ponens,[status(thm)],[23982, 24613])).
% 10.59/10.80 tff(24615,plain,
% 10.59/10.80 (r(s(s(s(elem!1))), elem!1)),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[230, 23959, 9])).
% 10.59/10.80 tff(24616,plain,
% 10.59/10.80 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24599])).
% 10.59/10.80 tff(24617,plain,
% 10.59/10.80 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 10.59/10.80 inference(transitivity,[status(thm)],[24616, 2123])).
% 10.59/10.80 tff(24618,plain,
% 10.59/10.80 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.59/10.80 inference(symmetry,[status(thm)],[24617])).
% 10.59/10.80 tff(24619,plain,
% 10.59/10.80 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24602])).
% 10.59/10.80 tff(24620,plain,
% 10.59/10.80 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 10.59/10.80 inference(symmetry,[status(thm)],[24619])).
% 10.59/10.80 tff(24621,plain,
% 10.59/10.80 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.59/10.80 inference(transitivity,[status(thm)],[24620, 24618])).
% 10.59/10.80 tff(24622,plain,
% 10.59/10.80 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24621])).
% 10.59/10.80 tff(24623,plain,
% 10.59/10.80 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.59/10.80 inference(modus_ponens,[status(thm)],[714, 24622])).
% 10.59/10.80 tff(24624,plain,
% 10.59/10.80 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[281, 24623])).
% 10.59/10.80 tff(24625,plain,
% 10.59/10.80 (s(z) = elem!1),
% 10.59/10.80 inference(symmetry,[status(thm)],[23954])).
% 10.59/10.80 tff(24626,plain,
% 10.59/10.80 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24625])).
% 10.59/10.80 tff(24627,plain,
% 10.59/10.80 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24626])).
% 10.59/10.80 tff(24628,plain,
% 10.59/10.80 (~(s(s(elem!1)) = elem!1)),
% 10.59/10.80 inference(modus_ponens,[status(thm)],[357, 24627])).
% 10.59/10.80 tff(24629,plain,
% 10.59/10.80 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24599])).
% 10.59/10.80 tff(24630,plain,
% 10.59/10.80 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 10.59/10.80 inference(symmetry,[status(thm)],[24629])).
% 10.59/10.80 tff(24631,plain,
% 10.59/10.80 (b(s(s(s(elem!1))), z)),
% 10.59/10.80 inference(modus_ponens,[status(thm)],[90, 24630])).
% 10.59/10.80 tff(24632,plain,
% 10.59/10.80 (r(z, elem!1)),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[141, 24594, 23980])).
% 10.59/10.80 tff(24633,plain,
% 10.59/10.80 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 10.59/10.80 inference(symmetry,[status(thm)],[3042])).
% 10.59/10.80 tff(24634,plain,
% 10.59/10.80 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24633])).
% 10.59/10.80 tff(24635,plain,
% 10.59/10.80 (~(z = s(s(s(elem!1))))),
% 10.59/10.80 inference(modus_ponens,[status(thm)],[50, 24634])).
% 10.59/10.80 tff(24636,plain,
% 10.59/10.80 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 10.59/10.80 inference(rewrite,[status(thm)],[])).
% 10.59/10.80 tff(24637,plain,
% 10.59/10.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 10.59/10.80 inference(monotonicity,[status(thm)],[24636])).
% 10.59/10.80 tff(24638,plain,
% 10.59/10.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 10.59/10.80 inference(transitivity,[status(thm)],[24637, 412])).
% 10.59/10.80 tff(24639,plain,
% 10.59/10.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 10.59/10.80 inference(quant_inst,[status(thm)],[])).
% 10.59/10.80 tff(24640,plain,
% 10.59/10.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 10.59/10.80 inference(modus_ponens,[status(thm)],[24639, 24638])).
% 10.59/10.80 tff(24641,plain,
% 10.59/10.80 (~r(z, s(s(s(elem!1))))),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[24640, 194, 411, 233, 410])).
% 10.59/10.80 tff(24642,plain,
% 10.59/10.80 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[56, 42, 24641])).
% 10.59/10.80 tff(24643,plain,
% 10.59/10.80 (b(z, s(s(s(elem!1))))),
% 10.59/10.80 inference(unit_resolution,[status(thm)],[24642, 24635])).
% 10.59/10.80 tff(24644,plain,
% 10.59/10.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.59/10.80 inference(rewrite,[status(thm)],[])).
% 10.59/10.80 tff(24645,plain,
% 10.59/10.80 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.59/10.80 inference(rewrite,[status(thm)],[])).
% 10.59/10.80 tff(24646,plain,
% 10.59/10.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))))),
% 10.59/10.81 inference(monotonicity,[status(thm)],[24645])).
% 10.59/10.81 tff(24647,plain,
% 10.59/10.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 10.59/10.81 inference(transitivity,[status(thm)],[24646, 24644])).
% 10.59/10.81 tff(24648,plain,
% 10.59/10.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 10.59/10.81 inference(quant_inst,[status(thm)],[])).
% 10.59/10.81 tff(24649,plain,
% 10.59/10.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 10.59/10.81 inference(modus_ponens,[status(thm)],[24648, 24647])).
% 10.59/10.81 tff(24650,plain,
% 10.59/10.81 ($false),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24649, 391, 665, 380, 10682, 591, 2122])).
% 10.59/10.81 tff(24651,plain,((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.81 tff(24652,plain,
% 10.59/10.81 (~b(s(elem!1), z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24651, 24643, 380, 665, 2122])).
% 10.59/10.81 tff(24653,plain,
% 10.59/10.81 (r(s(elem!1), z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[547, 42, 355, 24652])).
% 10.59/10.81 tff(24654,plain,
% 10.59/10.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~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))))))),
% 10.59/10.81 inference(rewrite,[status(thm)],[])).
% 10.59/10.81 tff(24655,plain,
% 10.59/10.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~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))))))),
% 10.59/10.81 inference(quant_inst,[status(thm)],[])).
% 10.59/10.81 tff(24656,plain,
% 10.59/10.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~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)))))),
% 10.59/10.81 inference(modus_ponens,[status(thm)],[24655, 24654])).
% 10.59/10.81 tff(24657,plain,
% 10.59/10.81 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24656, 194, 613, 24653, 2170])).
% 10.59/10.81 tff(24658,plain,
% 10.59/10.81 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[1354, 42, 270, 24657])).
% 10.59/10.81 tff(24659,plain,
% 10.59/10.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.59/10.81 inference(rewrite,[status(thm)],[])).
% 10.59/10.81 tff(24660,plain,
% 10.59/10.81 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.59/10.81 inference(rewrite,[status(thm)],[])).
% 10.59/10.81 tff(24661,plain,
% 10.59/10.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))))),
% 10.59/10.81 inference(monotonicity,[status(thm)],[24660])).
% 10.59/10.81 tff(24662,plain,
% 10.59/10.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.59/10.81 inference(transitivity,[status(thm)],[24661, 24659])).
% 10.59/10.81 tff(24663,plain,
% 10.59/10.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.59/10.81 inference(quant_inst,[status(thm)],[])).
% 10.59/10.81 tff(24664,plain,
% 10.59/10.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 10.59/10.81 inference(modus_ponens,[status(thm)],[24663, 24662])).
% 10.59/10.81 tff(24665,plain,
% 10.59/10.81 (~b(s(s(elem!1)), z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24664, 391, 380, 24643, 24658])).
% 10.59/10.81 tff(24666,plain,
% 10.59/10.81 (r(s(s(elem!1)), z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[2627, 42, 215, 24665])).
% 10.59/10.81 tff(24667,plain,
% 10.59/10.81 ($false),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24415, 194, 411, 24653, 2170, 24666])).
% 10.59/10.81 tff(24668,plain,((~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.81 tff(24669,plain,
% 10.59/10.81 (~r(s(s(elem!1)), s(elem!1))),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24668, 411, 380, 270, 613, 665, 2122, 233, 410])).
% 10.59/10.81 tff(24670,plain,
% 10.59/10.81 (b(s(s(elem!1)), s(elem!1))),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[1135, 24669, 285])).
% 10.59/10.81 tff(24671,plain,
% 10.59/10.81 (~b(s(s(elem!1)), elem!1)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[17814, 24643, 665, 24670, 2122])).
% 10.59/10.81 tff(24672,plain,
% 10.59/10.81 (r(s(s(elem!1)), elem!1)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[872, 24671, 249])).
% 10.59/10.81 tff(24673,plain,
% 10.59/10.81 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[4971, 194, 233, 24672, 410])).
% 10.59/10.81 tff(24674,plain,
% 10.59/10.81 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[1354, 42, 270, 24673])).
% 10.59/10.81 tff(24675,plain,
% 10.59/10.81 (~r(s(s(elem!1)), z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[19809, 194, 411, 24672, 410])).
% 10.59/10.81 tff(24676,plain,
% 10.59/10.81 (b(s(s(elem!1)), z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[2627, 42, 215, 24675])).
% 10.59/10.81 tff(24677,plain,
% 10.59/10.81 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.59/10.81 inference(rewrite,[status(thm)],[])).
% 10.59/10.81 tff(24678,plain,
% 10.59/10.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))))),
% 10.59/10.81 inference(monotonicity,[status(thm)],[24677])).
% 10.59/10.81 tff(24679,plain,
% 10.59/10.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.59/10.81 inference(transitivity,[status(thm)],[24678, 24659])).
% 10.59/10.81 tff(24680,plain,
% 10.59/10.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.59/10.81 inference(quant_inst,[status(thm)],[])).
% 10.59/10.81 tff(24681,plain,
% 10.59/10.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 10.59/10.81 inference(modus_ponens,[status(thm)],[24680, 24679])).
% 10.59/10.81 tff(24682,plain,
% 10.59/10.81 ($false),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24681, 391, 380, 24643, 24676, 24674])).
% 10.59/10.81 tff(24683,plain,((~r(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.81 tff(24684,plain,
% 10.59/10.81 (~b(elem!1, z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24683, 24632, 6124, 24606, 24631, 24628, 24624, 24615, 24614, 24610])).
% 10.59/10.81 tff(24685,plain,
% 10.59/10.81 (r(elem!1, z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[526, 24684, 23979])).
% 10.59/10.81 tff(24686,plain,
% 10.59/10.81 (~r(z, s(z))),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24540, 24685, 4028, 9, 23957, 24609, 10782, 23959])).
% 10.59/10.81 tff(24687,plain,
% 10.59/10.81 (b(z, s(z))),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[678, 24686])).
% 10.59/10.81 tff(24688,plain,
% 10.59/10.81 ($false),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24687, 24595])).
% 10.59/10.81 tff(24689,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1)))) | b(s(z), s(s(s(s(z))))) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.81 tff(24690,plain,
% 10.59/10.81 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[24689, 23929, 90, 11173, 53, 2881, 31, 1])).
% 10.59/10.81 tff(24691,plain,
% 10.59/10.81 (b(s(s(s(s(z)))), s(s(z)))),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[1714, 24690])).
% 10.59/10.81 tff(24692,plain,
% 10.59/10.81 (~b(s(s(z)), z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[20748, 24691, 90, 23910])).
% 10.59/10.81 tff(24693,plain,
% 10.59/10.81 (r(s(s(z)), z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[1211, 24692])).
% 10.59/10.81 tff(24694,plain,
% 10.59/10.81 (r(s(elem!1), z)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[3560, 24693, 23908])).
% 10.59/10.81 tff(24695,plain,
% 10.59/10.81 (~b(s(s(s(s(z)))), elem!1)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[9614, 23908, 23848])).
% 10.59/10.81 tff(24696,plain,
% 10.59/10.81 (~b(s(s(s(elem!1))), elem!1)),
% 10.59/10.81 inference(unit_resolution,[status(thm)],[1563, 24695, 23907])).
% 10.59/10.81 tff(24697,plain,
% 10.59/10.82 (r(z, elem!1) <=> r(z, s(z))),
% 10.59/10.82 inference(monotonicity,[status(thm)],[23907])).
% 10.59/10.82 tff(24698,plain,
% 10.59/10.82 (r(elem!1, s(s(s(elem!1))))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[424, 23929, 1])).
% 10.59/10.82 tff(24699,plain,
% 10.59/10.82 (~b(s(z), s(s(s(elem!1))))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[2884, 23907, 2881])).
% 10.59/10.82 tff(24700,plain,
% 10.59/10.82 (r(s(z), s(s(s(elem!1))))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[247, 24699])).
% 10.59/10.82 tff(24701,plain,
% 10.59/10.82 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 10.59/10.82 inference(monotonicity,[status(thm)],[169])).
% 10.59/10.82 tff(24702,plain,
% 10.59/10.82 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 10.59/10.82 inference(monotonicity,[status(thm)],[169])).
% 10.59/10.82 tff(24703,plain,
% 10.59/10.82 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 10.59/10.82 inference(symmetry,[status(thm)],[24702])).
% 10.59/10.82 tff(24704,plain,
% 10.59/10.82 (r(s(s(s(s(z)))), elem!1)),
% 10.59/10.82 inference(modus_ponens,[status(thm)],[723, 24703])).
% 10.59/10.82 tff(24705,plain,
% 10.59/10.82 (~b(s(s(z)), z)),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[20748, 3563, 90, 23965])).
% 10.59/10.82 tff(24706,plain,
% 10.59/10.82 (r(s(s(z)), z)),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[1211, 24705])).
% 10.59/10.82 tff(24707,plain,
% 10.59/10.82 (~b(z, s(elem!1))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[24258, 133, 1216, 127, 4028, 168, 23965, 24706, 24704, 8598])).
% 10.59/10.82 tff(24708,plain,
% 10.59/10.82 (r(z, s(elem!1))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[566, 24707])).
% 10.59/10.82 tff(24709,plain,
% 10.59/10.82 (r(z, s(s(z)))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[8520, 24708, 8598])).
% 10.59/10.82 tff(24710,plain,
% 10.59/10.82 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 10.59/10.82 inference(monotonicity,[status(thm)],[23969])).
% 10.59/10.82 tff(24711,plain,
% 10.59/10.82 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 10.59/10.82 inference(symmetry,[status(thm)],[24710])).
% 10.59/10.82 tff(24712,plain,
% 10.59/10.82 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 10.59/10.82 inference(monotonicity,[status(thm)],[1550])).
% 10.59/10.82 tff(24713,plain,
% 10.59/10.82 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 10.59/10.82 inference(symmetry,[status(thm)],[24712])).
% 10.59/10.82 tff(24714,plain,
% 10.59/10.82 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 10.59/10.82 inference(transitivity,[status(thm)],[24713, 24711])).
% 10.59/10.82 tff(24715,plain,
% 10.59/10.82 (b(s(s(s(elem!1))), s(elem!1))),
% 10.59/10.82 inference(modus_ponens,[status(thm)],[3563, 24714])).
% 10.59/10.82 tff(24716,plain,
% 10.59/10.82 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[287, 23983])).
% 10.59/10.82 tff(24717,plain,
% 10.59/10.82 (r(elem!1, z)),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[526, 484, 23979])).
% 10.59/10.82 tff(24718,plain,
% 10.59/10.82 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 10.59/10.82 inference(monotonicity,[status(thm)],[10937])).
% 10.59/10.82 tff(24719,plain,
% 10.59/10.82 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 10.59/10.82 inference(symmetry,[status(thm)],[24718])).
% 10.59/10.82 tff(24720,plain,
% 10.59/10.82 (b(s(s(s(elem!1))), z)),
% 10.59/10.82 inference(modus_ponens,[status(thm)],[90, 24719])).
% 10.59/10.82 tff(24721,plain,
% 10.59/10.82 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 10.59/10.82 inference(monotonicity,[status(thm)],[169])).
% 10.59/10.82 tff(24722,plain,
% 10.59/10.82 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 10.59/10.82 inference(symmetry,[status(thm)],[24721])).
% 10.59/10.82 tff(24723,plain,
% 10.59/10.82 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 10.59/10.82 inference(monotonicity,[status(thm)],[1550])).
% 10.59/10.82 tff(24724,plain,
% 10.59/10.82 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 10.59/10.82 inference(symmetry,[status(thm)],[24723])).
% 10.59/10.82 tff(24725,plain,
% 10.59/10.82 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 10.59/10.82 inference(transitivity,[status(thm)],[24724, 24722])).
% 10.59/10.82 tff(24726,plain,
% 10.59/10.82 (r(s(z), z)),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[7485, 484, 8598])).
% 10.59/10.82 tff(24727,plain,
% 10.59/10.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 10.59/10.82 inference(rewrite,[status(thm)],[])).
% 10.59/10.82 tff(24728,plain,
% 10.59/10.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 10.59/10.82 inference(quant_inst,[status(thm)],[])).
% 10.59/10.82 tff(24729,plain,
% 10.59/10.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 10.59/10.82 inference(modus_ponens,[status(thm)],[24728, 24727])).
% 10.59/10.82 tff(24730,plain,
% 10.59/10.82 (~r(s(s(z)), s(z))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[24729, 194, 24726, 3557, 8505])).
% 10.59/10.82 tff(24731,plain,
% 10.59/10.82 (b(s(s(z)), s(z))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[3778, 24730])).
% 10.59/10.82 tff(24732,plain,
% 10.59/10.82 (b(s(elem!1), elem!1)),
% 10.59/10.82 inference(modus_ponens,[status(thm)],[24731, 24725])).
% 10.59/10.82 tff(24733,plain,
% 10.59/10.82 (~r(z, s(s(elem!1)))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[24197, 24732, 10782, 24161, 168, 127, 4028, 8597, 24720, 23983, 133, 24717])).
% 10.59/10.82 tff(24734,plain,
% 10.59/10.82 (b(z, s(s(elem!1)))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[324, 24733])).
% 10.59/10.82 tff(24735,plain,
% 10.59/10.82 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[4039, 127, 168, 364, 4028])).
% 10.59/10.82 tff(24736,plain,
% 10.59/10.82 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[1370, 24735, 297])).
% 10.59/10.82 tff(24737,plain,
% 10.59/10.82 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[5875, 4031, 364, 4030])).
% 10.59/10.82 tff(24738,plain,
% 10.59/10.82 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[1356, 24737, 315])).
% 10.59/10.82 tff(24739,plain,
% 10.59/10.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.59/10.82 inference(rewrite,[status(thm)],[])).
% 10.59/10.82 tff(24740,plain,
% 10.59/10.82 (((~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(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.59/10.82 inference(rewrite,[status(thm)],[])).
% 10.59/10.82 tff(24741,plain,
% 10.59/10.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 10.59/10.82 inference(monotonicity,[status(thm)],[24740])).
% 10.59/10.82 tff(24742,plain,
% 10.59/10.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.59/10.82 inference(transitivity,[status(thm)],[24741, 24739])).
% 10.59/10.82 tff(24743,plain,
% 10.59/10.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 10.59/10.82 inference(quant_inst,[status(thm)],[])).
% 10.59/10.82 tff(24744,plain,
% 10.59/10.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 10.59/10.82 inference(modus_ponens,[status(thm)],[24743, 24742])).
% 10.59/10.82 tff(24745,plain,
% 10.59/10.82 ($false),
% 10.59/10.82 inference(unit_resolution,[status(thm)],[24744, 391, 1101, 10682, 1374, 3927, 328])).
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% 10.59/10.82 tff(24749,plain,
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% 10.59/10.82 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
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% 10.59/10.82 tff(24755,plain,
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% 10.59/10.82 tff(24757,plain,
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% 10.59/10.82 tff(24758,plain,
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% 10.59/10.83 inference(monotonicity,[status(thm)],[24762])).
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% 10.59/10.83 inference(modus_ponens,[status(thm)],[24765, 24764])).
% 10.59/10.83 tff(24767,plain,
% 10.59/10.83 ($false),
% 10.59/10.83 inference(unit_resolution,[status(thm)],[24766, 391, 24760, 23965, 24758, 24753, 24751])).
% 10.59/10.83 tff(24768,plain,(b(elem!1, z) | (~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1)))) | (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(z, elem!1)) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.83 tff(24769,plain,
% 10.59/10.83 (b(elem!1, z)),
% 10.59/10.83 inference(unit_resolution,[status(thm)],[24768, 133, 169, 1216, 4028, 90, 232, 11173, 53, 127, 24715, 168, 23969, 24706, 24709])).
% 10.59/10.83 tff(24770,plain,
% 10.59/10.83 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
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% 10.59/10.83 tff(24771,plain,
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% 10.59/10.83 tff(24772,plain,
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% 10.59/10.83 tff(24773,plain,
% 10.59/10.83 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(s(elem!1)))),
% 10.59/10.83 inference(monotonicity,[status(thm)],[24772])).
% 10.59/10.83 tff(24774,plain,
% 10.59/10.83 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(z)))),
% 10.59/10.83 inference(transitivity,[status(thm)],[24773, 9482])).
% 10.59/10.83 tff(24775,plain,
% 10.59/10.83 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
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% 10.59/10.83 tff(24776,plain,
% 10.59/10.83 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 10.59/10.83 inference(monotonicity,[status(thm)],[24775])).
% 10.59/10.83 tff(24777,plain,
% 10.59/10.83 (~(s(s(z)) = s(s(s(z))))),
% 10.59/10.83 inference(modus_ponens,[status(thm)],[23982, 24776])).
% 10.59/10.83 tff(24778,plain,
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% 10.59/10.83 inference(transitivity,[status(thm)],[212, 24770, 692])).
% 10.59/10.83 tff(24779,plain,
% 10.59/10.83 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 10.59/10.83 inference(monotonicity,[status(thm)],[24778])).
% 10.59/10.83 tff(24780,plain,
% 10.59/10.83 (~r(s(s(elem!1)), elem!1)),
% 10.59/10.83 inference(unit_resolution,[status(thm)],[24748, 3927, 10682, 4028, 1101, 127, 297, 168])).
% 10.59/10.83 tff(24781,plain,
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% 10.59/10.83 inference(unit_resolution,[status(thm)],[872, 24780, 6564, 249])).
% 10.59/10.83 tff(24782,plain,((~b(z, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), elem!1) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.83 tff(24783,plain,
% 10.59/10.83 (~b(z, s(s(elem!1)))),
% 10.59/10.83 inference(unit_resolution,[status(thm)],[24782, 24769, 10782, 4028, 24715, 127, 24716, 168, 8597, 133])).
% 10.59/10.83 tff(24784,plain,
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% 10.59/10.83 tff(24785,plain,
% 10.59/10.83 (r(z, s(s(s(z))))),
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% 10.59/10.83 tff(24786,plain,
% 10.59/10.83 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.59/10.83 inference(monotonicity,[status(thm)],[24092, 10938])).
% 10.59/10.83 tff(24787,plain,
% 10.59/10.83 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 10.59/10.83 inference(symmetry,[status(thm)],[24786])).
% 10.59/10.83 tff(24788,plain,
% 10.59/10.83 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 10.59/10.83 inference(monotonicity,[status(thm)],[10937])).
% 10.59/10.83 tff(24789,plain,
% 10.59/10.83 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.59/10.83 inference(symmetry,[status(thm)],[24788])).
% 10.59/10.83 tff(24790,plain,
% 10.59/10.83 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.59/10.83 inference(transitivity,[status(thm)],[24754, 24789])).
% 10.59/10.83 tff(24791,plain,
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% 10.59/10.83 tff(24794,plain,
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% 10.59/10.83 tff(24795,plain,
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% 10.59/10.83 tff(24796,plain,
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% 10.59/10.83 tff(24797,plain,
% 10.59/10.83 (~r(s(s(s(elem!1))), s(s(elem!1)))),
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% 10.59/10.83 tff(24798,plain,
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% 10.59/10.83 tff(24799,plain,
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% 10.59/10.83 tff(24800,plain,
% 10.59/10.83 (b(s(s(s(s(z)))), s(s(s(z))))),
% 10.59/10.83 inference(modus_ponens,[status(thm)],[24799, 24755])).
% 10.59/10.83 tff(24801,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
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% 10.59/10.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(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)))))),
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% 10.59/10.83 tff(24803,plain,
% 10.59/10.83 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(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)))))),
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% 10.59/10.83 tff(24804,plain,
% 10.59/10.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(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))))))),
% 10.59/10.83 inference(monotonicity,[status(thm)],[24803])).
% 10.59/10.83 tff(24805,plain,
% 10.59/10.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(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)))))),
% 10.59/10.83 inference(transitivity,[status(thm)],[24804, 24802])).
% 10.59/10.83 tff(24806,plain,
% 10.59/10.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(s(s(z))))))),
% 10.59/10.83 inference(quant_inst,[status(thm)],[])).
% 10.59/10.83 tff(24807,plain,
% 10.59/10.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 10.59/10.83 inference(modus_ponens,[status(thm)],[24806, 24805])).
% 10.59/10.83 tff(24808,plain,
% 10.59/10.83 ($false),
% 10.59/10.83 inference(unit_resolution,[status(thm)],[24807, 391, 3823, 3563, 7872, 24801])).
% 10.59/10.83 tff(24809,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(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))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.83 tff(24810,plain,
% 10.59/10.83 (~b(s(s(s(z))), s(s(z)))),
% 10.59/10.83 inference(unit_resolution,[status(thm)],[24809, 24800, 3563, 3823])).
% 10.59/10.83 tff(24811,plain,
% 10.59/10.83 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 10.59/10.83 inference(monotonicity,[status(thm)],[24091])).
% 10.59/10.83 tff(24812,plain,
% 10.59/10.83 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 10.59/10.83 inference(symmetry,[status(thm)],[24811])).
% 10.59/10.83 tff(24813,plain,
% 10.59/10.83 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 10.59/10.83 inference(transitivity,[status(thm)],[24701, 24812])).
% 10.59/10.83 tff(24814,plain,
% 10.59/10.83 (r(s(s(s(z))), s(z))),
% 10.59/10.83 inference(modus_ponens,[status(thm)],[364, 24813])).
% 10.59/10.83 tff(24815,plain,
% 10.59/10.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 10.59/10.83 inference(rewrite,[status(thm)],[])).
% 10.59/10.83 tff(24816,plain,
% 10.59/10.83 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 10.59/10.83 inference(rewrite,[status(thm)],[])).
% 10.59/10.83 tff(24817,plain,
% 10.59/10.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))))),
% 10.59/10.83 inference(monotonicity,[status(thm)],[24816])).
% 10.59/10.83 tff(24818,plain,
% 10.59/10.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 10.59/10.83 inference(transitivity,[status(thm)],[24817, 24815])).
% 10.59/10.83 tff(24819,plain,
% 10.59/10.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 10.59/10.83 inference(quant_inst,[status(thm)],[])).
% 10.59/10.83 tff(24820,plain,
% 10.59/10.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))),
% 10.59/10.83 inference(modus_ponens,[status(thm)],[24819, 24818])).
% 10.59/10.83 tff(24821,plain,
% 10.59/10.83 (~r(s(s(s(z))), s(s(z)))),
% 10.59/10.83 inference(unit_resolution,[status(thm)],[24820, 194, 1216, 2405, 24814])).
% 10.59/10.84 tff(24822,plain,
% 10.59/10.84 ($false),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[21897, 42, 24821, 24810, 21881])).
% 10.59/10.84 tff(24823,plain,((~r(s(s(elem!1)), elem!1)) | (s(s(s(z))) = s(s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.59/10.84 tff(24824,plain,
% 10.59/10.84 (~r(s(s(elem!1)), elem!1)),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[24823, 24795, 3563, 24796, 1216, 2405, 10937, 169, 297, 4028, 168, 127])).
% 10.59/10.84 tff(24825,plain,
% 10.59/10.84 (b(s(s(elem!1)), elem!1)),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[872, 24824, 8597])).
% 10.59/10.84 tff(24826,plain,
% 10.59/10.84 (b(s(s(s(z))), s(z))),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[16036, 24825, 8598])).
% 10.59/10.84 tff(24827,plain,
% 10.59/10.84 (~b(s(s(s(z))), z)),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[16043, 391, 1686, 23963, 24793, 24826])).
% 10.59/10.84 tff(24828,plain,
% 10.59/10.84 (r(s(s(s(z))), z)),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[8765, 42, 741, 24827])).
% 10.59/10.84 tff(24829,plain,
% 10.59/10.84 (~b(s(s(z)), z)),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[20748, 3563, 90, 1686])).
% 10.59/10.84 tff(24830,plain,
% 10.59/10.84 (r(s(s(z)), z)),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[1211, 24829])).
% 10.59/10.84 tff(24831,plain,
% 10.59/10.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 10.59/10.84 inference(rewrite,[status(thm)],[])).
% 10.59/10.84 tff(24832,plain,
% 10.59/10.84 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(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(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 10.59/10.84 inference(rewrite,[status(thm)],[])).
% 10.59/10.84 tff(24833,plain,
% 10.59/10.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 10.59/10.84 inference(monotonicity,[status(thm)],[24832])).
% 10.59/10.84 tff(24834,plain,
% 10.59/10.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 10.59/10.84 inference(transitivity,[status(thm)],[24833, 24831])).
% 10.59/10.84 tff(24835,plain,
% 10.59/10.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 10.59/10.84 inference(quant_inst,[status(thm)],[])).
% 10.59/10.84 tff(24836,plain,
% 10.59/10.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 10.59/10.84 inference(modus_ponens,[status(thm)],[24835, 24834])).
% 10.59/10.84 tff(24837,plain,
% 10.59/10.84 (~r(s(s(s(z))), s(s(z)))),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[24836, 194, 24830, 24828, 15510])).
% 10.59/10.84 tff(24838,plain,
% 10.59/10.84 (b(s(s(s(z))), s(s(z)))),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[21897, 42, 24837, 24796])).
% 10.59/10.84 tff(24839,plain,
% 10.59/10.84 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[24809, 24838, 3563, 24795])).
% 10.59/10.84 tff(24840,plain,
% 10.59/10.84 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.59/10.84 inference(modus_ponens,[status(thm)],[24839, 24791])).
% 10.59/10.84 tff(24841,plain,
% 10.59/10.84 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[1370, 24840, 297])).
% 10.59/10.84 tff(24842,plain,
% 10.59/10.84 (~r(s(s(z)), s(s(s(z))))),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[24069, 194, 24830, 24828, 15510])).
% 10.59/10.84 tff(24843,plain,
% 10.59/10.84 (b(s(s(z)), s(s(s(z))))),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[24076, 24842, 23946])).
% 10.59/10.84 tff(24844,plain,
% 10.59/10.84 (~r(s(s(s(s(s(z))))), z)),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[24137, 24843, 10937, 169, 24056, 24828, 15510, 24830])).
% 10.59/10.84 tff(24845,plain,
% 10.59/10.84 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(z))))), z)),
% 10.59/10.84 inference(monotonicity,[status(thm)],[24080])).
% 10.59/10.84 tff(24846,plain,
% 10.59/10.84 (r(s(s(s(s(s(z))))), z)),
% 10.59/10.84 inference(modus_ponens,[status(thm)],[12854, 24845])).
% 10.59/10.84 tff(24847,plain,
% 10.59/10.84 ($false),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[16524, 24846])).
% 10.59/10.84 tff(24848,plain,((~r(s(s(s(s(elem!1)))), z)) | r(s(s(s(s(s(z))))), z) | (~(s(s(s(elem!1))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.84 tff(24849,plain,
% 10.59/10.84 (~r(s(s(s(s(elem!1)))), z)),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[24848, 24844, 10937])).
% 10.59/10.84 tff(24850,plain,
% 10.59/10.84 (b(s(s(s(s(elem!1)))), z)),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[1626, 24849])).
% 10.59/10.84 tff(24851,plain,
% 10.59/10.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 10.59/10.84 inference(rewrite,[status(thm)],[])).
% 10.59/10.84 tff(24852,plain,
% 10.59/10.84 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 10.59/10.84 inference(rewrite,[status(thm)],[])).
% 10.59/10.84 tff(24853,plain,
% 10.59/10.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 10.59/10.84 inference(monotonicity,[status(thm)],[24852])).
% 10.59/10.84 tff(24854,plain,
% 10.59/10.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 10.59/10.84 inference(transitivity,[status(thm)],[24853, 24851])).
% 10.59/10.84 tff(24855,plain,
% 10.59/10.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 10.59/10.84 inference(quant_inst,[status(thm)],[])).
% 10.59/10.84 tff(24856,plain,
% 10.59/10.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 10.59/10.84 inference(modus_ponens,[status(thm)],[24855, 24854])).
% 10.59/10.84 tff(24857,plain,
% 10.59/10.84 ($false),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[24856, 391, 133, 665, 974, 17911])).
% 10.59/10.84 tff(24858,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.84 tff(24859,plain,
% 10.59/10.84 (~b(elem!1, s(s(s(s(elem!1)))))),
% 10.59/10.84 inference(unit_resolution,[status(thm)],[24858, 24850, 665, 133])).
% 10.59/10.85 tff(24860,plain,
% 10.59/10.85 (r(elem!1, s(s(s(s(elem!1)))))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[1018, 24859, 15611])).
% 10.59/10.85 tff(24861,plain,
% 10.59/10.85 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[1090, 24860, 410, 24841])).
% 10.59/10.85 tff(24862,plain,
% 10.59/10.85 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[1095, 24861, 310])).
% 10.59/10.85 tff(24863,plain,
% 10.59/10.85 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 10.59/10.85 inference(modus_ponens,[status(thm)],[24862, 24787])).
% 10.59/10.85 tff(24864,plain,
% 10.59/10.85 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 10.59/10.85 inference(monotonicity,[status(thm)],[24080])).
% 10.59/10.85 tff(24865,plain,
% 10.59/10.85 (b(s(s(s(s(s(z))))), z)),
% 10.59/10.85 inference(modus_ponens,[status(thm)],[24850, 24864])).
% 10.59/10.85 tff(24866,plain,
% 10.59/10.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 10.59/10.85 inference(rewrite,[status(thm)],[])).
% 10.59/10.85 tff(24867,plain,
% 10.59/10.85 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 10.59/10.85 inference(rewrite,[status(thm)],[])).
% 10.59/10.85 tff(24868,plain,
% 10.59/10.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 10.59/10.85 inference(monotonicity,[status(thm)],[24867])).
% 10.59/10.85 tff(24869,plain,
% 10.59/10.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 10.59/10.85 inference(transitivity,[status(thm)],[24868, 24866])).
% 10.59/10.85 tff(24870,plain,
% 10.59/10.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 10.59/10.85 inference(quant_inst,[status(thm)],[])).
% 10.59/10.85 tff(24871,plain,
% 10.59/10.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 10.59/10.85 inference(modus_ponens,[status(thm)],[24870, 24869])).
% 10.59/10.85 tff(24872,plain,
% 10.59/10.85 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[24871, 391, 90, 1686, 24865])).
% 10.59/10.85 tff(24873,plain,
% 10.59/10.85 ($false),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[24872, 24863])).
% 10.59/10.85 tff(24874,plain,((~r(s(s(z)), s(z))) | (~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = s(z))) | (~r(z, s(s(s(z))))) | (s(s(z)) = s(s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.59/10.85 tff(24875,plain,
% 10.59/10.85 (~r(s(s(z)), s(z))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[24874, 24769, 90, 23965, 410, 23969, 133, 24716, 3563, 169, 24785, 24777, 1216, 4028, 168, 127])).
% 10.59/10.85 tff(24876,plain,
% 10.59/10.85 (b(s(s(z)), s(z))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[3778, 24875])).
% 10.59/10.85 tff(24877,plain,
% 10.59/10.85 (b(s(elem!1), elem!1)),
% 10.59/10.85 inference(modus_ponens,[status(thm)],[24876, 24725])).
% 10.59/10.85 tff(24878,plain,
% 10.59/10.85 (~b(s(s(elem!1)), elem!1)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[5286, 24877, 24769, 133, 23983])).
% 10.59/10.85 tff(24879,plain,
% 10.59/10.85 (r(s(s(elem!1)), elem!1)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[872, 24878, 8597])).
% 10.59/10.85 tff(24880,plain,
% 10.59/10.85 (r(s(s(elem!1)), s(z))),
% 10.59/10.85 inference(modus_ponens,[status(thm)],[24879, 24701])).
% 10.59/10.85 tff(24881,plain,
% 10.59/10.85 (r(s(z), z)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[24157, 24877, 723, 169, 90, 23965, 1216, 10782, 11174, 232, 4028, 168, 127, 24706, 133])).
% 10.59/10.85 tff(24882,plain,
% 10.59/10.85 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[4039, 24879, 4028, 168, 127])).
% 10.59/10.85 tff(24883,plain,
% 10.59/10.85 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[1370, 24882, 24716])).
% 10.59/10.85 tff(24884,plain,
% 10.59/10.85 (~b(s(s(elem!1)), z)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[13177, 24883, 10782, 24164])).
% 10.59/10.85 tff(24885,plain,
% 10.59/10.85 (r(s(s(elem!1)), z)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[2629, 24884])).
% 10.59/10.85 tff(24886,plain,
% 10.59/10.85 (~r(s(s(elem!1)), s(z))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[2621, 24885, 24708, 24881])).
% 10.59/10.85 tff(24887,plain,
% 10.59/10.85 ($false),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[24886, 24880])).
% 10.59/10.85 tff(24888,plain,((~b(z, elem!1)) | (~(elem!1 = s(z))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.85 tff(24889,plain,
% 10.59/10.85 (~b(z, elem!1)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[24888, 23907, 23929, 24696, 9, 23849, 90, 2913, 24700, 24698, 24691, 11173, 53])).
% 10.59/10.85 tff(24890,plain,
% 10.59/10.85 (r(z, elem!1)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[141, 24889, 23931])).
% 10.59/10.85 tff(24891,plain,
% 10.59/10.85 (r(z, s(z))),
% 10.59/10.85 inference(modus_ponens,[status(thm)],[24890, 24697])).
% 10.59/10.85 tff(24892,plain,
% 10.59/10.85 (~r(s(elem!1), elem!1)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[541, 530, 1628, 411])).
% 10.59/10.85 tff(24893,plain,
% 10.59/10.85 (~b(s(s(z)), s(z))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[24540, 530, 4028, 127, 812, 722, 10682, 168])).
% 10.59/10.85 tff(24894,plain,
% 10.59/10.85 (r(s(s(z)), s(z))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[3778, 24893])).
% 10.59/10.85 tff(24895,plain,
% 10.59/10.85 ($false),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[9729, 24894, 24892, 812])).
% 10.59/10.85 tff(24896,plain,((~r(elem!1, z)) | (~(s(z) = elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(z))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.59/10.85 tff(24897,plain,
% 10.59/10.85 (~r(elem!1, z)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[24896, 23908, 24694, 24890, 23929, 9, 24891, 10782, 24696])).
% 10.59/10.85 tff(24898,plain,
% 10.59/10.85 (b(elem!1, z)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[526, 24897, 23930])).
% 10.59/10.85 tff(24899,plain,
% 10.59/10.85 (~r(s(s(z)), s(z))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[10610, 24891, 24693, 2913])).
% 10.59/10.85 tff(24900,plain,
% 10.59/10.85 (b(s(s(z)), s(z))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[3778, 24899])).
% 10.59/10.85 tff(24901,plain,
% 10.59/10.85 (s(z) = elem!1),
% 10.59/10.85 inference(symmetry,[status(thm)],[23907])).
% 10.59/10.85 tff(24902,plain,
% 10.59/10.85 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 10.59/10.85 inference(monotonicity,[status(thm)],[24901])).
% 10.59/10.85 tff(24903,plain,
% 10.59/10.85 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 10.59/10.85 inference(monotonicity,[status(thm)],[24902])).
% 10.59/10.85 tff(24904,plain,
% 10.59/10.85 (~(s(s(elem!1)) = elem!1)),
% 10.59/10.85 inference(modus_ponens,[status(thm)],[357, 24903])).
% 10.59/10.85 tff(24905,plain,
% 10.59/10.85 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 10.59/10.85 inference(monotonicity,[status(thm)],[23907])).
% 10.59/10.85 tff(24906,plain,
% 10.59/10.85 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 10.59/10.85 inference(symmetry,[status(thm)],[24905])).
% 10.59/10.85 tff(24907,plain,
% 10.59/10.85 (r(elem!1, s(s(s(s(z)))))),
% 10.59/10.85 inference(modus_ponens,[status(thm)],[2913, 24906])).
% 10.59/10.85 tff(24908,plain,
% 10.59/10.85 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 10.59/10.85 inference(monotonicity,[status(thm)],[23921])).
% 10.59/10.85 tff(24909,plain,
% 10.59/10.85 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 10.59/10.85 inference(symmetry,[status(thm)],[24908])).
% 10.59/10.85 tff(24910,plain,
% 10.59/10.85 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 10.59/10.85 inference(monotonicity,[status(thm)],[23925])).
% 10.59/10.85 tff(24911,plain,
% 10.59/10.85 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 10.59/10.85 inference(symmetry,[status(thm)],[24910])).
% 10.59/10.85 tff(24912,plain,
% 10.59/10.85 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 10.59/10.85 inference(transitivity,[status(thm)],[24911, 24909])).
% 10.59/10.85 tff(24913,plain,
% 10.59/10.85 (b(s(s(s(elem!1))), s(elem!1))),
% 10.59/10.85 inference(modus_ponens,[status(thm)],[24691, 24912])).
% 10.59/10.85 tff(24914,plain,
% 10.59/10.85 (~r(z, s(s(elem!1)))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[3014, 364, 2032, 411])).
% 10.59/10.85 tff(24915,plain,
% 10.59/10.85 (~b(z, s(s(elem!1)))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[24748, 364, 10682, 4028, 1101, 127, 297, 168])).
% 10.59/10.85 tff(24916,plain,
% 10.59/10.85 ($false),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[324, 24915, 24914])).
% 10.59/10.85 tff(24917,plain,((~r(s(s(elem!1)), elem!1)) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), elem!1) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.85 tff(24918,plain,
% 10.59/10.85 (~r(s(s(elem!1)), elem!1)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[24917, 23929, 10782, 24913, 9, 23935, 24696, 24907, 24890])).
% 10.59/10.85 tff(24919,plain,
% 10.59/10.85 (b(s(s(elem!1)), elem!1)),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[872, 24918, 24904])).
% 10.59/10.85 tff(24920,plain,
% 10.59/10.85 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 10.59/10.85 inference(monotonicity,[status(thm)],[24091])).
% 10.59/10.85 tff(24921,plain,
% 10.59/10.85 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 10.59/10.85 inference(symmetry,[status(thm)],[24920])).
% 10.59/10.85 tff(24922,plain,
% 10.59/10.85 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 10.59/10.85 inference(monotonicity,[status(thm)],[10937])).
% 10.59/10.85 tff(24923,plain,
% 10.59/10.85 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 10.59/10.85 inference(transitivity,[status(thm)],[24922, 24921])).
% 10.59/10.85 tff(24924,plain,
% 10.59/10.85 (r(s(s(s(s(z)))), s(s(s(z))))),
% 10.59/10.85 inference(modus_ponens,[status(thm)],[327, 24923])).
% 10.59/10.85 tff(24925,plain,
% 10.59/10.85 (b(s(s(s(z))), s(z))),
% 10.59/10.85 inference(unit_resolution,[status(thm)],[16036, 973, 8598])).
% 10.59/10.85 tff(24926,plain,
% 10.59/10.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 10.59/10.85 inference(rewrite,[status(thm)],[])).
% 10.59/10.85 tff(24927,plain,
% 10.59/10.85 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 10.59/10.85 inference(rewrite,[status(thm)],[])).
% 10.59/10.85 tff(24928,plain,
% 10.59/10.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 10.59/10.86 inference(monotonicity,[status(thm)],[24927])).
% 10.59/10.86 tff(24929,plain,
% 10.59/10.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 10.59/10.86 inference(transitivity,[status(thm)],[24928, 24926])).
% 10.59/10.86 tff(24930,plain,
% 10.59/10.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 10.59/10.86 inference(quant_inst,[status(thm)],[])).
% 10.59/10.86 tff(24931,plain,
% 10.59/10.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 10.59/10.86 inference(modus_ponens,[status(thm)],[24930, 24929])).
% 10.59/10.86 tff(24932,plain,
% 10.59/10.86 (~b(s(s(s(z))), s(s(z)))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[24931, 391, 1686, 1233, 24793, 24925])).
% 10.59/10.86 tff(24933,plain,
% 10.59/10.86 (r(s(s(s(z))), s(s(z)))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[21897, 42, 24932, 21881])).
% 10.59/10.86 tff(24934,plain,
% 10.59/10.86 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 10.59/10.86 inference(monotonicity,[status(thm)],[24091])).
% 10.59/10.86 tff(24935,plain,
% 10.59/10.86 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 10.59/10.86 inference(symmetry,[status(thm)],[24934])).
% 10.59/10.86 tff(24936,plain,
% 10.59/10.86 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 10.59/10.86 inference(transitivity,[status(thm)],[15599, 24935])).
% 10.59/10.86 tff(24937,plain,
% 10.59/10.86 (b(s(elem!1), elem!1)),
% 10.59/10.86 inference(modus_ponens,[status(thm)],[1233, 24725])).
% 10.59/10.86 tff(24938,plain,
% 10.59/10.86 (~b(s(s(elem!1)), s(elem!1))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[17814, 24937, 10682, 973, 665])).
% 10.59/10.86 tff(24939,plain,
% 10.59/10.86 (r(s(s(elem!1)), s(elem!1))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[1135, 24938, 285])).
% 10.59/10.86 tff(24940,plain,
% 10.59/10.86 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 10.59/10.86 inference(monotonicity,[status(thm)],[1550, 24079])).
% 10.59/10.86 tff(24941,plain,
% 10.59/10.86 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 10.59/10.86 inference(symmetry,[status(thm)],[24940])).
% 10.59/10.86 tff(24942,plain,
% 10.59/10.86 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 10.59/10.86 inference(monotonicity,[status(thm)],[24941])).
% 10.59/10.86 tff(24943,plain,
% 10.59/10.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 10.59/10.86 inference(rewrite,[status(thm)],[])).
% 10.59/10.86 tff(24944,plain,
% 10.59/10.86 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 10.59/10.86 inference(rewrite,[status(thm)],[])).
% 10.59/10.86 tff(24945,plain,
% 10.59/10.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))))),
% 10.59/10.86 inference(monotonicity,[status(thm)],[24944])).
% 10.59/10.86 tff(24946,plain,
% 10.59/10.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 10.59/10.86 inference(transitivity,[status(thm)],[24945, 24943])).
% 10.59/10.86 tff(24947,plain,
% 10.59/10.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 10.59/10.86 inference(quant_inst,[status(thm)],[])).
% 10.59/10.86 tff(24948,plain,
% 10.59/10.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))),
% 10.59/10.86 inference(modus_ponens,[status(thm)],[24947, 24946])).
% 10.59/10.86 tff(24949,plain,
% 10.59/10.86 (~b(s(s(z)), s(s(s(z))))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[24948, 391, 1686, 1233, 24793, 24925])).
% 10.59/10.86 tff(24950,plain,
% 10.59/10.86 (~b(s(elem!1), s(s(elem!1)))),
% 10.59/10.86 inference(modus_ponens,[status(thm)],[24949, 24942])).
% 10.59/10.86 tff(24951,plain,
% 10.59/10.86 (r(s(elem!1), s(s(elem!1)))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[8644, 24950, 8611])).
% 10.59/10.86 tff(24952,plain,
% 10.59/10.86 (~r(s(elem!1), s(s(s(elem!1))))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[8653, 24951, 327, 24939])).
% 10.59/10.86 tff(24953,plain,
% 10.59/10.86 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[3614, 24952, 8598])).
% 10.59/10.86 tff(24954,plain,
% 10.59/10.86 (b(s(s(z)), s(s(s(s(z)))))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[3652, 24953])).
% 10.59/10.86 tff(24955,plain,
% 10.59/10.86 (~b(z, s(s(z)))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[15550, 24954, 1686, 3563])).
% 10.59/10.86 tff(24956,plain,
% 10.59/10.86 (~b(z, s(elem!1))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[8527, 24955, 8598])).
% 10.59/10.86 tff(24957,plain,
% 10.59/10.86 (r(z, s(elem!1))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[566, 24956])).
% 10.59/10.86 tff(24958,plain,
% 10.59/10.86 (~r(z, s(s(elem!1)))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[2309, 24957, 1628, 24939])).
% 10.59/10.86 tff(24959,plain,
% 10.59/10.86 (b(z, s(s(elem!1)))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[324, 24958])).
% 10.59/10.86 tff(24960,plain,
% 10.59/10.86 (~b(elem!1, s(s(elem!1)))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[7297, 24959, 973, 665])).
% 10.59/10.86 tff(24961,plain,
% 10.59/10.86 (r(elem!1, s(s(elem!1)))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[1307, 24960, 15530])).
% 10.59/10.86 tff(24962,plain,
% 10.59/10.86 (r(s(z), s(s(s(z))))),
% 10.59/10.86 inference(modus_ponens,[status(thm)],[24961, 24936])).
% 10.59/10.86 tff(24963,plain,
% 10.59/10.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 10.59/10.86 inference(rewrite,[status(thm)],[])).
% 10.59/10.86 tff(24964,plain,
% 10.59/10.86 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 10.59/10.86 inference(rewrite,[status(thm)],[])).
% 10.59/10.86 tff(24965,plain,
% 10.59/10.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 10.59/10.86 inference(monotonicity,[status(thm)],[24964])).
% 10.59/10.86 tff(24966,plain,
% 10.59/10.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 10.59/10.86 inference(transitivity,[status(thm)],[24965, 24963])).
% 10.59/10.86 tff(24967,plain,
% 10.59/10.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 10.59/10.86 inference(quant_inst,[status(thm)],[])).
% 10.59/10.86 tff(24968,plain,
% 10.59/10.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 10.59/10.86 inference(modus_ponens,[status(thm)],[24967, 24966])).
% 10.59/10.86 tff(24969,plain,
% 10.59/10.86 ($false),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[24968, 194, 723, 24962, 24933, 24924])).
% 10.59/10.86 tff(24970,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (s(s(s(z))) = s(s(z))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.86 tff(24971,plain,
% 10.59/10.86 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[24970, 24919, 23921, 23907, 24900, 24898, 24694, 23910, 24691, 23849, 23952, 23949, 23934, 10782])).
% 10.59/10.86 tff(24972,plain,
% 10.59/10.86 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[1370, 24971, 23935])).
% 10.59/10.86 tff(24973,plain,
% 10.59/10.86 (~b(s(s(elem!1)), z)),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[13177, 24972, 10782, 23924])).
% 10.59/10.86 tff(24974,plain,
% 10.59/10.86 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 10.59/10.86 inference(monotonicity,[status(thm)],[23907])).
% 10.59/10.86 tff(24975,plain,
% 10.59/10.86 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 10.59/10.86 inference(symmetry,[status(thm)],[24974])).
% 10.59/10.86 tff(24976,plain,
% 10.59/10.86 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 10.59/10.86 inference(monotonicity,[status(thm)],[23925])).
% 10.59/10.86 tff(24977,plain,
% 10.59/10.86 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 10.59/10.86 inference(symmetry,[status(thm)],[24976])).
% 10.59/10.86 tff(24978,plain,
% 10.59/10.86 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 10.59/10.86 inference(transitivity,[status(thm)],[24977, 24975])).
% 10.59/10.86 tff(24979,plain,
% 10.59/10.86 (b(s(elem!1), elem!1)),
% 10.59/10.86 inference(modus_ponens,[status(thm)],[24900, 24978])).
% 10.59/10.86 tff(24980,plain,
% 10.59/10.86 (~b(s(s(elem!1)), s(elem!1))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[17814, 24919, 10782, 24979, 24898])).
% 10.59/10.86 tff(24981,plain,
% 10.59/10.86 (r(s(s(elem!1)), s(elem!1))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[1135, 24980, 23934])).
% 10.59/10.86 tff(24982,plain,
% 10.59/10.86 (~r(s(s(elem!1)), z)),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[24417, 24981, 24694, 24890])).
% 10.59/10.86 tff(24983,plain,
% 10.59/10.86 ($false),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[2629, 24982, 24973])).
% 10.59/10.86 tff(24984,plain,(b(elem!1, s(z)) | (~b(s(s(s(s(z)))), z)) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1)))) | b(s(z), s(s(s(s(z))))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.86 tff(24985,plain,
% 10.59/10.86 (b(elem!1, s(z))),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[24984, 11173, 90, 53, 2881, 1])).
% 10.59/10.86 tff(24986,plain,
% 10.59/10.86 ($false),
% 10.59/10.86 inference(unit_resolution,[status(thm)],[24985, 23869])).
% 10.59/10.86 tff(24987,plain,(b(s(s(s(elem!1))), s(z)) | (~b(s(s(s(s(z)))), z)) | r(z, s(s(s(elem!1)))) | b(s(z), s(s(s(s(z))))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.86 tff(24988,plain,
% 10.59/10.86 (elem!1 = s(s(s(elem!1)))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[24987, 22991, 90, 2881, 22986])).
% 10.59/10.87 tff(24989,plain,
% 10.59/10.87 ($false),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[129, 24988, 22988])).
% 10.59/10.87 tff(24990,plain,(r(elem!1, s(z)) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | (~r(s(z), z)) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.87 tff(24991,plain,
% 10.59/10.87 (r(elem!1, s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[24990, 1549, 2881, 181, 90, 31])).
% 10.59/10.87 tff(24992,plain,
% 10.59/10.87 (r(s(s(s(s(z)))), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[762, 720, 1549])).
% 10.59/10.87 tff(24993,plain,
% 10.59/10.87 (r(elem!1, s(s(s(s(z)))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[781, 770, 8536])).
% 10.59/10.87 tff(24994,plain,
% 10.59/10.87 ($false),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[10448, 194, 847, 24993, 24992, 1216])).
% 10.59/10.87 tff(24995,plain,((s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(s(z))))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.59/10.87 tff(24996,plain,
% 10.59/10.87 (s(s(s(s(z)))) = elem!1),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[24995, 24991, 2913, 22982, 1549])).
% 10.59/10.87 tff(24997,plain,
% 10.59/10.87 (~b(s(s(s(s(z)))), s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[11186, 24996, 31])).
% 10.59/10.87 tff(24998,plain,
% 10.59/10.87 (r(s(s(s(s(z)))), s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[749, 24997])).
% 10.59/10.87 tff(24999,plain,
% 10.59/10.87 (elem!1 = s(s(s(s(z))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[16908, 24996])).
% 10.59/10.87 tff(25000,plain,
% 10.59/10.87 (b(elem!1, z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[16358, 24999, 90])).
% 10.59/10.87 tff(25001,plain,
% 10.59/10.87 (~(s(s(s(elem!1))) = elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[1436, 24996])).
% 10.59/10.87 tff(25002,plain,
% 10.59/10.87 (~(elem!1 = s(s(s(elem!1))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[129, 25001])).
% 10.59/10.87 tff(25003,plain,
% 10.59/10.87 (~b(s(s(s(elem!1))), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[10743, 25000, 10682, 133])).
% 10.59/10.87 tff(25004,plain,
% 10.59/10.87 (~(s(z) = elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[10390, 25000, 91])).
% 10.59/10.87 tff(25005,plain,
% 10.59/10.87 (~b(elem!1, s(s(s(elem!1))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[16115, 25004, 31, 133, 10682, 664, 2913, 24991])).
% 10.59/10.87 tff(25006,plain,
% 10.59/10.87 (~r(elem!1, s(s(s(elem!1))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[10776, 838, 1216, 183])).
% 10.59/10.87 tff(25007,plain,
% 10.59/10.87 (~b(elem!1, s(s(s(elem!1))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[16115, 838, 10682, 31, 664, 133, 1216, 150])).
% 10.59/10.87 tff(25008,plain,
% 10.59/10.87 ($false),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[424, 25007, 25006, 1])).
% 10.59/10.87 tff(25009,plain,((s(z) = elem!1) | (elem!1 = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.87 tff(25010,plain,
% 10.59/10.87 (~r(s(s(s(elem!1))), s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[25009, 25004, 133, 31, 2913, 10682, 664, 25002])).
% 10.59/10.87 tff(25011,plain,
% 10.59/10.87 (b(s(s(s(elem!1))), s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[223, 25010])).
% 10.59/10.87 tff(25012,plain,
% 10.59/10.87 (r(elem!1, s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[837, 31, 15559])).
% 10.59/10.87 tff(25013,plain,
% 10.59/10.87 (~b(z, s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[15581, 168, 1526, 6124, 4028, 10682, 9])).
% 10.59/10.87 tff(25014,plain,
% 10.59/10.87 (r(z, s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[678, 25013])).
% 10.59/10.87 tff(25015,plain,
% 10.59/10.87 (~r(elem!1, s(s(s(s(z)))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[6347, 25012, 2913, 723])).
% 10.59/10.87 tff(25016,plain,
% 10.59/10.87 (elem!1 = s(s(s(s(z))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[781, 25015, 8536])).
% 10.59/10.87 tff(25017,plain,
% 10.59/10.87 (s(s(s(s(z)))) = elem!1),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[769, 25016])).
% 10.59/10.87 tff(25018,plain,
% 10.59/10.87 (~b(s(z), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[6252, 25017, 2881])).
% 10.59/10.87 tff(25019,plain,
% 10.59/10.87 (r(s(z), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[632, 25018, 4018])).
% 10.59/10.87 tff(25020,plain,
% 10.59/10.87 (~r(z, elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[14725, 25019, 25014, 25012])).
% 10.59/10.87 tff(25021,plain,
% 10.59/10.87 (b(z, elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[141, 25020, 24023])).
% 10.59/10.87 tff(25022,plain,
% 10.59/10.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[717, 25017])).
% 10.59/10.87 tff(25023,plain,
% 10.59/10.87 (~(s(s(elem!1)) = s(elem!1))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[2279, 25022])).
% 10.59/10.87 tff(25024,plain,
% 10.59/10.87 (~r(s(z), s(s(s(elem!1))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[5246, 5236, 233, 4018, 31])).
% 10.59/10.87 tff(25025,plain,
% 10.59/10.87 (b(s(z), s(s(s(elem!1))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[247, 25024])).
% 10.59/10.87 tff(25026,plain,
% 10.59/10.87 (~b(s(s(s(elem!1))), z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[11303, 25025, 10682, 590])).
% 10.59/10.87 tff(25027,plain,
% 10.59/10.87 (~r(elem!1, s(s(s(s(z)))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[6362, 590, 1526, 4631, 133, 25012, 1216])).
% 10.59/10.87 tff(25028,plain,
% 10.59/10.87 (elem!1 = s(s(s(s(z))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[781, 25027, 8536])).
% 10.59/10.87 tff(25029,plain,
% 10.59/10.87 (s(s(s(s(z)))) = elem!1),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[769, 25028])).
% 10.59/10.87 tff(25030,plain,
% 10.59/10.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[717, 25029])).
% 10.59/10.87 tff(25031,plain,
% 10.59/10.87 (~(s(s(elem!1)) = elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[451, 25030])).
% 10.59/10.87 tff(25032,plain,
% 10.59/10.87 ($false),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[12783, 25031, 25026, 4018, 665, 121, 133, 168, 590])).
% 10.59/10.87 tff(25033,plain,((~b(s(z), z)) | (~b(elem!1, z)) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | b(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | b(elem!1, s(z)) | b(elem!1, s(s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.87 tff(25034,plain,
% 10.59/10.87 (~b(s(z), z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[25033, 25021, 24024, 665, 168, 10682, 4097, 31, 8536, 1526, 2913])).
% 10.59/10.87 tff(25035,plain,
% 10.59/10.87 (r(s(z), z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[180, 25034])).
% 10.59/10.87 tff(25036,plain,
% 10.59/10.87 (~r(elem!1, z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[17266, 25035, 25014, 25012])).
% 10.59/10.87 tff(25037,plain,
% 10.59/10.87 (b(s(elem!1), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[13690, 25036, 10682, 4018, 25021, 665, 168, 24024, 4028])).
% 10.59/10.87 tff(25038,plain,
% 10.59/10.87 (~(s(s(elem!1)) = elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[451, 25022])).
% 10.59/10.87 tff(25039,plain,
% 10.59/10.87 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[287, 25023])).
% 10.59/10.87 tff(25040,plain,
% 10.59/10.87 (~r(s(s(elem!1)), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[12954, 25035, 10682, 4028, 1, 25019, 168, 25039])).
% 10.59/10.87 tff(25041,plain,
% 10.59/10.87 (b(s(s(elem!1)), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[872, 25040, 25038])).
% 10.59/10.87 tff(25042,plain,
% 10.59/10.87 ($false),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[5286, 25041, 25037, 665, 25023, 25021])).
% 10.59/10.87 tff(25043,plain,(b(elem!1, s(z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.87 tff(25044,plain,
% 10.59/10.87 ($false),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[25043, 25011, 25005, 31, 10682, 2881, 22982, 25003, 25002, 25000, 24998])).
% 10.59/10.87 tff(25045,plain,(b(s(s(s(s(z)))), elem!1) | b(elem!1, s(z)) | (~b(z, s(s(s(elem!1))))) | b(s(z), s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(z))) | b(s(z), z) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.87 tff(25046,plain,
% 10.59/10.87 (b(s(s(s(s(z)))), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[25045, 22965, 22898, 31, 133, 22903, 91, 88])).
% 10.59/10.87 tff(25047,plain,
% 10.59/10.87 (~(elem!1 = s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[11318, 10644, 2, 676])).
% 10.59/10.87 tff(25048,plain,
% 10.59/10.87 (r(elem!1, s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[837, 25047, 31])).
% 10.59/10.87 tff(25049,plain,
% 10.59/10.87 (~r(elem!1, z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[17062, 25048, 182, 10645])).
% 10.59/10.87 tff(25050,plain,
% 10.59/10.87 (b(elem!1, z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[526, 25049, 2])).
% 10.59/10.87 tff(25051,plain,
% 10.59/10.87 (~b(s(s(s(elem!1))), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[10743, 25050, 22924, 133])).
% 10.59/10.87 tff(25052,plain,
% 10.59/10.87 (~(s(z) = elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[1495, 25047])).
% 10.59/10.87 tff(25053,plain,
% 10.59/10.87 (b(s(elem!1), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[14657, 25051, 133, 22924, 25049, 25052, 2])).
% 10.59/10.87 tff(25054,plain,
% 10.59/10.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[14662, 25053, 25051])).
% 10.59/10.87 tff(25055,plain,
% 10.59/10.87 (~(s(s(elem!1)) = s(elem!1))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[2279, 25054])).
% 10.59/10.87 tff(25056,plain,
% 10.59/10.87 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[287, 25055])).
% 10.59/10.87 tff(25057,plain,
% 10.59/10.87 (~b(s(z), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[12158, 25050, 133, 1652, 182])).
% 10.59/10.87 tff(25058,plain,
% 10.59/10.87 (r(s(z), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[632, 25057, 25052])).
% 10.59/10.87 tff(25059,plain,
% 10.59/10.87 (~b(s(z), s(s(s(s(z)))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[22964, 676, 182, 90, 2, 31, 133])).
% 10.59/10.87 tff(25060,plain,
% 10.59/10.87 (r(s(z), s(s(s(s(z)))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[1230, 25059])).
% 10.59/10.87 tff(25061,plain,
% 10.59/10.87 (~b(elem!1, s(s(s(elem!1))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[16115, 25048, 31, 133, 22924, 22903, 25060, 25052])).
% 10.59/10.87 tff(25062,plain,
% 10.59/10.87 (~(s(s(elem!1)) = elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[451, 25054])).
% 10.59/10.87 tff(25063,plain,
% 10.59/10.87 (~b(s(s(elem!1)), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[5286, 25055, 133, 25050, 25053])).
% 10.59/10.87 tff(25064,plain,
% 10.59/10.87 (r(s(s(elem!1)), elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[872, 25063, 25062])).
% 10.59/10.87 tff(25065,plain,
% 10.59/10.87 (elem!1 = s(s(s(elem!1)))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[12954, 25064, 22924, 25061, 25058, 182, 25051, 25056])).
% 10.59/10.87 tff(25066,plain,
% 10.59/10.87 (s(s(s(elem!1))) = elem!1),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[129, 25065])).
% 10.59/10.87 tff(25067,plain,
% 10.59/10.87 (~b(s(s(s(elem!1))), s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[8400, 25066, 31])).
% 10.59/10.87 tff(25068,plain,
% 10.59/10.87 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[2849, 25052])).
% 10.59/10.87 tff(25069,plain,
% 10.59/10.87 (b(s(s(s(elem!1))), z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[9553, 25065, 25050])).
% 10.59/10.87 tff(25070,plain,
% 10.59/10.87 (~r(s(s(s(elem!1))), s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[23013, 25069, 90, 22924, 25060, 25068])).
% 10.59/10.87 tff(25071,plain,
% 10.59/10.87 ($false),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[223, 25070, 25067])).
% 10.59/10.87 tff(25072,plain,(b(z, s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | b(elem!1, s(z)) | (~r(s(z), z)) | (~b(z, elem!1)) | (elem!1 = z) | (~b(s(s(s(s(z)))), elem!1)) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.87 tff(25073,plain,
% 10.59/10.87 (b(z, s(s(s(s(z)))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[25072, 25046, 31, 181, 133, 2, 88, 676])).
% 10.59/10.87 tff(25074,plain,
% 10.59/10.87 (~b(elem!1, z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[4246, 25073, 88, 25046])).
% 10.59/10.87 tff(25075,plain,
% 10.59/10.87 (~b(elem!1, z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[4246, 1686, 88, 1652])).
% 10.59/10.87 tff(25076,plain,
% 10.59/10.87 (r(elem!1, z)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[526, 25075, 2])).
% 10.59/10.87 tff(25077,plain,
% 10.59/10.87 (~b(elem!1, s(s(s(s(z)))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[22981, 1686, 88, 133])).
% 10.59/10.87 tff(25078,plain,
% 10.59/10.87 (r(elem!1, s(s(s(s(z)))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[781, 25077, 8922])).
% 10.59/10.87 tff(25079,plain,
% 10.59/10.87 (~r(elem!1, s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[6347, 10646, 1216, 2032])).
% 10.59/10.87 tff(25080,plain,
% 10.59/10.87 (~(s(z) = elem!1)),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[9614, 9024, 1652])).
% 10.59/10.87 tff(25081,plain,
% 10.59/10.87 (~(elem!1 = s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[172, 25080])).
% 10.59/10.87 tff(25082,plain,
% 10.59/10.87 ($false),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[837, 25081, 25079, 31])).
% 10.59/10.87 tff(25083,plain,(b(s(s(s(s(z)))), s(z)) | b(elem!1, s(z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.87 tff(25084,plain,
% 10.59/10.87 (b(s(s(s(s(z)))), s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[25083, 25078, 2913, 31, 1652])).
% 10.59/10.87 tff(25085,plain,
% 10.59/10.87 (~r(z, s(s(s(elem!1))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[5941, 838, 182, 530])).
% 10.59/10.87 tff(25086,plain,
% 10.59/10.87 (~b(elem!1, s(s(s(elem!1))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[16115, 838, 31, 133, 10682, 664, 2913, 150])).
% 10.59/10.87 tff(25087,plain,
% 10.59/10.87 (b(s(s(s(elem!1))), s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[24987, 2881, 53, 88, 1])).
% 10.59/10.87 tff(25088,plain,
% 10.59/10.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 10.59/10.87 inference(rewrite,[status(thm)],[])).
% 10.59/10.87 tff(25089,plain,
% 10.59/10.87 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 10.59/10.87 inference(rewrite,[status(thm)],[])).
% 10.59/10.87 tff(25090,plain,
% 10.59/10.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))))),
% 10.59/10.87 inference(monotonicity,[status(thm)],[25089])).
% 10.59/10.87 tff(25091,plain,
% 10.59/10.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)))),
% 10.59/10.87 inference(transitivity,[status(thm)],[25090, 25088])).
% 10.59/10.87 tff(25092,plain,
% 10.59/10.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 10.59/10.87 inference(quant_inst,[status(thm)],[])).
% 10.59/10.87 tff(25093,plain,
% 10.59/10.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))),
% 10.59/10.87 inference(modus_ponens,[status(thm)],[25092, 25091])).
% 10.59/10.87 tff(25094,plain,
% 10.59/10.87 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[25093, 391, 10682, 1526, 90, 1235])).
% 10.59/10.87 tff(25095,plain,
% 10.59/10.87 (r(s(s(z)), s(s(s(s(z)))))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[3652, 25094])).
% 10.59/10.87 tff(25096,plain,
% 10.59/10.87 (~r(s(s(z)), s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[14395, 25095, 1216, 1697])).
% 10.59/10.87 tff(25097,plain,
% 10.59/10.87 (b(s(s(z)), s(z))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[3778, 25096])).
% 10.59/10.87 tff(25098,plain,
% 10.59/10.87 (~r(s(z), s(s(z)))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[23375, 194, 25095, 1216, 1697])).
% 10.59/10.87 tff(25099,plain,
% 10.59/10.87 (b(s(z), s(s(z)))),
% 10.59/10.87 inference(unit_resolution,[status(thm)],[1788, 25098])).
% 10.59/10.87 tff(25100,plain,
% 10.59/10.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.59/10.88 inference(rewrite,[status(thm)],[])).
% 10.59/10.88 tff(25101,plain,
% 10.59/10.88 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.59/10.88 inference(rewrite,[status(thm)],[])).
% 10.59/10.88 tff(25102,plain,
% 10.59/10.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 10.59/10.88 inference(monotonicity,[status(thm)],[25101])).
% 10.59/10.88 tff(25103,plain,
% 10.59/10.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.59/10.88 inference(transitivity,[status(thm)],[25102, 25100])).
% 10.59/10.88 tff(25104,plain,
% 10.59/10.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.59/10.88 inference(quant_inst,[status(thm)],[])).
% 10.59/10.88 tff(25105,plain,
% 10.59/10.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 10.59/10.88 inference(modus_ponens,[status(thm)],[25104, 25103])).
% 10.59/10.88 tff(25106,plain,
% 10.59/10.88 (~b(s(s(s(elem!1))), s(s(z)))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[25105, 391, 1526, 1235, 25099, 25097])).
% 10.59/10.88 tff(25107,plain,
% 10.59/10.88 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[10713, 42, 25106])).
% 10.59/10.88 tff(25108,plain,
% 10.59/10.88 (r(s(s(s(elem!1))), s(s(z)))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[25107, 10703])).
% 10.59/10.88 tff(25109,plain,
% 10.59/10.88 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[17508, 194, 25095, 1697, 25108])).
% 10.59/10.88 tff(25110,plain,
% 10.59/10.88 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[17519, 194, 25095, 1697, 25108])).
% 10.59/10.88 tff(25111,plain,
% 10.59/10.88 ($false),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[23863, 25110, 25109, 90, 10682, 3843])).
% 10.59/10.88 tff(25112,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.88 tff(25113,plain,
% 10.59/10.88 (~b(s(s(z)), z)),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[25112, 1697, 10682, 3843, 90, 1526, 1216])).
% 10.59/10.88 tff(25114,plain,
% 10.59/10.88 (r(s(s(z)), z)),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[1211, 25113])).
% 10.59/10.88 tff(25115,plain,
% 10.59/10.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.59/10.88 inference(rewrite,[status(thm)],[])).
% 10.59/10.88 tff(25116,plain,
% 10.59/10.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.59/10.88 inference(quant_inst,[status(thm)],[])).
% 10.59/10.88 tff(25117,plain,
% 10.59/10.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 10.59/10.88 inference(modus_ponens,[status(thm)],[25116, 25115])).
% 10.59/10.88 tff(25118,plain,
% 10.59/10.88 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[25117, 194, 3557, 1697, 11543])).
% 10.59/10.88 tff(25119,plain,
% 10.59/10.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.59/10.88 inference(rewrite,[status(thm)],[])).
% 10.59/10.88 tff(25120,plain,
% 10.59/10.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.59/10.88 inference(quant_inst,[status(thm)],[])).
% 10.59/10.88 tff(25121,plain,
% 10.59/10.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.59/10.88 inference(modus_ponens,[status(thm)],[25120, 25119])).
% 10.59/10.88 tff(25122,plain,
% 10.59/10.88 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[25121, 194, 3557, 1697, 11543])).
% 10.59/10.88 tff(25123,plain,
% 10.59/10.88 ($false),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[23863, 25122, 25118, 90, 10682, 3843])).
% 10.59/10.88 tff(25124,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.88 tff(25125,plain,
% 10.59/10.88 (~r(s(s(s(elem!1))), s(s(z)))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[25124, 25114, 10682, 3843, 90, 1697])).
% 10.59/10.88 tff(25126,plain,
% 10.59/10.88 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[10713, 42, 25125])).
% 10.59/10.88 tff(25127,plain,
% 10.59/10.88 (b(s(s(s(elem!1))), s(s(z)))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[25126, 10703])).
% 10.59/10.88 tff(25128,plain,
% 10.59/10.88 (~r(s(z), s(s(z)))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[11508, 25114, 1216, 1697])).
% 10.59/10.88 tff(25129,plain,
% 10.59/10.88 (b(s(z), s(s(z)))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[1788, 25128])).
% 10.59/10.88 tff(25130,plain,
% 10.59/10.88 (~b(s(s(z)), s(z))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[19018, 25129, 1526, 25127])).
% 10.59/10.88 tff(25131,plain,
% 10.59/10.88 (r(s(s(z)), s(z))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[3778, 25130])).
% 10.59/10.88 tff(25132,plain,
% 10.59/10.88 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[14395, 25131, 1216, 1697])).
% 10.59/10.88 tff(25133,plain,
% 10.59/10.88 (b(s(s(z)), s(s(s(s(z)))))),
% 10.59/10.88 inference(unit_resolution,[status(thm)],[3652, 25132])).
% 10.59/10.88 tff(25134,plain,
% 10.59/10.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.59/10.89 inference(rewrite,[status(thm)],[])).
% 10.59/10.89 tff(25135,plain,
% 10.59/10.89 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.59/10.89 inference(rewrite,[status(thm)],[])).
% 10.59/10.89 tff(25136,plain,
% 10.59/10.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 10.59/10.89 inference(monotonicity,[status(thm)],[25135])).
% 10.59/10.89 tff(25137,plain,
% 10.59/10.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.59/10.89 inference(transitivity,[status(thm)],[25136, 25134])).
% 10.59/10.89 tff(25138,plain,
% 10.59/10.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 10.59/10.89 inference(quant_inst,[status(thm)],[])).
% 10.59/10.89 tff(25139,plain,
% 10.59/10.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 10.59/10.89 inference(modus_ponens,[status(thm)],[25138, 25137])).
% 10.59/10.89 tff(25140,plain,
% 10.59/10.89 ($false),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[25139, 391, 1526, 25133, 90, 25129, 25127])).
% 10.59/10.89 tff(25141,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.89 tff(25142,plain,
% 10.59/10.89 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[25141, 4631, 90, 2913, 10682, 1526])).
% 10.59/10.89 tff(25143,plain,
% 10.59/10.89 (b(s(s(s(s(z)))), s(s(z)))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[1714, 25142])).
% 10.59/10.89 tff(25144,plain,
% 10.59/10.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.59/10.89 inference(rewrite,[status(thm)],[])).
% 10.59/10.89 tff(25145,plain,
% 10.59/10.89 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.59/10.89 inference(rewrite,[status(thm)],[])).
% 10.59/10.89 tff(25146,plain,
% 10.59/10.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 10.59/10.89 inference(monotonicity,[status(thm)],[25145])).
% 10.59/10.89 tff(25147,plain,
% 10.59/10.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.59/10.89 inference(transitivity,[status(thm)],[25146, 25144])).
% 10.59/10.89 tff(25148,plain,
% 10.59/10.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 10.59/10.89 inference(quant_inst,[status(thm)],[])).
% 10.59/10.89 tff(25149,plain,
% 10.59/10.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 10.59/10.89 inference(modus_ponens,[status(thm)],[25148, 25147])).
% 10.59/10.89 tff(25150,plain,
% 10.59/10.89 ($false),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[25149, 391, 10682, 1526, 90, 1235, 3563])).
% 10.59/10.89 tff(25151,plain,((~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.59/10.89 tff(25152,plain,
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% 10.59/10.89 tff(25153,plain,
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% 10.59/10.89 inference(unit_resolution,[status(thm)],[1211, 25152])).
% 10.59/10.89 tff(25154,plain,
% 10.59/10.89 (~r(s(s(z)), s(z))),
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% 10.59/10.89 tff(25155,plain,
% 10.59/10.89 (b(s(s(z)), s(z))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[3778, 25154])).
% 10.59/10.89 tff(25156,plain,
% 10.59/10.89 (~b(z, s(z))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[15581, 168, 1526, 410, 4028, 10682, 127])).
% 10.59/10.89 tff(25157,plain,
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% 10.59/10.89 inference(unit_resolution,[status(thm)],[678, 25156])).
% 10.59/10.89 tff(25158,plain,
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% 10.59/10.89 tff(25159,plain,
% 10.59/10.89 (~r(s(s(s(elem!1))), z)),
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% 10.59/10.89 tff(25160,plain,
% 10.59/10.89 (b(s(s(s(elem!1))), z)),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[377, 25159])).
% 10.59/10.89 tff(25161,plain,
% 10.59/10.89 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[23000, 391, 25160, 10682, 90])).
% 10.59/10.89 tff(25162,plain,
% 10.59/10.89 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[4313, 42, 25161, 16830])).
% 10.59/10.89 tff(25163,plain,
% 10.59/10.89 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[23009, 391, 25160, 10682, 90])).
% 10.59/10.89 tff(25164,plain,
% 10.59/10.89 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
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% 10.59/10.89 tff(25165,plain,
% 10.59/10.89 (~r(s(z), s(s(s(elem!1))))),
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% 10.59/10.89 tff(25166,plain,
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% 10.59/10.89 tff(25167,plain,
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% 10.59/10.89 tff(25168,plain,
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% 10.59/10.89 inference(unit_resolution,[status(thm)],[180, 25167])).
% 10.59/10.89 tff(25169,plain,
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% 10.59/10.89 inference(unit_resolution,[status(thm)],[17266, 25168, 722, 25158])).
% 10.59/10.89 tff(25170,plain,
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% 10.59/10.89 inference(unit_resolution,[status(thm)],[837, 25169, 173])).
% 10.59/10.89 tff(25171,plain,
% 10.59/10.89 (~r(s(s(z)), s(z))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[10610, 722, 3557, 2913])).
% 10.59/10.89 tff(25172,plain,
% 10.59/10.89 (b(s(s(z)), s(z))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[3778, 25171])).
% 10.59/10.89 tff(25173,plain,
% 10.59/10.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 10.59/10.89 inference(rewrite,[status(thm)],[])).
% 10.59/10.89 tff(25174,plain,
% 10.59/10.89 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 10.59/10.89 inference(rewrite,[status(thm)],[])).
% 10.59/10.89 tff(25175,plain,
% 10.59/10.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1))))),
% 10.59/10.89 inference(monotonicity,[status(thm)],[25174])).
% 10.59/10.89 tff(25176,plain,
% 10.59/10.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 10.59/10.89 inference(transitivity,[status(thm)],[25175, 25173])).
% 10.59/10.89 tff(25177,plain,
% 10.59/10.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 10.59/10.89 inference(quant_inst,[status(thm)],[])).
% 10.59/10.89 tff(25178,plain,
% 10.59/10.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 10.59/10.89 inference(modus_ponens,[status(thm)],[25177, 25176])).
% 10.59/10.89 tff(25179,plain,
% 10.59/10.89 ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[25178, 194])).
% 10.59/10.89 tff(25180,plain,
% 10.59/10.89 (~r(s(z), elem!1)),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[25179, 25168, 722, 25158])).
% 10.59/10.89 tff(25181,plain,
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% 10.59/10.89 inference(unit_resolution,[status(thm)],[632, 25180, 150])).
% 10.59/10.89 tff(25182,plain,
% 10.59/10.89 (~b(s(s(s(s(z)))), s(z))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[20714, 25181, 3563, 25172, 25170])).
% 10.59/10.89 tff(25183,plain,
% 10.59/10.89 (~r(elem!1, s(s(z)))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[18602, 25158, 722, 3557])).
% 10.59/10.89 tff(25184,plain,
% 10.59/10.89 (~r(z, s(s(s(s(z)))))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[2108, 25168, 2913, 25164])).
% 10.59/10.89 tff(25185,plain,
% 10.59/10.89 (b(z, s(s(s(s(z)))))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[800, 25184])).
% 10.59/10.89 tff(25186,plain,
% 10.59/10.89 (b(s(z), s(s(z)))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[20698, 25181, 25168, 25158, 90, 25185, 484, 2881])).
% 10.59/10.89 tff(25187,plain,
% 10.59/10.89 (~b(elem!1, s(s(z)))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[10150, 25186, 25170, 25172])).
% 10.59/10.89 tff(25188,plain,
% 10.59/10.89 (elem!1 = s(s(z))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[3394, 25187, 25183])).
% 10.59/10.89 tff(25189,plain,
% 10.59/10.89 (~b(s(s(elem!1)), s(z))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[9032, 25188, 25182])).
% 10.59/10.89 tff(25190,plain,
% 10.59/10.89 (r(s(s(elem!1)), s(z))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[362, 25189])).
% 10.59/10.89 tff(25191,plain,
% 10.59/10.89 (~(s(s(elem!1)) = elem!1)),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[4206, 25190, 25169])).
% 10.59/10.89 tff(25192,plain,
% 10.59/10.89 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.59/10.89 inference(unit_resolution,[status(thm)],[6159, 25191])).
% 10.59/10.89 tff(25193,plain,
% 10.59/10.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.90 inference(rewrite,[status(thm)],[])).
% 10.69/10.90 tff(25194,plain,
% 10.69/10.90 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.90 inference(rewrite,[status(thm)],[])).
% 10.69/10.90 tff(25195,plain,
% 10.69/10.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 10.69/10.90 inference(monotonicity,[status(thm)],[25194])).
% 10.69/10.90 tff(25196,plain,
% 10.69/10.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.90 inference(transitivity,[status(thm)],[25195, 25193])).
% 10.69/10.90 tff(25197,plain,
% 10.69/10.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.69/10.90 inference(quant_inst,[status(thm)],[])).
% 10.69/10.90 tff(25198,plain,
% 10.69/10.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 10.69/10.90 inference(modus_ponens,[status(thm)],[25197, 25196])).
% 10.69/10.90 tff(25199,plain,
% 10.69/10.90 (~r(elem!1, s(s(s(s(z)))))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[25198, 194, 410, 25164, 25162])).
% 10.69/10.90 tff(25200,plain,
% 10.69/10.90 (b(elem!1, s(s(s(s(z)))))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[781, 25199, 21768])).
% 10.69/10.90 tff(25201,plain,
% 10.69/10.90 (~b(z, elem!1)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[22981, 25185, 90, 25200])).
% 10.69/10.90 tff(25202,plain,
% 10.69/10.90 (r(z, elem!1)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[141, 25201, 24023])).
% 10.69/10.90 tff(25203,plain,
% 10.69/10.90 (~(s(s(elem!1)) = s(elem!1))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[264, 25191])).
% 10.69/10.90 tff(25204,plain,
% 10.69/10.90 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[9608, 25200, 25161])).
% 10.69/10.90 tff(25205,plain,
% 10.69/10.90 (~r(s(s(elem!1)), z)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[4103, 25190, 722, 25168])).
% 10.69/10.90 tff(25206,plain,
% 10.69/10.90 (b(s(s(elem!1)), z)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[2629, 25205])).
% 10.69/10.90 tff(25207,plain,
% 10.69/10.90 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[13177, 25206, 10682, 25160])).
% 10.69/10.90 tff(25208,plain,
% 10.69/10.90 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[1370, 25207, 25204])).
% 10.69/10.90 tff(25209,plain,
% 10.69/10.90 (~r(s(s(elem!1)), elem!1)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[4039, 25208, 4028, 168, 127])).
% 10.69/10.90 tff(25210,plain,
% 10.69/10.90 (b(s(s(elem!1)), elem!1)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[872, 25209, 25191])).
% 10.69/10.90 tff(25211,plain,
% 10.69/10.90 (~b(s(z), z)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[17206, 973, 121, 2122, 285, 150, 410, 380, 10682])).
% 10.69/10.90 tff(25212,plain,
% 10.69/10.90 (r(s(z), z)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[180, 25211])).
% 10.69/10.90 tff(25213,plain,
% 10.69/10.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 10.69/10.90 inference(rewrite,[status(thm)],[])).
% 10.69/10.90 tff(25214,plain,
% 10.69/10.90 (((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 10.69/10.90 inference(rewrite,[status(thm)],[])).
% 10.69/10.90 tff(25215,plain,
% 10.69/10.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))))),
% 10.69/10.90 inference(monotonicity,[status(thm)],[25214])).
% 10.69/10.90 tff(25216,plain,
% 10.69/10.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 10.69/10.90 inference(transitivity,[status(thm)],[25215, 25213])).
% 10.69/10.90 tff(25217,plain,
% 10.69/10.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 10.69/10.90 inference(quant_inst,[status(thm)],[])).
% 10.69/10.90 tff(25218,plain,
% 10.69/10.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 10.69/10.90 inference(modus_ponens,[status(thm)],[25217, 25216])).
% 10.69/10.90 tff(25219,plain,
% 10.69/10.90 (~r(elem!1, s(z))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[25218, 194, 411, 530, 25212])).
% 10.69/10.90 tff(25220,plain,
% 10.69/10.90 ((elem!1 = s(z)) | b(elem!1, s(z))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[835, 42, 25219])).
% 10.69/10.90 tff(25221,plain,
% 10.69/10.90 (b(elem!1, s(z))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[25220, 1746])).
% 10.69/10.90 tff(25222,plain,
% 10.69/10.90 (~r(s(z), elem!1)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[627, 25212, 530, 411])).
% 10.69/10.90 tff(25223,plain,
% 10.69/10.90 (b(s(z), elem!1)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[632, 25222, 150])).
% 10.69/10.90 tff(25224,plain,
% 10.69/10.90 (~b(s(z), s(elem!1))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[17171, 391, 25223, 2122, 25221])).
% 10.69/10.90 tff(25225,plain,
% 10.69/10.90 (r(s(z), s(elem!1))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[602, 42, 121, 25224])).
% 10.69/10.90 tff(25226,plain,
% 10.69/10.90 (~b(s(elem!1), s(s(elem!1)))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[17179, 391, 973, 25223, 2122, 25221])).
% 10.69/10.90 tff(25227,plain,
% 10.69/10.90 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[1111, 42, 25226])).
% 10.69/10.90 tff(25228,plain,
% 10.69/10.90 (r(s(elem!1), s(s(elem!1)))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[25227, 1100])).
% 10.69/10.90 tff(25229,plain,
% 10.69/10.90 (~b(s(z), s(s(elem!1)))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[17188, 391, 973, 25223, 25221])).
% 10.69/10.90 tff(25230,plain,
% 10.69/10.90 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[3414, 42, 25229])).
% 10.69/10.90 tff(25231,plain,
% 10.69/10.90 (r(s(z), s(s(elem!1)))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[25230, 3404])).
% 10.69/10.90 tff(25232,plain,
% 10.69/10.90 (~b(s(s(elem!1)), s(z))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[17196, 391, 973, 25223, 25221])).
% 10.69/10.90 tff(25233,plain,
% 10.69/10.90 (r(s(s(elem!1)), s(z))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[362, 25232])).
% 10.69/10.90 tff(25234,plain,
% 10.69/10.90 ($false),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[17204, 194, 25233, 25231, 25228, 25225])).
% 10.69/10.90 tff(25235,plain,((~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (s(z) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (s(z) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.90 tff(25236,plain,
% 10.69/10.90 (~b(s(elem!1), elem!1)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[25235, 25210, 10682, 410, 150, 24024, 25160, 25158, 25203, 25202])).
% 10.69/10.90 tff(25237,plain,
% 10.69/10.90 (r(s(elem!1), elem!1)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[2168, 25236, 4597])).
% 10.69/10.90 tff(25238,plain,
% 10.69/10.90 (~r(s(s(s(elem!1))), s(elem!1))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[13054, 25237, 4028, 127, 168])).
% 10.69/10.90 tff(25239,plain,
% 10.69/10.90 (b(s(s(s(elem!1))), s(elem!1))),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[588, 25238, 25192])).
% 10.69/10.90 tff(25240,plain,
% 10.69/10.90 (~r(s(elem!1), z)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[541, 25237, 25158, 25202])).
% 10.69/10.90 tff(25241,plain,
% 10.69/10.90 (b(s(elem!1), z)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[549, 25240])).
% 10.69/10.90 tff(25242,plain,
% 10.69/10.90 ($false),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[12799, 25241, 25239, 10682, 25160])).
% 10.69/10.90 tff(25243,plain,(b(elem!1, z) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (s(z) = elem!1) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.90 tff(25244,plain,
% 10.69/10.90 (b(elem!1, z)),
% 10.69/10.90 inference(unit_resolution,[status(thm)],[25243, 168, 4028, 127, 10682, 410, 4018, 25157, 90, 2881, 25143, 25153])).
% 10.69/10.90 tff(25245,plain,
% 10.69/10.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.69/10.90 inference(rewrite,[status(thm)],[])).
% 10.69/10.90 tff(25246,plain,
% 10.69/10.90 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.69/10.90 inference(rewrite,[status(thm)],[])).
% 10.69/10.90 tff(25247,plain,
% 10.69/10.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 10.69/10.90 inference(monotonicity,[status(thm)],[25246])).
% 10.69/10.90 tff(25248,plain,
% 10.69/10.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.69/10.90 inference(transitivity,[status(thm)],[25247, 25245])).
% 10.69/10.90 tff(25249,plain,
% 10.69/10.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.69/10.90 inference(quant_inst,[status(thm)],[])).
% 10.69/10.90 tff(25250,plain,
% 10.69/10.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 10.69/10.91 inference(modus_ponens,[status(thm)],[25249, 25248])).
% 10.69/10.91 tff(25251,plain,
% 10.69/10.91 (~b(s(s(s(s(z)))), elem!1)),
% 10.69/10.91 inference(unit_resolution,[status(thm)],[25250, 391, 25244, 10682, 1526, 90])).
% 10.69/10.91 tff(25252,plain,
% 10.69/10.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.91 inference(rewrite,[status(thm)],[])).
% 10.69/10.91 tff(25253,plain,
% 10.69/10.91 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.91 inference(rewrite,[status(thm)],[])).
% 10.69/10.91 tff(25254,plain,
% 10.69/10.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 10.69/10.91 inference(monotonicity,[status(thm)],[25253])).
% 10.69/10.91 tff(25255,plain,
% 10.69/10.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.91 inference(transitivity,[status(thm)],[25254, 25252])).
% 10.69/10.91 tff(25256,plain,
% 10.69/10.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.91 inference(quant_inst,[status(thm)],[])).
% 10.69/10.91 tff(25257,plain,
% 10.69/10.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 10.69/10.91 inference(modus_ponens,[status(thm)],[25256, 25255])).
% 10.69/10.91 tff(25258,plain,
% 10.69/10.91 (~b(elem!1, s(s(s(s(z)))))),
% 10.69/10.91 inference(unit_resolution,[status(thm)],[25257, 391, 25244, 10682, 1526, 90])).
% 10.69/10.91 tff(25259,plain,
% 10.69/10.91 (~r(z, elem!1)),
% 10.69/10.91 inference(unit_resolution,[status(thm)],[19185, 194, 722, 25012, 1216])).
% 10.69/10.91 tff(25260,plain,
% 10.69/10.91 (b(z, elem!1)),
% 10.69/10.91 inference(unit_resolution,[status(thm)],[141, 25259, 24023])).
% 10.69/10.91 tff(25261,plain,
% 10.69/10.91 (~b(s(z), z)),
% 10.69/10.91 inference(unit_resolution,[status(thm)],[25033, 25260, 24024, 665, 168, 10682, 233, 31, 8536, 1526, 1216])).
% 10.69/10.91 tff(25262,plain,
% 10.69/10.91 (r(s(z), z)),
% 10.69/10.91 inference(unit_resolution,[status(thm)],[180, 25261])).
% 10.69/10.91 tff(25263,plain,
% 10.69/10.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 10.69/10.91 inference(rewrite,[status(thm)],[])).
% 10.69/10.91 tff(25264,plain,
% 10.69/10.91 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 10.69/10.91 inference(rewrite,[status(thm)],[])).
% 10.69/10.91 tff(25265,plain,
% 10.69/10.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 10.69/10.91 inference(monotonicity,[status(thm)],[25264])).
% 10.69/10.91 tff(25266,plain,
% 10.69/10.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 10.69/10.91 inference(transitivity,[status(thm)],[25265, 25263])).
% 10.69/10.91 tff(25267,plain,
% 10.69/10.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 10.69/10.91 inference(quant_inst,[status(thm)],[])).
% 10.69/10.91 tff(25268,plain,
% 10.69/10.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 10.69/10.91 inference(modus_ponens,[status(thm)],[25267, 25266])).
% 10.69/10.91 tff(25269,plain,
% 10.69/10.91 (~r(elem!1, z)),
% 10.69/10.91 inference(unit_resolution,[status(thm)],[25268, 194, 722, 25012, 1216])).
% 10.69/10.91 tff(25270,plain,
% 10.69/10.91 (b(s(elem!1), elem!1)),
% 10.69/10.91 inference(unit_resolution,[status(thm)],[13690, 25260, 10682, 4018, 25269, 665, 168, 24024, 4028])).
% 10.69/10.91 tff(25271,plain,
% 10.69/10.91 (~b(z, s(elem!1))),
% 10.69/10.91 inference(unit_resolution,[status(thm)],[6555, 25260, 665, 25270])).
% 10.69/10.91 tff(25272,plain,
% 10.69/10.91 (r(z, s(elem!1))),
% 10.69/10.91 inference(unit_resolution,[status(thm)],[566, 25271])).
% 10.69/10.91 tff(25273,plain,
% 10.69/10.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 10.69/10.91 inference(rewrite,[status(thm)],[])).
% 10.69/10.91 tff(25274,plain,
% 10.69/10.91 (((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 10.69/10.91 inference(rewrite,[status(thm)],[])).
% 10.69/10.91 tff(25275,plain,
% 10.69/10.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))))),
% 10.69/10.91 inference(monotonicity,[status(thm)],[25274])).
% 10.69/10.91 tff(25276,plain,
% 10.69/10.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 10.69/10.91 inference(transitivity,[status(thm)],[25275, 25273])).
% 10.69/10.91 tff(25277,plain,
% 10.69/10.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 10.69/10.91 inference(quant_inst,[status(thm)],[])).
% 10.69/10.91 tff(25278,plain,
% 10.69/10.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))),
% 10.69/10.92 inference(modus_ponens,[status(thm)],[25277, 25276])).
% 10.69/10.92 tff(25279,plain,
% 10.69/10.92 ($false),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25278, 194, 25272, 25262, 3557, 1747])).
% 10.69/10.92 tff(25280,plain,(b(elem!1, s(z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~b(elem!1, z)) | b(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | b(elem!1, s(s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.92 tff(25281,plain,
% 10.69/10.92 (b(elem!1, s(z))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25280, 1747, 25153, 25244, 168, 10682, 4486, 25258, 1526, 2913, 4028, 25157])).
% 10.69/10.92 tff(25282,plain,
% 10.69/10.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 10.69/10.92 inference(rewrite,[status(thm)],[])).
% 10.69/10.92 tff(25283,plain,
% 10.69/10.92 (((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 10.69/10.92 inference(rewrite,[status(thm)],[])).
% 10.69/10.92 tff(25284,plain,
% 10.69/10.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 10.69/10.92 inference(monotonicity,[status(thm)],[25283])).
% 10.69/10.92 tff(25285,plain,
% 10.69/10.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 10.69/10.92 inference(transitivity,[status(thm)],[25284, 25282])).
% 10.69/10.92 tff(25286,plain,
% 10.69/10.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 10.69/10.92 inference(quant_inst,[status(thm)],[])).
% 10.69/10.92 tff(25287,plain,
% 10.69/10.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 10.69/10.92 inference(modus_ponens,[status(thm)],[25286, 25285])).
% 10.69/10.92 tff(25288,plain,
% 10.69/10.92 (~r(s(s(s(elem!1))), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25287, 194, 411, 233, 410])).
% 10.69/10.92 tff(25289,plain,
% 10.69/10.92 (b(s(s(s(elem!1))), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[377, 25288])).
% 10.69/10.92 tff(25290,plain,
% 10.69/10.92 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[23000, 391, 25289, 10682, 90])).
% 10.69/10.92 tff(25291,plain,
% 10.69/10.92 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[4313, 42, 25290, 16830])).
% 10.69/10.92 tff(25292,plain,
% 10.69/10.92 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[23009, 391, 25289, 10682, 90])).
% 10.69/10.92 tff(25293,plain,
% 10.69/10.92 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[2853, 42, 3363, 25292])).
% 10.69/10.92 tff(25294,plain,
% 10.69/10.92 (~r(s(z), s(s(s(elem!1))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[16927, 194, 2913, 25293, 25291])).
% 10.69/10.92 tff(25295,plain,
% 10.69/10.92 (b(s(z), s(s(s(elem!1))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[247, 25294])).
% 10.69/10.92 tff(25296,plain,
% 10.69/10.92 (~b(s(z), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[11303, 25295, 10682, 25289])).
% 10.69/10.92 tff(25297,plain,
% 10.69/10.92 (r(s(z), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[180, 25296])).
% 10.69/10.92 tff(25298,plain,
% 10.69/10.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.92 inference(rewrite,[status(thm)],[])).
% 10.69/10.92 tff(25299,plain,
% 10.69/10.92 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.92 inference(rewrite,[status(thm)],[])).
% 10.69/10.92 tff(25300,plain,
% 10.69/10.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 10.69/10.92 inference(monotonicity,[status(thm)],[25299])).
% 10.69/10.92 tff(25301,plain,
% 10.69/10.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.92 inference(transitivity,[status(thm)],[25300, 25298])).
% 10.69/10.92 tff(25302,plain,
% 10.69/10.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 10.69/10.92 inference(quant_inst,[status(thm)],[])).
% 10.69/10.92 tff(25303,plain,
% 10.69/10.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 10.69/10.92 inference(modus_ponens,[status(thm)],[25302, 25301])).
% 10.69/10.92 tff(25304,plain,
% 10.69/10.92 (~r(s(s(s(s(z)))), elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25303, 194, 410, 25293, 25291])).
% 10.69/10.92 tff(25305,plain,
% 10.69/10.92 (s(s(s(s(z)))) = elem!1),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[762, 25304, 1549])).
% 10.69/10.92 tff(25306,plain,
% 10.69/10.92 (~b(s(z), elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[6252, 25305, 2881])).
% 10.69/10.92 tff(25307,plain,
% 10.69/10.92 (r(s(z), elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[632, 25306, 150])).
% 10.69/10.92 tff(25308,plain,
% 10.69/10.92 (~r(elem!1, s(elem!1))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[2582, 25307, 25297, 411])).
% 10.69/10.92 tff(25309,plain,
% 10.69/10.92 (b(elem!1, s(elem!1))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[443, 25308, 437])).
% 10.69/10.92 tff(25310,plain,
% 10.69/10.92 (~r(z, s(s(s(s(z)))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[2108, 25297, 2913, 25293])).
% 10.69/10.92 tff(25311,plain,
% 10.69/10.92 (b(z, s(s(s(s(z)))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[800, 25310])).
% 10.69/10.92 tff(25312,plain,
% 10.69/10.92 (~b(s(elem!1), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[2050, 25311, 90, 665, 25309])).
% 10.69/10.92 tff(25313,plain,
% 10.69/10.92 (~r(s(elem!1), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[1930, 25309, 721, 121, 411, 25297])).
% 10.69/10.92 tff(25314,plain,
% 10.69/10.92 ($false),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[549, 25313, 25312])).
% 10.69/10.92 tff(25315,plain,((~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (elem!1 = s(elem!1)) | (s(z) = elem!1) | b(s(z), s(s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(s(z)))), elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.92 tff(25316,plain,
% 10.69/10.92 (~r(z, elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25315, 25281, 24024, 90, 25244, 4598, 4018, 2881, 10682, 25251, 410, 4486])).
% 10.69/10.92 tff(25317,plain,
% 10.69/10.92 (b(z, elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[141, 25316, 24023])).
% 10.69/10.92 tff(25318,plain,
% 10.69/10.92 (~b(s(z), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[13285, 25317, 25244, 25281])).
% 10.69/10.92 tff(25319,plain,
% 10.69/10.92 (r(s(z), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[180, 25318])).
% 10.69/10.92 tff(25320,plain,
% 10.69/10.92 (~r(z, s(s(elem!1)))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[3787, 25319, 25153, 1747])).
% 10.69/10.92 tff(25321,plain,
% 10.69/10.92 (b(z, s(s(elem!1)))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[324, 25320])).
% 10.69/10.92 tff(25322,plain,
% 10.69/10.92 (~b(s(s(elem!1)), elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[4944, 25321, 25244, 25317])).
% 10.69/10.92 tff(25323,plain,
% 10.69/10.92 (s(s(s(elem!1))) = s(elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[15730, 25321, 10682, 410, 4028, 168, 127, 25322])).
% 10.69/10.92 tff(25324,plain,
% 10.69/10.92 (r(s(elem!1), elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[472, 25323, 4486])).
% 10.69/10.92 tff(25325,plain,
% 10.69/10.92 (s(s(elem!1)) = elem!1),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[6159, 25323])).
% 10.69/10.92 tff(25326,plain,
% 10.69/10.92 (~b(s(elem!1), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[12727, 25325, 10682, 25244, 25317, 4018, 168, 24024])).
% 10.69/10.92 tff(25327,plain,
% 10.69/10.92 (r(s(elem!1), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[549, 25326])).
% 10.69/10.92 tff(25328,plain,
% 10.69/10.92 (~(s(s(s(s(z)))) = elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[717, 25323])).
% 10.69/10.92 tff(25329,plain,
% 10.69/10.92 (~(elem!1 = s(s(s(s(z)))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[769, 25328])).
% 10.69/10.92 tff(25330,plain,
% 10.69/10.92 (r(elem!1, s(s(s(s(z)))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[781, 25329, 25258])).
% 10.69/10.92 tff(25331,plain,
% 10.69/10.92 (r(s(s(s(s(z)))), elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[762, 25328, 25251])).
% 10.69/10.92 tff(25332,plain,
% 10.69/10.92 (~r(s(z), elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[14627, 25331, 2913, 25330])).
% 10.69/10.92 tff(25333,plain,
% 10.69/10.92 (b(s(z), elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[632, 25332, 4018])).
% 10.69/10.92 tff(25334,plain,
% 10.69/10.92 ($false),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[13276, 25333, 25327, 25317, 25244, 25324, 10682, 168, 4598, 4631, 24024])).
% 10.69/10.92 tff(25335,plain,((~r(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.92 tff(25336,plain,
% 10.69/10.92 (~r(s(z), s(s(z)))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25335, 168, 10682, 6124, 4028, 9, 90, 2881, 1526])).
% 10.69/10.92 tff(25337,plain,
% 10.69/10.92 (b(s(z), s(s(z)))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[1788, 25336])).
% 10.69/10.92 tff(25338,plain,
% 10.69/10.92 (~b(s(s(s(s(z)))), s(z))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[1795, 391, 25337, 25143, 25155])).
% 10.69/10.92 tff(25339,plain,
% 10.69/10.92 (r(s(s(s(s(z)))), s(z))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[749, 25338])).
% 10.69/10.92 tff(25340,plain,
% 10.69/10.92 (b(elem!1, z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25243, 168, 4028, 9, 10682, 6124, 4018, 25014, 90, 2881, 25143, 25153])).
% 10.69/10.92 tff(25341,plain,
% 10.69/10.92 (~b(elem!1, s(s(s(s(z)))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25257, 391, 25340, 10682, 1526, 90])).
% 10.69/10.92 tff(25342,plain,
% 10.69/10.92 (b(elem!1, s(z))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25043, 25340, 10682, 168, 4028, 1, 25341, 1526, 2881, 25339])).
% 10.69/10.92 tff(25343,plain,
% 10.69/10.92 (~b(s(s(s(s(z)))), elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25250, 391, 25340, 10682, 1526, 90])).
% 10.69/10.92 tff(25344,plain,
% 10.69/10.92 (~r(z, elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25315, 25342, 24024, 90, 25340, 427, 4018, 2881, 10682, 25343, 6124, 4097])).
% 10.69/10.92 tff(25345,plain,
% 10.69/10.92 (b(z, elem!1)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[141, 25344, 24023])).
% 10.69/10.92 tff(25346,plain,
% 10.69/10.92 (~b(s(z), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[13285, 25345, 25340, 25342])).
% 10.69/10.92 tff(25347,plain,
% 10.69/10.92 (r(s(z), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[180, 25346])).
% 10.69/10.92 tff(25348,plain,
% 10.69/10.92 (~b(s(s(z)), s(s(s(elem!1))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[17022, 391, 1526, 25337, 25155])).
% 10.69/10.92 tff(25349,plain,
% 10.69/10.92 (r(s(s(z)), s(s(s(elem!1))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[11041, 25348])).
% 10.69/10.92 tff(25350,plain,
% 10.69/10.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.69/10.92 inference(rewrite,[status(thm)],[])).
% 10.69/10.92 tff(25351,plain,
% 10.69/10.92 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.69/10.92 inference(rewrite,[status(thm)],[])).
% 10.69/10.92 tff(25352,plain,
% 10.69/10.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 10.69/10.92 inference(monotonicity,[status(thm)],[25351])).
% 10.69/10.92 tff(25353,plain,
% 10.69/10.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.69/10.92 inference(transitivity,[status(thm)],[25352, 25350])).
% 10.69/10.92 tff(25354,plain,
% 10.69/10.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))),
% 10.69/10.92 inference(quant_inst,[status(thm)],[])).
% 10.69/10.92 tff(25355,plain,
% 10.69/10.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 10.69/10.92 inference(modus_ponens,[status(thm)],[25354, 25353])).
% 10.69/10.92 tff(25356,plain,
% 10.69/10.92 (~r(elem!1, s(s(z)))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[25355, 194, 4097, 6124, 25349])).
% 10.69/10.92 tff(25357,plain,
% 10.69/10.92 (~b(elem!1, s(s(z)))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[10150, 25342, 25337, 25155])).
% 10.69/10.92 tff(25358,plain,
% 10.69/10.92 (elem!1 = s(s(z))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[3394, 25357, 25356])).
% 10.69/10.92 tff(25359,plain,
% 10.69/10.92 (~b(s(s(elem!1)), s(z))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[9032, 25358, 25338])).
% 10.69/10.92 tff(25360,plain,
% 10.69/10.92 (r(s(s(elem!1)), s(z))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[362, 25359])).
% 10.69/10.92 tff(25361,plain,
% 10.69/10.92 (~r(s(s(elem!1)), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[4103, 25360, 25014, 25347])).
% 10.69/10.92 tff(25362,plain,
% 10.69/10.92 (b(s(s(elem!1)), z)),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[2629, 25361])).
% 10.69/10.92 tff(25363,plain,
% 10.69/10.92 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[9253, 25358])).
% 10.69/10.92 tff(25364,plain,
% 10.69/10.92 (~(elem!1 = s(s(s(s(z)))))),
% 10.69/10.92 inference(unit_resolution,[status(thm)],[13738, 25342, 25338])).
% 10.69/10.93 tff(25365,plain,
% 10.69/10.93 (r(elem!1, s(s(s(s(z)))))),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[781, 25364, 25341])).
% 10.69/10.93 tff(25366,plain,
% 10.69/10.93 (~r(elem!1, s(z))),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[6347, 25365, 2913, 25339])).
% 10.69/10.93 tff(25367,plain,
% 10.69/10.93 (~(s(s(elem!1)) = elem!1)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[4206, 25360, 25366])).
% 10.69/10.93 tff(25368,plain,
% 10.69/10.93 (~r(s(z), elem!1)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[9108, 25364, 25341, 25343, 25339])).
% 10.69/10.93 tff(25369,plain,
% 10.69/10.93 (b(s(z), elem!1)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[632, 25368, 4018])).
% 10.69/10.93 tff(25370,plain,
% 10.69/10.93 (~b(s(s(elem!1)), elem!1)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[12771, 25369, 25345, 25340])).
% 10.69/10.93 tff(25371,plain,
% 10.69/10.93 (r(s(s(elem!1)), elem!1)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[872, 25370, 25367])).
% 10.69/10.93 tff(25372,plain,
% 10.69/10.93 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[4039, 25371, 4028, 168, 9])).
% 10.69/10.93 tff(25373,plain,
% 10.69/10.93 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[1370, 25372, 25363])).
% 10.69/10.93 tff(25374,plain,
% 10.69/10.93 (~r(s(s(s(elem!1))), z)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[12936, 25371, 10682, 1, 25363, 25345, 168, 25369, 25340])).
% 10.69/10.93 tff(25375,plain,
% 10.69/10.93 (b(s(s(s(elem!1))), z)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[377, 25374])).
% 10.69/10.93 tff(25376,plain,
% 10.69/10.93 ($false),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[13177, 25375, 25373, 10682, 25362])).
% 10.69/10.93 tff(25377,plain,(b(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.93 tff(25378,plain,
% 10.69/10.93 (b(s(s(s(elem!1))), elem!1)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[25377, 4028, 1, 10782, 88, 2881, 25087])).
% 10.69/10.93 tff(25379,plain,
% 10.69/10.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.93 inference(rewrite,[status(thm)],[])).
% 10.69/10.93 tff(25380,plain,
% 10.69/10.93 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.93 inference(rewrite,[status(thm)],[])).
% 10.69/10.93 tff(25381,plain,
% 10.69/10.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 10.69/10.93 inference(monotonicity,[status(thm)],[25380])).
% 10.69/10.93 tff(25382,plain,
% 10.69/10.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.93 inference(transitivity,[status(thm)],[25381, 25379])).
% 10.69/10.93 tff(25383,plain,
% 10.69/10.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 10.69/10.93 inference(quant_inst,[status(thm)],[])).
% 10.69/10.93 tff(25384,plain,
% 10.69/10.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 10.69/10.93 inference(modus_ponens,[status(thm)],[25383, 25382])).
% 10.69/10.93 tff(25385,plain,
% 10.69/10.93 ($false),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[25384, 391, 133, 900, 10682, 90, 2064])).
% 10.69/10.93 tff(25386,plain,((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.93 tff(25387,plain,
% 10.69/10.93 (~b(z, elem!1)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[25386, 2064, 10682, 90, 900])).
% 10.69/10.93 tff(25388,plain,
% 10.69/10.93 (r(z, elem!1)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[141, 25387, 24023])).
% 10.69/10.93 tff(25389,plain,
% 10.69/10.93 (~r(s(z), z)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[627, 5429, 530, 411])).
% 10.69/10.93 tff(25390,plain,
% 10.69/10.93 (b(s(z), z)),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[180, 25389])).
% 10.69/10.93 tff(25391,plain,
% 10.69/10.93 (~r(z, s(z))),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[16803, 5429, 530, 411])).
% 10.69/10.93 tff(25392,plain,
% 10.69/10.93 (b(z, s(z))),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[678, 25391])).
% 10.69/10.93 tff(25393,plain,
% 10.69/10.93 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.69/10.93 inference(rewrite,[status(thm)],[])).
% 10.69/10.93 tff(25394,plain,
% 10.69/10.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 10.69/10.93 inference(monotonicity,[status(thm)],[25393])).
% 10.69/10.93 tff(25395,plain,
% 10.69/10.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.69/10.93 inference(transitivity,[status(thm)],[25394, 10628])).
% 10.69/10.93 tff(25396,plain,
% 10.69/10.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.69/10.93 inference(quant_inst,[status(thm)],[])).
% 10.69/10.93 tff(25397,plain,
% 10.69/10.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 10.69/10.93 inference(modus_ponens,[status(thm)],[25396, 25395])).
% 10.69/10.93 tff(25398,plain,
% 10.69/10.93 (~b(s(s(s(elem!1))), s(z))),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[25397, 391, 380, 25392, 25390])).
% 10.69/10.93 tff(25399,plain,
% 10.69/10.93 (r(s(s(s(elem!1))), s(z))),
% 10.69/10.93 inference(unit_resolution,[status(thm)],[223, 25398])).
% 10.69/10.93 tff(25400,plain,
% 10.69/10.93 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 10.69/10.93 inference(rewrite,[status(thm)],[])).
% 10.69/10.93 tff(25401,plain,
% 10.69/10.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 10.69/10.94 inference(monotonicity,[status(thm)],[25400])).
% 10.69/10.94 tff(25402,plain,
% 10.69/10.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 10.69/10.94 inference(transitivity,[status(thm)],[25401, 11296])).
% 10.69/10.94 tff(25403,plain,
% 10.69/10.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 10.69/10.94 inference(quant_inst,[status(thm)],[])).
% 10.69/10.94 tff(25404,plain,
% 10.69/10.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 10.69/10.94 inference(modus_ponens,[status(thm)],[25403, 25402])).
% 10.69/10.94 tff(25405,plain,
% 10.69/10.94 (~b(s(z), z)),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[25404, 391, 380, 10682, 379])).
% 10.69/10.94 tff(25406,plain,
% 10.69/10.94 (r(s(z), z)),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[178, 42, 23, 25405])).
% 10.69/10.94 tff(25407,plain,
% 10.69/10.94 (~r(s(z), elem!1)),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[626, 194, 411, 530, 25406])).
% 10.69/10.94 tff(25408,plain,
% 10.69/10.94 (s(z) = elem!1),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[632, 25407, 2829])).
% 10.69/10.94 tff(25409,plain,
% 10.69/10.94 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 10.69/10.94 inference(monotonicity,[status(thm)],[25408])).
% 10.69/10.94 tff(25410,plain,
% 10.69/10.94 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 10.69/10.94 inference(symmetry,[status(thm)],[25409])).
% 10.69/10.94 tff(25411,plain,
% 10.69/10.94 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 10.69/10.94 inference(monotonicity,[status(thm)],[25410])).
% 10.69/10.94 tff(25412,plain,
% 10.69/10.94 (~b(s(z), s(s(s(elem!1))))),
% 10.69/10.94 inference(modus_ponens,[status(thm)],[4028, 25411])).
% 10.69/10.94 tff(25413,plain,
% 10.69/10.94 ($false),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[379, 25412])).
% 10.69/10.94 tff(25414,plain,((~b(s(z), s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | b(s(z), elem!1) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.94 tff(25415,plain,
% 10.69/10.94 (~b(s(z), s(s(s(elem!1))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[25414, 2829, 380, 530, 411, 4028, 10682])).
% 10.69/10.94 tff(25416,plain,
% 10.69/10.94 (r(s(z), s(s(s(elem!1))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[247, 25415])).
% 10.69/10.94 tff(25417,plain,
% 10.69/10.94 ($false),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[17163, 194, 410, 5429, 25416, 25399])).
% 10.69/10.94 tff(25418,plain,(b(s(z), elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.69/10.94 tff(25419,plain,
% 10.69/10.94 (~b(s(s(s(elem!1))), z)),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[25418, 2829, 10682, 4028, 150, 410, 530, 411])).
% 10.69/10.94 tff(25420,plain,
% 10.69/10.94 (r(s(s(s(elem!1))), z)),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[377, 25419])).
% 10.69/10.94 tff(25421,plain,
% 10.69/10.94 (~r(s(z), s(s(s(elem!1))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[5645, 25420, 410, 5429])).
% 10.69/10.94 tff(25422,plain,
% 10.69/10.94 (~r(z, s(z))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[14725, 5429, 411, 847])).
% 10.69/10.94 tff(25423,plain,
% 10.69/10.94 (b(z, s(z))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[678, 25422])).
% 10.69/10.94 tff(25424,plain,
% 10.69/10.94 (~b(s(z), s(s(s(elem!1))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[15561, 25423, 1526, 10682])).
% 10.69/10.94 tff(25425,plain,
% 10.69/10.94 ($false),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[247, 25424, 25421])).
% 10.69/10.94 tff(25426,plain,(b(s(z), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | b(elem!1, s(s(s(elem!1)))) | (s(z) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.94 tff(25427,plain,
% 10.69/10.94 (b(s(z), elem!1)),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[25426, 25388, 10682, 410, 1526, 847, 4028, 150, 530])).
% 10.69/10.94 tff(25428,plain,
% 10.69/10.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.94 inference(rewrite,[status(thm)],[])).
% 10.69/10.94 tff(25429,plain,
% 10.69/10.94 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.94 inference(rewrite,[status(thm)],[])).
% 10.69/10.94 tff(25430,plain,
% 10.69/10.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 10.69/10.94 inference(monotonicity,[status(thm)],[25429])).
% 10.69/10.94 tff(25431,plain,
% 10.69/10.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.94 inference(transitivity,[status(thm)],[25430, 25428])).
% 10.69/10.94 tff(25432,plain,
% 10.69/10.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.69/10.94 inference(quant_inst,[status(thm)],[])).
% 10.69/10.94 tff(25433,plain,
% 10.69/10.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 10.69/10.94 inference(modus_ponens,[status(thm)],[25432, 25431])).
% 10.69/10.94 tff(25434,plain,
% 10.69/10.94 ($false),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[25433, 391, 900, 25427, 1526, 90, 2064])).
% 10.69/10.94 tff(25435,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | b(elem!1, s(s(s(elem!1)))) | (s(z) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.94 tff(25436,plain,
% 10.69/10.94 (~b(elem!1, s(s(s(s(z)))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[25435, 25158, 1526, 90, 10682, 410, 847, 4028, 150, 900])).
% 10.69/10.94 tff(25437,plain,
% 10.69/10.94 (r(elem!1, s(s(s(s(z)))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[781, 25436, 21768])).
% 10.69/10.94 tff(25438,plain,
% 10.69/10.94 (~r(z, s(s(s(s(z)))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[17062, 182, 847, 530])).
% 10.69/10.94 tff(25439,plain,
% 10.69/10.94 (b(z, s(s(s(s(z)))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[800, 25438])).
% 10.69/10.94 tff(25440,plain,
% 10.69/10.94 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[23918, 25439, 90, 10682])).
% 10.69/10.94 tff(25441,plain,
% 10.69/10.94 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[4313, 42, 9606, 15348])).
% 10.69/10.94 tff(25442,plain,
% 10.69/10.94 ($false),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[25198, 194, 410, 2032, 2100, 25441])).
% 10.69/10.94 tff(25443,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.94 tff(25444,plain,
% 10.69/10.94 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[25443, 25440, 2032, 410, 16058])).
% 10.69/10.94 tff(25445,plain,
% 10.69/10.94 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[23863, 25444, 90, 10682, 3843])).
% 10.69/10.94 tff(25446,plain,
% 10.69/10.94 (~r(z, s(z))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[17266, 182, 847, 530])).
% 10.69/10.94 tff(25447,plain,
% 10.69/10.94 (b(z, s(z))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[678, 25446])).
% 10.69/10.94 tff(25448,plain,
% 10.69/10.94 (~b(s(z), s(s(s(elem!1))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[15561, 25447, 1526, 10682])).
% 10.69/10.94 tff(25449,plain,
% 10.69/10.94 (r(s(z), s(s(s(elem!1))))),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[247, 25448])).
% 10.69/10.94 tff(25450,plain,
% 10.69/10.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.94 inference(rewrite,[status(thm)],[])).
% 10.69/10.94 tff(25451,plain,
% 10.69/10.94 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, 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))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.94 inference(rewrite,[status(thm)],[])).
% 10.69/10.94 tff(25452,plain,
% 10.69/10.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 10.69/10.94 inference(monotonicity,[status(thm)],[25451])).
% 10.69/10.94 tff(25453,plain,
% 10.69/10.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.94 inference(transitivity,[status(thm)],[25452, 25450])).
% 10.69/10.94 tff(25454,plain,
% 10.69/10.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 10.69/10.94 inference(quant_inst,[status(thm)],[])).
% 10.69/10.94 tff(25455,plain,
% 10.69/10.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 10.69/10.94 inference(modus_ponens,[status(thm)],[25454, 25453])).
% 10.69/10.94 tff(25456,plain,
% 10.69/10.94 ($false),
% 10.69/10.94 inference(unit_resolution,[status(thm)],[25455, 194, 410, 25449, 847, 25445])).
% 10.69/10.95 tff(25457,plain,((~r(s(z), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.95 tff(25458,plain,
% 10.69/10.95 (~r(s(z), z)),
% 10.69/10.95 inference(unit_resolution,[status(thm)],[25457, 25437, 847, 90, 10682, 3363, 410, 1526, 25158])).
% 10.69/10.95 tff(25459,plain,
% 10.69/10.95 (b(s(z), z)),
% 10.69/10.95 inference(unit_resolution,[status(thm)],[180, 25458])).
% 10.69/10.95 tff(25460,plain,
% 10.69/10.95 (~r(s(s(s(s(z)))), s(z))),
% 10.69/10.95 inference(unit_resolution,[status(thm)],[6347, 25437, 1216, 847])).
% 10.69/10.95 tff(25461,plain,
% 10.69/10.95 (b(s(s(s(s(z)))), s(z))),
% 10.69/10.95 inference(unit_resolution,[status(thm)],[749, 25460])).
% 10.69/10.95 tff(25462,plain,
% 10.69/10.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 10.69/10.95 inference(rewrite,[status(thm)],[])).
% 10.69/10.95 tff(25463,plain,
% 10.69/10.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 10.69/10.95 inference(quant_inst,[status(thm)],[])).
% 10.69/10.95 tff(25464,plain,
% 10.69/10.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 10.69/10.95 inference(modus_ponens,[status(thm)],[25463, 25462])).
% 10.69/10.95 tff(25465,plain,
% 10.69/10.95 ($false),
% 10.69/10.95 inference(unit_resolution,[status(thm)],[25464, 391, 900, 10682, 90, 25461, 25459])).
% 10.69/10.95 tff(25466,plain,(b(elem!1, z) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.69/10.95 tff(25467,plain,
% 10.69/10.95 (b(elem!1, z)),
% 10.69/10.95 inference(unit_resolution,[status(thm)],[25466, 847, 10682, 90, 900, 410, 1526, 1216, 4028, 150])).
% 10.69/10.95 tff(25468,plain,
% 10.69/10.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 10.69/10.95 inference(rewrite,[status(thm)],[])).
% 10.69/10.95 tff(25469,plain,
% 10.69/10.95 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 10.69/10.95 inference(rewrite,[status(thm)],[])).
% 10.69/10.95 tff(25470,plain,
% 10.69/10.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 10.69/10.95 inference(monotonicity,[status(thm)],[25469])).
% 10.69/10.95 tff(25471,plain,
% 10.69/10.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 10.69/10.95 inference(transitivity,[status(thm)],[25470, 25468])).
% 10.69/10.95 tff(25472,plain,
% 10.69/10.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 10.69/10.95 inference(quant_inst,[status(thm)],[])).
% 10.69/10.95 tff(25473,plain,
% 10.69/10.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 10.69/10.95 inference(modus_ponens,[status(thm)],[25472, 25471])).
% 10.69/10.95 tff(25474,plain,
% 10.69/10.95 (~b(s(z), elem!1)),
% 10.69/10.95 inference(unit_resolution,[status(thm)],[25473, 391, 665, 900, 10682, 590])).
% 10.69/10.95 tff(25475,plain,
% 10.69/10.95 (r(s(z), elem!1)),
% 10.69/10.95 inference(unit_resolution,[status(thm)],[632, 25474, 150])).
% 10.69/10.95 tff(25476,plain,
% 10.69/10.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.95 inference(rewrite,[status(thm)],[])).
% 10.69/10.95 tff(25477,plain,
% 10.69/10.95 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.95 inference(rewrite,[status(thm)],[])).
% 10.69/10.95 tff(25478,plain,
% 10.69/10.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 10.69/10.95 inference(monotonicity,[status(thm)],[25477])).
% 10.69/10.95 tff(25479,plain,
% 10.69/10.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.95 inference(transitivity,[status(thm)],[25478, 25476])).
% 10.69/10.95 tff(25480,plain,
% 10.69/10.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 10.69/10.95 inference(quant_inst,[status(thm)],[])).
% 10.69/10.95 tff(25481,plain,
% 10.69/10.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 10.69/10.95 inference(modus_ponens,[status(thm)],[25480, 25479])).
% 10.69/10.96 tff(25482,plain,
% 10.69/10.96 (~b(elem!1, s(s(s(s(z)))))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[25481, 391, 665, 900, 10682, 90])).
% 10.69/10.96 tff(25483,plain,
% 10.69/10.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.69/10.96 inference(rewrite,[status(thm)],[])).
% 10.69/10.96 tff(25484,plain,
% 10.69/10.96 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.69/10.96 inference(rewrite,[status(thm)],[])).
% 10.69/10.96 tff(25485,plain,
% 10.69/10.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 10.69/10.96 inference(monotonicity,[status(thm)],[25484])).
% 10.69/10.96 tff(25486,plain,
% 10.69/10.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.69/10.96 inference(transitivity,[status(thm)],[25485, 25483])).
% 10.69/10.96 tff(25487,plain,
% 10.69/10.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.69/10.96 inference(quant_inst,[status(thm)],[])).
% 10.69/10.96 tff(25488,plain,
% 10.69/10.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 10.69/10.96 inference(modus_ponens,[status(thm)],[25487, 25486])).
% 10.69/10.96 tff(25489,plain,
% 10.69/10.96 (~b(s(s(s(s(z)))), elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[25488, 391, 665, 900, 10682, 90])).
% 10.69/10.96 tff(25490,plain,
% 10.69/10.96 (~b(s(s(s(s(z)))), s(z))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[25464, 391, 900, 10682, 90, 590])).
% 10.69/10.96 tff(25491,plain,
% 10.69/10.96 (r(s(s(s(s(z)))), s(z))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[749, 25490])).
% 10.69/10.96 tff(25492,plain,
% 10.69/10.96 (elem!1 = s(s(s(s(z))))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[9108, 25491, 25489, 25482, 25475])).
% 10.69/10.96 tff(25493,plain,
% 10.69/10.96 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 10.69/10.96 inference(monotonicity,[status(thm)],[25492])).
% 10.69/10.96 tff(25494,plain,
% 10.69/10.96 (~b(s(s(s(elem!1))), z)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[17249, 665, 10682, 900])).
% 10.69/10.96 tff(25495,plain,
% 10.69/10.96 (r(s(s(s(elem!1))), z)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[377, 25494])).
% 10.69/10.96 tff(25496,plain,
% 10.69/10.96 (~r(s(z), s(s(s(elem!1))))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[5645, 25475, 410, 25495])).
% 10.69/10.96 tff(25497,plain,
% 10.69/10.96 (b(s(z), s(s(s(elem!1))))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[247, 25496])).
% 10.69/10.96 tff(25498,plain,
% 10.69/10.96 (~b(z, s(z))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[15561, 25497, 1526, 10682])).
% 10.69/10.96 tff(25499,plain,
% 10.69/10.96 (r(z, s(z))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[678, 25498])).
% 10.69/10.96 tff(25500,plain,
% 10.69/10.96 (~r(z, elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[14725, 25499, 25475, 847])).
% 10.69/10.96 tff(25501,plain,
% 10.69/10.96 (b(z, elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[141, 25500, 115])).
% 10.69/10.96 tff(25502,plain,
% 10.69/10.96 (b(z, s(s(s(s(z)))))),
% 10.69/10.96 inference(modus_ponens,[status(thm)],[25501, 25493])).
% 10.69/10.96 tff(25503,plain,
% 10.69/10.96 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.69/10.96 inference(monotonicity,[status(thm)],[25492])).
% 10.69/10.96 tff(25504,plain,
% 10.69/10.96 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.69/10.96 inference(modus_ponens,[status(thm)],[900, 25503])).
% 10.69/10.96 tff(25505,plain,
% 10.69/10.96 ($false),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[23918, 25504, 25502, 90, 10682])).
% 10.69/10.96 tff(25506,plain,((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (z = elem!1) | (~r(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (s(z) = elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.96 tff(25507,plain,
% 10.69/10.96 (~b(s(z), z)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[25506, 847, 10682, 900, 24023, 90, 1526, 410, 150, 25467])).
% 10.69/10.96 tff(25508,plain,
% 10.69/10.96 (r(s(z), z)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[180, 25507])).
% 10.69/10.96 tff(25509,plain,
% 10.69/10.96 (~b(z, elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[10743, 25467, 900, 10682])).
% 10.69/10.96 tff(25510,plain,
% 10.69/10.96 (r(z, elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[141, 25509, 24023])).
% 10.69/10.96 tff(25511,plain,
% 10.69/10.96 (~r(s(z), elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[2475, 25510, 847, 25508])).
% 10.69/10.96 tff(25512,plain,
% 10.69/10.96 (b(s(z), elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[632, 25511, 150])).
% 10.69/10.96 tff(25513,plain,
% 10.69/10.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.69/10.96 inference(rewrite,[status(thm)],[])).
% 10.69/10.96 tff(25514,plain,
% 10.69/10.96 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.69/10.96 inference(rewrite,[status(thm)],[])).
% 10.69/10.96 tff(25515,plain,
% 10.69/10.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 10.69/10.96 inference(monotonicity,[status(thm)],[25514])).
% 10.69/10.96 tff(25516,plain,
% 10.69/10.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.69/10.96 inference(transitivity,[status(thm)],[25515, 25513])).
% 10.69/10.96 tff(25517,plain,
% 10.69/10.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.69/10.96 inference(quant_inst,[status(thm)],[])).
% 10.69/10.96 tff(25518,plain,
% 10.69/10.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 10.69/10.96 inference(modus_ponens,[status(thm)],[25517, 25516])).
% 10.69/10.96 tff(25519,plain,
% 10.69/10.96 ($false),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[25518, 391, 25467, 900, 10682, 25512, 1526])).
% 10.69/10.96 tff(25520,plain,((~r(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.96 tff(25521,plain,
% 10.69/10.96 (~r(elem!1, s(z))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[25520, 150, 10682, 1526, 900, 90, 410, 1216, 4028])).
% 10.69/10.96 tff(25522,plain,
% 10.69/10.96 (b(elem!1, s(z))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[837, 25521, 173])).
% 10.69/10.96 tff(25523,plain,
% 10.69/10.96 (~b(s(z), s(s(s(elem!1))))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[2907, 25522, 1526, 900])).
% 10.69/10.96 tff(25524,plain,
% 10.69/10.96 (r(s(z), s(s(s(elem!1))))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[247, 25523])).
% 10.69/10.96 tff(25525,plain,
% 10.69/10.96 (~b(s(z), elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[20387, 25522, 1526, 900])).
% 10.69/10.96 tff(25526,plain,
% 10.69/10.96 (r(s(z), elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[632, 25525, 150])).
% 10.69/10.96 tff(25527,plain,
% 10.69/10.96 (~r(s(s(s(elem!1))), z)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[5645, 25526, 410, 25524])).
% 10.69/10.96 tff(25528,plain,
% 10.69/10.96 (b(s(s(s(elem!1))), z)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[377, 25527])).
% 10.69/10.96 tff(25529,plain,
% 10.69/10.96 (~b(elem!1, z)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[17249, 25528, 10682, 900])).
% 10.69/10.96 tff(25530,plain,
% 10.69/10.96 (~(elem!1 = s(s(s(s(z)))))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[16358, 25529, 90])).
% 10.69/10.96 tff(25531,plain,
% 10.69/10.96 (r(elem!1, z)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[526, 25529, 24022])).
% 10.69/10.96 tff(25532,plain,
% 10.69/10.96 (~r(z, elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[25418, 25531, 10682, 4028, 150, 410, 25525, 25528])).
% 10.69/10.96 tff(25533,plain,
% 10.69/10.96 (b(z, elem!1)),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[141, 25532, 24023])).
% 10.69/10.96 tff(25534,plain,
% 10.69/10.96 (~b(elem!1, s(s(s(s(z)))))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[25386, 25533, 10682, 90, 900])).
% 10.69/10.96 tff(25535,plain,
% 10.69/10.96 (r(elem!1, s(s(s(s(z)))))),
% 10.69/10.96 inference(unit_resolution,[status(thm)],[781, 25534, 25530])).
% 10.69/10.96 tff(25536,plain,
% 10.69/10.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.96 inference(rewrite,[status(thm)],[])).
% 10.69/10.96 tff(25537,plain,
% 10.69/10.96 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.96 inference(rewrite,[status(thm)],[])).
% 10.69/10.96 tff(25538,plain,
% 10.69/10.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 10.69/10.96 inference(monotonicity,[status(thm)],[25537])).
% 10.69/10.96 tff(25539,plain,
% 10.69/10.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.97 inference(transitivity,[status(thm)],[25538, 25536])).
% 10.69/10.97 tff(25540,plain,
% 10.69/10.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.69/10.97 inference(quant_inst,[status(thm)],[])).
% 10.69/10.97 tff(25541,plain,
% 10.69/10.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[25540, 25539])).
% 10.69/10.97 tff(25542,plain,
% 10.69/10.97 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[25541, 391, 25533, 25528, 90, 25522])).
% 10.69/10.97 tff(25543,plain,
% 10.69/10.97 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[25443, 25542, 25535, 410, 16830])).
% 10.69/10.97 tff(25544,plain,
% 10.69/10.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.69/10.97 inference(rewrite,[status(thm)],[])).
% 10.69/10.97 tff(25545,plain,
% 10.69/10.97 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.69/10.97 inference(rewrite,[status(thm)],[])).
% 10.69/10.97 tff(25546,plain,
% 10.69/10.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25545])).
% 10.69/10.97 tff(25547,plain,
% 10.69/10.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.69/10.97 inference(transitivity,[status(thm)],[25546, 25544])).
% 10.69/10.97 tff(25548,plain,
% 10.69/10.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.69/10.97 inference(quant_inst,[status(thm)],[])).
% 10.69/10.97 tff(25549,plain,
% 10.69/10.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[25548, 25547])).
% 10.69/10.97 tff(25550,plain,
% 10.69/10.97 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[25549, 391, 25533, 25528, 90, 25522])).
% 10.69/10.97 tff(25551,plain,
% 10.69/10.97 ($false),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[2853, 42, 3363, 25550, 25543])).
% 10.69/10.97 tff(25552,plain,((s(z) = elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.97 tff(25553,plain,
% 10.69/10.97 (s(z) = elem!1),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[25552, 6124, 88, 10782, 25378, 4028, 25087, 2913])).
% 10.69/10.97 tff(25554,plain,
% 10.69/10.97 (s(s(z)) = s(elem!1)),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25553])).
% 10.69/10.97 tff(25555,plain,
% 10.69/10.97 (s(s(s(z))) = s(s(elem!1))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25554])).
% 10.69/10.97 tff(25556,plain,
% 10.69/10.97 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25555])).
% 10.69/10.97 tff(25557,plain,
% 10.69/10.97 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25556])).
% 10.69/10.97 tff(25558,plain,
% 10.69/10.97 (b(s(s(s(elem!1))), z)),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[88, 25557])).
% 10.69/10.97 tff(25559,plain,
% 10.69/10.97 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25554])).
% 10.69/10.97 tff(25560,plain,
% 10.69/10.97 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 10.69/10.97 inference(transitivity,[status(thm)],[25559, 582])).
% 10.69/10.97 tff(25561,plain,
% 10.69/10.97 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25560])).
% 10.69/10.97 tff(25562,plain,
% 10.69/10.97 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[1397, 25561])).
% 10.69/10.97 tff(25563,plain,
% 10.69/10.97 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25553])).
% 10.69/10.97 tff(25564,plain,
% 10.69/10.97 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25563])).
% 10.69/10.97 tff(25565,plain,
% 10.69/10.97 (~(s(s(elem!1)) = elem!1)),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[357, 25564])).
% 10.69/10.97 tff(25566,plain,
% 10.69/10.97 (elem!1 = s(z)),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[1495, 25553])).
% 10.69/10.97 tff(25567,plain,
% 10.69/10.97 (b(s(s(s(s(z)))), elem!1)),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[1563, 25566, 25378])).
% 10.69/10.97 tff(25568,plain,
% 10.69/10.97 (~r(z, s(s(s(s(z)))))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[10733, 25553, 53])).
% 10.69/10.97 tff(25569,plain,
% 10.69/10.97 (b(z, s(s(s(s(z)))))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[800, 25568])).
% 10.69/10.97 tff(25570,plain,
% 10.69/10.97 (~b(elem!1, z)),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[4246, 25569, 88, 25567])).
% 10.69/10.97 tff(25571,plain,
% 10.69/10.97 (r(elem!1, z)),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[526, 25570, 23979])).
% 10.69/10.97 tff(25572,plain,
% 10.69/10.97 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25556])).
% 10.69/10.97 tff(25573,plain,
% 10.69/10.97 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25572])).
% 10.69/10.97 tff(25574,plain,
% 10.69/10.97 (~r(s(s(s(elem!1))), z)),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[81, 25573])).
% 10.69/10.97 tff(25575,plain,
% 10.69/10.97 (~b(s(z), s(s(s(elem!1))))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[7796, 25553, 4028])).
% 10.69/10.97 tff(25576,plain,
% 10.69/10.97 (r(s(z), s(s(s(elem!1))))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[247, 25575])).
% 10.69/10.97 tff(25577,plain,
% 10.69/10.97 (b(s(s(s(s(z)))), s(z))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[9618, 25553, 25087])).
% 10.69/10.97 tff(25578,plain,
% 10.69/10.97 (~(s(elem!1) = s(z))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[123, 23981])).
% 10.69/10.97 tff(25579,plain,
% 10.69/10.97 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25554])).
% 10.69/10.97 tff(25580,plain,
% 10.69/10.97 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25579])).
% 10.69/10.97 tff(25581,plain,
% 10.69/10.97 (~(s(s(elem!1)) = s(elem!1))),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[23982, 25580])).
% 10.69/10.97 tff(25582,plain,
% 10.69/10.97 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 10.69/10.97 inference(transitivity,[status(thm)],[25579, 1098])).
% 10.69/10.97 tff(25583,plain,
% 10.69/10.97 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[25582])).
% 10.69/10.97 tff(25584,plain,
% 10.69/10.97 (~(s(elem!1) = s(s(elem!1)))),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[23982, 25583])).
% 10.69/10.97 tff(25585,plain,
% 10.69/10.97 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[299, 24165])).
% 10.69/10.97 tff(25586,plain,
% 10.69/10.97 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[307, 25585])).
% 10.69/10.97 tff(25587,plain,
% 10.69/10.97 (~b(s(z), s(s(z)))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[23366, 1235, 90, 1759, 664])).
% 10.69/10.97 tff(25588,plain,
% 10.69/10.97 (~r(s(z), s(s(z)))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[23399, 1235, 1216, 10682, 90, 900])).
% 10.69/10.97 tff(25589,plain,
% 10.69/10.97 ($false),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[1788, 25588, 25587])).
% 10.69/10.97 tff(25590,plain,((~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.97 tff(25591,plain,
% 10.69/10.97 (~b(s(s(z)), z)),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[25590, 7402, 10682, 90, 900, 1759, 1216])).
% 10.69/10.97 tff(25592,plain,
% 10.69/10.97 (r(s(s(z)), z)),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[1211, 25591])).
% 10.69/10.97 tff(25593,plain,
% 10.69/10.97 (r(s(elem!1), z)),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[3560, 25592, 812])).
% 10.69/10.97 tff(25594,plain,
% 10.69/10.97 (~b(elem!1, z)),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[4246, 1686, 90, 19955])).
% 10.69/10.97 tff(25595,plain,
% 10.69/10.97 (r(s(z), z)),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[7485, 25594, 812])).
% 10.69/10.97 tff(25596,plain,
% 10.69/10.97 (b(s(s(s(elem!1))), z)),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[90, 7494])).
% 10.69/10.97 tff(25597,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 10.69/10.97 tff(25598,plain,
% 10.69/10.97 (b(s(z), s(s(z)))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[1788, 25597])).
% 10.69/10.97 tff(25599,plain,
% 10.69/10.97 (b(elem!1, s(elem!1))),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[25598, 24223])).
% 10.69/10.97 tff(25600,plain,
% 10.69/10.97 ((~r(s(z), s(s(z)))) <=> (~r(elem!1, s(elem!1)))),
% 10.69/10.97 inference(monotonicity,[status(thm)],[19010])).
% 10.69/10.97 tff(25601,plain,
% 10.69/10.97 (~r(elem!1, s(elem!1))),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[25597, 25600])).
% 10.69/10.97 tff(25602,plain,
% 10.69/10.97 (~r(s(elem!1), s(s(elem!1)))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[7546, 485, 410, 364])).
% 10.69/10.97 tff(25603,plain,
% 10.69/10.97 (b(s(elem!1), s(s(elem!1)))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[8644, 25602, 8611])).
% 10.69/10.97 tff(25604,plain,
% 10.69/10.97 (~r(s(s(elem!1)), s(elem!1))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[7930, 485, 530, 364])).
% 10.69/10.97 tff(25605,plain,
% 10.69/10.97 (b(s(s(elem!1)), s(elem!1))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[1135, 25604, 285])).
% 10.69/10.97 tff(25606,plain,
% 10.69/10.97 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 10.69/10.97 inference(monotonicity,[status(thm)],[812])).
% 10.69/10.97 tff(25607,plain,
% 10.69/10.97 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 10.69/10.97 inference(symmetry,[status(thm)],[25606])).
% 10.69/10.97 tff(25608,plain,
% 10.69/10.97 (r(s(elem!1), s(z))),
% 10.69/10.97 inference(modus_ponens,[status(thm)],[485, 25607])).
% 10.69/10.97 tff(25609,plain,
% 10.69/10.97 (~r(z, s(elem!1))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[17381, 25608, 182, 1628])).
% 10.69/10.97 tff(25610,plain,
% 10.69/10.97 (b(z, s(elem!1))),
% 10.69/10.97 inference(unit_resolution,[status(thm)],[566, 25609])).
% 10.69/10.97 tff(25611,plain,
% 10.69/10.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(elem!1)))))),
% 10.69/10.97 inference(rewrite,[status(thm)],[])).
% 10.69/10.97 tff(25612,plain,
% 10.69/10.97 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(elem!1)))))),
% 10.69/10.97 inference(rewrite,[status(thm)],[])).
% 10.69/10.97 tff(25613,plain,
% 10.69/10.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(elem!1))))))),
% 10.69/10.98 inference(monotonicity,[status(thm)],[25612])).
% 10.69/10.98 tff(25614,plain,
% 10.69/10.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(elem!1)))))),
% 10.69/10.98 inference(transitivity,[status(thm)],[25613, 25611])).
% 10.69/10.98 tff(25615,plain,
% 10.69/10.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 10.69/10.98 inference(quant_inst,[status(thm)],[])).
% 10.69/10.98 tff(25616,plain,
% 10.69/10.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(s(elem!1))))),
% 10.69/10.98 inference(modus_ponens,[status(thm)],[25615, 25614])).
% 10.69/10.98 tff(25617,plain,
% 10.69/10.98 ($false),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[25616, 194, 1628, 326, 182, 13481])).
% 10.69/10.98 tff(25618,plain,((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.98 tff(25619,plain,
% 10.69/10.98 (~r(z, s(s(elem!1)))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[25618, 25608, 1628, 182])).
% 10.69/10.98 tff(25620,plain,
% 10.69/10.98 (b(z, s(s(elem!1)))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[324, 25619])).
% 10.69/10.98 tff(25621,plain,
% 10.69/10.98 ($false),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[7659, 391, 25620, 25610, 25605, 25603])).
% 10.69/10.98 tff(25622,plain,((~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.98 tff(25623,plain,
% 10.69/10.98 (~r(s(elem!1), elem!1)),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[25622, 364, 1628, 812, 8611, 285, 410, 182, 530])).
% 10.69/10.98 tff(25624,plain,
% 10.69/10.98 (~b(s(s(s(elem!1))), s(elem!1))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[2340, 25623, 900, 7437, 438])).
% 10.69/10.98 tff(25625,plain,
% 10.69/10.98 (r(s(s(s(elem!1))), s(elem!1))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[588, 25624, 7433])).
% 10.69/10.98 tff(25626,plain,
% 10.69/10.98 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[15594, 25625, 410, 364])).
% 10.69/10.98 tff(25627,plain,
% 10.69/10.98 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[1356, 25626, 7434])).
% 10.69/10.98 tff(25628,plain,
% 10.69/10.98 (r(s(s(elem!1)), s(z))),
% 10.69/10.98 inference(modus_ponens,[status(thm)],[364, 2216])).
% 10.69/10.98 tff(25629,plain,
% 10.69/10.98 (b(s(elem!1), elem!1)),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[2168, 25623, 164])).
% 10.69/10.98 tff(25630,plain,
% 10.69/10.98 (~b(z, s(elem!1))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[24246, 25629, 133, 802])).
% 10.69/10.98 tff(25631,plain,
% 10.69/10.98 (r(z, s(elem!1))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[566, 25630])).
% 10.69/10.98 tff(25632,plain,
% 10.69/10.98 (~r(s(s(elem!1)), z)),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[2621, 25631, 25628, 182])).
% 10.69/10.98 tff(25633,plain,
% 10.69/10.98 (b(s(s(elem!1)), z)),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[2629, 25632])).
% 10.69/10.98 tff(25634,plain,
% 10.69/10.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.69/10.98 inference(rewrite,[status(thm)],[])).
% 10.69/10.98 tff(25635,plain,
% 10.69/10.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 10.69/10.98 inference(quant_inst,[status(thm)],[])).
% 10.69/10.98 tff(25636,plain,
% 10.69/10.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 10.69/10.98 inference(modus_ponens,[status(thm)],[25635, 25634])).
% 10.69/10.98 tff(25637,plain,
% 10.69/10.98 ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[25636, 391])).
% 10.69/10.98 tff(25638,plain,
% 10.69/10.98 ($false),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[25637, 25633, 25627, 10682, 900, 802])).
% 10.69/10.98 tff(25639,plain,((~r(s(s(elem!1)), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | r(elem!1, s(elem!1)) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.98 tff(25640,plain,
% 10.69/10.98 (~r(s(s(elem!1)), elem!1)),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[25639, 25599, 900, 10682, 182, 410, 133, 25601, 164, 1628, 812, 8611, 285, 530])).
% 10.69/10.98 tff(25641,plain,
% 10.69/10.98 (b(s(s(elem!1)), elem!1)),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[872, 25640, 7422])).
% 10.69/10.98 tff(25642,plain,
% 10.69/10.98 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 10.69/10.98 inference(transitivity,[status(thm)],[7431, 2602])).
% 10.69/10.98 tff(25643,plain,
% 10.69/10.98 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 10.69/10.98 inference(monotonicity,[status(thm)],[25642])).
% 10.69/10.98 tff(25644,plain,
% 10.69/10.98 (~(s(elem!1) = s(s(s(elem!1))))),
% 10.69/10.98 inference(modus_ponens,[status(thm)],[1397, 25643])).
% 10.69/10.98 tff(25645,plain,
% 10.69/10.98 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 10.69/10.98 inference(monotonicity,[status(thm)],[812])).
% 10.69/10.98 tff(25646,plain,
% 10.69/10.98 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 10.69/10.98 inference(symmetry,[status(thm)],[25645])).
% 10.69/10.98 tff(25647,plain,
% 10.69/10.98 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(z)))),
% 10.69/10.98 inference(monotonicity,[status(thm)],[25646])).
% 10.69/10.98 tff(25648,plain,
% 10.69/10.98 (~b(s(elem!1), s(z))),
% 10.69/10.98 inference(modus_ponens,[status(thm)],[2163, 25647])).
% 10.69/10.98 tff(25649,plain,
% 10.69/10.98 (r(s(elem!1), s(z))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[13479, 25648, 11964])).
% 10.69/10.98 tff(25650,plain,
% 10.69/10.98 (~r(z, s(elem!1))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[17381, 25649, 182, 1628])).
% 10.69/10.98 tff(25651,plain,
% 10.69/10.98 (b(z, s(elem!1))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[566, 25650])).
% 10.69/10.98 tff(25652,plain,
% 10.69/10.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 10.69/10.98 inference(rewrite,[status(thm)],[])).
% 10.69/10.98 tff(25653,plain,
% 10.69/10.98 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 10.69/10.98 inference(rewrite,[status(thm)],[])).
% 10.69/10.98 tff(25654,plain,
% 10.69/10.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1)))))),
% 10.69/10.98 inference(monotonicity,[status(thm)],[25653])).
% 10.69/10.98 tff(25655,plain,
% 10.69/10.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 10.69/10.98 inference(transitivity,[status(thm)],[25654, 25652])).
% 10.69/10.98 tff(25656,plain,
% 10.69/10.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 10.69/10.98 inference(quant_inst,[status(thm)],[])).
% 10.69/10.98 tff(25657,plain,
% 10.69/10.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1)))),
% 10.69/10.98 inference(modus_ponens,[status(thm)],[25656, 25655])).
% 10.69/10.98 tff(25658,plain,
% 10.69/10.98 ($false),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[25657, 391, 900, 10682, 592, 802, 1036])).
% 10.69/10.98 tff(25659,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.98 tff(25660,plain,
% 10.69/10.98 (~b(s(elem!1), s(s(s(elem!1))))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[25659, 25651, 10682, 900, 802])).
% 10.69/10.98 tff(25661,plain,
% 10.69/10.98 (r(s(elem!1), s(s(s(elem!1))))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[579, 42, 25660, 25644])).
% 10.69/10.98 tff(25662,plain,
% 10.69/10.98 (~r(z, s(s(elem!1)))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[25618, 25649, 1628, 182])).
% 10.69/10.98 tff(25663,plain,
% 10.69/10.98 (b(z, s(s(elem!1)))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[324, 25662])).
% 10.69/10.98 tff(25664,plain,
% 10.69/10.98 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[8469, 25663, 973, 380, 802])).
% 10.69/10.98 tff(25665,plain,
% 10.69/10.98 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[1370, 25664, 297])).
% 10.69/10.98 tff(25666,plain,
% 10.69/10.98 (r(s(elem!1), elem!1)),
% 10.69/10.98 inference(unit_resolution,[status(thm)],[2168, 2163, 164])).
% 10.69/10.98 tff(25667,plain,
% 10.69/10.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.69/10.98 inference(rewrite,[status(thm)],[])).
% 10.69/10.98 tff(25668,plain,
% 10.69/10.98 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.69/10.98 inference(rewrite,[status(thm)],[])).
% 10.69/10.98 tff(25669,plain,
% 10.69/10.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 10.69/10.99 inference(monotonicity,[status(thm)],[25668])).
% 10.69/10.99 tff(25670,plain,
% 10.69/10.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.69/10.99 inference(transitivity,[status(thm)],[25669, 25667])).
% 10.69/10.99 tff(25671,plain,
% 10.69/10.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 10.69/10.99 inference(quant_inst,[status(thm)],[])).
% 10.69/10.99 tff(25672,plain,
% 10.69/10.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 10.69/10.99 inference(modus_ponens,[status(thm)],[25671, 25670])).
% 10.69/10.99 tff(25673,plain,
% 10.69/10.99 ($false),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[25672, 194, 25666, 410, 25665, 25661])).
% 10.69/10.99 tff(25674,plain,(b(s(elem!1), elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~(s(z) = elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.69/10.99 tff(25675,plain,
% 10.69/10.99 (b(s(elem!1), elem!1)),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[25674, 25641, 24165, 410, 380, 25599, 10682, 900, 182, 1628, 11964, 812, 164])).
% 10.69/10.99 tff(25676,plain,
% 10.69/10.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 10.69/10.99 inference(rewrite,[status(thm)],[])).
% 10.69/10.99 tff(25677,plain,
% 10.69/10.99 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 10.69/10.99 inference(rewrite,[status(thm)],[])).
% 10.69/10.99 tff(25678,plain,
% 10.69/10.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))))),
% 10.69/10.99 inference(monotonicity,[status(thm)],[25677])).
% 10.69/10.99 tff(25679,plain,
% 10.69/10.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 10.69/10.99 inference(transitivity,[status(thm)],[25678, 25676])).
% 10.69/10.99 tff(25680,plain,
% 10.69/10.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 10.69/10.99 inference(quant_inst,[status(thm)],[])).
% 10.69/10.99 tff(25681,plain,
% 10.69/10.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))),
% 10.69/10.99 inference(modus_ponens,[status(thm)],[25680, 25679])).
% 10.69/10.99 tff(25682,plain,
% 10.69/10.99 ($false),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[25681, 391, 133, 900, 380, 25599, 25675])).
% 10.69/10.99 tff(25683,plain,(r(s(z), s(s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~(s(z) = elem!1)) | (s(elem!1) = elem!1) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.99 tff(25684,plain,
% 10.69/10.99 (r(s(z), s(s(z)))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[25683, 133, 900, 25596, 410, 10682, 25595, 25593, 11964, 812, 164, 8611, 285, 530])).
% 10.69/10.99 tff(25685,plain,
% 10.69/10.99 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[11508, 25684, 1216, 25592])).
% 10.69/10.99 tff(25686,plain,
% 10.69/10.99 (b(s(s(s(s(z)))), s(s(z)))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[1714, 25685])).
% 10.69/10.99 tff(25687,plain,
% 10.69/10.99 (b(s(s(s(elem!1))), s(elem!1))),
% 10.69/10.99 inference(modus_ponens,[status(thm)],[25686, 19005])).
% 10.69/10.99 tff(25688,plain,
% 10.69/10.99 (~r(z, s(s(elem!1)))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[3787, 25684, 25592, 25595])).
% 10.69/10.99 tff(25689,plain,
% 10.69/10.99 (b(z, s(s(elem!1)))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[324, 25688])).
% 10.69/10.99 tff(25690,plain,
% 10.69/10.99 (~r(z, s(s(z)))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[20649, 25684, 25592, 25595])).
% 10.69/10.99 tff(25691,plain,
% 10.69/10.99 (~r(z, s(elem!1))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[8520, 25690, 812])).
% 10.69/10.99 tff(25692,plain,
% 10.69/10.99 (b(z, s(elem!1))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[566, 25691])).
% 10.69/10.99 tff(25693,plain,
% 10.69/10.99 (b(z, s(s(z)))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[8527, 25692, 812])).
% 10.69/10.99 tff(25694,plain,
% 10.69/10.99 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[15550, 25693, 1686, 25686])).
% 10.69/10.99 tff(25695,plain,
% 10.69/10.99 (r(s(s(z)), s(s(s(s(z)))))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[3652, 25694])).
% 10.69/10.99 tff(25696,plain,
% 10.69/10.99 (r(s(elem!1), s(s(s(elem!1))))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[3614, 25695, 812])).
% 10.69/10.99 tff(25697,plain,
% 10.69/10.99 (r(elem!1, s(elem!1))),
% 10.69/10.99 inference(modus_ponens,[status(thm)],[25684, 19010])).
% 10.69/10.99 tff(25698,plain,
% 10.69/10.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.69/10.99 inference(rewrite,[status(thm)],[])).
% 10.69/10.99 tff(25699,plain,
% 10.69/10.99 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.69/10.99 inference(rewrite,[status(thm)],[])).
% 10.69/10.99 tff(25700,plain,
% 10.69/10.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 10.69/10.99 inference(monotonicity,[status(thm)],[25699])).
% 10.69/10.99 tff(25701,plain,
% 10.69/10.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.69/10.99 inference(transitivity,[status(thm)],[25700, 25698])).
% 10.69/10.99 tff(25702,plain,
% 10.69/10.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 10.69/10.99 inference(quant_inst,[status(thm)],[])).
% 10.69/10.99 tff(25703,plain,
% 10.69/10.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 10.69/10.99 inference(modus_ponens,[status(thm)],[25702, 25701])).
% 10.69/10.99 tff(25704,plain,
% 10.69/10.99 ($false),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[25703, 194, 2251, 410, 327, 604])).
% 10.69/10.99 tff(25705,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.69/10.99 tff(25706,plain,
% 10.69/10.99 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[25705, 25697, 410, 25696])).
% 10.69/10.99 tff(25707,plain,
% 10.69/10.99 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[1370, 25706, 24165])).
% 10.69/10.99 tff(25708,plain,
% 10.69/10.99 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[12932, 25707, 10682, 25689])).
% 10.69/10.99 tff(25709,plain,
% 10.69/10.99 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[1356, 25708, 7434])).
% 10.69/10.99 tff(25710,plain,
% 10.69/10.99 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[12932, 1374, 10682, 3927])).
% 10.69/10.99 tff(25711,plain,
% 10.69/10.99 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.69/10.99 inference(unit_resolution,[status(thm)],[1356, 25710, 7434])).
% 10.69/10.99 tff(25712,plain,
% 10.69/10.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 10.69/10.99 inference(rewrite,[status(thm)],[])).
% 10.69/10.99 tff(25713,plain,
% 10.69/10.99 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 10.69/10.99 inference(rewrite,[status(thm)],[])).
% 10.69/10.99 tff(25714,plain,
% 10.69/10.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 10.69/10.99 inference(monotonicity,[status(thm)],[25713])).
% 10.69/10.99 tff(25715,plain,
% 10.69/10.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 10.69/11.00 inference(transitivity,[status(thm)],[25714, 25712])).
% 10.69/11.00 tff(25716,plain,
% 10.69/11.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 10.69/11.00 inference(quant_inst,[status(thm)],[])).
% 10.69/11.00 tff(25717,plain,
% 10.69/11.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 10.69/11.00 inference(modus_ponens,[status(thm)],[25716, 25715])).
% 10.69/11.00 tff(25718,plain,
% 10.69/11.00 ($false),
% 10.69/11.00 inference(unit_resolution,[status(thm)],[25717, 194, 364, 410, 1538, 1378])).
% 10.69/11.00 tff(25719,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.00 tff(25720,plain,
% 10.69/11.00 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.69/11.00 inference(unit_resolution,[status(thm)],[25719, 364, 410, 25711])).
% 10.69/11.00 tff(25721,plain,
% 10.69/11.00 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.69/11.00 inference(unit_resolution,[status(thm)],[1164, 25720, 25586])).
% 10.69/11.00 tff(25722,plain,
% 10.69/11.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 10.69/11.00 inference(rewrite,[status(thm)],[])).
% 10.69/11.00 tff(25723,plain,
% 10.69/11.00 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 10.69/11.00 inference(rewrite,[status(thm)],[])).
% 10.69/11.00 tff(25724,plain,
% 10.69/11.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 10.69/11.00 inference(monotonicity,[status(thm)],[25723])).
% 10.69/11.00 tff(25725,plain,
% 10.69/11.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 10.69/11.00 inference(transitivity,[status(thm)],[25724, 25722])).
% 10.69/11.00 tff(25726,plain,
% 10.69/11.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 10.69/11.00 inference(quant_inst,[status(thm)],[])).
% 10.69/11.00 tff(25727,plain,
% 10.69/11.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 10.69/11.00 inference(modus_ponens,[status(thm)],[25726, 25725])).
% 10.69/11.00 tff(25728,plain,
% 10.69/11.00 ($false),
% 10.69/11.00 inference(unit_resolution,[status(thm)],[25727, 391, 1101, 380, 10682, 1573, 17911])).
% 10.69/11.00 tff(25729,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.00 tff(25730,plain,
% 10.69/11.00 (~b(s(s(s(s(elem!1)))), z)),
% 10.69/11.00 inference(unit_resolution,[status(thm)],[25729, 25721, 380, 10682, 1101])).
% 10.69/11.00 tff(25731,plain,
% 10.69/11.00 (r(s(s(s(s(elem!1)))), z)),
% 10.69/11.00 inference(unit_resolution,[status(thm)],[1626, 25730])).
% 10.69/11.00 tff(25732,plain,
% 10.69/11.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.69/11.00 inference(rewrite,[status(thm)],[])).
% 10.69/11.00 tff(25733,plain,
% 10.69/11.00 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.69/11.00 inference(rewrite,[status(thm)],[])).
% 10.69/11.00 tff(25734,plain,
% 10.69/11.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 10.69/11.00 inference(monotonicity,[status(thm)],[25733])).
% 10.69/11.00 tff(25735,plain,
% 10.69/11.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 10.69/11.00 inference(transitivity,[status(thm)],[25734, 25732])).
% 10.69/11.00 tff(25736,plain,
% 10.69/11.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 10.69/11.00 inference(quant_inst,[status(thm)],[])).
% 10.69/11.00 tff(25737,plain,
% 10.69/11.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 10.69/11.01 inference(modus_ponens,[status(thm)],[25736, 25735])).
% 10.69/11.01 tff(25738,plain,
% 10.69/11.01 ($false),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[25737, 391, 380, 1374, 3927, 2698, 1152])).
% 10.69/11.01 tff(25739,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.01 tff(25740,plain,
% 10.69/11.01 (~b(s(s(s(s(elem!1)))), elem!1)),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[25739, 1152, 380, 3927, 1374])).
% 10.69/11.01 tff(25741,plain,
% 10.69/11.01 (r(s(s(s(s(elem!1)))), elem!1)),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[1004, 25740, 972])).
% 10.69/11.01 tff(25742,plain,
% 10.69/11.01 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[1741, 1152, 1573, 1374])).
% 10.69/11.01 tff(25743,plain,
% 10.69/11.01 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[1061, 25742, 1050])).
% 10.69/11.01 tff(25744,plain,
% 10.69/11.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 10.69/11.01 inference(rewrite,[status(thm)],[])).
% 10.69/11.01 tff(25745,plain,
% 10.69/11.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 10.69/11.01 inference(quant_inst,[status(thm)],[])).
% 10.69/11.01 tff(25746,plain,
% 10.69/11.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 10.69/11.01 inference(modus_ponens,[status(thm)],[25745, 25744])).
% 10.69/11.01 tff(25747,plain,
% 10.69/11.01 ($false),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[25746, 194, 530, 364, 25743, 25741])).
% 10.69/11.01 tff(25748,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.01 tff(25749,plain,
% 10.69/11.01 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[25748, 364, 530, 10228, 7473, 25721, 1374, 380, 3927])).
% 10.69/11.01 tff(25750,plain,
% 10.69/11.01 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[1048, 25749, 7435])).
% 10.69/11.01 tff(25751,plain,
% 10.69/11.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 10.69/11.01 inference(rewrite,[status(thm)],[])).
% 10.69/11.01 tff(25752,plain,
% 10.69/11.01 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 10.69/11.01 inference(rewrite,[status(thm)],[])).
% 10.69/11.01 tff(25753,plain,
% 10.69/11.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 10.69/11.01 inference(monotonicity,[status(thm)],[25752])).
% 10.69/11.01 tff(25754,plain,
% 10.69/11.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 10.69/11.01 inference(transitivity,[status(thm)],[25753, 25751])).
% 10.69/11.01 tff(25755,plain,
% 10.69/11.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 10.69/11.01 inference(quant_inst,[status(thm)],[])).
% 10.69/11.01 tff(25756,plain,
% 10.69/11.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 10.69/11.01 inference(modus_ponens,[status(thm)],[25755, 25754])).
% 10.69/11.01 tff(25757,plain,
% 10.69/11.01 ($false),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[25756, 391, 1101, 10682, 592, 974, 2122])).
% 10.69/11.01 tff(25758,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.01 tff(25759,plain,
% 10.69/11.01 (~b(elem!1, s(s(s(s(elem!1)))))),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[25758, 25629, 10682, 592, 1101])).
% 10.69/11.01 tff(25760,plain,
% 10.69/11.01 (r(elem!1, s(s(s(s(elem!1)))))),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[1018, 25759, 18176])).
% 10.69/11.01 tff(25761,plain,
% 10.69/11.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.69/11.01 inference(rewrite,[status(thm)],[])).
% 10.69/11.01 tff(25762,plain,
% 10.69/11.01 (((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.69/11.01 inference(rewrite,[status(thm)],[])).
% 10.69/11.01 tff(25763,plain,
% 10.69/11.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 10.69/11.01 inference(monotonicity,[status(thm)],[25762])).
% 10.69/11.01 tff(25764,plain,
% 10.69/11.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 10.69/11.01 inference(transitivity,[status(thm)],[25763, 25761])).
% 10.69/11.01 tff(25765,plain,
% 10.69/11.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))),
% 10.69/11.01 inference(quant_inst,[status(thm)],[])).
% 10.69/11.01 tff(25766,plain,
% 10.69/11.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 10.69/11.01 inference(modus_ponens,[status(thm)],[25765, 25764])).
% 10.69/11.01 tff(25767,plain,
% 10.69/11.01 ($false),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[25766, 194, 364, 25760, 25750, 25731])).
% 10.69/11.01 tff(25768,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.01 tff(25769,plain,
% 10.69/11.01 (~r(s(s(elem!1)), elem!1)),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[25768, 25707, 530, 25596, 25689, 10682, 25692, 25687, 410, 164, 25593, 812, 8611, 285, 25595])).
% 10.69/11.01 tff(25770,plain,
% 10.69/11.01 (b(s(s(elem!1)), elem!1)),
% 10.69/11.01 inference(unit_resolution,[status(thm)],[872, 25769, 7422])).
% 10.69/11.01 tff(25771,plain,
% 10.69/11.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 10.69/11.01 inference(rewrite,[status(thm)],[])).
% 10.69/11.01 tff(25772,plain,
% 10.69/11.01 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 10.69/11.01 inference(rewrite,[status(thm)],[])).
% 10.69/11.01 tff(25773,plain,
% 10.69/11.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 10.69/11.01 inference(monotonicity,[status(thm)],[25772])).
% 10.69/11.01 tff(25774,plain,
% 10.69/11.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 10.69/11.01 inference(transitivity,[status(thm)],[25773, 25771])).
% 10.69/11.01 tff(25775,plain,
% 10.69/11.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 10.69/11.02 inference(quant_inst,[status(thm)],[])).
% 10.69/11.02 tff(25776,plain,
% 10.69/11.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 10.69/11.02 inference(modus_ponens,[status(thm)],[25775, 25774])).
% 10.69/11.02 tff(25777,plain,
% 10.69/11.02 ($false),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25776, 391, 10682, 973, 1374, 3927, 974])).
% 10.69/11.02 tff(25778,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.02 tff(25779,plain,
% 10.69/11.02 (~b(elem!1, s(s(s(s(elem!1)))))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25778, 25770, 10682, 25707, 25689])).
% 10.69/11.02 tff(25780,plain,
% 10.69/11.02 (r(elem!1, s(s(s(s(elem!1)))))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[1018, 25779, 18176])).
% 10.69/11.02 tff(25781,plain,
% 10.69/11.02 (~b(elem!1, s(s(elem!1)))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[3979, 25770, 133, 25689])).
% 10.69/11.02 tff(25782,plain,
% 10.69/11.02 (r(elem!1, s(s(elem!1)))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[1307, 25781, 9651])).
% 10.69/11.02 tff(25783,plain,
% 10.69/11.02 (~b(s(s(s(s(elem!1)))), z)),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25729, 1573, 380, 10682, 1101])).
% 10.69/11.02 tff(25784,plain,
% 10.69/11.02 (r(s(s(s(s(elem!1)))), z)),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[1626, 25783])).
% 10.69/11.02 tff(25785,plain,
% 10.69/11.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 10.69/11.02 inference(rewrite,[status(thm)],[])).
% 10.69/11.02 tff(25786,plain,
% 10.69/11.02 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 10.69/11.02 inference(rewrite,[status(thm)],[])).
% 10.69/11.02 tff(25787,plain,
% 10.69/11.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 10.69/11.02 inference(monotonicity,[status(thm)],[25786])).
% 10.69/11.02 tff(25788,plain,
% 10.69/11.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 10.69/11.02 inference(transitivity,[status(thm)],[25787, 25785])).
% 10.69/11.02 tff(25789,plain,
% 10.69/11.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 10.69/11.02 inference(quant_inst,[status(thm)],[])).
% 10.69/11.02 tff(25790,plain,
% 10.69/11.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 10.69/11.02 inference(modus_ponens,[status(thm)],[25789, 25788])).
% 10.69/11.02 tff(25791,plain,
% 10.69/11.02 ($false),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25790, 194, 1064, 25743, 25741, 1378])).
% 10.69/11.02 tff(25792,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.02 tff(25793,plain,
% 10.69/11.02 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25792, 1573, 1378, 2712, 972, 1064, 1374, 380, 3927])).
% 10.69/11.02 tff(25794,plain,
% 10.69/11.02 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[1048, 25793, 1035])).
% 10.69/11.02 tff(25795,plain,
% 10.69/11.02 ($false),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[15258, 25794, 25784, 1064, 1063])).
% 10.69/11.02 tff(25796,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.02 tff(25797,plain,
% 10.69/11.02 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25796, 25782, 25780, 7435, 25709, 7473, 25707, 25596, 25689, 10682, 25687])).
% 10.69/11.02 tff(25798,plain,
% 10.69/11.02 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[1164, 25797, 25586])).
% 10.69/11.02 tff(25799,plain,
% 10.69/11.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 10.69/11.02 inference(rewrite,[status(thm)],[])).
% 10.69/11.02 tff(25800,plain,
% 10.69/11.02 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 10.69/11.02 inference(rewrite,[status(thm)],[])).
% 10.69/11.02 tff(25801,plain,
% 10.69/11.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 10.69/11.02 inference(monotonicity,[status(thm)],[25800])).
% 10.69/11.02 tff(25802,plain,
% 10.69/11.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 10.69/11.02 inference(transitivity,[status(thm)],[25801, 25799])).
% 10.69/11.02 tff(25803,plain,
% 10.69/11.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 10.69/11.02 inference(quant_inst,[status(thm)],[])).
% 10.69/11.02 tff(25804,plain,
% 10.69/11.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 10.69/11.02 inference(modus_ponens,[status(thm)],[25803, 25802])).
% 10.69/11.02 tff(25805,plain,
% 10.69/11.02 ($false),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25804, 194, 25697, 410, 25696, 25798])).
% 10.69/11.02 tff(25806,plain,((~b(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (s(elem!1) = elem!1) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.02 tff(25807,plain,
% 10.69/11.02 (~b(z, elem!1)),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25806, 6124, 10782, 25571, 426, 25553, 25584, 25581, 25569, 2913, 25378, 25578, 88, 25577])).
% 10.69/11.02 tff(25808,plain,
% 10.69/11.02 (r(z, elem!1)),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[141, 25807, 23980])).
% 10.69/11.02 tff(25809,plain,
% 10.69/11.02 (~(s(s(elem!1)) = s(elem!1))),
% 10.69/11.02 inference(modus_ponens,[status(thm)],[11940, 7411])).
% 10.69/11.02 tff(25810,plain,
% 10.69/11.02 (~r(elem!1, s(elem!1))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[24443, 411, 10682, 812, 530, 410, 25596])).
% 10.69/11.02 tff(25811,plain,
% 10.69/11.02 (b(elem!1, s(elem!1))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[443, 25810, 7437])).
% 10.69/11.02 tff(25812,plain,
% 10.69/11.02 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[287, 25809])).
% 10.69/11.02 tff(25813,plain,
% 10.69/11.02 (~(s(elem!1) = s(s(elem!1)))),
% 10.69/11.02 inference(modus_ponens,[status(thm)],[11940, 18180])).
% 10.69/11.02 tff(25814,plain,
% 10.69/11.02 (~r(elem!1, s(elem!1))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[24443, 411, 10682, 812, 530, 410, 380])).
% 10.69/11.02 tff(25815,plain,
% 10.69/11.02 (b(elem!1, s(elem!1))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[443, 25814, 7437])).
% 10.69/11.02 tff(25816,plain,
% 10.69/11.02 (~b(s(s(elem!1)), z)),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25637, 328, 10682, 900, 25815])).
% 10.69/11.02 tff(25817,plain,
% 10.69/11.02 (~b(s(elem!1), elem!1)),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[24431, 25816, 812, 10682, 530, 380, 957, 410, 7437, 411])).
% 10.69/11.02 tff(25818,plain,
% 10.69/11.02 (~b(s(elem!1), z)),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[3903, 328, 900, 25815, 973])).
% 10.69/11.02 tff(25819,plain,
% 10.69/11.02 (r(s(elem!1), z)),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[549, 25818])).
% 10.69/11.02 tff(25820,plain,
% 10.69/11.02 ($false),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25674, 25819, 25817, 297, 410, 380, 25815, 10682, 900, 182, 973, 11964, 812, 164])).
% 10.69/11.02 tff(25821,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = s(z)) | (~(s(z) = elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, z)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.69/11.02 tff(25822,plain,
% 10.69/11.02 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[25821, 973, 410, 25596, 10682, 900, 25595, 25812, 11956, 812, 164, 530, 957, 411])).
% 10.69/11.02 tff(25823,plain,
% 10.69/11.02 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[1356, 25822, 7434])).
% 10.69/11.02 tff(25824,plain,
% 10.69/11.02 (~r(s(s(z)), z)),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[3560, 544, 812])).
% 10.69/11.02 tff(25825,plain,
% 10.69/11.02 (b(s(s(z)), z)),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[1211, 25824])).
% 10.69/11.02 tff(25826,plain,
% 10.69/11.02 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[20748, 25825, 90, 1686])).
% 10.69/11.02 tff(25827,plain,
% 10.69/11.02 (r(s(s(s(s(z)))), s(s(z)))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[1714, 25826])).
% 10.69/11.02 tff(25828,plain,
% 10.69/11.02 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[4472, 25825, 90, 1686])).
% 10.69/11.02 tff(25829,plain,
% 10.69/11.02 (r(s(s(z)), s(s(s(s(z)))))),
% 10.69/11.02 inference(unit_resolution,[status(thm)],[3652, 25828])).
% 10.82/11.03 tff(25830,plain,
% 10.82/11.03 (~r(s(s(z)), s(z))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[14395, 25829, 1216, 25827])).
% 10.82/11.03 tff(25831,plain,
% 10.82/11.03 (b(s(s(z)), s(z))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[3778, 25830])).
% 10.82/11.03 tff(25832,plain,
% 10.82/11.03 (b(s(elem!1), elem!1)),
% 10.82/11.03 inference(modus_ponens,[status(thm)],[25831, 7399])).
% 10.82/11.03 tff(25833,plain,
% 10.82/11.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.82/11.03 inference(rewrite,[status(thm)],[])).
% 10.82/11.03 tff(25834,plain,
% 10.82/11.03 (((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.82/11.03 inference(rewrite,[status(thm)],[])).
% 10.82/11.03 tff(25835,plain,
% 10.82/11.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 10.82/11.03 inference(monotonicity,[status(thm)],[25834])).
% 10.82/11.03 tff(25836,plain,
% 10.82/11.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 10.82/11.03 inference(transitivity,[status(thm)],[25835, 25833])).
% 10.82/11.03 tff(25837,plain,
% 10.82/11.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 10.82/11.03 inference(quant_inst,[status(thm)],[])).
% 10.82/11.03 tff(25838,plain,
% 10.82/11.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 10.82/11.03 inference(modus_ponens,[status(thm)],[25837, 25836])).
% 10.82/11.03 tff(25839,plain,
% 10.82/11.03 (~b(s(elem!1), s(s(elem!1)))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[25838, 391, 973, 11937, 802, 25832])).
% 10.82/11.03 tff(25840,plain,
% 10.82/11.03 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 10.82/11.03 inference(monotonicity,[status(thm)],[1552])).
% 10.82/11.03 tff(25841,plain,
% 10.82/11.03 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 10.82/11.03 inference(symmetry,[status(thm)],[25840])).
% 10.82/11.03 tff(25842,plain,
% 10.82/11.03 (~r(s(s(z)), z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[3560, 8598, 544])).
% 10.82/11.03 tff(25843,plain,
% 10.82/11.03 (b(s(s(z)), z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[1211, 25842])).
% 10.82/11.03 tff(25844,plain,
% 10.82/11.03 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[3614, 8598, 3612])).
% 10.82/11.03 tff(25845,plain,
% 10.82/11.03 (b(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[3652, 25844])).
% 10.82/11.03 tff(25846,plain,
% 10.82/11.03 (~b(s(s(s(s(z)))), z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[4472, 25845, 1686, 25843])).
% 10.82/11.03 tff(25847,plain,
% 10.82/11.03 (r(s(s(s(s(z)))), z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[87, 25846])).
% 10.82/11.03 tff(25848,plain,
% 10.82/11.03 (r(s(s(s(elem!1))), z)),
% 10.82/11.03 inference(modus_ponens,[status(thm)],[25847, 25841])).
% 10.82/11.03 tff(25849,plain,
% 10.82/11.03 ($false),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[329, 25848])).
% 10.82/11.03 tff(25850,plain,((~(elem!1 = s(z))) | r(s(s(s(elem!1))), z) | (~b(z, s(s(s(s(z)))))) | r(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 10.82/11.03 tff(25851,plain,
% 10.82/11.03 (r(s(elem!1), s(s(s(elem!1))))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[25850, 544, 7866, 1686, 329])).
% 10.82/11.03 tff(25852,plain,
% 10.82/11.03 (~b(s(s(s(elem!1))), s(elem!1))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[12799, 11937, 10682, 25596])).
% 10.82/11.03 tff(25853,plain,
% 10.82/11.03 (r(s(s(s(elem!1))), s(elem!1))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[588, 25852, 7433])).
% 10.82/11.03 tff(25854,plain,
% 10.82/11.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.82/11.03 inference(rewrite,[status(thm)],[])).
% 10.82/11.03 tff(25855,plain,
% 10.82/11.03 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.82/11.03 inference(rewrite,[status(thm)],[])).
% 10.82/11.03 tff(25856,plain,
% 10.82/11.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 10.82/11.03 inference(monotonicity,[status(thm)],[25855])).
% 10.82/11.03 tff(25857,plain,
% 10.82/11.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.82/11.03 inference(transitivity,[status(thm)],[25856, 25854])).
% 10.82/11.03 tff(25858,plain,
% 10.82/11.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 10.82/11.03 inference(quant_inst,[status(thm)],[])).
% 10.82/11.03 tff(25859,plain,
% 10.82/11.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 10.82/11.03 inference(modus_ponens,[status(thm)],[25858, 25857])).
% 10.82/11.03 tff(25860,plain,
% 10.82/11.03 (~r(s(elem!1), s(s(elem!1)))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[25859, 194, 25853, 25851, 1378])).
% 10.82/11.03 tff(25861,plain,
% 10.82/11.03 ($false),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[8644, 25860, 25839, 8611])).
% 10.82/11.03 tff(25862,plain,(r(s(elem!1), z) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~(s(z) = elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 10.82/11.03 tff(25863,plain,
% 10.82/11.03 (r(s(elem!1), z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[25862, 25823, 25813, 973, 25811, 812, 1216, 90, 1686, 10682, 329])).
% 10.82/11.03 tff(25864,plain,
% 10.82/11.03 (b(s(elem!1), elem!1)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[25674, 25863, 25812, 410, 25596, 25811, 10682, 900, 25595, 973, 11956, 812, 164])).
% 10.82/11.03 tff(25865,plain,
% 10.82/11.03 (~b(s(s(elem!1)), s(elem!1))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[19494, 25864, 25811, 973])).
% 10.82/11.03 tff(25866,plain,
% 10.82/11.03 (r(s(s(s(elem!1))), s(elem!1))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[2594, 25863, 1526, 411, 25595, 121, 232])).
% 10.82/11.03 tff(25867,plain,
% 10.82/11.03 (~r(s(s(elem!1)), s(elem!1))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[24584, 25864, 410, 25809, 25823, 973, 9651, 25866])).
% 10.82/11.03 tff(25868,plain,
% 10.82/11.03 ($false),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[1135, 25867, 25865, 25809])).
% 10.82/11.03 tff(25869,plain,((~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1)) | (s(elem!1) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | r(s(s(s(elem!1))), z) | (~r(elem!1, z)) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.03 tff(25870,plain,
% 10.82/11.03 (~b(s(s(elem!1)), elem!1)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[25869, 6124, 10782, 25378, 25553, 426, 25087, 25808, 23981, 25576, 2913, 88, 25569, 25574, 25571, 930])).
% 10.82/11.03 tff(25871,plain,
% 10.82/11.03 (r(s(s(elem!1)), elem!1)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[872, 25870, 25565])).
% 10.82/11.03 tff(25872,plain,
% 10.82/11.03 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[281, 25562])).
% 10.82/11.03 tff(25873,plain,
% 10.82/11.03 (~r(elem!1, s(elem!1))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[24443, 25808, 10782, 25553, 25571, 6124, 25558])).
% 10.82/11.03 tff(25874,plain,
% 10.82/11.03 (b(elem!1, s(elem!1))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[443, 25873, 427])).
% 10.82/11.03 tff(25875,plain,
% 10.82/11.03 (~r(s(s(elem!1)), z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[8360, 25871, 25571, 25808])).
% 10.82/11.03 tff(25876,plain,
% 10.82/11.03 (b(s(s(elem!1)), z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[2629, 25875])).
% 10.82/11.03 tff(25877,plain,
% 10.82/11.03 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[25637, 25876, 10782, 25378, 25874])).
% 10.82/11.03 tff(25878,plain,
% 10.82/11.03 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[1356, 25877, 25872])).
% 10.82/11.03 tff(25879,plain,
% 10.82/11.03 (~r(s(s(s(elem!1))), s(elem!1))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[15594, 25878, 6124, 25871])).
% 10.82/11.03 tff(25880,plain,
% 10.82/11.03 (b(s(s(s(elem!1))), s(elem!1))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[588, 25879, 25562])).
% 10.82/11.03 tff(25881,plain,
% 10.82/11.03 (r(s(z), z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[7485, 25570, 25553])).
% 10.82/11.03 tff(25882,plain,
% 10.82/11.03 (~r(s(elem!1), z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[2594, 25879, 25087, 25808, 25881, 23981, 25576])).
% 10.82/11.03 tff(25883,plain,
% 10.82/11.03 (b(s(elem!1), z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[549, 25882])).
% 10.82/11.03 tff(25884,plain,
% 10.82/11.03 ($false),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[12799, 25883, 25880, 10782, 25558])).
% 10.82/11.03 tff(25885,plain,(b(elem!1, s(s(s(elem!1)))) | r(s(s(s(s(z)))), z) | r(z, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.03 tff(25886,plain,
% 10.82/11.03 ($false),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[25885, 25086, 25085, 81, 2881, 1])).
% 10.82/11.03 tff(25887,plain,((s(z) = elem!1) | r(s(s(s(s(z)))), z) | b(s(z), s(s(s(s(z))))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.03 tff(25888,plain,
% 10.82/11.03 (s(z) = elem!1),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[25887, 1, 2881, 81, 31, 133, 10682, 664, 182, 530])).
% 10.82/11.03 tff(25889,plain,
% 10.82/11.03 (elem!1 = s(z)),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[1495, 25888])).
% 10.82/11.03 tff(25890,plain,
% 10.82/11.03 (b(s(s(s(elem!1))), s(z))),
% 10.82/11.03 inference(unit_resolution,[status(thm)],[11177, 25889, 1759])).
% 10.82/11.04 tff(25891,plain,
% 10.82/11.04 (~b(elem!1, s(s(s(elem!1))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[8314, 25889, 2881])).
% 10.82/11.04 tff(25892,plain,
% 10.82/11.04 (b(s(s(s(elem!1))), elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[25377, 25891, 88, 10682, 2881, 1, 25890])).
% 10.82/11.04 tff(25893,plain,
% 10.82/11.04 (~b(s(s(z)), z)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[25590, 25892, 88, 10682, 664, 1759, 2913])).
% 10.82/11.04 tff(25894,plain,
% 10.82/11.04 (~b(s(z), s(s(s(elem!1))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[2884, 25889, 2881])).
% 10.82/11.04 tff(25895,plain,
% 10.82/11.04 (r(s(z), s(s(s(elem!1))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[247, 25894])).
% 10.82/11.04 tff(25896,plain,
% 10.82/11.04 (r(z, s(s(s(elem!1))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[25885, 25891, 81, 2881, 1])).
% 10.82/11.04 tff(25897,plain,
% 10.82/11.04 (~r(s(s(s(elem!1))), s(elem!1))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[641, 25896, 182, 25895])).
% 10.82/11.04 tff(25898,plain,
% 10.82/11.04 (~r(s(elem!1), z)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[6142, 25892, 25896, 25891, 530, 427, 25897])).
% 10.82/11.04 tff(25899,plain,
% 10.82/11.04 (~r(s(s(z)), z)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[3560, 25898, 25888])).
% 10.82/11.04 tff(25900,plain,
% 10.82/11.04 ($false),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[1211, 25899, 25893])).
% 10.82/11.04 tff(25901,plain,((elem!1 = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | b(s(z), s(s(s(s(z))))) | r(s(s(s(s(z)))), z) | b(elem!1, s(z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.04 tff(25902,plain,
% 10.82/11.04 (elem!1 = s(s(s(elem!1)))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[25901, 25084, 664, 22898, 25076, 182, 2881, 81, 31, 133])).
% 10.82/11.04 tff(25903,plain,
% 10.82/11.04 (s(elem!1) = s(s(s(s(elem!1))))),
% 10.82/11.04 inference(monotonicity,[status(thm)],[25902])).
% 10.82/11.04 tff(25904,plain,
% 10.82/11.04 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 10.82/11.04 inference(monotonicity,[status(thm)],[25903])).
% 10.82/11.04 tff(25905,plain,
% 10.82/11.04 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 10.82/11.04 inference(symmetry,[status(thm)],[25904])).
% 10.82/11.04 tff(25906,plain,
% 10.82/11.04 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.82/11.04 inference(monotonicity,[status(thm)],[25905])).
% 10.82/11.04 tff(25907,plain,
% 10.82/11.04 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 10.82/11.04 inference(symmetry,[status(thm)],[25906])).
% 10.82/11.04 tff(25908,plain,
% 10.82/11.04 (s(s(s(elem!1))) = elem!1),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[129, 25902])).
% 10.82/11.04 tff(25909,plain,
% 10.82/11.04 (r(s(s(s(elem!1))), z)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[533, 25908, 25076])).
% 10.82/11.04 tff(25910,plain,
% 10.82/11.04 (~b(s(s(s(elem!1))), s(z))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[8400, 25908, 31])).
% 10.82/11.04 tff(25911,plain,
% 10.82/11.04 (r(s(s(s(elem!1))), s(z))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[223, 25910])).
% 10.82/11.04 tff(25912,plain,
% 10.82/11.04 (~r(z, s(s(s(elem!1))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[202, 25911, 182, 25909])).
% 10.82/11.04 tff(25913,plain,
% 10.82/11.04 (~b(elem!1, s(s(s(elem!1))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[15370, 25908])).
% 10.82/11.04 tff(25914,plain,
% 10.82/11.04 (r(elem!1, s(z))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[8406, 25911, 25908])).
% 10.82/11.04 tff(25915,plain,
% 10.82/11.04 (~r(z, s(s(elem!1)))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[855, 25914, 182, 25076])).
% 10.82/11.04 tff(25916,plain,
% 10.82/11.04 (b(z, s(s(elem!1)))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[324, 25915])).
% 10.82/11.04 tff(25917,plain,
% 10.82/11.04 (~(elem!1 = s(s(s(s(z)))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[16358, 90, 484])).
% 10.82/11.04 tff(25918,plain,
% 10.82/11.04 (~(s(s(s(elem!1))) = elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[8406, 832, 11174])).
% 10.82/11.04 tff(25919,plain,
% 10.82/11.04 (~r(s(z), s(s(s(elem!1))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[24553, 25918, 4028, 530, 115, 2913, 90, 3927, 8329, 11173, 53, 2829])).
% 10.82/11.04 tff(25920,plain,
% 10.82/11.04 (b(s(z), s(s(s(elem!1))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[247, 25919])).
% 10.82/11.04 tff(25921,plain,
% 10.82/11.04 (~(elem!1 = s(z))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[2884, 25920, 2881])).
% 10.82/11.04 tff(25922,plain,
% 10.82/11.04 (b(elem!1, s(z))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[837, 25921, 832])).
% 10.82/11.04 tff(25923,plain,
% 10.82/11.04 (~(s(z) = elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[7796, 25920, 4028])).
% 10.82/11.04 tff(25924,plain,
% 10.82/11.04 (r(s(z), elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[632, 25923, 2829])).
% 10.82/11.04 tff(25925,plain,
% 10.82/11.04 (~r(s(s(s(elem!1))), elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[23283, 25924, 530, 11174])).
% 10.82/11.04 tff(25926,plain,
% 10.82/11.04 (b(s(s(s(elem!1))), elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[230, 25925, 25918])).
% 10.82/11.04 tff(25927,plain,
% 10.82/11.04 (~r(z, elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[627, 25924, 530, 182])).
% 10.82/11.04 tff(25928,plain,
% 10.82/11.04 (b(z, elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[141, 25927, 115])).
% 10.82/11.04 tff(25929,plain,
% 10.82/11.04 ($false),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[23274, 391, 25928, 25926, 10782, 25920, 25922])).
% 10.82/11.04 tff(25930,plain,(r(elem!1, s(z)) | (~r(elem!1, z)) | (z = elem!1) | (~r(s(z), z)) | b(s(z), elem!1) | b(s(z), s(s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.04 tff(25931,plain,
% 10.82/11.04 (r(elem!1, s(z))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[25930, 2829, 115, 182, 530, 2881, 4028, 90, 3927, 8329, 11173, 53])).
% 10.82/11.04 tff(25932,plain,
% 10.82/11.04 (~r(z, s(s(s(s(z)))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[17062, 25931, 182, 530])).
% 10.82/11.04 tff(25933,plain,
% 10.82/11.04 (b(z, s(s(s(s(z)))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[800, 25932])).
% 10.82/11.04 tff(25934,plain,
% 10.82/11.04 (~r(z, s(z))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[17266, 25931, 182, 530])).
% 10.82/11.04 tff(25935,plain,
% 10.82/11.04 (b(z, s(z))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[678, 25934])).
% 10.82/11.04 tff(25936,plain,
% 10.82/11.04 (~r(elem!1, s(s(s(elem!1))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[10774, 194, 11174, 25931, 2913])).
% 10.82/11.04 tff(25937,plain,
% 10.82/11.04 (elem!1 = s(s(s(elem!1)))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[424, 25936, 4028])).
% 10.82/11.04 tff(25938,plain,
% 10.82/11.04 (s(s(s(elem!1))) = elem!1),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[129, 25937])).
% 10.82/11.04 tff(25939,plain,
% 10.82/11.04 (r(s(s(s(elem!1))), z)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[533, 25938, 530])).
% 10.82/11.04 tff(25940,plain,
% 10.82/11.04 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.82/11.04 inference(monotonicity,[status(thm)],[25937])).
% 10.82/11.04 tff(25941,plain,
% 10.82/11.04 (~(s(s(s(s(z)))) = elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[1436, 25938])).
% 10.82/11.04 tff(25942,plain,
% 10.82/11.04 ((s(z) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 10.82/11.04 inference(monotonicity,[status(thm)],[25937])).
% 10.82/11.04 tff(25943,plain,
% 10.82/11.04 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 10.82/11.04 inference(symmetry,[status(thm)],[25942])).
% 10.82/11.04 tff(25944,plain,
% 10.82/11.04 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 10.82/11.04 inference(monotonicity,[status(thm)],[25943])).
% 10.82/11.04 tff(25945,plain,
% 10.82/11.04 (~(s(z) = elem!1)),
% 10.82/11.04 inference(modus_ponens,[status(thm)],[217, 25944])).
% 10.82/11.04 tff(25946,plain,
% 10.82/11.04 (r(s(z), elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[632, 25945, 2829])).
% 10.82/11.04 tff(25947,plain,
% 10.82/11.04 (~r(s(s(s(s(z)))), elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[6077, 25946, 2913, 530])).
% 10.82/11.04 tff(25948,plain,
% 10.82/11.04 (b(s(s(s(s(z)))), elem!1)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[762, 25947, 25941])).
% 10.82/11.04 tff(25949,plain,
% 10.82/11.04 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.82/11.04 inference(modus_ponens,[status(thm)],[25948, 25940])).
% 10.82/11.04 tff(25950,plain,
% 10.82/11.04 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 10.82/11.04 inference(monotonicity,[status(thm)],[25937])).
% 10.82/11.04 tff(25951,plain,
% 10.82/11.04 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(elem!1)))))),
% 10.82/11.04 inference(monotonicity,[status(thm)],[25950])).
% 10.82/11.04 tff(25952,plain,
% 10.82/11.04 (~b(s(z), s(s(s(elem!1))))),
% 10.82/11.04 inference(modus_ponens,[status(thm)],[2829, 25951])).
% 10.82/11.04 tff(25953,plain,
% 10.82/11.04 (r(s(z), s(s(s(elem!1))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[247, 25952])).
% 10.82/11.04 tff(25954,plain,
% 10.82/11.04 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[6684, 14905, 1216, 1747])).
% 10.82/11.04 tff(25955,plain,
% 10.82/11.04 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[6652, 42, 4995, 25954])).
% 10.82/11.04 tff(25956,plain,
% 10.82/11.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 10.82/11.04 inference(rewrite,[status(thm)],[])).
% 10.82/11.04 tff(25957,plain,
% 10.82/11.04 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 10.82/11.04 inference(rewrite,[status(thm)],[])).
% 10.82/11.04 tff(25958,plain,
% 10.82/11.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 10.82/11.04 inference(monotonicity,[status(thm)],[25957])).
% 10.82/11.04 tff(25959,plain,
% 10.82/11.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 10.82/11.04 inference(transitivity,[status(thm)],[25958, 25956])).
% 10.82/11.04 tff(25960,plain,
% 10.82/11.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 10.82/11.04 inference(quant_inst,[status(thm)],[])).
% 10.82/11.04 tff(25961,plain,
% 10.82/11.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 10.82/11.04 inference(modus_ponens,[status(thm)],[25960, 25959])).
% 10.82/11.04 tff(25962,plain,
% 10.82/11.04 ($false),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[25961, 391, 10682, 90, 3325, 14903, 25955])).
% 10.82/11.04 tff(25963,plain,((~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~(elem!1 = s(s(s(elem!1))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.04 tff(25964,plain,
% 10.82/11.04 (~b(s(s(z)), z)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[25963, 1747, 90, 9970, 125, 8922, 1216, 847, 1686, 10682])).
% 10.82/11.04 tff(25965,plain,
% 10.82/11.04 (r(s(s(z)), z)),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[1211, 25964])).
% 10.82/11.04 tff(25966,plain,
% 10.82/11.04 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[11508, 25965, 1216, 1747])).
% 10.82/11.04 tff(25967,plain,
% 10.82/11.04 (b(s(s(s(s(z)))), s(s(z)))),
% 10.82/11.04 inference(unit_resolution,[status(thm)],[1714, 25966])).
% 10.82/11.04 tff(25968,plain,
% 10.82/11.04 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(elem!1))))),
% 10.82/11.04 inference(monotonicity,[status(thm)],[125])).
% 10.82/11.05 tff(25969,plain,
% 10.82/11.05 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), elem!1)),
% 10.82/11.05 inference(symmetry,[status(thm)],[25968])).
% 10.82/11.05 tff(25970,plain,
% 10.82/11.05 ((~r(s(s(z)), s(s(s(elem!1))))) <=> (~r(s(s(z)), elem!1))),
% 10.82/11.05 inference(monotonicity,[status(thm)],[25969])).
% 10.82/11.05 tff(25971,plain,
% 10.82/11.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.82/11.05 inference(rewrite,[status(thm)],[])).
% 10.82/11.05 tff(25972,plain,
% 10.82/11.05 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.82/11.05 inference(rewrite,[status(thm)],[])).
% 10.82/11.05 tff(25973,plain,
% 10.82/11.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 10.82/11.05 inference(monotonicity,[status(thm)],[25972])).
% 10.82/11.05 tff(25974,plain,
% 10.82/11.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.82/11.05 inference(transitivity,[status(thm)],[25973, 25971])).
% 10.82/11.05 tff(25975,plain,
% 10.82/11.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 10.82/11.05 inference(quant_inst,[status(thm)],[])).
% 10.82/11.05 tff(25976,plain,
% 10.82/11.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 10.82/11.05 inference(modus_ponens,[status(thm)],[25975, 25974])).
% 10.82/11.05 tff(25977,plain,
% 10.82/11.05 ($false),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[25976, 194, 174, 232, 1747, 9130])).
% 10.82/11.05 tff(25978,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.05 tff(25979,plain,
% 10.82/11.05 (~r(s(s(z)), s(s(s(elem!1))))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[25978, 1747, 232, 174])).
% 10.82/11.05 tff(25980,plain,
% 10.82/11.05 (~r(s(s(z)), elem!1)),
% 10.82/11.05 inference(modus_ponens,[status(thm)],[25979, 25970])).
% 10.82/11.05 tff(25981,plain,
% 10.82/11.05 (b(s(s(z)), elem!1)),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[4730, 25980, 18819])).
% 10.82/11.05 tff(25982,plain,
% 10.82/11.05 (~b(elem!1, s(s(z)))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[11012, 25981, 1652, 25967])).
% 10.82/11.05 tff(25983,plain,
% 10.82/11.05 (r(elem!1, s(s(z)))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[3394, 25982, 3820])).
% 10.82/11.05 tff(25984,plain,
% 10.82/11.05 (r(s(s(s(elem!1))), s(s(z)))),
% 10.82/11.05 inference(modus_ponens,[status(thm)],[25983, 10018])).
% 10.82/11.05 tff(25985,plain,
% 10.82/11.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.05 inference(rewrite,[status(thm)],[])).
% 10.82/11.05 tff(25986,plain,
% 10.82/11.05 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.05 inference(rewrite,[status(thm)],[])).
% 10.82/11.05 tff(25987,plain,
% 10.82/11.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 10.82/11.05 inference(monotonicity,[status(thm)],[25986])).
% 10.82/11.05 tff(25988,plain,
% 10.82/11.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.05 inference(transitivity,[status(thm)],[25987, 25985])).
% 10.82/11.05 tff(25989,plain,
% 10.82/11.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 10.82/11.05 inference(quant_inst,[status(thm)],[])).
% 10.82/11.05 tff(25990,plain,
% 10.82/11.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 10.82/11.05 inference(modus_ponens,[status(thm)],[25989, 25988])).
% 10.82/11.05 tff(25991,plain,
% 10.82/11.05 ($false),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[25990, 194, 183, 25965, 1747, 25984])).
% 10.82/11.05 tff(25992,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.05 tff(25993,plain,
% 10.82/11.05 (~r(s(z), s(s(z)))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[25992, 25937, 11174, 25948, 25953, 25939, 2913, 90, 8922, 25931, 25933, 10782])).
% 10.82/11.05 tff(25994,plain,
% 10.82/11.05 (b(s(z), s(s(z)))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[1788, 25993])).
% 10.82/11.05 tff(25995,plain,
% 10.82/11.05 (r(s(s(s(elem!1))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 10.82/11.05 inference(symmetry,[status(thm)],[10018])).
% 10.82/11.05 tff(25996,plain,
% 10.82/11.05 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 10.82/11.05 inference(monotonicity,[status(thm)],[25995])).
% 10.82/11.05 tff(25997,plain,
% 10.82/11.05 (~b(z, s(s(z)))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[16242, 391, 2439, 1233, 664])).
% 10.82/11.05 tff(25998,plain,
% 10.82/11.05 ((z = s(s(z))) | r(z, s(s(z)))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[10164, 42, 25997])).
% 10.82/11.05 tff(25999,plain,
% 10.82/11.05 (r(z, s(s(z)))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[25998, 11718])).
% 10.82/11.05 tff(26000,plain,
% 10.82/11.05 (~b(s(s(z)), z)),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[16250, 391, 2439, 1233, 664])).
% 10.82/11.05 tff(26001,plain,
% 10.82/11.05 (r(s(s(z)), z)),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[1211, 26000])).
% 10.82/11.05 tff(26002,plain,
% 10.82/11.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.05 inference(rewrite,[status(thm)],[])).
% 10.82/11.05 tff(26003,plain,
% 10.82/11.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.05 inference(quant_inst,[status(thm)],[])).
% 10.82/11.05 tff(26004,plain,
% 10.82/11.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 10.82/11.05 inference(modus_ponens,[status(thm)],[26003, 26002])).
% 10.82/11.05 tff(26005,plain,
% 10.82/11.05 (~r(s(s(s(elem!1))), s(s(z)))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[26004, 194, 174, 26001, 25999])).
% 10.82/11.05 tff(26006,plain,
% 10.82/11.05 (~r(elem!1, s(s(z)))),
% 10.82/11.05 inference(modus_ponens,[status(thm)],[26005, 25996])).
% 10.82/11.05 tff(26007,plain,
% 10.82/11.05 (b(elem!1, s(s(z)))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[3394, 26006, 3820])).
% 10.82/11.05 tff(26008,plain,
% 10.82/11.05 (b(s(s(s(elem!1))), s(s(z)))),
% 10.82/11.05 inference(modus_ponens,[status(thm)],[26007, 3815])).
% 10.82/11.05 tff(26009,plain,
% 10.82/11.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.82/11.05 inference(rewrite,[status(thm)],[])).
% 10.82/11.05 tff(26010,plain,
% 10.82/11.05 (((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.82/11.05 inference(rewrite,[status(thm)],[])).
% 10.82/11.05 tff(26011,plain,
% 10.82/11.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 10.82/11.05 inference(monotonicity,[status(thm)],[26010])).
% 10.82/11.05 tff(26012,plain,
% 10.82/11.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.82/11.05 inference(transitivity,[status(thm)],[26011, 26009])).
% 10.82/11.05 tff(26013,plain,
% 10.82/11.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.82/11.05 inference(quant_inst,[status(thm)],[])).
% 10.82/11.05 tff(26014,plain,
% 10.82/11.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 10.82/11.05 inference(modus_ponens,[status(thm)],[26013, 26012])).
% 10.82/11.05 tff(26015,plain,
% 10.82/11.05 (~r(s(s(z)), s(s(s(elem!1))))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[26014, 194, 174, 26001, 25999])).
% 10.82/11.05 tff(26016,plain,
% 10.82/11.05 (b(s(s(z)), s(s(s(elem!1))))),
% 10.82/11.05 inference(unit_resolution,[status(thm)],[5163, 42, 1397, 26015])).
% 10.82/11.05 tff(26017,plain,
% 10.82/11.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.05 inference(rewrite,[status(thm)],[])).
% 10.82/11.05 tff(26018,plain,
% 10.82/11.05 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.06 inference(rewrite,[status(thm)],[])).
% 10.82/11.06 tff(26019,plain,
% 10.82/11.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 10.82/11.06 inference(monotonicity,[status(thm)],[26018])).
% 10.82/11.06 tff(26020,plain,
% 10.82/11.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.06 inference(transitivity,[status(thm)],[26019, 26017])).
% 10.82/11.06 tff(26021,plain,
% 10.82/11.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 10.82/11.06 inference(quant_inst,[status(thm)],[])).
% 10.82/11.06 tff(26022,plain,
% 10.82/11.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 10.82/11.06 inference(modus_ponens,[status(thm)],[26021, 26020])).
% 10.82/11.06 tff(26023,plain,
% 10.82/11.06 ($false),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[26022, 391, 10682, 90, 3325, 26016, 26008])).
% 10.82/11.06 tff(26024,plain,((~b(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.06 tff(26025,plain,
% 10.82/11.06 (~b(s(s(z)), s(z))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[26024, 25994, 90, 25949, 25937, 25939, 10782, 25935])).
% 10.82/11.06 tff(26026,plain,
% 10.82/11.06 (r(s(s(z)), s(z))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[3778, 26025])).
% 10.82/11.06 tff(26027,plain,
% 10.82/11.06 (s(s(s(elem!1))) = elem!1),
% 10.82/11.06 inference(symmetry,[status(thm)],[25937])).
% 10.82/11.06 tff(26028,plain,
% 10.82/11.06 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 10.82/11.06 inference(monotonicity,[status(thm)],[26027])).
% 10.82/11.06 tff(26029,plain,
% 10.82/11.06 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 10.82/11.06 inference(transitivity,[status(thm)],[26028, 698])).
% 10.82/11.06 tff(26030,plain,
% 10.82/11.06 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 10.82/11.06 inference(transitivity,[status(thm)],[26029, 8492])).
% 10.82/11.06 tff(26031,plain,
% 10.82/11.06 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 10.82/11.06 inference(monotonicity,[status(thm)],[26030])).
% 10.82/11.06 tff(26032,plain,
% 10.82/11.06 (~(s(s(z)) = elem!1)),
% 10.82/11.06 inference(modus_ponens,[status(thm)],[1397, 26031])).
% 10.82/11.06 tff(26033,plain,
% 10.82/11.06 (~r(s(s(z)), elem!1)),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[6674, 26026, 25931, 25946])).
% 10.82/11.06 tff(26034,plain,
% 10.82/11.06 (b(s(s(z)), elem!1)),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[4730, 26033, 26032])).
% 10.82/11.06 tff(26035,plain,
% 10.82/11.06 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 10.82/11.06 inference(monotonicity,[status(thm)],[26029])).
% 10.82/11.06 tff(26036,plain,
% 10.82/11.06 (~(elem!1 = s(s(z)))),
% 10.82/11.06 inference(modus_ponens,[status(thm)],[1397, 26035])).
% 10.82/11.06 tff(26037,plain,
% 10.82/11.06 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 10.82/11.06 inference(monotonicity,[status(thm)],[25937])).
% 10.82/11.06 tff(26038,plain,
% 10.82/11.06 (r(s(s(s(elem!1))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 10.82/11.06 inference(symmetry,[status(thm)],[26037])).
% 10.82/11.06 tff(26039,plain,
% 10.82/11.06 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 10.82/11.06 inference(monotonicity,[status(thm)],[26038])).
% 10.82/11.06 tff(26040,plain,
% 10.82/11.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.06 inference(rewrite,[status(thm)],[])).
% 10.82/11.06 tff(26041,plain,
% 10.82/11.06 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.06 inference(rewrite,[status(thm)],[])).
% 10.82/11.06 tff(26042,plain,
% 10.82/11.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 10.82/11.06 inference(monotonicity,[status(thm)],[26041])).
% 10.82/11.06 tff(26043,plain,
% 10.82/11.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.06 inference(transitivity,[status(thm)],[26042, 26040])).
% 10.82/11.06 tff(26044,plain,
% 10.82/11.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.82/11.06 inference(quant_inst,[status(thm)],[])).
% 10.82/11.06 tff(26045,plain,
% 10.82/11.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 10.82/11.06 inference(modus_ponens,[status(thm)],[26044, 26043])).
% 10.82/11.06 tff(26046,plain,
% 10.82/11.06 (~r(s(s(s(elem!1))), s(s(z)))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[26045, 194, 25953, 11174, 26026])).
% 10.82/11.06 tff(26047,plain,
% 10.82/11.06 (~r(elem!1, s(s(z)))),
% 10.82/11.06 inference(modus_ponens,[status(thm)],[26046, 26039])).
% 10.82/11.06 tff(26048,plain,
% 10.82/11.06 (b(elem!1, s(s(z)))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[3394, 26047, 26036])).
% 10.82/11.06 tff(26049,plain,
% 10.82/11.06 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[11012, 26048, 25948, 26034])).
% 10.82/11.06 tff(26050,plain,
% 10.82/11.06 (r(s(s(s(s(z)))), s(s(z)))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[1714, 26049])).
% 10.82/11.06 tff(26051,plain,
% 10.82/11.06 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[14395, 26050, 26026, 2913])).
% 10.82/11.06 tff(26052,plain,
% 10.82/11.06 (b(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[3652, 26051])).
% 10.82/11.06 tff(26053,plain,
% 10.82/11.06 (~b(s(s(z)), z)),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[4472, 26052, 25933, 90])).
% 10.82/11.06 tff(26054,plain,
% 10.82/11.06 (~r(s(s(s(s(z)))), s(z))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[2429, 26050, 25946, 26026])).
% 10.82/11.06 tff(26055,plain,
% 10.82/11.06 (b(s(s(s(s(z)))), s(z))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[749, 26054])).
% 10.82/11.06 tff(26056,plain,
% 10.82/11.06 (~r(elem!1, s(s(s(s(z)))))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[14900, 26050, 2913, 25931])).
% 10.82/11.06 tff(26057,plain,
% 10.82/11.06 (b(elem!1, s(s(s(s(z)))))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[781, 26056, 8922])).
% 10.82/11.06 tff(26058,plain,
% 10.82/11.06 (~r(s(s(z)), z)),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[13565, 26052, 26048, 26057, 2913, 26055])).
% 10.82/11.06 tff(26059,plain,
% 10.82/11.06 ($false),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[1211, 26058, 26053])).
% 10.82/11.06 tff(26060,plain,(b(s(z), elem!1) | (~b(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, z)) | b(elem!1, s(s(s(elem!1)))) | (~r(s(z), z)) | (z = elem!1) | b(s(z), s(s(s(s(z))))) | (~b(z, s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.06 tff(26061,plain,
% 10.82/11.06 (b(s(z), elem!1)),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[26060, 4028, 25917, 530, 90, 182, 115, 2881, 3927, 8329, 11173, 53])).
% 10.82/11.06 tff(26062,plain,
% 10.82/11.06 (~(s(s(s(s(z)))) = elem!1)),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[6252, 26061, 2881])).
% 10.82/11.06 tff(26063,plain,
% 10.82/11.06 (~(s(z) = elem!1)),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[10733, 719, 53])).
% 10.82/11.06 tff(26064,plain,
% 10.82/11.06 (~(elem!1 = s(z))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[172, 26063])).
% 10.82/11.06 tff(26065,plain,
% 10.82/11.06 (~r(elem!1, s(z))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[17062, 719, 182, 530])).
% 10.82/11.06 tff(26066,plain,
% 10.82/11.06 (b(elem!1, s(z))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[837, 26065, 26064])).
% 10.82/11.06 tff(26067,plain,
% 10.82/11.06 (~r(s(s(s(s(z)))), s(z))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[1224, 719, 182, 1216])).
% 10.82/11.06 tff(26068,plain,
% 10.82/11.06 (b(s(s(s(s(z)))), s(z))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[749, 26067])).
% 10.82/11.06 tff(26069,plain,
% 10.82/11.06 (~r(s(s(s(s(z)))), elem!1)),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[2720, 719, 182, 1216])).
% 10.82/11.06 tff(26070,plain,
% 10.82/11.06 (b(s(s(s(s(z)))), elem!1)),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[762, 26069, 720])).
% 10.82/11.06 tff(26071,plain,
% 10.82/11.06 ($false),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[1773, 391, 644, 26070, 26068, 26066])).
% 10.82/11.06 tff(26072,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, z)) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.06 tff(26073,plain,
% 10.82/11.06 (~r(z, s(s(s(s(z)))))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[26072, 26061, 26062, 182, 2913, 530, 53])).
% 10.82/11.06 tff(26074,plain,
% 10.82/11.06 (b(z, s(s(s(s(z)))))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[800, 26073])).
% 10.82/11.06 tff(26075,plain,
% 10.82/11.06 (b(s(z), s(s(z)))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[20696, 644, 1686, 182, 530, 2913, 90, 20619, 484])).
% 10.82/11.06 tff(26076,plain,
% 10.82/11.06 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[2849, 20633])).
% 10.82/11.06 tff(26077,plain,
% 10.82/11.06 (~(s(s(s(elem!1))) = elem!1)),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[8406, 832, 183])).
% 10.82/11.06 tff(26078,plain,
% 10.82/11.06 (~(elem!1 = s(s(s(elem!1))))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[129, 26077])).
% 10.82/11.06 tff(26079,plain,
% 10.82/11.06 (r(elem!1, s(s(s(elem!1))))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[424, 26078, 4028])).
% 10.82/11.06 tff(26080,plain,
% 10.82/11.06 (~r(elem!1, s(s(z)))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[16978, 194, 411, 530, 3557])).
% 10.82/11.06 tff(26081,plain,
% 10.82/11.06 (~b(elem!1, s(s(z)))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[10150, 3779, 2439, 721])).
% 10.82/11.06 tff(26082,plain,
% 10.82/11.06 (elem!1 = s(s(z))),
% 10.82/11.06 inference(unit_resolution,[status(thm)],[3394, 26081, 3816])).
% 10.82/11.06 tff(26083,plain,
% 10.82/11.06 (s(elem!1) = s(s(s(z)))),
% 10.82/11.06 inference(monotonicity,[status(thm)],[26082])).
% 10.82/11.06 tff(26084,plain,
% 10.82/11.06 (s(s(elem!1)) = s(s(s(s(z))))),
% 10.82/11.06 inference(monotonicity,[status(thm)],[26083])).
% 10.82/11.06 tff(26085,plain,
% 10.82/11.06 (b(elem!1, s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.06 inference(monotonicity,[status(thm)],[26082, 26084])).
% 10.82/11.06 tff(26086,plain,
% 10.82/11.06 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 10.82/11.06 inference(symmetry,[status(thm)],[26085])).
% 10.82/11.06 tff(26087,plain,
% 10.82/11.06 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.06 inference(monotonicity,[status(thm)],[26082])).
% 10.82/11.06 tff(26088,plain,
% 10.82/11.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.82/11.07 inference(rewrite,[status(thm)],[])).
% 10.82/11.07 tff(26089,plain,
% 10.82/11.07 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.82/11.07 inference(rewrite,[status(thm)],[])).
% 10.82/11.07 tff(26090,plain,
% 10.82/11.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 10.82/11.07 inference(monotonicity,[status(thm)],[26089])).
% 10.82/11.07 tff(26091,plain,
% 10.82/11.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.82/11.07 inference(transitivity,[status(thm)],[26090, 26088])).
% 10.82/11.07 tff(26092,plain,
% 10.82/11.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.82/11.07 inference(quant_inst,[status(thm)],[])).
% 10.82/11.07 tff(26093,plain,
% 10.82/11.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.82/11.07 inference(modus_ponens,[status(thm)],[26092, 26091])).
% 10.82/11.07 tff(26094,plain,
% 10.82/11.07 (~r(elem!1, s(s(s(s(z)))))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[26093, 194, 410, 183, 23011])).
% 10.82/11.07 tff(26095,plain,
% 10.82/11.07 (b(elem!1, s(s(s(s(z)))))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[781, 26094, 8922])).
% 10.82/11.07 tff(26096,plain,
% 10.82/11.07 (b(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.07 inference(modus_ponens,[status(thm)],[26095, 26087])).
% 10.82/11.07 tff(26097,plain,
% 10.82/11.07 (b(elem!1, s(s(elem!1)))),
% 10.82/11.07 inference(modus_ponens,[status(thm)],[26096, 26086])).
% 10.82/11.07 tff(26098,plain,
% 10.82/11.07 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[9608, 26095, 23001])).
% 10.82/11.07 tff(26099,plain,
% 10.82/11.07 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[1370, 26098, 8329])).
% 10.82/11.07 tff(26100,plain,
% 10.82/11.07 (~r(s(s(elem!1)), s(z))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[11169, 26099, 1216, 183])).
% 10.82/11.07 tff(26101,plain,
% 10.82/11.07 (b(s(s(elem!1)), s(z))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[362, 26100])).
% 10.82/11.07 tff(26102,plain,
% 10.82/11.07 (~b(elem!1, s(s(elem!1)))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[1302, 26101, 644, 721])).
% 10.82/11.07 tff(26103,plain,
% 10.82/11.07 ($false),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[26102, 26097])).
% 10.82/11.07 tff(26104,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | r(elem!1, s(s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(z), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.07 tff(26105,plain,
% 10.82/11.07 (~b(s(s(s(elem!1))), z)),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[26104, 26080, 721, 1216, 183, 644, 8329, 2439, 8922, 411, 182, 3557, 410, 3843, 10682, 90])).
% 10.82/11.07 tff(26106,plain,
% 10.82/11.07 (r(s(s(s(elem!1))), z)),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[377, 26105])).
% 10.82/11.07 tff(26107,plain,
% 10.82/11.07 ($false),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[21100, 194, 411, 26106, 183, 182])).
% 10.82/11.07 tff(26108,plain,((~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(z), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.07 tff(26109,plain,
% 10.82/11.07 (~r(z, elem!1)),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[26108, 3557, 182, 1491, 1216, 644, 8329, 2439, 8922, 183, 26079, 3843, 10682, 90, 530])).
% 10.82/11.07 tff(26110,plain,
% 10.82/11.07 (b(z, elem!1)),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[141, 26109, 115])).
% 10.82/11.07 tff(26111,plain,
% 10.82/11.07 (~b(z, s(z))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[23112, 26110, 644, 1491])).
% 10.82/11.07 tff(26112,plain,
% 10.82/11.07 (r(z, s(z))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[678, 26111])).
% 10.82/11.07 tff(26113,plain,
% 10.82/11.07 (~r(elem!1, s(s(z)))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[18602, 26112, 530, 3557])).
% 10.82/11.07 tff(26114,plain,
% 10.82/11.07 (~r(s(s(z)), s(z))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[12188, 194, 26112, 182, 3557])).
% 10.82/11.07 tff(26115,plain,
% 10.82/11.07 (b(s(s(z)), s(z))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[3778, 26114])).
% 10.82/11.07 tff(26116,plain,
% 10.82/11.07 (~b(elem!1, s(s(z)))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[10150, 26115, 2439, 1491])).
% 10.82/11.07 tff(26117,plain,
% 10.82/11.07 (elem!1 = s(s(z))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[3394, 26116, 26113])).
% 10.82/11.07 tff(26118,plain,
% 10.82/11.07 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[9253, 26117])).
% 10.82/11.07 tff(26119,plain,
% 10.82/11.07 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[1370, 26118, 8329])).
% 10.82/11.07 tff(26120,plain,
% 10.82/11.07 (~r(s(s(elem!1)), s(z))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[11169, 26119, 1216, 183])).
% 10.82/11.07 tff(26121,plain,
% 10.82/11.07 (b(s(s(elem!1)), s(z))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[362, 26120])).
% 10.82/11.07 tff(26122,plain,
% 10.82/11.07 (~r(s(z), elem!1)),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[25179, 26112, 530, 182])).
% 10.82/11.07 tff(26123,plain,
% 10.82/11.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 10.82/11.07 inference(rewrite,[status(thm)],[])).
% 10.82/11.07 tff(26124,plain,
% 10.82/11.07 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 10.82/11.07 inference(rewrite,[status(thm)],[])).
% 10.82/11.07 tff(26125,plain,
% 10.82/11.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))))),
% 10.82/11.07 inference(monotonicity,[status(thm)],[26124])).
% 10.82/11.07 tff(26126,plain,
% 10.82/11.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 10.82/11.07 inference(transitivity,[status(thm)],[26125, 26123])).
% 10.82/11.07 tff(26127,plain,
% 10.82/11.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 10.82/11.07 inference(quant_inst,[status(thm)],[])).
% 10.82/11.07 tff(26128,plain,
% 10.82/11.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 10.82/11.07 inference(modus_ponens,[status(thm)],[26127, 26126])).
% 10.82/11.07 tff(26129,plain,
% 10.82/11.07 (~r(s(s(s(elem!1))), z)),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[26128, 194, 183, 26112, 182])).
% 10.82/11.07 tff(26130,plain,
% 10.82/11.07 (b(s(s(s(elem!1))), z)),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[377, 26129])).
% 10.82/11.07 tff(26131,plain,
% 10.82/11.07 (~b(s(s(s(elem!1))), elem!1)),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[1505, 26130, 832, 831, 26110, 26122])).
% 10.82/11.07 tff(26132,plain,
% 10.82/11.07 (r(s(s(s(elem!1))), elem!1)),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[230, 26131, 26077])).
% 10.82/11.07 tff(26133,plain,
% 10.82/11.07 (~(s(elem!1) = elem!1)),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[158, 26077])).
% 10.82/11.07 tff(26134,plain,
% 10.82/11.07 (~(elem!1 = s(elem!1))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[166, 26133])).
% 10.82/11.07 tff(26135,plain,
% 10.82/11.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 10.82/11.07 inference(rewrite,[status(thm)],[])).
% 10.82/11.07 tff(26136,plain,
% 10.82/11.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 10.82/11.07 inference(quant_inst,[status(thm)],[])).
% 10.82/11.07 tff(26137,plain,
% 10.82/11.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 10.82/11.07 inference(modus_ponens,[status(thm)],[26136, 26135])).
% 10.82/11.07 tff(26138,plain,
% 10.82/11.07 (~r(s(s(s(elem!1))), s(elem!1))),
% 10.82/11.07 inference(unit_resolution,[status(thm)],[26137, 194, 530, 485, 233])).
% 10.82/11.07 tff(26139,plain,
% 10.82/11.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.82/11.07 inference(rewrite,[status(thm)],[])).
% 10.82/11.07 tff(26140,plain,
% 10.82/11.07 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), 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)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.82/11.07 inference(rewrite,[status(thm)],[])).
% 10.82/11.07 tff(26141,plain,
% 10.82/11.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 10.82/11.07 inference(monotonicity,[status(thm)],[26140])).
% 10.82/11.07 tff(26142,plain,
% 10.82/11.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.82/11.08 inference(transitivity,[status(thm)],[26141, 26139])).
% 10.82/11.08 tff(26143,plain,
% 10.82/11.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 10.82/11.08 inference(quant_inst,[status(thm)],[])).
% 10.82/11.08 tff(26144,plain,
% 10.82/11.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 10.82/11.08 inference(modus_ponens,[status(thm)],[26143, 26142])).
% 10.82/11.08 tff(26145,plain,
% 10.82/11.08 (~r(s(elem!1), s(s(s(elem!1))))),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[26144, 194, 530, 485, 233])).
% 10.82/11.08 tff(26146,plain,
% 10.82/11.08 (s(s(s(elem!1))) = s(elem!1)),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[12746, 591, 10682, 3612, 1575])).
% 10.82/11.08 tff(26147,plain,
% 10.82/11.08 (~(s(s(s(s(z)))) = elem!1)),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[717, 26146])).
% 10.82/11.08 tff(26148,plain,
% 10.82/11.08 (s(elem!1) = s(s(s(elem!1)))),
% 10.82/11.08 inference(symmetry,[status(thm)],[26146])).
% 10.82/11.08 tff(26149,plain,
% 10.82/11.08 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 10.82/11.08 inference(monotonicity,[status(thm)],[26148])).
% 10.82/11.08 tff(26150,plain,
% 10.82/11.08 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 10.82/11.08 inference(symmetry,[status(thm)],[26149])).
% 10.82/11.08 tff(26151,plain,
% 10.82/11.08 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 10.82/11.08 inference(monotonicity,[status(thm)],[26150])).
% 10.82/11.08 tff(26152,plain,
% 10.82/11.08 (~(s(s(s(s(z)))) = s(elem!1))),
% 10.82/11.08 inference(modus_ponens,[status(thm)],[3843, 26151])).
% 10.82/11.08 tff(26153,plain,
% 10.82/11.08 (~r(s(s(s(s(z)))), s(z))),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[11989, 194, 722, 182, 2053])).
% 10.82/11.08 tff(26154,plain,
% 10.82/11.08 (b(s(s(s(s(z)))), s(z))),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[749, 26153])).
% 10.82/11.08 tff(26155,plain,
% 10.82/11.08 (b(s(s(s(s(z)))), elem!1)),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[762, 18014, 720])).
% 10.82/11.08 tff(26156,plain,
% 10.82/11.08 (b(elem!1, s(s(s(s(z)))))),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[781, 18006, 770])).
% 10.82/11.08 tff(26157,plain,
% 10.82/11.08 ($false),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[17129, 391, 644, 26156, 26155, 26154])).
% 10.82/11.08 tff(26158,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.08 tff(26159,plain,
% 10.82/11.08 (~r(s(s(s(s(z)))), z)),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[26158, 26147, 644, 530, 722, 182])).
% 10.82/11.08 tff(26160,plain,
% 10.82/11.08 (b(s(s(s(s(z)))), z)),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[87, 26159])).
% 10.82/11.08 tff(26161,plain,
% 10.82/11.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 10.82/11.08 inference(rewrite,[status(thm)],[])).
% 10.82/11.08 tff(26162,plain,
% 10.82/11.08 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 10.82/11.08 inference(rewrite,[status(thm)],[])).
% 10.82/11.08 tff(26163,plain,
% 10.82/11.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 10.82/11.08 inference(monotonicity,[status(thm)],[26162])).
% 10.82/11.08 tff(26164,plain,
% 10.82/11.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 10.82/11.08 inference(transitivity,[status(thm)],[26163, 26161])).
% 10.82/11.08 tff(26165,plain,
% 10.82/11.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 10.82/11.08 inference(quant_inst,[status(thm)],[])).
% 10.82/11.08 tff(26166,plain,
% 10.82/11.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 10.82/11.08 inference(modus_ponens,[status(thm)],[26165, 26164])).
% 10.82/11.08 tff(26167,plain,
% 10.82/11.08 (~b(s(s(s(s(z)))), s(elem!1))),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[26166, 391, 133, 591, 26160, 721])).
% 10.82/11.08 tff(26168,plain,
% 10.82/11.08 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[2136, 42, 26167])).
% 10.82/11.08 tff(26169,plain,
% 10.82/11.08 (r(s(s(s(s(z)))), s(elem!1))),
% 10.82/11.08 inference(unit_resolution,[status(thm)],[26168, 26152])).
% 10.82/11.08 tff(26170,plain,
% 10.82/11.08 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 10.82/11.08 inference(monotonicity,[status(thm)],[26148])).
% 10.82/11.08 tff(26171,plain,
% 10.82/11.08 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 10.82/11.08 inference(transitivity,[status(thm)],[26170, 3928])).
% 10.82/11.08 tff(26172,plain,
% 10.82/11.08 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 10.82/11.08 inference(symmetry,[status(thm)],[26171])).
% 10.82/11.08 tff(26173,plain,
% 10.82/11.08 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 10.82/11.08 inference(monotonicity,[status(thm)],[26172])).
% 10.82/11.08 tff(26174,plain,
% 10.82/11.08 (~(s(elem!1) = s(s(s(s(z)))))),
% 10.82/11.08 inference(modus_ponens,[status(thm)],[3843, 26173])).
% 10.82/11.08 tff(26175,plain,
% 10.82/11.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 10.82/11.08 inference(rewrite,[status(thm)],[])).
% 10.82/11.08 tff(26176,plain,
% 10.82/11.08 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 10.82/11.08 inference(rewrite,[status(thm)],[])).
% 10.82/11.08 tff(26177,plain,
% 10.82/11.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 10.82/11.08 inference(monotonicity,[status(thm)],[26176])).
% 10.82/11.08 tff(26178,plain,
% 10.82/11.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 10.82/11.09 inference(transitivity,[status(thm)],[26177, 26175])).
% 10.82/11.09 tff(26179,plain,
% 10.82/11.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 10.82/11.09 inference(quant_inst,[status(thm)],[])).
% 10.82/11.09 tff(26180,plain,
% 10.82/11.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 10.82/11.09 inference(modus_ponens,[status(thm)],[26179, 26178])).
% 10.82/11.09 tff(26181,plain,
% 10.82/11.09 (~b(s(elem!1), s(s(s(s(z)))))),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[26180, 391, 133, 591, 26160, 721])).
% 10.82/11.09 tff(26182,plain,
% 10.82/11.09 ((s(elem!1) = s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[2142, 42, 26181])).
% 10.82/11.09 tff(26183,plain,
% 10.82/11.09 (r(s(elem!1), s(s(s(s(z)))))),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[26182, 26174])).
% 10.82/11.09 tff(26184,plain,
% 10.82/11.09 (~b(elem!1, s(elem!1))),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[4603, 26146, 4028])).
% 10.82/11.09 tff(26185,plain,
% 10.82/11.09 (r(elem!1, s(elem!1))),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[443, 26184, 437])).
% 10.82/11.09 tff(26186,plain,
% 10.82/11.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 10.82/11.09 inference(rewrite,[status(thm)],[])).
% 10.82/11.09 tff(26187,plain,
% 10.82/11.09 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 10.82/11.09 inference(rewrite,[status(thm)],[])).
% 10.82/11.09 tff(26188,plain,
% 10.82/11.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 10.82/11.09 inference(monotonicity,[status(thm)],[26187])).
% 10.82/11.09 tff(26189,plain,
% 10.82/11.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 10.82/11.09 inference(transitivity,[status(thm)],[26188, 26186])).
% 10.82/11.09 tff(26190,plain,
% 10.82/11.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))),
% 10.82/11.09 inference(quant_inst,[status(thm)],[])).
% 10.82/11.09 tff(26191,plain,
% 10.82/11.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 10.82/11.09 inference(modus_ponens,[status(thm)],[26190, 26189])).
% 10.82/11.09 tff(26192,plain,
% 10.82/11.09 (~r(s(s(s(s(z)))), elem!1)),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[26191, 194, 26185, 26183, 26169])).
% 10.82/11.09 tff(26193,plain,
% 10.82/11.09 (b(s(s(s(s(z)))), elem!1)),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[762, 26192, 26147])).
% 10.82/11.09 tff(26194,plain,
% 10.82/11.09 (~(elem!1 = s(s(s(s(z)))))),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[769, 26147])).
% 10.82/11.09 tff(26195,plain,
% 10.82/11.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 10.82/11.09 inference(rewrite,[status(thm)],[])).
% 10.82/11.09 tff(26196,plain,
% 10.82/11.09 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 10.82/11.09 inference(rewrite,[status(thm)],[])).
% 10.82/11.09 tff(26197,plain,
% 10.82/11.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 10.82/11.09 inference(monotonicity,[status(thm)],[26196])).
% 10.82/11.09 tff(26198,plain,
% 10.82/11.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 10.82/11.09 inference(transitivity,[status(thm)],[26197, 26195])).
% 10.82/11.09 tff(26199,plain,
% 10.82/11.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.82/11.09 inference(quant_inst,[status(thm)],[])).
% 10.82/11.09 tff(26200,plain,
% 10.82/11.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 10.82/11.09 inference(modus_ponens,[status(thm)],[26199, 26198])).
% 10.82/11.09 tff(26201,plain,
% 10.82/11.09 (~r(elem!1, s(s(s(s(z)))))),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[26200, 194, 26185, 26183, 26169])).
% 10.82/11.09 tff(26202,plain,
% 10.82/11.09 (b(elem!1, s(s(s(s(z)))))),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[781, 26201, 26194])).
% 10.82/11.09 tff(26203,plain,
% 10.82/11.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.82/11.09 inference(rewrite,[status(thm)],[])).
% 10.82/11.09 tff(26204,plain,
% 10.82/11.09 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.82/11.09 inference(rewrite,[status(thm)],[])).
% 10.82/11.09 tff(26205,plain,
% 10.82/11.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 10.82/11.09 inference(monotonicity,[status(thm)],[26204])).
% 10.82/11.09 tff(26206,plain,
% 10.82/11.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 10.82/11.09 inference(transitivity,[status(thm)],[26205, 26203])).
% 10.82/11.09 tff(26207,plain,
% 10.82/11.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 10.82/11.09 inference(quant_inst,[status(thm)],[])).
% 10.82/11.09 tff(26208,plain,
% 10.82/11.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 10.82/11.09 inference(modus_ponens,[status(thm)],[26207, 26206])).
% 10.82/11.09 tff(26209,plain,
% 10.82/11.09 ($false),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[26208, 391, 133, 26160, 26202, 26193])).
% 10.82/11.09 tff(26210,plain,((~b(s(elem!1), z)) | (~b(z, elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (elem!1 = s(elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | r(s(elem!1), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.09 tff(26211,plain,
% 10.82/11.09 (~b(s(elem!1), z)),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[26210, 26145, 3843, 721, 644, 530, 722, 182, 437, 4028, 10682, 133, 26138])).
% 10.82/11.09 tff(26212,plain,
% 10.82/11.09 (r(s(elem!1), z)),
% 10.82/11.09 inference(unit_resolution,[status(thm)],[549, 26211])).
% 10.82/11.09 tff(26213,plain,
% 10.82/11.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(z))))),
% 10.82/11.09 inference(rewrite,[status(thm)],[])).
% 10.82/11.09 tff(26214,plain,
% 10.82/11.09 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(z))))),
% 10.82/11.09 inference(rewrite,[status(thm)],[])).
% 10.82/11.09 tff(26215,plain,
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% 10.82/11.09 inference(monotonicity,[status(thm)],[26214])).
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% 10.82/11.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(z))))),
% 10.82/11.09 inference(transitivity,[status(thm)],[26215, 26213])).
% 10.82/11.09 tff(26217,plain,
% 10.82/11.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 10.82/11.09 inference(quant_inst,[status(thm)],[])).
% 10.82/11.09 tff(26218,plain,
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% 10.82/11.10 inference(modus_ponens,[status(thm)],[26217, 26216])).
% 10.82/11.10 tff(26219,plain,
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[26218, 194, 530, 485, 26212, 722])).
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% 10.82/11.10 tff(26221,plain,
% 10.82/11.10 (~r(s(elem!1), elem!1)),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[26220, 26132, 10682, 530, 644, 4028, 1491, 3843, 182, 26134, 26110, 26112])).
% 10.82/11.10 tff(26222,plain,
% 10.82/11.10 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[472, 26221, 26132])).
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[451, 26222])).
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% 10.82/11.10 (~r(s(s(elem!1)), elem!1)),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[4039, 26119, 26077, 4028, 26131])).
% 10.82/11.10 tff(26225,plain,
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[872, 26224, 26223])).
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[22561, 26225, 26121, 1491, 644])).
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% 10.82/11.10 tff(26228,plain,
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[26227, 832, 4028, 2913, 183, 8329, 10682, 530, 644, 182, 20620, 26076, 26075, 115, 25917, 90])).
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% 10.82/11.10 tff(26230,plain,
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[2884, 379, 2881])).
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[2849, 26231])).
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[26227, 26232, 4028, 2913, 183, 8329, 10682, 530, 644, 182, 2439, 832, 26230, 115, 25917, 90])).
% 10.82/11.10 tff(26234,plain,
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[1211, 26233])).
% 10.82/11.10 tff(26235,plain,
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[837, 26230, 832])).
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% 10.82/11.10 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[14891, 391, 90, 26234, 1686])).
% 10.82/11.10 tff(26237,plain,
% 10.82/11.10 (r(s(s(s(s(z)))), s(s(z)))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[1714, 26236])).
% 10.82/11.10 tff(26238,plain,
% 10.82/11.10 (~(elem!1 = s(s(z)))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[3589, 26234, 484])).
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% 10.82/11.10 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[4472, 26234, 1686, 90])).
% 10.82/11.10 tff(26240,plain,
% 10.82/11.10 (r(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[3652, 26239])).
% 10.82/11.10 tff(26241,plain,
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[14395, 26237, 26240, 2913])).
% 10.82/11.10 tff(26242,plain,
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[10150, 26242, 2439, 26235])).
% 10.82/11.10 tff(26244,plain,
% 10.82/11.10 (r(elem!1, s(s(z)))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[3394, 26243, 26238])).
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% 10.82/11.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 10.82/11.10 inference(rewrite,[status(thm)],[])).
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% 10.82/11.10 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 10.82/11.10 inference(rewrite,[status(thm)],[])).
% 10.82/11.10 tff(26247,plain,
% 10.82/11.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z))))))),
% 10.82/11.10 inference(monotonicity,[status(thm)],[26246])).
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% 10.82/11.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 10.82/11.10 inference(transitivity,[status(thm)],[26247, 26245])).
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% 10.82/11.10 inference(quant_inst,[status(thm)],[])).
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% 10.82/11.10 inference(modus_ponens,[status(thm)],[26249, 26248])).
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% 10.82/11.10 inference(unit_resolution,[status(thm)],[26250, 194, 26240, 26244, 26237])).
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% 10.82/11.10 inference(rewrite,[status(thm)],[])).
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% 10.82/11.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.82/11.10 inference(quant_inst,[status(thm)],[])).
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% 10.82/11.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.82/11.10 inference(modus_ponens,[status(thm)],[26256, 26255])).
% 10.82/11.10 tff(26258,plain,
% 10.82/11.10 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[26257, 194, 183, 182, 26254])).
% 10.82/11.10 tff(26259,plain,
% 10.82/11.10 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[2853, 42, 26232, 26258])).
% 10.82/11.10 tff(26260,plain,
% 10.82/11.10 (~(s(s(z)) = elem!1)),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[11003, 26238])).
% 10.82/11.10 tff(26261,plain,
% 10.82/11.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 10.82/11.10 inference(rewrite,[status(thm)],[])).
% 10.82/11.10 tff(26262,plain,
% 10.82/11.10 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 10.82/11.10 inference(rewrite,[status(thm)],[])).
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% 10.82/11.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 10.82/11.10 inference(monotonicity,[status(thm)],[26262])).
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% 10.82/11.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 10.82/11.10 inference(transitivity,[status(thm)],[26263, 26261])).
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% 10.82/11.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 10.82/11.10 inference(quant_inst,[status(thm)],[])).
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% 10.82/11.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 10.82/11.10 inference(modus_ponens,[status(thm)],[26265, 26264])).
% 10.82/11.10 tff(26267,plain,
% 10.82/11.10 (~b(s(s(z)), elem!1)),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[26266, 391, 644, 26242, 26235])).
% 10.82/11.10 tff(26268,plain,
% 10.82/11.10 (r(s(s(z)), elem!1)),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[4730, 26267, 26260])).
% 10.82/11.10 tff(26269,plain,
% 10.82/11.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.82/11.10 inference(rewrite,[status(thm)],[])).
% 10.82/11.10 tff(26270,plain,
% 10.82/11.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.82/11.10 inference(quant_inst,[status(thm)],[])).
% 10.82/11.10 tff(26271,plain,
% 10.82/11.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))),
% 10.82/11.10 inference(modus_ponens,[status(thm)],[26270, 26269])).
% 10.82/11.10 tff(26272,plain,
% 10.82/11.10 (~r(elem!1, s(s(s(s(z)))))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[26271, 194, 26240, 26244, 26237])).
% 10.82/11.10 tff(26273,plain,
% 10.82/11.10 (b(elem!1, s(s(s(s(z)))))),
% 10.82/11.10 inference(unit_resolution,[status(thm)],[781, 26272, 25917])).
% 10.82/11.10 tff(26274,plain,
% 10.82/11.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 10.82/11.11 inference(rewrite,[status(thm)],[])).
% 10.82/11.11 tff(26275,plain,
% 10.82/11.11 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 10.82/11.11 inference(rewrite,[status(thm)],[])).
% 10.82/11.11 tff(26276,plain,
% 10.82/11.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 10.82/11.11 inference(monotonicity,[status(thm)],[26275])).
% 10.82/11.11 tff(26277,plain,
% 10.82/11.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 10.82/11.11 inference(transitivity,[status(thm)],[26276, 26274])).
% 10.82/11.11 tff(26278,plain,
% 10.82/11.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 10.82/11.11 inference(quant_inst,[status(thm)],[])).
% 10.82/11.11 tff(26279,plain,
% 10.82/11.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 10.82/11.11 inference(modus_ponens,[status(thm)],[26278, 26277])).
% 10.82/11.11 tff(26280,plain,
% 10.82/11.11 ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[26279, 391])).
% 10.82/11.11 tff(26281,plain,
% 10.82/11.11 (~b(z, elem!1)),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[26280, 26273, 26235, 1686, 26252])).
% 10.82/11.11 tff(26282,plain,
% 10.82/11.11 (r(z, elem!1)),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[141, 26281, 115])).
% 10.82/11.11 tff(26283,plain,
% 10.82/11.11 (~r(z, s(s(z)))),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[8511, 194, 26282, 530, 26268])).
% 10.82/11.11 tff(26284,plain,
% 10.82/11.11 ((z = s(s(z))) | b(z, s(s(z)))),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[10164, 42, 26283])).
% 10.82/11.11 tff(26285,plain,
% 10.82/11.11 (b(z, s(s(z)))),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[26284, 11718])).
% 10.82/11.11 tff(26286,plain,
% 10.82/11.11 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 10.82/11.11 inference(modus_ponens,[status(thm)],[26232, 3930])).
% 10.82/11.11 tff(26287,plain,
% 10.82/11.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.82/11.11 inference(rewrite,[status(thm)],[])).
% 10.82/11.11 tff(26288,plain,
% 10.82/11.11 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.82/11.11 inference(rewrite,[status(thm)],[])).
% 10.82/11.11 tff(26289,plain,
% 10.82/11.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 10.82/11.11 inference(monotonicity,[status(thm)],[26288])).
% 10.82/11.11 tff(26290,plain,
% 10.82/11.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.82/11.11 inference(transitivity,[status(thm)],[26289, 26287])).
% 10.82/11.11 tff(26291,plain,
% 10.82/11.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.82/11.11 inference(quant_inst,[status(thm)],[])).
% 10.82/11.11 tff(26292,plain,
% 10.82/11.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 10.82/11.11 inference(modus_ponens,[status(thm)],[26291, 26290])).
% 10.82/11.11 tff(26293,plain,
% 10.82/11.11 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[26292, 194, 183, 182, 26254])).
% 10.82/11.11 tff(26294,plain,
% 10.82/11.11 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[4313, 42, 26293])).
% 10.82/11.11 tff(26295,plain,
% 10.82/11.11 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[26294, 26286])).
% 10.82/11.11 tff(26296,plain,
% 10.82/11.11 (~b(s(s(s(elem!1))), elem!1)),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[10959, 26295, 26273, 26259])).
% 10.82/11.11 tff(26297,plain,
% 10.82/11.11 (r(s(s(s(elem!1))), elem!1)),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[230, 26296, 26077])).
% 10.82/11.11 tff(26298,plain,
% 10.82/11.11 (~r(s(s(s(elem!1))), z)),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[23607, 26297, 530, 26282])).
% 10.82/11.11 tff(26299,plain,
% 10.82/11.11 (b(s(s(s(elem!1))), z)),
% 10.82/11.11 inference(unit_resolution,[status(thm)],[377, 26298])).
% 10.82/11.11 tff(26300,plain,
% 10.82/11.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.82/11.11 inference(rewrite,[status(thm)],[])).
% 10.82/11.11 tff(26301,plain,
% 10.82/11.11 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.82/11.11 inference(rewrite,[status(thm)],[])).
% 10.82/11.11 tff(26302,plain,
% 10.82/11.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 10.82/11.12 inference(monotonicity,[status(thm)],[26301])).
% 10.82/11.12 tff(26303,plain,
% 10.82/11.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.82/11.12 inference(transitivity,[status(thm)],[26302, 26300])).
% 10.82/11.12 tff(26304,plain,
% 10.82/11.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.82/11.12 inference(quant_inst,[status(thm)],[])).
% 10.82/11.12 tff(26305,plain,
% 10.82/11.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.82/11.12 inference(modus_ponens,[status(thm)],[26304, 26303])).
% 10.82/11.12 tff(26306,plain,
% 10.82/11.12 ($false),
% 10.82/11.12 inference(unit_resolution,[status(thm)],[26305, 391, 26299, 90, 26234, 26285, 26259])).
% 10.82/11.12 tff(26307,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (z = elem!1) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | b(elem!1, z) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | r(elem!1, s(z)) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 10.82/11.12 tff(26308,plain,
% 10.82/11.12 (~b(s(z), s(s(s(elem!1))))),
% 10.82/11.12 inference(unit_resolution,[status(thm)],[26307, 832, 530, 183, 182, 115, 1686, 26075, 644, 484, 4028, 8329, 10682, 90, 2881])).
% 10.82/11.12 tff(26309,plain,
% 10.82/11.12 (r(s(z), s(s(s(elem!1))))),
% 10.82/11.12 inference(unit_resolution,[status(thm)],[247, 26308])).
% 10.82/11.12 tff(26310,plain,
% 10.82/11.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 10.82/11.12 inference(rewrite,[status(thm)],[])).
% 10.82/11.12 tff(26311,plain,
% 10.82/11.12 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
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% 10.82/11.12 tff(26312,plain,
% 10.82/11.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 10.82/11.12 inference(monotonicity,[status(thm)],[26311])).
% 10.82/11.12 tff(26313,plain,
% 10.82/11.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 10.82/11.12 inference(transitivity,[status(thm)],[26312, 26310])).
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% 10.82/11.12 inference(quant_inst,[status(thm)],[])).
% 10.82/11.12 tff(26315,plain,
% 10.82/11.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 10.82/11.12 inference(modus_ponens,[status(thm)],[26314, 26313])).
% 10.82/11.12 tff(26316,plain,
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% 10.82/11.12 inference(unit_resolution,[status(thm)],[26315, 391, 10682, 1235, 2439])).
% 10.82/11.12 tff(26317,plain,
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% 10.82/11.12 inference(unit_resolution,[status(thm)],[8801, 26316, 644])).
% 10.82/11.12 tff(26318,plain,
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% 10.82/11.12 inference(unit_resolution,[status(thm)],[837, 26317, 832])).
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% 10.82/11.12 inference(unit_resolution,[status(thm)],[10150, 26318, 2439, 14907])).
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% 10.82/11.12 inference(unit_resolution,[status(thm)],[26250, 194, 14905, 26320, 14893])).
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% 10.82/11.13 inference(unit_resolution,[status(thm)],[23918, 26074, 90, 10782])).
% 10.82/11.13 tff(26371,plain,
% 10.82/11.13 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[4313, 42, 26370])).
% 10.82/11.13 tff(26372,plain,
% 10.82/11.13 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[26371, 26369])).
% 10.82/11.13 tff(26373,plain,
% 10.82/11.13 (b(s(z), s(s(z)))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[20696, 26061, 26074, 182, 530, 2913, 90, 26062, 484])).
% 10.82/11.13 tff(26374,plain,
% 10.82/11.13 (~b(s(s(s(elem!1))), z)),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[23013, 26368, 2913, 11174, 10782, 90])).
% 10.82/11.13 tff(26375,plain,
% 10.82/11.13 (r(s(s(s(elem!1))), z)),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[377, 26374])).
% 10.82/11.13 tff(26376,plain,
% 10.82/11.13 (~r(z, s(z))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[17266, 26360, 182, 530])).
% 10.82/11.13 tff(26377,plain,
% 10.82/11.13 (b(z, s(z))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[678, 26376])).
% 10.82/11.13 tff(26378,plain,
% 10.82/11.13 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.82/11.13 inference(monotonicity,[status(thm)],[26362])).
% 10.82/11.13 tff(26379,plain,
% 10.82/11.13 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 10.82/11.13 inference(symmetry,[status(thm)],[26378])).
% 10.82/11.13 tff(26380,plain,
% 10.82/11.13 (r(elem!1, s(s(s(s(z)))))),
% 10.82/11.13 inference(modus_ponens,[status(thm)],[26372, 26379])).
% 10.82/11.13 tff(26381,plain,
% 10.82/11.13 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[14900, 26380, 2913, 26360])).
% 10.82/11.13 tff(26382,plain,
% 10.82/11.13 (b(s(s(s(s(z)))), s(s(z)))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[1714, 26381])).
% 10.82/11.13 tff(26383,plain,
% 10.82/11.13 (~r(s(s(s(s(z)))), s(z))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[6347, 26380, 2913, 26360])).
% 10.82/11.13 tff(26384,plain,
% 10.82/11.13 (b(s(s(s(s(z)))), s(z))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[749, 26383])).
% 10.82/11.13 tff(26385,plain,
% 10.82/11.13 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[19085, 26384, 90, 26373, 26382])).
% 10.82/11.13 tff(26386,plain,
% 10.82/11.13 (r(s(s(z)), s(s(s(s(z)))))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[3652, 26385])).
% 10.82/11.13 tff(26387,plain,
% 10.82/11.13 (r(elem!1, s(s(z)))),
% 10.82/11.13 inference(unit_resolution,[status(thm)],[3394, 3820, 3583])).
% 10.82/11.13 tff(26388,plain,
% 10.82/11.13 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 10.92/11.13 inference(symmetry,[status(thm)],[14785])).
% 10.92/11.13 tff(26389,plain,
% 10.92/11.13 (r(elem!1, s(s(s(s(z)))))),
% 10.92/11.13 inference(modus_ponens,[status(thm)],[4317, 26388])).
% 10.92/11.13 tff(26390,plain,
% 10.92/11.13 (~r(s(s(s(s(z)))), s(z))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[6347, 26389, 1216, 847])).
% 10.92/11.13 tff(26391,plain,
% 10.92/11.13 (b(s(s(s(s(z)))), s(z))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[749, 26390])).
% 10.92/11.13 tff(26392,plain,
% 10.92/11.13 (~b(s(s(z)), s(z))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[26024, 9970, 90, 2439, 125, 174, 10682, 664])).
% 10.92/11.13 tff(26393,plain,
% 10.92/11.13 (~(s(z) = elem!1)),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[8502, 8498, 8500])).
% 10.92/11.13 tff(26394,plain,
% 10.92/11.13 (~r(s(z), s(s(z)))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[1775, 26393, 1759, 1652, 1749, 1748])).
% 10.92/11.13 tff(26395,plain,
% 10.92/11.13 (b(s(z), s(s(z)))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[1788, 26394])).
% 10.92/11.13 tff(26396,plain,
% 10.92/11.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 10.92/11.13 inference(rewrite,[status(thm)],[])).
% 10.92/11.13 tff(26397,plain,
% 10.92/11.13 (((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 10.92/11.13 inference(rewrite,[status(thm)],[])).
% 10.92/11.13 tff(26398,plain,
% 10.92/11.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))))),
% 10.92/11.13 inference(monotonicity,[status(thm)],[26397])).
% 10.92/11.13 tff(26399,plain,
% 10.92/11.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)))),
% 10.92/11.13 inference(transitivity,[status(thm)],[26398, 26396])).
% 10.92/11.13 tff(26400,plain,
% 10.92/11.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 10.92/11.13 inference(quant_inst,[status(thm)],[])).
% 10.92/11.13 tff(26401,plain,
% 10.92/11.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1))),
% 10.92/11.13 inference(modus_ponens,[status(thm)],[26400, 26399])).
% 10.92/11.13 tff(26402,plain,
% 10.92/11.13 ($false),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[26401, 391, 1759, 26395, 8498, 1686, 664])).
% 10.92/11.13 tff(26403,plain,((~b(s(s(z)), elem!1)) | (~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)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.13 tff(26404,plain,
% 10.92/11.13 (~b(s(s(z)), elem!1)),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[26403, 26392, 1686, 664, 1749, 1759, 1748, 1652])).
% 10.92/11.13 tff(26405,plain,
% 10.92/11.13 (r(s(s(z)), elem!1)),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[4730, 26404, 18819])).
% 10.92/11.13 tff(26406,plain,
% 10.92/11.13 (r(s(s(z)), s(s(s(elem!1))))),
% 10.92/11.13 inference(modus_ponens,[status(thm)],[26405, 25968])).
% 10.92/11.13 tff(26407,plain,
% 10.92/11.13 (r(s(s(z)), s(z))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[3778, 26392])).
% 10.92/11.13 tff(26408,plain,
% 10.92/11.13 ($false),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[11211, 194, 183, 1216, 26407, 26406])).
% 10.92/11.13 tff(26409,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.13 tff(26410,plain,
% 10.92/11.13 (~b(s(s(s(s(z)))), elem!1)),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[26409, 125, 1216, 183, 1686, 664, 1749, 26391, 26387, 90, 2439, 174, 10682])).
% 10.92/11.13 tff(26411,plain,
% 10.92/11.13 (r(s(s(s(s(z)))), elem!1)),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[762, 26410, 720])).
% 10.92/11.13 tff(26412,plain,
% 10.92/11.13 (~r(s(s(z)), s(z))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[4702, 26411, 1216, 1749])).
% 10.92/11.13 tff(26413,plain,
% 10.92/11.13 (b(s(s(z)), s(z))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[3778, 26412])).
% 10.92/11.13 tff(26414,plain,
% 10.92/11.13 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[14900, 26389, 1216, 847])).
% 10.92/11.13 tff(26415,plain,
% 10.92/11.13 (b(s(s(s(s(z)))), s(s(z)))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[1714, 26414])).
% 10.92/11.13 tff(26416,plain,
% 10.92/11.13 ($false),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[3794, 391, 26391, 2439, 26415, 26413])).
% 10.92/11.13 tff(26417,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.13 tff(26418,plain,
% 10.92/11.13 (b(elem!1, s(s(z)))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[26417, 26386, 2913, 26362, 26062, 11174, 26074, 26377, 90, 26375, 10782, 26373, 26360, 26372])).
% 10.92/11.13 tff(26419,plain,
% 10.92/11.13 (b(s(s(s(elem!1))), s(s(z)))),
% 10.92/11.13 inference(modus_ponens,[status(thm)],[26418, 26365])).
% 10.92/11.13 tff(26420,plain,
% 10.92/11.13 (s(s(s(elem!1))) = elem!1),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[129, 26362])).
% 10.92/11.13 tff(26421,plain,
% 10.92/11.13 (b(s(z), s(s(s(elem!1))))),
% 10.92/11.13 inference(unit_resolution,[status(thm)],[14872, 26420, 26061])).
% 10.92/11.13 tff(26422,plain,
% 10.92/11.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.92/11.13 inference(rewrite,[status(thm)],[])).
% 10.92/11.13 tff(26423,plain,
% 10.92/11.13 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.92/11.13 inference(rewrite,[status(thm)],[])).
% 10.92/11.13 tff(26424,plain,
% 10.92/11.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 10.92/11.13 inference(monotonicity,[status(thm)],[26423])).
% 10.92/11.13 tff(26425,plain,
% 10.92/11.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.92/11.14 inference(transitivity,[status(thm)],[26424, 26422])).
% 10.92/11.14 tff(26426,plain,
% 10.92/11.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 10.92/11.14 inference(quant_inst,[status(thm)],[])).
% 10.92/11.14 tff(26427,plain,
% 10.92/11.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 10.92/11.14 inference(modus_ponens,[status(thm)],[26426, 26425])).
% 10.92/11.14 tff(26428,plain,
% 10.92/11.14 (~b(s(s(s(elem!1))), s(s(z)))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[26427, 391, 26421, 26384, 26074, 26377])).
% 10.92/11.14 tff(26429,plain,
% 10.92/11.14 ($false),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[26428, 26419])).
% 10.92/11.14 tff(26430,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (z = elem!1) | b(elem!1, z) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(z), s(s(s(s(z))))) | r(z, s(s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.14 tff(26431,plain,
% 10.92/11.14 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[26430, 25916, 98, 88, 182, 25913, 2881, 25910, 25912, 25075, 25076])).
% 10.92/11.14 tff(26432,plain,
% 10.92/11.14 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 10.92/11.14 inference(modus_ponens,[status(thm)],[26431, 25907])).
% 10.92/11.14 tff(26433,plain,
% 10.92/11.14 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[12932, 26431, 22898, 25916])).
% 10.92/11.14 tff(26434,plain,
% 10.92/11.14 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 10.92/11.14 inference(monotonicity,[status(thm)],[25902])).
% 10.92/11.14 tff(26435,plain,
% 10.92/11.14 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), elem!1)),
% 10.92/11.14 inference(symmetry,[status(thm)],[26434])).
% 10.92/11.14 tff(26436,plain,
% 10.92/11.14 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 10.92/11.14 inference(monotonicity,[status(thm)],[26435])).
% 10.92/11.14 tff(26437,plain,
% 10.92/11.14 (~b(s(s(s(elem!1))), elem!1)),
% 10.92/11.14 inference(modus_ponens,[status(thm)],[463, 26436])).
% 10.92/11.14 tff(26438,plain,
% 10.92/11.14 (~(s(s(elem!1)) = elem!1)),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[1845, 26437, 26431])).
% 10.92/11.14 tff(26439,plain,
% 10.92/11.14 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[6159, 26438])).
% 10.92/11.14 tff(26440,plain,
% 10.92/11.14 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[281, 26439])).
% 10.92/11.14 tff(26441,plain,
% 10.92/11.14 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[1356, 26440, 26433])).
% 10.92/11.14 tff(26442,plain,
% 10.92/11.14 (~(elem!1 = s(z))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[11177, 25910, 25084])).
% 10.92/11.14 tff(26443,plain,
% 10.92/11.14 (~(s(z) = elem!1)),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[1495, 26442])).
% 10.92/11.14 tff(26444,plain,
% 10.92/11.14 (r(s(z), elem!1)),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[632, 22377, 150])).
% 10.92/11.14 tff(26445,plain,
% 10.92/11.14 (r(elem!1, s(z))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[8406, 183, 130])).
% 10.92/11.14 tff(26446,plain,
% 10.92/11.14 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[20820, 125, 1652])).
% 10.92/11.14 tff(26447,plain,
% 10.92/11.14 (~r(s(z), s(s(z)))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[25992, 20264, 90, 10682, 125, 1652, 1216, 174, 8922, 26445, 183, 1686])).
% 10.92/11.14 tff(26448,plain,
% 10.92/11.14 (b(s(z), s(s(z)))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[1788, 26447])).
% 10.92/11.14 tff(26449,plain,
% 10.92/11.14 (~b(s(s(z)), s(z))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[26024, 26448, 90, 10682, 26446, 174, 125, 664])).
% 10.92/11.14 tff(26450,plain,
% 10.92/11.14 (r(s(s(z)), s(z))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[3778, 26449])).
% 10.92/11.14 tff(26451,plain,
% 10.92/11.14 (~r(s(s(elem!1)), s(z))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[2201, 20264, 1378, 183])).
% 10.92/11.14 tff(26452,plain,
% 10.92/11.14 (b(s(s(elem!1)), s(z))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[362, 26451])).
% 10.92/11.14 tff(26453,plain,
% 10.92/11.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 10.92/11.14 inference(rewrite,[status(thm)],[])).
% 10.92/11.14 tff(26454,plain,
% 10.92/11.14 (((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 10.92/11.14 inference(rewrite,[status(thm)],[])).
% 10.92/11.14 tff(26455,plain,
% 10.92/11.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 10.92/11.14 inference(monotonicity,[status(thm)],[26454])).
% 10.92/11.14 tff(26456,plain,
% 10.92/11.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 10.92/11.14 inference(transitivity,[status(thm)],[26455, 26453])).
% 10.92/11.14 tff(26457,plain,
% 10.92/11.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 10.92/11.14 inference(quant_inst,[status(thm)],[])).
% 10.92/11.14 tff(26458,plain,
% 10.92/11.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 10.92/11.14 inference(modus_ponens,[status(thm)],[26457, 26456])).
% 10.92/11.14 tff(26459,plain,
% 10.92/11.14 ($false),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[26458, 391, 381, 3927, 2439, 8498, 664])).
% 10.92/11.14 tff(26460,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.14 tff(26461,plain,
% 10.92/11.14 (~b(s(s(z)), elem!1)),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[26460, 26448, 3927, 26452, 664])).
% 10.92/11.14 tff(26462,plain,
% 10.92/11.14 (r(s(s(z)), elem!1)),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[4730, 26461, 18819])).
% 10.92/11.14 tff(26463,plain,
% 10.92/11.14 ($false),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[6674, 26462, 26450, 26445, 26444])).
% 10.92/11.14 tff(26464,plain,(b(s(z), s(s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~(elem!1 = s(s(s(elem!1))))) | (s(z) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.14 tff(26465,plain,
% 10.92/11.14 (b(s(z), s(s(s(elem!1))))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[26464, 25916, 664, 88, 22898, 25909, 25902, 26443, 26441, 25911, 1652, 2913, 8922, 1686])).
% 10.92/11.14 tff(26466,plain,
% 10.92/11.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 10.92/11.14 inference(rewrite,[status(thm)],[])).
% 10.92/11.14 tff(26467,plain,
% 10.92/11.14 (((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 10.92/11.14 inference(rewrite,[status(thm)],[])).
% 10.92/11.14 tff(26468,plain,
% 10.92/11.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 10.92/11.14 inference(monotonicity,[status(thm)],[26467])).
% 10.92/11.14 tff(26469,plain,
% 10.92/11.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 10.92/11.14 inference(transitivity,[status(thm)],[26468, 26466])).
% 10.92/11.14 tff(26470,plain,
% 10.92/11.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 10.92/11.14 inference(quant_inst,[status(thm)],[])).
% 10.92/11.14 tff(26471,plain,
% 10.92/11.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 10.92/11.14 inference(modus_ponens,[status(thm)],[26470, 26469])).
% 10.92/11.14 tff(26472,plain,
% 10.92/11.14 ($false),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[26471, 391, 26465, 25084, 1686, 664, 26432])).
% 10.92/11.14 tff(26473,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~r(s(z), z)) | b(s(z), s(s(s(s(z))))) | b(elem!1, s(z)) | r(s(s(s(s(z)))), z) | (~b(z, elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 10.92/11.14 tff(26474,plain,
% 10.92/11.14 (elem!1 = s(s(s(s(z))))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[26473, 25073, 25046, 22903, 181, 22965, 31, 81, 133, 2])).
% 10.92/11.14 tff(26475,plain,
% 10.92/11.14 ($false),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[16358, 26474, 25074, 88])).
% 10.92/11.14 tff(26476,plain,(r(z, s(z)) | b(elem!1, s(z)) | r(s(s(s(s(z)))), z) | (~b(z, elem!1)) | (elem!1 = z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 10.92/11.14 tff(26477,plain,
% 10.92/11.14 (r(z, s(z))),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[26476, 31, 81, 22902, 2, 91])).
% 10.92/11.14 tff(26478,plain,
% 10.92/11.14 (~(s(z) = elem!1)),
% 10.92/11.14 inference(unit_resolution,[status(thm)],[17233, 26477, 80])).
% 10.92/11.14 tff(26479,plain,
% 10.92/11.14 (~(elem!1 = s(z))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[172, 26478])).
% 10.92/11.15 tff(26480,plain,
% 10.92/11.15 (r(elem!1, s(z))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[837, 26479, 31])).
% 10.92/11.15 tff(26481,plain,
% 10.92/11.15 (~r(elem!1, z)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[17266, 26480, 181, 26477])).
% 10.92/11.15 tff(26482,plain,
% 10.92/11.15 (b(elem!1, z)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[526, 26481, 2])).
% 10.92/11.15 tff(26483,plain,
% 10.92/11.15 (~b(s(s(s(elem!1))), elem!1)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[10743, 26482, 22898, 22902])).
% 10.92/11.15 tff(26484,plain,
% 10.92/11.15 (b(s(elem!1), elem!1)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[14657, 26483, 22902, 22898, 26481, 26478, 2])).
% 10.92/11.15 tff(26485,plain,
% 10.92/11.15 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[14662, 26484, 26483])).
% 10.92/11.15 tff(26486,plain,
% 10.92/11.15 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[281, 26485])).
% 10.92/11.15 tff(26487,plain,
% 10.92/11.15 (~(s(s(elem!1)) = s(elem!1))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[2279, 26485])).
% 10.92/11.15 tff(26488,plain,
% 10.92/11.15 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[287, 26487])).
% 10.92/11.15 tff(26489,plain,
% 10.92/11.15 (~(s(s(elem!1)) = elem!1)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[451, 26485])).
% 10.92/11.15 tff(26490,plain,
% 10.92/11.15 (~b(s(s(elem!1)), elem!1)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[5286, 26487, 22902, 26482, 26484])).
% 10.92/11.15 tff(26491,plain,
% 10.92/11.15 (r(s(s(elem!1)), elem!1)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[872, 26490, 26489])).
% 10.92/11.15 tff(26492,plain,
% 10.92/11.15 (~b(s(s(s(elem!1))), elem!1)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[10743, 665, 10682, 133])).
% 10.92/11.15 tff(26493,plain,
% 10.92/11.15 (r(s(s(s(elem!1))), elem!1)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[230, 9, 26492])).
% 10.92/11.15 tff(26494,plain,
% 10.92/11.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.92/11.15 inference(rewrite,[status(thm)],[])).
% 10.92/11.15 tff(26495,plain,
% 10.92/11.15 (((~r(elem!1, s(z))) | (~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)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.92/11.15 inference(rewrite,[status(thm)],[])).
% 10.92/11.15 tff(26496,plain,
% 10.92/11.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26495])).
% 10.92/11.15 tff(26497,plain,
% 10.92/11.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 10.92/11.15 inference(transitivity,[status(thm)],[26496, 26494])).
% 10.92/11.15 tff(26498,plain,
% 10.92/11.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~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))))))),
% 10.92/11.15 inference(quant_inst,[status(thm)],[])).
% 10.92/11.15 tff(26499,plain,
% 10.92/11.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 10.92/11.15 inference(modus_ponens,[status(thm)],[26498, 26497])).
% 10.92/11.15 tff(26500,plain,
% 10.92/11.15 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[26499, 194, 26493, 364, 838])).
% 10.92/11.15 tff(26501,plain,
% 10.92/11.15 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[1356, 26500, 270])).
% 10.92/11.15 tff(26502,plain,
% 10.92/11.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.92/11.15 inference(rewrite,[status(thm)],[])).
% 10.92/11.15 tff(26503,plain,
% 10.92/11.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.92/11.15 inference(quant_inst,[status(thm)],[])).
% 10.92/11.15 tff(26504,plain,
% 10.92/11.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 10.92/11.15 inference(modus_ponens,[status(thm)],[26503, 26502])).
% 10.92/11.15 tff(26505,plain,
% 10.92/11.15 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[26504, 194, 26493, 364, 838])).
% 10.92/11.15 tff(26506,plain,
% 10.92/11.15 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[1370, 26505, 297])).
% 10.92/11.15 tff(26507,plain,
% 10.92/11.15 (~b(z, s(s(elem!1)))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[12932, 26501, 10682, 26506])).
% 10.92/11.15 tff(26508,plain,
% 10.92/11.15 (r(z, s(s(elem!1)))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[324, 26507])).
% 10.92/11.15 tff(26509,plain,
% 10.92/11.15 (~b(s(z), s(s(s(elem!1))))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[3432, 26508, 182, 26506, 26501])).
% 10.92/11.15 tff(26510,plain,
% 10.92/11.15 (r(s(z), s(s(s(elem!1))))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[247, 26509])).
% 10.92/11.15 tff(26511,plain,
% 10.92/11.15 (b(s(z), elem!1)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[5246, 26510, 31, 150, 26493])).
% 10.92/11.15 tff(26512,plain,
% 10.92/11.15 (~r(s(s(s(elem!1))), z)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[12936, 26511, 10682, 133, 364, 26492, 1, 297, 665])).
% 10.92/11.15 tff(26513,plain,
% 10.92/11.15 (b(s(s(s(elem!1))), z)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[377, 26512])).
% 10.92/11.15 tff(26514,plain,
% 10.92/11.15 (~b(elem!1, s(s(s(elem!1))))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[10876, 26513, 133, 665])).
% 10.92/11.15 tff(26515,plain,
% 10.92/11.15 (r(elem!1, s(s(s(elem!1))))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[424, 26514, 1])).
% 10.92/11.15 tff(26516,plain,
% 10.92/11.15 ($false),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[15569, 194, 26493, 26515, 26510, 838])).
% 10.92/11.15 tff(26517,plain,((elem!1 = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | b(elem!1, s(z)) | (s(z) = elem!1) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.15 tff(26518,plain,
% 10.92/11.15 (elem!1 = s(s(s(elem!1)))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[26517, 26482, 22902, 22898, 26491, 26488, 31, 26478, 181, 26486])).
% 10.92/11.15 tff(26519,plain,
% 10.92/11.15 (s(s(s(elem!1))) = elem!1),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[129, 26518])).
% 10.92/11.15 tff(26520,plain,
% 10.92/11.15 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[11384, 26519])).
% 10.92/11.15 tff(26521,plain,
% 10.92/11.15 (s(elem!1) = s(s(s(s(elem!1))))),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26518])).
% 10.92/11.15 tff(26522,plain,
% 10.92/11.15 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26521])).
% 10.92/11.15 tff(26523,plain,
% 10.92/11.15 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26522])).
% 10.92/11.15 tff(26524,plain,
% 10.92/11.15 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 10.92/11.15 inference(symmetry,[status(thm)],[26523])).
% 10.92/11.15 tff(26525,plain,
% 10.92/11.15 ((~b(s(s(s(s(s(elem!1))))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26524])).
% 10.92/11.15 tff(26526,plain,
% 10.92/11.15 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 10.92/11.15 inference(symmetry,[status(thm)],[26522])).
% 10.92/11.15 tff(26527,plain,
% 10.92/11.15 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26526])).
% 10.92/11.15 tff(26528,plain,
% 10.92/11.15 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 10.92/11.15 inference(transitivity,[status(thm)],[26527, 1375])).
% 10.92/11.15 tff(26529,plain,
% 10.92/11.15 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 10.92/11.15 inference(symmetry,[status(thm)],[26528])).
% 10.92/11.15 tff(26530,plain,
% 10.92/11.15 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(s(z))))))),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26529])).
% 10.92/11.15 tff(26531,plain,
% 10.92/11.15 (s(s(s(elem!1))) = elem!1),
% 10.92/11.15 inference(symmetry,[status(thm)],[26518])).
% 10.92/11.15 tff(26532,plain,
% 10.92/11.15 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26531])).
% 10.92/11.15 tff(26533,plain,
% 10.92/11.15 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 10.92/11.15 inference(transitivity,[status(thm)],[26532, 698])).
% 10.92/11.15 tff(26534,plain,
% 10.92/11.15 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26533])).
% 10.92/11.15 tff(26535,plain,
% 10.92/11.15 (~(elem!1 = s(s(z)))),
% 10.92/11.15 inference(modus_ponens,[status(thm)],[1397, 26534])).
% 10.92/11.15 tff(26536,plain,
% 10.92/11.15 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[1407, 26535])).
% 10.92/11.15 tff(26537,plain,
% 10.92/11.15 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 10.92/11.15 inference(modus_ponens,[status(thm)],[26536, 26530])).
% 10.92/11.15 tff(26538,plain,
% 10.92/11.15 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26522])).
% 10.92/11.15 tff(26539,plain,
% 10.92/11.15 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.92/11.15 inference(monotonicity,[status(thm)],[26518])).
% 10.92/11.15 tff(26540,plain,
% 10.92/11.15 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.92/11.15 inference(modus_ponens,[status(thm)],[26491, 26539])).
% 10.92/11.15 tff(26541,plain,
% 10.92/11.15 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 10.92/11.15 inference(modus_ponens,[status(thm)],[26540, 26538])).
% 10.92/11.15 tff(26542,plain,
% 10.92/11.15 (~b(s(s(s(s(z)))), elem!1)),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[4086, 391, 22902, 26482, 88])).
% 10.92/11.15 tff(26543,plain,
% 10.92/11.15 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[2694, 26519, 26542])).
% 10.92/11.15 tff(26544,plain,
% 10.92/11.15 (~b(s(s(s(elem!1))), s(z))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[8400, 26519, 31])).
% 10.92/11.15 tff(26545,plain,
% 10.92/11.15 (r(s(s(s(elem!1))), s(z))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[223, 26544])).
% 10.92/11.15 tff(26546,plain,
% 10.92/11.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(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(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(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(s(s(s(z)))))))),
% 10.92/11.15 inference(rewrite,[status(thm)],[])).
% 10.92/11.15 tff(26547,plain,
% 10.92/11.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(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(s(s(s(z)))))))),
% 10.92/11.15 inference(quant_inst,[status(thm)],[])).
% 10.92/11.15 tff(26548,plain,
% 10.92/11.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(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(s(s(s(z))))))),
% 10.92/11.15 inference(modus_ponens,[status(thm)],[26547, 26546])).
% 10.92/11.15 tff(26549,plain,
% 10.92/11.15 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 10.92/11.15 inference(unit_resolution,[status(thm)],[26548, 194, 26545, 26543, 26541])).
% 10.92/11.15 tff(26550,plain,
% 10.92/11.16 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[16299, 42, 26549])).
% 10.92/11.16 tff(26551,plain,
% 10.92/11.16 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[26550, 26537])).
% 10.92/11.16 tff(26552,plain,
% 10.92/11.16 (~b(elem!1, s(s(s(s(z)))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[12445, 26482, 88, 22902])).
% 10.92/11.16 tff(26553,plain,
% 10.92/11.16 (~(s(s(s(s(z)))) = elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[1436, 26519])).
% 10.92/11.16 tff(26554,plain,
% 10.92/11.16 (~r(s(z), s(s(s(s(z)))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[24995, 26553, 26480, 26542, 26552])).
% 10.92/11.16 tff(26555,plain,
% 10.92/11.16 (b(s(z), s(s(s(s(z)))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[1230, 26554])).
% 10.92/11.16 tff(26556,plain,
% 10.92/11.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 10.92/11.16 inference(rewrite,[status(thm)],[])).
% 10.92/11.16 tff(26557,plain,
% 10.92/11.16 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 10.92/11.16 inference(rewrite,[status(thm)],[])).
% 10.92/11.16 tff(26558,plain,
% 10.92/11.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 10.92/11.16 inference(monotonicity,[status(thm)],[26557])).
% 10.92/11.16 tff(26559,plain,
% 10.92/11.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 10.92/11.16 inference(transitivity,[status(thm)],[26558, 26556])).
% 10.92/11.16 tff(26560,plain,
% 10.92/11.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(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))))),
% 10.92/11.16 inference(quant_inst,[status(thm)],[])).
% 10.92/11.16 tff(26561,plain,
% 10.92/11.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 10.92/11.16 inference(modus_ponens,[status(thm)],[26560, 26559])).
% 10.92/11.16 tff(26562,plain,
% 10.92/11.16 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[26561, 391, 22898, 88, 26555, 26551])).
% 10.92/11.16 tff(26563,plain,
% 10.92/11.16 (~b(s(s(elem!1)), s(z))),
% 10.92/11.16 inference(modus_ponens,[status(thm)],[26562, 26525])).
% 10.92/11.16 tff(26564,plain,
% 10.92/11.16 (r(s(s(elem!1)), s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[362, 26563])).
% 10.92/11.16 tff(26565,plain,
% 10.92/11.16 (~r(s(z), elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[1899, 26564, 26480, 26491])).
% 10.92/11.16 tff(26566,plain,
% 10.92/11.16 (b(s(z), elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[632, 26565, 26478])).
% 10.92/11.16 tff(26567,plain,
% 10.92/11.16 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[12150, 26566, 22902, 181, 26482])).
% 10.92/11.16 tff(26568,plain,
% 10.92/11.16 (r(s(s(s(s(z)))), elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[762, 26553, 26542])).
% 10.92/11.16 tff(26569,plain,
% 10.92/11.16 (~(elem!1 = s(s(s(s(z)))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[769, 26553])).
% 10.92/11.16 tff(26570,plain,
% 10.92/11.16 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[12326, 26566, 88, 22902, 26569, 26482, 181, 26555, 26568])).
% 10.92/11.16 tff(26571,plain,
% 10.92/11.16 ($false),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[8073, 26570, 26567, 26520])).
% 10.92/11.16 tff(26572,plain,(b(elem!1, s(z)) | (elem!1 = z) | r(z, elem!1) | r(s(s(s(s(z)))), z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 10.92/11.16 tff(26573,plain,
% 10.92/11.16 (b(elem!1, s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[26572, 91, 80, 81, 2])).
% 10.92/11.16 tff(26574,plain,
% 10.92/11.16 (r(z, s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[678, 675])).
% 10.92/11.16 tff(26575,plain,
% 10.92/11.16 (r(elem!1, s(z))),
% 10.92/11.16 inference(modus_ponens,[status(thm)],[722, 8827])).
% 10.92/11.16 tff(26576,plain,
% 10.92/11.16 ($false),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[832, 26575])).
% 10.92/11.16 tff(26577,plain,((~(elem!1 = z)) | r(elem!1, s(z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.16 tff(26578,plain,
% 10.92/11.16 (~(elem!1 = z)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[26577, 26574, 832])).
% 10.92/11.16 tff(26579,plain,
% 10.92/11.16 (b(z, s(s(s(elem!1))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[8231, 26578, 80])).
% 10.92/11.16 tff(26580,plain,
% 10.92/11.16 (~(z = elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[97, 26578])).
% 10.92/11.16 tff(26581,plain,
% 10.92/11.16 (b(z, elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[141, 26580, 80])).
% 10.92/11.16 tff(26582,plain,
% 10.92/11.16 (~(s(s(s(s(z)))) = elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[16908, 25917])).
% 10.92/11.16 tff(26583,plain,
% 10.92/11.16 (~(s(z) = elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[7485, 175, 484])).
% 10.92/11.16 tff(26584,plain,
% 10.92/11.16 (~(elem!1 = s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[172, 26583])).
% 10.92/11.16 tff(26585,plain,
% 10.92/11.16 (b(elem!1, s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[837, 26584, 832])).
% 10.92/11.16 tff(26586,plain,
% 10.92/11.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.16 inference(rewrite,[status(thm)],[])).
% 10.92/11.16 tff(26587,plain,
% 10.92/11.16 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.16 inference(rewrite,[status(thm)],[])).
% 10.92/11.16 tff(26588,plain,
% 10.92/11.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 10.92/11.16 inference(monotonicity,[status(thm)],[26587])).
% 10.92/11.16 tff(26589,plain,
% 10.92/11.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.16 inference(transitivity,[status(thm)],[26588, 26586])).
% 10.92/11.16 tff(26590,plain,
% 10.92/11.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.16 inference(quant_inst,[status(thm)],[])).
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% 10.92/11.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 10.92/11.16 inference(modus_ponens,[status(thm)],[26590, 26589])).
% 10.92/11.16 tff(26592,plain,
% 10.92/11.16 ($false),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[26591, 391, 133, 90, 1234, 5450, 26585])).
% 10.92/11.16 tff(26593,plain,(r(s(z), z) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | r(elem!1, s(z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 10.92/11.16 tff(26594,plain,
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% 10.92/11.16 inference(unit_resolution,[status(thm)],[26593, 90, 133, 1234, 832, 484])).
% 10.92/11.16 tff(26595,plain,
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% 10.92/11.16 inference(unit_resolution,[status(thm)],[26577, 722, 832])).
% 10.92/11.16 tff(26596,plain,
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% 10.92/11.16 tff(26597,plain,
% 10.92/11.16 (~r(s(s(s(s(z)))), s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[731, 719, 722, 182])).
% 10.92/11.16 tff(26598,plain,
% 10.92/11.16 (b(s(s(s(s(z)))), s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[749, 26597])).
% 10.92/11.16 tff(26599,plain,
% 10.92/11.16 (~r(s(z), elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[25179, 182, 722, 530])).
% 10.92/11.16 tff(26600,plain,
% 10.92/11.16 (~r(elem!1, s(s(s(s(z)))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[6399, 719, 530, 2112])).
% 10.92/11.16 tff(26601,plain,
% 10.92/11.16 (b(elem!1, s(s(s(s(z)))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[781, 26600, 8922])).
% 10.92/11.16 tff(26602,plain,
% 10.92/11.16 (~b(s(z), elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[6418, 26601, 90, 1234, 133])).
% 10.92/11.16 tff(26603,plain,
% 10.92/11.16 (s(z) = elem!1),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[632, 26602, 26599])).
% 10.92/11.16 tff(26604,plain,
% 10.92/11.16 (elem!1 = s(z)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[1495, 26603])).
% 10.92/11.16 tff(26605,plain,
% 10.92/11.16 (~b(s(s(s(elem!1))), elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[25386, 26601, 10682, 133, 90])).
% 10.92/11.16 tff(26606,plain,
% 10.92/11.16 (~b(s(s(s(elem!1))), s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[3938, 26603, 26605])).
% 10.92/11.16 tff(26607,plain,
% 10.92/11.16 ($false),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[11177, 26606, 26604, 26598])).
% 10.92/11.16 tff(26608,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.16 tff(26609,plain,
% 10.92/11.16 (~r(z, s(s(s(s(z)))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[26608, 182, 1234, 133, 10682, 25917, 26596, 2112, 722, 90])).
% 10.92/11.16 tff(26610,plain,
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% 10.92/11.16 tff(26611,plain,
% 10.92/11.16 (~b(elem!1, s(s(s(s(z)))))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[22981, 26610, 133, 90])).
% 10.92/11.16 tff(26612,plain,
% 10.92/11.16 (~(s(z) = elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[8539, 26611, 1234])).
% 10.92/11.16 tff(26613,plain,
% 10.92/11.16 (~(elem!1 = s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[172, 26612])).
% 10.92/11.16 tff(26614,plain,
% 10.92/11.16 (b(elem!1, s(z))),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[837, 26613, 832])).
% 10.92/11.16 tff(26615,plain,
% 10.92/11.16 (~r(s(z), elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[25179, 182, 722, 26596])).
% 10.92/11.16 tff(26616,plain,
% 10.92/11.16 (b(s(z), elem!1)),
% 10.92/11.16 inference(unit_resolution,[status(thm)],[632, 26612, 26615])).
% 10.92/11.16 tff(26617,plain,
% 10.92/11.16 (~b(s(s(s(s(z)))), s(s(z)))),
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% 10.92/11.16 tff(26618,plain,
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% 10.92/11.16 inference(unit_resolution,[status(thm)],[1714, 26617])).
% 10.92/11.17 tff(26619,plain,
% 10.92/11.17 (~r(s(s(z)), elem!1)),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[20852, 26618, 530, 2112])).
% 10.92/11.17 tff(26620,plain,
% 10.92/11.17 (b(s(s(z)), elem!1)),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[4730, 26619, 26332])).
% 10.92/11.17 tff(26621,plain,
% 10.92/11.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 10.92/11.17 inference(rewrite,[status(thm)],[])).
% 10.92/11.17 tff(26622,plain,
% 10.92/11.17 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 10.92/11.17 inference(rewrite,[status(thm)],[])).
% 10.92/11.17 tff(26623,plain,
% 10.92/11.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26622])).
% 10.92/11.17 tff(26624,plain,
% 10.92/11.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 10.92/11.17 inference(transitivity,[status(thm)],[26623, 26621])).
% 10.92/11.17 tff(26625,plain,
% 10.92/11.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 10.92/11.17 inference(quant_inst,[status(thm)],[])).
% 10.92/11.17 tff(26626,plain,
% 10.92/11.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 10.92/11.17 inference(modus_ponens,[status(thm)],[26625, 26624])).
% 10.92/11.17 tff(26627,plain,
% 10.92/11.17 ($false),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[26626, 391, 133, 644, 1235, 26620, 721])).
% 10.92/11.17 tff(26628,plain,((~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 10.92/11.17 tff(26629,plain,
% 10.92/11.17 (~b(s(s(z)), z)),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[26628, 26616, 133, 26614, 26596, 2112, 90, 26610, 484])).
% 10.92/11.17 tff(26630,plain,
% 10.92/11.17 (r(s(s(z)), z)),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[1211, 26629])).
% 10.92/11.17 tff(26631,plain,
% 10.92/11.17 (~r(elem!1, s(s(z)))),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[18602, 26630, 26596, 722])).
% 10.92/11.17 tff(26632,plain,
% 10.92/11.17 (~r(s(s(z)), s(z))),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[12188, 194, 722, 182, 26630])).
% 10.92/11.17 tff(26633,plain,
% 10.92/11.17 (b(s(s(z)), s(z))),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[3778, 26632])).
% 10.92/11.17 tff(26634,plain,
% 10.92/11.17 (~r(s(z), s(s(z)))),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[12646, 194, 722, 182, 26630])).
% 10.92/11.17 tff(26635,plain,
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% 10.92/11.17 inference(unit_resolution,[status(thm)],[1788, 26634])).
% 10.92/11.17 tff(26636,plain,
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% 10.92/11.17 inference(unit_resolution,[status(thm)],[10150, 26635, 26614, 26633])).
% 10.92/11.17 tff(26637,plain,
% 10.92/11.17 (elem!1 = s(s(z))),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[3394, 26636, 26631])).
% 10.92/11.17 tff(26638,plain,
% 10.92/11.17 (s(s(z)) = elem!1),
% 10.92/11.17 inference(symmetry,[status(thm)],[26637])).
% 10.92/11.17 tff(26639,plain,
% 10.92/11.17 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26638])).
% 10.92/11.17 tff(26640,plain,
% 10.92/11.17 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 10.92/11.17 inference(transitivity,[status(thm)],[26639, 3])).
% 10.92/11.17 tff(26641,plain,
% 10.92/11.17 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26640])).
% 10.92/11.17 tff(26642,plain,
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% 10.92/11.17 inference(modus_ponens,[status(thm)],[1397, 26641])).
% 10.92/11.17 tff(26643,plain,
% 10.92/11.17 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(z)))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26637])).
% 10.92/11.17 tff(26644,plain,
% 10.92/11.17 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 10.92/11.17 inference(symmetry,[status(thm)],[26643])).
% 10.92/11.17 tff(26645,plain,
% 10.92/11.17 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26644])).
% 10.92/11.17 tff(26646,plain,
% 10.92/11.17 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[2849, 26612])).
% 10.92/11.17 tff(26647,plain,
% 10.92/11.17 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26637])).
% 10.92/11.17 tff(26648,plain,
% 10.92/11.17 (r(s(s(s(s(z)))), s(s(z)))),
% 10.92/11.17 inference(modus_ponens,[status(thm)],[2112, 26647])).
% 10.92/11.17 tff(26649,plain,
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% 10.92/11.17 inference(unit_resolution,[status(thm)],[25124, 26648, 10682, 26646, 90, 26630])).
% 10.92/11.17 tff(26650,plain,
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% 10.92/11.17 inference(modus_ponens,[status(thm)],[26649, 26645])).
% 10.92/11.17 tff(26651,plain,
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% 10.92/11.17 inference(unit_resolution,[status(thm)],[230, 26650, 26642])).
% 10.92/11.17 tff(26652,plain,
% 10.92/11.17 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
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% 10.92/11.17 tff(26653,plain,
% 10.92/11.17 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26652])).
% 10.92/11.17 tff(26654,plain,
% 10.92/11.17 (~(elem!1 = s(s(s(elem!1))))),
% 10.92/11.17 inference(modus_ponens,[status(thm)],[1397, 26653])).
% 10.92/11.17 tff(26655,plain,
% 10.92/11.17 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26637])).
% 10.92/11.17 tff(26656,plain,
% 10.92/11.17 (r(s(s(z)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
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% 10.92/11.17 tff(26657,plain,
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% 10.92/11.17 inference(monotonicity,[status(thm)],[26637])).
% 10.92/11.17 tff(26658,plain,
% 10.92/11.17 (s(s(elem!1)) = s(s(s(s(z))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26657])).
% 10.92/11.17 tff(26659,plain,
% 10.92/11.17 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26658])).
% 10.92/11.17 tff(26660,plain,
% 10.92/11.17 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 10.92/11.17 inference(symmetry,[status(thm)],[26659])).
% 10.92/11.17 tff(26661,plain,
% 10.92/11.17 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26660])).
% 10.92/11.17 tff(26662,plain,
% 10.92/11.17 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(elem!1))))),
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% 10.92/11.17 tff(26663,plain,
% 10.92/11.17 ((~r(s(s(z)), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26662])).
% 10.92/11.17 tff(26664,plain,
% 10.92/11.17 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26660])).
% 10.92/11.17 tff(26665,plain,
% 10.92/11.17 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
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% 10.92/11.17 tff(26666,plain,
% 10.92/11.17 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26658])).
% 10.92/11.17 tff(26667,plain,
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% 10.92/11.17 inference(unit_resolution,[status(thm)],[9253, 26637])).
% 10.92/11.17 tff(26668,plain,
% 10.92/11.17 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26658])).
% 10.92/11.17 tff(26669,plain,
% 10.92/11.17 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.92/11.17 inference(symmetry,[status(thm)],[26668])).
% 10.92/11.17 tff(26670,plain,
% 10.92/11.17 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26669])).
% 10.92/11.17 tff(26671,plain,
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% 10.92/11.17 inference(unit_resolution,[status(thm)],[23918, 26610, 90, 10682])).
% 10.92/11.17 tff(26672,plain,
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% 10.92/11.17 inference(modus_ponens,[status(thm)],[26671, 26670])).
% 10.92/11.17 tff(26673,plain,
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% 10.92/11.17 inference(unit_resolution,[status(thm)],[1370, 26672, 26667])).
% 10.92/11.17 tff(26674,plain,
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% 10.92/11.17 tff(26675,plain,
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% 10.92/11.17 tff(26676,plain,
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% 10.92/11.17 inference(unit_resolution,[status(thm)],[5126, 26633, 1234, 133, 722, 182])).
% 10.92/11.17 tff(26677,plain,
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% 10.92/11.17 inference(unit_resolution,[status(thm)],[3652, 26676])).
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% 10.92/11.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 10.92/11.17 inference(rewrite,[status(thm)],[])).
% 10.92/11.17 tff(26679,plain,
% 10.92/11.17 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 10.92/11.17 inference(rewrite,[status(thm)],[])).
% 10.92/11.17 tff(26680,plain,
% 10.92/11.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 10.92/11.17 inference(monotonicity,[status(thm)],[26679])).
% 10.92/11.17 tff(26681,plain,
% 10.92/11.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 10.92/11.17 inference(transitivity,[status(thm)],[26680, 26678])).
% 10.92/11.17 tff(26682,plain,
% 10.92/11.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
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% 10.92/11.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 10.92/11.17 inference(modus_ponens,[status(thm)],[26682, 26681])).
% 10.92/11.17 tff(26684,plain,
% 10.92/11.17 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[26683, 194, 26677, 26648])).
% 10.92/11.17 tff(26685,plain,
% 10.92/11.17 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 10.92/11.17 inference(unit_resolution,[status(thm)],[26684, 26675])).
% 10.92/11.17 tff(26686,plain,
% 10.92/11.17 (~r(elem!1, s(s(s(elem!1))))),
% 10.92/11.17 inference(modus_ponens,[status(thm)],[26685, 26663])).
% 10.92/11.18 tff(26687,plain,
% 10.92/11.18 (b(elem!1, s(s(s(elem!1))))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[424, 26686, 26654])).
% 10.92/11.18 tff(26688,plain,
% 10.92/11.18 ($false),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[10845, 26687, 26651, 10682, 133])).
% 10.92/11.18 tff(26689,plain,((~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | b(elem!1, z) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.18 tff(26690,plain,
% 10.92/11.18 (~r(s(s(s(s(z)))), elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[26689, 26594, 133, 90, 10682, 1234, 722, 484, 832])).
% 10.92/11.18 tff(26691,plain,
% 10.92/11.18 (b(s(s(s(s(z)))), elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[762, 26690, 26582])).
% 10.92/11.18 tff(26692,plain,
% 10.92/11.18 (~r(s(z), elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[25179, 26594, 722, 26596])).
% 10.92/11.18 tff(26693,plain,
% 10.92/11.18 (b(s(s(s(elem!1))), s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[11177, 7866, 1759])).
% 10.92/11.18 tff(26694,plain,
% 10.92/11.18 (~b(s(s(s(elem!1))), elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[25386, 8540, 10682, 133, 90])).
% 10.92/11.18 tff(26695,plain,
% 10.92/11.18 ($false),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[3938, 26694, 26693, 812])).
% 10.92/11.18 tff(26696,plain,((~(s(z) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.18 tff(26697,plain,
% 10.92/11.18 (~(s(z) = elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[26696, 1759, 133, 90, 10682, 1234])).
% 10.92/11.18 tff(26698,plain,
% 10.92/11.18 (b(s(z), elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[632, 26697, 1492])).
% 10.92/11.18 tff(26699,plain,
% 10.92/11.18 (~(elem!1 = s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[172, 26697])).
% 10.92/11.18 tff(26700,plain,
% 10.92/11.18 (b(elem!1, s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[837, 26699, 832])).
% 10.92/11.18 tff(26701,plain,
% 10.92/11.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.18 inference(rewrite,[status(thm)],[])).
% 10.92/11.18 tff(26702,plain,
% 10.92/11.18 (((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.18 inference(rewrite,[status(thm)],[])).
% 10.92/11.18 tff(26703,plain,
% 10.92/11.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 10.92/11.18 inference(monotonicity,[status(thm)],[26702])).
% 10.92/11.18 tff(26704,plain,
% 10.92/11.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.18 inference(transitivity,[status(thm)],[26703, 26701])).
% 10.92/11.18 tff(26705,plain,
% 10.92/11.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 10.92/11.18 inference(quant_inst,[status(thm)],[])).
% 10.92/11.18 tff(26706,plain,
% 10.92/11.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 10.92/11.18 inference(modus_ponens,[status(thm)],[26705, 26704])).
% 10.92/11.18 tff(26707,plain,
% 10.92/11.18 ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[26706, 391])).
% 10.92/11.18 tff(26708,plain,
% 10.92/11.18 ($false),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[26707, 26700, 26698, 1652, 1234, 1759])).
% 10.92/11.18 tff(26709,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | r(elem!1, s(z)) | r(s(z), elem!1) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.18 tff(26710,plain,
% 10.92/11.18 (~b(s(s(s(s(z)))), s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[26709, 26691, 1234, 832, 26692, 133, 90, 10682])).
% 10.92/11.18 tff(26711,plain,
% 10.92/11.18 (~(s(z) = elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[9614, 26710, 26691])).
% 10.92/11.18 tff(26712,plain,
% 10.92/11.18 (~(elem!1 = s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[172, 26711])).
% 10.92/11.18 tff(26713,plain,
% 10.92/11.18 (b(elem!1, s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[837, 26712, 832])).
% 10.92/11.18 tff(26714,plain,
% 10.92/11.18 (b(s(z), elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[632, 26711, 26692])).
% 10.92/11.18 tff(26715,plain,
% 10.92/11.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.18 inference(rewrite,[status(thm)],[])).
% 10.92/11.18 tff(26716,plain,
% 10.92/11.18 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.18 inference(rewrite,[status(thm)],[])).
% 10.92/11.18 tff(26717,plain,
% 10.92/11.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 10.92/11.18 inference(monotonicity,[status(thm)],[26716])).
% 10.92/11.18 tff(26718,plain,
% 10.92/11.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.18 inference(transitivity,[status(thm)],[26717, 26715])).
% 10.92/11.18 tff(26719,plain,
% 10.92/11.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.92/11.18 inference(quant_inst,[status(thm)],[])).
% 10.92/11.18 tff(26720,plain,
% 10.92/11.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 10.92/11.18 inference(modus_ponens,[status(thm)],[26719, 26718])).
% 10.92/11.18 tff(26721,plain,
% 10.92/11.18 ($false),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[26720, 391, 26714, 26691, 1234, 26713])).
% 10.92/11.18 tff(26722,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | r(elem!1, s(z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 10.92/11.18 tff(26723,plain,
% 10.92/11.18 (~b(s(s(s(s(z)))), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[26722, 26581, 832, 1234, 26579, 26574, 484])).
% 10.92/11.18 tff(26724,plain,
% 10.92/11.18 (r(s(s(s(s(z)))), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[87, 26723])).
% 10.92/11.18 tff(26725,plain,
% 10.92/11.18 (r(elem!1, z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[526, 26578, 484])).
% 10.92/11.18 tff(26726,plain,
% 10.92/11.18 (s(s(s(s(z)))) = elem!1),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[20438, 1491, 1234, 18006, 18014])).
% 10.92/11.18 tff(26727,plain,
% 10.92/11.18 (elem!1 = s(s(s(s(z))))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[16908, 26726])).
% 10.92/11.18 tff(26728,plain,
% 10.92/11.18 (b(s(s(s(s(z)))), s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[13738, 26727, 1491])).
% 10.92/11.18 tff(26729,plain,
% 10.92/11.18 (b(s(z), elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[8916, 26726, 1234])).
% 10.92/11.18 tff(26730,plain,
% 10.92/11.18 (~b(s(z), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[4857, 26729, 133, 1491])).
% 10.92/11.18 tff(26731,plain,
% 10.92/11.18 (r(s(z), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[180, 26730])).
% 10.92/11.18 tff(26732,plain,
% 10.92/11.18 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[9635, 3557, 2053, 722])).
% 10.92/11.18 tff(26733,plain,
% 10.92/11.18 (b(s(s(z)), s(s(s(s(z)))))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[3652, 26732])).
% 10.92/11.18 tff(26734,plain,
% 10.92/11.18 (~b(s(s(z)), s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[5108, 26733, 1234, 1759])).
% 10.92/11.18 tff(26735,plain,
% 10.92/11.18 (r(s(s(z)), s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[3778, 26734])).
% 10.92/11.18 tff(26736,plain,
% 10.92/11.18 ($false),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[12188, 194, 722, 182, 3557, 26735])).
% 10.92/11.18 tff(26737,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.18 tff(26738,plain,
% 10.92/11.18 (~r(s(s(z)), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[26737, 26731, 722, 1234, 26728, 2053])).
% 10.92/11.18 tff(26739,plain,
% 10.92/11.18 (b(s(s(z)), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[1211, 26738])).
% 10.92/11.18 tff(26740,plain,
% 10.92/11.18 (~(s(s(s(elem!1))) = elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[1436, 26726])).
% 10.92/11.18 tff(26741,plain,
% 10.92/11.18 (~r(s(z), elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[25179, 26731, 722, 530])).
% 10.92/11.18 tff(26742,plain,
% 10.92/11.18 (~b(s(z), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[4857, 644, 133, 1491])).
% 10.92/11.18 tff(26743,plain,
% 10.92/11.18 (r(s(z), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[180, 26742])).
% 10.92/11.18 tff(26744,plain,
% 10.92/11.18 (~b(s(s(s(elem!1))), s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[20387, 900, 1491, 644])).
% 10.92/11.18 tff(26745,plain,
% 10.92/11.18 (r(s(s(s(elem!1))), s(z))),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[223, 26744])).
% 10.92/11.18 tff(26746,plain,
% 10.92/11.18 (~b(s(s(s(elem!1))), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[1505, 900, 133, 832, 1492, 831])).
% 10.92/11.18 tff(26747,plain,
% 10.92/11.18 (r(s(s(s(elem!1))), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[377, 26746])).
% 10.92/11.18 tff(26748,plain,
% 10.92/11.18 ($false),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[12916, 194, 26747, 26745, 722, 26743])).
% 10.92/11.18 tff(26749,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | r(elem!1, s(z)) | r(s(z), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.18 tff(26750,plain,
% 10.92/11.18 (~b(s(s(s(elem!1))), elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[26749, 26729, 722, 133, 832, 26741, 831])).
% 10.92/11.18 tff(26751,plain,
% 10.92/11.18 (r(s(s(s(elem!1))), elem!1)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[230, 26750, 26740])).
% 10.92/11.18 tff(26752,plain,
% 10.92/11.18 (~r(s(s(s(elem!1))), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[4113, 26751, 722, 530])).
% 10.92/11.18 tff(26753,plain,
% 10.92/11.18 (b(s(s(s(elem!1))), z)),
% 10.92/11.18 inference(unit_resolution,[status(thm)],[377, 26752])).
% 10.92/11.18 tff(26754,plain,
% 10.92/11.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.92/11.19 inference(rewrite,[status(thm)],[])).
% 10.92/11.19 tff(26755,plain,
% 10.92/11.19 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.92/11.19 inference(rewrite,[status(thm)],[])).
% 10.92/11.19 tff(26756,plain,
% 10.92/11.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 10.92/11.19 inference(monotonicity,[status(thm)],[26755])).
% 10.92/11.19 tff(26757,plain,
% 10.92/11.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.92/11.19 inference(transitivity,[status(thm)],[26756, 26754])).
% 10.92/11.19 tff(26758,plain,
% 10.92/11.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 10.92/11.19 inference(quant_inst,[status(thm)],[])).
% 10.92/11.19 tff(26759,plain,
% 10.92/11.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 10.92/11.19 inference(modus_ponens,[status(thm)],[26758, 26757])).
% 10.92/11.19 tff(26760,plain,
% 10.92/11.19 (~b(s(s(z)), s(s(s(elem!1))))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[26759, 391, 133, 26753, 26739, 1491])).
% 10.92/11.19 tff(26761,plain,
% 10.92/11.19 (r(s(s(z)), s(s(s(elem!1))))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[11041, 26760])).
% 10.92/11.19 tff(26762,plain,
% 10.92/11.19 (r(s(s(s(s(z)))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 10.92/11.19 inference(monotonicity,[status(thm)],[26726])).
% 10.92/11.19 tff(26763,plain,
% 10.92/11.19 (elem!1 = s(s(s(s(z))))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[16908, 688])).
% 10.92/11.19 tff(26764,plain,
% 10.92/11.19 (b(s(s(s(s(z)))), s(z))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[13738, 26763, 721])).
% 10.92/11.19 tff(26765,plain,
% 10.92/11.19 (~b(s(s(z)), s(z))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[20714, 3563, 26764, 721, 644])).
% 10.92/11.19 tff(26766,plain,
% 10.92/11.19 (r(s(s(z)), s(z))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[3778, 26765])).
% 10.92/11.19 tff(26767,plain,
% 10.92/11.19 (~b(s(z), z)),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[4857, 644, 133, 721])).
% 10.92/11.19 tff(26768,plain,
% 10.92/11.19 (r(s(z), z)),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[180, 26767])).
% 10.92/11.19 tff(26769,plain,
% 10.92/11.19 (~r(z, s(s(z)))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[1817, 194, 722, 26768, 26766])).
% 10.92/11.19 tff(26770,plain,
% 10.92/11.19 (b(z, s(s(z)))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[10164, 42, 26769, 8912])).
% 10.92/11.19 tff(26771,plain,
% 10.92/11.19 (b(elem!1, s(s(z)))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[11029, 3563, 688])).
% 10.92/11.19 tff(26772,plain,
% 10.92/11.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 10.92/11.19 inference(rewrite,[status(thm)],[])).
% 10.92/11.19 tff(26773,plain,
% 10.92/11.19 (((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 10.92/11.19 inference(rewrite,[status(thm)],[])).
% 10.92/11.19 tff(26774,plain,
% 10.92/11.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))))),
% 10.92/11.19 inference(monotonicity,[status(thm)],[26773])).
% 10.92/11.19 tff(26775,plain,
% 10.92/11.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 10.92/11.19 inference(transitivity,[status(thm)],[26774, 26772])).
% 10.92/11.19 tff(26776,plain,
% 10.92/11.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))),
% 10.92/11.19 inference(quant_inst,[status(thm)],[])).
% 10.92/11.19 tff(26777,plain,
% 10.92/11.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))),
% 10.92/11.19 inference(modus_ponens,[status(thm)],[26776, 26775])).
% 10.92/11.19 tff(26778,plain,
% 10.92/11.19 ($false),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[26777, 391, 133, 1235, 26771, 26770])).
% 10.92/11.19 tff(26779,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~(s(s(s(s(z)))) = elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.92/11.19 tff(26780,plain,
% 10.92/11.19 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[26779, 26739, 133, 722, 26726, 1491, 26729])).
% 10.92/11.19 tff(26781,plain,
% 10.92/11.19 (r(s(s(s(s(z)))), s(s(z)))),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[1714, 26780])).
% 10.92/11.19 tff(26782,plain,
% 10.92/11.19 (r(elem!1, s(s(z)))),
% 10.92/11.19 inference(modus_ponens,[status(thm)],[26781, 26762])).
% 10.92/11.19 tff(26783,plain,
% 10.92/11.19 (~r(s(s(s(elem!1))), z)),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[4113, 233, 722, 530])).
% 10.92/11.19 tff(26784,plain,
% 10.92/11.19 (b(s(s(s(elem!1))), z)),
% 10.92/11.19 inference(unit_resolution,[status(thm)],[377, 26783])).
% 10.92/11.19 tff(26785,plain,
% 10.92/11.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.92/11.19 inference(rewrite,[status(thm)],[])).
% 10.92/11.19 tff(26786,plain,
% 10.92/11.19 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.92/11.19 inference(rewrite,[status(thm)],[])).
% 10.92/11.19 tff(26787,plain,
% 10.92/11.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 10.92/11.20 inference(monotonicity,[status(thm)],[26786])).
% 10.92/11.20 tff(26788,plain,
% 10.92/11.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.92/11.20 inference(transitivity,[status(thm)],[26787, 26785])).
% 10.92/11.20 tff(26789,plain,
% 10.92/11.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 10.92/11.20 inference(quant_inst,[status(thm)],[])).
% 10.92/11.20 tff(26790,plain,
% 10.92/11.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 10.92/11.20 inference(modus_ponens,[status(thm)],[26789, 26788])).
% 10.92/11.20 tff(26791,plain,
% 10.92/11.20 (~b(s(s(s(elem!1))), s(s(z)))),
% 10.92/11.20 inference(unit_resolution,[status(thm)],[26790, 391, 133, 26784, 1235, 721])).
% 10.92/11.20 tff(26792,plain,
% 10.92/11.20 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 10.92/11.20 inference(unit_resolution,[status(thm)],[10713, 42, 26791])).
% 10.92/11.20 tff(26793,plain,
% 10.92/11.20 (r(s(s(s(elem!1))), s(s(z)))),
% 10.92/11.20 inference(unit_resolution,[status(thm)],[26792, 10703])).
% 10.92/11.20 tff(26794,plain,
% 10.92/11.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.92/11.20 inference(rewrite,[status(thm)],[])).
% 10.92/11.20 tff(26795,plain,
% 10.92/11.20 (((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.92/11.20 inference(rewrite,[status(thm)],[])).
% 10.92/11.20 tff(26796,plain,
% 10.92/11.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 10.92/11.20 inference(monotonicity,[status(thm)],[26795])).
% 10.92/11.20 tff(26797,plain,
% 10.92/11.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 10.92/11.20 inference(transitivity,[status(thm)],[26796, 26794])).
% 10.92/11.20 tff(26798,plain,
% 10.92/11.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 10.92/11.20 inference(quant_inst,[status(thm)],[])).
% 10.99/11.20 tff(26799,plain,
% 10.99/11.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 10.99/11.20 inference(modus_ponens,[status(thm)],[26798, 26797])).
% 10.99/11.20 tff(26800,plain,
% 10.99/11.20 ($false),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[26799, 194, 233, 1748, 2405, 26793])).
% 10.99/11.20 tff(26801,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.20 tff(26802,plain,
% 10.99/11.20 (~r(s(s(z)), s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[26801, 26751, 26782, 133, 26739, 1491, 722, 530])).
% 10.99/11.20 tff(26803,plain,
% 10.99/11.20 (b(s(s(z)), s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[3778, 26802])).
% 10.99/11.20 tff(26804,plain,
% 10.99/11.20 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[5126, 26803, 1234, 133, 722, 26731])).
% 10.99/11.20 tff(26805,plain,
% 10.99/11.20 (r(s(s(z)), s(s(s(s(z)))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[3652, 26804])).
% 10.99/11.20 tff(26806,plain,
% 10.99/11.20 (r(s(s(z)), elem!1)),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[5152, 26805, 26726])).
% 10.99/11.20 tff(26807,plain,
% 10.99/11.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 10.99/11.20 inference(rewrite,[status(thm)],[])).
% 10.99/11.20 tff(26808,plain,
% 10.99/11.20 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 10.99/11.20 inference(rewrite,[status(thm)],[])).
% 10.99/11.20 tff(26809,plain,
% 10.99/11.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1))))),
% 10.99/11.20 inference(monotonicity,[status(thm)],[26808])).
% 10.99/11.20 tff(26810,plain,
% 10.99/11.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 10.99/11.20 inference(transitivity,[status(thm)],[26809, 26807])).
% 10.99/11.20 tff(26811,plain,
% 10.99/11.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 10.99/11.20 inference(quant_inst,[status(thm)],[])).
% 10.99/11.20 tff(26812,plain,
% 10.99/11.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1))),
% 10.99/11.20 inference(modus_ponens,[status(thm)],[26811, 26810])).
% 10.99/11.20 tff(26813,plain,
% 10.99/11.20 ($false),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[26812, 194, 530, 26751, 26806, 26761])).
% 10.99/11.20 tff(26814,plain,((elem!1 = s(z)) | (~r(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | r(elem!1, s(z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.20 tff(26815,plain,
% 10.99/11.20 (elem!1 = s(z)),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[26814, 26725, 26581, 1234, 26574, 832, 26724])).
% 10.99/11.20 tff(26816,plain,
% 10.99/11.20 (b(z, elem!1) <=> b(z, s(z))),
% 10.99/11.20 inference(monotonicity,[status(thm)],[26815])).
% 10.99/11.20 tff(26817,plain,
% 10.99/11.20 (b(z, s(z)) <=> b(z, elem!1)),
% 10.99/11.20 inference(symmetry,[status(thm)],[26816])).
% 10.99/11.20 tff(26818,plain,
% 10.99/11.20 ((~b(z, s(z))) <=> (~b(z, elem!1))),
% 10.99/11.20 inference(monotonicity,[status(thm)],[26817])).
% 10.99/11.20 tff(26819,plain,
% 10.99/11.20 (~b(z, elem!1)),
% 10.99/11.20 inference(modus_ponens,[status(thm)],[675, 26818])).
% 10.99/11.20 tff(26820,plain,
% 10.99/11.20 ($false),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[26581, 26819])).
% 10.99/11.20 tff(26821,plain,(b(z, s(z)) | (~b(s(z), s(s(s(s(z)))))) | r(elem!1, s(z)) | b(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.20 tff(26822,plain,
% 10.99/11.20 (r(elem!1, s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[26821, 484, 80, 675, 1234])).
% 10.99/11.20 tff(26823,plain,
% 10.99/11.20 ($false),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[17266, 26822, 3618, 26574, 182])).
% 10.99/11.20 tff(26824,plain,(b(elem!1, z) | (~r(s(z), z)) | r(z, elem!1) | b(z, s(z)) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.20 tff(26825,plain,
% 10.99/11.20 (b(z, s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[26824, 484, 80, 182, 1234, 2])).
% 10.99/11.20 tff(26826,plain,
% 10.99/11.20 (~b(s(s(s(s(z)))), s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[22918, 26825, 90, 1234])).
% 10.99/11.20 tff(26827,plain,
% 10.99/11.20 (r(s(s(s(s(z)))), s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[749, 26826])).
% 10.99/11.20 tff(26828,plain,
% 10.99/11.20 (~b(s(z), elem!1)),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[23112, 26825, 22902, 721])).
% 10.99/11.20 tff(26829,plain,
% 10.99/11.20 (r(s(z), elem!1)),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[632, 26828, 21435])).
% 10.99/11.20 tff(26830,plain,
% 10.99/11.20 (b(elem!1, s(s(s(s(z)))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[9108, 26829, 1549, 26827, 21768])).
% 10.99/11.20 tff(26831,plain,
% 10.99/11.20 (~b(s(s(s(elem!1))), elem!1)),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[25386, 26830, 90, 22924, 22902])).
% 10.99/11.20 tff(26832,plain,
% 10.99/11.20 (r(s(s(s(elem!1))), elem!1)),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[230, 26831, 127])).
% 10.99/11.20 tff(26833,plain,
% 10.99/11.20 (~r(s(s(s(elem!1))), s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[23283, 26832, 26829, 3618])).
% 10.99/11.20 tff(26834,plain,
% 10.99/11.20 (b(s(s(s(elem!1))), s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[223, 26833])).
% 10.99/11.20 tff(26835,plain,
% 10.99/11.20 (~b(s(z), s(s(s(elem!1))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[15561, 26834, 22924, 26825])).
% 10.99/11.20 tff(26836,plain,
% 10.99/11.20 (r(s(z), s(s(s(elem!1))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[247, 26835])).
% 10.99/11.20 tff(26837,plain,
% 10.99/11.20 (b(elem!1, s(s(s(elem!1))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[5715, 26836, 127, 26829, 26831])).
% 10.99/11.20 tff(26838,plain,
% 10.99/11.20 (~b(s(s(s(s(z)))), s(s(z)))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[9010, 26837, 721, 26834, 1234])).
% 10.99/11.20 tff(26839,plain,
% 10.99/11.20 (r(s(s(s(s(z)))), s(s(z)))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[1714, 26838])).
% 10.99/11.20 tff(26840,plain,
% 10.99/11.20 (~r(s(s(z)), s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[2429, 26839, 26827, 26829])).
% 10.99/11.20 tff(26841,plain,
% 10.99/11.20 (b(s(s(z)), s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[3778, 26840])).
% 10.99/11.20 tff(26842,plain,
% 10.99/11.20 (~b(s(z), s(s(z)))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[23120, 26841, 22902, 721, 26825])).
% 10.99/11.20 tff(26843,plain,
% 10.99/11.20 (r(s(z), s(s(z)))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[1788, 26842])).
% 10.99/11.20 tff(26844,plain,
% 10.99/11.20 (~r(z, s(s(s(elem!1))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[1489, 26829, 182, 3618])).
% 10.99/11.20 tff(26845,plain,
% 10.99/11.20 (~b(z, s(s(s(s(z)))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[6914, 26825, 90, 22902, 1234])).
% 10.99/11.20 tff(26846,plain,
% 10.99/11.20 (r(z, s(s(s(s(z)))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[800, 26845])).
% 10.99/11.20 tff(26847,plain,
% 10.99/11.20 (~r(elem!1, s(z))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[17062, 26846, 182, 3618])).
% 10.99/11.20 tff(26848,plain,
% 10.99/11.20 (~r(s(s(z)), s(s(s(s(z)))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[9076, 26843, 26827, 26839])).
% 10.99/11.20 tff(26849,plain,
% 10.99/11.20 (b(s(s(z)), s(s(s(s(z)))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[3652, 26848])).
% 10.99/11.20 tff(26850,plain,
% 10.99/11.20 (~b(s(s(z)), z)),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[23843, 26849, 90, 80, 26832, 26836, 26847, 26844])).
% 10.99/11.20 tff(26851,plain,
% 10.99/11.20 (r(s(s(z)), z)),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[1211, 26850])).
% 10.99/11.20 tff(26852,plain,
% 10.99/11.20 (~r(z, s(s(elem!1)))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[3787, 26851, 182, 26843])).
% 10.99/11.20 tff(26853,plain,
% 10.99/11.20 (b(z, s(s(elem!1)))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[324, 26852])).
% 10.99/11.20 tff(26854,plain,
% 10.99/11.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.20 inference(rewrite,[status(thm)],[])).
% 10.99/11.20 tff(26855,plain,
% 10.99/11.20 (((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.20 inference(rewrite,[status(thm)],[])).
% 10.99/11.20 tff(26856,plain,
% 10.99/11.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 10.99/11.20 inference(monotonicity,[status(thm)],[26855])).
% 10.99/11.20 tff(26857,plain,
% 10.99/11.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.20 inference(transitivity,[status(thm)],[26856, 26854])).
% 10.99/11.20 tff(26858,plain,
% 10.99/11.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 10.99/11.20 inference(quant_inst,[status(thm)],[])).
% 10.99/11.20 tff(26859,plain,
% 10.99/11.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 10.99/11.20 inference(modus_ponens,[status(thm)],[26858, 26857])).
% 10.99/11.20 tff(26860,plain,
% 10.99/11.20 ($false),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[26859, 391, 133, 973, 448, 3927, 1526])).
% 10.99/11.20 tff(26861,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.20 tff(26862,plain,
% 10.99/11.20 (~b(s(s(elem!1)), elem!1)),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[26861, 26853, 22902, 26834, 26837])).
% 10.99/11.20 tff(26863,plain,
% 10.99/11.20 (r(s(s(s(s(z)))), elem!1)),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[762, 21778, 1549])).
% 10.99/11.20 tff(26864,plain,
% 10.99/11.20 (~r(elem!1, s(s(z)))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[9117, 26827, 26863, 26829])).
% 10.99/11.20 tff(26865,plain,
% 10.99/11.20 (~r(s(s(z)), s(s(s(elem!1))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[9138, 26843, 26839, 26827])).
% 10.99/11.20 tff(26866,plain,
% 10.99/11.20 (b(s(s(z)), s(s(s(elem!1))))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[11041, 26865])).
% 10.99/11.20 tff(26867,plain,
% 10.99/11.20 (~b(elem!1, s(s(z)))),
% 10.99/11.20 inference(unit_resolution,[status(thm)],[8561, 26866, 26834, 26837, 1234])).
% 10.99/11.21 tff(26868,plain,
% 10.99/11.21 (elem!1 = s(s(z))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[3394, 26867, 26864])).
% 10.99/11.21 tff(26869,plain,
% 10.99/11.21 (~b(s(s(elem!1)), s(z))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[9032, 26868, 26826])).
% 10.99/11.21 tff(26870,plain,
% 10.99/11.21 (r(s(s(elem!1)), s(z))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[362, 26869])).
% 10.99/11.21 tff(26871,plain,
% 10.99/11.21 (~(s(s(elem!1)) = elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[4206, 26870, 26847])).
% 10.99/11.21 tff(26872,plain,
% 10.99/11.21 (~b(s(s(s(elem!1))), z)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[4905, 26871, 3618, 26837, 26862, 26832, 22902])).
% 10.99/11.21 tff(26873,plain,
% 10.99/11.21 (b(s(elem!1), s(z))),
% 10.99/11.21 inference(modus_ponens,[status(thm)],[1526, 11405])).
% 10.99/11.21 tff(26874,plain,
% 10.99/11.21 (s(s(elem!1)) = elem!1),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[6159, 465])).
% 10.99/11.21 tff(26875,plain,
% 10.99/11.21 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[23479, 26874, 437, 168])).
% 10.99/11.21 tff(26876,plain,
% 10.99/11.21 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 10.99/11.21 inference(monotonicity,[status(thm)],[26874])).
% 10.99/11.21 tff(26877,plain,
% 10.99/11.21 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 10.99/11.21 inference(symmetry,[status(thm)],[26876])).
% 10.99/11.21 tff(26878,plain,
% 10.99/11.21 (r(s(s(elem!1)), z)),
% 10.99/11.21 inference(modus_ponens,[status(thm)],[530, 26877])).
% 10.99/11.21 tff(26879,plain,
% 10.99/11.21 (~r(s(z), s(s(elem!1)))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[4840, 26878, 26875, 232])).
% 10.99/11.21 tff(26880,plain,
% 10.99/11.21 (~r(s(z), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[4847, 26879, 26874])).
% 10.99/11.21 tff(26881,plain,
% 10.99/11.21 (b(s(z), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[632, 26880, 150])).
% 10.99/11.21 tff(26882,plain,
% 10.99/11.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 10.99/11.21 inference(rewrite,[status(thm)],[])).
% 10.99/11.21 tff(26883,plain,
% 10.99/11.21 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 10.99/11.21 inference(rewrite,[status(thm)],[])).
% 10.99/11.21 tff(26884,plain,
% 10.99/11.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))))),
% 10.99/11.21 inference(monotonicity,[status(thm)],[26883])).
% 10.99/11.21 tff(26885,plain,
% 10.99/11.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 10.99/11.21 inference(transitivity,[status(thm)],[26884, 26882])).
% 10.99/11.21 tff(26886,plain,
% 10.99/11.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 10.99/11.21 inference(quant_inst,[status(thm)],[])).
% 10.99/11.21 tff(26887,plain,
% 10.99/11.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 10.99/11.21 inference(modus_ponens,[status(thm)],[26886, 26885])).
% 10.99/11.21 tff(26888,plain,
% 10.99/11.21 ($false),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26887, 391, 133, 26881, 802, 664, 26873])).
% 10.99/11.21 tff(26889,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(z))) | (s(z) = elem!1) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~b(s(s(s(elem!1))), s(z))) | (elem!1 = s(elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.21 tff(26890,plain,
% 10.99/11.21 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26889, 802, 133, 664, 150, 15563, 530, 1526, 7437, 168])).
% 10.99/11.21 tff(26891,plain,
% 10.99/11.21 (~b(s(elem!1), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[24246, 802, 133, 592])).
% 10.99/11.21 tff(26892,plain,
% 10.99/11.21 (r(s(elem!1), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[2168, 26891, 164])).
% 10.99/11.21 tff(26893,plain,
% 10.99/11.21 (~r(s(s(s(elem!1))), s(elem!1))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26137, 194, 530, 26892, 233])).
% 10.99/11.21 tff(26894,plain,
% 10.99/11.21 (b(s(s(s(elem!1))), s(elem!1))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[588, 26890, 26893])).
% 10.99/11.21 tff(26895,plain,
% 10.99/11.21 (~b(s(s(elem!1)), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[7912, 26894, 448, 133, 3927])).
% 10.99/11.21 tff(26896,plain,
% 10.99/11.21 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[1356, 5680, 1350])).
% 10.99/11.21 tff(26897,plain,
% 10.99/11.21 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[12932, 26896, 10682, 3927])).
% 10.99/11.21 tff(26898,plain,
% 10.99/11.21 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[1370, 26897, 6452])).
% 10.99/11.21 tff(26899,plain,
% 10.99/11.21 ($false),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[4883, 194, 530, 233, 15174, 26898])).
% 10.99/11.21 tff(26900,plain,((s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.21 tff(26901,plain,
% 10.99/11.21 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26900, 26895, 233, 10682, 3927, 530, 26890])).
% 10.99/11.21 tff(26902,plain,
% 10.99/11.21 (~(s(s(elem!1)) = elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[451, 26890])).
% 10.99/11.21 tff(26903,plain,
% 10.99/11.21 (r(s(s(elem!1)), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[872, 26895, 26902])).
% 10.99/11.21 tff(26904,plain,
% 10.99/11.21 ($false),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[4878, 194, 530, 233, 26903, 26901])).
% 10.99/11.21 tff(26905,plain,((~b(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (s(z) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), elem!1) | (s(elem!1) = elem!1) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.21 tff(26906,plain,
% 10.99/11.21 (~b(elem!1, s(elem!1))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26905, 133, 233, 10682, 3927, 448, 530, 664, 150, 1526, 168, 164, 592])).
% 10.99/11.21 tff(26907,plain,
% 10.99/11.21 (r(elem!1, s(elem!1))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[443, 26906, 7437])).
% 10.99/11.21 tff(26908,plain,
% 10.99/11.21 (~b(s(s(elem!1)), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26861, 133, 448, 3927, 1526])).
% 10.99/11.21 tff(26909,plain,
% 10.99/11.21 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26900, 4017, 233, 10682, 3927, 530, 279])).
% 10.99/11.21 tff(26910,plain,
% 10.99/11.21 (r(s(s(elem!1)), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[872, 4017, 5625])).
% 10.99/11.21 tff(26911,plain,
% 10.99/11.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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))))))),
% 10.99/11.21 inference(rewrite,[status(thm)],[])).
% 10.99/11.21 tff(26912,plain,
% 10.99/11.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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))))))),
% 10.99/11.21 inference(quant_inst,[status(thm)],[])).
% 10.99/11.21 tff(26913,plain,
% 10.99/11.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 10.99/11.21 inference(modus_ponens,[status(thm)],[26912, 26911])).
% 10.99/11.21 tff(26914,plain,
% 10.99/11.21 ($false),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26913, 194, 233, 2251, 364, 1378])).
% 10.99/11.21 tff(26915,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.21 tff(26916,plain,
% 10.99/11.21 ($false),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26915, 26910, 26909, 233, 2251])).
% 10.99/11.21 tff(26917,plain,(b(s(s(elem!1)), elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.21 tff(26918,plain,
% 10.99/11.21 (s(s(s(elem!1))) = s(elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26917, 26908, 26907, 10682, 3927, 530, 233])).
% 10.99/11.21 tff(26919,plain,
% 10.99/11.21 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 10.99/11.21 inference(monotonicity,[status(thm)],[26918])).
% 10.99/11.21 tff(26920,plain,
% 10.99/11.21 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(elem!1))))),
% 10.99/11.21 inference(symmetry,[status(thm)],[26919])).
% 10.99/11.21 tff(26921,plain,
% 10.99/11.21 ((~b(elem!1, s(elem!1))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 10.99/11.21 inference(monotonicity,[status(thm)],[26920])).
% 10.99/11.21 tff(26922,plain,
% 10.99/11.21 (~b(elem!1, s(s(s(elem!1))))),
% 10.99/11.21 inference(modus_ponens,[status(thm)],[26906, 26921])).
% 10.99/11.21 tff(26923,plain,
% 10.99/11.21 ($false),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[448, 26922])).
% 10.99/11.21 tff(26924,plain,((~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (s(z) = elem!1) | b(s(s(s(elem!1))), elem!1) | (s(elem!1) = elem!1) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.21 tff(26925,plain,
% 10.99/11.21 (~b(z, s(elem!1))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26924, 26853, 22924, 22902, 26834, 26832, 3618, 26825, 21435, 26831, 4597, 26837])).
% 10.99/11.21 tff(26926,plain,
% 10.99/11.21 (r(z, s(elem!1))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[566, 26925])).
% 10.99/11.21 tff(26927,plain,
% 10.99/11.21 (~r(s(s(s(elem!1))), z)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[4255, 26926, 3618, 26832])).
% 10.99/11.21 tff(26928,plain,
% 10.99/11.21 ($false),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[377, 26927, 26872])).
% 10.99/11.21 tff(26929,plain,(b(elem!1, z) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | r(z, elem!1) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(s(z)))), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.21 tff(26930,plain,
% 10.99/11.21 (b(elem!1, z)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[26929, 9, 1234, 90, 80, 721, 182, 1549, 2])).
% 10.99/11.21 tff(26931,plain,
% 10.99/11.21 (~b(s(s(s(elem!1))), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[10743, 26930, 22924, 22902])).
% 10.99/11.21 tff(26932,plain,
% 10.99/11.21 (~b(elem!1, s(s(s(s(z)))))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[12445, 665, 90, 133])).
% 10.99/11.21 tff(26933,plain,
% 10.99/11.21 (r(s(z), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[632, 2829, 21435])).
% 10.99/11.21 tff(26934,plain,
% 10.99/11.21 (~r(s(s(s(s(z)))), s(z))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[9108, 26933, 1549, 26932, 8919])).
% 10.99/11.21 tff(26935,plain,
% 10.99/11.21 (b(s(s(s(s(z)))), s(z))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[749, 26934])).
% 10.99/11.21 tff(26936,plain,
% 10.99/11.21 (~b(z, s(z))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[22918, 26935, 90, 1234])).
% 10.99/11.21 tff(26937,plain,
% 10.99/11.21 (r(z, s(z))),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[678, 26936])).
% 10.99/11.21 tff(26938,plain,
% 10.99/11.21 (~r(s(s(s(elem!1))), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[23411, 1484, 183, 410])).
% 10.99/11.21 tff(26939,plain,
% 10.99/11.21 (b(s(s(s(elem!1))), elem!1)),
% 10.99/11.21 inference(unit_resolution,[status(thm)],[230, 26938, 127])).
% 10.99/11.21 tff(26940,plain,
% 10.99/11.22 (~b(s(z), s(s(s(elem!1))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[23276, 26939, 721, 10682, 133])).
% 10.99/11.22 tff(26941,plain,
% 10.99/11.22 (r(s(z), s(s(s(elem!1))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[247, 26940])).
% 10.99/11.22 tff(26942,plain,
% 10.99/11.22 ($false),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[17163, 194, 410, 1484, 26941, 183])).
% 10.99/11.22 tff(26943,plain,((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.22 tff(26944,plain,
% 10.99/11.22 (~r(elem!1, s(s(s(elem!1))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[26943, 26933, 133, 721, 10682, 183, 9])).
% 10.99/11.22 tff(26945,plain,
% 10.99/11.22 (b(elem!1, s(s(s(elem!1))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[424, 26944, 1])).
% 10.99/11.22 tff(26946,plain,
% 10.99/11.22 (~b(s(s(s(elem!1))), z)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[10876, 26945, 133, 665])).
% 10.99/11.22 tff(26947,plain,
% 10.99/11.22 (r(s(s(s(elem!1))), z)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[377, 26946])).
% 10.99/11.22 tff(26948,plain,
% 10.99/11.22 ($false),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[17465, 26947, 26937, 26933, 183])).
% 10.99/11.22 tff(26949,plain,(b(s(z), elem!1) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.22 tff(26950,plain,
% 10.99/11.22 (b(s(z), elem!1)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[26949, 183, 133, 665, 90, 1234, 1, 721, 22924, 1549])).
% 10.99/11.22 tff(26951,plain,
% 10.99/11.22 (~b(z, s(z))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[23112, 26950, 133, 721])).
% 10.99/11.22 tff(26952,plain,
% 10.99/11.22 (r(z, s(z))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[678, 26951])).
% 10.99/11.22 tff(26953,plain,
% 10.99/11.22 (~r(s(s(s(elem!1))), z)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[26128, 194, 183, 26952, 182])).
% 10.99/11.22 tff(26954,plain,
% 10.99/11.22 (b(s(s(s(elem!1))), z)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[377, 26953])).
% 10.99/11.22 tff(26955,plain,
% 10.99/11.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.99/11.22 inference(rewrite,[status(thm)],[])).
% 10.99/11.22 tff(26956,plain,
% 10.99/11.22 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.99/11.22 inference(rewrite,[status(thm)],[])).
% 10.99/11.22 tff(26957,plain,
% 10.99/11.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 10.99/11.22 inference(monotonicity,[status(thm)],[26956])).
% 10.99/11.22 tff(26958,plain,
% 10.99/11.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.99/11.22 inference(transitivity,[status(thm)],[26957, 26955])).
% 10.99/11.22 tff(26959,plain,
% 10.99/11.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 10.99/11.22 inference(quant_inst,[status(thm)],[])).
% 10.99/11.22 tff(26960,plain,
% 10.99/11.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 10.99/11.22 inference(modus_ponens,[status(thm)],[26959, 26958])).
% 10.99/11.22 tff(26961,plain,
% 10.99/11.22 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[26960, 391, 133, 665, 26954, 90])).
% 10.99/11.22 tff(26962,plain,
% 10.99/11.22 (~b(elem!1, s(s(s(elem!1))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[10876, 26954, 133, 665])).
% 10.99/11.22 tff(26963,plain,
% 10.99/11.22 (r(elem!1, s(s(s(elem!1))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[424, 26962, 1])).
% 10.99/11.22 tff(26964,plain,
% 10.99/11.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.22 inference(rewrite,[status(thm)],[])).
% 10.99/11.22 tff(26965,plain,
% 10.99/11.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.22 inference(quant_inst,[status(thm)],[])).
% 10.99/11.22 tff(26966,plain,
% 10.99/11.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.99/11.22 inference(modus_ponens,[status(thm)],[26965, 26964])).
% 10.99/11.22 tff(26967,plain,
% 10.99/11.22 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[26966, 391, 133, 665, 26954, 90])).
% 10.99/11.22 tff(26968,plain,
% 10.99/11.22 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[2853, 42, 21769, 26967])).
% 10.99/11.22 tff(26969,plain,
% 10.99/11.22 (~r(elem!1, s(s(s(s(z)))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[25443, 26968, 26963, 26961, 21770])).
% 10.99/11.22 tff(26970,plain,
% 10.99/11.22 (elem!1 = s(s(s(s(z))))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[781, 26969, 26932])).
% 10.99/11.22 tff(26971,plain,
% 10.99/11.22 (s(elem!1) = s(s(s(s(s(z)))))),
% 10.99/11.22 inference(monotonicity,[status(thm)],[26970])).
% 10.99/11.22 tff(26972,plain,
% 10.99/11.22 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 10.99/11.22 inference(monotonicity,[status(thm)],[26971])).
% 10.99/11.22 tff(26973,plain,
% 10.99/11.22 (~b(s(s(s(elem!1))), elem!1)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[10743, 665, 22924, 133])).
% 10.99/11.22 tff(26974,plain,
% 10.99/11.22 (~b(s(s(elem!1)), elem!1)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[12771, 26950, 133, 665])).
% 10.99/11.22 tff(26975,plain,
% 10.99/11.22 (s(s(s(s(z)))) = elem!1),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[769, 26970])).
% 10.99/11.22 tff(26976,plain,
% 10.99/11.22 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[717, 26975])).
% 10.99/11.22 tff(26977,plain,
% 10.99/11.22 (~(s(s(elem!1)) = elem!1)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[451, 26976])).
% 10.99/11.22 tff(26978,plain,
% 10.99/11.22 (r(s(s(elem!1)), elem!1)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[872, 26977, 26974])).
% 10.99/11.22 tff(26979,plain,
% 10.99/11.22 (~b(z, s(s(elem!1)))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[15730, 26976, 22924, 26963, 26962, 26973, 9, 26974])).
% 10.99/11.22 tff(26980,plain,
% 10.99/11.22 (r(z, s(s(elem!1)))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[324, 26979])).
% 10.99/11.22 tff(26981,plain,
% 10.99/11.22 (~(elem!1 = s(s(elem!1)))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[1292, 26977])).
% 10.99/11.22 tff(26982,plain,
% 10.99/11.22 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[8251, 9])).
% 10.99/11.22 tff(26983,plain,
% 10.99/11.22 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[4039, 26978, 9, 26962, 26973])).
% 10.99/11.22 tff(26984,plain,
% 10.99/11.22 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[1370, 26983, 26982])).
% 10.99/11.22 tff(26985,plain,
% 10.99/11.22 (~b(s(s(elem!1)), z)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[13177, 26984, 22924, 26954])).
% 10.99/11.22 tff(26986,plain,
% 10.99/11.22 (r(s(s(elem!1)), z)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[2629, 26985])).
% 10.99/11.22 tff(26987,plain,
% 10.99/11.22 (~r(s(s(elem!1)), s(z))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[4103, 26986, 182, 26952])).
% 10.99/11.22 tff(26988,plain,
% 10.99/11.22 (b(s(s(elem!1)), s(z))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[362, 26987])).
% 10.99/11.22 tff(26989,plain,
% 10.99/11.22 (~b(elem!1, s(s(elem!1)))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[1302, 26988, 721, 26950])).
% 10.99/11.22 tff(26990,plain,
% 10.99/11.22 (r(elem!1, s(s(elem!1)))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[1307, 26989, 26981])).
% 10.99/11.22 tff(26991,plain,
% 10.99/11.22 (~r(elem!1, z)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[2231, 26990, 26980, 26978])).
% 10.99/11.22 tff(26992,plain,
% 10.99/11.22 (b(s(elem!1), elem!1)),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[14657, 26991, 133, 22924, 26973, 21435, 2])).
% 10.99/11.22 tff(26993,plain,
% 10.99/11.22 (~b(z, s(elem!1))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[6555, 26992, 133, 665])).
% 10.99/11.22 tff(26994,plain,
% 10.99/11.22 (r(z, s(elem!1))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[566, 26993])).
% 10.99/11.22 tff(26995,plain,
% 10.99/11.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 10.99/11.22 inference(rewrite,[status(thm)],[])).
% 10.99/11.22 tff(26996,plain,
% 10.99/11.22 (((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 10.99/11.22 inference(rewrite,[status(thm)],[])).
% 10.99/11.22 tff(26997,plain,
% 10.99/11.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 10.99/11.22 inference(monotonicity,[status(thm)],[26996])).
% 10.99/11.22 tff(26998,plain,
% 10.99/11.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 10.99/11.22 inference(transitivity,[status(thm)],[26997, 26995])).
% 10.99/11.22 tff(26999,plain,
% 10.99/11.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 10.99/11.22 inference(quant_inst,[status(thm)],[])).
% 10.99/11.22 tff(27000,plain,
% 10.99/11.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 10.99/11.22 inference(modus_ponens,[status(thm)],[26999, 26998])).
% 10.99/11.22 tff(27001,plain,
% 10.99/11.22 ($false),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[27000, 194, 2144, 722, 182, 13481])).
% 10.99/11.22 tff(27002,plain,((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.22 tff(27003,plain,
% 10.99/11.22 (~r(s(elem!1), s(z))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[27002, 26994, 182, 26952])).
% 10.99/11.22 tff(27004,plain,
% 10.99/11.22 (b(s(elem!1), s(z))),
% 10.99/11.22 inference(unit_resolution,[status(thm)],[13479, 27003, 124])).
% 10.99/11.22 tff(27005,plain,
% 10.99/11.22 (b(s(s(s(s(s(z))))), s(z))),
% 10.99/11.22 inference(modus_ponens,[status(thm)],[27004, 26972])).
% 10.99/11.23 tff(27006,plain,
% 10.99/11.23 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 10.99/11.23 inference(monotonicity,[status(thm)],[26971])).
% 10.99/11.23 tff(27007,plain,
% 10.99/11.23 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 10.99/11.23 inference(monotonicity,[status(thm)],[26970])).
% 10.99/11.23 tff(27008,plain,
% 10.99/11.23 (b(s(elem!1), s(s(s(s(z)))))),
% 10.99/11.23 inference(modus_ponens,[status(thm)],[26992, 27007])).
% 10.99/11.23 tff(27009,plain,
% 10.99/11.23 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 10.99/11.23 inference(modus_ponens,[status(thm)],[27008, 27006])).
% 10.99/11.23 tff(27010,plain,
% 10.99/11.23 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 10.99/11.23 inference(monotonicity,[status(thm)],[26970])).
% 10.99/11.23 tff(27011,plain,
% 10.99/11.23 (b(z, s(s(s(s(z)))))),
% 10.99/11.23 inference(modus_ponens,[status(thm)],[133, 27010])).
% 10.99/11.23 tff(27012,plain,
% 10.99/11.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 10.99/11.23 inference(rewrite,[status(thm)],[])).
% 10.99/11.23 tff(27013,plain,
% 10.99/11.23 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 10.99/11.23 inference(rewrite,[status(thm)],[])).
% 10.99/11.23 tff(27014,plain,
% 10.99/11.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 10.99/11.23 inference(monotonicity,[status(thm)],[27013])).
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% 10.99/11.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 10.99/11.23 inference(transitivity,[status(thm)],[27014, 27012])).
% 10.99/11.23 tff(27016,plain,
% 10.99/11.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 10.99/11.23 inference(quant_inst,[status(thm)],[])).
% 10.99/11.23 tff(27017,plain,
% 10.99/11.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 10.99/11.23 inference(modus_ponens,[status(thm)],[27016, 27015])).
% 10.99/11.23 tff(27018,plain,
% 10.99/11.23 ($false),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[27017, 391, 90, 1234, 27011, 27009, 27005])).
% 10.99/11.23 tff(27019,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~r(s(z), z)) | (~b(elem!1, z)) | (elem!1 = z) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(elem!1)))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.23 tff(27020,plain,
% 10.99/11.23 (~r(s(s(s(elem!1))), s(z))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[27019, 26930, 1234, 22902, 182, 90, 2, 721, 1, 1549])).
% 10.99/11.23 tff(27021,plain,
% 10.99/11.23 (b(s(s(s(elem!1))), s(z))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[223, 27020])).
% 10.99/11.23 tff(27022,plain,
% 10.99/11.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.99/11.23 inference(rewrite,[status(thm)],[])).
% 10.99/11.23 tff(27023,plain,
% 10.99/11.23 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.99/11.23 inference(rewrite,[status(thm)],[])).
% 10.99/11.23 tff(27024,plain,
% 10.99/11.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 10.99/11.23 inference(monotonicity,[status(thm)],[27023])).
% 10.99/11.23 tff(27025,plain,
% 10.99/11.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 10.99/11.23 inference(transitivity,[status(thm)],[27024, 27022])).
% 10.99/11.23 tff(27026,plain,
% 10.99/11.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 10.99/11.23 inference(quant_inst,[status(thm)],[])).
% 10.99/11.23 tff(27027,plain,
% 10.99/11.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 10.99/11.23 inference(modus_ponens,[status(thm)],[27026, 27025])).
% 10.99/11.23 tff(27028,plain,
% 10.99/11.23 (~b(elem!1, s(s(s(elem!1))))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[27027, 391, 27021, 90, 1234, 721])).
% 10.99/11.23 tff(27029,plain,
% 10.99/11.23 (r(elem!1, s(s(s(elem!1))))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[424, 27028, 1])).
% 10.99/11.23 tff(27030,plain,
% 10.99/11.23 (~b(z, s(z))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[15581, 27029, 22924, 27028, 26931, 27021, 9])).
% 10.99/11.23 tff(27031,plain,
% 10.99/11.23 (r(z, s(z))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[678, 27030])).
% 10.99/11.23 tff(27032,plain,
% 10.99/11.23 (~r(elem!1, z)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[25179, 1484, 182, 722])).
% 10.99/11.23 tff(27033,plain,
% 10.99/11.23 (b(s(elem!1), elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[14657, 27032, 133, 10682, 26492, 150, 2])).
% 10.99/11.23 tff(27034,plain,
% 10.99/11.23 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[14662, 27033, 26492])).
% 10.99/11.23 tff(27035,plain,
% 10.99/11.23 (~(s(s(elem!1)) = s(elem!1))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[2279, 27034])).
% 10.99/11.23 tff(27036,plain,
% 10.99/11.23 (~r(s(s(elem!1)), elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[12954, 1484, 10682, 1, 4028, 182, 26492, 26982])).
% 10.99/11.23 tff(27037,plain,
% 10.99/11.23 (~(s(s(elem!1)) = elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[451, 27034])).
% 10.99/11.23 tff(27038,plain,
% 10.99/11.23 (b(s(s(elem!1)), elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[872, 27037, 27036])).
% 10.99/11.23 tff(27039,plain,
% 10.99/11.23 ($false),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[5286, 27038, 27035, 133, 665, 27033])).
% 10.99/11.23 tff(27040,plain,((~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1) | (elem!1 = z) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.23 tff(27041,plain,
% 10.99/11.23 (~r(s(z), elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[27040, 26930, 22902, 22924, 21435, 2, 1, 27028, 182, 27031])).
% 10.99/11.23 tff(27042,plain,
% 10.99/11.23 (b(s(z), elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[632, 27041, 21435])).
% 10.99/11.23 tff(27043,plain,
% 10.99/11.23 (r(s(s(s(elem!1))), elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[230, 26931, 9])).
% 10.99/11.23 tff(27044,plain,
% 10.99/11.23 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[314, 26982])).
% 10.99/11.23 tff(27045,plain,
% 10.99/11.23 (r(s(s(s(elem!1))), elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[230, 26492, 9])).
% 10.99/11.23 tff(27046,plain,
% 10.99/11.23 (~b(elem!1, s(s(s(elem!1))))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[27027, 391, 1526, 90, 1234, 721])).
% 10.99/11.23 tff(27047,plain,
% 10.99/11.23 (r(elem!1, s(s(s(elem!1))))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[424, 27046, 1])).
% 10.99/11.23 tff(27048,plain,
% 10.99/11.23 (b(s(z), elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[632, 1492, 21435])).
% 10.99/11.23 tff(27049,plain,
% 10.99/11.23 (~b(s(s(elem!1)), elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[12771, 27048, 133, 665])).
% 10.99/11.23 tff(27050,plain,
% 10.99/11.23 (r(s(s(elem!1)), elem!1)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[872, 5625, 27049])).
% 10.99/11.23 tff(27051,plain,
% 10.99/11.23 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[5875, 27050, 27047, 27045])).
% 10.99/11.23 tff(27052,plain,
% 10.99/11.23 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[1356, 27051, 27044])).
% 10.99/11.23 tff(27053,plain,
% 10.99/11.23 (~b(z, s(s(elem!1)))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[15730, 279, 10682, 27047, 27046, 26492, 9, 27049])).
% 10.99/11.23 tff(27054,plain,
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% 10.99/11.23 tff(27056,plain,
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% 10.99/11.23 tff(27057,plain,
% 10.99/11.23 (~b(s(z), s(s(s(elem!1))))),
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% 10.99/11.23 tff(27058,plain,
% 10.99/11.23 (r(s(z), s(s(s(elem!1))))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[247, 27057])).
% 10.99/11.23 tff(27059,plain,
% 10.99/11.23 (~r(s(s(s(elem!1))), z)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[12936, 27050, 10682, 133, 27048, 26492, 1, 26982, 665])).
% 10.99/11.23 tff(27060,plain,
% 10.99/11.23 (b(s(s(s(elem!1))), z)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[377, 27059])).
% 10.99/11.23 tff(27061,plain,
% 10.99/11.23 (~b(z, s(z))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[15581, 27047, 10682, 27046, 26492, 1526, 9])).
% 10.99/11.23 tff(27062,plain,
% 10.99/11.23 (r(z, s(z))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[678, 27061])).
% 10.99/11.23 tff(27063,plain,
% 10.99/11.23 (~b(s(s(elem!1)), z)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[13177, 27056, 10682, 27060])).
% 10.99/11.23 tff(27064,plain,
% 10.99/11.23 (r(s(s(elem!1)), z)),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[2629, 27063])).
% 10.99/11.23 tff(27065,plain,
% 10.99/11.23 (~r(s(s(elem!1)), s(z))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[4103, 27064, 182, 27062])).
% 10.99/11.23 tff(27066,plain,
% 10.99/11.23 (b(s(s(elem!1)), s(z))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[362, 27065])).
% 10.99/11.23 tff(27067,plain,
% 10.99/11.23 (~b(s(s(s(s(z)))), s(z))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[3263, 27066, 1234, 1526, 27056])).
% 10.99/11.23 tff(27068,plain,
% 10.99/11.23 (r(s(s(s(s(z)))), s(z))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[749, 27067])).
% 10.99/11.23 tff(27069,plain,
% 10.99/11.23 (~r(z, s(s(s(s(z)))))),
% 10.99/11.23 inference(unit_resolution,[status(thm)],[731, 27068, 182, 27062])).
% 10.99/11.24 tff(27070,plain,
% 10.99/11.24 (b(z, s(s(s(s(z)))))),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[800, 27069])).
% 10.99/11.24 tff(27071,plain,
% 10.99/11.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.24 inference(rewrite,[status(thm)],[])).
% 10.99/11.24 tff(27072,plain,
% 10.99/11.24 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.24 inference(rewrite,[status(thm)],[])).
% 10.99/11.24 tff(27073,plain,
% 10.99/11.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 10.99/11.24 inference(monotonicity,[status(thm)],[27072])).
% 10.99/11.24 tff(27074,plain,
% 10.99/11.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.24 inference(transitivity,[status(thm)],[27073, 27071])).
% 10.99/11.24 tff(27075,plain,
% 10.99/11.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))),
% 10.99/11.24 inference(quant_inst,[status(thm)],[])).
% 10.99/11.24 tff(27076,plain,
% 10.99/11.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.99/11.24 inference(modus_ponens,[status(thm)],[27075, 27074])).
% 10.99/11.24 tff(27077,plain,
% 10.99/11.24 ($false),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[27076, 391, 380, 10682, 1686, 3325])).
% 10.99/11.24 tff(27078,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.24 tff(27079,plain,
% 10.99/11.24 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[27078, 27070, 10682, 27060])).
% 10.99/11.24 tff(27080,plain,
% 10.99/11.24 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[20877, 27070, 90, 182, 1234, 27054])).
% 10.99/11.24 tff(27081,plain,
% 10.99/11.24 (r(s(s(z)), s(s(s(s(z)))))),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[3652, 27080])).
% 10.99/11.24 tff(27082,plain,
% 10.99/11.24 (~r(s(s(z)), s(z))),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[20881, 27081, 182, 27068])).
% 10.99/11.24 tff(27083,plain,
% 10.99/11.24 (b(s(s(z)), s(z))),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[3778, 27082])).
% 10.99/11.24 tff(27084,plain,
% 10.99/11.24 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[2853, 42, 2863])).
% 10.99/11.24 tff(27085,plain,
% 10.99/11.24 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[27084, 3363])).
% 10.99/11.24 tff(27086,plain,
% 10.99/11.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.24 inference(rewrite,[status(thm)],[])).
% 10.99/11.24 tff(27087,plain,
% 10.99/11.24 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.24 inference(rewrite,[status(thm)],[])).
% 10.99/11.24 tff(27088,plain,
% 10.99/11.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 10.99/11.24 inference(monotonicity,[status(thm)],[27087])).
% 10.99/11.24 tff(27089,plain,
% 10.99/11.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.24 inference(transitivity,[status(thm)],[27088, 27086])).
% 10.99/11.24 tff(27090,plain,
% 10.99/11.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))),
% 10.99/11.24 inference(quant_inst,[status(thm)],[])).
% 10.99/11.24 tff(27091,plain,
% 10.99/11.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.99/11.24 inference(modus_ponens,[status(thm)],[27090, 27089])).
% 10.99/11.24 tff(27092,plain,
% 10.99/11.24 (~r(s(s(s(s(z)))), s(z))),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[27091, 194, 233, 232, 27085])).
% 10.99/11.24 tff(27093,plain,
% 10.99/11.24 (b(s(s(s(s(z)))), s(z))),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[749, 27092])).
% 10.99/11.24 tff(27094,plain,
% 10.99/11.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.24 inference(rewrite,[status(thm)],[])).
% 10.99/11.24 tff(27095,plain,
% 10.99/11.24 (((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.24 inference(rewrite,[status(thm)],[])).
% 10.99/11.24 tff(27096,plain,
% 10.99/11.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 10.99/11.24 inference(monotonicity,[status(thm)],[27095])).
% 10.99/11.24 tff(27097,plain,
% 10.99/11.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.24 inference(transitivity,[status(thm)],[27096, 27094])).
% 10.99/11.24 tff(27098,plain,
% 10.99/11.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 10.99/11.24 inference(quant_inst,[status(thm)],[])).
% 10.99/11.24 tff(27099,plain,
% 10.99/11.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.99/11.24 inference(modus_ponens,[status(thm)],[27098, 27097])).
% 10.99/11.24 tff(27100,plain,
% 10.99/11.24 (~r(s(s(s(s(z)))), elem!1)),
% 10.99/11.24 inference(unit_resolution,[status(thm)],[27099, 194, 233, 410, 27085])).
% 10.99/11.24 tff(27101,plain,
% 10.99/11.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.24 inference(rewrite,[status(thm)],[])).
% 10.99/11.24 tff(27102,plain,
% 10.99/11.24 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.25 inference(rewrite,[status(thm)],[])).
% 10.99/11.25 tff(27103,plain,
% 10.99/11.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 10.99/11.25 inference(monotonicity,[status(thm)],[27102])).
% 10.99/11.25 tff(27104,plain,
% 10.99/11.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.25 inference(transitivity,[status(thm)],[27103, 27101])).
% 10.99/11.25 tff(27105,plain,
% 10.99/11.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 10.99/11.25 inference(quant_inst,[status(thm)],[])).
% 10.99/11.25 tff(27106,plain,
% 10.99/11.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.99/11.25 inference(modus_ponens,[status(thm)],[27105, 27104])).
% 10.99/11.25 tff(27107,plain,
% 10.99/11.25 (~r(s(z), s(s(s(s(z)))))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[27106, 194, 233, 232, 27085])).
% 10.99/11.25 tff(27108,plain,
% 10.99/11.25 (b(s(z), s(s(s(s(z)))))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[1230, 27107])).
% 10.99/11.25 tff(27109,plain,
% 10.99/11.25 (~b(s(s(z)), s(s(s(s(z)))))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[5108, 27093, 27108, 1233])).
% 10.99/11.25 tff(27110,plain,
% 10.99/11.25 (r(s(s(z)), s(s(s(s(z)))))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[3652, 27109])).
% 10.99/11.25 tff(27111,plain,
% 10.99/11.25 (~(s(s(s(s(z)))) = elem!1)),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[5152, 27110, 5149])).
% 10.99/11.25 tff(27112,plain,
% 10.99/11.25 (b(s(s(s(s(z)))), elem!1)),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[762, 27111, 27100])).
% 10.99/11.25 tff(27113,plain,
% 10.99/11.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.25 inference(rewrite,[status(thm)],[])).
% 10.99/11.25 tff(27114,plain,
% 10.99/11.25 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.25 inference(rewrite,[status(thm)],[])).
% 10.99/11.25 tff(27115,plain,
% 10.99/11.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 10.99/11.25 inference(monotonicity,[status(thm)],[27114])).
% 10.99/11.25 tff(27116,plain,
% 10.99/11.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 10.99/11.25 inference(transitivity,[status(thm)],[27115, 27113])).
% 10.99/11.25 tff(27117,plain,
% 10.99/11.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 10.99/11.25 inference(quant_inst,[status(thm)],[])).
% 10.99/11.25 tff(27118,plain,
% 10.99/11.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 10.99/11.25 inference(modus_ponens,[status(thm)],[27117, 27116])).
% 10.99/11.25 tff(27119,plain,
% 10.99/11.25 (~r(elem!1, s(s(s(s(z)))))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[27118, 194, 233, 410, 27085])).
% 10.99/11.25 tff(27120,plain,
% 10.99/11.25 (~(elem!1 = s(s(s(s(z)))))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[769, 27111])).
% 10.99/11.25 tff(27121,plain,
% 10.99/11.25 (b(elem!1, s(s(s(s(z)))))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[781, 27120, 27119])).
% 10.99/11.25 tff(27122,plain,
% 10.99/11.25 (b(s(z), elem!1)),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[632, 150, 1492])).
% 10.99/11.25 tff(27123,plain,
% 10.99/11.25 ($false),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[14958, 391, 27122, 90, 27121, 27112, 27093])).
% 10.99/11.25 tff(27124,plain,((s(z) = elem!1) | (~b(s(s(s(s(z)))), z)) | r(s(s(z)), elem!1) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.25 tff(27125,plain,
% 10.99/11.25 (r(s(s(z)), elem!1)),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[27124, 27083, 21435, 27045, 1492, 27079, 27047, 27058, 90])).
% 10.99/11.25 tff(27126,plain,
% 10.99/11.25 (~(elem!1 = s(s(s(s(z)))))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[13738, 27067, 721])).
% 10.99/11.25 tff(27127,plain,
% 10.99/11.25 (r(elem!1, s(s(s(s(z)))))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[781, 27126, 26932])).
% 10.99/11.25 tff(27128,plain,
% 10.99/11.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 10.99/11.25 inference(rewrite,[status(thm)],[])).
% 10.99/11.25 tff(27129,plain,
% 10.99/11.25 (((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 10.99/11.25 inference(rewrite,[status(thm)],[])).
% 10.99/11.25 tff(27130,plain,
% 10.99/11.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))))),
% 10.99/11.25 inference(monotonicity,[status(thm)],[27129])).
% 10.99/11.25 tff(27131,plain,
% 10.99/11.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 10.99/11.25 inference(transitivity,[status(thm)],[27130, 27128])).
% 10.99/11.25 tff(27132,plain,
% 10.99/11.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 10.99/11.25 inference(quant_inst,[status(thm)],[])).
% 10.99/11.25 tff(27133,plain,
% 10.99/11.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))),
% 10.99/11.25 inference(modus_ponens,[status(thm)],[27132, 27131])).
% 10.99/11.25 tff(27134,plain,
% 10.99/11.25 ($false),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[27133, 194, 27081, 27127, 27068, 27125])).
% 10.99/11.25 tff(27135,plain,((s(s(s(elem!1))) = s(elem!1)) | r(s(z), elem!1) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.25 tff(27136,plain,
% 10.99/11.25 (s(s(s(elem!1))) = s(elem!1)),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[27135, 27041, 90, 182, 22924, 1234, 721, 27021, 22902, 1, 26930])).
% 10.99/11.25 tff(27137,plain,
% 10.99/11.25 (r(s(elem!1), elem!1)),
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% 10.99/11.25 tff(27138,plain,
% 10.99/11.25 (~b(s(elem!1), elem!1)),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[14662, 27136, 26931])).
% 10.99/11.25 tff(27139,plain,
% 10.99/11.25 (r(s(elem!1), z)),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[13110, 27138, 22902, 21435, 26931, 26930, 22924, 118])).
% 10.99/11.25 tff(27140,plain,
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% 10.99/11.25 inference(unit_resolution,[status(thm)],[13276, 27139, 27137, 22902, 27042, 26930, 22924, 26931, 427, 21769, 118])).
% 10.99/11.25 tff(27141,plain,((elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (elem!1 = z) | b(s(s(s(s(z)))), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.25 tff(27142,plain,
% 10.99/11.25 (elem!1 = s(s(s(elem!1)))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[27141, 1234, 182, 90, 721, 2, 1549, 80])).
% 10.99/11.25 tff(27143,plain,
% 10.99/11.25 (s(s(s(elem!1))) = elem!1),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[129, 27142])).
% 10.99/11.25 tff(27144,plain,
% 10.99/11.25 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[11384, 27143])).
% 10.99/11.25 tff(27145,plain,
% 10.99/11.25 (~b(s(s(s(s(z)))), s(z))),
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% 10.99/11.25 tff(27146,plain,
% 10.99/11.25 (r(s(s(s(s(z)))), s(z))),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[749, 27145])).
% 10.99/11.25 tff(27147,plain,
% 10.99/11.25 (~b(s(z), elem!1)),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[23112, 664, 133, 721])).
% 10.99/11.25 tff(27148,plain,
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% 10.99/11.25 inference(unit_resolution,[status(thm)],[632, 27147, 21435])).
% 10.99/11.25 tff(27149,plain,
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% 10.99/11.25 inference(unit_resolution,[status(thm)],[9108, 27148, 1549, 27146, 3810])).
% 10.99/11.25 tff(27150,plain,
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% 10.99/11.25 tff(27151,plain,
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% 10.99/11.25 tff(27152,plain,
% 10.99/11.25 (~r(s(s(z)), s(s(s(s(z)))))),
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% 10.99/11.25 tff(27153,plain,
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% 10.99/11.25 tff(27158,plain,
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% 10.99/11.25 tff(27159,plain,
% 10.99/11.25 ($false),
% 10.99/11.25 inference(unit_resolution,[status(thm)],[5136, 27158, 27153, 90, 133, 721])).
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% 10.99/11.25 ((~r(s(s(s(s(s(elem!1))))), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
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% 10.99/11.26 inference(modus_ponens,[status(thm)],[27178, 27177])).
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% 10.99/11.26 inference(modus_ponens,[status(thm)],[27182, 18695])).
% 10.99/11.26 tff(27184,plain,
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% 10.99/11.26 tff(27201,plain,
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% 10.99/11.26 tff(27210,plain,
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% 10.99/11.26 inference(unit_resolution,[status(thm)],[27209, 1549, 182, 2, 88, 80, 721])).
% 10.99/11.26 tff(27211,plain,
% 10.99/11.26 (~(elem!1 = s(z))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[172, 21435])).
% 10.99/11.26 tff(27212,plain,
% 10.99/11.26 (~r(s(z), elem!1)),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[6077, 26863, 2913, 3618])).
% 10.99/11.26 tff(27213,plain,
% 10.99/11.26 (b(s(z), elem!1)),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[632, 27212, 21435])).
% 10.99/11.26 tff(27214,plain,
% 10.99/11.26 (~b(z, s(z))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[23112, 27213, 133, 721])).
% 10.99/11.26 tff(27215,plain,
% 10.99/11.26 (r(z, s(z))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[678, 27214])).
% 10.99/11.26 tff(27216,plain,
% 10.99/11.26 (~r(z, s(s(s(s(z)))))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[2720, 26863, 182, 2913])).
% 10.99/11.26 tff(27217,plain,
% 10.99/11.26 (b(z, s(s(s(s(z)))))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[800, 27216])).
% 10.99/11.26 tff(27218,plain,
% 10.99/11.26 (~b(elem!1, s(s(s(s(z)))))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[22981, 27217, 90, 133])).
% 10.99/11.26 tff(27219,plain,
% 10.99/11.26 (~r(elem!1, s(z))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[24995, 27218, 2913, 1549, 21778])).
% 10.99/11.26 tff(27220,plain,
% 10.99/11.26 (~b(s(s(s(elem!1))), elem!1)),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[26749, 27219, 133, 27213, 27215, 27212, 27211])).
% 10.99/11.26 tff(27221,plain,
% 10.99/11.26 (r(s(s(s(elem!1))), elem!1)),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[230, 27220, 9])).
% 10.99/11.26 tff(27222,plain,
% 10.99/11.26 (~r(s(s(s(elem!1))), z)),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[4113, 27221, 3618, 27215])).
% 10.99/11.26 tff(27223,plain,
% 10.99/11.26 (b(s(s(s(elem!1))), z)),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[377, 27222])).
% 10.99/11.26 tff(27224,plain,
% 10.99/11.26 (~r(s(s(s(elem!1))), s(z))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[23013, 27223, 90, 22924, 2913, 21769])).
% 10.99/11.26 tff(27225,plain,
% 10.99/11.26 (b(s(s(s(elem!1))), s(z))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[223, 27224])).
% 10.99/11.26 tff(27226,plain,
% 10.99/11.26 (~r(s(z), s(s(s(elem!1))))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[12394, 27223, 90, 182, 2913, 21769, 26863])).
% 10.99/11.26 tff(27227,plain,
% 10.99/11.26 (b(s(z), s(s(s(elem!1))))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[247, 27226])).
% 10.99/11.26 tff(27228,plain,
% 10.99/11.26 (~b(elem!1, s(s(s(elem!1))))),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[4026, 27227, 27213, 27225])).
% 10.99/11.26 tff(27229,plain,
% 10.99/11.26 ($false),
% 10.99/11.26 inference(unit_resolution,[status(thm)],[25377, 27228, 27225, 90, 22924, 2881, 1, 27220])).
% 10.99/11.26 tff(27230,plain,(b(elem!1, z) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), z)) | (~b(z, elem!1)) | b(s(s(s(s(z)))), elem!1) | (~b(elem!1, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.27 tff(27231,plain,
% 10.99/11.27 (b(elem!1, z)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[27230, 1, 2881, 88, 182, 133, 1549, 721, 2])).
% 10.99/11.27 tff(27232,plain,
% 10.99/11.27 (~b(s(s(s(elem!1))), elem!1)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[10743, 27231, 22898, 133])).
% 10.99/11.27 tff(27233,plain,
% 10.99/11.27 (~b(elem!1, s(s(s(s(z)))))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[12445, 27231, 88, 133])).
% 10.99/11.27 tff(27234,plain,
% 10.99/11.27 (~(s(s(s(s(z)))) = elem!1)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[16908, 8922])).
% 10.99/11.27 tff(27235,plain,
% 10.99/11.27 (r(s(s(s(s(z)))), elem!1)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[762, 27234, 1549])).
% 10.99/11.27 tff(27236,plain,
% 10.99/11.27 ($false),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[14627, 27235, 9101, 1216, 1484])).
% 10.99/11.27 tff(27237,plain,((elem!1 = s(s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.27 tff(27238,plain,
% 10.99/11.27 (elem!1 = s(s(s(s(z))))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[27237, 1484, 2913, 1549, 27233])).
% 10.99/11.27 tff(27239,plain,
% 10.99/11.27 (s(s(s(s(z)))) = elem!1),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[769, 27238])).
% 10.99/11.27 tff(27240,plain,
% 10.99/11.27 (~(s(s(s(elem!1))) = s(elem!1))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[717, 27239])).
% 10.99/11.27 tff(27241,plain,
% 10.99/11.27 (~(s(s(elem!1)) = elem!1)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[451, 27240])).
% 10.99/11.27 tff(27242,plain,
% 10.99/11.27 (~(s(s(elem!1)) = s(elem!1))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[2279, 27240])).
% 10.99/11.27 tff(27243,plain,
% 10.99/11.27 (r(elem!1, z) <=> r(s(s(s(s(z)))), z)),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27238])).
% 10.99/11.27 tff(27244,plain,
% 10.99/11.27 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 10.99/11.27 inference(symmetry,[status(thm)],[27243])).
% 10.99/11.27 tff(27245,plain,
% 10.99/11.27 ((~r(s(s(s(s(z)))), z)) <=> (~r(elem!1, z))),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27244])).
% 10.99/11.27 tff(27246,plain,
% 10.99/11.27 (~r(elem!1, z)),
% 10.99/11.27 inference(modus_ponens,[status(thm)],[81, 27245])).
% 10.99/11.27 tff(27247,plain,
% 10.99/11.27 (b(s(elem!1), elem!1)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[14657, 27246, 133, 22898, 27232, 21435, 2])).
% 10.99/11.27 tff(27248,plain,
% 10.99/11.27 (~b(s(s(elem!1)), elem!1)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[5286, 27247, 133, 27231, 27242])).
% 10.99/11.27 tff(27249,plain,
% 10.99/11.27 (r(s(s(elem!1)), elem!1)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[872, 27248, 27241])).
% 10.99/11.27 tff(27250,plain,
% 10.99/11.27 (b(elem!1, s(s(s(elem!1))))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[12954, 27249, 22898, 1, 1484, 182, 27232, 26982])).
% 10.99/11.27 tff(27251,plain,
% 10.99/11.27 (~b(s(s(s(elem!1))), z)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[10876, 27250, 133, 27231])).
% 10.99/11.27 tff(27252,plain,
% 10.99/11.27 (r(s(s(s(elem!1))), z)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[377, 27251])).
% 10.99/11.27 tff(27253,plain,
% 10.99/11.27 (b(s(s(s(s(z)))), s(z))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[13738, 27238, 721])).
% 10.99/11.27 tff(27254,plain,
% 10.99/11.27 ((elem!1 = s(s(z))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27238])).
% 10.99/11.27 tff(27255,plain,
% 10.99/11.27 ((elem!1 = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 10.99/11.27 inference(transitivity,[status(thm)],[27254, 940])).
% 10.99/11.27 tff(27256,plain,
% 10.99/11.27 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 10.99/11.27 inference(symmetry,[status(thm)],[27255])).
% 10.99/11.27 tff(27257,plain,
% 10.99/11.27 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(z))))),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27256])).
% 10.99/11.27 tff(27258,plain,
% 10.99/11.27 (~(elem!1 = s(s(z)))),
% 10.99/11.27 inference(modus_ponens,[status(thm)],[714, 27257])).
% 10.99/11.27 tff(27259,plain,
% 10.99/11.27 (r(s(s(s(elem!1))), elem!1)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[230, 27232, 9])).
% 10.99/11.27 tff(27260,plain,
% 10.99/11.27 (~r(elem!1, s(s(z)))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[14370, 27250, 721, 1484, 27259])).
% 10.99/11.27 tff(27261,plain,
% 10.99/11.27 (b(elem!1, s(s(z)))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[3394, 27260, 27258])).
% 10.99/11.27 tff(27262,plain,
% 10.99/11.27 (~b(s(s(z)), z)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[13448, 27261, 133, 27231])).
% 10.99/11.27 tff(27263,plain,
% 10.99/11.27 (r(s(s(z)), z)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[1211, 27262])).
% 10.99/11.27 tff(27264,plain,
% 10.99/11.27 (~r(s(s(s(elem!1))), s(z))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[23356, 27263, 88, 22898, 2913, 27211, 1, 27253])).
% 10.99/11.27 tff(27265,plain,
% 10.99/11.27 (b(s(s(s(elem!1))), s(z))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[223, 27264])).
% 10.99/11.27 tff(27266,plain,
% 10.99/11.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.27 inference(rewrite,[status(thm)],[])).
% 10.99/11.27 tff(27267,plain,
% 10.99/11.27 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.27 inference(rewrite,[status(thm)],[])).
% 10.99/11.27 tff(27268,plain,
% 10.99/11.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27267])).
% 10.99/11.27 tff(27269,plain,
% 10.99/11.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.27 inference(transitivity,[status(thm)],[27268, 27266])).
% 10.99/11.27 tff(27270,plain,
% 10.99/11.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 10.99/11.27 inference(quant_inst,[status(thm)],[])).
% 10.99/11.27 tff(27271,plain,
% 10.99/11.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 10.99/11.27 inference(modus_ponens,[status(thm)],[27270, 27269])).
% 10.99/11.27 tff(27272,plain,
% 10.99/11.27 (~b(elem!1, z)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[27271, 391, 10682, 448, 1526, 5450])).
% 10.99/11.27 tff(27273,plain,
% 10.99/11.27 (elem!1 = z),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[526, 27272, 2282])).
% 10.99/11.27 tff(27274,plain,
% 10.99/11.27 (s(elem!1) = s(z)),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27273])).
% 10.99/11.27 tff(27275,plain,
% 10.99/11.27 (s(s(elem!1)) = s(s(z))),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27274])).
% 10.99/11.27 tff(27276,plain,
% 10.99/11.27 (s(s(s(elem!1))) = s(s(s(z)))),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27275])).
% 10.99/11.27 tff(27277,plain,
% 10.99/11.27 (s(s(s(z))) = s(s(s(elem!1)))),
% 10.99/11.27 inference(symmetry,[status(thm)],[27276])).
% 10.99/11.27 tff(27278,plain,
% 10.99/11.27 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27277])).
% 10.99/11.27 tff(27279,plain,
% 10.99/11.27 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 10.99/11.27 inference(symmetry,[status(thm)],[27278])).
% 10.99/11.27 tff(27280,plain,
% 10.99/11.27 (b(s(s(s(z))), s(z))),
% 10.99/11.27 inference(modus_ponens,[status(thm)],[1526, 27279])).
% 10.99/11.27 tff(27281,plain,
% 10.99/11.27 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27276])).
% 10.99/11.27 tff(27282,plain,
% 10.99/11.27 (b(z, s(s(s(z))))),
% 10.99/11.27 inference(modus_ponens,[status(thm)],[10682, 27281])).
% 10.99/11.27 tff(27283,plain,
% 10.99/11.27 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27276])).
% 10.99/11.27 tff(27284,plain,
% 10.99/11.27 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[8883, 27273])).
% 10.99/11.27 tff(27285,plain,
% 10.99/11.27 (r(s(s(s(z))), z)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[4409, 27273, 174])).
% 10.99/11.27 tff(27286,plain,
% 10.99/11.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 10.99/11.27 inference(rewrite,[status(thm)],[])).
% 10.99/11.27 tff(27287,plain,
% 10.99/11.27 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 10.99/11.27 inference(rewrite,[status(thm)],[])).
% 10.99/11.27 tff(27288,plain,
% 10.99/11.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 10.99/11.27 inference(monotonicity,[status(thm)],[27287])).
% 10.99/11.27 tff(27289,plain,
% 10.99/11.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 10.99/11.27 inference(transitivity,[status(thm)],[27288, 27286])).
% 10.99/11.27 tff(27290,plain,
% 10.99/11.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 10.99/11.27 inference(quant_inst,[status(thm)],[])).
% 10.99/11.27 tff(27291,plain,
% 10.99/11.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 10.99/11.27 inference(modus_ponens,[status(thm)],[27290, 27289])).
% 10.99/11.27 tff(27292,plain,
% 10.99/11.27 (~b(s(s(s(s(z)))), s(z))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[27291, 391, 10682, 1526, 90, 5450])).
% 10.99/11.27 tff(27293,plain,
% 10.99/11.27 (r(s(s(s(s(z)))), s(z))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[749, 27292])).
% 10.99/11.27 tff(27294,plain,
% 10.99/11.27 (z = elem!1),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[5453, 27273])).
% 10.99/11.27 tff(27295,plain,
% 10.99/11.27 (~r(s(z), elem!1)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[5433, 27294, 175])).
% 10.99/11.27 tff(27296,plain,
% 10.99/11.27 (b(s(z), elem!1)),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[632, 27295, 150])).
% 10.99/11.27 tff(27297,plain,
% 10.99/11.27 (~b(s(z), s(s(s(elem!1))))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[4026, 27296, 1526, 448])).
% 10.99/11.27 tff(27298,plain,
% 10.99/11.27 (r(s(z), s(s(s(elem!1))))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[247, 27297])).
% 10.99/11.27 tff(27299,plain,
% 10.99/11.27 (r(s(z), s(s(s(z))))),
% 10.99/11.27 inference(unit_resolution,[status(thm)],[23224, 27298, 27273])).
% 10.99/11.27 tff(27300,plain,
% 10.99/11.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 10.99/11.28 inference(rewrite,[status(thm)],[])).
% 10.99/11.28 tff(27301,plain,
% 10.99/11.28 (((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 10.99/11.28 inference(rewrite,[status(thm)],[])).
% 10.99/11.28 tff(27302,plain,
% 10.99/11.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 10.99/11.28 inference(monotonicity,[status(thm)],[27301])).
% 10.99/11.28 tff(27303,plain,
% 10.99/11.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 10.99/11.28 inference(transitivity,[status(thm)],[27302, 27300])).
% 10.99/11.28 tff(27304,plain,
% 10.99/11.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 10.99/11.28 inference(quant_inst,[status(thm)],[])).
% 10.99/11.28 tff(27305,plain,
% 10.99/11.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 10.99/11.28 inference(modus_ponens,[status(thm)],[27304, 27303])).
% 10.99/11.28 tff(27306,plain,
% 10.99/11.28 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[27305, 194, 723, 4428, 15705])).
% 10.99/11.28 tff(27307,plain,
% 10.99/11.28 ($false),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[27306, 23229])).
% 10.99/11.28 tff(27308,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.28 tff(27309,plain,
% 10.99/11.28 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[27308, 27299, 27293, 27285, 27273])).
% 10.99/11.28 tff(27310,plain,
% 10.99/11.28 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[1095, 27309, 27284])).
% 10.99/11.28 tff(27311,plain,
% 10.99/11.28 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 10.99/11.28 inference(monotonicity,[status(thm)],[490])).
% 10.99/11.28 tff(27312,plain,
% 10.99/11.28 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.99/11.28 inference(symmetry,[status(thm)],[27311])).
% 10.99/11.28 tff(27313,plain,
% 10.99/11.28 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.99/11.28 inference(transitivity,[status(thm)],[23220, 27312])).
% 10.99/11.28 tff(27314,plain,
% 10.99/11.28 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.99/11.28 inference(modus_ponens,[status(thm)],[1114, 27313])).
% 10.99/11.28 tff(27315,plain,
% 10.99/11.28 ($false),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[2863, 27314])).
% 10.99/11.28 tff(27316,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.28 tff(27317,plain,
% 10.99/11.28 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[27316, 27310, 27273])).
% 10.99/11.28 tff(27318,plain,
% 10.99/11.28 (b(s(s(s(s(z)))), s(s(s(z))))),
% 10.99/11.28 inference(modus_ponens,[status(thm)],[27317, 27283])).
% 10.99/11.28 tff(27319,plain,
% 10.99/11.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 10.99/11.28 inference(rewrite,[status(thm)],[])).
% 10.99/11.28 tff(27320,plain,
% 10.99/11.28 (((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 10.99/11.28 inference(rewrite,[status(thm)],[])).
% 10.99/11.28 tff(27321,plain,
% 10.99/11.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 10.99/11.28 inference(monotonicity,[status(thm)],[27320])).
% 10.99/11.28 tff(27322,plain,
% 10.99/11.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 10.99/11.28 inference(transitivity,[status(thm)],[27321, 27319])).
% 10.99/11.28 tff(27323,plain,
% 10.99/11.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 10.99/11.28 inference(quant_inst,[status(thm)],[])).
% 10.99/11.28 tff(27324,plain,
% 10.99/11.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 10.99/11.28 inference(modus_ponens,[status(thm)],[27323, 27322])).
% 10.99/11.28 tff(27325,plain,
% 10.99/11.28 ($false),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[27324, 391, 90, 5450, 27318, 27282, 27280])).
% 10.99/11.28 tff(27326,plain,(r(s(z), z) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (s(z) = elem!1) | (~r(s(s(s(elem!1))), z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.28 tff(27327,plain,
% 10.99/11.28 (r(s(z), z)),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[27326, 2282, 1526, 10682, 448, 10902, 174, 90])).
% 10.99/11.28 tff(27328,plain,
% 10.99/11.28 (r(s(elem!1), z)),
% 10.99/11.28 inference(modus_ponens,[status(thm)],[182, 17617])).
% 10.99/11.28 tff(27329,plain,
% 10.99/11.28 ($false),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[544, 27328])).
% 10.99/11.28 tff(27330,plain,((~(elem!1 = z)) | r(s(elem!1), z) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.28 tff(27331,plain,
% 10.99/11.28 (~(elem!1 = z)),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[27330, 544, 182])).
% 10.99/11.28 tff(27332,plain,
% 10.99/11.28 (b(elem!1, z)),
% 10.99/11.28 inference(unit_resolution,[status(thm)],[526, 27331, 2282])).
% 10.99/11.28 tff(27333,plain,
% 10.99/11.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.29 inference(rewrite,[status(thm)],[])).
% 10.99/11.29 tff(27334,plain,
% 10.99/11.29 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.29 inference(rewrite,[status(thm)],[])).
% 10.99/11.29 tff(27335,plain,
% 10.99/11.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 10.99/11.29 inference(monotonicity,[status(thm)],[27334])).
% 10.99/11.29 tff(27336,plain,
% 10.99/11.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.29 inference(transitivity,[status(thm)],[27335, 27333])).
% 10.99/11.29 tff(27337,plain,
% 10.99/11.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 10.99/11.29 inference(quant_inst,[status(thm)],[])).
% 10.99/11.29 tff(27338,plain,
% 10.99/11.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 10.99/11.29 inference(modus_ponens,[status(thm)],[27337, 27336])).
% 10.99/11.29 tff(27339,plain,
% 10.99/11.29 (~b(s(elem!1), elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[27338, 391, 27332, 10682, 1526, 11937])).
% 10.99/11.29 tff(27340,plain,
% 10.99/11.29 (r(s(elem!1), elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[2168, 27339, 164])).
% 10.99/11.29 tff(27341,plain,
% 10.99/11.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.29 inference(rewrite,[status(thm)],[])).
% 10.99/11.29 tff(27342,plain,
% 10.99/11.29 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.29 inference(rewrite,[status(thm)],[])).
% 10.99/11.29 tff(27343,plain,
% 10.99/11.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 10.99/11.29 inference(monotonicity,[status(thm)],[27342])).
% 10.99/11.29 tff(27344,plain,
% 10.99/11.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 10.99/11.29 inference(transitivity,[status(thm)],[27343, 27341])).
% 10.99/11.29 tff(27345,plain,
% 10.99/11.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 10.99/11.29 inference(quant_inst,[status(thm)],[])).
% 10.99/11.29 tff(27346,plain,
% 10.99/11.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 10.99/11.29 inference(modus_ponens,[status(thm)],[27345, 27344])).
% 10.99/11.29 tff(27347,plain,
% 10.99/11.29 (~b(elem!1, s(elem!1))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[27346, 391, 27332, 10682, 1526, 11937])).
% 10.99/11.29 tff(27348,plain,
% 10.99/11.29 (r(elem!1, s(elem!1))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[443, 27347, 7437])).
% 10.99/11.29 tff(27349,plain,
% 10.99/11.29 (s(s(s(elem!1))) = s(elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[12962, 27348, 233, 10682, 11937, 27340])).
% 10.99/11.29 tff(27350,plain,
% 10.99/11.29 (~(s(s(s(s(z)))) = elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[717, 27349])).
% 10.99/11.29 tff(27351,plain,
% 10.99/11.29 (~b(elem!1, s(s(s(s(z)))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[25257, 391, 27332, 10682, 1526, 90])).
% 10.99/11.29 tff(27352,plain,
% 10.99/11.29 (~(z = elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[97, 27331])).
% 10.99/11.29 tff(27353,plain,
% 10.99/11.29 (~b(z, elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[14657, 27339, 10682, 150, 168, 2282, 27331])).
% 10.99/11.29 tff(27354,plain,
% 10.99/11.29 (r(z, elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[141, 27353, 27352])).
% 10.99/11.29 tff(27355,plain,
% 10.99/11.29 (~r(elem!1, s(s(s(s(z)))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[22246, 27354, 174, 233])).
% 10.99/11.29 tff(27356,plain,
% 10.99/11.29 (elem!1 = s(s(s(s(z))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[781, 27355, 27351])).
% 10.99/11.29 tff(27357,plain,
% 10.99/11.29 ($false),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[769, 27356, 27350])).
% 10.99/11.29 tff(27358,plain,(r(s(elem!1), z) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(elem!1, z) | (s(elem!1) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.29 tff(27359,plain,
% 10.99/11.29 (r(s(elem!1), z)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[27358, 2282, 233, 10682, 10902, 168, 174, 164, 1526, 90, 27327])).
% 10.99/11.29 tff(27360,plain,
% 10.99/11.29 (~r(s(s(s(s(z)))), s(s(z)))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[25141, 10936, 90, 2913, 10682, 1526])).
% 10.99/11.29 tff(27361,plain,
% 10.99/11.29 (b(s(s(s(s(z)))), s(s(z)))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[1714, 27360])).
% 10.99/11.29 tff(27362,plain,
% 10.99/11.29 (~b(s(s(z)), z)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[25151, 27361, 1526, 90, 10682])).
% 10.99/11.29 tff(27363,plain,
% 10.99/11.29 (r(s(s(z)), z)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[1211, 27362])).
% 10.99/11.29 tff(27364,plain,
% 10.99/11.29 (b(elem!1, z)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[526, 10680, 2282])).
% 10.99/11.29 tff(27365,plain,
% 10.99/11.29 (~b(s(z), s(s(z)))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[14507, 27364, 10682, 1526, 448])).
% 10.99/11.29 tff(27366,plain,
% 10.99/11.29 (r(s(z), s(s(z)))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[1788, 27365])).
% 10.99/11.29 tff(27367,plain,
% 10.99/11.29 (~b(elem!1, s(s(s(s(z)))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[25257, 391, 27364, 10682, 1526, 90])).
% 10.99/11.29 tff(27368,plain,
% 10.99/11.29 (~b(elem!1, s(z))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[1930, 411, 1628, 802, 121, 182])).
% 10.99/11.29 tff(27369,plain,
% 10.99/11.29 (b(s(z), elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[13708, 27368, 10682, 448, 10902, 233, 665])).
% 10.99/11.29 tff(27370,plain,
% 10.99/11.29 (~r(elem!1, s(s(s(s(z)))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[22246, 411, 174, 233])).
% 10.99/11.29 tff(27371,plain,
% 10.99/11.29 (elem!1 = s(s(s(s(z))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[781, 27370, 8536])).
% 10.99/11.29 tff(27372,plain,
% 10.99/11.29 (s(s(s(s(z)))) = elem!1),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[769, 27371])).
% 10.99/11.29 tff(27373,plain,
% 10.99/11.29 ($false),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[6252, 27372, 27369, 2881])).
% 10.99/11.29 tff(27374,plain,((~r(z, elem!1)) | b(s(z), s(s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | b(elem!1, s(s(s(s(z))))) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.29 tff(27375,plain,
% 10.99/11.29 (~r(z, elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[27374, 27364, 10682, 448, 233, 2881, 27367, 1628, 802, 10968, 27327, 174])).
% 10.99/11.29 tff(27376,plain,
% 10.99/11.29 (b(z, elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[141, 27375, 115])).
% 10.99/11.29 tff(27377,plain,
% 10.99/11.29 (b(s(elem!1), elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[14657, 27376, 10682, 10902, 168, 2282, 10680])).
% 10.99/11.29 tff(27378,plain,
% 10.99/11.29 (~b(z, s(elem!1))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[6555, 27376, 27377, 27364])).
% 10.99/11.29 tff(27379,plain,
% 10.99/11.29 (r(z, s(elem!1))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[566, 27378])).
% 10.99/11.29 tff(27380,plain,
% 10.99/11.29 ($false),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[25278, 194, 27379, 27327, 27363, 27366])).
% 10.99/11.29 tff(27381,plain,((z = elem!1) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | r(elem!1, z) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | b(s(z), s(s(s(s(z))))) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.29 tff(27382,plain,
% 10.99/11.29 (~b(elem!1, s(elem!1))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[27381, 2282, 168, 115, 448, 233, 2881, 27359, 10682, 174, 1526, 90])).
% 10.99/11.29 tff(27383,plain,
% 10.99/11.29 (r(elem!1, s(elem!1))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[443, 27382, 7437])).
% 10.99/11.29 tff(27384,plain,
% 10.99/11.29 (~r(s(elem!1), s(s(s(elem!1))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[7450, 194, 25666, 233, 2251])).
% 10.99/11.29 tff(27385,plain,
% 10.99/11.29 (~r(s(s(s(elem!1))), s(elem!1))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[7744, 25666, 233, 2251])).
% 10.99/11.29 tff(27386,plain,
% 10.99/11.29 (~b(z, elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[14657, 10680, 10682, 150, 168, 2282, 2163])).
% 10.99/11.29 tff(27387,plain,
% 10.99/11.29 (r(z, elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[141, 27386, 115])).
% 10.99/11.29 tff(27388,plain,
% 10.99/11.29 (~r(s(z), s(s(s(elem!1))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[2594, 27387, 1526, 1628, 182, 1575, 10968])).
% 10.99/11.29 tff(27389,plain,
% 10.99/11.29 (b(s(z), s(s(s(elem!1))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[247, 27388])).
% 10.99/11.29 tff(27390,plain,
% 10.99/11.29 (~r(s(z), elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[2582, 27387, 182, 2251])).
% 10.99/11.29 tff(27391,plain,
% 10.99/11.29 (b(s(z), elem!1)),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[632, 27390, 150])).
% 10.99/11.29 tff(27392,plain,
% 10.99/11.29 ($false),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[4026, 27391, 27389, 1526, 448])).
% 10.99/11.29 tff(27393,plain,((z = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (s(z) = elem!1) | (~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | r(s(s(s(elem!1))), s(elem!1)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | r(elem!1, z) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 10.99/11.29 tff(27394,plain,
% 10.99/11.29 (z = elem!1),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[27393, 27385, 448, 150, 182, 2251, 1628, 1526, 10682, 168, 2282, 2163])).
% 10.99/11.29 tff(27395,plain,
% 10.99/11.29 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 10.99/11.29 inference(monotonicity,[status(thm)],[932])).
% 10.99/11.29 tff(27396,plain,
% 10.99/11.29 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 10.99/11.29 inference(transitivity,[status(thm)],[27395, 267])).
% 10.99/11.29 tff(27397,plain,
% 10.99/11.29 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 10.99/11.29 inference(monotonicity,[status(thm)],[27396])).
% 10.99/11.29 tff(27398,plain,
% 10.99/11.29 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 10.99/11.29 inference(modus_ponens,[status(thm)],[1397, 27397])).
% 10.99/11.29 tff(27399,plain,
% 10.99/11.29 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 10.99/11.29 inference(monotonicity,[status(thm)],[931])).
% 10.99/11.29 tff(27400,plain,
% 10.99/11.29 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 10.99/11.29 inference(symmetry,[status(thm)],[27399])).
% 10.99/11.29 tff(27401,plain,
% 10.99/11.29 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 10.99/11.29 inference(monotonicity,[status(thm)],[27400])).
% 10.99/11.29 tff(27402,plain,
% 10.99/11.29 (~r(s(z), s(s(s(elem!1))))),
% 10.99/11.29 inference(modus_ponens,[status(thm)],[3612, 27401])).
% 10.99/11.29 tff(27403,plain,
% 10.99/11.29 (b(s(z), s(s(s(elem!1))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[247, 27402])).
% 10.99/11.29 tff(27404,plain,
% 10.99/11.29 (r(s(s(z)), elem!1)),
% 10.99/11.29 inference(modus_ponens,[status(thm)],[3557, 1199])).
% 10.99/11.29 tff(27405,plain,
% 10.99/11.29 (r(s(s(elem!1)), elem!1)),
% 10.99/11.29 inference(modus_ponens,[status(thm)],[27404, 1201])).
% 10.99/11.29 tff(27406,plain,
% 10.99/11.29 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 10.99/11.29 inference(monotonicity,[status(thm)],[94])).
% 10.99/11.29 tff(27407,plain,
% 10.99/11.29 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 10.99/11.29 inference(symmetry,[status(thm)],[27406])).
% 10.99/11.29 tff(27408,plain,
% 10.99/11.29 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), z)),
% 10.99/11.29 inference(transitivity,[status(thm)],[1201, 27407])).
% 10.99/11.29 tff(27409,plain,
% 10.99/11.29 (r(s(s(elem!1)), z)),
% 10.99/11.29 inference(modus_ponens,[status(thm)],[27404, 27408])).
% 10.99/11.29 tff(27410,plain,
% 10.99/11.29 (~r(z, s(s(elem!1)))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[13840, 27409, 174, 27405, 27403, 27398, 182])).
% 10.99/11.29 tff(27411,plain,
% 10.99/11.29 (b(z, s(s(elem!1)))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[324, 27410])).
% 10.99/11.29 tff(27412,plain,
% 10.99/11.29 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 10.99/11.29 inference(transitivity,[status(thm)],[27396, 268])).
% 10.99/11.29 tff(27413,plain,
% 10.99/11.29 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 10.99/11.29 inference(monotonicity,[status(thm)],[27412])).
% 10.99/11.29 tff(27414,plain,
% 10.99/11.29 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 10.99/11.29 inference(modus_ponens,[status(thm)],[1397, 27413])).
% 10.99/11.29 tff(27415,plain,
% 10.99/11.29 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[1356, 27414, 1350])).
% 10.99/11.29 tff(27416,plain,
% 10.99/11.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.99/11.29 inference(rewrite,[status(thm)],[])).
% 10.99/11.29 tff(27417,plain,
% 10.99/11.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 10.99/11.29 inference(quant_inst,[status(thm)],[])).
% 10.99/11.29 tff(27418,plain,
% 10.99/11.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 10.99/11.29 inference(modus_ponens,[status(thm)],[27417, 27416])).
% 10.99/11.29 tff(27419,plain,
% 10.99/11.29 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[27418, 194, 233, 2251, 27405])).
% 10.99/11.29 tff(27420,plain,
% 10.99/11.29 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[1370, 27419, 27398])).
% 10.99/11.29 tff(27421,plain,
% 10.99/11.29 ($false),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[12932, 27420, 27415, 10682, 27411])).
% 10.99/11.29 tff(27422,plain,((~(z = elem!1)) | (~b(z, s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | r(s(elem!1), s(s(s(elem!1)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 10.99/11.29 tff(27423,plain,
% 10.99/11.29 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 10.99/11.29 inference(unit_resolution,[status(thm)],[27422, 27394, 10682, 174, 182, 233, 2251, 27384, 3557])).
% 10.99/11.29 tff(27424,plain,
% 10.99/11.29 (s(z) = s(elem!1)),
% 11.09/11.30 inference(monotonicity,[status(thm)],[27394])).
% 11.09/11.30 tff(27425,plain,
% 11.09/11.30 (s(s(z)) = s(s(elem!1))),
% 11.09/11.30 inference(monotonicity,[status(thm)],[27424])).
% 11.09/11.30 tff(27426,plain,
% 11.09/11.30 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 11.09/11.30 inference(monotonicity,[status(thm)],[27425])).
% 11.09/11.30 tff(27427,plain,
% 11.09/11.30 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 11.09/11.30 inference(monotonicity,[status(thm)],[27394])).
% 11.09/11.30 tff(27428,plain,
% 11.09/11.30 (r(s(s(z)), elem!1)),
% 11.09/11.30 inference(modus_ponens,[status(thm)],[3557, 27427])).
% 11.09/11.30 tff(27429,plain,
% 11.09/11.30 (r(s(s(elem!1)), elem!1)),
% 11.09/11.30 inference(modus_ponens,[status(thm)],[27428, 27426])).
% 11.09/11.30 tff(27430,plain,
% 11.09/11.30 ($false),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[26913, 194, 233, 2251, 27429, 27423])).
% 11.09/11.30 tff(27431,plain,(b(s(elem!1), elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (s(z) = elem!1) | (~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), elem!1) | r(elem!1, z) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.30 tff(27432,plain,
% 11.09/11.30 (b(s(elem!1), elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[27431, 27383, 168, 27363, 10682, 174, 27327, 448, 10902, 2282, 1526, 233, 27359, 164])).
% 11.09/11.30 tff(27433,plain,
% 11.09/11.30 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[14662, 27432, 168])).
% 11.09/11.30 tff(27434,plain,
% 11.09/11.30 (~r(z, s(s(elem!1)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[3787, 27366, 27363, 27327])).
% 11.09/11.30 tff(27435,plain,
% 11.09/11.30 (b(z, s(s(elem!1)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[324, 27434])).
% 11.09/11.30 tff(27436,plain,
% 11.09/11.30 (~b(elem!1, s(s(elem!1)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[7297, 27435, 973, 27364])).
% 11.09/11.30 tff(27437,plain,
% 11.09/11.30 (~b(z, elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[4944, 27435, 973, 27364])).
% 11.09/11.30 tff(27438,plain,
% 11.09/11.30 (r(z, elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[141, 27437, 115])).
% 11.09/11.30 tff(27439,plain,
% 11.09/11.30 (~r(s(z), elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[2582, 27438, 27327, 2251])).
% 11.09/11.30 tff(27440,plain,
% 11.09/11.30 (b(s(z), elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[632, 27439, 10902])).
% 11.09/11.30 tff(27441,plain,
% 11.09/11.30 (~b(s(z), s(s(s(elem!1))))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[4026, 27440, 1526, 448])).
% 11.09/11.30 tff(27442,plain,
% 11.09/11.30 (r(s(z), s(s(s(elem!1))))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[247, 27441])).
% 11.09/11.30 tff(27443,plain,
% 11.09/11.30 (r(s(s(s(elem!1))), s(elem!1))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[2594, 27442, 1526, 1628, 27327, 27438, 10968])).
% 11.09/11.30 tff(27444,plain,
% 11.09/11.30 (~r(s(elem!1), elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[7744, 27443, 233, 2251])).
% 11.09/11.30 tff(27445,plain,
% 11.09/11.30 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[472, 27444, 233])).
% 11.09/11.30 tff(27446,plain,
% 11.09/11.30 (~(s(s(elem!1)) = elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[451, 27445])).
% 11.09/11.30 tff(27447,plain,
% 11.09/11.30 (~(elem!1 = s(s(elem!1)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[1292, 27446])).
% 11.09/11.30 tff(27448,plain,
% 11.09/11.30 (~r(elem!1, s(s(s(s(z)))))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[22246, 27438, 174, 233])).
% 11.09/11.30 tff(27449,plain,
% 11.09/11.30 (~(s(s(s(s(z)))) = elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[6252, 27440, 2881])).
% 11.09/11.30 tff(27450,plain,
% 11.09/11.30 (~(elem!1 = s(s(s(s(z)))))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[769, 27449])).
% 11.09/11.30 tff(27451,plain,
% 11.09/11.30 (b(elem!1, s(s(s(s(z)))))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[781, 27450, 27448])).
% 11.09/11.30 tff(27452,plain,
% 11.09/11.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 11.09/11.30 inference(rewrite,[status(thm)],[])).
% 11.09/11.30 tff(27453,plain,
% 11.09/11.30 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 11.09/11.30 inference(rewrite,[status(thm)],[])).
% 11.09/11.30 tff(27454,plain,
% 11.09/11.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 11.09/11.30 inference(monotonicity,[status(thm)],[27453])).
% 11.09/11.30 tff(27455,plain,
% 11.09/11.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 11.09/11.30 inference(transitivity,[status(thm)],[27454, 27452])).
% 11.09/11.30 tff(27456,plain,
% 11.09/11.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 11.09/11.30 inference(quant_inst,[status(thm)],[])).
% 11.09/11.30 tff(27457,plain,
% 11.09/11.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 11.09/11.30 inference(modus_ponens,[status(thm)],[27456, 27455])).
% 11.09/11.30 tff(27458,plain,
% 11.09/11.30 ($false),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[27457, 391, 381, 973, 644, 90, 2064])).
% 11.09/11.30 tff(27459,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.30 tff(27460,plain,
% 11.09/11.30 (~b(s(s(elem!1)), s(z))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[27459, 27451, 90, 973, 27440])).
% 11.09/11.30 tff(27461,plain,
% 11.09/11.30 (r(s(s(elem!1)), s(z))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[362, 27460])).
% 11.09/11.30 tff(27462,plain,
% 11.09/11.30 (~r(s(s(s(s(z)))), s(z))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[3236, 27451, 2913, 27364, 27327, 27438])).
% 11.09/11.30 tff(27463,plain,
% 11.09/11.30 (b(s(s(s(s(z)))), s(z))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[749, 27462])).
% 11.09/11.30 tff(27464,plain,
% 11.09/11.30 (~b(elem!1, s(z))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[3150, 27463, 27440, 27451, 27364])).
% 11.09/11.30 tff(27465,plain,
% 11.09/11.30 (r(elem!1, s(z))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[837, 27464, 10901])).
% 11.09/11.30 tff(27466,plain,
% 11.09/11.30 (~r(elem!1, s(s(elem!1)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[6408, 27465, 2913, 27461])).
% 11.09/11.30 tff(27467,plain,
% 11.09/11.30 ($false),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[1307, 27466, 27447, 27436])).
% 11.09/11.30 tff(27468,plain,((z = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | b(s(z), s(s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.30 tff(27469,plain,
% 11.09/11.30 (~b(s(s(elem!1)), elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[27468, 27383, 115, 90, 27359, 1526, 233, 448, 2881, 174, 10682, 2282])).
% 11.09/11.30 tff(27470,plain,
% 11.09/11.30 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[25141, 3363, 90, 1216, 10682, 1526])).
% 11.09/11.30 tff(27471,plain,
% 11.09/11.30 (b(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[1714, 27470])).
% 11.09/11.30 tff(27472,plain,
% 11.09/11.30 (~b(s(s(z)), z)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[25151, 27471, 1526, 90, 10682])).
% 11.09/11.30 tff(27473,plain,
% 11.09/11.30 (r(s(s(z)), z)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[1211, 27472])).
% 11.09/11.30 tff(27474,plain,
% 11.09/11.30 (r(s(z), z)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[27326, 2282, 1526, 10682, 448, 150, 174, 90])).
% 11.09/11.30 tff(27475,plain,
% 11.09/11.30 (~b(s(s(s(s(z)))), elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[25250, 391, 27364, 10682, 1526, 90])).
% 11.09/11.30 tff(27476,plain,
% 11.09/11.30 (r(s(elem!1), elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[472, 465, 233])).
% 11.09/11.30 tff(27477,plain,
% 11.09/11.30 (r(elem!1, s(s(s(s(z)))))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[781, 5511, 8536])).
% 11.09/11.30 tff(27478,plain,
% 11.09/11.30 (~r(s(z), elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[14627, 13137, 1216, 27477])).
% 11.09/11.30 tff(27479,plain,
% 11.09/11.30 (b(s(z), elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[632, 27478, 150])).
% 11.09/11.30 tff(27480,plain,
% 11.09/11.30 (~r(z, elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[22246, 27477, 174, 233])).
% 11.09/11.30 tff(27481,plain,
% 11.09/11.30 (b(z, elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[141, 27480, 115])).
% 11.09/11.30 tff(27482,plain,
% 11.09/11.30 ($false),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[13276, 27481, 27479, 1628, 665, 27476, 10682, 168, 437, 3363, 10968])).
% 11.09/11.30 tff(27483,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(elem!1)) | (z = elem!1) | (s(z) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(s(s(s(z))))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.30 tff(27484,plain,
% 11.09/11.30 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[27483, 27364, 1628, 10682, 168, 437, 115, 150, 174, 233, 1216, 27367, 27475])).
% 11.09/11.30 tff(27485,plain,
% 11.09/11.30 (~(s(s(elem!1)) = s(elem!1))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[2279, 27484])).
% 11.09/11.30 tff(27486,plain,
% 11.09/11.30 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[287, 27485])).
% 11.09/11.30 tff(27487,plain,
% 11.09/11.30 (~r(z, s(s(elem!1)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[3787, 27366, 27473, 27474])).
% 11.09/11.30 tff(27488,plain,
% 11.09/11.30 (b(z, s(s(elem!1)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[324, 27487])).
% 11.09/11.30 tff(27489,plain,
% 11.09/11.30 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[281, 27484])).
% 11.09/11.30 tff(27490,plain,
% 11.09/11.30 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[1356, 27489, 1350])).
% 11.09/11.30 tff(27491,plain,
% 11.09/11.30 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[12932, 27490, 10682, 27488])).
% 11.09/11.30 tff(27492,plain,
% 11.09/11.30 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[1370, 27491, 27486])).
% 11.09/11.30 tff(27493,plain,
% 11.09/11.30 (~(s(s(elem!1)) = elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[451, 27484])).
% 11.09/11.30 tff(27494,plain,
% 11.09/11.30 (r(s(s(elem!1)), elem!1)),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[872, 27493, 4017])).
% 11.09/11.30 tff(27495,plain,
% 11.09/11.30 ($false),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[27418, 194, 233, 2251, 27494, 27492])).
% 11.09/11.30 tff(27496,plain,((z = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(elem!1)))) | b(s(s(elem!1)), elem!1) | (~r(s(elem!1), z)) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(elem!1)) | (s(z) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(elem!1))))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.30 tff(27497,plain,
% 11.09/11.30 (z = elem!1),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[27496, 1350, 2251, 10682, 233, 4017, 1628, 168, 437, 150, 174, 1216, 1526, 90, 448, 2282])).
% 11.09/11.30 tff(27498,plain,
% 11.09/11.30 (r(s(elem!1), s(s(s(elem!1))))),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[27422, 27497, 10682, 174, 27474, 233, 2251, 1350, 27473])).
% 11.09/11.30 tff(27499,plain,
% 11.09/11.30 (elem!1 = z),
% 11.09/11.30 inference(unit_resolution,[status(thm)],[97, 27497])).
% 11.09/11.31 tff(27500,plain,
% 11.09/11.31 (r(z, s(elem!1))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[2288, 27499, 2251])).
% 11.09/11.31 tff(27501,plain,
% 11.09/11.31 ($false),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[7760, 27500, 27498, 174, 1628])).
% 11.09/11.31 tff(27502,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | b(s(s(elem!1)), elem!1) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(elem!1)) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(elem!1))))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.31 tff(27503,plain,
% 11.09/11.31 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[27502, 4017, 2282, 174, 10682, 233, 1628, 168, 437, 150, 1216, 1526, 90, 448, 2251])).
% 11.09/11.31 tff(27504,plain,
% 11.09/11.31 (r(s(s(elem!1)), elem!1)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[872, 4017, 249])).
% 11.09/11.31 tff(27505,plain,
% 11.09/11.31 ($false),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[5875, 27504, 27503, 233, 410])).
% 11.09/11.31 tff(27506,plain,(b(s(s(elem!1)), elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | r(elem!1, z) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(elem!1)) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.31 tff(27507,plain,
% 11.09/11.31 (s(s(elem!1)) = elem!1),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[27506, 27469, 410, 233, 2282, 174, 10682, 27359, 168, 7437, 10902, 2913, 1526, 90, 448, 27383])).
% 11.09/11.31 tff(27508,plain,
% 11.09/11.31 ($false),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[451, 27507, 27433])).
% 11.09/11.31 tff(27509,plain,(r(elem!1, z) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (z = elem!1) | b(s(z), s(s(s(s(z))))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.31 tff(27510,plain,
% 11.09/11.31 (~r(elem!1, s(s(s(elem!1))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[27509, 27265, 88, 22898, 27250, 27232, 27259, 27252, 27246, 98, 2881, 426])).
% 11.09/11.31 tff(27511,plain,
% 11.09/11.31 (z = elem!1),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[27381, 802, 168, 2282, 448, 233, 2881, 1628, 10682, 174, 1526, 90])).
% 11.09/11.31 tff(27512,plain,
% 11.09/11.31 (b(z, s(z)) <=> b(elem!1, s(z))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27511])).
% 11.09/11.31 tff(27513,plain,
% 11.09/11.31 (b(elem!1, s(z)) <=> b(z, s(z))),
% 11.09/11.31 inference(symmetry,[status(thm)],[27512])).
% 11.09/11.31 tff(27514,plain,
% 11.09/11.31 (s(z) = s(elem!1)),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27511])).
% 11.09/11.31 tff(27515,plain,
% 11.09/11.31 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27514])).
% 11.09/11.31 tff(27516,plain,
% 11.09/11.31 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 11.09/11.31 inference(symmetry,[status(thm)],[27515])).
% 11.09/11.31 tff(27517,plain,
% 11.09/11.31 (b(elem!1, s(elem!1)) <=> b(z, s(z))),
% 11.09/11.31 inference(transitivity,[status(thm)],[27516, 27513])).
% 11.09/11.31 tff(27518,plain,
% 11.09/11.31 (b(z, s(z))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[802, 27517])).
% 11.09/11.31 tff(27519,plain,
% 11.09/11.31 (~b(s(z), s(s(s(elem!1))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[15561, 27518, 1526, 10682])).
% 11.09/11.31 tff(27520,plain,
% 11.09/11.31 (r(s(z), s(s(s(elem!1))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[247, 27519])).
% 11.09/11.31 tff(27521,plain,
% 11.09/11.31 (s(s(z)) = s(s(elem!1))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27514])).
% 11.09/11.31 tff(27522,plain,
% 11.09/11.31 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27514, 27521])).
% 11.09/11.31 tff(27523,plain,
% 11.09/11.31 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 11.09/11.31 inference(symmetry,[status(thm)],[27522])).
% 11.09/11.31 tff(27524,plain,
% 11.09/11.31 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(z), s(s(z))))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27523])).
% 11.09/11.31 tff(27525,plain,
% 11.09/11.31 (elem!1 = z),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[97, 27511])).
% 11.09/11.31 tff(27526,plain,
% 11.09/11.31 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[8883, 27525])).
% 11.09/11.31 tff(27527,plain,
% 11.09/11.31 (r(s(s(s(z))), z)),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[4409, 27525, 174])).
% 11.09/11.31 tff(27528,plain,
% 11.09/11.31 (r(s(z), s(s(s(z))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[23224, 27520, 27525])).
% 11.09/11.31 tff(27529,plain,
% 11.09/11.31 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[23238, 27528, 2913, 27527, 27525])).
% 11.09/11.31 tff(27530,plain,
% 11.09/11.31 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[1095, 27529, 27526])).
% 11.09/11.31 tff(27531,plain,
% 11.09/11.31 (s(s(s(z))) = s(s(s(elem!1)))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27521])).
% 11.09/11.31 tff(27532,plain,
% 11.09/11.31 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27531])).
% 11.09/11.31 tff(27533,plain,
% 11.09/11.31 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27532])).
% 11.09/11.31 tff(27534,plain,
% 11.09/11.31 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27511])).
% 11.09/11.31 tff(27535,plain,
% 11.09/11.31 (b(s(s(s(s(z)))), elem!1)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[90, 27534])).
% 11.09/11.31 tff(27536,plain,
% 11.09/11.31 (b(s(s(s(s(elem!1)))), elem!1)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[27535, 27533])).
% 11.09/11.31 tff(27537,plain,
% 11.09/11.31 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27514])).
% 11.09/11.31 tff(27538,plain,
% 11.09/11.31 (b(s(s(s(elem!1))), s(elem!1))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[1526, 27537])).
% 11.09/11.31 tff(27539,plain,
% 11.09/11.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(27540,plain,
% 11.09/11.31 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 11.09/11.31 inference(rewrite,[status(thm)],[])).
% 11.09/11.31 tff(27541,plain,
% 11.09/11.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27540])).
% 11.09/11.31 tff(27542,plain,
% 11.09/11.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 11.09/11.31 inference(transitivity,[status(thm)],[27541, 27539])).
% 11.09/11.31 tff(27543,plain,
% 11.09/11.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 11.09/11.31 inference(quant_inst,[status(thm)],[])).
% 11.09/11.31 tff(27544,plain,
% 11.09/11.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[27543, 27542])).
% 11.09/11.31 tff(27545,plain,
% 11.09/11.31 ($false),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[27544, 391, 1101, 448, 7625, 2698, 1114])).
% 11.09/11.31 tff(27546,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.31 tff(27547,plain,
% 11.09/11.31 (~b(s(elem!1), s(s(elem!1)))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[27546, 27538, 448, 27536, 27530])).
% 11.09/11.31 tff(27548,plain,
% 11.09/11.31 (~b(s(z), s(s(z)))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[27547, 27524])).
% 11.09/11.31 tff(27549,plain,
% 11.09/11.31 (r(s(z), s(s(z)))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[1788, 27548])).
% 11.09/11.31 tff(27550,plain,
% 11.09/11.31 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27511])).
% 11.09/11.31 tff(27551,plain,
% 11.09/11.31 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 11.09/11.31 inference(symmetry,[status(thm)],[27550])).
% 11.09/11.31 tff(27552,plain,
% 11.09/11.31 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27521])).
% 11.09/11.31 tff(27553,plain,
% 11.09/11.31 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), z)),
% 11.09/11.31 inference(transitivity,[status(thm)],[27552, 27551])).
% 11.09/11.31 tff(27554,plain,
% 11.09/11.31 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27511])).
% 11.09/11.31 tff(27555,plain,
% 11.09/11.31 (r(s(s(z)), elem!1)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[27363, 27554])).
% 11.09/11.31 tff(27556,plain,
% 11.09/11.31 (r(s(s(elem!1)), z)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[27555, 27553])).
% 11.09/11.31 tff(27557,plain,
% 11.09/11.31 (r(s(z), z) <=> r(s(z), elem!1)),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27511])).
% 11.09/11.31 tff(27558,plain,
% 11.09/11.31 (r(s(z), elem!1)),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[27327, 27557])).
% 11.09/11.31 tff(27559,plain,
% 11.09/11.31 (~r(elem!1, s(s(s(s(elem!1)))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[14585, 27520, 233, 27558])).
% 11.09/11.31 tff(27560,plain,
% 11.09/11.31 (~r(z, s(s(s(s(z)))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[23210, 27559, 27525])).
% 11.09/11.31 tff(27561,plain,
% 11.09/11.31 (b(z, s(s(s(s(z)))))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[800, 27560])).
% 11.09/11.31 tff(27562,plain,
% 11.09/11.31 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27511])).
% 11.09/11.31 tff(27563,plain,
% 11.09/11.31 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 11.09/11.31 inference(symmetry,[status(thm)],[27562])).
% 11.09/11.31 tff(27564,plain,
% 11.09/11.31 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27531])).
% 11.09/11.31 tff(27565,plain,
% 11.09/11.31 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 11.09/11.31 inference(symmetry,[status(thm)],[27564])).
% 11.09/11.31 tff(27566,plain,
% 11.09/11.31 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 11.09/11.31 inference(transitivity,[status(thm)],[27565, 27563])).
% 11.09/11.31 tff(27567,plain,
% 11.09/11.31 (b(z, s(s(s(z))))),
% 11.09/11.31 inference(modus_ponens,[status(thm)],[448, 27566])).
% 11.09/11.31 tff(27568,plain,
% 11.09/11.31 (r(s(z), s(s(elem!1)))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[23186, 27549, 27525])).
% 11.09/11.31 tff(27569,plain,
% 11.09/11.31 (~b(s(s(z)), s(z))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[23249, 27568, 27525, 27567, 27520, 2913, 27527, 27561, 27556])).
% 11.09/11.31 tff(27570,plain,
% 11.09/11.31 (r(s(s(z)), s(z))),
% 11.09/11.31 inference(unit_resolution,[status(thm)],[3778, 27569])).
% 11.09/11.31 tff(27571,plain,
% 11.09/11.31 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 11.09/11.31 inference(monotonicity,[status(thm)],[27511])).
% 11.09/11.31 tff(27572,plain,
% 11.09/11.31 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 11.09/11.31 inference(transitivity,[status(thm)],[27571, 698])).
% 11.09/11.31 tff(27573,plain,
% 11.09/11.32 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27572])).
% 11.09/11.32 tff(27574,plain,
% 11.09/11.32 (~(elem!1 = s(s(z)))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[1207, 27573])).
% 11.09/11.32 tff(27575,plain,
% 11.09/11.32 (b(elem!1, s(z))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[802, 27516])).
% 11.09/11.32 tff(27576,plain,
% 11.09/11.32 (~r(elem!1, s(s(z)))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[14370, 27575, 233, 27558, 448])).
% 11.09/11.32 tff(27577,plain,
% 11.09/11.32 (b(elem!1, s(s(z)))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[3394, 27576, 27574])).
% 11.09/11.32 tff(27578,plain,
% 11.09/11.32 (~r(s(s(z)), s(s(s(elem!1))))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[25978, 27549, 174, 27520])).
% 11.09/11.32 tff(27579,plain,
% 11.09/11.32 (b(s(s(z)), s(s(s(elem!1))))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[11041, 27578])).
% 11.09/11.32 tff(27580,plain,
% 11.09/11.32 (r(s(s(s(elem!1))), s(s(z)))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[14450, 27579, 448, 27538, 27577])).
% 11.09/11.32 tff(27581,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[11551, 27580, 27570, 27549, 27520])).
% 11.09/11.32 tff(27582,plain,((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | b(s(s(s(elem!1))), elem!1) | r(elem!1, z) | b(s(z), s(s(s(s(z))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.32 tff(27583,plain,
% 11.09/11.32 (~b(elem!1, s(elem!1))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27582, 2282, 174, 233, 1526, 10682, 90, 168, 448, 2881, 27359])).
% 11.09/11.32 tff(27584,plain,
% 11.09/11.32 (r(elem!1, s(elem!1))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[443, 27583, 7437])).
% 11.09/11.32 tff(27585,plain,
% 11.09/11.32 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27502, 2251, 1628, 174, 10682, 233, 4017, 168, 437, 150, 1216, 1526, 90, 448, 2282])).
% 11.09/11.32 tff(27586,plain,
% 11.09/11.32 (~r(s(s(elem!1)), elem!1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[26915, 2251, 233, 27585])).
% 11.09/11.32 tff(27587,plain,
% 11.09/11.32 (s(s(elem!1)) = elem!1),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[872, 27586, 4017])).
% 11.09/11.32 tff(27588,plain,
% 11.09/11.32 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27587])).
% 11.09/11.32 tff(27589,plain,
% 11.09/11.32 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.09/11.32 inference(symmetry,[status(thm)],[27588])).
% 11.09/11.32 tff(27590,plain,
% 11.09/11.32 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27589])).
% 11.09/11.32 tff(27591,plain,
% 11.09/11.32 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[2567, 27590])).
% 11.09/11.32 tff(27592,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27585, 27591])).
% 11.09/11.32 tff(27593,plain,((~r(elem!1, s(elem!1))) | r(elem!1, s(s(s(elem!1)))) | b(s(s(elem!1)), elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(elem!1)) | (s(z) = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(elem!1))))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.32 tff(27594,plain,
% 11.09/11.32 (b(s(s(elem!1)), elem!1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27593, 27584, 2567, 233, 27359, 174, 10682, 168, 7437, 10902, 2913, 1526, 90, 448, 2282])).
% 11.09/11.32 tff(27595,plain,
% 11.09/11.32 (z = elem!1),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27468, 27584, 233, 90, 27594, 1526, 27359, 448, 2881, 174, 10682, 2282])).
% 11.09/11.32 tff(27596,plain,
% 11.09/11.32 (s(z) = s(elem!1)),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27595])).
% 11.09/11.32 tff(27597,plain,
% 11.09/11.32 (s(s(z)) = s(s(elem!1))),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27596])).
% 11.09/11.32 tff(27598,plain,
% 11.09/11.32 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27597])).
% 11.09/11.32 tff(27599,plain,
% 11.09/11.32 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 11.09/11.32 inference(symmetry,[status(thm)],[27598])).
% 11.09/11.32 tff(27600,plain,
% 11.09/11.32 (b(s(s(z)), elem!1)),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[27594, 27599])).
% 11.09/11.32 tff(27601,plain,
% 11.09/11.32 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27595])).
% 11.09/11.32 tff(27602,plain,
% 11.09/11.32 ((~b(s(s(z)), z)) <=> (~b(s(s(z)), elem!1))),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27601])).
% 11.09/11.32 tff(27603,plain,
% 11.09/11.32 (~b(s(s(z)), elem!1)),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[27362, 27602])).
% 11.09/11.32 tff(27604,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27603, 27600])).
% 11.09/11.32 tff(27605,plain,(r(elem!1, z) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | b(s(z), s(s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | r(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.32 tff(27606,plain,
% 11.09/11.32 (r(elem!1, z)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27605, 4486, 90, 1526, 448, 2881, 174, 10682, 2567, 168, 4597])).
% 11.09/11.32 tff(27607,plain,
% 11.09/11.32 (~r(z, elem!1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[23607, 27606, 174, 4486])).
% 11.09/11.32 tff(27608,plain,
% 11.09/11.32 (~r(z, s(elem!1))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[4255, 27606, 174, 4486])).
% 11.09/11.32 tff(27609,plain,
% 11.09/11.32 (b(z, s(elem!1))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[566, 27608])).
% 11.09/11.32 tff(27610,plain,
% 11.09/11.32 (~r(z, s(z))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[4113, 27606, 174, 4486])).
% 11.09/11.32 tff(27611,plain,
% 11.09/11.32 (b(z, s(z))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[678, 27610])).
% 11.09/11.32 tff(27612,plain,
% 11.09/11.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(27613,plain,
% 11.09/11.32 (((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(27614,plain,
% 11.09/11.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))))),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27613])).
% 11.09/11.32 tff(27615,plain,
% 11.09/11.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 11.09/11.32 inference(transitivity,[status(thm)],[27614, 27612])).
% 11.09/11.32 tff(27616,plain,
% 11.09/11.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 11.09/11.32 inference(quant_inst,[status(thm)],[])).
% 11.09/11.32 tff(27617,plain,
% 11.09/11.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[27616, 27615])).
% 11.09/11.32 tff(27618,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27617, 194, 530, 174, 233, 326])).
% 11.09/11.32 tff(27619,plain,((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.32 tff(27620,plain,
% 11.09/11.32 (~r(z, s(s(elem!1)))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27619, 27606, 174, 4486])).
% 11.09/11.32 tff(27621,plain,
% 11.09/11.32 (b(z, s(s(elem!1)))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[324, 27620])).
% 11.09/11.32 tff(27622,plain,
% 11.09/11.32 (~b(z, elem!1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[26924, 27621, 10682, 448, 27606, 4486, 1526, 27611, 10902, 168, 4597, 27609])).
% 11.09/11.32 tff(27623,plain,
% 11.09/11.32 (z = elem!1),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[141, 27622, 27607])).
% 11.09/11.32 tff(27624,plain,
% 11.09/11.32 (r(elem!1, z) <=> r(elem!1, elem!1)),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27623])).
% 11.09/11.32 tff(27625,plain,
% 11.09/11.32 (r(elem!1, elem!1) <=> r(elem!1, z)),
% 11.09/11.32 inference(symmetry,[status(thm)],[27624])).
% 11.09/11.32 tff(27626,plain,
% 11.09/11.32 ((~r(elem!1, elem!1)) <=> (~r(elem!1, z))),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27625])).
% 11.09/11.32 tff(27627,plain,
% 11.09/11.32 (~r(elem!1, z)),
% 11.09/11.32 inference(modus_ponens,[status(thm)],[17665, 27626])).
% 11.09/11.32 tff(27628,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27606, 27627])).
% 11.09/11.32 tff(27629,plain,(b(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | r(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.32 tff(27630,plain,
% 11.09/11.32 ($false),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27629, 27510, 27265, 88, 22898, 2881, 27232, 27250, 27252, 9])).
% 11.09/11.32 tff(27631,plain,((~r(s(z), elem!1)) | b(s(z), s(s(s(s(z))))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (elem!1 = z) | r(s(s(s(s(z)))), z) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.32 tff(27632,plain,
% 11.09/11.32 (~r(s(z), elem!1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[27631, 1, 2881, 133, 721, 182, 2, 81, 1549])).
% 11.09/11.32 tff(27633,plain,
% 11.09/11.32 (b(s(z), elem!1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[632, 27632, 21435])).
% 11.09/11.32 tff(27634,plain,
% 11.09/11.32 (~(s(s(s(s(z)))) = elem!1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[6252, 27633, 2881])).
% 11.09/11.32 tff(27635,plain,
% 11.09/11.32 (r(s(s(s(s(z)))), elem!1)),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[762, 27634, 1549])).
% 11.09/11.32 tff(27636,plain,
% 11.09/11.32 (~r(z, s(s(s(s(z)))))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[2720, 27635, 182, 2913])).
% 11.09/11.32 tff(27637,plain,
% 11.09/11.32 (b(z, s(s(s(s(z)))))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[800, 27636])).
% 11.09/11.32 tff(27638,plain,
% 11.09/11.32 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[23918, 27637, 88, 22898])).
% 11.09/11.32 tff(27639,plain,
% 11.09/11.32 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[15351, 27638, 21770])).
% 11.09/11.32 tff(27640,plain,
% 11.09/11.32 (~(elem!1 = s(s(s(s(z)))))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[769, 27634])).
% 11.09/11.32 tff(27641,plain,
% 11.09/11.32 (r(elem!1, s(s(s(s(z)))))),
% 11.09/11.32 inference(unit_resolution,[status(thm)],[781, 27640, 27233])).
% 11.09/11.32 tff(27642,plain,
% 11.09/11.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(27643,plain,
% 11.09/11.32 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.09/11.32 inference(rewrite,[status(thm)],[])).
% 11.09/11.32 tff(27644,plain,
% 11.09/11.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 11.09/11.32 inference(monotonicity,[status(thm)],[27643])).
% 11.09/11.33 tff(27645,plain,
% 11.09/11.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.09/11.33 inference(transitivity,[status(thm)],[27644, 27642])).
% 11.09/11.33 tff(27646,plain,
% 11.09/11.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.09/11.33 inference(quant_inst,[status(thm)],[])).
% 11.09/11.33 tff(27647,plain,
% 11.09/11.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[27646, 27645])).
% 11.09/11.33 tff(27648,plain,
% 11.09/11.33 ($false),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[27647, 194, 27259, 27641, 27635, 27639])).
% 11.09/11.33 tff(27649,plain,((elem!1 = s(s(s(elem!1)))) | (~r(s(z), z)) | b(s(s(s(s(z)))), elem!1) | b(s(z), s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (elem!1 = z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.33 tff(27650,plain,
% 11.09/11.33 (elem!1 = s(s(s(elem!1)))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[27649, 1549, 182, 27210, 22902, 721, 2, 81])).
% 11.09/11.33 tff(27651,plain,
% 11.09/11.33 (s(elem!1) = s(s(s(s(elem!1))))),
% 11.09/11.33 inference(monotonicity,[status(thm)],[27650])).
% 11.09/11.33 tff(27652,plain,
% 11.09/11.33 (s(s(s(s(elem!1)))) = s(elem!1)),
% 11.09/11.33 inference(symmetry,[status(thm)],[27651])).
% 11.09/11.33 tff(27653,plain,
% 11.09/11.33 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(elem!1), s(z))),
% 11.09/11.33 inference(monotonicity,[status(thm)],[27652])).
% 11.09/11.33 tff(27654,plain,
% 11.09/11.33 (b(s(elem!1), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 11.09/11.33 inference(symmetry,[status(thm)],[27653])).
% 11.09/11.33 tff(27655,plain,
% 11.09/11.33 (r(s(z), s(s(s(s(z)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[1230, 27210])).
% 11.09/11.33 tff(27656,plain,
% 11.09/11.33 (s(s(s(elem!1))) = elem!1),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[129, 27650])).
% 11.09/11.33 tff(27657,plain,
% 11.09/11.33 (~(s(s(s(s(z)))) = elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[1436, 27656])).
% 11.09/11.33 tff(27658,plain,
% 11.09/11.33 (~(elem!1 = s(s(s(s(z)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[769, 27657])).
% 11.09/11.33 tff(27659,plain,
% 11.09/11.33 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[2694, 27656, 1549])).
% 11.09/11.33 tff(27660,plain,
% 11.09/11.33 (~r(z, s(s(s(s(z)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[2108, 27659, 182, 27655])).
% 11.09/11.33 tff(27661,plain,
% 11.09/11.33 (b(z, s(s(s(s(z)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[800, 27660])).
% 11.09/11.33 tff(27662,plain,
% 11.09/11.33 (~b(elem!1, s(s(s(s(z)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[22981, 27661, 88, 22902])).
% 11.09/11.33 tff(27663,plain,
% 11.09/11.33 (~r(s(z), elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[27237, 27662, 27655, 1549, 27658])).
% 11.09/11.33 tff(27664,plain,
% 11.09/11.33 (b(s(z), elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[632, 27663, 21435])).
% 11.09/11.33 tff(27665,plain,
% 11.09/11.33 (~b(z, s(z))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[23112, 27664, 22902, 721])).
% 11.09/11.33 tff(27666,plain,
% 11.09/11.33 (r(z, s(z))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[678, 27665])).
% 11.09/11.33 tff(27667,plain,
% 11.09/11.33 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[23918, 27661, 88, 22898])).
% 11.09/11.33 tff(27668,plain,
% 11.09/11.33 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[15351, 27667, 21770])).
% 11.09/11.33 tff(27669,plain,
% 11.09/11.33 (r(s(s(s(s(z)))), elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[762, 27657, 1549])).
% 11.09/11.33 tff(27670,plain,
% 11.09/11.33 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[20997, 27664, 721, 27655, 27650, 27669, 27668])).
% 11.09/11.33 tff(27671,plain,
% 11.09/11.33 (b(s(s(z)), s(s(s(s(z)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[3652, 27670])).
% 11.09/11.33 tff(27672,plain,
% 11.09/11.33 (~b(s(s(z)), z)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[5136, 27671, 88, 22902, 721])).
% 11.09/11.33 tff(27673,plain,
% 11.09/11.33 (r(s(s(z)), z)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[1211, 27672])).
% 11.09/11.33 tff(27674,plain,
% 11.09/11.33 (~r(elem!1, s(z))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[24995, 27662, 27655, 1549, 27657])).
% 11.09/11.33 tff(27675,plain,
% 11.09/11.33 (~r(s(s(s(elem!1))), s(z))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[8406, 27674, 27656])).
% 11.09/11.33 tff(27676,plain,
% 11.09/11.33 (b(s(s(s(elem!1))), s(z))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[223, 27675])).
% 11.09/11.33 tff(27677,plain,
% 11.09/11.33 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[25141, 27676, 88, 22898, 21769, 27655])).
% 11.09/11.33 tff(27678,plain,
% 11.09/11.33 (b(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[1714, 27677])).
% 11.09/11.33 tff(27679,plain,
% 11.09/11.33 (~b(z, s(s(z)))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[15550, 27678, 27671, 27661])).
% 11.09/11.33 tff(27680,plain,
% 11.09/11.33 (r(z, s(s(z)))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[18613, 27679])).
% 11.09/11.33 tff(27681,plain,
% 11.09/11.33 (~r(s(z), s(s(z)))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[20649, 27680, 182, 27673])).
% 11.09/11.33 tff(27682,plain,
% 11.09/11.33 (b(s(z), s(s(z)))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[1788, 27681])).
% 11.09/11.33 tff(27683,plain,
% 11.09/11.33 (s(s(s(elem!1))) = elem!1),
% 11.09/11.33 inference(symmetry,[status(thm)],[27650])).
% 11.09/11.33 tff(27684,plain,
% 11.09/11.33 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.09/11.33 inference(monotonicity,[status(thm)],[27683])).
% 11.09/11.33 tff(27685,plain,
% 11.09/11.33 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 11.09/11.33 inference(transitivity,[status(thm)],[27684, 698])).
% 11.09/11.33 tff(27686,plain,
% 11.09/11.33 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 11.09/11.33 inference(monotonicity,[status(thm)],[27685])).
% 11.09/11.33 tff(27687,plain,
% 11.09/11.33 (~(elem!1 = s(s(z)))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[1397, 27686])).
% 11.09/11.33 tff(27688,plain,
% 11.09/11.33 (~r(elem!1, z)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[20742, 27687, 721, 27673, 27682, 27666, 27655])).
% 11.09/11.33 tff(27689,plain,
% 11.09/11.33 (b(elem!1, z)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[526, 27688, 2])).
% 11.09/11.33 tff(27690,plain,
% 11.09/11.33 (b(s(z), s(s(s(elem!1))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[14872, 27664, 27656])).
% 11.09/11.33 tff(27691,plain,
% 11.09/11.33 (~b(s(s(s(elem!1))), elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[2907, 27676, 721, 27690])).
% 11.09/11.33 tff(27692,plain,
% 11.09/11.33 (b(s(elem!1), elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[14657, 27688, 22902, 22898, 27691, 21435, 2])).
% 11.09/11.33 tff(27693,plain,
% 11.09/11.33 (~b(s(elem!1), z)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[7777, 27692, 22902, 27689])).
% 11.09/11.33 tff(27694,plain,
% 11.09/11.33 (r(s(elem!1), z)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[549, 27693])).
% 11.09/11.33 tff(27695,plain,
% 11.09/11.33 (~b(z, s(elem!1))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[6555, 27692, 22902, 27689])).
% 11.09/11.33 tff(27696,plain,
% 11.09/11.33 (r(z, s(elem!1))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[566, 27695])).
% 11.09/11.33 tff(27697,plain,
% 11.09/11.33 (~r(s(elem!1), s(z))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[17381, 27696, 182, 27694])).
% 11.09/11.33 tff(27698,plain,
% 11.09/11.33 (b(s(elem!1), s(z))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[13479, 27697, 124])).
% 11.09/11.33 tff(27699,plain,
% 11.09/11.33 (b(s(s(s(s(elem!1)))), s(z))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[27698, 27654])).
% 11.09/11.33 tff(27700,plain,
% 11.09/11.33 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[14662, 27692, 27691])).
% 11.09/11.33 tff(27701,plain,
% 11.09/11.33 (~(s(s(elem!1)) = s(elem!1))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[2279, 27700])).
% 11.09/11.33 tff(27702,plain,
% 11.09/11.33 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[287, 27701])).
% 11.09/11.33 tff(27703,plain,
% 11.09/11.33 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[299, 27702])).
% 11.09/11.33 tff(27704,plain,
% 11.09/11.33 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.09/11.33 inference(monotonicity,[status(thm)],[27651])).
% 11.09/11.33 tff(27705,plain,
% 11.09/11.33 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(elem!1))))),
% 11.09/11.33 inference(monotonicity,[status(thm)],[27650])).
% 11.09/11.33 tff(27706,plain,
% 11.09/11.33 (r(s(elem!1), elem!1) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.09/11.33 inference(transitivity,[status(thm)],[27705, 27704])).
% 11.09/11.33 tff(27707,plain,
% 11.09/11.33 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 11.09/11.33 inference(monotonicity,[status(thm)],[27706])).
% 11.09/11.33 tff(27708,plain,
% 11.09/11.33 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[2686, 27700])).
% 11.09/11.33 tff(27709,plain,
% 11.09/11.33 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[2711, 27708])).
% 11.09/11.33 tff(27710,plain,
% 11.09/11.33 (r(elem!1, s(s(s(s(z)))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[781, 27662, 27658])).
% 11.09/11.33 tff(27711,plain,
% 11.09/11.33 (~b(s(s(elem!1)), elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[12771, 27689, 22902, 27664])).
% 11.09/11.33 tff(27712,plain,
% 11.09/11.33 (~(s(s(elem!1)) = elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[451, 27700])).
% 11.09/11.33 tff(27713,plain,
% 11.09/11.33 (r(s(s(elem!1)), elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[872, 27712, 27711])).
% 11.09/11.33 tff(27714,plain,
% 11.09/11.33 (~r(s(elem!1), elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[13245, 27713, 27656, 27669, 27710, 27701, 27709])).
% 11.09/11.33 tff(27715,plain,
% 11.09/11.33 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[27714, 27707])).
% 11.09/11.33 tff(27716,plain,
% 11.09/11.33 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[1095, 27715, 27703])).
% 11.09/11.33 tff(27717,plain,
% 11.09/11.33 (b(s(s(s(elem!1))), z)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[9553, 27689, 27650])).
% 11.09/11.33 tff(27718,plain,
% 11.09/11.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(27719,plain,
% 11.09/11.33 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 11.09/11.33 inference(rewrite,[status(thm)],[])).
% 11.09/11.33 tff(27720,plain,
% 11.09/11.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 11.09/11.33 inference(monotonicity,[status(thm)],[27719])).
% 11.09/11.33 tff(27721,plain,
% 11.09/11.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 11.09/11.33 inference(transitivity,[status(thm)],[27720, 27718])).
% 11.09/11.33 tff(27722,plain,
% 11.09/11.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 11.09/11.33 inference(quant_inst,[status(thm)],[])).
% 11.09/11.33 tff(27723,plain,
% 11.09/11.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 11.09/11.33 inference(modus_ponens,[status(thm)],[27722, 27721])).
% 11.09/11.33 tff(27724,plain,
% 11.09/11.33 (~b(s(s(s(s(elem!1)))), s(z))),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[27723, 391, 27717, 22898, 27690, 27716])).
% 11.09/11.33 tff(27725,plain,
% 11.09/11.33 ($false),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[27724, 27699])).
% 11.09/11.33 tff(27726,plain,(b(s(s(s(s(z)))), elem!1) | (~r(s(z), z)) | (elem!1 = z) | (~b(elem!1, s(z))) | r(s(s(s(s(z)))), z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.33 tff(27727,plain,
% 11.09/11.33 (b(s(s(s(s(z)))), elem!1)),
% 11.09/11.33 inference(unit_resolution,[status(thm)],[27726, 181, 2, 26573, 81, 80])).
% 11.09/11.33 tff(27728,plain,
% 11.09/11.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 11.09/11.34 inference(rewrite,[status(thm)],[])).
% 11.09/11.34 tff(27729,plain,
% 11.09/11.34 (((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 11.09/11.34 inference(rewrite,[status(thm)],[])).
% 11.09/11.34 tff(27730,plain,
% 11.09/11.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 11.09/11.34 inference(monotonicity,[status(thm)],[27729])).
% 11.09/11.34 tff(27731,plain,
% 11.09/11.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 11.09/11.34 inference(transitivity,[status(thm)],[27730, 27728])).
% 11.09/11.34 tff(27732,plain,
% 11.09/11.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 11.09/11.34 inference(quant_inst,[status(thm)],[])).
% 11.09/11.34 tff(27733,plain,
% 11.09/11.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 11.09/11.34 inference(modus_ponens,[status(thm)],[27732, 27731])).
% 11.09/11.34 tff(27734,plain,
% 11.09/11.34 ($false),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[27733, 391, 133, 90, 1652, 1234, 721])).
% 11.09/11.34 tff(27735,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.34 tff(27736,plain,
% 11.09/11.34 (~b(s(z), s(s(s(s(z)))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[27735, 27727, 88, 22902, 26573])).
% 11.09/11.34 tff(27737,plain,
% 11.09/11.34 (b(s(s(s(elem!1))), s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[24987, 53, 88, 2881, 1])).
% 11.09/11.34 tff(27738,plain,
% 11.09/11.34 (b(elem!1, s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[25885, 53, 81, 1, 2881])).
% 11.09/11.34 tff(27739,plain,
% 11.09/11.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 11.09/11.34 inference(rewrite,[status(thm)],[])).
% 11.09/11.34 tff(27740,plain,
% 11.09/11.34 (((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 11.09/11.34 inference(rewrite,[status(thm)],[])).
% 11.09/11.34 tff(27741,plain,
% 11.09/11.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 11.09/11.34 inference(monotonicity,[status(thm)],[27740])).
% 11.09/11.34 tff(27742,plain,
% 11.09/11.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 11.09/11.34 inference(transitivity,[status(thm)],[27741, 27739])).
% 11.09/11.34 tff(27743,plain,
% 11.09/11.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 11.09/11.34 inference(quant_inst,[status(thm)],[])).
% 11.09/11.34 tff(27744,plain,
% 11.09/11.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 11.09/11.34 inference(modus_ponens,[status(thm)],[27743, 27742])).
% 11.09/11.34 tff(27745,plain,
% 11.09/11.34 ($false),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[27744, 391, 133, 27738, 27737, 88, 1652])).
% 11.09/11.34 tff(27746,plain,(r(z, s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(z)))), z) | (elem!1 = s(s(s(elem!1)))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.34 tff(27747,plain,
% 11.09/11.34 (r(z, s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[27746, 2881, 1652, 81, 1, 133])).
% 11.09/11.34 tff(27748,plain,
% 11.09/11.34 (~b(z, s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[23112, 27048, 133, 721])).
% 11.09/11.34 tff(27749,plain,
% 11.09/11.34 (r(z, s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[678, 27748])).
% 11.09/11.34 tff(27750,plain,
% 11.09/11.34 (~r(elem!1, s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[17266, 27749, 182, 530])).
% 11.09/11.34 tff(27751,plain,
% 11.09/11.34 (~b(s(s(s(elem!1))), elem!1)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[26749, 27749, 133, 27750, 27048, 1492, 27211])).
% 11.09/11.34 tff(27752,plain,
% 11.09/11.34 (r(s(s(s(elem!1))), elem!1)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[230, 27751, 9])).
% 11.09/11.34 tff(27753,plain,
% 11.09/11.34 (~r(s(s(s(elem!1))), z)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[4113, 27752, 530, 27749])).
% 11.09/11.34 tff(27754,plain,
% 11.09/11.34 (b(s(s(s(elem!1))), z)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[377, 27753])).
% 11.09/11.34 tff(27755,plain,
% 11.09/11.34 (~r(s(s(s(elem!1))), s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[23013, 27754, 90, 10682, 2913, 21769])).
% 11.09/11.34 tff(27756,plain,
% 11.09/11.34 (b(s(s(s(elem!1))), s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[223, 27755])).
% 11.09/11.34 tff(27757,plain,
% 11.09/11.34 (b(elem!1, s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[25377, 27756, 90, 10682, 1, 2881, 27751])).
% 11.09/11.34 tff(27758,plain,
% 11.09/11.34 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[25141, 27756, 90, 10682, 21769, 2913])).
% 11.09/11.34 tff(27759,plain,
% 11.09/11.34 (b(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[1714, 27758])).
% 11.09/11.34 tff(27760,plain,
% 11.09/11.34 (~b(s(s(z)), z)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[25151, 27759, 90, 10682, 27756])).
% 11.09/11.34 tff(27761,plain,
% 11.09/11.34 (r(s(s(z)), z)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[1211, 27760])).
% 11.09/11.34 tff(27762,plain,
% 11.09/11.34 (~r(s(s(z)), s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[10610, 27761, 27749, 2913])).
% 11.09/11.34 tff(27763,plain,
% 11.09/11.34 (b(s(s(z)), s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[3778, 27762])).
% 11.09/11.34 tff(27764,plain,
% 11.09/11.34 (~b(s(z), s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[4026, 27757, 27048, 27756])).
% 11.09/11.34 tff(27765,plain,
% 11.09/11.34 (r(s(z), s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[247, 27764])).
% 11.09/11.34 tff(27766,plain,
% 11.09/11.34 (~r(z, s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[241, 27765, 182, 27752])).
% 11.09/11.34 tff(27767,plain,
% 11.09/11.34 (~r(z, s(s(s(s(z)))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[26072, 27766, 182, 2913, 530, 21778, 27048])).
% 11.09/11.34 tff(27768,plain,
% 11.09/11.34 (b(z, s(s(s(s(z)))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[800, 27767])).
% 11.09/11.34 tff(27769,plain,
% 11.09/11.34 (b(s(z), s(s(z)))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[20698, 27768, 90, 182, 2881, 484, 27048, 530])).
% 11.09/11.34 tff(27770,plain,
% 11.09/11.34 ($false),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[9961, 27769, 27763, 721, 27756, 27757])).
% 11.09/11.34 tff(27771,plain,(r(s(z), elem!1) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | b(s(z), s(s(s(s(z))))) | b(elem!1, z) | (~r(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.34 tff(27772,plain,
% 11.09/11.34 (r(s(z), elem!1)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[27771, 484, 90, 182, 2881, 721, 3618, 22924, 1, 133])).
% 11.09/11.34 tff(27773,plain,
% 11.09/11.34 ($false),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[1489, 27772, 3618, 182, 184])).
% 11.09/11.34 tff(27774,plain,(b(elem!1, z) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.34 tff(27775,plain,
% 11.09/11.34 (b(elem!1, z)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[27774, 27747, 182, 88, 2881, 721, 1, 133, 2])).
% 11.09/11.34 tff(27776,plain,
% 11.09/11.34 (~b(s(s(s(elem!1))), elem!1)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[10743, 27775, 22898, 133])).
% 11.09/11.34 tff(27777,plain,
% 11.09/11.34 (~b(elem!1, s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[10895, 27775, 22898, 133, 1652, 21769])).
% 11.09/11.34 tff(27778,plain,
% 11.09/11.34 (~b(s(s(s(elem!1))), s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[25377, 27777, 88, 22898, 1, 2881, 27776])).
% 11.09/11.34 tff(27779,plain,
% 11.09/11.34 (~b(s(z), elem!1)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[12158, 27775, 133, 1652, 182])).
% 11.09/11.34 tff(27780,plain,
% 11.09/11.34 (r(s(z), elem!1)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[632, 27779, 21435])).
% 11.09/11.34 tff(27781,plain,
% 11.09/11.34 (r(elem!1, s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[424, 27777, 1])).
% 11.09/11.34 tff(27782,plain,
% 11.09/11.34 (~r(s(s(s(elem!1))), s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[26943, 27781, 133, 721, 22898, 27780, 9])).
% 11.09/11.34 tff(27783,plain,
% 11.09/11.34 ($false),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[223, 27782, 27778])).
% 11.09/11.34 tff(27784,plain,(b(s(z), s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (elem!1 = z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.34 tff(27785,plain,
% 11.09/11.34 (elem!1 = s(s(s(elem!1)))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[27784, 27736, 26573, 22902, 27727, 181, 2, 81])).
% 11.09/11.34 tff(27786,plain,
% 11.09/11.34 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[20820, 27785, 27727])).
% 11.09/11.34 tff(27787,plain,
% 11.09/11.34 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 11.09/11.34 inference(monotonicity,[status(thm)],[27785])).
% 11.09/11.34 tff(27788,plain,
% 11.09/11.34 ((~r(z, elem!1)) <=> (~r(z, s(s(s(elem!1)))))),
% 11.09/11.34 inference(monotonicity,[status(thm)],[27787])).
% 11.09/11.34 tff(27789,plain,
% 11.09/11.34 (~r(z, s(s(s(elem!1))))),
% 11.09/11.34 inference(modus_ponens,[status(thm)],[80, 27788])).
% 11.09/11.34 tff(27790,plain,
% 11.09/11.34 (r(s(s(s(elem!1))), z)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[533, 3618, 130])).
% 11.09/11.34 tff(27791,plain,
% 11.09/11.34 (~b(s(z), s(s(s(s(z)))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[27735, 1652, 90, 133, 721])).
% 11.09/11.34 tff(27792,plain,
% 11.09/11.34 (r(s(z), s(s(s(s(z)))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[1230, 27791])).
% 11.09/11.34 tff(27793,plain,
% 11.09/11.34 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[25141, 20468, 90, 22924, 21769, 27792])).
% 11.09/11.34 tff(27794,plain,
% 11.09/11.34 (b(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[1714, 27793])).
% 11.09/11.34 tff(27795,plain,
% 11.09/11.34 (~b(s(s(z)), z)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[25151, 27794, 90, 22924, 20468])).
% 11.09/11.34 tff(27796,plain,
% 11.09/11.34 (r(s(s(z)), z)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[1211, 27795])).
% 11.09/11.34 tff(27797,plain,
% 11.09/11.34 (~r(z, s(s(s(s(z)))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[26072, 644, 182, 2913, 530, 720, 53])).
% 11.09/11.34 tff(27798,plain,
% 11.09/11.34 (b(z, s(s(s(s(z)))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[800, 27797])).
% 11.09/11.34 tff(27799,plain,
% 11.09/11.34 (~b(z, s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[23112, 644, 133, 721])).
% 11.09/11.34 tff(27800,plain,
% 11.09/11.34 (r(z, s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[678, 27799])).
% 11.09/11.34 tff(27801,plain,
% 11.09/11.34 (~b(s(z), s(s(z)))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[20742, 27800, 721, 1405, 3557, 530, 2913])).
% 11.09/11.34 tff(27802,plain,
% 11.09/11.34 ($false),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[20698, 27801, 27798, 90, 182, 2881, 484, 644, 530])).
% 11.09/11.34 tff(27803,plain,((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | b(s(z), s(s(s(s(z))))) | b(elem!1, z) | (~r(elem!1, z)) | (~b(elem!1, s(z))) | (elem!1 = s(s(z))) | (~r(s(s(z)), z)) | (s(s(s(s(z)))) = elem!1) | r(z, s(s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.34 tff(27804,plain,
% 11.09/11.34 (~b(s(z), elem!1)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[27803, 484, 182, 27791, 90, 3618, 721, 3820, 27796, 2642, 53, 133])).
% 11.09/11.34 tff(27805,plain,
% 11.09/11.34 (r(s(z), elem!1)),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[632, 27804, 21435])).
% 11.09/11.34 tff(27806,plain,
% 11.09/11.34 (~r(z, s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[25179, 27805, 182, 3618])).
% 11.09/11.34 tff(27807,plain,
% 11.09/11.34 (b(z, s(z))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[678, 27806])).
% 11.09/11.34 tff(27808,plain,
% 11.09/11.34 (~b(s(z), s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[15561, 27807, 22924, 20468])).
% 11.09/11.34 tff(27809,plain,
% 11.09/11.34 (r(s(z), s(s(s(elem!1))))),
% 11.09/11.34 inference(unit_resolution,[status(thm)],[247, 27808])).
% 11.09/11.34 tff(27810,plain,
% 11.09/11.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 11.09/11.34 inference(rewrite,[status(thm)],[])).
% 11.09/11.34 tff(27811,plain,
% 11.09/11.34 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 11.09/11.34 inference(rewrite,[status(thm)],[])).
% 11.09/11.34 tff(27812,plain,
% 11.09/11.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))))),
% 11.09/11.35 inference(monotonicity,[status(thm)],[27811])).
% 11.09/11.35 tff(27813,plain,
% 11.09/11.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 11.09/11.35 inference(transitivity,[status(thm)],[27812, 27810])).
% 11.09/11.35 tff(27814,plain,
% 11.09/11.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 11.09/11.35 inference(quant_inst,[status(thm)],[])).
% 11.09/11.35 tff(27815,plain,
% 11.09/11.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))),
% 11.09/11.35 inference(modus_ponens,[status(thm)],[27814, 27813])).
% 11.09/11.35 tff(27816,plain,
% 11.09/11.35 ($false),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[27815, 194, 174, 232, 182, 719])).
% 11.09/11.35 tff(27817,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.35 tff(27818,plain,
% 11.09/11.35 (~r(z, s(s(s(s(z)))))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[27817, 27809, 27790, 182])).
% 11.09/11.35 tff(27819,plain,
% 11.09/11.35 (b(z, s(s(s(s(z)))))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[800, 27818])).
% 11.09/11.35 tff(27820,plain,
% 11.09/11.35 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[23918, 27819, 90, 22924])).
% 11.09/11.35 tff(27821,plain,
% 11.09/11.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.09/11.35 inference(rewrite,[status(thm)],[])).
% 11.09/11.35 tff(27822,plain,
% 11.09/11.35 (((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.09/11.35 inference(rewrite,[status(thm)],[])).
% 11.09/11.35 tff(27823,plain,
% 11.09/11.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 11.09/11.35 inference(monotonicity,[status(thm)],[27822])).
% 11.09/11.35 tff(27824,plain,
% 11.09/11.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.09/11.35 inference(transitivity,[status(thm)],[27823, 27821])).
% 11.09/11.35 tff(27825,plain,
% 11.09/11.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 11.09/11.35 inference(quant_inst,[status(thm)],[])).
% 11.09/11.35 tff(27826,plain,
% 11.09/11.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 11.09/11.35 inference(modus_ponens,[status(thm)],[27825, 27824])).
% 11.09/11.35 tff(27827,plain,
% 11.09/11.35 ($false),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[27826, 391, 10682, 1526, 90, 2439, 3325])).
% 11.09/11.35 tff(27828,plain,((~b(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.35 tff(27829,plain,
% 11.09/11.35 (~b(s(z), s(s(z)))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[27828, 20468, 22924, 90, 26446])).
% 11.09/11.35 tff(27830,plain,
% 11.09/11.35 (r(s(z), s(s(z)))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[1788, 27829])).
% 11.09/11.35 tff(27831,plain,
% 11.09/11.35 (~r(z, s(s(s(s(z)))))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[27817, 174, 232, 182])).
% 11.09/11.35 tff(27832,plain,
% 11.09/11.35 (b(z, s(s(s(s(z)))))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[800, 27831])).
% 11.09/11.35 tff(27833,plain,
% 11.09/11.35 (~r(z, s(s(z)))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[20649, 1747, 182, 3557])).
% 11.09/11.35 tff(27834,plain,
% 11.09/11.35 (b(z, s(s(z)))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[18613, 27833])).
% 11.09/11.35 tff(27835,plain,
% 11.09/11.35 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[22399, 27834, 721, 1652, 27832])).
% 11.09/11.35 tff(27836,plain,
% 11.09/11.35 (r(s(s(z)), s(s(s(s(z)))))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[3652, 27835])).
% 11.09/11.35 tff(27837,plain,
% 11.09/11.35 (~r(elem!1, s(s(z)))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[1775, 27836, 1652, 21435, 1759, 1747])).
% 11.09/11.35 tff(27838,plain,
% 11.09/11.35 (b(elem!1, s(s(z)))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[3394, 27837, 3820])).
% 11.09/11.35 tff(27839,plain,
% 11.09/11.35 (~b(s(s(z)), elem!1)),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[11012, 27838, 3563, 1652])).
% 11.09/11.35 tff(27840,plain,
% 11.09/11.35 (r(s(s(z)), elem!1)),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[4730, 27839, 18819])).
% 11.09/11.35 tff(27841,plain,
% 11.09/11.35 (r(s(s(z)), s(s(s(elem!1))))),
% 11.09/11.35 inference(modus_ponens,[status(thm)],[27840, 25968])).
% 11.09/11.35 tff(27842,plain,
% 11.09/11.35 (~r(s(s(z)), s(s(s(elem!1))))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[25978, 1747, 174, 232])).
% 11.09/11.35 tff(27843,plain,
% 11.09/11.35 ($false),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[27842, 27841])).
% 11.09/11.35 tff(27844,plain,((~r(s(z), s(s(z)))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.35 tff(27845,plain,
% 11.09/11.35 (~b(s(s(s(s(z)))), s(z))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[27844, 27809, 27794, 1652, 125, 721, 27830, 27790, 182, 27796])).
% 11.09/11.35 tff(27846,plain,
% 11.09/11.35 (r(s(s(s(s(z)))), s(z))),
% 11.09/11.35 inference(unit_resolution,[status(thm)],[749, 27845])).
% 11.09/11.35 tff(27847,plain,
% 11.09/11.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.09/11.35 inference(rewrite,[status(thm)],[])).
% 11.09/11.35 tff(27848,plain,
% 11.09/11.35 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.09/11.36 inference(rewrite,[status(thm)],[])).
% 11.09/11.36 tff(27849,plain,
% 11.09/11.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27848])).
% 11.09/11.36 tff(27850,plain,
% 11.09/11.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.09/11.36 inference(transitivity,[status(thm)],[27849, 27847])).
% 11.09/11.36 tff(27851,plain,
% 11.09/11.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 11.09/11.36 inference(quant_inst,[status(thm)],[])).
% 11.09/11.36 tff(27852,plain,
% 11.09/11.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.09/11.36 inference(modus_ponens,[status(thm)],[27851, 27850])).
% 11.09/11.36 tff(27853,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27852, 194, 232, 1216, 723, 4317])).
% 11.09/11.36 tff(27854,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27855,plain,
% 11.09/11.36 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27854, 27846, 27792, 27809])).
% 11.09/11.36 tff(27856,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[15351, 27855, 27820, 21770])).
% 11.09/11.36 tff(27857,plain,(b(elem!1, z) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~r(s(z), z)) | r(z, s(s(s(elem!1)))) | (~b(z, elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27858,plain,
% 11.09/11.36 (b(elem!1, z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27857, 27727, 88, 27785, 26573, 181, 27789, 22902, 2])).
% 11.09/11.36 tff(27859,plain,
% 11.09/11.36 (b(s(s(s(elem!1))), z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[9553, 27858, 27785])).
% 11.09/11.36 tff(27860,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[23009, 391, 27859, 22898, 88, 27786])).
% 11.09/11.36 tff(27861,plain,(b(s(z), z) | (elem!1 = z) | r(z, elem!1) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27862,plain,
% 11.09/11.36 (b(s(z), z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27861, 80, 2, 81])).
% 11.09/11.36 tff(27863,plain,
% 11.09/11.36 (~(s(z) = elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[7485, 484, 175])).
% 11.09/11.36 tff(27864,plain,
% 11.09/11.36 (~(elem!1 = s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[172, 27863])).
% 11.09/11.36 tff(27865,plain,
% 11.09/11.36 (r(elem!1, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[837, 27864, 31])).
% 11.09/11.36 tff(27866,plain,
% 11.09/11.36 (b(elem!1, s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[24995, 27865, 2913, 1549, 21778])).
% 11.09/11.36 tff(27867,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[25386, 27866, 90, 22924, 133])).
% 11.09/11.36 tff(27868,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[230, 27867, 9])).
% 11.09/11.36 tff(27869,plain,
% 11.09/11.36 (~r(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[10856, 27868, 2913, 27865])).
% 11.09/11.36 tff(27870,plain,
% 11.09/11.36 (b(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[223, 27869])).
% 11.09/11.36 tff(27871,plain,
% 11.09/11.36 (b(elem!1, s(s(s(elem!1))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[25377, 27870, 90, 22924, 1, 2881, 27867])).
% 11.09/11.36 tff(27872,plain,
% 11.09/11.36 (~b(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[10690, 27870, 22924, 590])).
% 11.09/11.36 tff(27873,plain,
% 11.09/11.36 (r(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[678, 27872])).
% 11.09/11.36 tff(27874,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[18052, 27873, 27871, 133, 22924, 31, 3618, 27863, 9])).
% 11.09/11.36 tff(27875,plain,(b(elem!1, z) | (~b(z, elem!1)) | b(elem!1, s(z)) | (~b(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(elem!1)))) | b(s(z), s(s(s(s(z))))) | (~b(s(z), z)) | b(s(s(s(s(z)))), elem!1) | r(s(z), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27876,plain,
% 11.09/11.36 (b(elem!1, z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27875, 175, 31, 90, 1, 2881, 590, 1549, 22902, 2])).
% 11.09/11.36 tff(27877,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[10743, 27876, 22924, 22902])).
% 11.09/11.36 tff(27878,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[230, 27877, 9])).
% 11.09/11.36 tff(27879,plain,
% 11.09/11.36 (~b(elem!1, s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[12445, 27876, 90, 22902])).
% 11.09/11.36 tff(27880,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[25033, 27879, 22924, 590, 2913, 27877, 118, 31, 22902, 27878, 27876])).
% 11.09/11.36 tff(27881,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[223, 27880])).
% 11.09/11.36 tff(27882,plain,
% 11.09/11.36 (~r(elem!1, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[10856, 27881, 2913, 27878])).
% 11.09/11.36 tff(27883,plain,
% 11.09/11.36 (elem!1 = s(z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[837, 27882, 31])).
% 11.09/11.36 tff(27884,plain,
% 11.09/11.36 (s(elem!1) = s(s(z))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27883])).
% 11.09/11.36 tff(27885,plain,
% 11.09/11.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27884])).
% 11.09/11.36 tff(27886,plain,
% 11.09/11.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(elem!1))))),
% 11.09/11.36 inference(transitivity,[status(thm)],[27885, 10700])).
% 11.09/11.36 tff(27887,plain,
% 11.09/11.36 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 11.09/11.36 inference(symmetry,[status(thm)],[27886])).
% 11.09/11.36 tff(27888,plain,
% 11.09/11.36 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27887])).
% 11.09/11.36 tff(27889,plain,
% 11.09/11.36 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.09/11.36 inference(modus_ponens,[status(thm)],[1397, 27888])).
% 11.09/11.36 tff(27890,plain,
% 11.09/11.36 (~b(elem!1, s(s(s(elem!1))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[8314, 27883, 2881])).
% 11.09/11.36 tff(27891,plain,
% 11.09/11.36 (s(z) = elem!1),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[172, 27883])).
% 11.09/11.36 tff(27892,plain,
% 11.09/11.36 (r(z, s(s(s(elem!1))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[24987, 27880, 90, 2881, 1])).
% 11.09/11.36 tff(27893,plain,
% 11.09/11.36 (s(s(z)) = s(elem!1)),
% 11.09/11.36 inference(symmetry,[status(thm)],[27884])).
% 11.09/11.36 tff(27894,plain,
% 11.09/11.36 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27893])).
% 11.09/11.36 tff(27895,plain,
% 11.09/11.36 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27894])).
% 11.09/11.36 tff(27896,plain,
% 11.09/11.36 (~(s(s(elem!1)) = s(elem!1))),
% 11.09/11.36 inference(modus_ponens,[status(thm)],[2680, 27895])).
% 11.09/11.36 tff(27897,plain,
% 11.09/11.36 (~b(s(elem!1), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[7822, 27896, 22902, 175, 27892, 27891, 27878, 27876])).
% 11.09/11.36 tff(27898,plain,
% 11.09/11.36 (r(s(elem!1), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[2168, 27897, 426])).
% 11.09/11.36 tff(27899,plain,
% 11.09/11.36 (~r(s(s(s(elem!1))), s(elem!1))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[13054, 27898, 9, 27877, 27890])).
% 11.09/11.36 tff(27900,plain,
% 11.09/11.36 (s(z) = elem!1),
% 11.09/11.36 inference(symmetry,[status(thm)],[27883])).
% 11.09/11.36 tff(27901,plain,
% 11.09/11.36 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27900])).
% 11.09/11.36 tff(27902,plain,
% 11.09/11.36 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27901])).
% 11.09/11.36 tff(27903,plain,
% 11.09/11.36 (~(s(s(elem!1)) = elem!1)),
% 11.09/11.36 inference(modus_ponens,[status(thm)],[357, 27902])).
% 11.09/11.36 tff(27904,plain,
% 11.09/11.36 (s(s(elem!1)) = s(s(s(z)))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27884])).
% 11.09/11.36 tff(27905,plain,
% 11.09/11.36 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27904])).
% 11.09/11.36 tff(27906,plain,
% 11.09/11.36 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27905])).
% 11.09/11.36 tff(27907,plain,
% 11.09/11.36 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27906, 27904])).
% 11.09/11.36 tff(27908,plain,
% 11.09/11.36 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 11.09/11.36 inference(transitivity,[status(thm)],[27907, 8583])).
% 11.09/11.36 tff(27909,plain,
% 11.09/11.36 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 11.09/11.36 inference(symmetry,[status(thm)],[27908])).
% 11.09/11.36 tff(27910,plain,
% 11.09/11.36 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 11.09/11.36 inference(transitivity,[status(thm)],[27909, 1021])).
% 11.09/11.36 tff(27911,plain,
% 11.09/11.36 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27910])).
% 11.09/11.36 tff(27912,plain,
% 11.09/11.36 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 11.09/11.36 inference(modus_ponens,[status(thm)],[8593, 27911])).
% 11.09/11.36 tff(27913,plain,
% 11.09/11.36 (~r(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[17233, 27891, 80])).
% 11.09/11.36 tff(27914,plain,
% 11.09/11.36 (b(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[678, 27913])).
% 11.09/11.36 tff(27915,plain,
% 11.09/11.36 (~b(s(s(s(s(z)))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[11177, 27883, 27880])).
% 11.09/11.36 tff(27916,plain,
% 11.09/11.36 (r(s(s(s(s(z)))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[749, 27915])).
% 11.09/11.36 tff(27917,plain,
% 11.09/11.36 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 11.09/11.36 inference(monotonicity,[status(thm)],[27905])).
% 11.09/11.36 tff(27918,plain,
% 11.09/11.36 (r(z, s(s(s(s(z)))))),
% 11.09/11.36 inference(modus_ponens,[status(thm)],[27892, 27917])).
% 11.09/11.36 tff(27919,plain,
% 11.09/11.36 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[16415, 27918, 590, 27914, 27916, 2913])).
% 11.09/11.36 tff(27920,plain,
% 11.09/11.36 (b(s(s(z)), s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[3652, 27919])).
% 11.09/11.36 tff(27921,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), s(elem!1))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[7579, 27920, 27891, 27914, 27892, 27890, 27912, 27876, 27896, 27903, 590, 27044])).
% 11.09/11.36 tff(27922,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[588, 27921, 27899, 27889])).
% 11.09/11.36 tff(27923,plain,(r(s(z), z) | (~b(s(z), z)) | r(z, elem!1) | b(s(z), s(s(s(s(z))))) | b(elem!1, s(z)) | (~b(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(elem!1)))) | b(s(s(s(s(z)))), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27924,plain,
% 11.09/11.36 (r(s(z), z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27923, 1549, 80, 2881, 31, 90, 1, 590, 2])).
% 11.09/11.36 tff(27925,plain,
% 11.09/11.36 (r(elem!1, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[24990, 27924, 31, 1549, 90, 2881])).
% 11.09/11.36 tff(27926,plain,
% 11.09/11.36 (~r(z, s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[22971, 27924, 31, 2913, 1549])).
% 11.09/11.36 tff(27927,plain,
% 11.09/11.36 (b(z, s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[800, 27926])).
% 11.09/11.36 tff(27928,plain,
% 11.09/11.36 (~b(elem!1, s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[22981, 27927, 90, 22902])).
% 11.09/11.36 tff(27929,plain,
% 11.09/11.36 (s(s(s(s(z)))) = elem!1),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[24995, 27928, 2913, 1549, 27925])).
% 11.09/11.36 tff(27930,plain,
% 11.09/11.36 (elem!1 = s(s(s(s(z))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[16908, 27929])).
% 11.09/11.36 tff(27931,plain,
% 11.09/11.36 (b(elem!1, z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[16358, 27930, 90])).
% 11.09/11.36 tff(27932,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[10743, 27931, 22924, 22902])).
% 11.09/11.36 tff(27933,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[230, 27932, 9])).
% 11.09/11.36 tff(27934,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[25033, 27932, 22924, 590, 2913, 27928, 118, 31, 22902, 27933, 27931])).
% 11.09/11.36 tff(27935,plain,
% 11.09/11.36 (~r(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[10856, 27933, 2913, 27925])).
% 11.09/11.36 tff(27936,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[223, 27935, 27934])).
% 11.09/11.36 tff(27937,plain,(b(s(s(s(s(z)))), elem!1) | (~b(s(z), z)) | b(elem!1, s(z)) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | r(z, elem!1) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27938,plain,
% 11.09/11.36 (b(s(s(s(s(z)))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27937, 2881, 31, 88, 27862, 80, 1, 2])).
% 11.09/11.36 tff(27939,plain,
% 11.09/11.36 (r(z, s(s(s(elem!1))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27746, 27938, 1, 81, 2881, 22902])).
% 11.09/11.36 tff(27940,plain,
% 11.09/11.36 (~b(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[14978, 665, 90, 590, 1652])).
% 11.09/11.36 tff(27941,plain,
% 11.09/11.36 (r(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[678, 27940])).
% 11.09/11.36 tff(27942,plain,
% 11.09/11.36 (~(s(z) = elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[17233, 27941, 80])).
% 11.09/11.36 tff(27943,plain,
% 11.09/11.36 (~(elem!1 = s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[172, 27942])).
% 11.09/11.36 tff(27944,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[230, 26492, 127])).
% 11.09/11.36 tff(27945,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[25033, 27944, 10682, 590, 1216, 26492, 121, 31, 133, 665, 26932])).
% 11.09/11.36 tff(27946,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[223, 27945])).
% 11.09/11.36 tff(27947,plain,
% 11.09/11.36 (~r(elem!1, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[10856, 27946, 1216, 27944])).
% 11.09/11.36 tff(27948,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[837, 27947, 27943, 31])).
% 11.09/11.36 tff(27949,plain,((~b(elem!1, z)) | b(elem!1, s(z)) | (~r(s(z), s(s(s(s(z)))))) | r(z, elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27950,plain,
% 11.09/11.36 (~b(elem!1, z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27949, 2913, 31, 80, 22898, 27862, 118, 22902, 9, 88, 27938])).
% 11.09/11.36 tff(27951,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[6505, 484, 133, 184, 27863, 427, 1, 2])).
% 11.09/11.36 tff(27952,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[230, 27951, 9])).
% 11.09/11.36 tff(27953,plain,
% 11.09/11.36 (~r(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[10856, 27952, 1216, 27865])).
% 11.09/11.36 tff(27954,plain,
% 11.09/11.36 (b(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[223, 27953])).
% 11.09/11.36 tff(27955,plain,
% 11.09/11.36 (~b(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[10690, 27954, 10682, 590])).
% 11.09/11.36 tff(27956,plain,
% 11.09/11.36 (~r(elem!1, s(s(s(elem!1))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[4772, 27952, 184, 3618])).
% 11.09/11.36 tff(27957,plain,
% 11.09/11.36 (b(elem!1, s(s(s(elem!1))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[424, 27956, 1])).
% 11.09/11.36 tff(27958,plain,
% 11.09/11.36 (~r(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[18052, 27957, 133, 10682, 31, 3618, 27863, 9])).
% 11.09/11.36 tff(27959,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[678, 27958, 27955])).
% 11.09/11.36 tff(27960,plain,(b(elem!1, z) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(z)) | (~b(s(z), z)) | (elem!1 = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (elem!1 = z) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27961,plain,
% 11.09/11.36 (r(s(z), z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27960, 27950, 22898, 31, 27862, 1, 27939, 2913, 2, 22902])).
% 11.09/11.36 tff(27962,plain,
% 11.09/11.36 (r(elem!1, z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[526, 27950, 2])).
% 11.09/11.36 tff(27963,plain,
% 11.09/11.36 (~r(elem!1, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[5941, 27961, 27939, 27962])).
% 11.09/11.36 tff(27964,plain,
% 11.09/11.36 (elem!1 = s(z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[837, 27963, 31])).
% 11.09/11.36 tff(27965,plain,
% 11.09/11.36 (s(z) = elem!1),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[172, 27964])).
% 11.09/11.36 tff(27966,plain,
% 11.09/11.36 (b(s(s(s(s(z)))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[9614, 27965, 27938])).
% 11.09/11.36 tff(27967,plain,
% 11.09/11.36 (~r(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[17233, 27965, 80])).
% 11.09/11.36 tff(27968,plain,
% 11.09/11.36 (b(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[678, 27967])).
% 11.09/11.36 tff(27969,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[25901, 27968, 27966, 31, 22898, 1, 27962, 2881, 81, 27961, 22902])).
% 11.09/11.36 tff(27970,plain,(b(s(z), s(s(s(s(z))))) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | r(s(s(s(s(z)))), z) | r(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27971,plain,
% 11.09/11.36 (b(s(z), s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27970, 1, 31, 81, 80, 2])).
% 11.09/11.36 tff(27972,plain,
% 11.09/11.36 (~b(z, s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[22664, 27971, 88, 27862])).
% 11.09/11.36 tff(27973,plain,
% 11.09/11.36 (~r(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[17233, 812, 80])).
% 11.09/11.36 tff(27974,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[11318, 27973, 7866, 2, 10644])).
% 11.09/11.36 tff(27975,plain,((~(s(z) = elem!1)) | (elem!1 = z) | b(z, s(s(s(s(z))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27976,plain,
% 11.09/11.36 (~(s(z) = elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27975, 27972, 2, 80])).
% 11.09/11.36 tff(27977,plain,
% 11.09/11.36 (~(elem!1 = s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[172, 27976])).
% 11.09/11.36 tff(27978,plain,
% 11.09/11.36 (r(elem!1, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[837, 27977, 31])).
% 11.09/11.36 tff(27979,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[25386, 2064, 90, 10682, 133])).
% 11.09/11.36 tff(27980,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[230, 27979, 127])).
% 11.09/11.36 tff(27981,plain,
% 11.09/11.36 (~b(s(z), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[6418, 2064, 90, 133, 1234])).
% 11.09/11.36 tff(27982,plain,
% 11.09/11.36 (r(s(z), elem!1)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[632, 27981, 150])).
% 11.09/11.36 tff(27983,plain,
% 11.09/11.36 (~r(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[23283, 27982, 530, 27980])).
% 11.09/11.36 tff(27984,plain,
% 11.09/11.36 (b(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[223, 27983])).
% 11.09/11.36 tff(27985,plain,
% 11.09/11.36 (~b(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[10690, 27984, 10682, 590])).
% 11.09/11.36 tff(27986,plain,
% 11.09/11.36 (r(z, s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[678, 27985])).
% 11.09/11.36 tff(27987,plain,
% 11.09/11.36 (~r(s(z), s(s(s(elem!1))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[5246, 27980, 31, 150, 27981])).
% 11.09/11.36 tff(27988,plain,
% 11.09/11.36 (b(s(z), s(s(s(elem!1))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[247, 27987])).
% 11.09/11.36 tff(27989,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[11303, 27988, 10682, 590])).
% 11.09/11.36 tff(27990,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[377, 27989])).
% 11.09/11.36 tff(27991,plain,
% 11.09/11.36 ($false),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[4113, 27990, 27986, 530, 27980])).
% 11.09/11.36 tff(27992,plain,((~b(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | b(elem!1, s(z)) | (s(z) = elem!1) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.36 tff(27993,plain,
% 11.09/11.36 (~b(elem!1, s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[27992, 3618, 22924, 590, 31, 150, 9, 90, 133, 1234])).
% 11.09/11.36 tff(27994,plain,
% 11.09/11.36 (r(elem!1, s(s(s(s(z)))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[781, 27993, 21768])).
% 11.09/11.36 tff(27995,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[6382, 27994, 133, 90, 22666, 3363, 838, 3618, 590])).
% 11.09/11.36 tff(27996,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), s(z))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[223, 27995])).
% 11.09/11.36 tff(27997,plain,
% 11.09/11.36 (~r(s(z), s(s(s(elem!1))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[22961, 27996, 22924, 133, 1, 838])).
% 11.09/11.36 tff(27998,plain,
% 11.09/11.36 (b(s(z), s(s(s(elem!1))))),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[247, 27997])).
% 11.09/11.36 tff(27999,plain,
% 11.09/11.36 (~b(s(s(s(elem!1))), z)),
% 11.09/11.36 inference(unit_resolution,[status(thm)],[11303, 27998, 22924, 590])).
% 11.09/11.36 tff(28000,plain,
% 11.09/11.36 (r(s(s(s(elem!1))), z)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[377, 27999])).
% 11.09/11.37 tff(28001,plain,
% 11.09/11.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))))),
% 11.09/11.37 inference(rewrite,[status(thm)],[])).
% 11.09/11.37 tff(28002,plain,
% 11.09/11.37 (((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))))),
% 11.09/11.37 inference(rewrite,[status(thm)],[])).
% 11.09/11.37 tff(28003,plain,
% 11.09/11.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z))))))))),
% 11.09/11.37 inference(monotonicity,[status(thm)],[28002])).
% 11.09/11.37 tff(28004,plain,
% 11.09/11.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))))),
% 11.09/11.37 inference(transitivity,[status(thm)],[28003, 28001])).
% 11.09/11.37 tff(28005,plain,
% 11.09/11.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 11.09/11.37 inference(quant_inst,[status(thm)],[])).
% 11.09/11.37 tff(28006,plain,
% 11.09/11.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z))))))),
% 11.09/11.37 inference(modus_ponens,[status(thm)],[28005, 28004])).
% 11.09/11.37 tff(28007,plain,
% 11.09/11.37 (~r(s(s(s(elem!1))), elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[28006, 194, 3618, 28000, 22666])).
% 11.09/11.37 tff(28008,plain,
% 11.09/11.37 (b(s(s(s(elem!1))), elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[230, 28007, 9])).
% 11.09/11.37 tff(28009,plain,
% 11.09/11.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 11.09/11.37 inference(rewrite,[status(thm)],[])).
% 11.09/11.37 tff(28010,plain,
% 11.09/11.37 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 11.09/11.37 inference(rewrite,[status(thm)],[])).
% 11.09/11.37 tff(28011,plain,
% 11.09/11.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))))),
% 11.09/11.37 inference(monotonicity,[status(thm)],[28010])).
% 11.09/11.37 tff(28012,plain,
% 11.09/11.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 11.09/11.37 inference(transitivity,[status(thm)],[28011, 28009])).
% 11.09/11.37 tff(28013,plain,
% 11.09/11.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 11.09/11.37 inference(quant_inst,[status(thm)],[])).
% 11.09/11.37 tff(28014,plain,
% 11.09/11.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))),
% 11.09/11.37 inference(modus_ponens,[status(thm)],[28013, 28012])).
% 11.09/11.37 tff(28015,plain,
% 11.09/11.37 (~r(elem!1, s(s(s(elem!1))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[28014, 194, 3618, 28000, 22666])).
% 11.09/11.37 tff(28016,plain,
% 11.09/11.37 (b(elem!1, s(s(s(elem!1))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[424, 28015, 1])).
% 11.09/11.37 tff(28017,plain,
% 11.09/11.37 ($false),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[10845, 28016, 28008, 22924, 133])).
% 11.09/11.37 tff(28018,plain,(b(elem!1, z) | (~b(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | b(elem!1, s(z)) | (s(z) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.37 tff(28019,plain,
% 11.09/11.37 (b(elem!1, z)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[28018, 1, 22902, 27862, 88, 31, 27976, 27971, 2])).
% 11.09/11.37 tff(28020,plain,
% 11.09/11.37 (~b(s(z), elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[5231, 28019, 22902, 27862])).
% 11.09/11.37 tff(28021,plain,
% 11.09/11.37 (~(s(s(s(s(z)))) = elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[8916, 28020, 27971])).
% 11.09/11.37 tff(28022,plain,
% 11.09/11.37 (r(s(z), elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[632, 28020, 27976])).
% 11.09/11.37 tff(28023,plain,
% 11.09/11.37 ($false),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[5398, 28022, 28021, 88, 22902, 27862, 28019, 27978])).
% 11.09/11.37 tff(28024,plain,((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(z)) | (elem!1 = z) | r(z, elem!1) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.37 tff(28025,plain,
% 11.09/11.37 (elem!1 = s(s(s(elem!1)))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[28024, 31, 2, 80, 81])).
% 11.09/11.37 tff(28026,plain,
% 11.09/11.37 (s(s(s(elem!1))) = elem!1),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[129, 28025])).
% 11.09/11.37 tff(28027,plain,
% 11.09/11.37 (~(s(s(s(s(z)))) = elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[1436, 28026])).
% 11.09/11.37 tff(28028,plain,
% 11.09/11.37 (~(elem!1 = s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[769, 28027])).
% 11.09/11.37 tff(28029,plain,
% 11.09/11.37 (~b(s(s(s(elem!1))), s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[8400, 130, 31])).
% 11.09/11.37 tff(28030,plain,
% 11.09/11.37 (r(s(s(s(elem!1))), s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[223, 28029])).
% 11.09/11.37 tff(28031,plain,
% 11.09/11.37 (~b(s(s(s(elem!1))), z)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[23013, 1216, 90, 22924, 28030, 20445])).
% 11.09/11.37 tff(28032,plain,
% 11.09/11.37 (r(s(s(s(elem!1))), z)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[377, 28031])).
% 11.09/11.37 tff(28033,plain,
% 11.09/11.37 (~r(z, s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[16377, 28032, 28030, 1216])).
% 11.09/11.37 tff(28034,plain,
% 11.09/11.37 (b(z, s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[678, 28033])).
% 11.09/11.37 tff(28035,plain,
% 11.09/11.37 (r(elem!1, s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[8406, 28030, 130])).
% 11.09/11.37 tff(28036,plain,
% 11.09/11.37 (~b(elem!1, z)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[9553, 28031, 125])).
% 11.09/11.37 tff(28037,plain,
% 11.09/11.37 (r(elem!1, z)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[526, 28036, 2])).
% 11.09/11.37 tff(28038,plain,
% 11.09/11.37 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.09/11.37 inference(modus_ponens,[status(thm)],[2064, 3811])).
% 11.09/11.37 tff(28039,plain,
% 11.09/11.37 (~b(z, s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[22981, 2064, 90, 133])).
% 11.09/11.37 tff(28040,plain,
% 11.09/11.37 (r(z, s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[800, 28039])).
% 11.09/11.37 tff(28041,plain,
% 11.09/11.37 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[16434, 28040, 590, 90, 125, 664, 530, 1216])).
% 11.09/11.37 tff(28042,plain,
% 11.09/11.37 ($false),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[28041, 28038])).
% 11.09/11.37 tff(28043,plain,((~b(elem!1, s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.37 tff(28044,plain,
% 11.09/11.37 (~b(elem!1, s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[28043, 28034, 590, 90, 125, 28037, 1216, 133])).
% 11.09/11.37 tff(28045,plain,
% 11.09/11.37 (b(s(s(s(s(z)))), elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[24995, 28044, 1216, 2642, 28035])).
% 11.09/11.37 tff(28046,plain,
% 11.09/11.37 (r(elem!1, s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[781, 28044, 3810])).
% 11.09/11.37 tff(28047,plain,
% 11.09/11.37 (b(s(s(s(s(z)))), s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[25083, 28046, 31, 1216, 28045])).
% 11.09/11.37 tff(28048,plain,
% 11.09/11.37 ($false),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[5575, 391, 90, 28047, 28034, 590])).
% 11.09/11.37 tff(28049,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | b(elem!1, s(z)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(z, elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.37 tff(28050,plain,
% 11.09/11.37 (~r(s(z), s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[28049, 31, 27862, 88, 28025, 22902, 2])).
% 11.09/11.37 tff(28051,plain,
% 11.09/11.37 (b(s(z), s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[1230, 28050])).
% 11.09/11.37 tff(28052,plain,
% 11.09/11.37 (~b(z, s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[22664, 28051, 88, 27862])).
% 11.09/11.37 tff(28053,plain,
% 11.09/11.37 (r(z, s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[800, 28052])).
% 11.09/11.37 tff(28054,plain,
% 11.09/11.37 (~b(s(s(s(elem!1))), s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[8400, 28026, 31])).
% 11.09/11.37 tff(28055,plain,
% 11.09/11.37 (r(s(s(s(elem!1))), s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[223, 28054])).
% 11.09/11.37 tff(28056,plain,
% 11.09/11.37 (r(elem!1, s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[8406, 28055, 28026])).
% 11.09/11.37 tff(28057,plain,
% 11.09/11.37 ((s(z) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 11.09/11.37 inference(monotonicity,[status(thm)],[28025])).
% 11.09/11.37 tff(28058,plain,
% 11.09/11.37 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 11.09/11.37 inference(symmetry,[status(thm)],[28057])).
% 11.09/11.37 tff(28059,plain,
% 11.09/11.37 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 11.09/11.37 inference(monotonicity,[status(thm)],[28058])).
% 11.09/11.37 tff(28060,plain,
% 11.09/11.37 (~(s(z) = elem!1)),
% 11.09/11.37 inference(modus_ponens,[status(thm)],[217, 28059])).
% 11.09/11.37 tff(28061,plain,
% 11.09/11.37 (~b(s(z), elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[5231, 665, 133, 590])).
% 11.09/11.37 tff(28062,plain,
% 11.09/11.37 (~r(s(z), elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[5398, 665, 90, 133, 590, 720, 847])).
% 11.09/11.37 tff(28063,plain,
% 11.09/11.37 ($false),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[632, 28062, 28061, 150])).
% 11.09/11.37 tff(28064,plain,((~b(elem!1, z)) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.37 tff(28065,plain,
% 11.09/11.37 (~b(elem!1, z)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[28064, 28060, 88, 22902, 27862, 28027, 28056])).
% 11.09/11.37 tff(28066,plain,
% 11.09/11.37 (r(elem!1, z)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[526, 28065, 2])).
% 11.09/11.37 tff(28067,plain,
% 11.09/11.37 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[2694, 1549, 130])).
% 11.09/11.37 tff(28068,plain,
% 11.09/11.37 (r(s(s(s(s(z)))), elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[762, 1549, 2642])).
% 11.09/11.37 tff(28069,plain,
% 11.09/11.37 (~r(elem!1, s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[6399, 28068, 719, 530])).
% 11.09/11.37 tff(28070,plain,
% 11.09/11.37 (b(elem!1, s(s(s(s(z)))))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[781, 28069, 3810])).
% 11.09/11.37 tff(28071,plain,
% 11.09/11.37 (~b(s(z), elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[6418, 28070, 90, 133, 1234])).
% 11.09/11.37 tff(28072,plain,
% 11.09/11.37 (r(s(z), elem!1)),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[632, 28071, 20601])).
% 11.09/11.37 tff(28073,plain,
% 11.09/11.37 (~r(z, s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[17465, 28072, 183, 21024])).
% 11.09/11.37 tff(28074,plain,
% 11.09/11.37 (b(z, s(z))),
% 11.09/11.37 inference(unit_resolution,[status(thm)],[678, 28073])).
% 11.09/11.37 tff(28075,plain,
% 11.09/11.37 (~b(s(s(s(s(z)))), s(z))),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[22918, 28074, 90, 1234])).
% 11.09/11.38 tff(28076,plain,
% 11.09/11.38 (r(s(s(s(s(z)))), s(z))),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[749, 28075])).
% 11.09/11.38 tff(28077,plain,
% 11.09/11.38 (r(s(z), s(s(s(elem!1))))),
% 11.09/11.38 inference(modus_ponens,[status(thm)],[28072, 9967])).
% 11.09/11.38 tff(28078,plain,
% 11.09/11.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.09/11.38 inference(rewrite,[status(thm)],[])).
% 11.09/11.38 tff(28079,plain,
% 11.09/11.38 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.09/11.38 inference(rewrite,[status(thm)],[])).
% 11.09/11.38 tff(28080,plain,
% 11.09/11.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 11.09/11.38 inference(monotonicity,[status(thm)],[28079])).
% 11.09/11.38 tff(28081,plain,
% 11.09/11.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.09/11.38 inference(transitivity,[status(thm)],[28080, 28078])).
% 11.09/11.38 tff(28082,plain,
% 11.09/11.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))),
% 11.09/11.38 inference(quant_inst,[status(thm)],[])).
% 11.09/11.38 tff(28083,plain,
% 11.09/11.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 11.09/11.38 inference(modus_ponens,[status(thm)],[28082, 28081])).
% 11.09/11.38 tff(28084,plain,
% 11.09/11.38 ($false),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[28083, 194, 21024, 28077, 28076, 28067])).
% 11.09/11.38 tff(28085,plain,(b(s(s(s(s(z)))), elem!1) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.38 tff(28086,plain,
% 11.09/11.38 (b(s(s(s(s(z)))), elem!1)),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[28085, 28066, 88, 28051, 28055, 22902, 28053, 28025])).
% 11.09/11.38 tff(28087,plain,
% 11.09/11.38 ($false),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[18955, 391, 90, 1234, 664, 590])).
% 11.09/11.38 tff(28088,plain,((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.38 tff(28089,plain,
% 11.09/11.38 (~b(z, s(z))),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[28088, 28051, 88, 27862])).
% 11.09/11.38 tff(28090,plain,
% 11.09/11.38 (r(z, s(z))),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[678, 28089])).
% 11.09/11.38 tff(28091,plain,
% 11.09/11.38 (r(s(s(s(elem!1))), z)),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[533, 28066, 28026])).
% 11.09/11.38 tff(28092,plain,
% 11.09/11.38 (~r(s(z), elem!1)),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[17465, 28091, 28055, 28090])).
% 11.09/11.38 tff(28093,plain,
% 11.09/11.38 (b(s(z), elem!1)),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[632, 28092, 28060])).
% 11.09/11.38 tff(28094,plain,
% 11.09/11.38 (~b(elem!1, s(s(s(s(z)))))),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[18589, 28093, 28051, 28086])).
% 11.09/11.38 tff(28095,plain,
% 11.09/11.38 (r(elem!1, s(s(s(s(z)))))),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[781, 28094, 28028])).
% 11.09/11.38 tff(28096,plain,
% 11.09/11.38 (s(s(s(elem!1))) = elem!1),
% 11.09/11.38 inference(symmetry,[status(thm)],[28025])).
% 11.09/11.38 tff(28097,plain,
% 11.09/11.38 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.09/11.38 inference(monotonicity,[status(thm)],[28096])).
% 11.09/11.38 tff(28098,plain,
% 11.09/11.38 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 11.09/11.38 inference(transitivity,[status(thm)],[28097, 698])).
% 11.09/11.38 tff(28099,plain,
% 11.09/11.38 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 11.09/11.38 inference(monotonicity,[status(thm)],[28098])).
% 11.09/11.38 tff(28100,plain,
% 11.09/11.38 (~(elem!1 = s(s(z)))),
% 11.09/11.38 inference(modus_ponens,[status(thm)],[1397, 28099])).
% 11.09/11.38 tff(28101,plain,
% 11.09/11.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.09/11.38 inference(rewrite,[status(thm)],[])).
% 11.09/11.38 tff(28102,plain,
% 11.09/11.38 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.09/11.38 inference(rewrite,[status(thm)],[])).
% 11.09/11.38 tff(28103,plain,
% 11.09/11.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 11.09/11.38 inference(monotonicity,[status(thm)],[28102])).
% 11.09/11.38 tff(28104,plain,
% 11.09/11.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.09/11.38 inference(transitivity,[status(thm)],[28103, 28101])).
% 11.09/11.38 tff(28105,plain,
% 11.09/11.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 11.09/11.38 inference(quant_inst,[status(thm)],[])).
% 11.09/11.38 tff(28106,plain,
% 11.09/11.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 11.09/11.38 inference(modus_ponens,[status(thm)],[28105, 28104])).
% 11.09/11.38 tff(28107,plain,
% 11.09/11.38 ($false),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[28106, 391, 10682, 90, 1234, 590, 17493])).
% 11.09/11.38 tff(28108,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.38 tff(28109,plain,
% 11.09/11.38 (~b(s(s(s(elem!1))), s(s(z)))),
% 11.09/11.38 inference(unit_resolution,[status(thm)],[28108, 28051, 88, 22898, 27862])).
% 11.09/11.38 tff(28110,plain,
% 11.09/11.38 (~b(elem!1, s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[16425, 28109, 28025])).
% 11.09/11.39 tff(28111,plain,
% 11.09/11.39 (r(elem!1, s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[3394, 28110, 28100])).
% 11.09/11.39 tff(28112,plain,
% 11.09/11.39 (~r(s(s(z)), z)),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[18602, 28066, 28090, 28111])).
% 11.09/11.39 tff(28113,plain,
% 11.09/11.39 (b(s(s(z)), z)),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[1211, 28112])).
% 11.09/11.39 tff(28114,plain,
% 11.09/11.39 (~r(s(s(s(s(z)))), elem!1)),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[6399, 28095, 28053, 28066])).
% 11.09/11.39 tff(28115,plain,
% 11.09/11.39 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 11.09/11.39 inference(monotonicity,[status(thm)],[28025])).
% 11.09/11.39 tff(28116,plain,
% 11.09/11.39 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.09/11.39 inference(transitivity,[status(thm)],[28115, 3928])).
% 11.09/11.39 tff(28117,plain,
% 11.09/11.39 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 11.09/11.39 inference(transitivity,[status(thm)],[28116, 3929])).
% 11.09/11.39 tff(28118,plain,
% 11.09/11.39 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 11.09/11.39 inference(monotonicity,[status(thm)],[28117])).
% 11.09/11.39 tff(28119,plain,
% 11.09/11.39 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 11.09/11.39 inference(modus_ponens,[status(thm)],[28028, 28118])).
% 11.09/11.39 tff(28120,plain,
% 11.09/11.39 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[20820, 28086, 28025])).
% 11.09/11.39 tff(28121,plain,
% 11.09/11.39 (~r(s(z), s(s(s(elem!1))))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[16770, 28066, 28090, 28056])).
% 11.09/11.39 tff(28122,plain,
% 11.09/11.39 (b(s(z), s(s(s(elem!1))))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[247, 28121])).
% 11.09/11.39 tff(28123,plain,
% 11.09/11.39 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[17481, 28122, 22898, 27862, 28120])).
% 11.09/11.39 tff(28124,plain,
% 11.09/11.39 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[15351, 28123, 28119])).
% 11.09/11.39 tff(28125,plain,
% 11.09/11.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.09/11.39 inference(rewrite,[status(thm)],[])).
% 11.09/11.39 tff(28126,plain,
% 11.09/11.39 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.09/11.39 inference(rewrite,[status(thm)],[])).
% 11.09/11.39 tff(28127,plain,
% 11.09/11.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 11.09/11.39 inference(monotonicity,[status(thm)],[28126])).
% 11.09/11.39 tff(28128,plain,
% 11.09/11.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.09/11.39 inference(transitivity,[status(thm)],[28127, 28125])).
% 11.09/11.39 tff(28129,plain,
% 11.09/11.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))),
% 11.09/11.39 inference(quant_inst,[status(thm)],[])).
% 11.09/11.39 tff(28130,plain,
% 11.09/11.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.09/11.39 inference(modus_ponens,[status(thm)],[28129, 28128])).
% 11.09/11.39 tff(28131,plain,
% 11.09/11.39 ($false),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[28130, 194, 174, 723, 719, 4317])).
% 11.09/11.39 tff(28132,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.39 tff(28133,plain,
% 11.09/11.39 (~r(s(s(s(s(z)))), s(z))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[28132, 28124, 28053, 28091])).
% 11.09/11.39 tff(28134,plain,
% 11.09/11.39 (b(s(s(s(s(z)))), s(z))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[749, 28133])).
% 11.09/11.39 tff(28135,plain,
% 11.09/11.39 (~b(elem!1, s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[18622, 1235, 1652, 644, 1759])).
% 11.09/11.39 tff(28136,plain,
% 11.09/11.39 (r(elem!1, s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[3394, 28135, 1405])).
% 11.09/11.39 tff(28137,plain,
% 11.09/11.39 (~b(z, s(z))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[28088, 1234, 90, 590])).
% 11.09/11.39 tff(28138,plain,
% 11.09/11.39 (r(z, s(z))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[678, 28137])).
% 11.09/11.39 tff(28139,plain,
% 11.09/11.39 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[18451, 2405, 2032, 1748])).
% 11.09/11.39 tff(28140,plain,
% 11.09/11.39 (b(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[1714, 28139])).
% 11.09/11.39 tff(28141,plain,
% 11.09/11.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.09/11.39 inference(rewrite,[status(thm)],[])).
% 11.09/11.39 tff(28142,plain,
% 11.09/11.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.09/11.39 inference(quant_inst,[status(thm)],[])).
% 11.09/11.39 tff(28143,plain,
% 11.09/11.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 11.09/11.39 inference(modus_ponens,[status(thm)],[28142, 28141])).
% 11.09/11.39 tff(28144,plain,
% 11.09/11.39 ($false),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[28143, 391, 133, 1235, 1234, 2439, 3563])).
% 11.09/11.39 tff(28145,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.39 tff(28146,plain,
% 11.09/11.39 (~b(s(z), s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[28145, 28140, 133, 1234, 1235])).
% 11.09/11.39 tff(28147,plain,
% 11.09/11.39 (r(s(z), s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[1788, 28146])).
% 11.09/11.39 tff(28148,plain,
% 11.09/11.39 (~b(z, s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[15053, 28140, 90, 1235])).
% 11.09/11.39 tff(28149,plain,
% 11.09/11.39 (r(z, s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[18613, 28148])).
% 11.09/11.39 tff(28150,plain,
% 11.09/11.39 ($false),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[9720, 28149, 28147, 722, 2405])).
% 11.09/11.39 tff(28151,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.39 tff(28152,plain,
% 11.09/11.39 (~r(s(s(z)), s(z))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[28151, 1235, 90, 28138, 133, 1234, 2032, 28136])).
% 11.09/11.39 tff(28153,plain,
% 11.09/11.39 (b(s(s(z)), s(z))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[3778, 28152])).
% 11.09/11.39 tff(28154,plain,
% 11.09/11.39 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[5108, 28153, 1234, 1759])).
% 11.09/11.39 tff(28155,plain,
% 11.09/11.39 (r(s(s(z)), s(s(s(s(z)))))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[3652, 28154])).
% 11.09/11.39 tff(28156,plain,
% 11.09/11.39 (~b(z, s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[17567, 28155, 847, 1405, 6221, 1235, 644, 590])).
% 11.09/11.39 tff(28157,plain,
% 11.09/11.39 (r(z, s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[18613, 28156])).
% 11.09/11.39 tff(28158,plain,
% 11.09/11.39 (~r(s(z), s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[1775, 28155, 1652, 150, 28136, 1759])).
% 11.09/11.39 tff(28159,plain,
% 11.09/11.39 (b(s(z), s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[1788, 28158])).
% 11.09/11.39 tff(28160,plain,
% 11.09/11.39 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[28145, 28159, 133, 1234, 1235])).
% 11.09/11.39 tff(28161,plain,
% 11.09/11.39 (r(s(s(s(s(z)))), s(s(z)))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[1714, 28160])).
% 11.09/11.39 tff(28162,plain,
% 11.09/11.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.09/11.39 inference(rewrite,[status(thm)],[])).
% 11.09/11.39 tff(28163,plain,
% 11.09/11.39 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.09/11.39 inference(rewrite,[status(thm)],[])).
% 11.09/11.39 tff(28164,plain,
% 11.09/11.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 11.09/11.39 inference(monotonicity,[status(thm)],[28163])).
% 11.09/11.39 tff(28165,plain,
% 11.09/11.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.09/11.39 inference(transitivity,[status(thm)],[28164, 28162])).
% 11.09/11.39 tff(28166,plain,
% 11.09/11.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 11.09/11.39 inference(quant_inst,[status(thm)],[])).
% 11.09/11.39 tff(28167,plain,
% 11.09/11.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 11.09/11.39 inference(modus_ponens,[status(thm)],[28166, 28165])).
% 11.09/11.39 tff(28168,plain,
% 11.09/11.39 ($false),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[28167, 194, 28155, 28161, 22666, 28157])).
% 11.09/11.39 tff(28169,plain,((~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (elem!1 = s(s(z))) | r(s(s(s(s(z)))), elem!1) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.09/11.39 tff(28170,plain,
% 11.09/11.39 ($false),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[28169, 28134, 28114, 28051, 28056, 28100, 22902, 28093, 27862, 28086, 28060, 28113, 88, 28095])).
% 11.09/11.39 tff(28171,plain,(b(elem!1, s(z)) | (elem!1 = z) | r(z, elem!1) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.39 tff(28172,plain,
% 11.09/11.39 (b(elem!1, s(z))),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[28171, 80, 2, 81])).
% 11.09/11.39 tff(28173,plain,
% 11.09/11.39 (~b(elem!1, z)),
% 11.09/11.39 inference(unit_resolution,[status(thm)],[13285, 28172, 22902, 27862])).
% 11.09/11.39 tff(28174,plain,
% 11.09/11.40 (~(elem!1 = s(s(s(s(z)))))),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[16358, 28173, 88])).
% 11.09/11.40 tff(28175,plain,
% 11.09/11.40 (~(s(s(s(s(z)))) = elem!1)),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[16908, 28174])).
% 11.09/11.40 tff(28176,plain,
% 11.09/11.40 (r(elem!1, z)),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[526, 28173, 2])).
% 11.09/11.40 tff(28177,plain,
% 11.09/11.40 (~(s(z) = elem!1)),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[20271, 28172])).
% 11.09/11.40 tff(28178,plain,
% 11.09/11.40 (~b(s(z), elem!1)),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[4857, 28172, 22902, 27862])).
% 11.09/11.40 tff(28179,plain,
% 11.09/11.40 (r(s(z), elem!1)),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[632, 28178, 28177])).
% 11.09/11.40 tff(28180,plain,
% 11.09/11.40 (~b(s(z), s(s(s(s(z)))))),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[26591, 391, 22902, 88, 27862, 28172])).
% 11.09/11.40 tff(28181,plain,
% 11.09/11.40 (r(s(z), s(s(s(s(z)))))),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[1230, 28180])).
% 11.09/11.40 tff(28182,plain,
% 11.09/11.40 (~r(s(s(s(s(z)))), elem!1)),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[6077, 28181, 28179, 28176])).
% 11.09/11.40 tff(28183,plain,
% 11.09/11.40 (b(s(s(s(s(z)))), elem!1)),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[762, 28182, 28175])).
% 11.09/11.40 tff(28184,plain,
% 11.09/11.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 11.09/11.40 inference(rewrite,[status(thm)],[])).
% 11.09/11.40 tff(28185,plain,
% 11.09/11.40 (((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 11.09/11.40 inference(rewrite,[status(thm)],[])).
% 11.09/11.40 tff(28186,plain,
% 11.09/11.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 11.09/11.40 inference(monotonicity,[status(thm)],[28185])).
% 11.09/11.40 tff(28187,plain,
% 11.09/11.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 11.09/11.40 inference(transitivity,[status(thm)],[28186, 28184])).
% 11.09/11.40 tff(28188,plain,
% 11.09/11.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 11.09/11.40 inference(quant_inst,[status(thm)],[])).
% 11.09/11.40 tff(28189,plain,
% 11.09/11.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 11.09/11.40 inference(modus_ponens,[status(thm)],[28188, 28187])).
% 11.09/11.40 tff(28190,plain,
% 11.09/11.40 ($false),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[28189, 391, 22902, 88, 28183, 27862, 28172])).
% 11.09/11.40 tff(28191,plain,(r(z, elem!1) | (elem!1 = z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.09/11.40 tff(28192,plain,
% 11.09/11.40 (r(z, elem!1)),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[28191, 81, 2])).
% 11.09/11.40 tff(28193,plain,
% 11.09/11.40 (~b(elem!1, z)),
% 11.09/11.40 inference(unit_resolution,[status(thm)],[10464, 31, 28192, 150, 181, 2881])).
% 11.18/11.40 tff(28194,plain,
% 11.18/11.40 (r(elem!1, z)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[526, 28193, 2])).
% 11.18/11.40 tff(28195,plain,
% 11.18/11.40 (~r(z, s(s(s(s(z)))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[17062, 28194, 181, 13696])).
% 11.18/11.40 tff(28196,plain,
% 11.18/11.40 (b(z, s(s(s(s(z)))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[800, 28195])).
% 11.18/11.40 tff(28197,plain,
% 11.18/11.40 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[23918, 28196, 88, 22898])).
% 11.18/11.40 tff(28198,plain,
% 11.18/11.40 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[15351, 28197, 16830])).
% 11.18/11.40 tff(28199,plain,
% 11.18/11.40 (~r(s(z), elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[2475, 13696, 28192, 181])).
% 11.18/11.40 tff(28200,plain,
% 11.18/11.40 (~r(z, s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[8411, 13696, 91, 28199, 28193])).
% 11.18/11.40 tff(28201,plain,
% 11.18/11.40 (~(s(s(s(elem!1))) = elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[10792, 28200, 28192])).
% 11.18/11.40 tff(28202,plain,
% 11.18/11.40 (~(elem!1 = s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[129, 28201])).
% 11.18/11.40 tff(28203,plain,
% 11.18/11.40 (b(s(s(s(elem!1))), s(z))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[24987, 28202, 88, 2881, 28200])).
% 11.18/11.40 tff(28204,plain,
% 11.18/11.40 (b(s(z), elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[632, 28199, 150])).
% 11.18/11.40 tff(28205,plain,
% 11.18/11.40 (b(elem!1, s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[25885, 28202, 81, 28200, 2881])).
% 11.18/11.40 tff(28206,plain,
% 11.18/11.40 (~b(s(z), s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[4026, 28205, 28204, 28203])).
% 11.18/11.40 tff(28207,plain,
% 11.18/11.40 (r(s(z), s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[247, 28206])).
% 11.18/11.40 tff(28208,plain,
% 11.18/11.40 (~r(s(s(s(s(z)))), s(z))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[27854, 28207, 28198, 2913])).
% 11.18/11.40 tff(28209,plain,
% 11.18/11.40 (b(s(s(s(s(z)))), s(z))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[749, 28208])).
% 11.18/11.40 tff(28210,plain,
% 11.18/11.40 (~(elem!1 = s(s(s(s(z)))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[16358, 28193, 88])).
% 11.18/11.40 tff(28211,plain,
% 11.18/11.40 (~(s(s(s(s(z)))) = elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[16908, 28210])).
% 11.18/11.40 tff(28212,plain,
% 11.18/11.40 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[25141, 10936, 90, 2913, 10782, 1526])).
% 11.18/11.40 tff(28213,plain,
% 11.18/11.40 (b(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[1714, 28212])).
% 11.18/11.40 tff(28214,plain,
% 11.18/11.40 (~b(s(s(z)), z)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[25151, 28213, 1526, 90, 10782])).
% 11.18/11.40 tff(28215,plain,
% 11.18/11.40 (r(s(s(z)), z)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[1211, 28214])).
% 11.18/11.40 tff(28216,plain,
% 11.18/11.40 (~b(elem!1, z)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[10911, 391, 900, 10682, 448])).
% 11.18/11.40 tff(28217,plain,
% 11.18/11.40 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 11.18/11.40 inference(monotonicity,[status(thm)],[11])).
% 11.18/11.40 tff(28218,plain,
% 11.18/11.40 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 11.18/11.40 inference(symmetry,[status(thm)],[28217])).
% 11.18/11.40 tff(28219,plain,
% 11.18/11.40 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 11.18/11.40 inference(monotonicity,[status(thm)],[28218])).
% 11.18/11.40 tff(28220,plain,
% 11.18/11.40 (~b(s(s(s(elem!1))), elem!1)),
% 11.18/11.40 inference(modus_ponens,[status(thm)],[9550, 28219])).
% 11.18/11.40 tff(28221,plain,
% 11.18/11.40 ($false),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[900, 28220])).
% 11.18/11.40 tff(28222,plain,((~(elem!1 = z)) | (~b(s(s(s(elem!1))), elem!1)) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.40 tff(28223,plain,
% 11.18/11.40 (~(elem!1 = z)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[28222, 900, 9550])).
% 11.18/11.40 tff(28224,plain,
% 11.18/11.40 (r(elem!1, z)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[526, 28223, 28216])).
% 11.18/11.40 tff(28225,plain,
% 11.18/11.40 (~b(z, elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[10845, 900, 10682, 448])).
% 11.18/11.40 tff(28226,plain,
% 11.18/11.40 (~(z = elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[97, 28223])).
% 11.18/11.40 tff(28227,plain,
% 11.18/11.40 (r(z, elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[141, 28226, 28225])).
% 11.18/11.40 tff(28228,plain,
% 11.18/11.40 (~r(s(s(z)), elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[15383, 194, 28227, 28224, 3557])).
% 11.18/11.40 tff(28229,plain,
% 11.18/11.40 (~r(s(s(z)), s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[23046, 194, 28227, 12778, 3557])).
% 11.18/11.40 tff(28230,plain,
% 11.18/11.40 (b(s(s(z)), s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[11041, 28229])).
% 11.18/11.40 tff(28231,plain,
% 11.18/11.40 (~b(s(s(z)), elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[15437, 391, 900, 448, 28230])).
% 11.18/11.40 tff(28232,plain,
% 11.18/11.40 (s(s(z)) = elem!1),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[4730, 28231, 28228])).
% 11.18/11.40 tff(28233,plain,
% 11.18/11.40 (r(s(z), s(s(elem!1)))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[11275, 28232, 1216])).
% 11.18/11.40 tff(28234,plain,
% 11.18/11.40 (~(s(z) = s(elem!1))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[117, 28226])).
% 11.18/11.40 tff(28235,plain,
% 11.18/11.40 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[4584, 28232, 28234])).
% 11.18/11.40 tff(28236,plain,
% 11.18/11.40 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[281, 28235])).
% 11.18/11.40 tff(28237,plain,
% 11.18/11.40 (s(s(s(z))) = s(elem!1)),
% 11.18/11.40 inference(monotonicity,[status(thm)],[28232])).
% 11.18/11.40 tff(28238,plain,
% 11.18/11.40 (s(s(s(s(z)))) = s(s(elem!1))),
% 11.18/11.40 inference(monotonicity,[status(thm)],[28237])).
% 11.18/11.40 tff(28239,plain,
% 11.18/11.40 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 11.18/11.40 inference(monotonicity,[status(thm)],[28238])).
% 11.18/11.40 tff(28240,plain,
% 11.18/11.40 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 11.18/11.40 inference(monotonicity,[status(thm)],[28232])).
% 11.18/11.40 tff(28241,plain,
% 11.18/11.40 (b(s(s(s(s(z)))), elem!1)),
% 11.18/11.40 inference(modus_ponens,[status(thm)],[3563, 28240])).
% 11.18/11.40 tff(28242,plain,
% 11.18/11.40 (b(s(s(elem!1)), elem!1)),
% 11.18/11.40 inference(modus_ponens,[status(thm)],[28241, 28239])).
% 11.18/11.40 tff(28243,plain,
% 11.18/11.40 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[920, 391, 900, 28242, 448])).
% 11.18/11.40 tff(28244,plain,
% 11.18/11.40 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[1356, 28243, 28236])).
% 11.18/11.40 tff(28245,plain,
% 11.18/11.40 (~r(elem!1, s(s(z)))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[16978, 194, 28227, 28224, 3557])).
% 11.18/11.40 tff(28246,plain,
% 11.18/11.40 (~b(elem!1, s(s(z)))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[15450, 391, 900, 448, 28230])).
% 11.18/11.40 tff(28247,plain,
% 11.18/11.40 (elem!1 = s(s(z))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[3394, 28246, 28245])).
% 11.18/11.40 tff(28248,plain,
% 11.18/11.40 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[9253, 28247])).
% 11.18/11.40 tff(28249,plain,
% 11.18/11.40 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[22105, 391, 900, 28242, 448])).
% 11.18/11.40 tff(28250,plain,
% 11.18/11.40 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[1370, 28249, 28248])).
% 11.18/11.40 tff(28251,plain,
% 11.18/11.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 11.18/11.40 inference(rewrite,[status(thm)],[])).
% 11.18/11.40 tff(28252,plain,
% 11.18/11.40 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 11.18/11.40 inference(rewrite,[status(thm)],[])).
% 11.18/11.40 tff(28253,plain,
% 11.18/11.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 11.18/11.40 inference(monotonicity,[status(thm)],[28252])).
% 11.18/11.40 tff(28254,plain,
% 11.18/11.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 11.18/11.40 inference(transitivity,[status(thm)],[28253, 28251])).
% 11.18/11.40 tff(28255,plain,
% 11.18/11.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 11.18/11.40 inference(quant_inst,[status(thm)],[])).
% 11.18/11.40 tff(28256,plain,
% 11.18/11.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 11.18/11.40 inference(modus_ponens,[status(thm)],[28255, 28254])).
% 11.18/11.40 tff(28257,plain,
% 11.18/11.40 (~r(s(z), s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[28256, 194, 28250, 28244, 28233])).
% 11.18/11.40 tff(28258,plain,
% 11.18/11.40 (b(s(z), s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[247, 28257])).
% 11.18/11.40 tff(28259,plain,
% 11.18/11.40 (~b(elem!1, s(z))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[2907, 28258, 1526, 900])).
% 11.18/11.40 tff(28260,plain,
% 11.18/11.40 (r(elem!1, s(z))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[837, 28259, 831])).
% 11.18/11.40 tff(28261,plain,
% 11.18/11.40 (~b(s(z), elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[4026, 28258, 1526, 448])).
% 11.18/11.40 tff(28262,plain,
% 11.18/11.40 (r(s(z), elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[632, 28261, 1496])).
% 11.18/11.40 tff(28263,plain,
% 11.18/11.40 (~b(z, s(z))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[15561, 28258, 1526, 10682])).
% 11.18/11.40 tff(28264,plain,
% 11.18/11.40 (r(z, s(z))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[678, 28263])).
% 11.18/11.40 tff(28265,plain,
% 11.18/11.40 ($false),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[14725, 28264, 28262, 28227, 28260])).
% 11.18/11.40 tff(28266,plain,((~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.40 tff(28267,plain,
% 11.18/11.40 (~b(s(s(s(elem!1))), elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[28266, 9550, 1526, 10782, 448, 28213, 2913, 28215, 10901])).
% 11.18/11.40 tff(28268,plain,
% 11.18/11.40 (r(s(s(s(elem!1))), elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[230, 28267, 127])).
% 11.18/11.40 tff(28269,plain,
% 11.18/11.40 (r(elem!1, s(s(s(elem!1))))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[27629, 28267, 448, 1526, 12778, 90, 2881, 10782, 127])).
% 11.18/11.40 tff(28270,plain,
% 11.18/11.40 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 11.18/11.40 inference(symmetry,[status(thm)],[962])).
% 11.18/11.40 tff(28271,plain,
% 11.18/11.40 (r(z, s(s(s(elem!1))))),
% 11.18/11.40 inference(modus_ponens,[status(thm)],[410, 28270])).
% 11.18/11.40 tff(28272,plain,
% 11.18/11.40 ($false),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[53, 28271])).
% 11.18/11.40 tff(28273,plain,((~(z = elem!1)) | r(z, s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.40 tff(28274,plain,
% 11.18/11.40 (~(z = elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[28273, 28269, 53])).
% 11.18/11.40 tff(28275,plain,
% 11.18/11.40 (r(elem!1, z)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[27509, 28269, 28268, 12778, 10782, 28267, 1526, 90, 448, 28274, 2881, 4597])).
% 11.18/11.40 tff(28276,plain,
% 11.18/11.40 (~r(z, s(elem!1))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[4255, 28275, 12778, 28268])).
% 11.18/11.40 tff(28277,plain,
% 11.18/11.40 (b(z, s(elem!1))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[566, 28276])).
% 11.18/11.40 tff(28278,plain,
% 11.18/11.40 (~r(z, s(z))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[4113, 28275, 12778, 28268])).
% 11.18/11.40 tff(28279,plain,
% 11.18/11.40 (b(z, s(z))),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[678, 28278])).
% 11.18/11.40 tff(28280,plain,
% 11.18/11.40 (~r(z, elem!1)),
% 11.18/11.40 inference(unit_resolution,[status(thm)],[23607, 28275, 12778, 28268])).
% 11.18/11.40 tff(28281,plain,
% 11.18/11.40 (b(z, elem!1)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[141, 28280, 28274])).
% 11.18/11.41 tff(28282,plain,
% 11.18/11.41 (~r(z, s(s(elem!1)))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[27619, 28275, 12778, 28268])).
% 11.18/11.41 tff(28283,plain,
% 11.18/11.41 (b(z, s(s(elem!1)))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[324, 28282])).
% 11.18/11.41 tff(28284,plain,
% 11.18/11.41 ($false),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[26924, 28283, 28281, 10782, 448, 28275, 28268, 1526, 28279, 10902, 28267, 4597, 28277])).
% 11.18/11.41 tff(28285,plain,(b(s(s(s(elem!1))), z) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | r(z, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.41 tff(28286,plain,
% 11.18/11.41 (b(s(s(s(elem!1))), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[28285, 28205, 88, 2881, 28203, 28200, 28201])).
% 11.18/11.41 tff(28287,plain,
% 11.18/11.41 (~r(s(s(s(s(z)))), elem!1)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[12394, 28207, 88, 181, 2913, 3363, 28286])).
% 11.18/11.41 tff(28288,plain,
% 11.18/11.41 (b(s(s(s(s(z)))), elem!1)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[762, 28287, 28211])).
% 11.18/11.41 tff(28289,plain,
% 11.18/11.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 11.18/11.41 inference(rewrite,[status(thm)],[])).
% 11.18/11.41 tff(28290,plain,
% 11.18/11.41 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 11.18/11.41 inference(rewrite,[status(thm)],[])).
% 11.18/11.41 tff(28291,plain,
% 11.18/11.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 11.18/11.41 inference(monotonicity,[status(thm)],[28290])).
% 11.18/11.41 tff(28292,plain,
% 11.18/11.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 11.18/11.41 inference(transitivity,[status(thm)],[28291, 28289])).
% 11.18/11.41 tff(28293,plain,
% 11.18/11.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 11.18/11.41 inference(quant_inst,[status(thm)],[])).
% 11.18/11.41 tff(28294,plain,
% 11.18/11.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 11.18/11.41 inference(modus_ponens,[status(thm)],[28293, 28292])).
% 11.18/11.41 tff(28295,plain,
% 11.18/11.41 ($false),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[28294, 391, 28286, 28205, 28204, 28288, 28209])).
% 11.18/11.41 tff(28296,plain,(b(elem!1, s(z)) | b(s(z), s(s(s(s(z))))) | r(s(s(s(s(z)))), z) | (s(z) = elem!1) | (elem!1 = z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.41 tff(28297,plain,
% 11.18/11.41 (b(s(z), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[28296, 150, 81, 31, 2, 2881])).
% 11.18/11.41 tff(28298,plain,
% 11.18/11.41 (~b(s(s(s(elem!1))), s(z))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[10690, 664, 10682, 590])).
% 11.18/11.41 tff(28299,plain,
% 11.18/11.41 (r(s(s(s(elem!1))), s(z))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[223, 28298])).
% 11.18/11.41 tff(28300,plain,
% 11.18/11.41 (~r(s(s(s(s(z)))), s(z))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[23906, 28299, 90, 10682, 31, 9, 1216, 831])).
% 11.18/11.41 tff(28301,plain,
% 11.18/11.41 (b(s(s(s(s(z)))), s(z))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[749, 28300])).
% 11.18/11.41 tff(28302,plain,
% 11.18/11.41 (~r(s(s(z)), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[23356, 28301, 90, 10682, 1216, 831, 1, 28299])).
% 11.18/11.41 tff(28303,plain,
% 11.18/11.41 (~r(s(s(s(elem!1))), elem!1)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[10856, 28299, 1216, 1810])).
% 11.18/11.41 tff(28304,plain,
% 11.18/11.41 (b(s(s(s(elem!1))), elem!1)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[230, 28303, 9])).
% 11.18/11.41 tff(28305,plain,
% 11.18/11.41 (~b(s(s(z)), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[25590, 28304, 90, 10682, 664, 28301, 1216])).
% 11.18/11.41 tff(28306,plain,
% 11.18/11.41 ($false),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[1211, 28305, 28302])).
% 11.18/11.41 tff(28307,plain,((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (elem!1 = s(z)) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.41 tff(28308,plain,
% 11.18/11.41 (~b(z, s(z))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[28307, 173, 22898, 2913, 88, 1, 31, 28297])).
% 11.18/11.41 tff(28309,plain,
% 11.18/11.41 (r(z, s(z))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[678, 28308])).
% 11.18/11.41 tff(28310,plain,
% 11.18/11.41 (~r(s(z), s(s(s(elem!1))))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[16770, 28309, 838, 530])).
% 11.18/11.41 tff(28311,plain,
% 11.18/11.41 (b(s(z), s(s(s(elem!1))))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[247, 28310])).
% 11.18/11.41 tff(28312,plain,
% 11.18/11.41 (~b(s(s(s(elem!1))), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[11303, 28311, 22898, 28297])).
% 11.18/11.41 tff(28313,plain,
% 11.18/11.41 (r(s(s(s(elem!1))), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[377, 28312])).
% 11.18/11.41 tff(28314,plain,
% 11.18/11.41 (b(s(z), elem!1)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[19761, 28309, 28192, 31, 150])).
% 11.18/11.41 tff(28315,plain,
% 11.18/11.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.18/11.41 inference(rewrite,[status(thm)],[])).
% 11.18/11.41 tff(28316,plain,
% 11.18/11.41 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.18/11.41 inference(rewrite,[status(thm)],[])).
% 11.18/11.41 tff(28317,plain,
% 11.18/11.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 11.18/11.41 inference(monotonicity,[status(thm)],[28316])).
% 11.18/11.41 tff(28318,plain,
% 11.18/11.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.18/11.41 inference(transitivity,[status(thm)],[28317, 28315])).
% 11.18/11.41 tff(28319,plain,
% 11.18/11.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 11.18/11.41 inference(quant_inst,[status(thm)],[])).
% 11.18/11.41 tff(28320,plain,
% 11.18/11.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 11.18/11.41 inference(modus_ponens,[status(thm)],[28319, 28318])).
% 11.18/11.41 tff(28321,plain,
% 11.18/11.41 ($false),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[28320, 391, 10682, 644, 379, 1526, 590])).
% 11.18/11.41 tff(28322,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.41 tff(28323,plain,
% 11.18/11.41 (~b(s(s(s(elem!1))), s(z))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[28322, 28311, 22898, 28297, 28314])).
% 11.18/11.41 tff(28324,plain,
% 11.18/11.41 (r(s(s(s(elem!1))), s(z))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[223, 28323])).
% 11.18/11.41 tff(28325,plain,
% 11.18/11.41 ($false),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[16377, 28324, 28313, 28309, 2913])).
% 11.18/11.41 tff(28326,plain,((s(z) = elem!1) | b(elem!1, s(z)) | (~r(elem!1, z)) | (elem!1 = s(s(s(elem!1)))) | r(s(s(s(s(z)))), z) | (elem!1 = z) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.41 tff(28327,plain,
% 11.18/11.41 (s(z) = elem!1),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[28326, 530, 31, 1, 81, 2, 2881])).
% 11.18/11.41 tff(28328,plain,
% 11.18/11.41 (elem!1 = s(z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[1495, 28327])).
% 11.18/11.41 tff(28329,plain,
% 11.18/11.41 (~b(elem!1, s(s(s(elem!1))))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[8314, 28328, 2881])).
% 11.18/11.41 tff(28330,plain,
% 11.18/11.41 (r(elem!1, s(s(s(elem!1))))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[424, 28329, 1])).
% 11.18/11.41 tff(28331,plain,
% 11.18/11.41 (~b(s(z), s(s(s(elem!1))))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[2884, 28328, 2881])).
% 11.18/11.41 tff(28332,plain,
% 11.18/11.41 (r(s(z), s(s(s(elem!1))))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[247, 28331])).
% 11.18/11.41 tff(28333,plain,
% 11.18/11.41 (r(s(z), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[7479, 28327, 530])).
% 11.18/11.41 tff(28334,plain,
% 11.18/11.41 (r(z, s(s(s(elem!1))))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[25885, 28329, 81, 1, 2881])).
% 11.18/11.41 tff(28335,plain,
% 11.18/11.41 (~r(s(s(s(elem!1))), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[1867, 28334, 28333, 28332])).
% 11.18/11.41 tff(28336,plain,
% 11.18/11.41 (b(s(s(s(elem!1))), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[377, 28335])).
% 11.18/11.41 tff(28337,plain,
% 11.18/11.41 (~r(elem!1, s(elem!1))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[24443, 28336, 22898, 28192, 28327, 530, 28330])).
% 11.18/11.41 tff(28338,plain,
% 11.18/11.41 (b(elem!1, s(elem!1))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[443, 28337, 427])).
% 11.18/11.41 tff(28339,plain,
% 11.18/11.41 (~r(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[641, 28332, 28334, 28333])).
% 11.18/11.41 tff(28340,plain,
% 11.18/11.41 (b(s(s(s(elem!1))), elem!1)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[10519, 28334, 28192, 1, 28329])).
% 11.18/11.41 tff(28341,plain,
% 11.18/11.41 (~r(s(elem!1), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[6142, 28340, 28334, 28329, 530, 427, 28339])).
% 11.18/11.41 tff(28342,plain,
% 11.18/11.41 (b(s(elem!1), z)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[549, 28341])).
% 11.18/11.41 tff(28343,plain,
% 11.18/11.41 (~b(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[12799, 28342, 22898, 28336])).
% 11.18/11.41 tff(28344,plain,
% 11.18/11.41 (s(s(s(elem!1))) = s(elem!1)),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[588, 28343, 28339])).
% 11.18/11.41 tff(28345,plain,
% 11.18/11.41 ($false),
% 11.18/11.41 inference(unit_resolution,[status(thm)],[4603, 28344, 28338, 28329])).
% 11.18/11.41 tff(28346,plain,((~r(elem!1, z)) | (elem!1 = s(s(s(elem!1)))) | r(s(s(s(s(z)))), z) | b(s(z), s(s(s(s(z))))) | b(elem!1, s(z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.42 tff(28347,plain,
% 11.18/11.42 (~r(elem!1, z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[28346, 31, 81, 2881, 1, 2])).
% 11.18/11.42 tff(28348,plain,
% 11.18/11.42 (b(elem!1, z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[526, 28347, 2])).
% 11.18/11.42 tff(28349,plain,
% 11.18/11.42 (~(s(s(s(s(z)))) = elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[6252, 28314, 2881])).
% 11.18/11.42 tff(28350,plain,
% 11.18/11.42 (~(elem!1 = s(s(s(s(z)))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[769, 28349])).
% 11.18/11.42 tff(28351,plain,
% 11.18/11.42 (~r(s(s(s(s(z)))), elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[10450, 28350, 28192, 28348, 838])).
% 11.18/11.42 tff(28352,plain,
% 11.18/11.42 (b(s(s(s(s(z)))), elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[762, 28351, 28349])).
% 11.18/11.42 tff(28353,plain,
% 11.18/11.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 11.18/11.42 inference(rewrite,[status(thm)],[])).
% 11.18/11.42 tff(28354,plain,
% 11.18/11.42 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 11.18/11.42 inference(rewrite,[status(thm)],[])).
% 11.18/11.42 tff(28355,plain,
% 11.18/11.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 11.18/11.42 inference(monotonicity,[status(thm)],[28354])).
% 11.18/11.42 tff(28356,plain,
% 11.18/11.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 11.18/11.42 inference(transitivity,[status(thm)],[28355, 28353])).
% 11.18/11.42 tff(28357,plain,
% 11.18/11.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 11.18/11.42 inference(quant_inst,[status(thm)],[])).
% 11.18/11.42 tff(28358,plain,
% 11.18/11.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 11.18/11.42 inference(modus_ponens,[status(thm)],[28357, 28356])).
% 11.18/11.42 tff(28359,plain,
% 11.18/11.42 (~b(s(s(s(s(z)))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[28358, 391, 28348, 22898, 28314, 28352])).
% 11.18/11.42 tff(28360,plain,
% 11.18/11.42 (r(s(s(s(s(z)))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[749, 28359])).
% 11.18/11.42 tff(28361,plain,
% 11.18/11.42 (~r(s(s(s(elem!1))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[23906, 28360, 88, 22898, 31, 9, 2913, 173])).
% 11.18/11.42 tff(28362,plain,
% 11.18/11.42 (b(s(s(s(elem!1))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[223, 28361])).
% 11.18/11.42 tff(28363,plain,
% 11.18/11.42 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[23575, 28314, 22898, 28348, 28297])).
% 11.18/11.42 tff(28364,plain,
% 11.18/11.42 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[1370, 28363, 26982])).
% 11.18/11.42 tff(28365,plain,
% 11.18/11.42 (~b(s(z), s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[28322, 28362, 22898, 28297, 28314])).
% 11.18/11.42 tff(28366,plain,
% 11.18/11.42 (r(s(z), s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[247, 28365])).
% 11.18/11.42 tff(28367,plain,
% 11.18/11.42 (~r(elem!1, s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[18031, 28366, 838, 28364])).
% 11.18/11.42 tff(28368,plain,
% 11.18/11.42 (b(elem!1, s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[424, 28367, 1])).
% 11.18/11.42 tff(28369,plain,
% 11.18/11.42 (~b(s(z), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[14507, 28368, 22898, 28348, 28362])).
% 11.18/11.42 tff(28370,plain,
% 11.18/11.42 (~(elem!1 = s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[11253, 28369, 28314])).
% 11.18/11.42 tff(28371,plain,
% 11.18/11.42 (~(s(s(z)) = elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[11003, 28370])).
% 11.18/11.42 tff(28372,plain,
% 11.18/11.42 ($false),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[14968, 28371, 28370, 2913, 28348, 838, 88, 28309, 28350, 28352, 150, 28192])).
% 11.18/11.42 tff(28373,plain,((s(z) = elem!1) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(z)) | b(s(z), s(s(s(s(z))))) | r(s(s(s(s(z)))), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.42 tff(28374,plain,
% 11.18/11.42 (s(z) = elem!1),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[28373, 31, 1, 2881, 81, 2])).
% 11.18/11.42 tff(28375,plain,
% 11.18/11.42 (elem!1 = s(z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[1495, 28374])).
% 11.18/11.42 tff(28376,plain,
% 11.18/11.42 (~b(elem!1, s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[8314, 28375, 2881])).
% 11.18/11.42 tff(28377,plain,
% 11.18/11.42 (r(z, s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[25885, 28376, 81, 1, 2881])).
% 11.18/11.42 tff(28378,plain,
% 11.18/11.42 (b(s(s(s(elem!1))), elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[10519, 28377, 28192, 1, 28376])).
% 11.18/11.42 tff(28379,plain,
% 11.18/11.42 (b(s(s(s(elem!1))), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[19694, 28377, 28192, 28348, 28376])).
% 11.18/11.42 tff(28380,plain,
% 11.18/11.42 ($false),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[17249, 28379, 28378, 22898, 28348])).
% 11.18/11.42 tff(28381,plain,(b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | r(s(s(s(s(z)))), z) | b(s(z), s(s(s(s(z))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.42 tff(28382,plain,
% 11.18/11.42 (b(elem!1, s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[28381, 2881, 81, 22901, 2])).
% 11.18/11.42 tff(28383,plain,
% 11.18/11.42 (~(s(z) = elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[20271, 28382])).
% 11.18/11.42 tff(28384,plain,
% 11.18/11.42 (b(elem!1, s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[28381, 2881, 81, 1, 2])).
% 11.18/11.42 tff(28385,plain,
% 11.18/11.42 (~(s(z) = elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[20271, 28384])).
% 11.18/11.42 tff(28386,plain,
% 11.18/11.42 (~r(s(z), elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[627, 3618, 411, 182])).
% 11.18/11.42 tff(28387,plain,
% 11.18/11.42 (b(s(z), elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[632, 28386, 150])).
% 11.18/11.42 tff(28388,plain,
% 11.18/11.42 (~b(s(s(s(elem!1))), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[23013, 11174, 90, 10682, 2913, 3843])).
% 11.18/11.42 tff(28389,plain,
% 11.18/11.42 (r(z, s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[24987, 11173, 90, 2881, 1])).
% 11.18/11.42 tff(28390,plain,
% 11.18/11.42 (~r(s(s(s(elem!1))), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[202, 28389, 182, 11174])).
% 11.18/11.42 tff(28391,plain,
% 11.18/11.42 ($false),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[377, 28390, 28388])).
% 11.18/11.42 tff(28392,plain,(b(s(s(s(elem!1))), s(z)) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(z), s(s(s(s(z))))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.42 tff(28393,plain,
% 11.18/11.42 (b(s(s(s(elem!1))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[28392, 1, 90, 10682, 3843, 2881, 182])).
% 11.18/11.42 tff(28394,plain,
% 11.18/11.42 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[25141, 28393, 90, 10682, 3843, 2913])).
% 11.18/11.42 tff(28395,plain,
% 11.18/11.42 (b(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[1714, 28394])).
% 11.18/11.42 tff(28396,plain,
% 11.18/11.42 (~b(s(s(z)), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[25151, 28395, 90, 10682, 28393])).
% 11.18/11.42 tff(28397,plain,
% 11.18/11.42 (r(s(s(z)), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[1211, 28396])).
% 11.18/11.42 tff(28398,plain,
% 11.18/11.42 (~b(s(s(s(elem!1))), elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[20387, 28393, 721, 644])).
% 11.18/11.42 tff(28399,plain,
% 11.18/11.42 (b(elem!1, s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[25377, 28398, 90, 10682, 2881, 1, 28393])).
% 11.18/11.42 tff(28400,plain,
% 11.18/11.42 (~r(z, s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[21676, 28393, 411, 182, 721, 9, 530])).
% 11.18/11.42 tff(28401,plain,
% 11.18/11.42 (~r(z, s(s(s(s(z)))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[26072, 28400, 182, 2913, 530, 21778, 644])).
% 11.18/11.42 tff(28402,plain,
% 11.18/11.42 (b(z, s(s(s(s(z)))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[800, 28401])).
% 11.18/11.42 tff(28403,plain,
% 11.18/11.42 (b(s(z), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[20696, 28402, 90, 182, 2913, 644, 530, 21778, 484])).
% 11.18/11.42 tff(28404,plain,
% 11.18/11.42 (~b(s(s(z)), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[9961, 28403, 721, 28393, 28399])).
% 11.18/11.42 tff(28405,plain,
% 11.18/11.42 (r(s(s(z)), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[3778, 28404])).
% 11.18/11.42 tff(28406,plain,
% 11.18/11.42 (~r(z, s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[10610, 28405, 28397, 2913])).
% 11.18/11.42 tff(28407,plain,
% 11.18/11.42 (~b(s(z), s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[4026, 28399, 644, 28393])).
% 11.18/11.42 tff(28408,plain,
% 11.18/11.42 (r(s(z), s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[247, 28407])).
% 11.18/11.42 tff(28409,plain,
% 11.18/11.42 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[23918, 28402, 90, 10682])).
% 11.18/11.42 tff(28410,plain,
% 11.18/11.42 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[15351, 28409, 16058])).
% 11.18/11.42 tff(28411,plain,
% 11.18/11.42 (~r(s(s(s(s(z)))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[27854, 28410, 28408, 2913])).
% 11.18/11.42 tff(28412,plain,
% 11.18/11.42 (b(s(s(s(s(z)))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[749, 28411])).
% 11.18/11.42 tff(28413,plain,
% 11.18/11.42 (~b(z, s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[20920, 28412, 90, 721, 644])).
% 11.18/11.42 tff(28414,plain,
% 11.18/11.42 ($false),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[678, 28413, 28406])).
% 11.18/11.42 tff(28415,plain,((elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | b(elem!1, z) | (~b(z, s(s(s(elem!1))))) | b(s(z), s(s(s(s(z))))) | (~r(z, elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.42 tff(28416,plain,
% 11.18/11.42 (elem!1 = s(s(s(elem!1)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[28415, 28387, 721, 90, 182, 3618, 484, 22924, 2881, 411, 3363])).
% 11.18/11.42 tff(28417,plain,
% 11.18/11.42 (s(s(s(elem!1))) = elem!1),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[129, 28416])).
% 11.18/11.42 tff(28418,plain,
% 11.18/11.42 (r(s(s(s(elem!1))), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[533, 28417, 3618])).
% 11.18/11.42 tff(28419,plain,
% 11.18/11.42 (r(z, s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[10792, 28417, 411])).
% 11.18/11.42 tff(28420,plain,
% 11.18/11.42 (~r(s(s(s(elem!1))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[202, 28419, 182, 28418])).
% 11.18/11.42 tff(28421,plain,
% 11.18/11.42 (b(s(s(s(elem!1))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[223, 28420])).
% 11.18/11.42 tff(28422,plain,
% 11.18/11.42 (b(s(z), s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[14872, 28417, 28387])).
% 11.18/11.42 tff(28423,plain,
% 11.18/11.42 (~b(z, s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[15561, 28421, 22924, 28422])).
% 11.18/11.42 tff(28424,plain,
% 11.18/11.42 (r(z, s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[678, 28423])).
% 11.18/11.42 tff(28425,plain,
% 11.18/11.42 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[25141, 28421, 90, 22924, 3363, 2913])).
% 11.18/11.42 tff(28426,plain,
% 11.18/11.42 (b(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[1714, 28425])).
% 11.18/11.42 tff(28427,plain,
% 11.18/11.42 (~b(s(s(z)), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[25151, 28426, 90, 22924, 28421])).
% 11.18/11.42 tff(28428,plain,
% 11.18/11.42 (r(s(s(z)), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[1211, 28427])).
% 11.18/11.42 tff(28429,plain,
% 11.18/11.42 (~r(s(s(z)), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[10610, 28428, 28424, 2913])).
% 11.18/11.42 tff(28430,plain,
% 11.18/11.42 (b(s(s(z)), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[3778, 28429])).
% 11.18/11.42 tff(28431,plain,
% 11.18/11.42 (~r(s(s(s(s(z)))), elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[20856, 28430, 90, 411, 3618, 28424, 28416, 28422, 28421])).
% 11.18/11.42 tff(28432,plain,
% 11.18/11.42 (b(s(s(s(s(z)))), elem!1)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[762, 28431, 21778])).
% 11.18/11.42 tff(28433,plain,
% 11.18/11.42 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[20820, 28432, 28416])).
% 11.18/11.42 tff(28434,plain,
% 11.18/11.42 (~b(s(z), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[27828, 28433, 22924, 90, 28421])).
% 11.18/11.42 tff(28435,plain,
% 11.18/11.42 (~b(s(s(s(s(z)))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[20714, 28430, 721, 28387, 28426])).
% 11.18/11.42 tff(28436,plain,
% 11.18/11.42 (r(s(s(s(s(z)))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[749, 28435])).
% 11.18/11.42 tff(28437,plain,
% 11.18/11.42 (~r(z, s(s(s(s(z)))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[731, 28436, 182, 28424])).
% 11.18/11.42 tff(28438,plain,
% 11.18/11.42 (b(z, s(s(s(s(z)))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[800, 28437])).
% 11.18/11.42 tff(28439,plain,
% 11.18/11.42 ($false),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[20698, 28438, 28434, 90, 182, 2881, 484, 28387, 3618])).
% 11.18/11.42 tff(28440,plain,(b(elem!1, z) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | b(s(z), s(s(s(s(z))))) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (s(z) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.42 tff(28441,plain,
% 11.18/11.42 (~r(s(z), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[28440, 484, 88, 2881, 28384, 28192, 28385, 2])).
% 11.18/11.42 tff(28442,plain,
% 11.18/11.42 (b(s(z), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[180, 28441])).
% 11.18/11.42 tff(28443,plain,
% 11.18/11.42 (~r(s(z), s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[21913, 184, 411, 90, 127, 721, 590, 484, 2])).
% 11.18/11.42 tff(28444,plain,
% 11.18/11.42 (~b(s(z), s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[22138, 184, 411, 721, 127, 590, 3618])).
% 11.18/11.42 tff(28445,plain,
% 11.18/11.42 ($false),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[247, 28444, 28443])).
% 11.18/11.42 tff(28446,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = elem!1) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | b(elem!1, z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.42 tff(28447,plain,
% 11.18/11.42 (~r(z, s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[28446, 28442, 28384, 9, 28192, 88, 484, 2])).
% 11.18/11.42 tff(28448,plain,
% 11.18/11.42 (b(elem!1, s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[25885, 28447, 81, 1, 2881])).
% 11.18/11.42 tff(28449,plain,
% 11.18/11.42 (b(s(s(s(elem!1))), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[24987, 28447, 88, 2881, 1])).
% 11.18/11.42 tff(28450,plain,
% 11.18/11.42 (~b(z, s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[10690, 28449, 22898, 28442])).
% 11.18/11.42 tff(28451,plain,
% 11.18/11.42 (r(z, s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[678, 28450])).
% 11.18/11.42 tff(28452,plain,
% 11.18/11.42 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[2849, 28385])).
% 11.18/11.42 tff(28453,plain,
% 11.18/11.42 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[25141, 28449, 88, 22898, 28452, 2913])).
% 11.18/11.42 tff(28454,plain,
% 11.18/11.42 (b(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[1714, 28453])).
% 11.18/11.42 tff(28455,plain,
% 11.18/11.42 (~b(s(s(z)), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[25151, 28454, 88, 22898, 28449])).
% 11.18/11.42 tff(28456,plain,
% 11.18/11.42 (r(s(s(z)), z)),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[1211, 28455])).
% 11.18/11.42 tff(28457,plain,
% 11.18/11.42 (~r(s(s(z)), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[10610, 28456, 28451, 2913])).
% 11.18/11.42 tff(28458,plain,
% 11.18/11.42 (b(s(s(z)), s(z))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[3778, 28457])).
% 11.18/11.42 tff(28459,plain,
% 11.18/11.42 (~b(s(z), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[9961, 28458, 28384, 28449, 28448])).
% 11.18/11.42 tff(28460,plain,
% 11.18/11.42 (r(s(z), s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[1788, 28459])).
% 11.18/11.42 tff(28461,plain,
% 11.18/11.42 (~r(elem!1, s(s(z)))),
% 11.18/11.42 inference(unit_resolution,[status(thm)],[18602, 28456, 3618, 28451])).
% 11.18/11.42 tff(28462,plain,
% 11.18/11.42 (~r(s(z), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[16803, 28451, 28192, 3618])).
% 11.18/11.43 tff(28463,plain,
% 11.18/11.43 (b(s(z), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[632, 28462, 28385])).
% 11.18/11.43 tff(28464,plain,
% 11.18/11.43 (~(elem!1 = s(s(z)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[11253, 28459, 28463])).
% 11.18/11.43 tff(28465,plain,
% 11.18/11.43 (b(elem!1, s(s(z)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[3394, 28464, 28461])).
% 11.18/11.43 tff(28466,plain,
% 11.18/11.43 (~b(s(s(s(s(z)))), s(z))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[20714, 28458, 28384, 28463, 28454])).
% 11.18/11.43 tff(28467,plain,
% 11.18/11.43 (r(s(s(s(s(z)))), s(z))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[749, 28466])).
% 11.18/11.43 tff(28468,plain,
% 11.18/11.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[16396, 28460, 2913, 28467])).
% 11.18/11.43 tff(28469,plain,
% 11.18/11.43 (b(s(s(z)), s(s(s(s(z)))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[3652, 28468])).
% 11.18/11.43 tff(28470,plain,
% 11.18/11.43 (~(elem!1 = s(s(s(s(z)))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[16358, 484, 88])).
% 11.18/11.43 tff(28471,plain,
% 11.18/11.43 (b(s(s(s(elem!1))), z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[28285, 28447, 88, 2881, 28449, 28448, 9])).
% 11.18/11.43 tff(28472,plain,
% 11.18/11.43 (~b(z, s(s(s(s(z)))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[6325, 28449, 28442, 28471, 88])).
% 11.18/11.43 tff(28473,plain,
% 11.18/11.43 (r(z, s(s(s(s(z)))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[800, 28472])).
% 11.18/11.43 tff(28474,plain,
% 11.18/11.43 (~r(elem!1, s(s(s(s(z)))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[15063, 28467, 28192, 28473])).
% 11.18/11.43 tff(28475,plain,
% 11.18/11.43 (b(elem!1, s(s(s(s(z)))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[781, 28474, 28470])).
% 11.18/11.43 tff(28476,plain,
% 11.18/11.43 ($false),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[22690, 28475, 28469, 88, 2913, 28465, 28460])).
% 11.18/11.43 tff(28477,plain,(b(elem!1, z) | b(s(z), s(s(s(s(z))))) | (elem!1 = s(s(s(elem!1)))) | r(s(s(s(s(z)))), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.43 tff(28478,plain,
% 11.18/11.43 (b(elem!1, z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[28477, 2881, 22901, 81, 2])).
% 11.18/11.43 tff(28479,plain,
% 11.18/11.43 (b(s(s(s(elem!1))), s(z))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[28392, 1, 90, 10682, 3363, 2881, 182])).
% 11.18/11.43 tff(28480,plain,
% 11.18/11.43 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[25141, 28479, 90, 10682, 3363, 2913])).
% 11.18/11.43 tff(28481,plain,
% 11.18/11.43 (b(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[1714, 28480])).
% 11.18/11.43 tff(28482,plain,
% 11.18/11.43 (~b(s(s(z)), z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[25151, 28481, 90, 10682, 28479])).
% 11.18/11.43 tff(28483,plain,
% 11.18/11.43 (r(s(s(z)), z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[1211, 28482])).
% 11.18/11.43 tff(28484,plain,
% 11.18/11.43 (~b(elem!1, s(s(s(s(z)))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[25257, 391, 665, 10682, 28479, 90])).
% 11.18/11.43 tff(28485,plain,
% 11.18/11.43 (~b(s(s(s(s(z)))), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[25250, 391, 665, 10682, 28479, 90])).
% 11.18/11.43 tff(28486,plain,
% 11.18/11.43 (elem!1 = s(s(s(s(z))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[27237, 1484, 1549, 8536, 1216])).
% 11.18/11.43 tff(28487,plain,
% 11.18/11.43 (s(s(s(s(z)))) = elem!1),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[769, 28486])).
% 11.18/11.43 tff(28488,plain,
% 11.18/11.43 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[717, 28487])).
% 11.18/11.43 tff(28489,plain,
% 11.18/11.43 (b(elem!1, s(elem!1))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[443, 21575, 437])).
% 11.18/11.43 tff(28490,plain,
% 11.18/11.43 (~r(s(elem!1), z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[1930, 28489, 411, 182, 121, 721])).
% 11.18/11.43 tff(28491,plain,
% 11.18/11.43 (b(s(elem!1), z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[549, 28490])).
% 11.18/11.43 tff(28492,plain,
% 11.18/11.43 (~b(s(s(s(elem!1))), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[17249, 10682, 665, 380])).
% 11.18/11.43 tff(28493,plain,
% 11.18/11.43 (~b(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[12799, 10682, 591, 380])).
% 11.18/11.43 tff(28494,plain,
% 11.18/11.43 (r(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[588, 28493, 279])).
% 11.18/11.43 tff(28495,plain,
% 11.18/11.43 (~(s(s(s(elem!1))) = elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[13062, 28494, 438])).
% 11.18/11.43 tff(28496,plain,
% 11.18/11.43 (b(elem!1, s(s(s(elem!1))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[5715, 28495, 1484, 28492, 232])).
% 11.18/11.43 tff(28497,plain,
% 11.18/11.43 ($false),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[19544, 391, 665, 380, 10682, 28496])).
% 11.18/11.43 tff(28498,plain,((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | r(elem!1, s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.43 tff(28499,plain,
% 11.18/11.43 (~b(s(s(s(elem!1))), z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[28498, 28491, 10682, 665, 232, 1484, 28488, 21575])).
% 11.18/11.43 tff(28500,plain,
% 11.18/11.43 (~b(z, s(s(s(s(z)))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[16124, 28487, 89])).
% 11.18/11.43 tff(28501,plain,
% 11.18/11.43 (r(z, s(s(s(s(z)))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[800, 28500])).
% 11.18/11.43 tff(28502,plain,
% 11.18/11.43 (~r(s(s(s(elem!1))), z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[27817, 28501, 182, 232])).
% 11.18/11.43 tff(28503,plain,
% 11.18/11.43 ($false),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[377, 28502, 28499])).
% 11.18/11.43 tff(28504,plain,((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | b(z, elem!1) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(elem!1)) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.43 tff(28505,plain,
% 11.18/11.43 (~r(s(z), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[28504, 232, 182, 10682, 665, 89, 411, 121, 721, 427, 28485, 28484, 2913])).
% 11.18/11.43 tff(28506,plain,
% 11.18/11.43 (b(s(z), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[632, 28505, 150])).
% 11.18/11.43 tff(28507,plain,
% 11.18/11.43 (~b(s(s(s(elem!1))), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[20387, 28506, 721, 28479])).
% 11.18/11.43 tff(28508,plain,
% 11.18/11.43 (r(s(s(s(elem!1))), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[230, 28507, 9])).
% 11.18/11.43 tff(28509,plain,
% 11.18/11.43 (~r(z, s(s(s(elem!1))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[241, 28508, 232, 182])).
% 11.18/11.43 tff(28510,plain,
% 11.18/11.43 (b(elem!1, s(s(s(elem!1))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[25377, 28507, 90, 10682, 2881, 1, 28479])).
% 11.18/11.43 tff(28511,plain,
% 11.18/11.43 (~(s(s(s(s(z)))) = elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[6252, 28506, 2881])).
% 11.18/11.43 tff(28512,plain,
% 11.18/11.43 (r(s(s(s(s(z)))), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[762, 28511, 28485])).
% 11.18/11.43 tff(28513,plain,
% 11.18/11.43 (~b(s(s(s(elem!1))), z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[12394, 28512, 90, 182, 2913, 3363, 232])).
% 11.18/11.43 tff(28514,plain,
% 11.18/11.43 ($false),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[28285, 28513, 28510, 90, 2881, 28479, 28509, 9])).
% 11.18/11.43 tff(28515,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, s(z))) | (s(z) = elem!1) | (~b(elem!1, z)) | b(z, elem!1) | (~r(z, elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.43 tff(28516,plain,
% 11.18/11.43 (~r(s(z), s(s(s(elem!1))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[28515, 1, 2881, 182, 10682, 90, 721, 150, 665, 89, 411, 121])).
% 11.18/11.43 tff(28517,plain,
% 11.18/11.43 (b(s(z), s(s(s(elem!1))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[247, 28516])).
% 11.18/11.43 tff(28518,plain,
% 11.18/11.43 (~b(s(s(s(elem!1))), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[2907, 28517, 721, 28479])).
% 11.18/11.43 tff(28519,plain,
% 11.18/11.43 (b(elem!1, s(s(s(elem!1))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[25377, 28518, 90, 10682, 2881, 1, 28479])).
% 11.18/11.43 tff(28520,plain,
% 11.18/11.43 (~b(s(z), s(s(z)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[14507, 28519, 10682, 665, 28479])).
% 11.18/11.43 tff(28521,plain,
% 11.18/11.43 (r(s(z), s(s(z)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[1788, 28520])).
% 11.18/11.43 tff(28522,plain,
% 11.18/11.43 (~r(z, s(s(elem!1)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[3787, 28521, 182, 28483])).
% 11.18/11.43 tff(28523,plain,
% 11.18/11.43 (b(z, s(s(elem!1)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[324, 28522])).
% 11.18/11.43 tff(28524,plain,
% 11.18/11.43 (~b(z, s(z))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[15561, 28517, 10682, 28479])).
% 11.18/11.43 tff(28525,plain,
% 11.18/11.43 (r(z, s(z))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[678, 28524])).
% 11.18/11.43 tff(28526,plain,
% 11.18/11.43 (~b(s(z), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[4026, 28519, 28517, 28479])).
% 11.18/11.43 tff(28527,plain,
% 11.18/11.43 (r(s(z), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[632, 28526, 150])).
% 11.18/11.43 tff(28528,plain,
% 11.18/11.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 11.18/11.43 inference(rewrite,[status(thm)],[])).
% 11.18/11.43 tff(28529,plain,
% 11.18/11.43 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 11.18/11.43 inference(rewrite,[status(thm)],[])).
% 11.18/11.43 tff(28530,plain,
% 11.18/11.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1))))))),
% 11.18/11.43 inference(monotonicity,[status(thm)],[28529])).
% 11.18/11.43 tff(28531,plain,
% 11.18/11.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 11.18/11.43 inference(transitivity,[status(thm)],[28530, 28528])).
% 11.18/11.43 tff(28532,plain,
% 11.18/11.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 11.18/11.43 inference(quant_inst,[status(thm)],[])).
% 11.18/11.43 tff(28533,plain,
% 11.18/11.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 11.18/11.43 inference(modus_ponens,[status(thm)],[28532, 28531])).
% 11.18/11.43 tff(28534,plain,
% 11.18/11.43 ($false),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[28533, 194, 411, 1484, 1064, 722])).
% 11.18/11.43 tff(28535,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.43 tff(28536,plain,
% 11.18/11.43 (~r(elem!1, s(s(elem!1)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[28535, 28527, 411, 28525])).
% 11.18/11.43 tff(28537,plain,
% 11.18/11.43 (elem!1 = s(s(s(s(z))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[27237, 28527, 28485, 28484, 2913])).
% 11.18/11.43 tff(28538,plain,
% 11.18/11.43 (s(s(s(s(z)))) = elem!1),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[769, 28537])).
% 11.18/11.43 tff(28539,plain,
% 11.18/11.43 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[717, 28538])).
% 11.18/11.43 tff(28540,plain,
% 11.18/11.43 (~(s(s(elem!1)) = elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[451, 28539])).
% 11.18/11.43 tff(28541,plain,
% 11.18/11.43 (~(elem!1 = s(s(elem!1)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[1292, 28540])).
% 11.18/11.43 tff(28542,plain,
% 11.18/11.43 (b(elem!1, s(s(elem!1)))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[1307, 28541, 28536])).
% 11.18/11.43 tff(28543,plain,
% 11.18/11.43 (r(s(s(s(elem!1))), elem!1)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[230, 28518, 9])).
% 11.18/11.43 tff(28544,plain,
% 11.18/11.43 (~r(elem!1, s(s(s(elem!1))))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[25315, 28543, 90, 10682, 121, 411, 150, 721, 2881, 665, 427, 28485])).
% 11.18/11.43 tff(28545,plain,
% 11.18/11.43 (~r(s(s(s(elem!1))), z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[27629, 28544, 90, 10682, 2881, 28519, 28479, 28518, 9])).
% 11.18/11.43 tff(28546,plain,
% 11.18/11.43 (b(s(s(s(elem!1))), z)),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[377, 28545])).
% 11.18/11.43 tff(28547,plain,
% 11.18/11.43 (~b(s(s(elem!1)), s(z))),
% 11.18/11.43 inference(unit_resolution,[status(thm)],[19556, 28523, 665, 28519, 28546])).
% 11.18/11.44 tff(28548,plain,
% 11.18/11.44 (r(s(s(elem!1)), s(z))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[362, 28547])).
% 11.18/11.44 tff(28549,plain,
% 11.18/11.44 (~r(s(s(elem!1)), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[9045, 28548, 28525, 28521])).
% 11.18/11.44 tff(28550,plain,
% 11.18/11.44 (b(s(s(elem!1)), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[2629, 28549])).
% 11.18/11.44 tff(28551,plain,
% 11.18/11.44 ($false),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[20366, 28550, 28542, 28523, 665])).
% 11.18/11.44 tff(28552,plain,((elem!1 = s(s(s(elem!1)))) | (~b(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | b(s(z), s(s(s(s(z))))) | (s(z) = s(elem!1)) | (~b(elem!1, s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.44 tff(28553,plain,
% 11.18/11.44 (~r(s(z), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[28552, 28478, 22901, 28192, 28383, 88, 22898, 2881, 118, 28382, 89])).
% 11.18/11.44 tff(28554,plain,
% 11.18/11.44 (b(s(z), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[180, 28553])).
% 11.18/11.44 tff(28555,plain,
% 11.18/11.44 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[2849, 28383])).
% 11.18/11.44 tff(28556,plain,
% 11.18/11.44 (~b(z, s(z))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[21922, 28554, 28382, 28478])).
% 11.18/11.44 tff(28557,plain,
% 11.18/11.44 (r(z, s(z))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[678, 28556])).
% 11.18/11.44 tff(28558,plain,
% 11.18/11.44 (~b(s(s(s(elem!1))), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[23013, 183, 90, 10682, 1216, 3843])).
% 11.18/11.44 tff(28559,plain,
% 11.18/11.44 (~r(s(s(s(elem!1))), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[16377, 183, 722, 1216])).
% 11.18/11.44 tff(28560,plain,
% 11.18/11.44 ($false),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[377, 28559, 28558])).
% 11.18/11.44 tff(28561,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.44 tff(28562,plain,
% 11.18/11.44 (~r(s(s(s(elem!1))), s(z))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[28561, 28557, 2913, 88, 22898, 28555])).
% 11.18/11.44 tff(28563,plain,
% 11.18/11.44 (b(s(s(s(elem!1))), s(z))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[223, 28562])).
% 11.18/11.44 tff(28564,plain,
% 11.18/11.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 11.18/11.44 inference(rewrite,[status(thm)],[])).
% 11.18/11.44 tff(28565,plain,
% 11.18/11.44 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 11.18/11.44 inference(rewrite,[status(thm)],[])).
% 11.18/11.44 tff(28566,plain,
% 11.18/11.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 11.18/11.44 inference(monotonicity,[status(thm)],[28565])).
% 11.18/11.44 tff(28567,plain,
% 11.18/11.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 11.18/11.44 inference(transitivity,[status(thm)],[28566, 28564])).
% 11.18/11.44 tff(28568,plain,
% 11.18/11.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 11.18/11.44 inference(quant_inst,[status(thm)],[])).
% 11.18/11.44 tff(28569,plain,
% 11.18/11.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 11.18/11.44 inference(modus_ponens,[status(thm)],[28568, 28567])).
% 11.18/11.44 tff(28570,plain,
% 11.18/11.44 ($false),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[28569, 391, 28478, 22898, 28563, 28554, 28382])).
% 11.18/11.44 tff(28571,plain,(b(s(z), s(s(s(s(z))))) | b(z, elem!1) | r(s(s(s(s(z)))), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.44 tff(28572,plain,
% 11.18/11.44 (b(s(z), s(s(s(s(z)))))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[28571, 89, 81, 2])).
% 11.18/11.44 tff(28573,plain,
% 11.18/11.44 (~(s(s(s(elem!1))) = elem!1)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[8, 22901])).
% 11.18/11.44 tff(28574,plain,
% 11.18/11.44 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 11.18/11.44 inference(monotonicity,[status(thm)],[8081])).
% 11.18/11.44 tff(28575,plain,
% 11.18/11.44 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 11.18/11.44 inference(symmetry,[status(thm)],[28574])).
% 11.18/11.44 tff(28576,plain,
% 11.18/11.44 (elem!1 = s(z)),
% 11.18/11.44 inference(symmetry,[status(thm)],[812])).
% 11.18/11.44 tff(28577,plain,
% 11.18/11.44 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 11.18/11.44 inference(monotonicity,[status(thm)],[28576])).
% 11.18/11.44 tff(28578,plain,
% 11.18/11.44 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 11.18/11.44 inference(symmetry,[status(thm)],[28577])).
% 11.18/11.44 tff(28579,plain,
% 11.18/11.44 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 11.18/11.44 inference(monotonicity,[status(thm)],[28578])).
% 11.18/11.44 tff(28580,plain,
% 11.18/11.44 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 11.18/11.44 inference(modus_ponens,[status(thm)],[5065, 28579])).
% 11.18/11.44 tff(28581,plain,
% 11.18/11.44 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 11.18/11.44 inference(monotonicity,[status(thm)],[8081, 812])).
% 11.18/11.44 tff(28582,plain,
% 11.18/11.44 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 11.18/11.44 inference(monotonicity,[status(thm)],[28576])).
% 11.18/11.44 tff(28583,plain,
% 11.18/11.44 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 11.18/11.44 inference(transitivity,[status(thm)],[28582, 28581])).
% 11.18/11.44 tff(28584,plain,
% 11.18/11.44 ((~b(s(s(s(s(s(elem!1))))), elem!1)) <=> (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 11.18/11.44 inference(monotonicity,[status(thm)],[28583])).
% 11.18/11.44 tff(28585,plain,
% 11.18/11.44 (~b(elem!1, z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[19544, 391, 25596, 22924, 18086])).
% 11.18/11.44 tff(28586,plain,
% 11.18/11.44 (r(elem!1, z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[526, 28585, 2])).
% 11.18/11.44 tff(28587,plain,
% 11.18/11.44 (~(s(elem!1) = s(s(elem!1)))),
% 11.18/11.44 inference(modus_ponens,[status(thm)],[2680, 18180])).
% 11.18/11.44 tff(28588,plain,
% 11.18/11.44 (~r(z, s(s(elem!1)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[867, 27504, 411, 530])).
% 11.18/11.44 tff(28589,plain,
% 11.18/11.44 (b(z, s(s(elem!1)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[324, 28588])).
% 11.18/11.44 tff(28590,plain,
% 11.18/11.44 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[26900, 28589, 10682, 530, 233, 279, 4017])).
% 11.18/11.44 tff(28591,plain,
% 11.18/11.44 ($false),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[4878, 194, 530, 233, 27504, 28590])).
% 11.18/11.44 tff(28592,plain,(b(s(s(elem!1)), elem!1) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.44 tff(28593,plain,
% 11.18/11.44 (b(s(s(elem!1)), elem!1)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[28592, 4486, 530, 10682, 7433, 411, 7422])).
% 11.18/11.44 tff(28594,plain,
% 11.18/11.44 (~r(s(elem!1), elem!1)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[541, 1628, 411, 530])).
% 11.18/11.44 tff(28595,plain,
% 11.18/11.44 (b(s(elem!1), elem!1)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[2168, 28594, 164])).
% 11.18/11.44 tff(28596,plain,
% 11.18/11.44 (~r(elem!1, s(elem!1))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[9766, 1628, 411, 530])).
% 11.18/11.44 tff(28597,plain,
% 11.18/11.44 (b(elem!1, s(elem!1))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[443, 28596, 7437])).
% 11.18/11.44 tff(28598,plain,
% 11.18/11.44 (~b(s(s(elem!1)), s(elem!1))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[19494, 28597, 973, 28595])).
% 11.18/11.44 tff(28599,plain,
% 11.18/11.44 (r(s(s(elem!1)), s(elem!1))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[1135, 28598, 285])).
% 11.18/11.44 tff(28600,plain,
% 11.18/11.44 (~r(s(s(elem!1)), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[24417, 28599, 411, 1628])).
% 11.18/11.44 tff(28601,plain,
% 11.18/11.44 (b(s(s(elem!1)), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[2629, 28600])).
% 11.18/11.44 tff(28602,plain,
% 11.18/11.44 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[13177, 28601, 10682, 380])).
% 11.18/11.44 tff(28603,plain,
% 11.18/11.44 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[1370, 28602, 297])).
% 11.18/11.44 tff(28604,plain,
% 11.18/11.44 (~r(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[19498, 28603, 973, 448, 380, 28595, 8611, 285, 28597])).
% 11.18/11.44 tff(28605,plain,
% 11.18/11.44 (b(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[588, 28604, 279])).
% 11.18/11.44 tff(28606,plain,
% 11.18/11.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(elem!1), elem!1)))),
% 11.18/11.44 inference(rewrite,[status(thm)],[])).
% 11.18/11.44 tff(28607,plain,
% 11.18/11.44 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), 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)))))) <=> ((~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(elem!1), elem!1)))),
% 11.18/11.44 inference(rewrite,[status(thm)],[])).
% 11.18/11.44 tff(28608,plain,
% 11.18/11.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), elem!1))))),
% 11.18/11.44 inference(monotonicity,[status(thm)],[28607])).
% 11.18/11.44 tff(28609,plain,
% 11.18/11.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(elem!1), elem!1)))),
% 11.18/11.44 inference(transitivity,[status(thm)],[28608, 28606])).
% 11.18/11.44 tff(28610,plain,
% 11.18/11.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), 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))))))),
% 11.18/11.44 inference(quant_inst,[status(thm)],[])).
% 11.18/11.44 tff(28611,plain,
% 11.18/11.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))),
% 11.18/11.44 inference(modus_ponens,[status(thm)],[28610, 28609])).
% 11.18/11.44 tff(28612,plain,
% 11.18/11.44 ($false),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[28611, 391, 28605, 448, 28597, 28595])).
% 11.18/11.44 tff(28613,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), z)) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.44 tff(28614,plain,
% 11.18/11.44 (~r(s(elem!1), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[28613, 28593, 7433, 448, 25596, 8611, 285, 15838, 10682, 411, 4597, 530])).
% 11.18/11.44 tff(28615,plain,
% 11.18/11.44 (b(s(elem!1), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[549, 28614])).
% 11.18/11.44 tff(28616,plain,
% 11.18/11.44 ($false),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[12746, 26138, 26145, 10682, 591, 279])).
% 11.18/11.44 tff(28617,plain,((~r(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.44 tff(28618,plain,
% 11.18/11.44 (~r(s(elem!1), elem!1)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[28617, 28615, 530, 4486, 10682, 7433])).
% 11.18/11.44 tff(28619,plain,
% 11.18/11.44 (b(s(elem!1), elem!1)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[2168, 28618, 4597])).
% 11.18/11.44 tff(28620,plain,
% 11.18/11.44 (~r(s(s(z)), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[3560, 28614, 812])).
% 11.18/11.44 tff(28621,plain,
% 11.18/11.44 (b(s(s(z)), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[1211, 28620])).
% 11.18/11.44 tff(28622,plain,
% 11.18/11.44 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[20748, 28621, 90, 18104])).
% 11.18/11.44 tff(28623,plain,
% 11.18/11.44 (r(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[1714, 28622])).
% 11.18/11.44 tff(28624,plain,
% 11.18/11.44 (~b(s(s(s(s(z)))), s(z))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[11177, 7408, 7866])).
% 11.18/11.44 tff(28625,plain,
% 11.18/11.44 (r(s(s(s(s(z)))), s(z))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[749, 28624])).
% 11.18/11.44 tff(28626,plain,
% 11.18/11.44 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[4472, 28621, 90, 18104])).
% 11.18/11.44 tff(28627,plain,
% 11.18/11.44 (r(s(s(z)), s(s(s(s(z)))))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[3652, 28626])).
% 11.18/11.44 tff(28628,plain,
% 11.18/11.44 (~r(s(z), s(s(z)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[9076, 28627, 28625, 28623])).
% 11.18/11.44 tff(28629,plain,
% 11.18/11.44 (b(s(z), s(s(z)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[1788, 28628])).
% 11.18/11.44 tff(28630,plain,
% 11.18/11.44 (b(elem!1, s(elem!1))),
% 11.18/11.44 inference(modus_ponens,[status(thm)],[28629, 24223])).
% 11.18/11.44 tff(28631,plain,
% 11.18/11.44 (~b(s(elem!1), s(s(elem!1)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[25838, 391, 28593, 28615, 28630, 28619])).
% 11.18/11.44 tff(28632,plain,
% 11.18/11.44 (r(s(elem!1), s(s(elem!1)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[8644, 28631, 8611])).
% 11.18/11.44 tff(28633,plain,
% 11.18/11.44 (~b(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[12799, 28615, 10682, 25596])).
% 11.18/11.44 tff(28634,plain,
% 11.18/11.44 (r(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[588, 28633, 7433])).
% 11.18/11.44 tff(28635,plain,
% 11.18/11.44 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[19498, 28630, 28593, 448, 25596, 28619, 8611, 285, 28634])).
% 11.18/11.44 tff(28636,plain,
% 11.18/11.44 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[1370, 28635, 15838])).
% 11.18/11.44 tff(28637,plain,
% 11.18/11.44 (~b(elem!1, z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[19544, 391, 25596, 10682, 448])).
% 11.18/11.44 tff(28638,plain,
% 11.18/11.44 (r(s(z), z)),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[7485, 28637, 812])).
% 11.18/11.44 tff(28639,plain,
% 11.18/11.44 (~b(z, s(s(elem!1)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[8469, 28636, 25596, 28593, 28630])).
% 11.18/11.44 tff(28640,plain,
% 11.18/11.44 (r(z, s(s(elem!1)))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[324, 28639])).
% 11.18/11.44 tff(28641,plain,
% 11.18/11.44 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[3432, 28640, 28638, 19981, 28636])).
% 11.18/11.44 tff(28642,plain,
% 11.18/11.44 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[1356, 28641, 21729])).
% 11.18/11.44 tff(28643,plain,
% 11.18/11.44 (~b(s(s(elem!1)), s(elem!1))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[24390, 391, 28593, 28615, 28630, 28619])).
% 11.18/11.44 tff(28644,plain,
% 11.18/11.44 (r(s(s(elem!1)), s(elem!1))),
% 11.18/11.44 inference(unit_resolution,[status(thm)],[1135, 28643, 285])).
% 11.18/11.45 tff(28645,plain,
% 11.18/11.45 ($false),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[24582, 194, 28634, 28644, 28642, 28632])).
% 11.18/11.45 tff(28646,plain,(b(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.45 tff(28647,plain,
% 11.18/11.45 (b(s(s(s(elem!1))), elem!1)),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[28646, 7412, 28587, 18086, 812, 90, 28586, 22924, 411, 127])).
% 11.18/11.45 tff(28648,plain,
% 11.18/11.45 (b(z, s(s(s(s(z)))))),
% 11.18/11.45 inference(modus_ponens,[status(thm)],[22924, 18103])).
% 11.18/11.45 tff(28649,plain,
% 11.18/11.45 (~r(s(elem!1), elem!1)),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[541, 19022, 411, 530])).
% 11.18/11.45 tff(28650,plain,
% 11.18/11.45 (~r(elem!1, s(elem!1))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[9766, 19022, 411, 530])).
% 11.18/11.45 tff(28651,plain,
% 11.18/11.45 (~b(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[2340, 28650, 900, 7437, 28649])).
% 11.18/11.45 tff(28652,plain,
% 11.18/11.45 (r(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[588, 28651, 7433])).
% 11.18/11.45 tff(28653,plain,
% 11.18/11.45 (b(s(elem!1), elem!1)),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[2168, 28649, 164])).
% 11.18/11.45 tff(28654,plain,
% 11.18/11.45 ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 11.18/11.45 inference(monotonicity,[status(thm)],[7945])).
% 11.18/11.45 tff(28655,plain,
% 11.18/11.45 ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 11.18/11.45 inference(transitivity,[status(thm)],[28654, 8179])).
% 11.18/11.45 tff(28656,plain,
% 11.18/11.45 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 11.18/11.45 inference(symmetry,[status(thm)],[28655])).
% 11.18/11.45 tff(28657,plain,
% 11.18/11.45 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))))),
% 11.18/11.45 inference(monotonicity,[status(thm)],[28656])).
% 11.18/11.45 tff(28658,plain,
% 11.18/11.45 (~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 11.18/11.45 inference(modus_ponens,[status(thm)],[4995, 28657])).
% 11.18/11.45 tff(28659,plain,
% 11.18/11.45 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 11.18/11.45 inference(monotonicity,[status(thm)],[818])).
% 11.18/11.45 tff(28660,plain,
% 11.18/11.45 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 11.18/11.45 inference(monotonicity,[status(thm)],[28659])).
% 11.18/11.45 tff(28661,plain,
% 11.18/11.45 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 11.18/11.45 inference(modus_ponens,[status(thm)],[5009, 28660])).
% 11.18/11.45 tff(28662,plain,
% 11.18/11.45 (b(s(s(s(s(z)))), elem!1)),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[1563, 900, 7866])).
% 11.18/11.45 tff(28663,plain,
% 11.18/11.45 (b(s(s(s(s(z)))), s(z))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[9614, 28662, 812])).
% 11.18/11.45 tff(28664,plain,
% 11.18/11.45 (b(s(s(s(elem!1))), s(z))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[11177, 28663, 7866])).
% 11.18/11.45 tff(28665,plain,
% 11.18/11.45 (~r(elem!1, s(s(z)))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[18602, 3557, 530, 815])).
% 11.18/11.45 tff(28666,plain,
% 11.18/11.45 (b(elem!1, s(s(z)))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[3394, 28665, 19053])).
% 11.18/11.45 tff(28667,plain,
% 11.18/11.45 (~b(s(s(z)), s(s(s(elem!1))))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[8561, 28666, 1234, 18086, 28664])).
% 11.18/11.45 tff(28668,plain,
% 11.18/11.45 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[8551, 28667, 812])).
% 11.18/11.45 tff(28669,plain,
% 11.18/11.45 (r(s(s(z)), s(s(s(s(z)))))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[3652, 28668])).
% 11.18/11.45 tff(28670,plain,
% 11.18/11.45 (r(s(elem!1), s(s(s(elem!1))))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[3614, 28669, 812])).
% 11.18/11.45 tff(28671,plain,
% 11.18/11.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 11.18/11.45 inference(rewrite,[status(thm)],[])).
% 11.18/11.45 tff(28672,plain,
% 11.18/11.45 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 11.18/11.45 inference(rewrite,[status(thm)],[])).
% 11.18/11.45 tff(28673,plain,
% 11.18/11.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 11.18/11.45 inference(monotonicity,[status(thm)],[28672])).
% 11.18/11.45 tff(28674,plain,
% 11.18/11.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 11.18/11.45 inference(transitivity,[status(thm)],[28673, 28671])).
% 11.18/11.45 tff(28675,plain,
% 11.18/11.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 11.18/11.45 inference(quant_inst,[status(thm)],[])).
% 11.18/11.45 tff(28676,plain,
% 11.18/11.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 11.18/11.45 inference(modus_ponens,[status(thm)],[28675, 28674])).
% 11.18/11.45 tff(28677,plain,
% 11.18/11.45 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[28676, 391, 900, 448, 2122, 8042])).
% 11.18/11.45 tff(28678,plain,
% 11.18/11.45 (r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[13326, 42, 13323, 28677])).
% 11.18/11.45 tff(28679,plain,
% 11.18/11.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 11.18/11.45 inference(rewrite,[status(thm)],[])).
% 11.18/11.45 tff(28680,plain,
% 11.18/11.45 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 11.18/11.45 inference(rewrite,[status(thm)],[])).
% 11.18/11.45 tff(28681,plain,
% 11.18/11.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 11.18/11.45 inference(monotonicity,[status(thm)],[28680])).
% 11.18/11.45 tff(28682,plain,
% 11.18/11.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 11.18/11.45 inference(transitivity,[status(thm)],[28681, 28679])).
% 11.18/11.45 tff(28683,plain,
% 11.18/11.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 11.18/11.45 inference(quant_inst,[status(thm)],[])).
% 11.18/11.45 tff(28684,plain,
% 11.18/11.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 11.18/11.45 inference(modus_ponens,[status(thm)],[28683, 28682])).
% 11.18/11.45 tff(28685,plain,
% 11.18/11.45 (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[28684, 391, 900, 448, 8042])).
% 11.18/11.45 tff(28686,assumption,(~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))), introduced(assumption)).
% 11.18/11.45 tff(28687,plain,
% 11.18/11.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 11.18/11.45 inference(rewrite,[status(thm)],[])).
% 11.18/11.45 tff(28688,plain,
% 11.18/11.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 11.18/11.45 inference(quant_inst,[status(thm)],[])).
% 11.18/11.45 tff(28689,plain,
% 11.18/11.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 11.18/11.45 inference(modus_ponens,[status(thm)],[28688, 28687])).
% 11.18/11.45 tff(28690,plain,
% 11.18/11.45 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 11.18/11.45 inference(unit_resolution,[status(thm)],[28689, 42, 28686, 28685])).
% 11.18/11.45 tff(28691,plain,
% 11.18/11.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 11.18/11.45 inference(rewrite,[status(thm)],[])).
% 11.18/11.45 tff(28692,plain,
% 11.18/11.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 11.18/11.45 inference(quant_inst,[status(thm)],[])).
% 11.18/11.45 tff(28693,plain,
% 11.18/11.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 11.18/11.46 inference(modus_ponens,[status(thm)],[28692, 28691])).
% 11.18/11.46 tff(28694,plain,
% 11.18/11.46 ($false),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[28693, 194, 613, 604, 28690, 28678])).
% 11.18/11.46 tff(28695,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.46 tff(28696,plain,
% 11.18/11.46 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[28695, 28670, 900, 28661, 28658, 28653, 18086, 28652])).
% 11.18/11.46 tff(28697,plain,
% 11.18/11.46 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[8073, 28696, 28580])).
% 11.18/11.46 tff(28698,plain,
% 11.18/11.46 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 11.18/11.46 inference(modus_ponens,[status(thm)],[28697, 28575])).
% 11.18/11.46 tff(28699,plain,
% 11.18/11.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 11.18/11.46 inference(rewrite,[status(thm)],[])).
% 11.18/11.46 tff(28700,plain,
% 11.18/11.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 11.18/11.46 inference(quant_inst,[status(thm)],[])).
% 11.18/11.46 tff(28701,plain,
% 11.18/11.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), z))),
% 11.18/11.46 inference(modus_ponens,[status(thm)],[28700, 28699])).
% 11.18/11.46 tff(28702,plain,
% 11.18/11.46 (~r(s(s(s(s(s(elem!1))))), z)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[28701, 194, 411, 530, 28698])).
% 11.18/11.46 tff(28703,plain,
% 11.18/11.46 (b(s(s(s(s(s(elem!1))))), z)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[18703, 28702])).
% 11.18/11.46 tff(28704,plain,
% 11.18/11.46 (~b(s(s(elem!1)), elem!1)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[28613, 19022, 7433, 18086, 380, 8611, 285, 297, 10682, 411, 164, 530])).
% 11.18/11.46 tff(28705,plain,
% 11.18/11.46 (r(s(s(elem!1)), elem!1)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[872, 28704, 7422])).
% 11.18/11.46 tff(28706,plain,
% 11.18/11.46 (~r(s(s(elem!1)), z)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[8360, 28705, 411, 530])).
% 11.18/11.46 tff(28707,plain,
% 11.18/11.46 (b(s(s(elem!1)), z)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[2629, 28706])).
% 11.18/11.46 tff(28708,plain,
% 11.18/11.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 11.18/11.46 inference(rewrite,[status(thm)],[])).
% 11.18/11.46 tff(28709,plain,
% 11.18/11.46 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 11.18/11.46 inference(rewrite,[status(thm)],[])).
% 11.18/11.46 tff(28710,plain,
% 11.18/11.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 11.18/11.46 inference(monotonicity,[status(thm)],[28709])).
% 11.18/11.46 tff(28711,plain,
% 11.18/11.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 11.18/11.46 inference(transitivity,[status(thm)],[28710, 28708])).
% 11.18/11.46 tff(28712,plain,
% 11.18/11.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 11.18/11.46 inference(quant_inst,[status(thm)],[])).
% 11.18/11.46 tff(28713,plain,
% 11.18/11.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 11.18/11.46 inference(modus_ponens,[status(thm)],[28712, 28711])).
% 11.18/11.46 tff(28714,plain,
% 11.18/11.46 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[28713, 391, 900, 10682, 28707, 28703])).
% 11.18/11.46 tff(28715,plain,
% 11.18/11.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 11.18/11.46 inference(rewrite,[status(thm)],[])).
% 11.18/11.46 tff(28716,plain,
% 11.18/11.46 (((~r(elem!1, z)) | (~r(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(elem!1)))))))) <=> ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 11.18/11.46 inference(rewrite,[status(thm)],[])).
% 11.18/11.46 tff(28717,plain,
% 11.18/11.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(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(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 11.18/11.46 inference(monotonicity,[status(thm)],[28716])).
% 11.18/11.46 tff(28718,plain,
% 11.18/11.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(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(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 11.18/11.46 inference(transitivity,[status(thm)],[28717, 28715])).
% 11.18/11.46 tff(28719,plain,
% 11.18/11.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(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(elem!1))))))))),
% 11.18/11.46 inference(quant_inst,[status(thm)],[])).
% 11.18/11.46 tff(28720,plain,
% 11.18/11.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 11.18/11.46 inference(modus_ponens,[status(thm)],[28719, 28718])).
% 11.18/11.46 tff(28721,plain,
% 11.18/11.46 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[28720, 194, 530, 28705, 28698])).
% 11.18/11.46 tff(28722,plain,
% 11.18/11.46 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[8127, 42, 28721])).
% 11.18/11.46 tff(28723,plain,
% 11.18/11.46 ($false),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[28722, 28714, 8095])).
% 11.18/11.46 tff(28724,plain,((~r(s(s(z)), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(elem!1) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.46 tff(28725,plain,
% 11.18/11.46 (~r(s(s(z)), z)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[28724, 28647, 22924, 812, 411, 28586, 4597, 1234, 25596, 28587, 7412, 15838])).
% 11.18/11.46 tff(28726,plain,
% 11.18/11.46 (b(s(s(z)), z)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[1211, 28725])).
% 11.18/11.46 tff(28727,plain,
% 11.18/11.46 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[4472, 28726, 90, 28648])).
% 11.18/11.46 tff(28728,plain,
% 11.18/11.46 (r(s(s(z)), s(s(s(s(z)))))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[3652, 28727])).
% 11.18/11.46 tff(28729,plain,
% 11.18/11.46 (r(s(elem!1), s(s(s(elem!1))))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[3614, 28728, 812])).
% 11.18/11.46 tff(28730,plain,
% 11.18/11.46 (b(s(elem!1), z)),
% 11.18/11.46 inference(modus_ponens,[status(thm)],[28726, 9630])).
% 11.18/11.46 tff(28731,plain,
% 11.18/11.46 (~b(elem!1, z)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[17249, 380, 10682, 900])).
% 11.18/11.46 tff(28732,plain,
% 11.18/11.46 (r(elem!1, z)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[526, 28731, 2])).
% 11.18/11.46 tff(28733,plain,
% 11.18/11.46 ($false),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[8360, 28732, 23565, 411, 364])).
% 11.18/11.46 tff(28734,plain,((~b(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.46 tff(28735,plain,
% 11.18/11.46 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[28734, 364, 10682, 411, 2, 380, 900])).
% 11.18/11.46 tff(28736,plain,
% 11.18/11.46 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[1370, 28735, 297])).
% 11.18/11.46 tff(28737,plain,
% 11.18/11.46 (~r(s(s(elem!1)), z)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[8360, 364, 411, 530])).
% 11.18/11.46 tff(28738,plain,
% 11.18/11.46 (b(s(s(elem!1)), z)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[2629, 28737])).
% 11.18/11.46 tff(28739,plain,
% 11.18/11.46 ($false),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[17760, 28738, 28736, 10682, 591, 604, 8611, 285, 900])).
% 11.18/11.46 tff(28740,plain,((~r(s(s(elem!1)), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.46 tff(28741,plain,
% 11.18/11.46 (~r(s(s(elem!1)), elem!1)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[28740, 28730, 22924, 28729, 28587, 7412, 28647, 15838, 411, 28586, 2, 25596])).
% 11.18/11.46 tff(28742,plain,
% 11.18/11.46 (b(s(s(elem!1)), elem!1)),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[872, 28741, 7422])).
% 11.18/11.46 tff(28743,plain,
% 11.18/11.46 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[6001, 28742, 18086, 28647])).
% 11.18/11.46 tff(28744,plain,
% 11.18/11.46 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[1356, 28743, 21729])).
% 11.18/11.46 tff(28745,plain,
% 11.18/11.46 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.46 inference(unit_resolution,[status(thm)],[20748, 28726, 90, 28648])).
% 11.18/11.47 tff(28746,plain,
% 11.18/11.47 (r(s(s(s(s(z)))), s(s(z)))),
% 11.18/11.47 inference(unit_resolution,[status(thm)],[1714, 28745])).
% 11.18/11.47 tff(28747,plain,
% 11.18/11.47 (r(s(s(s(elem!1))), s(elem!1))),
% 11.18/11.47 inference(modus_ponens,[status(thm)],[28746, 19452])).
% 11.18/11.47 tff(28748,plain,
% 11.18/11.47 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 11.18/11.47 inference(monotonicity,[status(thm)],[8081, 8082])).
% 11.18/11.47 tff(28749,plain,
% 11.18/11.47 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 11.18/11.47 inference(symmetry,[status(thm)],[28748])).
% 11.18/11.47 tff(28750,plain,
% 11.18/11.47 ((~(s(s(s(s(s(s(z)))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 11.18/11.47 inference(monotonicity,[status(thm)],[28749])).
% 11.18/11.47 tff(28751,plain,
% 11.18/11.47 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 11.18/11.47 inference(modus_ponens,[status(thm)],[8094, 28750])).
% 11.18/11.47 tff(28752,assumption,(b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 11.18/11.47 tff(28753,plain,
% 11.18/11.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 11.18/11.47 inference(rewrite,[status(thm)],[])).
% 11.18/11.47 tff(28754,plain,
% 11.18/11.47 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 11.18/11.47 inference(rewrite,[status(thm)],[])).
% 11.18/11.47 tff(28755,plain,
% 11.18/11.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 11.18/11.47 inference(monotonicity,[status(thm)],[28754])).
% 11.18/11.47 tff(28756,plain,
% 11.18/11.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 11.18/11.47 inference(transitivity,[status(thm)],[28755, 28753])).
% 11.18/11.47 tff(28757,plain,
% 11.18/11.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 11.18/11.47 inference(quant_inst,[status(thm)],[])).
% 11.18/11.47 tff(28758,plain,
% 11.18/11.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 11.18/11.47 inference(modus_ponens,[status(thm)],[28757, 28756])).
% 11.18/11.47 tff(28759,plain,
% 11.18/11.47 ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 11.18/11.47 inference(unit_resolution,[status(thm)],[28758, 391, 900, 973, 448])).
% 11.18/11.47 tff(28760,plain,
% 11.18/11.47 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 11.18/11.47 inference(unit_resolution,[status(thm)],[28759, 28752])).
% 11.18/11.47 tff(28761,plain,
% 11.18/11.47 (((~![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))))),
% 11.18/11.47 inference(rewrite,[status(thm)],[])).
% 11.18/11.47 tff(28762,plain,
% 11.18/11.47 ((~![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))))),
% 11.18/11.47 inference(quant_inst,[status(thm)],[])).
% 11.18/11.47 tff(28763,plain,
% 11.18/11.47 ((~![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)))),
% 11.18/11.47 inference(modus_ponens,[status(thm)],[28762, 28761])).
% 11.18/11.47 tff(28764,plain,
% 11.18/11.47 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 11.18/11.47 inference(unit_resolution,[status(thm)],[28763, 42, 28760])).
% 11.18/11.47 tff(28765,plain,
% 11.18/11.47 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 11.18/11.47 inference(unit_resolution,[status(thm)],[28764, 28751])).
% 11.18/11.47 tff(28766,plain,
% 11.18/11.47 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 11.18/11.47 inference(monotonicity,[status(thm)],[8081])).
% 11.18/11.47 tff(28767,plain,
% 11.18/11.47 ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 11.18/11.47 inference(symmetry,[status(thm)],[28766])).
% 11.18/11.47 tff(28768,plain,
% 11.18/11.47 ((~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 11.18/11.47 inference(monotonicity,[status(thm)],[28767])).
% 11.18/11.47 tff(28769,plain,
% 11.18/11.47 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 11.18/11.47 inference(modus_ponens,[status(thm)],[28658, 28768])).
% 11.18/11.47 tff(28770,plain,
% 11.18/11.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(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))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(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))))), elem!1)))),
% 11.18/11.47 inference(rewrite,[status(thm)],[])).
% 11.18/11.47 tff(28771,plain,
% 11.18/11.47 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(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))))), elem!1)))),
% 11.18/11.47 inference(rewrite,[status(thm)],[])).
% 11.18/11.47 tff(28772,plain,
% 11.18/11.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(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))))), elem!1))))),
% 11.18/11.47 inference(monotonicity,[status(thm)],[28771])).
% 11.18/11.47 tff(28773,plain,
% 11.18/11.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(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))))), elem!1)))),
% 11.18/11.48 inference(transitivity,[status(thm)],[28772, 28770])).
% 11.18/11.48 tff(28774,plain,
% 11.18/11.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 11.18/11.48 inference(quant_inst,[status(thm)],[])).
% 11.18/11.48 tff(28775,plain,
% 11.18/11.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(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))))), elem!1))),
% 11.18/11.48 inference(modus_ponens,[status(thm)],[28774, 28773])).
% 11.18/11.48 tff(28776,plain,
% 11.18/11.48 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28775, 391, 900, 448])).
% 11.18/11.48 tff(28777,plain,
% 11.18/11.48 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28776, 28752])).
% 11.18/11.48 tff(28778,plain,
% 11.18/11.48 ((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))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[8191, 42, 28777])).
% 11.18/11.48 tff(28779,plain,
% 11.18/11.48 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28778, 28769])).
% 11.18/11.48 tff(28780,plain,
% 11.18/11.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 11.18/11.48 inference(rewrite,[status(thm)],[])).
% 11.18/11.48 tff(28781,plain,
% 11.18/11.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 11.18/11.48 inference(quant_inst,[status(thm)],[])).
% 11.18/11.48 tff(28782,plain,
% 11.18/11.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 11.18/11.48 inference(modus_ponens,[status(thm)],[28781, 28780])).
% 11.18/11.48 tff(28783,plain,
% 11.18/11.48 ($false),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28782, 194, 613, 1378, 28779, 28765])).
% 11.18/11.48 tff(28784,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.48 tff(28785,plain,
% 11.18/11.48 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28784, 28747, 28744, 812, 28647, 28742, 18086])).
% 11.18/11.48 tff(28786,plain,
% 11.18/11.48 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 11.18/11.48 inference(modus_ponens,[status(thm)],[28785, 28584])).
% 11.18/11.48 tff(28787,plain,
% 11.18/11.48 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[8073, 28786, 28580])).
% 11.18/11.48 tff(28788,plain,
% 11.18/11.48 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 11.18/11.48 inference(modus_ponens,[status(thm)],[28787, 28575])).
% 11.18/11.48 tff(28789,plain,
% 11.18/11.48 (b(s(s(s(s(z)))), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[1563, 28647, 7866])).
% 11.18/11.48 tff(28790,plain,
% 11.18/11.48 (b(s(s(s(s(z)))), s(z))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[9614, 28789, 812])).
% 11.18/11.48 tff(28791,plain,
% 11.18/11.48 (b(s(s(s(elem!1))), s(z))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[11177, 28790, 7866])).
% 11.18/11.48 tff(28792,plain,
% 11.18/11.48 (b(s(z), s(s(s(elem!1))))),
% 11.18/11.48 inference(modus_ponens,[status(thm)],[18086, 7582])).
% 11.18/11.48 tff(28793,plain,
% 11.18/11.48 (~r(s(s(elem!1)), s(z))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[2220, 28741, 812])).
% 11.18/11.48 tff(28794,plain,
% 11.18/11.48 (b(s(s(elem!1)), s(z))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[362, 28793])).
% 11.18/11.48 tff(28795,plain,
% 11.18/11.48 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[4762, 28794, 28792, 28791])).
% 11.18/11.48 tff(28796,plain,
% 11.18/11.48 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[1370, 28795, 15838])).
% 11.18/11.48 tff(28797,plain,
% 11.18/11.48 (~b(s(elem!1), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[8697, 28796, 28647, 18086, 28729, 28587, 7412, 28742])).
% 11.18/11.48 tff(28798,plain,
% 11.18/11.48 (r(s(elem!1), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[2168, 28797, 4597])).
% 11.18/11.48 tff(28799,plain,
% 11.18/11.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 11.18/11.48 inference(rewrite,[status(thm)],[])).
% 11.18/11.48 tff(28800,plain,
% 11.18/11.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 11.18/11.48 inference(quant_inst,[status(thm)],[])).
% 11.18/11.48 tff(28801,plain,
% 11.18/11.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 11.18/11.48 inference(modus_ponens,[status(thm)],[28800, 28799])).
% 11.18/11.48 tff(28802,plain,
% 11.18/11.48 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28801, 194, 28586, 28798, 28788])).
% 11.18/11.48 tff(28803,plain,
% 11.18/11.48 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 11.18/11.48 inference(quant_inst,[status(thm)],[])).
% 11.18/11.48 tff(28804,plain,
% 11.18/11.48 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28803, 106])).
% 11.18/11.48 tff(28805,assumption,(s(s(s(s(s(elem!1))))) = s(elem!1)), introduced(assumption)).
% 11.18/11.48 tff(28806,plain,
% 11.18/11.48 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(elem!1))),
% 11.18/11.48 inference(monotonicity,[status(thm)],[28805])).
% 11.18/11.48 tff(28807,plain,
% 11.18/11.48 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(elem!1))))))),
% 11.18/11.48 inference(symmetry,[status(thm)],[28806])).
% 11.18/11.48 tff(28808,plain,
% 11.18/11.48 (elem!1 = s(s(s(s(elem!1))))),
% 11.18/11.48 inference(transitivity,[status(thm)],[261, 28807, 28804])).
% 11.18/11.48 tff(28809,plain,
% 11.18/11.48 ($false),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[14203, 28808])).
% 11.18/11.48 tff(28810,plain,((~(s(s(s(s(s(elem!1))))) = s(elem!1))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.48 tff(28811,plain,
% 11.18/11.48 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28810, 18176])).
% 11.18/11.48 tff(28812,plain,
% 11.18/11.48 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[8108, 42, 28811, 28802])).
% 11.18/11.48 tff(28813,plain,
% 11.18/11.48 (~r(s(s(s(s(s(elem!1))))), z)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28701, 194, 411, 28586, 28788])).
% 11.18/11.48 tff(28814,plain,
% 11.18/11.48 (b(s(s(s(s(s(elem!1))))), z)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[18703, 28813])).
% 11.18/11.48 tff(28815,plain,
% 11.18/11.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 11.18/11.48 inference(rewrite,[status(thm)],[])).
% 11.18/11.48 tff(28816,plain,
% 11.18/11.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 11.18/11.48 inference(quant_inst,[status(thm)],[])).
% 11.18/11.48 tff(28817,plain,
% 11.18/11.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 11.18/11.48 inference(modus_ponens,[status(thm)],[28816, 28815])).
% 11.18/11.48 tff(28818,plain,
% 11.18/11.48 ($false),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28817, 391, 28647, 22924, 28730, 28814, 28812])).
% 11.18/11.48 tff(28819,plain,((~(s(z) = elem!1)) | (~r(z, elem!1)) | (elem!1 = z) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.48 tff(28820,plain,
% 11.18/11.48 (~(s(z) = elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28819, 28572, 2, 88, 28192, 28573])).
% 11.18/11.48 tff(28821,plain,
% 11.18/11.48 (~b(z, s(s(s(s(z)))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[10438, 847, 411, 1234, 90])).
% 11.18/11.48 tff(28822,plain,
% 11.18/11.48 (r(z, s(s(s(s(z)))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[800, 28821])).
% 11.18/11.48 tff(28823,plain,
% 11.18/11.48 (~r(s(z), z)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[17062, 530, 847, 28822])).
% 11.18/11.48 tff(28824,plain,
% 11.18/11.48 (b(s(z), z)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[180, 28823])).
% 11.18/11.48 tff(28825,plain,
% 11.18/11.48 (~b(z, s(z))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28088, 28824, 90, 1234])).
% 11.18/11.48 tff(28826,plain,
% 11.18/11.48 (r(z, s(z))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[678, 28825])).
% 11.18/11.48 tff(28827,plain,
% 11.18/11.48 (~r(s(z), s(s(s(elem!1))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[16770, 28826, 847, 530])).
% 11.18/11.48 tff(28828,plain,
% 11.18/11.48 (b(s(z), s(s(s(elem!1))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[247, 28827])).
% 11.18/11.48 tff(28829,plain,
% 11.18/11.48 (~b(s(s(s(elem!1))), z)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[11303, 28828, 10682, 28824])).
% 11.18/11.48 tff(28830,plain,
% 11.18/11.48 (r(s(s(s(elem!1))), z)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[377, 28829])).
% 11.18/11.48 tff(28831,plain,
% 11.18/11.48 (~r(s(s(s(elem!1))), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[23607, 28830, 411, 530])).
% 11.18/11.48 tff(28832,plain,
% 11.18/11.48 (b(s(s(s(elem!1))), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[230, 28831, 9])).
% 11.18/11.48 tff(28833,plain,
% 11.18/11.48 (~b(elem!1, s(s(s(elem!1))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[16827, 28832, 411, 847, 150, 530, 28826])).
% 11.18/11.48 tff(28834,plain,
% 11.18/11.48 (r(elem!1, s(s(s(elem!1))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[424, 28833, 1])).
% 11.18/11.48 tff(28835,plain,
% 11.18/11.48 ($false),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[9837, 194, 411, 530, 28830, 28834])).
% 11.18/11.48 tff(28836,plain,((~r(elem!1, z)) | (~r(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.48 tff(28837,plain,
% 11.18/11.48 (~r(elem!1, z)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28836, 838, 1, 411, 150, 22924, 90, 1234])).
% 11.18/11.48 tff(28838,plain,
% 11.18/11.48 (b(elem!1, z)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[526, 28837, 2])).
% 11.18/11.48 tff(28839,plain,
% 11.18/11.48 (~r(z, s(z))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[845, 182, 411, 847])).
% 11.18/11.48 tff(28840,plain,
% 11.18/11.48 (b(z, s(z))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[678, 28839])).
% 11.18/11.48 tff(28841,plain,
% 11.18/11.48 (~r(s(z), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[2475, 182, 411, 847])).
% 11.18/11.48 tff(28842,plain,
% 11.18/11.48 (b(s(z), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[632, 28841, 150])).
% 11.18/11.48 tff(28843,plain,
% 11.18/11.48 (~r(s(s(s(s(z)))), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[10418, 28822, 411, 847])).
% 11.18/11.48 tff(28844,plain,
% 11.18/11.48 (~b(s(s(s(s(z)))), s(z))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[22918, 28840, 90, 1234])).
% 11.18/11.48 tff(28845,plain,
% 11.18/11.48 (r(s(s(s(s(z)))), s(z))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[749, 28844])).
% 11.18/11.48 tff(28846,plain,
% 11.18/11.48 (~r(elem!1, s(s(s(s(z)))))),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[15063, 28845, 411, 28822])).
% 11.18/11.48 tff(28847,plain,
% 11.18/11.48 (s(s(s(s(z)))) = elem!1),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[18869, 28846, 1234, 28843, 28842])).
% 11.18/11.48 tff(28848,plain,
% 11.18/11.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 11.18/11.48 inference(rewrite,[status(thm)],[])).
% 11.18/11.48 tff(28849,plain,
% 11.18/11.48 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 11.18/11.48 inference(rewrite,[status(thm)],[])).
% 11.18/11.48 tff(28850,plain,
% 11.18/11.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 11.18/11.48 inference(monotonicity,[status(thm)],[28849])).
% 11.18/11.48 tff(28851,plain,
% 11.18/11.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 11.18/11.48 inference(transitivity,[status(thm)],[28850, 28848])).
% 11.18/11.48 tff(28852,plain,
% 11.18/11.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 11.18/11.48 inference(quant_inst,[status(thm)],[])).
% 11.18/11.48 tff(28853,plain,
% 11.18/11.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 11.18/11.48 inference(modus_ponens,[status(thm)],[28852, 28851])).
% 11.18/11.48 tff(28854,plain,
% 11.18/11.48 ($false),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28853, 391, 665, 900, 10682, 644, 379])).
% 11.18/11.48 tff(28855,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.48 tff(28856,plain,
% 11.18/11.48 (~b(s(s(s(elem!1))), elem!1)),
% 11.18/11.48 inference(unit_resolution,[status(thm)],[28855, 379, 10682, 644, 665])).
% 11.18/11.48 tff(28857,plain,
% 11.18/11.48 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 11.18/11.48 inference(monotonicity,[status(thm)],[688])).
% 11.18/11.48 tff(28858,plain,
% 11.18/11.48 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.18/11.48 inference(symmetry,[status(thm)],[28857])).
% 11.18/11.48 tff(28859,plain,
% 11.18/11.48 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.18/11.48 inference(monotonicity,[status(thm)],[28858])).
% 11.18/11.49 tff(28860,plain,
% 11.18/11.49 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.18/11.49 inference(modus_ponens,[status(thm)],[168, 28859])).
% 11.18/11.49 tff(28861,plain,
% 11.18/11.49 ($false),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[1669, 28860])).
% 11.18/11.49 tff(28862,plain,(b(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.49 tff(28863,plain,
% 11.18/11.49 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28862, 28856, 688])).
% 11.18/11.49 tff(28864,plain,
% 11.18/11.49 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[15351, 28863, 15348])).
% 11.18/11.49 tff(28865,plain,
% 11.18/11.49 (~r(s(s(s(elem!1))), z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28132, 28864, 719, 723])).
% 11.18/11.49 tff(28866,plain,
% 11.18/11.49 (b(s(s(s(elem!1))), z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[377, 28865])).
% 11.18/11.49 tff(28867,plain,
% 11.18/11.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.18/11.49 inference(rewrite,[status(thm)],[])).
% 11.18/11.49 tff(28868,plain,
% 11.18/11.49 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.18/11.49 inference(rewrite,[status(thm)],[])).
% 11.18/11.49 tff(28869,plain,
% 11.18/11.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 11.18/11.49 inference(monotonicity,[status(thm)],[28868])).
% 11.18/11.49 tff(28870,plain,
% 11.18/11.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.18/11.49 inference(transitivity,[status(thm)],[28869, 28867])).
% 11.18/11.49 tff(28871,plain,
% 11.18/11.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 11.18/11.49 inference(quant_inst,[status(thm)],[])).
% 11.18/11.49 tff(28872,plain,
% 11.18/11.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 11.18/11.49 inference(modus_ponens,[status(thm)],[28871, 28870])).
% 11.18/11.49 tff(28873,plain,
% 11.18/11.49 ($false),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28872, 391, 28866, 10682, 379, 664])).
% 11.18/11.49 tff(28874,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.49 tff(28875,plain,
% 11.18/11.49 (~b(s(z), s(s(s(elem!1))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28874, 28840, 10682, 28822, 28845, 16830, 28847, 28842, 665])).
% 11.18/11.49 tff(28876,plain,
% 11.18/11.49 (r(s(z), s(s(s(elem!1))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[247, 28875])).
% 11.18/11.49 tff(28877,plain,
% 11.18/11.49 (~r(s(s(s(elem!1))), z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[27817, 28876, 28822, 182])).
% 11.18/11.49 tff(28878,plain,
% 11.18/11.49 (b(s(s(s(elem!1))), z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[377, 28877])).
% 11.18/11.49 tff(28879,plain,
% 11.18/11.49 (b(s(s(s(elem!1))), elem!1)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[230, 22958, 127])).
% 11.18/11.49 tff(28880,plain,
% 11.18/11.49 (~b(elem!1, z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[17249, 28879, 10682, 380])).
% 11.18/11.49 tff(28881,plain,
% 11.18/11.49 (elem!1 = z),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[526, 28880, 2282])).
% 11.18/11.49 tff(28882,plain,
% 11.18/11.49 (r(elem!1, s(z)) <=> r(z, s(z))),
% 11.18/11.49 inference(monotonicity,[status(thm)],[28881])).
% 11.18/11.49 tff(28883,plain,
% 11.18/11.49 (r(z, s(z)) <=> r(elem!1, s(z))),
% 11.18/11.49 inference(symmetry,[status(thm)],[28882])).
% 11.18/11.49 tff(28884,plain,
% 11.18/11.49 ((~r(z, s(z))) <=> (~r(elem!1, s(z)))),
% 11.18/11.49 inference(monotonicity,[status(thm)],[28883])).
% 11.18/11.49 tff(28885,plain,
% 11.18/11.49 (~r(elem!1, s(z))),
% 11.18/11.49 inference(modus_ponens,[status(thm)],[676, 28884])).
% 11.18/11.49 tff(28886,plain,
% 11.18/11.49 ($false),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[847, 28885])).
% 11.18/11.49 tff(28887,plain,((~r(elem!1, s(z))) | r(z, s(z)) | r(elem!1, z) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = elem!1) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.49 tff(28888,plain,
% 11.18/11.49 (~r(s(s(s(elem!1))), s(z))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28887, 28878, 10682, 127, 847, 2282, 28839, 28876])).
% 11.18/11.49 tff(28889,plain,
% 11.18/11.49 (b(s(s(s(elem!1))), s(z))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[223, 28888])).
% 11.18/11.49 tff(28890,plain,
% 11.18/11.49 ($false),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[2520, 391, 665, 28878, 28842, 28889, 28840])).
% 11.18/11.49 tff(28891,plain,((~r(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(z))) | r(elem!1, z) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.49 tff(28892,plain,
% 11.18/11.49 (~r(s(z), z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28891, 28838, 22924, 9, 838, 28837, 1234, 411, 90, 150])).
% 11.18/11.49 tff(28893,plain,
% 11.18/11.49 (b(s(z), z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[180, 28892])).
% 11.18/11.49 tff(28894,plain,
% 11.18/11.49 (~b(z, s(z))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28088, 28893, 90, 1234])).
% 11.18/11.49 tff(28895,plain,
% 11.18/11.49 (r(z, s(z))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[678, 28894])).
% 11.18/11.49 tff(28896,plain,
% 11.18/11.49 (b(s(z), elem!1)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[19761, 28895, 411, 31, 150])).
% 11.18/11.49 tff(28897,plain,
% 11.18/11.49 (~b(z, s(s(s(s(z)))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[10438, 838, 411, 1234, 90])).
% 11.18/11.49 tff(28898,plain,
% 11.18/11.49 (r(z, s(s(s(s(z)))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[800, 28897])).
% 11.18/11.49 tff(28899,plain,
% 11.18/11.49 (~r(s(s(s(s(z)))), elem!1)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[10418, 28898, 411, 838])).
% 11.18/11.49 tff(28900,plain,
% 11.18/11.49 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[23575, 28896, 22924, 28838, 28893])).
% 11.18/11.49 tff(28901,plain,
% 11.18/11.49 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[1370, 28900, 26982])).
% 11.18/11.49 tff(28902,plain,
% 11.18/11.49 ($false),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[16153, 391, 665, 900, 10682, 448])).
% 11.18/11.49 tff(28903,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.18/11.49 tff(28904,plain,
% 11.18/11.49 (~b(s(s(s(elem!1))), elem!1)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28903, 448, 10682, 665])).
% 11.18/11.49 tff(28905,plain,
% 11.18/11.49 (r(s(s(s(elem!1))), elem!1)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[230, 28904, 127])).
% 11.18/11.49 tff(28906,plain,
% 11.18/11.49 (~r(s(s(s(elem!1))), z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[19265, 194, 411, 28905, 847])).
% 11.18/11.49 tff(28907,plain,
% 11.18/11.49 (b(s(s(s(elem!1))), z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[377, 28906])).
% 11.18/11.49 tff(28908,plain,
% 11.18/11.49 ($false),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[23581, 391, 665, 28907, 10682, 448])).
% 11.18/11.49 tff(28909,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.18/11.49 tff(28910,plain,
% 11.18/11.49 (~b(elem!1, s(s(s(elem!1))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28909, 28838, 22924, 411, 838, 9])).
% 11.18/11.49 tff(28911,plain,
% 11.18/11.49 (r(elem!1, s(s(s(elem!1))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[424, 28910, 1])).
% 11.18/11.49 tff(28912,plain,
% 11.18/11.49 (~r(s(z), s(s(s(elem!1))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[18031, 28911, 838, 28901])).
% 11.18/11.49 tff(28913,plain,
% 11.18/11.49 (b(s(z), s(s(s(elem!1))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[247, 28912])).
% 11.18/11.49 tff(28914,plain,
% 11.18/11.49 (~b(s(s(s(elem!1))), elem!1)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28855, 28913, 22924, 28896, 28838])).
% 11.18/11.49 tff(28915,plain,
% 11.18/11.49 (r(s(s(s(elem!1))), elem!1)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[230, 28914, 9])).
% 11.18/11.49 tff(28916,plain,
% 11.18/11.49 (~b(s(s(s(elem!1))), z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[11303, 28913, 22924, 28893])).
% 11.18/11.49 tff(28917,plain,
% 11.18/11.49 (r(s(s(s(elem!1))), z)),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[377, 28916])).
% 11.18/11.49 tff(28918,plain,
% 11.18/11.49 (~r(elem!1, s(s(s(s(z)))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[22246, 28917, 411, 28915])).
% 11.18/11.49 tff(28919,plain,
% 11.18/11.49 (s(s(s(s(z)))) = elem!1),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[18869, 28918, 1234, 28899, 28896])).
% 11.18/11.49 tff(28920,plain,
% 11.18/11.49 (~r(z, s(s(s(elem!1))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[8380, 411, 174, 410])).
% 11.18/11.49 tff(28921,plain,
% 11.18/11.49 (b(z, s(s(s(elem!1))))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[58, 28920])).
% 11.18/11.49 tff(28922,plain,
% 11.18/11.49 (~b(s(s(s(elem!1))), s(z))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[28322, 28921, 644, 379, 590])).
% 11.18/11.49 tff(28923,plain,
% 11.18/11.49 (r(s(s(s(elem!1))), s(z))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[223, 28922])).
% 11.18/11.49 tff(28924,plain,
% 11.18/11.49 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[23575, 28921, 665, 644, 590])).
% 11.18/11.49 tff(28925,plain,
% 11.18/11.49 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.18/11.49 inference(unit_resolution,[status(thm)],[1370, 28924, 297])).
% 11.18/11.49 tff(28926,plain,
% 11.18/11.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 11.18/11.49 inference(rewrite,[status(thm)],[])).
% 11.18/11.49 tff(28927,plain,
% 11.18/11.49 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 11.18/11.49 inference(rewrite,[status(thm)],[])).
% 11.18/11.49 tff(28928,plain,
% 11.18/11.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))))),
% 11.18/11.49 inference(monotonicity,[status(thm)],[28927])).
% 11.18/11.49 tff(28929,plain,
% 11.18/11.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 11.18/11.49 inference(transitivity,[status(thm)],[28928, 28926])).
% 11.18/11.49 tff(28930,plain,
% 11.18/11.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 11.28/11.50 inference(quant_inst,[status(thm)],[])).
% 11.28/11.50 tff(28931,plain,
% 11.28/11.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))),
% 11.28/11.50 inference(modus_ponens,[status(thm)],[28930, 28929])).
% 11.28/11.50 tff(28932,plain,
% 11.28/11.50 (~b(s(z), s(s(elem!1)))),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[28931, 391, 665, 10682, 973, 644])).
% 11.28/11.50 tff(28933,plain,
% 11.28/11.50 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[3414, 42, 28932])).
% 11.28/11.50 tff(28934,plain,
% 11.28/11.50 (r(s(z), s(s(elem!1)))),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[28933, 3404])).
% 11.28/11.50 tff(28935,plain,
% 11.28/11.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 11.28/11.50 inference(rewrite,[status(thm)],[])).
% 11.28/11.50 tff(28936,plain,
% 11.28/11.50 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 11.28/11.50 inference(rewrite,[status(thm)],[])).
% 11.28/11.50 tff(28937,plain,
% 11.28/11.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))))),
% 11.28/11.50 inference(monotonicity,[status(thm)],[28936])).
% 11.28/11.50 tff(28938,plain,
% 11.28/11.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 11.28/11.50 inference(transitivity,[status(thm)],[28937, 28935])).
% 11.28/11.50 tff(28939,plain,
% 11.28/11.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 11.28/11.50 inference(quant_inst,[status(thm)],[])).
% 11.28/11.50 tff(28940,plain,
% 11.28/11.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))),
% 11.28/11.50 inference(modus_ponens,[status(thm)],[28939, 28938])).
% 11.28/11.50 tff(28941,plain,
% 11.28/11.50 (~b(s(s(elem!1)), s(z))),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[28940, 391, 665, 10682, 973, 644])).
% 11.28/11.50 tff(28942,plain,
% 11.28/11.50 (r(s(s(elem!1)), s(z))),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[362, 28941])).
% 11.28/11.50 tff(28943,plain,
% 11.28/11.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 11.28/11.50 inference(rewrite,[status(thm)],[])).
% 11.28/11.50 tff(28944,plain,
% 11.28/11.50 (((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 11.28/11.50 inference(rewrite,[status(thm)],[])).
% 11.28/11.50 tff(28945,plain,
% 11.28/11.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 11.28/11.50 inference(monotonicity,[status(thm)],[28944])).
% 11.28/11.50 tff(28946,plain,
% 11.28/11.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 11.28/11.50 inference(transitivity,[status(thm)],[28945, 28943])).
% 11.28/11.50 tff(28947,plain,
% 11.28/11.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 11.28/11.50 inference(quant_inst,[status(thm)],[])).
% 11.28/11.50 tff(28948,plain,
% 11.28/11.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 11.28/11.50 inference(modus_ponens,[status(thm)],[28947, 28946])).
% 11.28/11.50 tff(28949,plain,
% 11.28/11.50 ($false),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[28948, 194, 28942, 327, 183, 28934])).
% 11.28/11.50 tff(28950,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.50 tff(28951,plain,
% 11.28/11.50 (~b(s(s(elem!1)), elem!1)),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[28950, 28925, 28923, 665, 28921, 644])).
% 11.28/11.50 tff(28952,plain,
% 11.28/11.50 (r(s(s(elem!1)), elem!1)),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[872, 28951, 249])).
% 11.28/11.50 tff(28953,plain,
% 11.28/11.50 (~r(z, s(s(elem!1)))),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[2562, 28952, 410, 411])).
% 11.28/11.50 tff(28954,plain,
% 11.28/11.50 (b(z, s(s(elem!1)))),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[324, 28953])).
% 11.28/11.50 tff(28955,plain,
% 11.28/11.50 (~b(s(s(elem!1)), z)),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[19801, 28954, 644, 665, 590])).
% 11.28/11.50 tff(28956,plain,
% 11.28/11.50 (r(s(s(elem!1)), z)),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[2629, 28955])).
% 11.28/11.50 tff(28957,plain,
% 11.28/11.50 ($false),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[19809, 194, 411, 28952, 410, 28956])).
% 11.28/11.50 tff(28958,plain,((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (s(s(elem!1)) = elem!1) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.50 tff(28959,plain,
% 11.28/11.50 (s(s(elem!1)) = elem!1),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[28958, 28917, 411, 28838, 28893, 28896, 28911, 26982, 28913])).
% 11.28/11.50 tff(28960,plain,
% 11.28/11.50 (s(s(s(elem!1))) = s(elem!1)),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[451, 28959])).
% 11.28/11.50 tff(28961,plain,
% 11.28/11.50 ($false),
% 11.28/11.50 inference(unit_resolution,[status(thm)],[717, 28960, 28919])).
% 11.28/11.50 tff(28962,plain,((s(z) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(z)) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.51 tff(28963,plain,
% 11.28/11.51 (b(elem!1, s(z))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[28962, 28820, 28192, 22901, 28572, 88, 2])).
% 11.28/11.51 tff(28964,plain,
% 11.28/11.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.28/11.51 inference(rewrite,[status(thm)],[])).
% 11.28/11.51 tff(28965,plain,
% 11.28/11.51 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.28/11.51 inference(rewrite,[status(thm)],[])).
% 11.28/11.51 tff(28966,plain,
% 11.28/11.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.28/11.51 inference(monotonicity,[status(thm)],[28965])).
% 11.28/11.51 tff(28967,plain,
% 11.28/11.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.28/11.51 inference(transitivity,[status(thm)],[28966, 28964])).
% 11.28/11.51 tff(28968,plain,
% 11.28/11.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 11.28/11.51 inference(quant_inst,[status(thm)],[])).
% 11.28/11.51 tff(28969,plain,
% 11.28/11.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 11.28/11.51 inference(modus_ponens,[status(thm)],[28968, 28967])).
% 11.28/11.51 tff(28970,plain,
% 11.28/11.51 ($false),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[28969, 391, 10682, 90, 2064, 1234, 721])).
% 11.28/11.51 tff(28971,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.51 tff(28972,plain,
% 11.28/11.51 (~b(elem!1, s(s(s(s(z)))))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[28971, 28572, 88, 22898, 28963])).
% 11.28/11.51 tff(28973,plain,
% 11.28/11.51 (~(s(z) = elem!1)),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[28819, 1234, 2, 90, 411, 9])).
% 11.28/11.51 tff(28974,plain,
% 11.28/11.51 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[2849, 28973])).
% 11.28/11.51 tff(28975,plain,
% 11.28/11.51 (b(elem!1, s(z))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[28962, 28973, 411, 1, 1234, 90, 2])).
% 11.28/11.51 tff(28976,plain,
% 11.28/11.51 (~b(elem!1, s(s(s(s(z)))))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[28971, 1234, 90, 22924, 28975])).
% 11.28/11.51 tff(28977,plain,
% 11.28/11.51 (r(elem!1, s(s(s(s(z)))))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[781, 21768, 28976])).
% 11.28/11.51 tff(28978,plain,
% 11.28/11.51 (~r(s(s(s(elem!1))), z)),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[23607, 233, 411, 530])).
% 11.28/11.51 tff(28979,plain,
% 11.28/11.51 (b(s(s(s(elem!1))), z)),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[377, 28978])).
% 11.28/11.51 tff(28980,plain,
% 11.28/11.51 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[23000, 391, 28979, 10682, 90])).
% 11.28/11.51 tff(28981,plain,
% 11.28/11.51 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[15351, 28980, 16058])).
% 11.28/11.51 tff(28982,plain,
% 11.28/11.51 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[23009, 391, 28979, 10682, 90])).
% 11.28/11.51 tff(28983,plain,
% 11.28/11.51 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 28982])).
% 11.28/11.51 tff(28984,plain,
% 11.28/11.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.28/11.51 inference(rewrite,[status(thm)],[])).
% 11.28/11.51 tff(28985,plain,
% 11.28/11.51 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.28/11.51 inference(rewrite,[status(thm)],[])).
% 11.28/11.51 tff(28986,plain,
% 11.28/11.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 11.28/11.51 inference(monotonicity,[status(thm)],[28985])).
% 11.28/11.51 tff(28987,plain,
% 11.28/11.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.28/11.51 inference(transitivity,[status(thm)],[28986, 28984])).
% 11.28/11.51 tff(28988,plain,
% 11.28/11.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 11.28/11.51 inference(quant_inst,[status(thm)],[])).
% 11.28/11.51 tff(28989,plain,
% 11.28/11.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.28/11.51 inference(modus_ponens,[status(thm)],[28988, 28987])).
% 11.28/11.51 tff(28990,plain,
% 11.28/11.51 ($false),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[28989, 194, 233, 2032, 28983, 28981])).
% 11.28/11.51 tff(28991,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.51 tff(28992,plain,
% 11.28/11.51 (~r(s(s(s(elem!1))), elem!1)),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[28991, 28977, 28974, 22924, 90, 411, 3618])).
% 11.28/11.51 tff(28993,plain,
% 11.28/11.51 (b(s(s(s(elem!1))), elem!1)),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[230, 28992, 9])).
% 11.28/11.51 tff(28994,plain,
% 11.28/11.51 (~r(z, s(s(s(s(z)))))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[15063, 27146, 411, 2032])).
% 11.28/11.51 tff(28995,plain,
% 11.28/11.51 (b(z, s(s(s(s(z)))))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[800, 28994])).
% 11.28/11.51 tff(28996,plain,
% 11.28/11.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.28/11.51 inference(rewrite,[status(thm)],[])).
% 11.28/11.51 tff(28997,plain,
% 11.28/11.51 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.28/11.51 inference(rewrite,[status(thm)],[])).
% 11.28/11.51 tff(28998,plain,
% 11.28/11.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.28/11.51 inference(monotonicity,[status(thm)],[28997])).
% 11.28/11.51 tff(28999,plain,
% 11.28/11.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.28/11.51 inference(transitivity,[status(thm)],[28998, 28996])).
% 11.28/11.51 tff(29000,plain,
% 11.28/11.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 11.28/11.51 inference(quant_inst,[status(thm)],[])).
% 11.28/11.51 tff(29001,plain,
% 11.28/11.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 11.28/11.51 inference(modus_ponens,[status(thm)],[29000, 28999])).
% 11.28/11.51 tff(29002,plain,
% 11.28/11.51 ($false),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[29001, 391, 10682, 90, 1234, 28995, 664])).
% 11.28/11.51 tff(29003,plain,((~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.51 tff(29004,plain,
% 11.28/11.51 (~b(z, s(z))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[29003, 28977, 90, 1234, 411, 22924])).
% 11.28/11.51 tff(29005,plain,
% 11.28/11.51 (r(z, s(z))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[678, 29004])).
% 11.28/11.51 tff(29006,plain,
% 11.28/11.51 (~r(s(z), elem!1)),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[16803, 29005, 411, 3618])).
% 11.28/11.51 tff(29007,plain,
% 11.28/11.51 (b(s(z), elem!1)),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[632, 29006, 28973])).
% 11.28/11.51 tff(29008,plain,
% 11.28/11.51 (~b(s(s(s(elem!1))), s(z))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[20387, 29007, 28975, 28993])).
% 11.28/11.51 tff(29009,plain,
% 11.28/11.51 (r(s(s(s(elem!1))), s(z))),
% 11.28/11.51 inference(unit_resolution,[status(thm)],[223, 29008])).
% 11.28/11.51 tff(29010,plain,
% 11.28/11.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 11.28/11.52 inference(rewrite,[status(thm)],[])).
% 11.28/11.52 tff(29011,plain,
% 11.28/11.52 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 11.28/11.52 inference(rewrite,[status(thm)],[])).
% 11.28/11.52 tff(29012,plain,
% 11.28/11.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 11.28/11.52 inference(monotonicity,[status(thm)],[29011])).
% 11.28/11.52 tff(29013,plain,
% 11.28/11.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 11.28/11.52 inference(transitivity,[status(thm)],[29012, 29010])).
% 11.28/11.52 tff(29014,plain,
% 11.28/11.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 11.28/11.52 inference(quant_inst,[status(thm)],[])).
% 11.28/11.52 tff(29015,plain,
% 11.28/11.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 11.28/11.52 inference(modus_ponens,[status(thm)],[29014, 29013])).
% 11.28/11.52 tff(29016,plain,
% 11.28/11.52 (~b(s(z), s(s(s(elem!1))))),
% 11.28/11.52 inference(unit_resolution,[status(thm)],[29015, 391, 28993, 29007, 28975])).
% 11.28/11.52 tff(29017,plain,
% 11.28/11.52 (r(s(z), s(s(s(elem!1))))),
% 11.28/11.52 inference(unit_resolution,[status(thm)],[247, 29016])).
% 11.28/11.52 tff(29018,plain,
% 11.28/11.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 11.28/11.52 inference(rewrite,[status(thm)],[])).
% 11.28/11.52 tff(29019,plain,
% 11.28/11.52 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 11.28/11.52 inference(rewrite,[status(thm)],[])).
% 11.28/11.52 tff(29020,plain,
% 11.28/11.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 11.28/11.52 inference(monotonicity,[status(thm)],[29019])).
% 11.28/11.52 tff(29021,plain,
% 11.28/11.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 11.28/11.52 inference(transitivity,[status(thm)],[29020, 29018])).
% 11.28/11.52 tff(29022,plain,
% 11.28/11.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 11.28/11.52 inference(quant_inst,[status(thm)],[])).
% 11.28/11.52 tff(29023,plain,
% 11.28/11.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 11.28/11.52 inference(modus_ponens,[status(thm)],[29022, 29021])).
% 11.28/11.52 tff(29024,plain,
% 11.28/11.52 (~r(s(s(s(elem!1))), z)),
% 11.28/11.52 inference(unit_resolution,[status(thm)],[29023, 194, 29017, 29009, 29005])).
% 11.28/11.52 tff(29025,plain,
% 11.28/11.52 (b(s(s(s(elem!1))), z)),
% 11.28/11.52 inference(unit_resolution,[status(thm)],[377, 29024])).
% 11.28/11.52 tff(29026,plain,
% 11.28/11.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.28/11.52 inference(rewrite,[status(thm)],[])).
% 11.28/11.52 tff(29027,plain,
% 11.28/11.52 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.28/11.52 inference(rewrite,[status(thm)],[])).
% 11.28/11.52 tff(29028,plain,
% 11.28/11.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 11.28/11.52 inference(monotonicity,[status(thm)],[29027])).
% 11.28/11.52 tff(29029,plain,
% 11.28/11.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.28/11.52 inference(transitivity,[status(thm)],[29028, 29026])).
% 11.28/11.52 tff(29030,plain,
% 11.28/11.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.28/11.52 inference(quant_inst,[status(thm)],[])).
% 11.28/11.52 tff(29031,plain,
% 11.28/11.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.28/11.52 inference(modus_ponens,[status(thm)],[29030, 29029])).
% 11.28/11.52 tff(29032,plain,
% 11.28/11.52 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.28/11.52 inference(unit_resolution,[status(thm)],[29031, 391, 28993, 29025, 22924, 90])).
% 11.28/11.52 tff(29033,plain,
% 11.28/11.52 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 11.28/11.52 inference(unit_resolution,[status(thm)],[10940, 28974])).
% 11.28/11.52 tff(29034,plain,
% 11.28/11.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.28/11.52 inference(rewrite,[status(thm)],[])).
% 11.28/11.52 tff(29035,plain,
% 11.28/11.52 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.28/11.52 inference(rewrite,[status(thm)],[])).
% 11.28/11.52 tff(29036,plain,
% 11.28/11.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 11.28/11.52 inference(monotonicity,[status(thm)],[29035])).
% 11.28/11.52 tff(29037,plain,
% 11.28/11.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.28/11.52 inference(transitivity,[status(thm)],[29036, 29034])).
% 11.28/11.52 tff(29038,plain,
% 11.28/11.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.28/11.52 inference(quant_inst,[status(thm)],[])).
% 11.28/11.52 tff(29039,plain,
% 11.28/11.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 11.28/11.52 inference(modus_ponens,[status(thm)],[29038, 29037])).
% 11.28/11.53 tff(29040,plain,
% 11.28/11.53 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[29039, 391, 28993, 29025, 22924, 90])).
% 11.28/11.53 tff(29041,plain,
% 11.28/11.53 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[2853, 42, 28974, 29040])).
% 11.28/11.53 tff(29042,plain,
% 11.28/11.53 (~r(elem!1, s(s(s(elem!1))))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[25443, 29041, 29033, 28977, 29032])).
% 11.28/11.53 tff(29043,plain,
% 11.28/11.53 (b(elem!1, s(s(s(elem!1))))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[424, 29042, 1])).
% 11.28/11.53 tff(29044,plain,
% 11.28/11.53 (~r(z, s(s(s(s(z)))))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[6337, 29041, 28977, 3618])).
% 11.28/11.53 tff(29045,plain,
% 11.28/11.53 (b(z, s(s(s(s(z)))))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[800, 29044])).
% 11.28/11.53 tff(29046,plain,
% 11.28/11.53 (~b(s(z), z)),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[22664, 29045, 90, 1234])).
% 11.28/11.53 tff(29047,plain,
% 11.28/11.53 (r(s(z), z)),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[180, 29046])).
% 11.28/11.53 tff(29048,plain,
% 11.28/11.53 (~b(elem!1, s(elem!1))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[1930, 1628, 411, 721, 121, 182])).
% 11.28/11.53 tff(29049,plain,
% 11.28/11.53 ($false),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[443, 29048, 28596, 437])).
% 11.28/11.53 tff(29050,plain,((~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.53 tff(29051,plain,
% 11.28/11.53 (~r(s(elem!1), z)),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[29050, 29047, 411, 28975, 118, 427, 3618])).
% 11.28/11.53 tff(29052,plain,
% 11.28/11.53 (b(s(elem!1), z)),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[549, 29051])).
% 11.28/11.53 tff(29053,plain,
% 11.28/11.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 11.28/11.53 inference(rewrite,[status(thm)],[])).
% 11.28/11.53 tff(29054,plain,
% 11.28/11.53 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 11.28/11.53 inference(rewrite,[status(thm)],[])).
% 11.28/11.53 tff(29055,plain,
% 11.28/11.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 11.28/11.53 inference(monotonicity,[status(thm)],[29054])).
% 11.28/11.53 tff(29056,plain,
% 11.28/11.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 11.28/11.53 inference(transitivity,[status(thm)],[29055, 29053])).
% 11.28/11.53 tff(29057,plain,
% 11.28/11.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 11.28/11.53 inference(quant_inst,[status(thm)],[])).
% 11.28/11.53 tff(29058,plain,
% 11.28/11.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 11.28/11.53 inference(modus_ponens,[status(thm)],[29057, 29056])).
% 11.28/11.53 tff(29059,plain,
% 11.28/11.53 (~b(s(elem!1), s(s(s(s(z)))))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[29058, 391, 28993, 22924, 29052, 90])).
% 11.28/11.53 tff(29060,plain,
% 11.28/11.53 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[15351, 29032, 29033])).
% 11.28/11.53 tff(29061,plain,
% 11.28/11.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.28/11.53 inference(rewrite,[status(thm)],[])).
% 11.28/11.53 tff(29062,plain,
% 11.28/11.53 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.28/11.53 inference(rewrite,[status(thm)],[])).
% 11.28/11.53 tff(29063,plain,
% 11.28/11.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 11.28/11.53 inference(monotonicity,[status(thm)],[29062])).
% 11.28/11.53 tff(29064,plain,
% 11.28/11.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.28/11.53 inference(transitivity,[status(thm)],[29063, 29061])).
% 11.28/11.53 tff(29065,plain,
% 11.28/11.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))),
% 11.28/11.53 inference(quant_inst,[status(thm)],[])).
% 11.28/11.53 tff(29066,plain,
% 11.28/11.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.28/11.53 inference(modus_ponens,[status(thm)],[29065, 29064])).
% 11.28/11.53 tff(29067,plain,
% 11.28/11.53 (~r(s(s(s(s(z)))), s(z))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[29066, 194, 29017, 29041, 29060])).
% 11.28/11.53 tff(29068,plain,
% 11.28/11.53 (b(s(s(s(s(z)))), s(z))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[749, 29067])).
% 11.28/11.53 tff(29069,plain,
% 11.28/11.53 (~b(s(s(s(s(z)))), elem!1)),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[26707, 29068, 1234, 28975, 29007])).
% 11.28/11.53 tff(29070,plain,
% 11.28/11.53 (r(s(s(s(s(z)))), elem!1)),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[762, 29069, 21778])).
% 11.28/11.53 tff(29071,plain,
% 11.28/11.53 (~b(s(z), z)),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[22664, 1686, 90, 1234])).
% 11.28/11.53 tff(29072,plain,
% 11.28/11.53 (r(s(z), z)),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[180, 29071])).
% 11.28/11.53 tff(29073,plain,
% 11.28/11.53 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 11.28/11.53 inference(monotonicity,[status(thm)],[26874])).
% 11.28/11.53 tff(29074,plain,
% 11.28/11.53 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 11.28/11.53 inference(symmetry,[status(thm)],[29073])).
% 11.28/11.53 tff(29075,plain,
% 11.28/11.53 (r(z, s(s(elem!1)))),
% 11.28/11.53 inference(modus_ponens,[status(thm)],[411, 29074])).
% 11.28/11.53 tff(29076,plain,
% 11.28/11.53 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[20877, 29075, 90, 1234, 1686, 29072])).
% 11.28/11.53 tff(29077,plain,
% 11.28/11.53 (r(s(s(z)), s(s(s(s(z)))))),
% 11.28/11.53 inference(unit_resolution,[status(thm)],[3652, 29076])).
% 11.28/11.53 tff(29078,plain,
% 11.28/11.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 11.28/11.53 inference(rewrite,[status(thm)],[])).
% 11.28/11.53 tff(29079,plain,
% 11.28/11.53 (((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 11.28/11.54 inference(rewrite,[status(thm)],[])).
% 11.28/11.54 tff(29080,plain,
% 11.28/11.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))))),
% 11.28/11.54 inference(monotonicity,[status(thm)],[29079])).
% 11.28/11.54 tff(29081,plain,
% 11.28/11.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 11.28/11.54 inference(transitivity,[status(thm)],[29080, 29078])).
% 11.28/11.54 tff(29082,plain,
% 11.28/11.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 11.28/11.54 inference(quant_inst,[status(thm)],[])).
% 11.28/11.54 tff(29083,plain,
% 11.28/11.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))),
% 11.28/11.54 inference(modus_ponens,[status(thm)],[29082, 29081])).
% 11.28/11.54 tff(29084,plain,
% 11.28/11.54 ($false),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[29083, 194, 530, 1749, 2112, 6669])).
% 11.28/11.54 tff(29085,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.54 tff(29086,plain,
% 11.28/11.54 (~r(s(s(z)), elem!1)),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[29085, 29077, 2112, 530])).
% 11.28/11.54 tff(29087,plain,
% 11.28/11.54 (b(s(s(z)), elem!1)),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[4730, 29086, 5536])).
% 11.28/11.54 tff(29088,plain,
% 11.28/11.54 (b(elem!1, s(elem!1))),
% 11.28/11.54 inference(modus_ponens,[status(thm)],[448, 4599])).
% 11.28/11.54 tff(29089,plain,
% 11.28/11.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 11.28/11.54 inference(rewrite,[status(thm)],[])).
% 11.28/11.54 tff(29090,plain,
% 11.28/11.54 (((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 11.28/11.54 inference(rewrite,[status(thm)],[])).
% 11.28/11.54 tff(29091,plain,
% 11.28/11.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))))),
% 11.28/11.54 inference(monotonicity,[status(thm)],[29090])).
% 11.28/11.54 tff(29092,plain,
% 11.28/11.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 11.28/11.54 inference(transitivity,[status(thm)],[29091, 29089])).
% 11.28/11.54 tff(29093,plain,
% 11.28/11.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 11.28/11.54 inference(quant_inst,[status(thm)],[])).
% 11.28/11.54 tff(29094,plain,
% 11.28/11.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))),
% 11.28/11.54 inference(modus_ponens,[status(thm)],[29093, 29092])).
% 11.28/11.54 tff(29095,plain,
% 11.28/11.54 (~b(s(s(z)), s(elem!1))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[29094, 391, 591, 29088, 2465, 29087])).
% 11.28/11.54 tff(29096,plain,
% 11.28/11.54 ((s(elem!1) = s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[2142, 42, 2139])).
% 11.28/11.54 tff(29097,plain,
% 11.28/11.54 (r(s(elem!1), s(s(s(s(z)))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[29096, 13135])).
% 11.28/11.54 tff(29098,plain,
% 11.28/11.54 (~r(s(s(z)), s(elem!1))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[6930, 194, 29077, 2112, 29097])).
% 11.28/11.54 tff(29099,plain,
% 11.28/11.54 ($false),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[4693, 42, 2494, 29098, 29095])).
% 11.28/11.54 tff(29100,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | b(s(elem!1), s(s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.54 tff(29101,plain,
% 11.28/11.54 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[29100, 29052, 29070, 3618, 90, 1234, 29045, 411, 29043, 28993, 29059, 28974, 118])).
% 11.28/11.54 tff(29102,plain,
% 11.28/11.54 (~r(s(elem!1), s(s(s(elem!1))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[28740, 15191, 10682, 900, 591, 5682, 15174, 297, 411, 530, 2, 380])).
% 11.28/11.54 tff(29103,plain,
% 11.28/11.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 11.28/11.54 inference(rewrite,[status(thm)],[])).
% 11.28/11.54 tff(29104,plain,
% 11.28/11.54 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 11.28/11.54 inference(rewrite,[status(thm)],[])).
% 11.28/11.54 tff(29105,plain,
% 11.28/11.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))))),
% 11.28/11.54 inference(monotonicity,[status(thm)],[29104])).
% 11.28/11.54 tff(29106,plain,
% 11.28/11.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 11.28/11.54 inference(transitivity,[status(thm)],[29105, 29103])).
% 11.28/11.54 tff(29107,plain,
% 11.28/11.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 11.28/11.54 inference(quant_inst,[status(thm)],[])).
% 11.28/11.54 tff(29108,plain,
% 11.28/11.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 11.28/11.54 inference(modus_ponens,[status(thm)],[29107, 29106])).
% 11.28/11.54 tff(29109,plain,
% 11.28/11.54 (~b(s(elem!1), s(s(s(elem!1))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[29108, 391, 900, 380, 10682, 591])).
% 11.28/11.54 tff(29110,plain,
% 11.28/11.54 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[579, 42, 29109])).
% 11.28/11.54 tff(29111,plain,
% 11.28/11.54 (s(elem!1) = s(s(s(elem!1)))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[29110, 29102])).
% 11.28/11.54 tff(29112,plain,
% 11.28/11.54 (s(s(s(elem!1))) = s(elem!1)),
% 11.28/11.54 inference(modus_ponens,[status(thm)],[29111, 582])).
% 11.28/11.54 tff(29113,plain,
% 11.28/11.54 ($false),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[279, 29112])).
% 11.28/11.54 tff(29114,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), z)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.54 tff(29115,plain,
% 11.28/11.54 (b(s(s(elem!1)), elem!1)),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[29114, 29101, 28993, 29052, 26982, 411, 3618, 2, 29025, 22924])).
% 11.28/11.54 tff(29116,plain,
% 11.28/11.54 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[6001, 29115, 29043, 28993])).
% 11.28/11.54 tff(29117,plain,
% 11.28/11.54 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[1356, 29116, 27044])).
% 11.28/11.54 tff(29118,plain,
% 11.28/11.54 (~b(s(s(elem!1)), s(z))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[22561, 29115, 28975, 29007])).
% 11.28/11.54 tff(29119,plain,
% 11.28/11.54 (r(s(s(elem!1)), s(z))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[362, 29118])).
% 11.28/11.54 tff(29120,plain,
% 11.28/11.54 ($false),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[2201, 29119, 29117, 29017, 29009])).
% 11.28/11.54 tff(29121,plain,(b(elem!1, z) | (~r(z, elem!1)) | (elem!1 = z) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.54 tff(29122,plain,
% 11.28/11.54 (b(elem!1, z)),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[29121, 28572, 2, 88, 28192, 22901])).
% 11.28/11.54 tff(29123,plain,
% 11.28/11.54 (~b(elem!1, s(s(s(s(z)))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[28971, 1234, 90, 10682, 721])).
% 11.28/11.54 tff(29124,plain,
% 11.28/11.54 ($false),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[25287, 194, 411, 174, 233, 410])).
% 11.28/11.54 tff(29125,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.54 tff(29126,plain,
% 11.28/11.54 (~r(elem!1, s(s(s(elem!1))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[29125, 174, 411, 233])).
% 11.28/11.54 tff(29127,plain,
% 11.28/11.54 (b(elem!1, s(s(s(elem!1))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[424, 29126, 1])).
% 11.28/11.54 tff(29128,plain,
% 11.28/11.54 (elem!1 = s(s(s(s(z))))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[781, 22247, 29123])).
% 11.28/11.54 tff(29129,plain,
% 11.28/11.54 (b(s(s(s(s(z)))), s(z))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[13738, 29128, 721])).
% 11.28/11.54 tff(29130,plain,
% 11.28/11.54 (~b(z, s(z))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[22918, 29129, 90, 1234])).
% 11.28/11.54 tff(29131,plain,
% 11.28/11.54 (r(z, s(z))),
% 11.28/11.54 inference(unit_resolution,[status(thm)],[678, 29130])).
% 11.28/11.55 tff(29132,plain,
% 11.28/11.55 (s(s(s(s(z)))) = elem!1),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[769, 29128])).
% 11.28/11.55 tff(29133,plain,
% 11.28/11.55 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[2865, 29132, 29127])).
% 11.28/11.55 tff(29134,plain,
% 11.28/11.55 (~b(s(s(s(elem!1))), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[6372, 29133, 90, 1234, 29129])).
% 11.28/11.55 tff(29135,plain,
% 11.28/11.55 (r(s(s(s(elem!1))), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[223, 29134])).
% 11.28/11.55 tff(29136,plain,
% 11.28/11.55 (~r(elem!1, s(elem!1))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[18138, 174, 411, 233])).
% 11.28/11.55 tff(29137,plain,
% 11.28/11.55 (b(elem!1, s(elem!1))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[443, 29136, 7437])).
% 11.28/11.55 tff(29138,plain,
% 11.28/11.55 (~(elem!1 = s(s(s(s(z)))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[13738, 27145, 721])).
% 11.28/11.55 tff(29139,plain,
% 11.28/11.55 (b(elem!1, s(s(s(s(z)))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[781, 29138, 3222])).
% 11.28/11.55 tff(29140,plain,
% 11.28/11.55 (~b(s(z), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[21922, 664, 721, 665])).
% 11.28/11.55 tff(29141,plain,
% 11.28/11.55 (r(s(z), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[180, 29140])).
% 11.28/11.55 tff(29142,plain,
% 11.28/11.55 (~r(z, s(s(s(s(z)))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[27817, 29141, 174, 232])).
% 11.28/11.55 tff(29143,plain,
% 11.28/11.55 (b(z, s(s(s(s(z)))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[800, 29142])).
% 11.28/11.55 tff(29144,plain,
% 11.28/11.55 ($false),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[3234, 29143, 29139, 90, 665])).
% 11.28/11.55 tff(29145,plain,((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | r(elem!1, s(s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.55 tff(29146,plain,
% 11.28/11.55 (~b(z, s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[29145, 232, 665, 3222, 174, 90, 721, 1234])).
% 11.28/11.55 tff(29147,plain,
% 11.28/11.55 (r(z, s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[678, 29146])).
% 11.28/11.55 tff(29148,plain,
% 11.28/11.55 ($false),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[29023, 194, 174, 232, 183, 29147])).
% 11.28/11.55 tff(29149,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | r(elem!1, s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.55 tff(29150,plain,
% 11.28/11.55 (~r(s(z), s(s(s(elem!1))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[29149, 183, 174, 665, 22247, 90, 721, 1234])).
% 11.28/11.55 tff(29151,plain,
% 11.28/11.55 (b(s(z), s(s(s(elem!1))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[247, 29150])).
% 11.28/11.55 tff(29152,plain,
% 11.28/11.55 (~r(s(z), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[17465, 722, 183, 174])).
% 11.28/11.55 tff(29153,plain,
% 11.28/11.55 (b(s(z), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[632, 29152, 150])).
% 11.28/11.55 tff(29154,plain,
% 11.28/11.55 (~b(s(z), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[22273, 29153, 411, 721, 233, 174, 183, 90, 665, 297, 29151, 448])).
% 11.28/11.55 tff(29155,plain,
% 11.28/11.55 (r(s(z), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[180, 29154])).
% 11.28/11.55 tff(29156,plain,
% 11.28/11.55 (~r(s(elem!1), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[1930, 29155, 411, 721, 121, 29137])).
% 11.28/11.55 tff(29157,plain,
% 11.28/11.55 (b(s(elem!1), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[549, 29156])).
% 11.28/11.55 tff(29158,plain,
% 11.28/11.55 (~b(z, s(s(s(s(z)))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[2050, 29157, 90, 665, 29137])).
% 11.28/11.55 tff(29159,plain,
% 11.28/11.55 (r(z, s(s(s(s(z)))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[800, 29158])).
% 11.28/11.55 tff(29160,plain,
% 11.28/11.55 (~r(s(s(s(s(z)))), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[731, 29159, 29155, 722])).
% 11.28/11.55 tff(29161,plain,
% 11.28/11.55 (b(s(s(s(s(z)))), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[749, 29160])).
% 11.28/11.55 tff(29162,plain,
% 11.28/11.55 (s(s(s(s(z)))) = elem!1),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[2097, 29161, 411, 1234, 721, 29159])).
% 11.28/11.55 tff(29163,plain,
% 11.28/11.55 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[717, 29162])).
% 11.28/11.55 tff(29164,plain,
% 11.28/11.55 (~(s(s(elem!1)) = elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[451, 29163])).
% 11.28/11.55 tff(29165,plain,
% 11.28/11.55 (~(elem!1 = s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[1292, 29164])).
% 11.28/11.55 tff(29166,plain,
% 11.28/11.55 (~r(s(s(elem!1)), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[22176, 29153, 411, 174, 448, 315, 29151])).
% 11.28/11.55 tff(29167,plain,
% 11.28/11.55 (b(s(s(elem!1)), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[2629, 29166])).
% 11.28/11.55 tff(29168,plain,
% 11.28/11.55 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[22200, 29151, 411, 721, 174, 448, 315])).
% 11.28/11.55 tff(29169,plain,
% 11.28/11.55 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[1370, 29168, 297])).
% 11.28/11.55 tff(29170,plain,
% 11.28/11.55 (~b(s(s(elem!1)), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[28950, 29153, 10682, 665, 183, 29169])).
% 11.28/11.55 tff(29171,plain,
% 11.28/11.55 (r(s(s(elem!1)), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[872, 29164, 29170])).
% 11.28/11.55 tff(29172,plain,
% 11.28/11.55 (~r(z, s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[13828, 29171, 29169, 174])).
% 11.28/11.55 tff(29173,plain,
% 11.28/11.55 (b(z, s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[324, 29172])).
% 11.28/11.55 tff(29174,plain,
% 11.28/11.55 (~b(elem!1, s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[20366, 29173, 665, 29167])).
% 11.28/11.55 tff(29175,plain,
% 11.28/11.55 (~(s(s(elem!1)) = s(elem!1))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[2279, 29163])).
% 11.28/11.55 tff(29176,plain,
% 11.28/11.55 (~(s(elem!1) = s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[9802, 29175])).
% 11.28/11.55 tff(29177,plain,
% 11.28/11.55 (~r(elem!1, s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[15211, 29173, 665, 29167, 164, 29157, 29171, 29176])).
% 11.28/11.55 tff(29178,plain,
% 11.28/11.55 ($false),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[1307, 29177, 29174, 29165])).
% 11.28/11.55 tff(29179,plain,((~r(z, s(z))) | (~b(elem!1, z)) | (s(elem!1) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (s(z) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.55 tff(29180,plain,
% 11.28/11.55 ($false),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[29179, 29135, 29131, 426, 665, 411, 1234, 721, 90, 121, 10682, 174, 233, 26982, 29127, 150])).
% 11.28/11.55 tff(29181,plain,((~r(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | (s(z) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(z) = elem!1) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.55 tff(29182,plain,
% 11.28/11.55 (~r(s(s(s(elem!1))), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[29181, 4097, 411, 1234, 721, 90, 121, 10682, 665, 150, 1])).
% 11.28/11.55 tff(29183,plain,
% 11.28/11.55 (b(s(s(s(elem!1))), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[377, 29182])).
% 11.28/11.55 tff(29184,plain,
% 11.28/11.55 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[23000, 391, 29183, 10682, 90])).
% 11.28/11.55 tff(29185,plain,
% 11.28/11.55 (~b(elem!1, s(s(s(elem!1))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[23581, 391, 665, 29183, 10682])).
% 11.28/11.55 tff(29186,plain,
% 11.28/11.55 (r(elem!1, s(s(s(elem!1))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[424, 29185, 1])).
% 11.28/11.55 tff(29187,plain,
% 11.28/11.55 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[23009, 391, 29183, 10682, 90])).
% 11.28/11.55 tff(29188,plain,
% 11.28/11.55 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[2853, 42, 3363, 29187])).
% 11.28/11.55 tff(29189,plain,
% 11.28/11.55 (~r(elem!1, s(s(s(s(z)))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[25443, 29188, 16830, 29186, 29184])).
% 11.28/11.55 tff(29190,plain,
% 11.28/11.55 (elem!1 = s(s(s(s(z))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[781, 29189, 29123])).
% 11.28/11.55 tff(29191,plain,
% 11.28/11.55 (b(s(s(s(s(z)))), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[13738, 29190, 721])).
% 11.28/11.55 tff(29192,plain,
% 11.28/11.55 (~b(z, s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[22918, 29191, 90, 1234])).
% 11.28/11.55 tff(29193,plain,
% 11.28/11.55 (r(z, s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[678, 29192])).
% 11.28/11.55 tff(29194,plain,
% 11.28/11.55 (s(s(s(s(z)))) = elem!1),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[769, 29190])).
% 11.28/11.55 tff(29195,plain,
% 11.28/11.55 (b(s(z), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[8916, 29194, 1234])).
% 11.28/11.55 tff(29196,plain,
% 11.28/11.55 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[717, 29194])).
% 11.28/11.55 tff(29197,plain,
% 11.28/11.55 (~(s(s(elem!1)) = elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[451, 29196])).
% 11.28/11.55 tff(29198,plain,
% 11.28/11.55 (~r(s(s(elem!1)), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[2562, 326, 410, 411])).
% 11.28/11.55 tff(29199,plain,
% 11.28/11.55 (b(s(s(elem!1)), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[872, 29198, 249])).
% 11.28/11.55 tff(29200,plain,
% 11.28/11.55 (~b(s(z), s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[28931, 391, 665, 10682, 29199, 644])).
% 11.28/11.55 tff(29201,plain,
% 11.28/11.55 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[3414, 42, 29200])).
% 11.28/11.55 tff(29202,plain,
% 11.28/11.55 (r(s(z), s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[29201, 3404])).
% 11.28/11.55 tff(29203,plain,
% 11.28/11.55 (~b(s(s(elem!1)), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[28940, 391, 665, 10682, 29199, 644])).
% 11.28/11.55 tff(29204,plain,
% 11.28/11.55 (r(s(s(elem!1)), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[362, 29203])).
% 11.28/11.55 tff(29205,plain,
% 11.28/11.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 11.28/11.55 inference(rewrite,[status(thm)],[])).
% 11.28/11.55 tff(29206,plain,
% 11.28/11.55 (((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 11.28/11.55 inference(rewrite,[status(thm)],[])).
% 11.28/11.55 tff(29207,plain,
% 11.28/11.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))))),
% 11.28/11.55 inference(monotonicity,[status(thm)],[29206])).
% 11.28/11.55 tff(29208,plain,
% 11.28/11.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 11.28/11.55 inference(transitivity,[status(thm)],[29207, 29205])).
% 11.28/11.55 tff(29209,plain,
% 11.28/11.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 11.28/11.55 inference(quant_inst,[status(thm)],[])).
% 11.28/11.55 tff(29210,plain,
% 11.28/11.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))),
% 11.28/11.55 inference(modus_ponens,[status(thm)],[29209, 29208])).
% 11.28/11.55 tff(29211,plain,
% 11.28/11.55 ($false),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[29210, 194, 29204, 326, 722, 29202])).
% 11.28/11.55 tff(29212,plain,((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.55 tff(29213,plain,
% 11.28/11.55 (~r(z, s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[29212, 29193, 10682, 411, 665, 29186, 29195, 29197])).
% 11.28/11.55 tff(29214,plain,
% 11.28/11.55 (b(z, s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[324, 29213])).
% 11.28/11.55 tff(29215,plain,
% 11.28/11.55 (b(s(s(elem!1)), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[15730, 29214, 10682, 29185, 29196, 168, 9, 29186])).
% 11.28/11.55 tff(29216,plain,
% 11.28/11.55 (~b(s(s(elem!1)), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[22561, 29215, 721, 29195])).
% 11.28/11.55 tff(29217,plain,
% 11.28/11.55 (r(s(s(elem!1)), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[362, 29216])).
% 11.28/11.55 tff(29218,plain,
% 11.28/11.55 (~(elem!1 = s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[1292, 29197])).
% 11.28/11.55 tff(29219,plain,
% 11.28/11.55 (~b(elem!1, s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[7297, 29215, 665, 29214])).
% 11.28/11.55 tff(29220,plain,
% 11.28/11.55 (r(elem!1, s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[1307, 29219, 29218])).
% 11.28/11.55 tff(29221,plain,
% 11.28/11.55 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[4159, 29220, 29186, 29217])).
% 11.28/11.55 tff(29222,plain,
% 11.28/11.55 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[1370, 29221, 26982])).
% 11.28/11.55 tff(29223,plain,
% 11.28/11.55 (~b(s(z), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[23575, 29222, 10682, 665, 29195])).
% 11.28/11.55 tff(29224,plain,
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% 11.28/11.55 inference(unit_resolution,[status(thm)],[180, 29223])).
% 11.28/11.55 tff(29225,plain,
% 11.28/11.55 (~b(s(s(elem!1)), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[13177, 29222, 10682, 29183])).
% 11.28/11.55 tff(29226,plain,
% 11.28/11.55 (r(s(s(elem!1)), z)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[2629, 29225])).
% 11.28/11.55 tff(29227,plain,
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% 11.28/11.55 inference(unit_resolution,[status(thm)],[4103, 29226, 29224, 29217, 29193])).
% 11.28/11.55 tff(29228,plain,(b(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.55 tff(29229,plain,
% 11.28/11.55 (b(s(s(s(elem!1))), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[29228, 29122, 22898, 28963, 28192, 88, 28572, 22901, 118, 28820])).
% 11.28/11.55 tff(29230,plain,
% 11.28/11.55 (~(elem!1 = s(s(s(elem!1))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[22900, 89, 10682])).
% 11.28/11.55 tff(29231,plain,
% 11.28/11.55 (~b(elem!1, s(s(s(elem!1))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[28903, 900, 10682, 665])).
% 11.28/11.55 tff(29232,plain,
% 11.28/11.55 (r(elem!1, s(s(s(elem!1))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[424, 29231, 29230])).
% 11.28/11.55 tff(29233,plain,
% 11.28/11.55 (~(s(s(s(elem!1))) = elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[8, 29230])).
% 11.28/11.55 tff(29234,plain,
% 11.28/11.55 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[8251, 29233])).
% 11.28/11.55 tff(29235,plain,
% 11.28/11.55 (~b(z, s(s(s(s(z)))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[22664, 590, 90, 1234])).
% 11.28/11.55 tff(29236,plain,
% 11.28/11.55 (r(z, s(s(s(s(z)))))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[800, 29235])).
% 11.28/11.55 tff(29237,plain,
% 11.28/11.55 (~r(s(s(s(s(z)))), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[8972, 29236, 411, 410])).
% 11.28/11.55 tff(29238,plain,
% 11.28/11.55 (s(s(s(s(z)))) = elem!1),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[762, 29237, 25489])).
% 11.28/11.55 tff(29239,plain,
% 11.28/11.55 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[717, 29238])).
% 11.28/11.55 tff(29240,plain,
% 11.28/11.55 (~(s(s(elem!1)) = elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[451, 29239])).
% 11.28/11.55 tff(29241,plain,
% 11.28/11.55 (b(s(z), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[8916, 29238, 1234])).
% 11.28/11.55 tff(29242,plain,
% 11.28/11.55 (~r(s(s(elem!1)), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[19811, 29241, 411, 665, 410, 590])).
% 11.28/11.55 tff(29243,plain,
% 11.28/11.55 (b(s(s(elem!1)), elem!1)),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[872, 29242, 29240])).
% 11.28/11.55 tff(29244,plain,
% 11.28/11.55 (~b(s(s(s(elem!1))), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[20387, 29241, 721, 900])).
% 11.28/11.55 tff(29245,plain,
% 11.28/11.55 (r(s(s(s(elem!1))), s(z))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[223, 29244])).
% 11.28/11.55 tff(29246,plain,
% 11.28/11.55 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[23575, 29241, 10682, 665, 590])).
% 11.28/11.55 tff(29247,plain,
% 11.28/11.55 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.55 inference(unit_resolution,[status(thm)],[1370, 29246, 297])).
% 11.28/11.55 tff(29248,plain,
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% 11.28/11.55 inference(unit_resolution,[status(thm)],[28950, 29247, 29245, 10682, 665, 29241, 29243])).
% 11.28/11.56 tff(29249,plain,((~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29250,plain,
% 11.28/11.56 (~b(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29249, 665, 10682, 29234, 411, 29232, 721, 900, 1234, 90])).
% 11.28/11.56 tff(29251,plain,
% 11.28/11.56 (r(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[180, 29250])).
% 11.28/11.56 tff(29252,plain,
% 11.28/11.56 (~r(z, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[731, 10646, 182, 722])).
% 11.28/11.56 tff(29253,plain,
% 11.28/11.56 (b(z, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[800, 29252])).
% 11.28/11.56 tff(29254,plain,
% 11.28/11.56 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[23918, 29253, 90, 10682])).
% 11.28/11.56 tff(29255,plain,
% 11.28/11.56 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[15351, 29254, 16830])).
% 11.28/11.56 tff(29256,plain,
% 11.28/11.56 (~r(s(z), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[9108, 13739, 8536, 25489, 10646])).
% 11.28/11.56 tff(29257,plain,
% 11.28/11.56 (b(s(z), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[632, 29256, 150])).
% 11.28/11.56 tff(29258,plain,
% 11.28/11.56 (~b(s(s(s(elem!1))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[20387, 29257, 721, 900])).
% 11.28/11.56 tff(29259,plain,
% 11.28/11.56 (r(s(s(s(elem!1))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[223, 29258])).
% 11.28/11.56 tff(29260,plain,
% 11.28/11.56 (~b(s(z), s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28855, 29257, 10682, 665, 900])).
% 11.28/11.56 tff(29261,plain,
% 11.28/11.56 (r(s(z), s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[247, 29260])).
% 11.28/11.56 tff(29262,plain,
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% 11.28/11.56 inference(unit_resolution,[status(thm)],[26348, 194, 29261, 29259, 10646, 29255])).
% 11.28/11.56 tff(29263,plain,(b(s(s(s(s(z)))), s(z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (s(z) = elem!1) | b(elem!1, s(s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29264,plain,
% 11.28/11.56 (b(s(s(s(s(z)))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29263, 722, 900, 10682, 665, 90, 150, 29123, 29251, 721])).
% 11.28/11.56 tff(29265,plain,
% 11.28/11.56 (~b(s(s(s(elem!1))), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[17249, 900, 10682, 665])).
% 11.28/11.56 tff(29266,plain,
% 11.28/11.56 (r(s(s(s(elem!1))), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[377, 29265])).
% 11.28/11.56 tff(29267,plain,
% 11.28/11.56 (~r(s(z), s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[27817, 719, 29266, 182])).
% 11.28/11.56 tff(29268,plain,
% 11.28/11.56 (b(s(z), s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[247, 29267])).
% 11.28/11.56 tff(29269,plain,
% 11.28/11.56 (s(s(s(s(z)))) = elem!1),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[2097, 719, 411, 1234, 721, 1759])).
% 11.28/11.56 tff(29270,plain,
% 11.28/11.56 (b(s(z), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[8916, 29269, 1234])).
% 11.28/11.56 tff(29271,plain,
% 11.28/11.56 ($false),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28855, 29270, 29268, 10682, 665, 900])).
% 11.28/11.56 tff(29272,plain,((~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29273,plain,
% 11.28/11.56 (~r(z, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29272, 29264, 665, 900, 1234, 411, 721, 10682, 29251])).
% 11.28/11.56 tff(29274,plain,
% 11.28/11.56 (b(z, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[800, 29273])).
% 11.28/11.56 tff(29275,plain,
% 11.28/11.56 (~(s(s(s(s(z)))) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[16124, 29274, 89])).
% 11.28/11.56 tff(29276,plain,
% 11.28/11.56 (~(elem!1 = s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[769, 29275])).
% 11.28/11.56 tff(29277,plain,
% 11.28/11.56 (r(elem!1, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[781, 29276, 29123])).
% 11.28/11.56 tff(29278,plain,
% 11.28/11.56 (~r(s(z), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[21996, 29277, 411, 722])).
% 11.28/11.56 tff(29279,plain,
% 11.28/11.56 (b(s(z), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[632, 29278, 150])).
% 11.28/11.56 tff(29280,plain,
% 11.28/11.56 (~b(s(s(s(elem!1))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[20387, 29279, 721, 900])).
% 11.28/11.56 tff(29281,plain,
% 11.28/11.56 (r(s(s(s(elem!1))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[223, 29280])).
% 11.28/11.56 tff(29282,plain,
% 11.28/11.56 (~b(s(z), s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28855, 29279, 10682, 665, 900])).
% 11.28/11.56 tff(29283,plain,
% 11.28/11.56 (r(s(z), s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[247, 29282])).
% 11.28/11.56 tff(29284,plain,
% 11.28/11.56 ($false),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29023, 194, 29266, 29283, 29281, 722])).
% 11.28/11.56 tff(29285,plain,((~r(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (s(z) = elem!1) | (~r(z, elem!1)) | b(z, elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29286,plain,
% 11.28/11.56 (~r(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29285, 28963, 29229, 22898, 29122, 28820, 28192, 89, 28572, 88])).
% 11.28/11.56 tff(29287,plain,
% 11.28/11.56 (b(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[678, 29286])).
% 11.28/11.56 tff(29288,plain,
% 11.28/11.56 (~r(elem!1, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29003, 29287, 88, 28572, 28192, 22898])).
% 11.28/11.56 tff(29289,plain,
% 11.28/11.56 (~b(s(s(s(s(z)))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[22918, 29287, 88, 28572])).
% 11.28/11.56 tff(29290,plain,
% 11.28/11.56 (~(elem!1 = s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[13738, 29289, 28963])).
% 11.28/11.56 tff(29291,plain,
% 11.28/11.56 ($false),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[781, 29290, 29288, 28972])).
% 11.28/11.56 tff(29292,plain,(b(z, elem!1) | (elem!1 = z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29293,plain,
% 11.28/11.56 (b(z, elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29292, 81, 2])).
% 11.28/11.56 tff(29294,plain,
% 11.28/11.56 (elem!1 = s(s(s(elem!1)))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28381, 31, 81, 2881, 2])).
% 11.28/11.56 tff(29295,plain,
% 11.28/11.56 (s(s(s(elem!1))) = elem!1),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[129, 29294])).
% 11.28/11.56 tff(29296,plain,
% 11.28/11.56 (~b(s(s(s(elem!1))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[8400, 29295, 31])).
% 11.28/11.56 tff(29297,plain,
% 11.28/11.56 (r(s(s(s(elem!1))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[223, 29296])).
% 11.28/11.56 tff(29298,plain,
% 11.28/11.56 (~b(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28049, 29294, 2913, 88, 31, 29293, 2])).
% 11.28/11.56 tff(29299,plain,
% 11.28/11.56 (r(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[180, 29298])).
% 11.28/11.56 tff(29300,plain,
% 11.28/11.56 (r(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[26476, 29298, 81, 29293, 2, 31])).
% 11.28/11.56 tff(29301,plain,
% 11.28/11.56 (~r(elem!1, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[845, 29300, 28192, 29299])).
% 11.28/11.56 tff(29302,plain,
% 11.28/11.56 ($false),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[8406, 29301, 29297, 29295])).
% 11.28/11.56 tff(29303,plain,(b(elem!1, s(z)) | r(s(s(s(s(z)))), z) | (elem!1 = z) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29304,plain,
% 11.28/11.56 (b(elem!1, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29303, 2881, 2, 81])).
% 11.28/11.56 tff(29305,plain,
% 11.28/11.56 (~r(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28440, 484, 90, 2881, 721, 411, 21435, 2])).
% 11.28/11.56 tff(29306,plain,
% 11.28/11.56 (b(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[180, 29305])).
% 11.28/11.56 tff(29307,plain,
% 11.28/11.56 (~b(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[5970, 29306, 133, 721])).
% 11.28/11.56 tff(29308,plain,
% 11.28/11.56 (r(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[678, 29307])).
% 11.28/11.56 tff(29309,plain,
% 11.28/11.56 (~b(s(z), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[4857, 29306, 133, 721])).
% 11.28/11.56 tff(29310,plain,
% 11.28/11.56 (r(s(z), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[632, 29309, 21435])).
% 11.28/11.56 tff(29311,plain,
% 11.28/11.56 ($false),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[16803, 29310, 29308, 411, 3618])).
% 11.28/11.56 tff(29312,plain,(b(elem!1, z) | (~r(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(s(z))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29313,plain,
% 11.28/11.56 (b(elem!1, z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29312, 29304, 29293, 28192, 88, 2881, 2])).
% 11.28/11.56 tff(29314,plain,
% 11.28/11.56 (~b(s(s(s(elem!1))), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[10743, 29313, 22898, 29293])).
% 11.28/11.56 tff(29315,plain,
% 11.28/11.56 (~(s(z) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[20271, 29304])).
% 11.28/11.56 tff(29316,plain,
% 11.28/11.56 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[2849, 29315])).
% 11.28/11.56 tff(29317,plain,
% 11.28/11.56 (~b(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[13285, 29313, 29293, 29304])).
% 11.28/11.56 tff(29318,plain,
% 11.28/11.56 (r(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[180, 29317])).
% 11.28/11.56 tff(29319,plain,
% 11.28/11.56 (~b(s(s(s(s(z)))), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[4086, 391, 29293, 29313, 88])).
% 11.28/11.56 tff(29320,plain,
% 11.28/11.56 (elem!1 = s(s(s(elem!1)))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[27649, 29319, 29293, 2881, 29304, 29318, 2, 81])).
% 11.28/11.56 tff(29321,plain,
% 11.28/11.56 (b(s(s(s(elem!1))), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[9553, 29320, 29313])).
% 11.28/11.56 tff(29322,plain,
% 11.28/11.56 (~r(s(s(s(elem!1))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[23013, 29321, 88, 22898, 2913, 29316])).
% 11.28/11.56 tff(29323,plain,
% 11.28/11.56 (b(s(s(s(elem!1))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[223, 29322])).
% 11.28/11.56 tff(29324,plain,
% 11.28/11.56 (s(s(s(elem!1))) = elem!1),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[129, 29320])).
% 11.28/11.56 tff(29325,plain,
% 11.28/11.56 (~(s(s(s(s(z)))) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[1436, 29324])).
% 11.28/11.56 tff(29326,plain,
% 11.28/11.56 (r(s(s(s(s(z)))), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[762, 29325, 29319])).
% 11.28/11.56 tff(29327,plain,
% 11.28/11.56 (~r(s(z), s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[12394, 29326, 88, 2913, 29316, 29318, 29321])).
% 11.28/11.56 tff(29328,plain,
% 11.28/11.56 (b(s(z), s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[247, 29327])).
% 11.28/11.56 tff(29329,plain,
% 11.28/11.56 (~b(elem!1, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[12445, 29313, 88, 29293])).
% 11.28/11.56 tff(29330,plain,
% 11.28/11.56 (~(elem!1 = s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[769, 29325])).
% 11.28/11.56 tff(29331,plain,
% 11.28/11.56 (~r(s(z), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[27237, 29330, 2913, 29329, 29319])).
% 11.28/11.56 tff(29332,plain,
% 11.28/11.56 (b(s(z), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[632, 29331, 29315])).
% 11.28/11.56 tff(29333,plain,
% 11.28/11.56 (~b(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[23112, 29332, 29293, 29304])).
% 11.28/11.56 tff(29334,plain,
% 11.28/11.56 (r(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[678, 29333])).
% 11.28/11.56 tff(29335,plain,
% 11.28/11.56 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[25141, 29323, 88, 22898, 2913, 29316])).
% 11.28/11.56 tff(29336,plain,
% 11.28/11.56 (b(s(s(s(s(z)))), s(s(z)))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[1714, 29335])).
% 11.28/11.56 tff(29337,plain,
% 11.28/11.56 (~b(s(s(z)), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[25151, 29336, 88, 22898, 29323])).
% 11.28/11.56 tff(29338,plain,
% 11.28/11.56 (r(s(s(z)), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[1211, 29337])).
% 11.28/11.56 tff(29339,plain,
% 11.28/11.56 (~r(s(s(z)), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[10610, 29338, 2913, 29334])).
% 11.28/11.56 tff(29340,plain,
% 11.28/11.56 (b(s(s(z)), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[3778, 29339])).
% 11.28/11.56 tff(29341,plain,
% 11.28/11.56 (~r(elem!1, z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[20856, 29340, 88, 28192, 29320, 29326, 29334, 29328, 29323])).
% 11.28/11.56 tff(29342,plain,
% 11.28/11.56 (b(s(elem!1), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[14657, 29341, 29293, 22898, 29314, 29315, 2])).
% 11.28/11.56 tff(29343,plain,
% 11.28/11.56 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[14662, 29342, 29314])).
% 11.28/11.56 tff(29344,plain,
% 11.28/11.56 (~(s(s(elem!1)) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[451, 29343])).
% 11.28/11.56 tff(29345,plain,
% 11.28/11.56 (~(s(elem!1) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[1943, 29344])).
% 11.28/11.56 tff(29346,plain,
% 11.28/11.56 (~(elem!1 = s(elem!1))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[166, 29345])).
% 11.28/11.56 tff(29347,plain,
% 11.28/11.56 (~b(s(elem!1), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[7777, 29342, 29293, 29313])).
% 11.28/11.56 tff(29348,plain,
% 11.28/11.56 (r(s(elem!1), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[549, 29347])).
% 11.28/11.56 tff(29349,plain,
% 11.28/11.56 (~b(elem!1, s(elem!1))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[1930, 29348, 28192, 29304, 118, 29318])).
% 11.28/11.56 tff(29350,plain,
% 11.28/11.56 (~b(z, s(elem!1))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[6555, 29342, 29293, 29313])).
% 11.28/11.56 tff(29351,plain,
% 11.28/11.56 (r(z, s(elem!1))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[566, 29350])).
% 11.28/11.56 tff(29352,plain,
% 11.28/11.56 (~r(elem!1, s(elem!1))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[19851, 29351, 28192, 29348])).
% 11.28/11.56 tff(29353,plain,
% 11.28/11.56 ($false),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[443, 29352, 29349, 29346])).
% 11.28/11.56 tff(29354,plain,(b(s(z), s(s(s(s(z))))) | (elem!1 = z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29355,plain,
% 11.28/11.56 (b(s(z), s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29354, 81, 2])).
% 11.28/11.56 tff(29356,plain,
% 11.28/11.56 (elem!1 = s(s(s(elem!1)))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29121, 484, 2, 90, 411, 1234])).
% 11.28/11.56 tff(29357,plain,
% 11.28/11.56 (s(s(s(elem!1))) = elem!1),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[129, 29356])).
% 11.28/11.56 tff(29358,plain,
% 11.28/11.56 (~b(elem!1, s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[15370, 29357])).
% 11.28/11.56 tff(29359,plain,
% 11.28/11.56 (~(s(z) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[8542, 29358, 1234])).
% 11.28/11.56 tff(29360,plain,
% 11.28/11.56 (r(s(s(s(elem!1))), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[533, 29357, 3618])).
% 11.28/11.56 tff(29361,plain,
% 11.28/11.56 (r(z, s(s(s(elem!1))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[10792, 29357, 411])).
% 11.28/11.56 tff(29362,plain,
% 11.28/11.56 (~b(s(s(s(elem!1))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[8400, 29357, 31])).
% 11.28/11.56 tff(29363,plain,
% 11.28/11.56 (r(s(s(s(elem!1))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[223, 29362])).
% 11.28/11.56 tff(29364,plain,
% 11.28/11.56 (~r(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[202, 29363, 29361, 29360])).
% 11.28/11.56 tff(29365,plain,
% 11.28/11.56 (b(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[180, 29364])).
% 11.28/11.56 tff(29366,plain,
% 11.28/11.56 (~b(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28088, 29365, 90, 1234])).
% 11.28/11.56 tff(29367,plain,
% 11.28/11.56 (r(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[678, 29366])).
% 11.28/11.56 tff(29368,plain,
% 11.28/11.56 (b(s(z), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[19761, 29367, 411, 31, 29359])).
% 11.28/11.56 tff(29369,plain,
% 11.28/11.56 (r(elem!1, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[8406, 29363, 29357])).
% 11.28/11.56 tff(29370,plain,
% 11.28/11.56 (~b(z, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[10438, 29369, 411, 1234, 90])).
% 11.28/11.56 tff(29371,plain,
% 11.28/11.56 (r(z, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[800, 29370])).
% 11.28/11.56 tff(29372,plain,
% 11.28/11.56 (b(s(s(s(s(z)))), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28085, 29371, 90, 133, 1234, 3618, 29363, 29356])).
% 11.28/11.56 tff(29373,plain,
% 11.28/11.56 (~r(s(s(s(s(z)))), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[10418, 29371, 411, 29369])).
% 11.28/11.56 tff(29374,plain,
% 11.28/11.56 (r(elem!1, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[18869, 29373, 1234, 21778, 29368])).
% 11.28/11.56 tff(29375,plain,
% 11.28/11.56 (~r(s(s(s(s(z)))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[15063, 29374, 411, 29371])).
% 11.28/11.56 tff(29376,plain,
% 11.28/11.56 (b(s(s(s(s(z)))), s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[749, 29375])).
% 11.28/11.56 tff(29377,plain,
% 11.28/11.56 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[15016, 29374, 411, 29371])).
% 11.28/11.56 tff(29378,plain,
% 11.28/11.56 (b(s(s(s(s(z)))), s(s(z)))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[1714, 29377])).
% 11.28/11.56 tff(29379,plain,
% 11.28/11.56 ($false),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[18640, 29378, 29376, 411, 1234, 3618, 29357, 29367, 29372, 90, 29368])).
% 11.28/11.56 tff(29380,plain,(b(elem!1, z) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | b(elem!1, s(z)) | (~b(z, elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29381,plain,
% 11.28/11.56 (b(elem!1, z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29380, 31, 29355, 88, 28192, 29293, 2])).
% 11.28/11.56 tff(29382,plain,
% 11.28/11.56 (~b(elem!1, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[12445, 29381, 88, 29293])).
% 11.28/11.56 tff(29383,plain,
% 11.28/11.56 (~(s(z) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[8539, 29382, 29355])).
% 11.28/11.56 tff(29384,plain,
% 11.28/11.56 (~(elem!1 = s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[172, 29383])).
% 11.28/11.56 tff(29385,plain,
% 11.28/11.56 (r(elem!1, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[837, 29384, 31])).
% 11.28/11.56 tff(29386,plain,
% 11.28/11.56 (elem!1 = s(s(s(elem!1)))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28962, 29383, 28192, 31, 29355, 88, 2])).
% 11.28/11.56 tff(29387,plain,
% 11.28/11.56 (s(s(s(elem!1))) = elem!1),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[129, 29386])).
% 11.28/11.56 tff(29388,plain,
% 11.28/11.56 (~(s(s(s(s(z)))) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[1436, 29387])).
% 11.28/11.56 tff(29389,plain,
% 11.28/11.56 (~b(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28064, 29388, 88, 29293, 29381, 29383, 29385])).
% 11.28/11.56 tff(29390,plain,
% 11.28/11.56 (r(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[180, 29389])).
% 11.28/11.56 tff(29391,plain,
% 11.28/11.56 (r(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[26476, 29389, 81, 29293, 2, 31])).
% 11.28/11.56 tff(29392,plain,
% 11.28/11.56 ($false),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[845, 29391, 29390, 28192, 29385])).
% 11.28/11.56 tff(29393,plain,(b(elem!1, s(z)) | r(s(s(s(s(z)))), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29394,plain,
% 11.28/11.56 (b(elem!1, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29393, 81, 2])).
% 11.28/11.56 tff(29395,plain,
% 11.28/11.56 (~(s(z) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[20271, 29394])).
% 11.28/11.56 tff(29396,plain,
% 11.28/11.56 (~b(s(s(s(s(z)))), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[27735, 721, 90, 133, 1234])).
% 11.28/11.56 tff(29397,plain,
% 11.28/11.56 (~b(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[27160, 29356, 133, 1234, 90, 721, 29396])).
% 11.28/11.56 tff(29398,plain,
% 11.28/11.56 (r(z, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[678, 29397])).
% 11.28/11.56 tff(29399,plain,
% 11.28/11.56 (r(elem!1, s(z))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[26722, 29398, 90, 22924, 133, 1234, 484])).
% 11.28/11.56 tff(29400,plain,
% 11.28/11.56 (~b(elem!1, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[28971, 721, 90, 22924, 1234])).
% 11.28/11.56 tff(29401,plain,
% 11.28/11.56 (r(elem!1, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[781, 21768, 29400])).
% 11.28/11.56 tff(29402,plain,
% 11.28/11.56 (r(s(s(s(s(z)))), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[762, 21778, 29396])).
% 11.28/11.56 tff(29403,plain,
% 11.28/11.56 (~r(z, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[6399, 29402, 29401, 3618])).
% 11.28/11.56 tff(29404,plain,
% 11.28/11.56 (b(z, s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[800, 29403])).
% 11.28/11.56 tff(29405,plain,
% 11.28/11.56 ($false),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[10438, 29404, 29399, 411, 1234, 90])).
% 11.28/11.56 tff(29406,plain,(b(elem!1, z) | (~r(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.56 tff(29407,plain,
% 11.28/11.56 (b(elem!1, z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29406, 28192, 29355, 88, 29293, 29394, 2])).
% 11.28/11.56 tff(29408,plain,
% 11.28/11.56 (~b(s(s(s(elem!1))), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[10743, 29407, 22898, 29293])).
% 11.28/11.56 tff(29409,plain,
% 11.28/11.56 (elem!1 = s(s(s(elem!1)))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[29228, 29408, 22898, 29355, 28192, 88, 29394, 29407, 118, 29395])).
% 11.28/11.56 tff(29410,plain,
% 11.28/11.56 (s(s(s(elem!1))) = elem!1),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[129, 29409])).
% 11.28/11.56 tff(29411,plain,
% 11.28/11.56 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[11384, 29410])).
% 11.28/11.56 tff(29412,plain,
% 11.28/11.56 (~(s(s(s(s(z)))) = elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[1436, 29410])).
% 11.28/11.56 tff(29413,plain,
% 11.28/11.56 (~(elem!1 = s(s(s(s(z)))))),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[769, 29412])).
% 11.28/11.56 tff(29414,plain,
% 11.28/11.56 (~b(s(s(s(s(z)))), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[27735, 29394, 88, 29293, 29355])).
% 11.28/11.56 tff(29415,plain,
% 11.28/11.56 (r(s(s(s(s(z)))), elem!1)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[762, 29412, 29414])).
% 11.28/11.56 tff(29416,plain,
% 11.28/11.56 (~b(s(z), z)),
% 11.28/11.56 inference(unit_resolution,[status(thm)],[13285, 29407, 29293, 29394])).
% 11.28/11.57 tff(29417,plain,
% 11.28/11.57 (r(s(z), z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[180, 29416])).
% 11.28/11.57 tff(29418,plain,
% 11.28/11.57 (~b(z, s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[27160, 29409, 29293, 29355, 88, 29394, 29414])).
% 11.28/11.57 tff(29419,plain,
% 11.28/11.57 (r(z, s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[678, 29418])).
% 11.28/11.57 tff(29420,plain,
% 11.28/11.57 (~r(s(z), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[27200, 29419, 88, 29293, 29355, 29407, 29395, 2, 29409, 29417, 29414])).
% 11.28/11.57 tff(29421,plain,
% 11.28/11.57 (b(s(z), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[632, 29420, 29395])).
% 11.28/11.57 tff(29422,plain,
% 11.28/11.57 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[12326, 29421, 88, 29293, 29355, 29407, 29417, 29415, 29413])).
% 11.28/11.57 tff(29423,plain,
% 11.28/11.57 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[12150, 29421, 29293, 29417, 29407])).
% 11.28/11.57 tff(29424,plain,
% 11.28/11.57 ($false),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[8073, 29423, 29422, 29411])).
% 11.28/11.57 tff(29425,plain,(r(s(s(s(s(z)))), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.57 tff(29426,plain,
% 11.28/11.57 (r(s(s(s(s(z)))), z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[29425, 2])).
% 11.28/11.57 tff(29427,plain,
% 11.28/11.57 (b(z, s(s(s(elem!1))))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[8231, 80, 2])).
% 11.28/11.57 tff(29428,plain,
% 11.28/11.57 (~r(z, s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[10620, 1216, 29426])).
% 11.28/11.57 tff(29429,plain,
% 11.28/11.57 (b(z, s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[678, 29428])).
% 11.28/11.57 tff(29430,plain,
% 11.28/11.57 (~b(s(s(s(elem!1))), s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[10690, 5450, 29427, 29429])).
% 11.28/11.57 tff(29431,plain,
% 11.28/11.57 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 11.28/11.57 inference(monotonicity,[status(thm)],[2841])).
% 11.28/11.57 tff(29432,plain,
% 11.28/11.57 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 11.28/11.57 inference(symmetry,[status(thm)],[29431])).
% 11.28/11.57 tff(29433,plain,
% 11.28/11.57 (b(s(s(s(s(z)))), z)),
% 11.28/11.57 inference(modus_ponens,[status(thm)],[380, 29432])).
% 11.28/11.57 tff(29434,plain,
% 11.28/11.57 ($false),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[3446, 29433])).
% 11.28/11.57 tff(29435,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | b(s(s(s(s(z)))), z) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.57 tff(29436,plain,
% 11.28/11.57 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[29435, 380, 3446])).
% 11.28/11.57 tff(29437,plain,
% 11.28/11.57 ($false),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[3843, 15469])).
% 11.28/11.57 tff(29438,plain,((~(elem!1 = s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.57 tff(29439,plain,
% 11.28/11.57 (~(elem!1 = s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[29438, 29436])).
% 11.28/11.57 tff(29440,plain,
% 11.28/11.57 (r(elem!1, s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[837, 29439, 31])).
% 11.28/11.57 tff(29441,plain,
% 11.28/11.57 (~r(elem!1, s(s(s(elem!1))))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[22955, 194, 232, 183, 29440])).
% 11.28/11.57 tff(29442,plain,
% 11.28/11.57 (b(elem!1, s(s(s(elem!1))))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[424, 29441, 1])).
% 11.28/11.57 tff(29443,plain,
% 11.28/11.57 (~r(s(s(s(elem!1))), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[5762, 194, 232, 183, 29440])).
% 11.28/11.57 tff(29444,plain,
% 11.28/11.57 (b(s(s(s(elem!1))), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[230, 29443, 9])).
% 11.28/11.57 tff(29445,plain,
% 11.28/11.57 (~b(z, elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[10845, 29444, 10782, 29442])).
% 11.28/11.57 tff(29446,plain,
% 11.28/11.57 (z = elem!1),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[141, 29445, 80])).
% 11.28/11.57 tff(29447,plain,
% 11.28/11.57 (r(elem!1, z) <=> r(elem!1, elem!1)),
% 11.28/11.57 inference(monotonicity,[status(thm)],[94])).
% 11.28/11.57 tff(29448,plain,
% 11.28/11.57 (r(elem!1, elem!1) <=> r(elem!1, z)),
% 11.28/11.57 inference(symmetry,[status(thm)],[29447])).
% 11.28/11.57 tff(29449,plain,
% 11.28/11.57 ((~r(elem!1, elem!1)) <=> (~r(elem!1, z))),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29448])).
% 11.28/11.57 tff(29450,plain,
% 11.28/11.57 (~r(elem!1, z)),
% 11.28/11.57 inference(modus_ponens,[status(thm)],[17665, 29449])).
% 11.28/11.57 tff(29451,plain,
% 11.28/11.57 ($false),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[530, 29450])).
% 11.28/11.57 tff(29452,plain,((~(z = elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.57 tff(29453,plain,
% 11.28/11.57 (~r(elem!1, z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[29452, 29446])).
% 11.28/11.57 tff(29454,plain,
% 11.28/11.57 (r(z, s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[28887, 29453, 29440, 10782, 380, 9, 232, 183])).
% 11.28/11.57 tff(29455,plain,
% 11.28/11.57 (r(elem!1, s(s(s(elem!1))))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[2570, 812, 232])).
% 11.28/11.57 tff(29456,plain,
% 11.28/11.57 (~(z = elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[28273, 29455, 53])).
% 11.28/11.57 tff(29457,plain,
% 11.28/11.57 (b(z, elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[141, 29456, 80])).
% 11.28/11.57 tff(29458,plain,
% 11.28/11.57 (~(elem!1 = z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[5453, 29456])).
% 11.28/11.57 tff(29459,plain,
% 11.28/11.57 (b(elem!1, z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[526, 29458, 2282])).
% 11.28/11.57 tff(29460,plain,
% 11.28/11.57 ($false),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[10876, 29459, 29457, 380, 18086])).
% 11.28/11.57 tff(29461,plain,((~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), z)) | r(elem!1, z) | r(z, elem!1) | r(z, s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.57 tff(29462,plain,
% 11.28/11.57 (~(s(z) = elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[29461, 1234, 2282, 80, 53, 232, 380])).
% 11.28/11.57 tff(29463,plain,
% 11.28/11.57 (~(elem!1 = s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[172, 29462])).
% 11.28/11.57 tff(29464,plain,
% 11.28/11.57 (r(elem!1, s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[837, 29463, 31])).
% 11.28/11.57 tff(29465,plain,
% 11.28/11.57 (~r(s(s(s(elem!1))), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[5762, 194, 232, 183, 29464])).
% 11.28/11.57 tff(29466,plain,
% 11.28/11.57 (b(s(s(s(elem!1))), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[230, 29465, 127])).
% 11.28/11.57 tff(29467,plain,
% 11.28/11.57 (~b(elem!1, z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[17249, 29466, 10782, 380])).
% 11.28/11.57 tff(29468,plain,
% 11.28/11.57 (elem!1 = z),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[526, 29467, 2282])).
% 11.28/11.57 tff(29469,plain,
% 11.28/11.57 (s(elem!1) = s(z)),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29468])).
% 11.28/11.57 tff(29470,plain,
% 11.28/11.57 (s(s(elem!1)) = s(s(z))),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29469])).
% 11.28/11.57 tff(29471,plain,
% 11.28/11.57 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29470])).
% 11.28/11.57 tff(29472,plain,
% 11.28/11.57 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 11.28/11.57 inference(symmetry,[status(thm)],[29471])).
% 11.28/11.57 tff(29473,plain,
% 11.28/11.57 (r(z, s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[28887, 29464, 2282, 10782, 380, 127, 232, 183])).
% 11.28/11.57 tff(29474,plain,
% 11.28/11.57 (r(s(z), s(s(s(z))))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[23224, 29468, 232])).
% 11.28/11.57 tff(29475,plain,
% 11.28/11.57 (~r(s(s(s(s(z)))), s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[18419, 29474, 2053, 29473])).
% 11.28/11.57 tff(29476,plain,
% 11.28/11.57 (b(s(s(s(s(z)))), s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[749, 29475])).
% 11.28/11.57 tff(29477,plain,
% 11.28/11.57 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[5108, 29476, 1233, 1234])).
% 11.28/11.57 tff(29478,plain,
% 11.28/11.57 (r(s(s(z)), s(s(s(s(z)))))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[3652, 29477])).
% 11.28/11.57 tff(29479,plain,
% 11.28/11.57 (~r(s(s(z)), z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[9635, 29478, 2053, 29473])).
% 11.28/11.57 tff(29480,plain,
% 11.28/11.57 (b(s(s(z)), z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[1211, 29479])).
% 11.28/11.57 tff(29481,plain,
% 11.28/11.57 (b(s(s(elem!1)), z)),
% 11.28/11.57 inference(modus_ponens,[status(thm)],[29480, 29472])).
% 11.28/11.57 tff(29482,plain,
% 11.28/11.57 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[13177, 29481, 10782, 380])).
% 11.28/11.57 tff(29483,plain,
% 11.28/11.57 (b(s(elem!1), z) <=> b(s(z), z)),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29469])).
% 11.28/11.57 tff(29484,plain,
% 11.28/11.57 (b(s(z), z) <=> b(s(elem!1), z)),
% 11.28/11.57 inference(symmetry,[status(thm)],[29483])).
% 11.28/11.57 tff(29485,plain,
% 11.28/11.57 (~b(elem!1, z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[10390, 812, 91])).
% 11.28/11.57 tff(29486,plain,
% 11.28/11.57 (elem!1 = z),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[526, 29485, 2282])).
% 11.28/11.57 tff(29487,plain,
% 11.28/11.57 ($false),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[5453, 29456, 29486])).
% 11.28/11.57 tff(29488,plain,((~(s(z) = elem!1)) | r(z, s(s(s(elem!1)))) | r(elem!1, z) | (~r(s(z), s(s(s(elem!1))))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.57 tff(29489,plain,
% 11.28/11.57 (~(s(z) = elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[29488, 2282, 53, 232, 91])).
% 11.28/11.57 tff(29490,plain,
% 11.28/11.57 (~(elem!1 = s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[172, 29489])).
% 11.28/11.57 tff(29491,plain,
% 11.28/11.57 (r(elem!1, s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[837, 29490, 31])).
% 11.28/11.57 tff(29492,plain,
% 11.28/11.57 (~r(s(s(s(elem!1))), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[5762, 194, 232, 183, 29491])).
% 11.28/11.57 tff(29493,plain,
% 11.28/11.57 (b(s(s(s(elem!1))), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[230, 29492, 127])).
% 11.28/11.57 tff(29494,plain,
% 11.28/11.57 (~b(elem!1, z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[17249, 29493, 10782, 380])).
% 11.28/11.57 tff(29495,plain,
% 11.28/11.57 (elem!1 = z),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[526, 29494, 2282])).
% 11.28/11.57 tff(29496,plain,
% 11.28/11.57 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), z)),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29495])).
% 11.28/11.57 tff(29497,plain,
% 11.28/11.57 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = z)),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29495])).
% 11.28/11.57 tff(29498,plain,
% 11.28/11.57 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 11.28/11.57 inference(symmetry,[status(thm)],[29497])).
% 11.28/11.57 tff(29499,plain,
% 11.28/11.57 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29498])).
% 11.28/11.57 tff(29500,plain,
% 11.28/11.57 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 11.28/11.57 inference(modus_ponens,[status(thm)],[6638, 29499])).
% 11.28/11.57 tff(29501,plain,
% 11.28/11.57 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29495])).
% 11.28/11.57 tff(29502,plain,
% 11.28/11.57 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 11.28/11.57 inference(symmetry,[status(thm)],[29501])).
% 11.28/11.57 tff(29503,plain,
% 11.28/11.57 (r(s(s(s(s(z)))), elem!1)),
% 11.28/11.57 inference(modus_ponens,[status(thm)],[2053, 29502])).
% 11.28/11.57 tff(29504,plain,
% 11.28/11.57 (r(s(z), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[3205, 29495, 91])).
% 11.28/11.57 tff(29505,plain,
% 11.28/11.57 (r(elem!1, s(z)) <=> r(z, s(z))),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29495])).
% 11.28/11.57 tff(29506,plain,
% 11.28/11.57 (r(z, s(z))),
% 11.28/11.57 inference(modus_ponens,[status(thm)],[29491, 29505])).
% 11.28/11.57 tff(29507,plain,
% 11.28/11.57 (~r(s(s(s(s(z)))), s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[11989, 194, 29506, 181, 2053])).
% 11.28/11.57 tff(29508,plain,
% 11.28/11.57 (b(s(s(s(s(z)))), s(z))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[749, 29507])).
% 11.28/11.57 tff(29509,plain,
% 11.28/11.57 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[11865, 29508, 29491, 29504, 29503])).
% 11.28/11.57 tff(29510,plain,
% 11.28/11.57 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[8073, 29509, 29500])).
% 11.28/11.57 tff(29511,plain,
% 11.28/11.57 (b(s(s(s(s(s(s(z)))))), z)),
% 11.28/11.57 inference(modus_ponens,[status(thm)],[29510, 29496])).
% 11.28/11.57 tff(29512,plain,
% 11.28/11.57 (b(s(s(s(z))), z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[1680, 29495, 380])).
% 11.28/11.57 tff(29513,plain,
% 11.28/11.57 (s(elem!1) = s(z)),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29495])).
% 11.28/11.57 tff(29514,plain,
% 11.28/11.57 (s(s(elem!1)) = s(s(z))),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29513])).
% 11.28/11.57 tff(29515,plain,
% 11.28/11.57 (s(s(s(elem!1))) = s(s(s(z)))),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29514])).
% 11.28/11.57 tff(29516,plain,
% 11.28/11.57 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29515])).
% 11.28/11.57 tff(29517,plain,
% 11.28/11.57 (b(z, s(s(s(z))))),
% 11.28/11.57 inference(modus_ponens,[status(thm)],[10782, 29516])).
% 11.28/11.57 tff(29518,plain,
% 11.28/11.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.28/11.57 inference(rewrite,[status(thm)],[])).
% 11.28/11.57 tff(29519,plain,
% 11.28/11.57 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.28/11.57 inference(rewrite,[status(thm)],[])).
% 11.28/11.57 tff(29520,plain,
% 11.28/11.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 11.28/11.57 inference(monotonicity,[status(thm)],[29519])).
% 11.28/11.57 tff(29521,plain,
% 11.28/11.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.28/11.57 inference(transitivity,[status(thm)],[29520, 29518])).
% 11.28/11.57 tff(29522,plain,
% 11.28/11.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.28/11.57 inference(quant_inst,[status(thm)],[])).
% 11.28/11.57 tff(29523,plain,
% 11.28/11.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 11.28/11.57 inference(modus_ponens,[status(thm)],[29522, 29521])).
% 11.28/11.57 tff(29524,plain,
% 11.28/11.57 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[29523, 391, 29517, 29512, 29511])).
% 11.28/11.57 tff(29525,plain,
% 11.28/11.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(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(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 11.28/11.57 inference(rewrite,[status(thm)],[])).
% 11.28/11.57 tff(29526,plain,
% 11.28/11.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 11.28/11.57 inference(quant_inst,[status(thm)],[])).
% 11.28/11.57 tff(29527,plain,
% 11.28/11.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 11.28/11.57 inference(modus_ponens,[status(thm)],[29526, 29525])).
% 11.28/11.57 tff(29528,plain,
% 11.28/11.57 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[29527, 42, 8094, 29524])).
% 11.28/11.57 tff(29529,plain,
% 11.28/11.57 (~r(s(s(z)), z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[26737, 29508, 2053, 181, 29506, 1234])).
% 11.28/11.57 tff(29530,plain,
% 11.28/11.57 (b(s(s(z)), z)),
% 11.28/11.57 inference(unit_resolution,[status(thm)],[1211, 29529])).
% 11.28/11.57 tff(29531,plain,
% 11.28/11.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.28/11.57 inference(rewrite,[status(thm)],[])).
% 11.28/11.57 tff(29532,plain,
% 11.28/11.57 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.28/11.58 inference(rewrite,[status(thm)],[])).
% 11.28/11.58 tff(29533,plain,
% 11.28/11.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29532])).
% 11.28/11.58 tff(29534,plain,
% 11.28/11.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.28/11.58 inference(transitivity,[status(thm)],[29533, 29531])).
% 11.28/11.58 tff(29535,plain,
% 11.28/11.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 11.28/11.58 inference(quant_inst,[status(thm)],[])).
% 11.28/11.58 tff(29536,plain,
% 11.28/11.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[29535, 29534])).
% 11.28/11.58 tff(29537,plain,
% 11.28/11.58 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[29536, 391, 29530, 29517, 29512, 29511])).
% 11.28/11.58 tff(29538,plain,
% 11.28/11.58 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 29537])).
% 11.28/11.58 tff(29539,plain,
% 11.28/11.58 (~(s(s(z)) = s(s(s(z))))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[8879, 29495])).
% 11.28/11.58 tff(29540,plain,
% 11.28/11.58 (~b(s(s(z)), s(s(s(z))))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[8632, 391, 29530, 29517, 29512])).
% 11.28/11.58 tff(29541,plain,
% 11.28/11.58 (r(s(s(z)), s(s(s(z))))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[24076, 29540, 29539])).
% 11.28/11.58 tff(29542,plain,
% 11.28/11.58 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29514])).
% 11.28/11.58 tff(29543,plain,
% 11.28/11.58 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 11.28/11.58 inference(symmetry,[status(thm)],[29542])).
% 11.28/11.58 tff(29544,plain,
% 11.28/11.58 (b(s(s(elem!1)), z)),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[29530, 29543])).
% 11.28/11.58 tff(29545,plain,
% 11.28/11.58 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[13177, 29544, 10782, 380])).
% 11.28/11.58 tff(29546,plain,
% 11.28/11.58 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[1370, 29545, 15838])).
% 11.28/11.58 tff(29547,plain,
% 11.28/11.58 (r(s(s(s(z))), s(s(z)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[4385, 29546, 29495])).
% 11.28/11.58 tff(29548,plain,
% 11.28/11.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 11.28/11.58 inference(rewrite,[status(thm)],[])).
% 11.28/11.58 tff(29549,plain,
% 11.28/11.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 11.28/11.58 inference(quant_inst,[status(thm)],[])).
% 11.28/11.58 tff(29550,plain,
% 11.28/11.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[29549, 29548])).
% 11.28/11.58 tff(29551,plain,
% 11.28/11.58 ($false),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[29550, 194, 29547, 29541, 29538, 29528])).
% 11.28/11.58 tff(29552,plain,(r(elem!1, z) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | b(s(z), z) | (s(s(s(elem!1))) = elem!1) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | b(elem!1, s(z)) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.58 tff(29553,plain,
% 11.28/11.58 (b(s(z), z)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[29552, 1234, 2053, 380, 2282, 127, 232, 183, 31, 53])).
% 11.28/11.58 tff(29554,plain,
% 11.28/11.58 (b(s(elem!1), z)),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[29553, 29484])).
% 11.28/11.58 tff(29555,plain,
% 11.28/11.58 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29469])).
% 11.28/11.58 tff(29556,plain,
% 11.28/11.58 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 11.28/11.58 inference(symmetry,[status(thm)],[29555])).
% 11.28/11.58 tff(29557,plain,
% 11.28/11.58 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29556])).
% 11.28/11.58 tff(29558,plain,
% 11.28/11.58 (~(s(s(elem!1)) = s(elem!1))),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[357, 29557])).
% 11.28/11.58 tff(29559,plain,
% 11.28/11.58 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(s(elem!1)))),
% 11.28/11.58 inference(transitivity,[status(thm)],[29556, 1098])).
% 11.28/11.58 tff(29560,plain,
% 11.28/11.58 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29559])).
% 11.28/11.58 tff(29561,plain,
% 11.28/11.58 (~(s(elem!1) = s(s(elem!1)))),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[357, 29560])).
% 11.28/11.58 tff(29562,plain,
% 11.28/11.58 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29469])).
% 11.28/11.58 tff(29563,plain,
% 11.28/11.58 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 11.28/11.58 inference(symmetry,[status(thm)],[29562])).
% 11.28/11.58 tff(29564,plain,
% 11.28/11.58 (r(s(elem!1), s(s(s(elem!1))))),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[232, 29563])).
% 11.28/11.58 tff(29565,plain,
% 11.28/11.58 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[17760, 29481, 10782, 29466, 29564, 29561, 29558, 29554])).
% 11.28/11.58 tff(29566,plain,
% 11.28/11.58 ($false),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[1370, 29565, 29482, 15838])).
% 11.28/11.58 tff(29567,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | r(elem!1, z) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | b(elem!1, s(z)) | r(z, elem!1) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.58 tff(29568,plain,
% 11.28/11.58 (~b(s(z), s(s(s(s(z)))))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[29567, 29453, 232, 3447, 1233, 380, 9, 183, 31, 80, 53])).
% 11.28/11.58 tff(29569,plain,
% 11.28/11.58 (r(s(z), s(s(s(s(z)))))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[1230, 29568])).
% 11.28/11.58 tff(29570,plain,
% 11.28/11.58 ($false),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[10620, 29569, 29454, 3447])).
% 11.28/11.58 tff(29571,plain,((~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | b(elem!1, s(z)) | r(z, elem!1) | r(z, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.58 tff(29572,plain,
% 11.28/11.58 (~b(s(s(s(elem!1))), z)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[29571, 53, 11174, 1233, 31, 80, 20264, 1, 3446])).
% 11.28/11.58 tff(29573,plain,
% 11.28/11.58 (r(s(s(s(elem!1))), z)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[377, 29572])).
% 11.28/11.58 tff(29574,plain,
% 11.28/11.58 (~(z = elem!1)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[9853, 22958, 174])).
% 11.28/11.58 tff(29575,plain,
% 11.28/11.58 (~b(z, elem!1)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[10845, 22959, 10682, 22957])).
% 11.28/11.58 tff(29576,plain,
% 11.28/11.58 ($false),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[141, 29575, 29574, 80])).
% 11.28/11.58 tff(29577,plain,((~r(elem!1, s(z))) | r(z, elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.58 tff(29578,plain,
% 11.28/11.58 (~r(elem!1, s(z))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[29577, 10782, 80, 29573, 1, 20264, 11174])).
% 11.28/11.58 tff(29579,plain,
% 11.28/11.58 (elem!1 = s(z)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[837, 29578, 31])).
% 11.28/11.58 tff(29580,plain,
% 11.28/11.58 (s(z) = elem!1),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[172, 29579])).
% 11.28/11.58 tff(29581,plain,
% 11.28/11.58 (b(s(elem!1), elem!1)),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[1233, 7399])).
% 11.28/11.58 tff(29582,plain,
% 11.28/11.58 ($false),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[2163, 29581])).
% 11.28/11.58 tff(29583,plain,((~b(s(s(z)), s(z))) | b(s(elem!1), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.58 tff(29584,plain,
% 11.28/11.58 (b(s(elem!1), elem!1)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[29583, 29580, 1233])).
% 11.28/11.58 tff(29585,plain,
% 11.28/11.58 (~b(s(s(s(s(z)))), s(z))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[11177, 29579, 11173])).
% 11.28/11.58 tff(29586,plain,
% 11.28/11.58 (~b(s(s(s(s(z)))), elem!1)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[9614, 29580, 29585])).
% 11.28/11.58 tff(29587,plain,
% 11.28/11.58 (~b(s(s(s(elem!1))), elem!1)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[1563, 29586, 29579])).
% 11.28/11.58 tff(29588,plain,
% 11.28/11.58 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[14662, 29587, 29584])).
% 11.28/11.58 tff(29589,plain,
% 11.28/11.58 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29579])).
% 11.28/11.58 tff(29590,plain,
% 11.28/11.58 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 11.28/11.58 inference(symmetry,[status(thm)],[29589])).
% 11.28/11.58 tff(29591,plain,
% 11.28/11.58 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29590])).
% 11.28/11.58 tff(29592,plain,
% 11.28/11.58 (~b(elem!1, s(s(s(elem!1))))),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[14870, 29591])).
% 11.28/11.58 tff(29593,plain,
% 11.28/11.58 (r(elem!1, s(s(s(elem!1))))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[2570, 29580, 20264])).
% 11.28/11.58 tff(29594,plain,
% 11.28/11.58 (r(s(s(s(elem!1))), elem!1)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[230, 29587, 9])).
% 11.28/11.58 tff(29595,plain,
% 11.28/11.58 (~(z = elem!1)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[28273, 29593, 53])).
% 11.28/11.58 tff(29596,plain,
% 11.28/11.58 (s(elem!1) = s(s(z))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29579])).
% 11.28/11.58 tff(29597,plain,
% 11.28/11.58 (s(s(elem!1)) = s(s(s(z)))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29596])).
% 11.28/11.58 tff(29598,plain,
% 11.28/11.58 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29597])).
% 11.28/11.58 tff(29599,plain,
% 11.28/11.58 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29598])).
% 11.28/11.58 tff(29600,plain,
% 11.28/11.58 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(s(z))))))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[29599])).
% 11.28/11.58 tff(29601,plain,
% 11.28/11.58 (~b(s(z), s(s(s(s(z)))))),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[14870, 29600])).
% 11.28/11.58 tff(29602,plain,
% 11.28/11.58 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[16257, 29601, 31, 29595, 3446])).
% 11.28/11.58 tff(29603,plain,
% 11.28/11.58 (b(z, elem!1)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[141, 29595, 80])).
% 11.28/11.58 tff(29604,plain,
% 11.28/11.58 (~(s(s(elem!1)) = s(elem!1))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[2279, 29588])).
% 11.28/11.58 tff(29605,plain,
% 11.28/11.58 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[1374, 3473])).
% 11.28/11.58 tff(29606,plain,
% 11.28/11.58 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 11.28/11.58 inference(monotonicity,[status(thm)],[1552])).
% 11.28/11.58 tff(29607,plain,
% 11.28/11.58 (r(s(z), s(s(s(s(z)))))),
% 11.28/11.58 inference(modus_ponens,[status(thm)],[232, 29606])).
% 11.28/11.58 tff(29608,plain,
% 11.28/11.58 (~r(s(z), s(s(z)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[16234, 1749, 2053, 1216])).
% 11.28/11.58 tff(29609,plain,
% 11.28/11.58 (b(s(z), s(s(z)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[1788, 29608])).
% 11.28/11.58 tff(29610,plain,
% 11.28/11.58 (~b(z, s(s(z)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[16242, 391, 29609, 1233, 10679])).
% 11.28/11.58 tff(29611,plain,
% 11.28/11.58 (r(z, s(s(z)))),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[18613, 29610])).
% 11.28/11.58 tff(29612,plain,
% 11.28/11.58 (~b(s(s(z)), z)),
% 11.28/11.58 inference(unit_resolution,[status(thm)],[16250, 391, 29609, 1233, 10679])).
% 11.28/11.59 tff(29613,plain,
% 11.28/11.59 (r(s(s(z)), z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[1211, 29612])).
% 11.28/11.59 tff(29614,plain,
% 11.28/11.59 ($false),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[16255, 194, 1749, 2053, 29613, 29611])).
% 11.28/11.59 tff(29615,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.59 tff(29616,plain,
% 11.28/11.59 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[29615, 29607, 1233, 2053])).
% 11.28/11.59 tff(29617,plain,
% 11.28/11.59 (b(s(s(z)), s(s(s(s(z)))))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[3652, 29616])).
% 11.28/11.59 tff(29618,plain,
% 11.28/11.59 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 11.28/11.59 inference(monotonicity,[status(thm)],[1551])).
% 11.28/11.59 tff(29619,plain,
% 11.28/11.59 (b(s(z), z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[29488, 2282, 53, 232, 8598])).
% 11.28/11.59 tff(29620,plain,
% 11.28/11.59 (~b(z, s(s(elem!1)))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[24044, 29619, 10782, 1374, 183, 232, 270])).
% 11.28/11.59 tff(29621,plain,
% 11.28/11.59 (r(z, s(s(elem!1)))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[324, 29620])).
% 11.28/11.59 tff(29622,plain,
% 11.28/11.59 (r(z, s(s(s(z))))),
% 11.28/11.59 inference(modus_ponens,[status(thm)],[29621, 29618])).
% 11.28/11.59 tff(29623,plain,
% 11.28/11.59 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[3482, 1374, 169])).
% 11.28/11.59 tff(29624,plain,
% 11.28/11.59 (~b(s(s(z)), z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[20484, 29619, 29623, 23965, 1233])).
% 11.28/11.59 tff(29625,plain,
% 11.28/11.59 (r(s(s(z)), z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[1211, 29624])).
% 11.28/11.59 tff(29626,plain,
% 11.28/11.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.28/11.59 inference(rewrite,[status(thm)],[])).
% 11.28/11.59 tff(29627,plain,
% 11.28/11.59 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.28/11.59 inference(rewrite,[status(thm)],[])).
% 11.28/11.59 tff(29628,plain,
% 11.28/11.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 11.28/11.59 inference(monotonicity,[status(thm)],[29627])).
% 11.28/11.59 tff(29629,plain,
% 11.28/11.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.28/11.59 inference(transitivity,[status(thm)],[29628, 29626])).
% 11.28/11.59 tff(29630,plain,
% 11.28/11.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.28/11.59 inference(quant_inst,[status(thm)],[])).
% 11.28/11.59 tff(29631,plain,
% 11.28/11.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 11.28/11.59 inference(modus_ponens,[status(thm)],[29630, 29629])).
% 11.28/11.59 tff(29632,plain,
% 11.28/11.59 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[29631, 194, 2053, 29625, 29622])).
% 11.28/11.59 tff(29633,plain,
% 11.28/11.59 (b(s(s(s(s(z)))), s(s(z)))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[1714, 29632])).
% 11.28/11.59 tff(29634,plain,
% 11.28/11.59 (~b(s(s(s(z))), s(s(z)))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[24809, 29633, 29617, 29605])).
% 11.28/11.59 tff(29635,plain,
% 11.28/11.59 (~b(s(s(elem!1)), s(elem!1))),
% 11.28/11.59 inference(modus_ponens,[status(thm)],[29634, 8618])).
% 11.28/11.59 tff(29636,plain,
% 11.28/11.59 (b(s(elem!1), elem!1)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[29583, 8598, 1233])).
% 11.28/11.59 tff(29637,plain,
% 11.28/11.59 (r(elem!1, s(s(s(elem!1))))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[2570, 8598, 232])).
% 11.28/11.59 tff(29638,plain,
% 11.28/11.59 (~(z = elem!1)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[28273, 29637, 53])).
% 11.28/11.59 tff(29639,plain,
% 11.28/11.59 (~(elem!1 = z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[5453, 29638])).
% 11.28/11.59 tff(29640,plain,
% 11.28/11.59 (b(elem!1, z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[526, 2282, 29639])).
% 11.28/11.59 tff(29641,plain,
% 11.28/11.59 (~b(s(elem!1), z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[7777, 29640, 133, 29636])).
% 11.28/11.59 tff(29642,plain,
% 11.28/11.59 (r(s(elem!1), z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[549, 29641])).
% 11.28/11.59 tff(29643,plain,
% 11.28/11.59 (~b(z, s(elem!1))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[6555, 29640, 133, 29636])).
% 11.28/11.59 tff(29644,plain,
% 11.28/11.59 (r(z, s(elem!1))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[566, 29643])).
% 11.28/11.59 tff(29645,plain,
% 11.28/11.59 (~r(s(s(elem!1)), s(elem!1))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[2309, 29644, 29642, 29621])).
% 11.28/11.59 tff(29646,plain,
% 11.28/11.59 (b(s(s(elem!1)), s(elem!1))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[1135, 29645, 285])).
% 11.28/11.59 tff(29647,plain,
% 11.28/11.59 ($false),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[29646, 29635])).
% 11.28/11.59 tff(29648,plain,(r(elem!1, z) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), z)) | (s(s(elem!1)) = s(elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.59 tff(29649,plain,
% 11.28/11.59 (r(elem!1, z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[29648, 29579, 3447, 29604, 29603, 1233, 29602, 11174, 20264, 27044, 53])).
% 11.28/11.59 tff(29650,plain,
% 11.28/11.59 (~r(z, s(s(elem!1)))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[27619, 29649, 29573, 29594])).
% 11.28/11.59 tff(29651,plain,
% 11.28/11.59 (b(z, s(s(elem!1)))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[324, 29650])).
% 11.28/11.59 tff(29652,plain,
% 11.28/11.59 (b(s(s(elem!1)), elem!1)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[15730, 29651, 10782, 29593, 29592, 29587, 9, 29588])).
% 11.28/11.59 tff(29653,plain,
% 11.28/11.59 (b(s(s(s(z))), s(z))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[16036, 29652, 29580])).
% 11.28/11.59 tff(29654,plain,
% 11.28/11.59 (r(s(s(s(s(z)))), s(z))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[749, 29585])).
% 11.28/11.59 tff(29655,plain,
% 11.28/11.59 (~(elem!1 = s(s(s(s(z)))))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[2674, 29654, 29578])).
% 11.28/11.59 tff(29656,plain,
% 11.28/11.59 (~(s(s(s(s(z)))) = elem!1)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[16908, 29655])).
% 11.28/11.59 tff(29657,plain,
% 11.28/11.59 (r(s(s(s(s(z)))), elem!1)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[762, 29656, 29586])).
% 11.28/11.59 tff(29658,plain,
% 11.28/11.59 (~r(z, s(elem!1))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[6087, 29649, 3447, 29657])).
% 11.28/11.59 tff(29659,plain,
% 11.28/11.59 (b(z, s(elem!1))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[566, 29658])).
% 11.28/11.59 tff(29660,plain,
% 11.28/11.59 (b(z, s(s(z)))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[8527, 29659, 29580])).
% 11.28/11.59 tff(29661,plain,
% 11.28/11.59 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 11.28/11.59 inference(monotonicity,[status(thm)],[29598, 29597])).
% 11.28/11.59 tff(29662,plain,
% 11.28/11.59 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.28/11.59 inference(modus_ponens,[status(thm)],[29602, 29661])).
% 11.28/11.59 tff(29663,plain,
% 11.28/11.59 (~r(z, s(s(s(s(z)))))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[10733, 29580, 53])).
% 11.28/11.59 tff(29664,plain,
% 11.28/11.59 (b(z, s(s(s(s(z)))))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[800, 29663])).
% 11.28/11.59 tff(29665,plain,
% 11.28/11.59 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 11.28/11.59 inference(monotonicity,[status(thm)],[29598])).
% 11.28/11.59 tff(29666,plain,
% 11.28/11.59 (r(s(z), s(s(s(s(z)))))),
% 11.28/11.59 inference(modus_ponens,[status(thm)],[20264, 29665])).
% 11.28/11.59 tff(29667,plain,
% 11.28/11.59 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[29615, 29666, 1233, 3447])).
% 11.28/11.59 tff(29668,plain,
% 11.28/11.59 (b(s(s(z)), s(s(s(s(z)))))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[3652, 29667])).
% 11.28/11.59 tff(29669,plain,
% 11.28/11.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 11.28/11.59 inference(rewrite,[status(thm)],[])).
% 11.28/11.59 tff(29670,plain,
% 11.28/11.59 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 11.28/11.59 inference(rewrite,[status(thm)],[])).
% 11.28/11.59 tff(29671,plain,
% 11.28/11.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z))))))),
% 11.28/11.59 inference(monotonicity,[status(thm)],[29670])).
% 11.28/11.59 tff(29672,plain,
% 11.28/11.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 11.28/11.59 inference(transitivity,[status(thm)],[29671, 29669])).
% 11.28/11.59 tff(29673,plain,
% 11.28/11.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 11.28/11.59 inference(quant_inst,[status(thm)],[])).
% 11.28/11.59 tff(29674,plain,
% 11.28/11.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z))))),
% 11.28/11.59 inference(modus_ponens,[status(thm)],[29673, 29672])).
% 11.28/11.59 tff(29675,plain,
% 11.28/11.59 ($false),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[29674, 391, 29668, 29664, 29662, 29660, 29653])).
% 11.28/11.59 tff(29676,plain,(r(z, s(s(s(elem!1)))) | (~b(s(s(z)), s(z))) | b(elem!1, s(z)) | b(s(s(s(s(z)))), z) | b(s(z), s(s(s(elem!1)))) | r(z, elem!1) | b(s(s(s(elem!1))), s(z)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.59 tff(29677,plain,
% 11.28/11.59 (r(z, s(s(s(elem!1))))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[29676, 1233, 31, 3446, 14870, 80, 11173, 1])).
% 11.28/11.59 tff(29678,plain,
% 11.28/11.59 (~r(z, s(z))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[20248, 194, 29677, 20264, 11174])).
% 11.28/11.59 tff(29679,plain,
% 11.28/11.59 (~r(s(z), z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[3499, 29677, 11174, 20264])).
% 11.28/11.59 tff(29680,plain,
% 11.28/11.59 (b(s(z), z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[180, 29679])).
% 11.28/11.59 tff(29681,plain,
% 11.28/11.59 (b(z, s(z))),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[678, 29678])).
% 11.28/11.59 tff(29682,plain,
% 11.28/11.59 (~b(s(s(z)), z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[9065, 391, 1233, 29681, 29680])).
% 11.28/11.59 tff(29683,plain,
% 11.28/11.59 (r(s(s(z)), z)),
% 11.28/11.59 inference(unit_resolution,[status(thm)],[1211, 29682])).
% 11.28/11.59 tff(29684,plain,
% 11.28/11.59 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[14746, 29683, 3447, 29677])).
% 11.28/11.60 tff(29685,plain,
% 11.28/11.60 (b(s(s(z)), s(s(s(s(z)))))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[3652, 29684])).
% 11.28/11.60 tff(29686,plain,
% 11.28/11.60 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[14769, 29683, 3447, 29677])).
% 11.28/11.60 tff(29687,plain,
% 11.28/11.60 (b(s(s(s(s(z)))), s(s(z)))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[1714, 29686])).
% 11.28/11.60 tff(29688,plain,
% 11.28/11.60 (~b(s(z), s(s(s(s(z)))))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[9374, 29687, 1233, 29685])).
% 11.28/11.60 tff(29689,plain,
% 11.28/11.60 (r(s(z), s(s(s(s(z)))))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[1230, 29688])).
% 11.28/11.60 tff(29690,plain,
% 11.28/11.60 (~b(z, s(s(z)))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[22414, 391, 1233, 29681, 29680])).
% 11.28/11.60 tff(29691,plain,
% 11.28/11.60 (elem!1 = z),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[8231, 10, 80])).
% 11.28/11.60 tff(29692,plain,
% 11.28/11.60 (~b(elem!1, s(s(s(elem!1))))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[8846, 29691, 10])).
% 11.28/11.60 tff(29693,plain,
% 11.28/11.60 (r(elem!1, s(s(s(elem!1))))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[424, 29692, 1])).
% 11.28/11.60 tff(29694,plain,
% 11.28/11.60 (~r(elem!1, s(z))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[10776, 29693, 1216, 183])).
% 11.28/11.60 tff(29695,plain,
% 11.28/11.60 (elem!1 = s(z)),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[837, 29694, 31])).
% 11.28/11.60 tff(29696,plain,
% 11.28/11.60 (s(z) = elem!1),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[172, 29695])).
% 11.28/11.60 tff(29697,plain,
% 11.28/11.60 (~r(z, s(elem!1))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[8832, 29694, 29691])).
% 11.28/11.60 tff(29698,plain,
% 11.28/11.60 (b(z, s(elem!1))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[566, 29697])).
% 11.28/11.60 tff(29699,plain,
% 11.28/11.60 ($false),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[8527, 29698, 29696, 3373])).
% 11.28/11.60 tff(29700,plain,(b(z, s(s(s(elem!1)))) | b(z, s(s(z))) | b(elem!1, s(z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.60 tff(29701,plain,
% 11.28/11.60 (b(z, s(s(s(elem!1))))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[29700, 29690, 31, 29689, 11174, 1, 80])).
% 11.28/11.60 tff(29702,plain,
% 11.28/11.60 (~b(s(s(s(s(z)))), s(z))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[11177, 169, 11173])).
% 11.28/11.60 tff(29703,plain,
% 11.28/11.60 (~b(s(s(s(s(z)))), elem!1)),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[9614, 8598, 29702])).
% 11.28/11.60 tff(29704,plain,
% 11.28/11.60 (~b(s(s(s(elem!1))), elem!1)),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[1563, 29703, 169])).
% 11.28/11.60 tff(29705,plain,
% 11.28/11.60 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[14662, 29704, 29636])).
% 11.28/11.60 tff(29706,plain,
% 11.28/11.60 (~b(z, s(s(z)))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[22414, 391, 1233, 664, 5450])).
% 11.28/11.60 tff(29707,plain,
% 11.28/11.60 (~b(z, s(elem!1))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[8527, 8598, 29706])).
% 11.28/11.60 tff(29708,plain,
% 11.28/11.60 (r(z, s(elem!1))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[566, 29707])).
% 11.28/11.60 tff(29709,plain,
% 11.28/11.60 (~b(s(s(z)), z)),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[9065, 391, 1233, 664, 5450])).
% 11.28/11.60 tff(29710,plain,
% 11.28/11.60 (r(s(s(z)), z)),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[1211, 29709])).
% 11.28/11.60 tff(29711,plain,
% 11.28/11.60 (r(s(elem!1), z)),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[3560, 8598, 29710])).
% 11.28/11.60 tff(29712,plain,
% 11.28/11.60 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[29438, 169])).
% 11.28/11.60 tff(29713,plain,
% 11.28/11.60 (~b(s(s(s(elem!1))), z)),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[29435, 29712, 3446])).
% 11.28/11.60 tff(29714,plain,
% 11.28/11.60 (r(s(s(s(elem!1))), z)),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[377, 29713])).
% 11.28/11.60 tff(29715,plain,
% 11.28/11.60 (s(s(elem!1)) = s(elem!1)),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[7768, 29714, 184, 29711, 664, 29708, 175, 8598])).
% 11.28/11.60 tff(29716,plain,
% 11.28/11.60 ($false),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[2279, 29715, 29705])).
% 11.28/11.60 tff(29717,plain,((~(elem!1 = s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | r(s(z), z) | b(s(s(s(s(z)))), z) | (~b(s(s(z)), s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 11.28/11.60 tff(29718,plain,
% 11.28/11.60 (~(elem!1 = s(z))),
% 11.28/11.60 inference(unit_resolution,[status(thm)],[29717, 29677, 29681, 29679, 3446, 1233, 11173])).
% 11.38/11.60 tff(29719,plain,
% 11.38/11.60 (r(elem!1, s(z))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[837, 29718, 31])).
% 11.38/11.60 tff(29720,plain,
% 11.38/11.60 (~b(s(s(s(elem!1))), z)),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[28887, 847, 2282, 10682, 676, 9, 232, 183])).
% 11.38/11.60 tff(29721,plain,
% 11.38/11.60 (~r(s(s(s(elem!1))), z)),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[29577, 847, 80, 10682, 1, 232, 183])).
% 11.38/11.60 tff(29722,plain,
% 11.38/11.60 ($false),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[377, 29721, 29720])).
% 11.38/11.60 tff(29723,plain,((~r(elem!1, s(z))) | r(z, elem!1) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | r(elem!1, z) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.60 tff(29724,plain,
% 11.38/11.60 (r(elem!1, z)),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[29723, 29719, 29701, 1, 20264, 11174, 80, 29678])).
% 11.38/11.60 tff(29725,plain,
% 11.38/11.60 (~(s(z) = elem!1)),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[1495, 29718])).
% 11.38/11.60 tff(29726,plain,
% 11.38/11.60 (~b(z, elem!1)),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[25009, 29725, 29689, 31, 1, 29701, 29681, 11174])).
% 11.38/11.60 tff(29727,plain,
% 11.38/11.60 (z = elem!1),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[141, 29726, 80])).
% 11.38/11.60 tff(29728,plain,
% 11.38/11.60 ($false),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[29452, 29727, 29724])).
% 11.38/11.60 tff(29729,plain,((~b(s(s(z)), s(z))) | r(z, elem!1) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(z)) | b(s(s(s(s(z)))), z) | b(s(s(s(elem!1))), s(z)) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.60 tff(29730,plain,
% 11.38/11.60 (~b(s(s(z)), s(z))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[29729, 14870, 1, 31, 3446, 11173, 80])).
% 11.38/11.60 tff(29731,plain,
% 11.38/11.60 (r(s(s(z)), s(z))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[3778, 29730])).
% 11.38/11.60 tff(29732,plain,
% 11.38/11.60 (~r(s(s(s(elem!1))), s(s(z)))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[26045, 194, 20264, 11174, 29731])).
% 11.38/11.60 tff(29733,plain,
% 11.38/11.60 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[10713, 42, 29732])).
% 11.38/11.60 tff(29734,plain,
% 11.38/11.60 (b(s(s(s(elem!1))), s(s(z)))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[29733, 10703])).
% 11.38/11.60 tff(29735,plain,
% 11.38/11.60 (~r(s(s(z)), s(s(s(elem!1))))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[18934, 194, 20264, 11174, 29731])).
% 11.38/11.60 tff(29736,plain,
% 11.38/11.60 (b(s(s(z)), s(s(s(elem!1))))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[11041, 29735])).
% 11.38/11.60 tff(29737,plain,
% 11.38/11.60 (r(s(s(s(z))), s(z))),
% 11.38/11.60 inference(modus_ponens,[status(thm)],[183, 493])).
% 11.38/11.60 tff(29738,assumption,(~r(s(s(s(z))), s(z))), introduced(assumption)).
% 11.38/11.60 tff(29739,plain,
% 11.38/11.60 ($false),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[29738, 29737])).
% 11.38/11.60 tff(29740,plain,(r(s(s(s(z))), s(z)) | (~r(s(s(s(elem!1))), s(z))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.60 tff(29741,plain,
% 11.38/11.60 (r(s(s(s(z))), s(z))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[29740, 29691, 183])).
% 11.38/11.60 tff(29742,plain,
% 11.38/11.60 (s(elem!1) = s(z)),
% 11.38/11.60 inference(monotonicity,[status(thm)],[29691])).
% 11.38/11.60 tff(29743,plain,
% 11.38/11.60 (s(s(elem!1)) = s(s(z))),
% 11.38/11.60 inference(monotonicity,[status(thm)],[29742])).
% 11.38/11.60 tff(29744,plain,
% 11.38/11.60 (s(s(s(elem!1))) = s(s(s(z)))),
% 11.38/11.60 inference(monotonicity,[status(thm)],[29743])).
% 11.38/11.60 tff(29745,plain,
% 11.38/11.60 (s(s(s(z))) = s(s(s(elem!1)))),
% 11.38/11.60 inference(symmetry,[status(thm)],[29744])).
% 11.38/11.60 tff(29746,plain,
% 11.38/11.60 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 11.38/11.60 inference(monotonicity,[status(thm)],[29745])).
% 11.38/11.60 tff(29747,plain,
% 11.38/11.60 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 11.38/11.60 inference(symmetry,[status(thm)],[29746])).
% 11.38/11.60 tff(29748,plain,
% 11.38/11.60 (r(z, s(s(s(z))))),
% 11.38/11.60 inference(modus_ponens,[status(thm)],[59, 29747])).
% 11.38/11.60 tff(29749,plain,
% 11.38/11.60 (r(s(z), s(s(s(z))))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[23224, 29691, 232])).
% 11.38/11.60 tff(29750,plain,
% 11.38/11.60 (r(elem!1, s(z)) <=> r(z, s(z))),
% 11.38/11.60 inference(monotonicity,[status(thm)],[29691])).
% 11.38/11.60 tff(29751,plain,
% 11.38/11.60 (~r(s(z), z)),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[3499, 59, 183, 232])).
% 11.38/11.60 tff(29752,plain,
% 11.38/11.60 ((~r(s(z), z)) <=> (~r(s(elem!1), z))),
% 11.38/11.60 inference(monotonicity,[status(thm)],[17617])).
% 11.38/11.60 tff(29753,plain,
% 11.38/11.60 (~r(s(elem!1), z)),
% 11.38/11.60 inference(modus_ponens,[status(thm)],[175, 29752])).
% 11.38/11.60 tff(29754,plain,
% 11.38/11.60 ($false),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[511, 29753])).
% 11.38/11.60 tff(29755,plain,((~(elem!1 = z)) | r(s(z), z) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.60 tff(29756,plain,
% 11.38/11.60 (~r(s(elem!1), elem!1)),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[29755, 29691, 29751])).
% 11.38/11.60 tff(29757,plain,
% 11.38/11.60 (~(s(z) = elem!1)),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[9729, 29756, 2405])).
% 11.38/11.60 tff(29758,plain,
% 11.38/11.60 (~(elem!1 = s(z))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[172, 29757])).
% 11.38/11.60 tff(29759,plain,
% 11.38/11.60 (r(elem!1, s(z))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[837, 29758, 31])).
% 11.38/11.60 tff(29760,plain,
% 11.38/11.60 (r(z, s(z))),
% 11.38/11.60 inference(modus_ponens,[status(thm)],[29759, 29750])).
% 11.38/11.60 tff(29761,plain,
% 11.38/11.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 11.38/11.60 inference(rewrite,[status(thm)],[])).
% 11.38/11.60 tff(29762,plain,
% 11.38/11.60 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 11.38/11.60 inference(rewrite,[status(thm)],[])).
% 11.38/11.60 tff(29763,plain,
% 11.38/11.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 11.38/11.60 inference(monotonicity,[status(thm)],[29762])).
% 11.38/11.60 tff(29764,plain,
% 11.38/11.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 11.38/11.60 inference(transitivity,[status(thm)],[29763, 29761])).
% 11.38/11.60 tff(29765,plain,
% 11.38/11.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 11.38/11.60 inference(quant_inst,[status(thm)],[])).
% 11.38/11.60 tff(29766,plain,
% 11.38/11.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 11.38/11.60 inference(modus_ponens,[status(thm)],[29765, 29764])).
% 11.38/11.60 tff(29767,plain,
% 11.38/11.60 ($false),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[29766, 194, 29760, 29749, 29748, 29741])).
% 11.38/11.60 tff(29768,plain,(b(z, s(s(s(elem!1)))) | b(elem!1, s(z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.38/11.60 tff(29769,plain,
% 11.38/11.60 (b(z, s(s(s(elem!1))))),
% 11.38/11.60 inference(unit_resolution,[status(thm)],[29768, 29731, 31, 11174, 20264, 80])).
% 11.38/11.60 tff(29770,plain,
% 11.38/11.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.38/11.60 inference(rewrite,[status(thm)],[])).
% 11.38/11.60 tff(29771,plain,
% 11.38/11.60 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.38/11.61 inference(rewrite,[status(thm)],[])).
% 11.38/11.61 tff(29772,plain,
% 11.38/11.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29771])).
% 11.38/11.61 tff(29773,plain,
% 11.38/11.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.38/11.61 inference(transitivity,[status(thm)],[29772, 29770])).
% 11.38/11.61 tff(29774,plain,
% 11.38/11.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))))),
% 11.38/11.61 inference(quant_inst,[status(thm)],[])).
% 11.38/11.61 tff(29775,plain,
% 11.38/11.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[29774, 29773])).
% 11.38/11.61 tff(29776,plain,
% 11.38/11.61 (~b(z, s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[29775, 391, 29769, 29736, 29734])).
% 11.38/11.61 tff(29777,plain,
% 11.38/11.61 (r(z, s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[18613, 29776])).
% 11.38/11.61 tff(29778,plain,
% 11.38/11.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.38/11.61 inference(rewrite,[status(thm)],[])).
% 11.38/11.61 tff(29779,plain,
% 11.38/11.61 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.38/11.61 inference(rewrite,[status(thm)],[])).
% 11.38/11.61 tff(29780,plain,
% 11.38/11.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29779])).
% 11.38/11.61 tff(29781,plain,
% 11.38/11.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.38/11.61 inference(transitivity,[status(thm)],[29780, 29778])).
% 11.38/11.61 tff(29782,plain,
% 11.38/11.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 11.38/11.61 inference(quant_inst,[status(thm)],[])).
% 11.38/11.61 tff(29783,plain,
% 11.38/11.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[29782, 29781])).
% 11.38/11.61 tff(29784,plain,
% 11.38/11.61 (~b(s(s(z)), z)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[29783, 391, 29769, 29736, 29734])).
% 11.38/11.61 tff(29785,plain,
% 11.38/11.61 (r(s(s(z)), z)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[1211, 29784])).
% 11.38/11.61 tff(29786,plain,
% 11.38/11.61 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[16255, 194, 3447, 29785, 29777])).
% 11.38/11.61 tff(29787,plain,
% 11.38/11.61 (b(s(s(z)), s(s(s(s(z)))))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[3652, 29786])).
% 11.38/11.61 tff(29788,plain,
% 11.38/11.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[18433, 8505, 2053, 2405])).
% 11.38/11.61 tff(29789,plain,
% 11.38/11.61 (b(s(s(s(s(z)))), s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[1714, 29788])).
% 11.38/11.61 tff(29790,plain,
% 11.38/11.61 (~r(s(z), s(s(s(s(z)))))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[10620, 722, 2053])).
% 11.38/11.61 tff(29791,plain,
% 11.38/11.61 (b(s(z), s(s(s(s(z)))))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[1230, 29790])).
% 11.38/11.61 tff(29792,plain,
% 11.38/11.61 (~r(s(z), s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[9720, 722, 8505, 2405])).
% 11.38/11.61 tff(29793,plain,
% 11.38/11.61 (b(s(z), s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[1788, 29792])).
% 11.38/11.61 tff(29794,plain,
% 11.38/11.61 ($false),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[6275, 29793, 29791, 29789, 3823])).
% 11.38/11.61 tff(29795,plain,((~r(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.61 tff(29796,plain,
% 11.38/11.61 (~r(z, s(z))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[29795, 29787, 29777, 29731, 3447])).
% 11.38/11.61 tff(29797,plain,
% 11.38/11.61 (~r(elem!1, s(z))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[29723, 2282, 29769, 1, 20264, 11174, 80, 29796])).
% 11.38/11.61 tff(29798,plain,
% 11.38/11.61 (elem!1 = s(z)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[837, 29797, 31])).
% 11.38/11.61 tff(29799,plain,
% 11.38/11.61 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[29438, 29798])).
% 11.38/11.61 tff(29800,plain,
% 11.38/11.61 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29799])).
% 11.38/11.61 tff(29801,plain,
% 11.38/11.61 (s(s(s(z))) = s(s(elem!1))),
% 11.38/11.61 inference(transitivity,[status(thm)],[693, 29800, 211])).
% 11.38/11.61 tff(29802,plain,
% 11.38/11.61 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29801])).
% 11.38/11.61 tff(29803,plain,
% 11.38/11.61 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 11.38/11.61 inference(symmetry,[status(thm)],[29802])).
% 11.38/11.61 tff(29804,plain,
% 11.38/11.61 (s(z) = elem!1),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[172, 29798])).
% 11.38/11.61 tff(29805,plain,
% 11.38/11.61 (~b(z, s(elem!1))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[8527, 29804, 29776])).
% 11.38/11.61 tff(29806,plain,
% 11.38/11.61 (r(z, s(elem!1))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[566, 29805])).
% 11.38/11.61 tff(29807,plain,
% 11.38/11.61 (~(elem!1 = z)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[8832, 29806, 29797])).
% 11.38/11.61 tff(29808,plain,
% 11.38/11.61 (~(z = elem!1)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[97, 29807])).
% 11.38/11.61 tff(29809,plain,
% 11.38/11.61 (~(s(z) = s(elem!1))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[117, 29808])).
% 11.38/11.61 tff(29810,plain,
% 11.38/11.61 (~(s(s(elem!1)) = s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[1962, 29809])).
% 11.38/11.61 tff(29811,plain,
% 11.38/11.61 (b(elem!1, z)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[526, 29807, 2282])).
% 11.38/11.61 tff(29812,plain,
% 11.38/11.61 (b(s(z), z)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[10390, 29811, 29804])).
% 11.38/11.61 tff(29813,plain,
% 11.38/11.61 (b(z, s(z))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[678, 29796])).
% 11.38/11.61 tff(29814,plain,
% 11.38/11.61 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(s(elem!1)))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29801])).
% 11.38/11.61 tff(29815,plain,
% 11.38/11.61 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(z)))),
% 11.38/11.61 inference(transitivity,[status(thm)],[29814, 9482])).
% 11.38/11.61 tff(29816,plain,
% 11.38/11.61 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 11.38/11.61 inference(symmetry,[status(thm)],[29815])).
% 11.38/11.61 tff(29817,plain,
% 11.38/11.61 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(z))) = s(s(z)))),
% 11.38/11.61 inference(transitivity,[status(thm)],[29816, 21829])).
% 11.38/11.61 tff(29818,plain,
% 11.38/11.61 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(s(z))) = s(s(z))))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29817])).
% 11.38/11.61 tff(29819,plain,
% 11.38/11.61 (~(s(s(s(z))) = s(s(z)))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[29810, 29818])).
% 11.38/11.61 tff(29820,plain,
% 11.38/11.61 (~b(s(s(s(s(z)))), s(z))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[11177, 29798, 11173])).
% 11.38/11.61 tff(29821,plain,
% 11.38/11.61 (~b(s(s(s(s(z)))), elem!1)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[9614, 29804, 29820])).
% 11.38/11.61 tff(29822,plain,
% 11.38/11.61 (~b(s(s(s(elem!1))), elem!1)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[1563, 29821, 29798])).
% 11.38/11.61 tff(29823,plain,
% 11.38/11.61 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29798])).
% 11.38/11.61 tff(29824,plain,
% 11.38/11.61 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 11.38/11.61 inference(symmetry,[status(thm)],[29823])).
% 11.38/11.61 tff(29825,plain,
% 11.38/11.61 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29824])).
% 11.38/11.61 tff(29826,plain,
% 11.38/11.61 (~b(elem!1, s(s(s(elem!1))))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[14870, 29825])).
% 11.38/11.61 tff(29827,plain,
% 11.38/11.61 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[29799, 3929])).
% 11.38/11.61 tff(29828,plain,
% 11.38/11.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[18433, 29777, 3447, 29731])).
% 11.38/11.61 tff(29829,plain,
% 11.38/11.61 (b(s(s(s(s(z)))), s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[1714, 29828])).
% 11.38/11.61 tff(29830,plain,
% 11.38/11.61 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(elem!1))))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29799])).
% 11.38/11.61 tff(29831,plain,
% 11.38/11.61 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 11.38/11.61 inference(symmetry,[status(thm)],[29830])).
% 11.38/11.61 tff(29832,plain,
% 11.38/11.61 (r(s(z), s(s(s(s(z)))))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[20264, 29831])).
% 11.38/11.61 tff(29833,plain,
% 11.38/11.61 (~r(s(s(elem!1)), elem!1)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[24823, 29832, 29731, 26982, 29829, 29827, 29787, 29798, 9, 29826, 29822, 29819])).
% 11.38/11.61 tff(29834,plain,
% 11.38/11.61 (~r(s(s(elem!1)), s(z))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[2220, 29833, 29804])).
% 11.38/11.61 tff(29835,plain,
% 11.38/11.61 (b(s(s(elem!1)), s(z))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[362, 29834])).
% 11.38/11.61 tff(29836,plain,
% 11.38/11.61 (~b(s(s(elem!1)), z)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[16170, 391, 29835, 29769, 29813, 29812])).
% 11.38/11.61 tff(29837,plain,
% 11.38/11.61 (r(s(s(elem!1)), z)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[2629, 29836])).
% 11.38/11.61 tff(29838,plain,
% 11.38/11.61 (s(z) = elem!1),
% 11.38/11.61 inference(symmetry,[status(thm)],[29798])).
% 11.38/11.61 tff(29839,plain,
% 11.38/11.61 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29838])).
% 11.38/11.61 tff(29840,plain,
% 11.38/11.61 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29839])).
% 11.38/11.61 tff(29841,plain,
% 11.38/11.61 (~(s(s(elem!1)) = elem!1)),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[357, 29840])).
% 11.38/11.61 tff(29842,plain,
% 11.38/11.61 (b(z, elem!1)),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[141, 29808, 80])).
% 11.38/11.61 tff(29843,plain,
% 11.38/11.61 (s(elem!1) = s(s(z))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29798])).
% 11.38/11.61 tff(29844,plain,
% 11.38/11.61 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29843])).
% 11.38/11.61 tff(29845,plain,
% 11.38/11.61 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 11.38/11.61 inference(symmetry,[status(thm)],[29844])).
% 11.38/11.61 tff(29846,plain,
% 11.38/11.61 (b(s(s(s(elem!1))), s(elem!1))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[29734, 29845])).
% 11.38/11.61 tff(29847,plain,
% 11.38/11.61 (~b(z, s(s(elem!1)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[24782, 29846, 29769, 29826, 26982, 29811, 9, 29822, 29842, 29841])).
% 11.38/11.61 tff(29848,plain,
% 11.38/11.61 (r(z, s(s(elem!1)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[324, 29847])).
% 11.38/11.61 tff(29849,plain,
% 11.38/11.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)))),
% 11.38/11.61 inference(rewrite,[status(thm)],[])).
% 11.38/11.61 tff(29850,plain,
% 11.38/11.61 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)))),
% 11.38/11.61 inference(rewrite,[status(thm)],[])).
% 11.38/11.61 tff(29851,plain,
% 11.38/11.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z))))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29850])).
% 11.38/11.61 tff(29852,plain,
% 11.38/11.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)))),
% 11.38/11.61 inference(transitivity,[status(thm)],[29851, 29849])).
% 11.38/11.61 tff(29853,plain,
% 11.38/11.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 11.38/11.61 inference(quant_inst,[status(thm)],[])).
% 11.38/11.61 tff(29854,plain,
% 11.38/11.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[29853, 29852])).
% 11.38/11.61 tff(29855,plain,
% 11.38/11.61 (~r(s(s(elem!1)), s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[29854, 194, 29848, 29785, 29837])).
% 11.38/11.61 tff(29856,plain,
% 11.38/11.61 (b(s(s(elem!1)), s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[5174, 42, 29855, 29810])).
% 11.38/11.61 tff(29857,plain,
% 11.38/11.61 (b(s(s(s(z))), s(s(z)))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[29856, 29803])).
% 11.38/11.61 tff(29858,plain,
% 11.38/11.61 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29799, 29801])).
% 11.38/11.61 tff(29859,plain,
% 11.38/11.61 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 11.38/11.61 inference(symmetry,[status(thm)],[29858])).
% 11.38/11.61 tff(29860,plain,
% 11.38/11.61 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(elem!1))))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29799])).
% 11.38/11.61 tff(29861,plain,
% 11.38/11.61 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 11.38/11.61 inference(symmetry,[status(thm)],[29860])).
% 11.38/11.61 tff(29862,plain,
% 11.38/11.61 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(s(z))))))),
% 11.38/11.61 inference(monotonicity,[status(thm)],[29861])).
% 11.38/11.61 tff(29863,plain,
% 11.38/11.61 (~b(s(z), s(s(s(s(z)))))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[14870, 29862])).
% 11.38/11.61 tff(29864,plain,
% 11.38/11.61 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[16228, 29863, 31, 3446, 29787, 29808])).
% 11.38/11.61 tff(29865,plain,
% 11.38/11.61 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.38/11.61 inference(modus_ponens,[status(thm)],[29864, 29859])).
% 11.38/11.61 tff(29866,plain,
% 11.38/11.61 (~b(s(s(s(z))), s(s(z)))),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[24809, 29865, 29787, 29829])).
% 11.38/11.61 tff(29867,plain,
% 11.38/11.61 ($false),
% 11.38/11.61 inference(unit_resolution,[status(thm)],[29866, 29857])).
% 11.38/11.62 tff(29868,plain,(r(elem!1, z) | b(elem!1, s(z)) | b(s(s(s(s(z)))), z) | b(s(z), s(s(s(elem!1)))) | r(z, elem!1) | b(s(s(s(elem!1))), s(z)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.62 tff(29869,plain,
% 11.38/11.62 (r(elem!1, z)),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[29868, 14870, 3446, 31, 80, 11173, 1])).
% 11.38/11.62 tff(29870,plain,
% 11.38/11.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 11.38/11.62 inference(rewrite,[status(thm)],[])).
% 11.38/11.62 tff(29871,plain,
% 11.38/11.62 (((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 11.38/11.62 inference(rewrite,[status(thm)],[])).
% 11.38/11.62 tff(29872,plain,
% 11.38/11.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 11.38/11.62 inference(monotonicity,[status(thm)],[29871])).
% 11.38/11.62 tff(29873,plain,
% 11.38/11.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 11.38/11.62 inference(transitivity,[status(thm)],[29872, 29870])).
% 11.38/11.62 tff(29874,plain,
% 11.38/11.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 11.38/11.62 inference(quant_inst,[status(thm)],[])).
% 11.38/11.62 tff(29875,plain,
% 11.38/11.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 11.38/11.62 inference(modus_ponens,[status(thm)],[29874, 29873])).
% 11.38/11.62 tff(29876,plain,
% 11.38/11.62 (~r(s(s(s(s(z)))), elem!1)),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[29875, 194, 29869, 3447, 29777])).
% 11.38/11.62 tff(29877,plain,
% 11.38/11.62 (~(z = elem!1)),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[29452, 29869])).
% 11.38/11.62 tff(29878,plain,
% 11.38/11.62 (b(z, elem!1)),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[141, 29877, 80])).
% 11.38/11.62 tff(29879,plain,
% 11.38/11.62 (~r(elem!1, s(z))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[22961, 29769, 29878, 1, 20264, 11174])).
% 11.38/11.62 tff(29880,plain,
% 11.38/11.62 (elem!1 = s(z)),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[837, 29879, 31])).
% 11.38/11.62 tff(29881,plain,
% 11.38/11.62 (~b(s(s(s(s(z)))), s(z))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[11177, 29880, 11173])).
% 11.38/11.62 tff(29882,plain,
% 11.38/11.62 (s(z) = elem!1),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[172, 29880])).
% 11.38/11.62 tff(29883,plain,
% 11.38/11.62 (~b(s(s(s(s(z)))), elem!1)),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[9614, 29882, 29881])).
% 11.38/11.62 tff(29884,plain,
% 11.38/11.62 (s(s(s(s(z)))) = elem!1),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[762, 29883, 29876])).
% 11.38/11.62 tff(29885,plain,
% 11.38/11.62 (r(s(s(s(s(z)))), s(z))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[749, 29881])).
% 11.38/11.62 tff(29886,plain,
% 11.38/11.62 (~(elem!1 = s(s(s(s(z)))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[2674, 29885, 29879])).
% 11.38/11.62 tff(29887,plain,
% 11.38/11.62 ($false),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[16908, 29886, 29884])).
% 11.38/11.62 tff(29888,plain,(b(s(z), s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z)) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.38/11.62 tff(29889,plain,
% 11.38/11.62 (b(s(z), s(s(s(elem!1))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[29888, 31, 11173, 1, 80, 3446])).
% 11.38/11.62 tff(29890,plain,
% 11.38/11.62 (~(elem!1 = s(z))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[2884, 2881, 379])).
% 11.38/11.62 tff(29891,plain,
% 11.38/11.62 (r(elem!1, s(z))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[837, 29890, 31])).
% 11.38/11.62 tff(29892,plain,
% 11.38/11.62 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 11.38/11.62 inference(monotonicity,[status(thm)],[29691])).
% 11.38/11.62 tff(29893,plain,
% 11.38/11.62 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 11.38/11.62 inference(symmetry,[status(thm)],[29892])).
% 11.38/11.62 tff(29894,plain,
% 11.38/11.62 (r(s(s(s(s(z)))), elem!1)),
% 11.38/11.62 inference(modus_ponens,[status(thm)],[2053, 29893])).
% 11.38/11.62 tff(29895,plain,
% 11.38/11.62 ((elem!1 = s(s(z))) <=> (z = s(s(z)))),
% 11.38/11.62 inference(monotonicity,[status(thm)],[29691])).
% 11.38/11.62 tff(29896,plain,
% 11.38/11.62 ((elem!1 = s(s(z))) <=> (s(s(z)) = z)),
% 11.38/11.62 inference(transitivity,[status(thm)],[29895, 11715])).
% 11.38/11.62 tff(29897,plain,
% 11.38/11.62 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 11.38/11.62 inference(symmetry,[status(thm)],[29896])).
% 11.38/11.62 tff(29898,plain,
% 11.38/11.62 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 11.38/11.62 inference(monotonicity,[status(thm)],[29897])).
% 11.38/11.62 tff(29899,plain,
% 11.38/11.62 (~(elem!1 = s(s(z)))),
% 11.38/11.62 inference(modus_ponens,[status(thm)],[1207, 29898])).
% 11.38/11.62 tff(29900,plain,
% 11.38/11.62 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[299, 26982])).
% 11.38/11.62 tff(29901,plain,
% 11.38/11.62 (~(s(z) = elem!1)),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[7796, 29692, 379])).
% 11.38/11.62 tff(29902,plain,
% 11.38/11.62 (~(elem!1 = s(z))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[172, 29901])).
% 11.38/11.62 tff(29903,plain,
% 11.38/11.62 (r(elem!1, s(z))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[837, 29902, 31])).
% 11.38/11.62 tff(29904,plain,
% 11.38/11.62 (r(z, s(z))),
% 11.38/11.62 inference(modus_ponens,[status(thm)],[29903, 29750])).
% 11.38/11.62 tff(29905,plain,
% 11.38/11.62 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[2849, 29901])).
% 11.38/11.62 tff(29906,plain,
% 11.38/11.62 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[10940, 29905])).
% 11.38/11.62 tff(29907,plain,
% 11.38/11.62 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 11.38/11.62 inference(monotonicity,[status(thm)],[29745])).
% 11.38/11.62 tff(29908,plain,
% 11.38/11.62 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 11.38/11.62 inference(symmetry,[status(thm)],[29907])).
% 11.38/11.62 tff(29909,plain,
% 11.38/11.62 (b(s(z), s(s(s(z))))),
% 11.38/11.62 inference(modus_ponens,[status(thm)],[379, 29908])).
% 11.38/11.62 tff(29910,plain,
% 11.38/11.62 (~r(s(z), s(s(s(s(z)))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[10776, 29903, 29693, 183])).
% 11.38/11.62 tff(29911,plain,
% 11.38/11.62 (b(s(z), s(s(s(s(z)))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[1230, 29910])).
% 11.38/11.62 tff(29912,plain,
% 11.38/11.62 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.38/11.62 inference(monotonicity,[status(thm)],[17612])).
% 11.38/11.62 tff(29913,plain,
% 11.38/11.62 (r(s(s(s(z))), z)),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[4409, 174, 11])).
% 11.38/11.62 tff(29914,plain,
% 11.38/11.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)))),
% 11.38/11.62 inference(rewrite,[status(thm)],[])).
% 11.38/11.62 tff(29915,plain,
% 11.38/11.62 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)))),
% 11.38/11.62 inference(rewrite,[status(thm)],[])).
% 11.38/11.62 tff(29916,plain,
% 11.38/11.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z))))),
% 11.38/11.62 inference(monotonicity,[status(thm)],[29915])).
% 11.38/11.62 tff(29917,plain,
% 11.38/11.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)))),
% 11.38/11.62 inference(transitivity,[status(thm)],[29916, 29914])).
% 11.38/11.62 tff(29918,plain,
% 11.38/11.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 11.38/11.62 inference(quant_inst,[status(thm)],[])).
% 11.38/11.62 tff(29919,plain,
% 11.38/11.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z))),
% 11.38/11.62 inference(modus_ponens,[status(thm)],[29918, 29917])).
% 11.38/11.62 tff(29920,plain,
% 11.38/11.62 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[29919, 194, 722, 2053, 29913])).
% 11.38/11.62 tff(29921,plain,
% 11.38/11.62 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.38/11.62 inference(modus_ponens,[status(thm)],[29920, 29912])).
% 11.38/11.62 tff(29922,plain,
% 11.38/11.62 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[15351, 29921, 15348])).
% 11.38/11.62 tff(29923,plain,
% 11.38/11.62 (b(s(s(s(z))), s(s(s(s(z)))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[1673, 29922, 11])).
% 11.38/11.62 tff(29924,plain,
% 11.38/11.62 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[15335, 174, 2053, 184])).
% 11.38/11.62 tff(29925,plain,
% 11.38/11.62 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 11.38/11.62 inference(monotonicity,[status(thm)],[490])).
% 11.38/11.62 tff(29926,plain,
% 11.38/11.62 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.38/11.62 inference(symmetry,[status(thm)],[29925])).
% 11.38/11.62 tff(29927,plain,
% 11.38/11.62 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 11.38/11.62 inference(monotonicity,[status(thm)],[2401, 490])).
% 11.38/11.62 tff(29928,plain,
% 11.38/11.62 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.38/11.62 inference(transitivity,[status(thm)],[29927, 29926])).
% 11.38/11.62 tff(29929,plain,
% 11.38/11.62 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.38/11.62 inference(modus_ponens,[status(thm)],[1082, 29928])).
% 11.38/11.62 tff(29930,plain,
% 11.38/11.62 ($false),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[2114, 29929])).
% 11.38/11.62 tff(29931,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.62 tff(29932,plain,
% 11.38/11.62 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[29931, 29924, 11])).
% 11.38/11.62 tff(29933,plain,
% 11.38/11.62 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.38/11.62 inference(unit_resolution,[status(thm)],[1095, 29932, 305])).
% 11.38/11.62 tff(29934,plain,
% 11.38/11.62 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.38/11.62 inference(modus_ponens,[status(thm)],[29933, 23220])).
% 11.38/11.62 tff(29935,plain,
% 11.38/11.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.62 inference(rewrite,[status(thm)],[])).
% 11.38/11.62 tff(29936,plain,
% 11.38/11.62 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.62 inference(rewrite,[status(thm)],[])).
% 11.38/11.62 tff(29937,plain,
% 11.38/11.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.38/11.63 inference(monotonicity,[status(thm)],[29936])).
% 11.38/11.63 tff(29938,plain,
% 11.38/11.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.63 inference(transitivity,[status(thm)],[29937, 29935])).
% 11.38/11.63 tff(29939,plain,
% 11.38/11.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 11.38/11.63 inference(quant_inst,[status(thm)],[])).
% 11.38/11.63 tff(29940,plain,
% 11.38/11.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[29939, 29938])).
% 11.38/11.63 tff(29941,plain,
% 11.38/11.63 ($false),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[29940, 391, 1234, 29934, 4415, 29923])).
% 11.38/11.63 tff(29942,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.63 tff(29943,plain,
% 11.38/11.63 (~r(s(s(s(elem!1))), z)),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[29942, 29911, 29909, 29691, 29906, 29904, 2053, 29900, 59])).
% 11.38/11.63 tff(29944,plain,
% 11.38/11.63 (b(s(s(s(elem!1))), z)),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[377, 29943])).
% 11.38/11.63 tff(29945,plain,
% 11.38/11.63 (b(s(s(s(z))), z)),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[1680, 29944, 29691])).
% 11.38/11.63 tff(29946,plain,
% 11.38/11.63 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 11.38/11.63 inference(monotonicity,[status(thm)],[29691])).
% 11.38/11.63 tff(29947,plain,
% 11.38/11.63 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 11.38/11.63 inference(symmetry,[status(thm)],[29946])).
% 11.38/11.63 tff(29948,plain,
% 11.38/11.63 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 11.38/11.63 inference(monotonicity,[status(thm)],[29743])).
% 11.38/11.63 tff(29949,plain,
% 11.38/11.63 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 11.38/11.63 inference(symmetry,[status(thm)],[29948])).
% 11.38/11.63 tff(29950,plain,
% 11.38/11.63 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 11.38/11.63 inference(transitivity,[status(thm)],[29949, 29947])).
% 11.38/11.63 tff(29951,plain,
% 11.38/11.63 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 11.38/11.63 inference(monotonicity,[status(thm)],[29742])).
% 11.38/11.63 tff(29952,plain,
% 11.38/11.63 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 11.38/11.63 inference(symmetry,[status(thm)],[29951])).
% 11.38/11.63 tff(29953,plain,
% 11.38/11.63 (b(s(elem!1), s(s(s(elem!1))))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[379, 29952])).
% 11.38/11.63 tff(29954,plain,
% 11.38/11.63 (~r(s(s(s(elem!1))), elem!1)),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[406, 29943, 29691])).
% 11.38/11.63 tff(29955,plain,
% 11.38/11.63 (b(s(s(s(elem!1))), elem!1)),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[230, 29954, 9])).
% 11.38/11.63 tff(29956,plain,
% 11.38/11.63 (~r(s(s(s(elem!1))), z)),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[29942, 1234, 4415, 11, 15348, 722, 2053, 310, 59])).
% 11.38/11.63 tff(29957,plain,
% 11.38/11.63 (b(s(s(s(elem!1))), z)),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[377, 29956])).
% 11.38/11.63 tff(29958,plain,
% 11.38/11.63 (b(s(s(s(z))), z)),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[1680, 29957, 11])).
% 11.38/11.63 tff(29959,plain,
% 11.38/11.63 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 11.38/11.63 inference(symmetry,[status(thm)],[18402])).
% 11.38/11.63 tff(29960,plain,
% 11.38/11.63 (r(z, s(s(z)))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[18613, 3373])).
% 11.38/11.63 tff(29961,plain,
% 11.38/11.63 (r(z, s(s(elem!1)))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[29960, 29959])).
% 11.38/11.63 tff(29962,plain,
% 11.38/11.63 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[18433, 29960, 2053, 2405])).
% 11.38/11.63 tff(29963,plain,
% 11.38/11.63 (b(s(s(s(s(z)))), s(s(z)))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[1714, 29962])).
% 11.38/11.63 tff(29964,plain,
% 11.38/11.63 (r(z, s(s(s(z))))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[59, 500])).
% 11.38/11.63 tff(29965,plain,
% 11.38/11.63 ((~b(z, s(s(z)))) <=> (~b(z, s(s(elem!1))))),
% 11.38/11.63 inference(monotonicity,[status(thm)],[3368])).
% 11.38/11.63 tff(29966,plain,
% 11.38/11.63 (~b(z, s(s(elem!1)))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[3373, 29965])).
% 11.38/11.63 tff(29967,plain,
% 11.38/11.63 (b(s(z), z)),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[3924, 29966, 297, 10])).
% 11.38/11.63 tff(29968,plain,
% 11.38/11.63 (r(s(s(elem!1)), s(z))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[2405, 18396])).
% 11.38/11.63 tff(29969,plain,
% 11.38/11.63 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 11.38/11.63 inference(monotonicity,[status(thm)],[11])).
% 11.38/11.63 tff(29970,plain,
% 11.38/11.63 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 11.38/11.63 inference(symmetry,[status(thm)],[29969])).
% 11.38/11.63 tff(29971,plain,
% 11.38/11.63 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 11.38/11.63 inference(transitivity,[status(thm)],[29959, 29970])).
% 11.38/11.63 tff(29972,plain,
% 11.38/11.63 (r(elem!1, s(s(elem!1)))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[29960, 29971])).
% 11.38/11.63 tff(29973,plain,
% 11.38/11.63 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[4159, 29972, 410, 29968])).
% 11.38/11.63 tff(29974,plain,
% 11.38/11.63 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[1370, 29973, 297])).
% 11.38/11.63 tff(29975,plain,
% 11.38/11.63 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[3563, 2421])).
% 11.38/11.63 tff(29976,plain,
% 11.38/11.63 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 11.38/11.63 inference(monotonicity,[status(thm)],[11])).
% 11.38/11.63 tff(29977,plain,
% 11.38/11.63 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 11.38/11.63 inference(symmetry,[status(thm)],[29976])).
% 11.38/11.63 tff(29978,plain,
% 11.38/11.63 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 11.38/11.63 inference(monotonicity,[status(thm)],[2401])).
% 11.38/11.63 tff(29979,plain,
% 11.38/11.63 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 11.38/11.63 inference(symmetry,[status(thm)],[29978])).
% 11.38/11.63 tff(29980,plain,
% 11.38/11.63 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 11.38/11.63 inference(transitivity,[status(thm)],[29979, 29977])).
% 11.38/11.63 tff(29981,plain,
% 11.38/11.63 (r(s(s(s(s(elem!1)))), elem!1)),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[2053, 29980])).
% 11.38/11.63 tff(29982,plain,
% 11.38/11.63 (~b(z, s(s(s(s(z)))))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[17288, 3563, 1234, 1235, 590])).
% 11.38/11.63 tff(29983,plain,
% 11.38/11.63 (r(z, s(s(s(s(z)))))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[800, 29982])).
% 11.38/11.63 tff(29984,plain,
% 11.38/11.63 (r(z, s(s(s(s(elem!1)))))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[29983, 18458])).
% 11.38/11.63 tff(29985,plain,
% 11.38/11.63 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[2800, 29984, 326, 29981])).
% 11.38/11.63 tff(29986,plain,
% 11.38/11.63 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[1048, 29985, 1035])).
% 11.38/11.63 tff(29987,plain,
% 11.38/11.63 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[1741, 29986, 29975, 1374])).
% 11.38/11.63 tff(29988,plain,
% 11.38/11.63 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[1164, 29987, 1373])).
% 11.38/11.63 tff(29989,plain,
% 11.38/11.63 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[29988, 17614])).
% 11.38/11.63 tff(29990,plain,
% 11.38/11.63 (r(s(s(s(z))), s(s(s(s(z)))))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[29989, 17613])).
% 11.38/11.63 tff(29991,plain,
% 11.38/11.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 11.38/11.63 inference(rewrite,[status(thm)],[])).
% 11.38/11.63 tff(29992,plain,
% 11.38/11.63 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 11.38/11.63 inference(rewrite,[status(thm)],[])).
% 11.38/11.63 tff(29993,plain,
% 11.38/11.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))))),
% 11.38/11.63 inference(monotonicity,[status(thm)],[29992])).
% 11.38/11.63 tff(29994,plain,
% 11.38/11.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 11.38/11.63 inference(transitivity,[status(thm)],[29993, 29991])).
% 11.38/11.63 tff(29995,plain,
% 11.38/11.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 11.38/11.63 inference(quant_inst,[status(thm)],[])).
% 11.38/11.63 tff(29996,plain,
% 11.38/11.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[29995, 29994])).
% 11.38/11.63 tff(29997,plain,
% 11.38/11.63 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[29996, 194, 2053, 29983, 15510])).
% 11.38/11.63 tff(29998,plain,
% 11.38/11.63 ($false),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[29997, 29990])).
% 11.38/11.63 tff(29999,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.63 tff(30000,plain,
% 11.38/11.63 ($false),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[29999, 29974, 29967, 2053, 11, 311, 29964, 2419, 1234, 1235, 29963, 29961])).
% 11.38/11.63 tff(30001,plain,(b(z, s(s(z))) | (~r(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.63 tff(30002,plain,
% 11.38/11.63 (b(z, s(s(z)))),
% 11.38/11.63 inference(unit_resolution,[status(thm)],[30001, 10584, 11, 1234, 2053, 297, 10, 410, 2405])).
% 11.38/11.63 tff(30003,plain,
% 11.38/11.63 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 11.38/11.63 inference(monotonicity,[status(thm)],[489])).
% 11.38/11.63 tff(30004,plain,
% 11.38/11.63 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 11.38/11.63 inference(symmetry,[status(thm)],[18437])).
% 11.38/11.63 tff(30005,plain,
% 11.38/11.63 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 11.38/11.63 inference(symmetry,[status(thm)],[18436])).
% 11.38/11.63 tff(30006,plain,
% 11.38/11.63 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 11.38/11.63 inference(transitivity,[status(thm)],[30005, 30004])).
% 11.38/11.63 tff(30007,plain,
% 11.38/11.63 (b(s(s(elem!1)), elem!1)),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[10584, 30006])).
% 11.38/11.63 tff(30008,plain,
% 11.38/11.63 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 11.38/11.63 inference(monotonicity,[status(thm)],[11])).
% 11.38/11.63 tff(30009,plain,
% 11.38/11.63 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 11.38/11.63 inference(symmetry,[status(thm)],[30008])).
% 11.38/11.63 tff(30010,plain,
% 11.38/11.63 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 11.38/11.63 inference(transitivity,[status(thm)],[3368, 30009])).
% 11.38/11.63 tff(30011,plain,
% 11.38/11.63 (b(elem!1, s(s(elem!1)))),
% 11.38/11.63 inference(modus_ponens,[status(thm)],[30002, 30010])).
% 11.38/11.64 tff(30012,plain,
% 11.38/11.64 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.64 inference(unit_resolution,[status(thm)],[1467, 30011, 900, 30007])).
% 11.38/11.64 tff(30013,plain,
% 11.38/11.64 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.64 inference(unit_resolution,[status(thm)],[1370, 30012, 297])).
% 11.38/11.64 tff(30014,plain,
% 11.38/11.64 (r(s(s(s(elem!1))), s(s(z)))),
% 11.38/11.64 inference(modus_ponens,[status(thm)],[30013, 30003])).
% 11.38/11.64 tff(30015,plain,
% 11.38/11.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.38/11.64 inference(rewrite,[status(thm)],[])).
% 11.38/11.64 tff(30016,plain,
% 11.38/11.64 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.38/11.64 inference(rewrite,[status(thm)],[])).
% 11.38/11.64 tff(30017,plain,
% 11.38/11.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 11.38/11.64 inference(monotonicity,[status(thm)],[30016])).
% 11.38/11.64 tff(30018,plain,
% 11.38/11.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.38/11.64 inference(transitivity,[status(thm)],[30017, 30015])).
% 11.38/11.64 tff(30019,plain,
% 11.38/11.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 11.38/11.64 inference(quant_inst,[status(thm)],[])).
% 11.38/11.64 tff(30020,plain,
% 11.38/11.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 11.38/11.64 inference(modus_ponens,[status(thm)],[30019, 30018])).
% 11.38/11.64 tff(30021,plain,
% 11.38/11.64 ($false),
% 11.38/11.64 inference(unit_resolution,[status(thm)],[30020, 194, 184, 2053, 2100, 11543])).
% 11.38/11.64 tff(30022,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.64 tff(30023,plain,
% 11.38/11.64 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.38/11.64 inference(unit_resolution,[status(thm)],[30022, 30014, 2053, 59])).
% 11.38/11.64 tff(30024,plain,
% 11.38/11.64 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.38/11.64 inference(unit_resolution,[status(thm)],[29931, 30023, 11])).
% 11.38/11.64 tff(30025,plain,
% 11.38/11.64 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.38/11.64 inference(unit_resolution,[status(thm)],[1095, 30024, 310])).
% 11.38/11.64 tff(30026,plain,
% 11.38/11.64 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.38/11.64 inference(modus_ponens,[status(thm)],[30025, 23220])).
% 11.38/11.64 tff(30027,plain,
% 11.38/11.64 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 11.38/11.64 inference(monotonicity,[status(thm)],[11])).
% 11.38/11.64 tff(30028,plain,
% 11.38/11.64 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 11.38/11.64 inference(symmetry,[status(thm)],[30027])).
% 11.38/11.64 tff(30029,plain,
% 11.38/11.64 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 11.38/11.64 inference(transitivity,[status(thm)],[30028, 2206])).
% 11.38/11.64 tff(30030,plain,
% 11.38/11.64 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 11.38/11.64 inference(monotonicity,[status(thm)],[30029])).
% 11.38/11.64 tff(30031,plain,
% 11.38/11.64 (~(elem!1 = s(s(elem!1)))),
% 11.38/11.64 inference(modus_ponens,[status(thm)],[215, 30030])).
% 11.38/11.64 tff(30032,plain,
% 11.38/11.64 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 11.38/11.64 inference(monotonicity,[status(thm)],[488])).
% 11.38/11.64 tff(30033,plain,
% 11.38/11.64 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 11.38/11.64 inference(symmetry,[status(thm)],[30032])).
% 11.38/11.64 tff(30034,plain,
% 11.38/11.64 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 11.38/11.64 inference(transitivity,[status(thm)],[18396, 30033])).
% 11.38/11.64 tff(30035,plain,
% 11.38/11.64 (r(s(s(elem!1)), s(elem!1))),
% 11.38/11.64 inference(modus_ponens,[status(thm)],[2405, 30034])).
% 11.38/11.64 tff(30036,plain,
% 11.38/11.64 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 11.38/11.64 inference(monotonicity,[status(thm)],[488])).
% 11.38/11.64 tff(30037,plain,
% 11.38/11.64 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 11.38/11.64 inference(symmetry,[status(thm)],[30036])).
% 11.38/11.64 tff(30038,plain,
% 11.38/11.64 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 11.38/11.64 inference(monotonicity,[status(thm)],[30037])).
% 11.38/11.64 tff(30039,plain,
% 11.38/11.64 (~(s(s(elem!1)) = s(elem!1))),
% 11.38/11.64 inference(modus_ponens,[status(thm)],[357, 30038])).
% 11.38/11.64 tff(30040,plain,
% 11.38/11.64 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 11.38/11.64 inference(monotonicity,[status(thm)],[489])).
% 11.38/11.64 tff(30041,plain,
% 11.38/11.64 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.38/11.64 inference(symmetry,[status(thm)],[30040])).
% 11.38/11.64 tff(30042,plain,
% 11.38/11.64 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 11.38/11.64 inference(monotonicity,[status(thm)],[491])).
% 11.38/11.64 tff(30043,plain,
% 11.38/11.64 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.38/11.64 inference(transitivity,[status(thm)],[30042, 30041])).
% 11.38/11.64 tff(30044,plain,
% 11.38/11.64 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 11.38/11.64 inference(monotonicity,[status(thm)],[30043])).
% 11.38/11.64 tff(30045,plain,
% 11.38/11.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 11.38/11.64 inference(rewrite,[status(thm)],[])).
% 11.38/11.64 tff(30046,plain,
% 11.38/11.64 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 11.38/11.64 inference(rewrite,[status(thm)],[])).
% 11.38/11.64 tff(30047,plain,
% 11.38/11.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))))),
% 11.38/11.64 inference(monotonicity,[status(thm)],[30046])).
% 11.38/11.64 tff(30048,plain,
% 11.38/11.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 11.38/11.64 inference(transitivity,[status(thm)],[30047, 30045])).
% 11.38/11.64 tff(30049,plain,
% 11.38/11.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 11.38/11.64 inference(quant_inst,[status(thm)],[])).
% 11.38/11.64 tff(30050,plain,
% 11.38/11.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))),
% 11.38/11.65 inference(modus_ponens,[status(thm)],[30049, 30048])).
% 11.38/11.65 tff(30051,plain,
% 11.38/11.65 (~b(s(s(z)), s(s(s(z))))),
% 11.38/11.65 inference(unit_resolution,[status(thm)],[30050, 391, 10584, 30002, 1685])).
% 11.38/11.65 tff(30052,plain,
% 11.38/11.65 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.38/11.65 inference(modus_ponens,[status(thm)],[30051, 30044])).
% 11.38/11.65 tff(30053,plain,
% 11.38/11.65 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.38/11.65 inference(unit_resolution,[status(thm)],[1356, 30052, 315])).
% 11.38/11.65 tff(30054,plain,
% 11.38/11.65 (~b(s(elem!1), elem!1)),
% 11.38/11.65 inference(unit_resolution,[status(thm)],[24584, 30053, 410, 613, 30039, 30035, 30031, 30007])).
% 11.38/11.65 tff(30055,plain,
% 11.38/11.65 (r(s(elem!1), elem!1)),
% 11.38/11.65 inference(unit_resolution,[status(thm)],[2168, 30054, 164])).
% 11.38/11.65 tff(30056,plain,
% 11.38/11.65 (r(s(z), z)),
% 11.38/11.65 inference(unit_resolution,[status(thm)],[29755, 30055, 11])).
% 11.38/11.65 tff(30057,plain,
% 11.38/11.65 (~r(s(s(s(s(z)))), s(z))),
% 11.38/11.65 inference(unit_resolution,[status(thm)],[20881, 30056, 2405, 1749])).
% 11.38/11.65 tff(30058,plain,
% 11.38/11.65 (b(s(s(s(s(z)))), s(z))),
% 11.38/11.65 inference(unit_resolution,[status(thm)],[749, 30057])).
% 11.38/11.65 tff(30059,plain,
% 11.38/11.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(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(z)))))),
% 11.38/11.65 inference(rewrite,[status(thm)],[])).
% 11.38/11.65 tff(30060,plain,
% 11.38/11.65 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(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(z)))))),
% 11.38/11.65 inference(rewrite,[status(thm)],[])).
% 11.38/11.65 tff(30061,plain,
% 11.38/11.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(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(z))))))),
% 11.38/11.65 inference(monotonicity,[status(thm)],[30060])).
% 11.38/11.65 tff(30062,plain,
% 11.38/11.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(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(z)))))),
% 11.38/11.65 inference(transitivity,[status(thm)],[30061, 30059])).
% 11.38/11.65 tff(30063,plain,
% 11.38/11.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.38/11.65 inference(quant_inst,[status(thm)],[])).
% 11.38/11.65 tff(30064,plain,
% 11.38/11.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z))))),
% 11.38/11.65 inference(modus_ponens,[status(thm)],[30063, 30062])).
% 11.38/11.65 tff(30065,plain,
% 11.38/11.65 ($false),
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% 11.38/11.65 tff(30067,plain,
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% 11.38/11.65 inference(unit_resolution,[status(thm)],[30066, 2405, 29958, 11, 4415, 164, 410, 23202, 2053, 297, 900, 1234, 10, 722])).
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% 11.38/11.65 inference(unit_resolution,[status(thm)],[18613, 30069])).
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% 11.38/11.65 tff(30080,plain,
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% 11.38/11.65 tff(30084,plain,((~r(z, s(s(elem!1)))) | r(z, s(s(z))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
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% 11.38/11.65 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 11.38/11.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.65 inference(rewrite,[status(thm)],[])).
% 11.38/11.65 tff(30097,plain,
% 11.38/11.65 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.65 inference(rewrite,[status(thm)],[])).
% 11.38/11.65 tff(30098,plain,
% 11.38/11.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
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% 11.38/11.65 inference(transitivity,[status(thm)],[30098, 30096])).
% 11.38/11.65 tff(30100,plain,
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% 11.38/11.65 inference(modus_ponens,[status(thm)],[30100, 30099])).
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% 11.38/11.65 inference(unit_resolution,[status(thm)],[30101, 391, 1234, 30095, 30070, 4415, 29958])).
% 11.38/11.65 tff(30103,plain,((~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (s(elem!1) = elem!1) | (~r(elem!1, s(s(s(elem!1))))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.65 tff(30104,plain,
% 11.38/11.65 (~r(s(s(z)), s(z))),
% 11.38/11.65 inference(unit_resolution,[status(thm)],[30103, 29911, 29909, 29691, 2053, 26982, 29955, 29953, 29906, 183, 29904, 426, 29693, 10])).
% 11.38/11.65 tff(30105,plain,
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% 11.38/11.65 inference(unit_resolution,[status(thm)],[3778, 30104])).
% 11.38/11.65 tff(30106,plain,
% 11.38/11.65 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.38/11.65 inference(unit_resolution,[status(thm)],[14746, 3557, 2053, 184])).
% 11.38/11.65 tff(30107,plain,
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% 11.38/11.65 inference(unit_resolution,[status(thm)],[3652, 30106])).
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% 11.38/11.65 inference(unit_resolution,[status(thm)],[9374, 30107, 14771, 1234, 1233])).
% 11.38/11.65 tff(30109,plain,((~r(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.65 tff(30110,plain,
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% 11.38/11.65 inference(unit_resolution,[status(thm)],[30109, 29911, 30105, 2053, 59])).
% 11.38/11.65 tff(30111,plain,
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% 11.38/11.66 tff(30112,plain,
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% 11.38/11.66 tff(30113,plain,
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% 11.38/11.66 tff(30114,plain,
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% 11.38/11.66 tff(30115,plain,
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% 11.38/11.66 tff(30116,plain,
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% 11.38/11.66 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 11.38/11.66 tff(30118,plain,
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% 11.38/11.66 tff(30119,plain,
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% 11.38/11.66 tff(30120,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.66 tff(30121,plain,
% 11.38/11.66 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[30120, 15045, 1234, 4415, 1685])).
% 11.38/11.66 tff(30122,plain,
% 11.38/11.66 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.38/11.66 inference(modus_ponens,[status(thm)],[30121, 30118])).
% 11.38/11.66 tff(30123,plain,
% 11.38/11.66 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 11.38/11.66 tff(30124,plain,
% 11.38/11.66 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[29931, 30123, 11])).
% 11.38/11.66 tff(30125,plain,
% 11.38/11.66 (~r(s(s(s(elem!1))), s(s(z)))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[30022, 30124, 2053, 184])).
% 11.38/11.66 tff(30126,plain,
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% 11.38/11.66 inference(unit_resolution,[status(thm)],[30125, 30116])).
% 11.38/11.66 tff(30127,plain,((~b(z, s(s(z)))) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (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(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.66 tff(30128,plain,
% 11.38/11.66 (~b(z, s(s(z)))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[30127, 29691, 2053, 59, 26982, 29955, 30112, 29911, 29909, 29945])).
% 11.38/11.66 tff(30129,plain,
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% 11.38/11.66 tff(30130,plain,
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% 11.38/11.66 tff(30131,plain,
% 11.38/11.66 (b(z, elem!1) <=> b(z, z)),
% 11.38/11.66 inference(monotonicity,[status(thm)],[29691])).
% 11.38/11.66 tff(30132,plain,
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% 11.38/11.66 inference(symmetry,[status(thm)],[30131])).
% 11.38/11.66 tff(30133,plain,
% 11.38/11.66 ((~b(z, z)) <=> (~b(z, elem!1))),
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% 11.38/11.66 tff(30134,plain,
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% 11.38/11.66 tff(30135,plain,
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% 11.38/11.66 inference(unit_resolution,[status(thm)],[30134, 461])).
% 11.38/11.66 tff(30136,plain,
% 11.38/11.66 (~b(z, elem!1)),
% 11.38/11.66 inference(modus_ponens,[status(thm)],[30135, 30133])).
% 11.38/11.66 tff(30137,plain,
% 11.38/11.66 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 11.38/11.66 inference(monotonicity,[status(thm)],[29691])).
% 11.38/11.66 tff(30138,plain,
% 11.38/11.66 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 11.38/11.66 inference(symmetry,[status(thm)],[30137])).
% 11.38/11.66 tff(30139,plain,
% 11.38/11.66 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 11.38/11.66 inference(monotonicity,[status(thm)],[29743])).
% 11.38/11.66 tff(30140,plain,
% 11.38/11.66 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 11.38/11.66 inference(symmetry,[status(thm)],[30139])).
% 11.38/11.66 tff(30141,plain,
% 11.38/11.66 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 11.38/11.66 inference(transitivity,[status(thm)],[30140, 30138])).
% 11.38/11.66 tff(30142,plain,
% 11.38/11.66 ((~r(s(s(z)), z)) <=> (~r(s(s(elem!1)), elem!1))),
% 11.38/11.66 inference(monotonicity,[status(thm)],[30141])).
% 11.38/11.66 tff(30143,plain,
% 11.38/11.66 (~r(s(s(elem!1)), elem!1)),
% 11.38/11.66 inference(modus_ponens,[status(thm)],[30110, 30142])).
% 11.38/11.66 tff(30144,plain,
% 11.38/11.66 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 11.38/11.66 inference(monotonicity,[status(thm)],[29691])).
% 11.38/11.66 tff(30145,plain,
% 11.38/11.66 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 11.38/11.66 inference(symmetry,[status(thm)],[30144])).
% 11.38/11.66 tff(30146,plain,
% 11.38/11.66 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 11.38/11.66 inference(monotonicity,[status(thm)],[30145])).
% 11.38/11.66 tff(30147,plain,
% 11.38/11.66 (~(s(s(elem!1)) = elem!1)),
% 11.38/11.66 inference(modus_ponens,[status(thm)],[215, 30146])).
% 11.38/11.66 tff(30148,plain,
% 11.38/11.66 (b(elem!1, z) <=> b(z, z)),
% 11.38/11.66 inference(monotonicity,[status(thm)],[29691])).
% 11.38/11.66 tff(30149,plain,
% 11.38/11.66 (b(z, z) <=> b(elem!1, z)),
% 11.38/11.66 inference(symmetry,[status(thm)],[30148])).
% 11.38/11.66 tff(30150,plain,
% 11.38/11.66 ((~b(z, z)) <=> (~b(elem!1, z))),
% 11.38/11.66 inference(monotonicity,[status(thm)],[30149])).
% 11.38/11.66 tff(30151,plain,
% 11.38/11.66 (~b(elem!1, z)),
% 11.38/11.66 inference(modus_ponens,[status(thm)],[30135, 30150])).
% 11.38/11.66 tff(30152,plain,
% 11.38/11.66 (r(z, s(s(z)))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[18613, 30128])).
% 11.38/11.66 tff(30153,plain,
% 11.38/11.66 (r(s(s(s(elem!1))), s(s(z)))),
% 11.38/11.66 inference(modus_ponens,[status(thm)],[327, 30003])).
% 11.38/11.66 tff(30154,plain,
% 11.38/11.66 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[30022, 30153, 2053, 184])).
% 11.38/11.66 tff(30155,plain,
% 11.38/11.66 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[29931, 30154, 11])).
% 11.38/11.66 tff(30156,plain,
% 11.38/11.66 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[1095, 30155, 305])).
% 11.38/11.66 tff(30157,plain,
% 11.38/11.66 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.38/11.66 inference(modus_ponens,[status(thm)],[30156, 23220])).
% 11.38/11.66 tff(30158,plain,
% 11.38/11.66 (r(s(s(s(z))), s(s(z)))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[4385, 327, 11])).
% 11.38/11.66 tff(30159,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 11.38/11.66 tff(30160,plain,
% 11.38/11.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 11.38/11.66 inference(rewrite,[status(thm)],[])).
% 11.38/11.66 tff(30161,plain,
% 11.38/11.66 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 11.38/11.66 inference(rewrite,[status(thm)],[])).
% 11.38/11.66 tff(30162,plain,
% 11.38/11.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 11.38/11.66 inference(monotonicity,[status(thm)],[30161])).
% 11.38/11.66 tff(30163,plain,
% 11.38/11.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 11.38/11.66 inference(transitivity,[status(thm)],[30162, 30160])).
% 11.38/11.66 tff(30164,plain,
% 11.38/11.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 11.38/11.66 inference(quant_inst,[status(thm)],[])).
% 11.38/11.66 tff(30165,plain,
% 11.38/11.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 11.38/11.66 inference(modus_ponens,[status(thm)],[30164, 30163])).
% 11.38/11.66 tff(30166,plain,
% 11.38/11.66 ($false),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[30165, 194, 1749, 15510, 8505, 30159])).
% 11.38/11.66 tff(30167,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.66 tff(30168,plain,
% 11.38/11.66 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[30167, 30158, 8505, 501])).
% 11.38/11.66 tff(30169,plain,
% 11.38/11.66 (b(s(s(z)), s(s(s(s(z)))))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[3652, 30168])).
% 11.38/11.66 tff(30170,plain,
% 11.38/11.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.66 inference(rewrite,[status(thm)],[])).
% 11.38/11.66 tff(30171,plain,
% 11.38/11.66 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.66 inference(rewrite,[status(thm)],[])).
% 11.38/11.66 tff(30172,plain,
% 11.38/11.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.38/11.66 inference(monotonicity,[status(thm)],[30171])).
% 11.38/11.66 tff(30173,plain,
% 11.38/11.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.66 inference(transitivity,[status(thm)],[30172, 30170])).
% 11.38/11.66 tff(30174,plain,
% 11.38/11.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 11.38/11.66 inference(quant_inst,[status(thm)],[])).
% 11.38/11.66 tff(30175,plain,
% 11.38/11.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 11.38/11.66 inference(modus_ponens,[status(thm)],[30174, 30173])).
% 11.38/11.66 tff(30176,plain,
% 11.38/11.66 ($false),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[30175, 391, 30169, 1234, 1233, 30157, 1685])).
% 11.38/11.66 tff(30177,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.66 tff(30178,plain,
% 11.38/11.66 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[30177, 30152, 30105, 29945, 29911, 29691, 29900, 2053, 59])).
% 11.38/11.66 tff(30179,plain,
% 11.38/11.66 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[1370, 30178, 26982])).
% 11.38/11.66 tff(30180,plain,
% 11.38/11.66 (r(s(z), z)),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[7485, 812, 484])).
% 11.38/11.66 tff(30181,plain,
% 11.38/11.66 (~b(s(z), s(s(s(elem!1))))),
% 11.38/11.66 inference(unit_resolution,[status(thm)],[7796, 812, 4028])).
% 11.38/11.67 tff(30182,plain,
% 11.38/11.67 (r(s(z), s(s(s(elem!1))))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[247, 30181])).
% 11.38/11.67 tff(30183,plain,
% 11.38/11.67 (~r(s(s(s(elem!1))), s(z))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[3499, 30182, 184, 30180])).
% 11.38/11.67 tff(30184,plain,
% 11.38/11.67 (b(s(s(s(elem!1))), s(z))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[223, 30183])).
% 11.38/11.67 tff(30185,plain,
% 11.38/11.67 (b(s(s(s(elem!1))), elem!1)),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[3938, 30184, 812])).
% 11.38/11.67 tff(30186,plain,
% 11.38/11.67 (~r(s(s(elem!1)), s(z))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[2220, 812, 888])).
% 11.38/11.67 tff(30187,plain,
% 11.38/11.67 (b(s(s(elem!1)), s(z))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[362, 30186])).
% 11.38/11.67 tff(30188,plain,
% 11.38/11.67 (~b(s(s(s(s(z)))), elem!1)),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[1660, 30184, 1234, 1374, 30187])).
% 11.38/11.67 tff(30189,plain,
% 11.38/11.67 ($false),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[1563, 30188, 30185, 7866])).
% 11.38/11.67 tff(30190,plain,((~(s(z) = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | r(s(s(elem!1)), elem!1) | b(elem!1, s(s(s(elem!1)))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 11.38/11.67 tff(30191,plain,
% 11.38/11.67 (~(s(z) = elem!1)),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[30190, 888, 1374, 59, 1234, 4028, 484])).
% 11.38/11.67 tff(30192,plain,
% 11.38/11.67 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[2849, 30191])).
% 11.38/11.67 tff(30193,plain,
% 11.38/11.67 (b(s(z), elem!1)),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[632, 30191, 1492])).
% 11.38/11.67 tff(30194,plain,
% 11.38/11.67 (b(s(s(elem!1)), elem!1)),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[872, 888, 249])).
% 11.38/11.67 tff(30195,plain,
% 11.38/11.67 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[2686, 6160])).
% 11.38/11.67 tff(30196,plain,
% 11.38/11.67 (~(elem!1 = s(z))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[172, 30191])).
% 11.38/11.67 tff(30197,plain,
% 11.38/11.67 (r(elem!1, s(z))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[837, 30196, 31])).
% 11.38/11.67 tff(30198,plain,
% 11.38/11.67 (~b(s(s(s(elem!1))), s(z))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[18559, 30197, 30195, 1374, 1234, 30194, 225, 30193, 308, 30192, 484, 10, 89, 1293, 4028, 31])).
% 11.38/11.67 tff(30199,plain,
% 11.38/11.67 (r(s(s(s(elem!1))), s(z))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[223, 30198])).
% 11.38/11.67 tff(30200,plain,
% 11.38/11.67 (b(s(z), z)),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[8411, 30197, 59, 484, 1492])).
% 11.38/11.67 tff(30201,plain,
% 11.38/11.67 (~r(elem!1, s(s(s(elem!1))))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[6132, 530, 184, 183])).
% 11.38/11.67 tff(30202,plain,
% 11.38/11.67 (elem!1 = s(s(s(elem!1)))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[424, 30201, 4028])).
% 11.38/11.67 tff(30203,plain,
% 11.38/11.67 (s(elem!1) = s(s(s(s(elem!1))))),
% 11.38/11.67 inference(monotonicity,[status(thm)],[30202])).
% 11.38/11.67 tff(30204,plain,
% 11.38/11.67 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 11.38/11.67 inference(monotonicity,[status(thm)],[30203])).
% 11.38/11.67 tff(30205,plain,
% 11.38/11.67 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 11.38/11.67 inference(symmetry,[status(thm)],[30204])).
% 11.38/11.67 tff(30206,plain,
% 11.38/11.67 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.38/11.67 inference(monotonicity,[status(thm)],[30205])).
% 11.38/11.67 tff(30207,plain,
% 11.38/11.67 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 11.38/11.67 inference(symmetry,[status(thm)],[30206])).
% 11.38/11.67 tff(30208,plain,
% 11.38/11.67 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[1887, 30202, 973])).
% 11.38/11.67 tff(30209,plain,
% 11.38/11.67 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 11.38/11.67 inference(modus_ponens,[status(thm)],[30208, 30207])).
% 11.38/11.67 tff(30210,plain,
% 11.38/11.67 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.67 inference(monotonicity,[status(thm)],[30205])).
% 11.38/11.67 tff(30211,plain,
% 11.38/11.67 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 11.38/11.67 inference(symmetry,[status(thm)],[30210])).
% 11.38/11.67 tff(30212,plain,
% 11.38/11.67 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 11.38/11.67 inference(modus_ponens,[status(thm)],[1374, 30211])).
% 11.38/11.67 tff(30213,plain,
% 11.38/11.67 (s(s(s(elem!1))) = elem!1),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[129, 30202])).
% 11.38/11.67 tff(30214,plain,
% 11.38/11.67 (b(s(z), s(s(s(elem!1))))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[14872, 30213, 644])).
% 11.38/11.67 tff(30215,assumption,(b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 11.38/11.67 tff(30216,plain,
% 11.38/11.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 11.38/11.67 inference(rewrite,[status(thm)],[])).
% 11.38/11.67 tff(30217,plain,
% 11.38/11.67 (((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 11.38/11.67 inference(rewrite,[status(thm)],[])).
% 11.38/11.67 tff(30218,plain,
% 11.38/11.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 11.38/11.67 inference(monotonicity,[status(thm)],[30217])).
% 11.38/11.67 tff(30219,plain,
% 11.38/11.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 11.38/11.67 inference(transitivity,[status(thm)],[30218, 30216])).
% 11.38/11.67 tff(30220,plain,
% 11.38/11.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.67 inference(quant_inst,[status(thm)],[])).
% 11.38/11.67 tff(30221,plain,
% 11.38/11.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 11.38/11.67 inference(modus_ponens,[status(thm)],[30220, 30219])).
% 11.38/11.67 tff(30222,plain,
% 11.38/11.67 ($false),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[30221, 391, 379, 1234, 3325, 30215, 9469])).
% 11.38/11.67 tff(30223,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.67 tff(30224,plain,
% 11.38/11.67 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[30223, 30214, 1234, 30212, 30209])).
% 11.38/11.67 tff(30225,plain,
% 11.38/11.67 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 30224])).
% 11.38/11.67 tff(30226,plain,
% 11.38/11.67 (r(s(s(s(elem!1))), z)),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[533, 30213, 530])).
% 11.38/11.67 tff(30227,plain,
% 11.38/11.67 (~r(z, s(s(s(s(z)))))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[4324, 194, 30226, 184, 30225])).
% 11.38/11.67 tff(30228,plain,
% 11.38/11.67 (b(z, s(s(s(s(z)))))),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[800, 30227])).
% 11.38/11.67 tff(30229,plain,
% 11.38/11.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.38/11.67 inference(rewrite,[status(thm)],[])).
% 11.38/11.67 tff(30230,plain,
% 11.38/11.67 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.38/11.67 inference(rewrite,[status(thm)],[])).
% 11.38/11.67 tff(30231,plain,
% 11.38/11.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 11.38/11.67 inference(monotonicity,[status(thm)],[30230])).
% 11.38/11.67 tff(30232,plain,
% 11.38/11.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.38/11.67 inference(transitivity,[status(thm)],[30231, 30229])).
% 11.38/11.67 tff(30233,plain,
% 11.38/11.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 11.38/11.67 inference(quant_inst,[status(thm)],[])).
% 11.38/11.67 tff(30234,plain,
% 11.38/11.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 11.38/11.67 inference(modus_ponens,[status(thm)],[30233, 30232])).
% 11.38/11.67 tff(30235,plain,
% 11.38/11.67 (~r(s(s(s(s(z)))), z)),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[30234, 194, 30226, 184, 30225])).
% 11.38/11.67 tff(30236,plain,
% 11.38/11.67 (b(s(s(s(s(z)))), z)),
% 11.38/11.67 inference(unit_resolution,[status(thm)],[87, 30235])).
% 11.38/11.67 tff(30237,plain,
% 11.38/11.67 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.67 inference(rewrite,[status(thm)],[])).
% 11.38/11.67 tff(30238,plain,
% 11.38/11.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.38/11.67 inference(monotonicity,[status(thm)],[30237])).
% 11.38/11.67 tff(30239,plain,
% 11.38/11.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.68 inference(transitivity,[status(thm)],[30238, 10429])).
% 11.38/11.68 tff(30240,plain,
% 11.38/11.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.68 inference(quant_inst,[status(thm)],[])).
% 11.38/11.68 tff(30241,plain,
% 11.38/11.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30240, 30239])).
% 11.38/11.68 tff(30242,plain,
% 11.38/11.68 ($false),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[30241, 391, 30236, 1234, 30228, 590])).
% 11.38/11.68 tff(30243,plain,((~r(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.68 tff(30244,plain,
% 11.38/11.68 (~r(elem!1, z)),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[30243, 30200, 1234, 59, 30192, 1374, 30193, 30194, 4028, 30199])).
% 11.38/11.68 tff(30245,plain,
% 11.38/11.68 (elem!1 = z),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[526, 30244, 484])).
% 11.38/11.68 tff(30246,plain,
% 11.38/11.68 (s(elem!1) = s(z)),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30245])).
% 11.38/11.68 tff(30247,plain,
% 11.38/11.68 (s(s(elem!1)) = s(s(z))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30246])).
% 11.38/11.68 tff(30248,plain,
% 11.38/11.68 (s(s(s(elem!1))) = s(s(s(z)))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30247])).
% 11.38/11.68 tff(30249,plain,
% 11.38/11.68 (s(s(s(z))) = s(s(s(elem!1)))),
% 11.38/11.68 inference(symmetry,[status(thm)],[30248])).
% 11.38/11.68 tff(30250,plain,
% 11.38/11.68 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30249])).
% 11.38/11.68 tff(30251,plain,
% 11.38/11.68 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 11.38/11.68 inference(symmetry,[status(thm)],[30250])).
% 11.38/11.68 tff(30252,plain,
% 11.38/11.68 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30249])).
% 11.38/11.68 tff(30253,plain,
% 11.38/11.68 ((~r(s(z), s(s(s(z))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30252])).
% 11.38/11.68 tff(30254,plain,
% 11.38/11.68 (r(s(s(s(z))), s(z))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[29740, 30199, 30245])).
% 11.38/11.68 tff(30255,plain,
% 11.38/11.68 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30249])).
% 11.38/11.68 tff(30256,plain,
% 11.38/11.68 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 11.38/11.68 inference(symmetry,[status(thm)],[30255])).
% 11.38/11.68 tff(30257,plain,
% 11.38/11.68 (r(z, s(s(s(z))))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[59, 30256])).
% 11.38/11.68 tff(30258,plain,
% 11.38/11.68 (r(elem!1, s(z)) <=> r(z, s(z))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30245])).
% 11.38/11.68 tff(30259,plain,
% 11.38/11.68 (r(z, s(z))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30197, 30258])).
% 11.38/11.68 tff(30260,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 11.38/11.68 tff(30261,plain,
% 11.38/11.68 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 11.38/11.68 inference(rewrite,[status(thm)],[])).
% 11.38/11.68 tff(30262,plain,
% 11.38/11.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30261])).
% 11.38/11.68 tff(30263,plain,
% 11.38/11.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 11.38/11.68 inference(transitivity,[status(thm)],[30262, 29761])).
% 11.38/11.68 tff(30264,plain,
% 11.38/11.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 11.38/11.68 inference(quant_inst,[status(thm)],[])).
% 11.38/11.68 tff(30265,plain,
% 11.38/11.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30264, 30263])).
% 11.38/11.68 tff(30266,plain,
% 11.38/11.68 ($false),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[30265, 194, 722, 15705, 15510, 30260])).
% 11.38/11.68 tff(30267,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.68 tff(30268,plain,
% 11.38/11.68 (~r(s(z), s(s(s(z))))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[30267, 30259, 30257, 30254])).
% 11.38/11.68 tff(30269,plain,
% 11.38/11.68 (~r(s(z), s(s(s(elem!1))))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30268, 30253])).
% 11.38/11.68 tff(30270,plain,
% 11.38/11.68 (b(s(z), s(s(s(elem!1))))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[247, 30269])).
% 11.38/11.68 tff(30271,plain,
% 11.38/11.68 (b(s(z), s(s(s(z))))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30270, 30251])).
% 11.38/11.68 tff(30272,plain,
% 11.38/11.68 (b(s(s(s(z))), s(s(z)))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[2986, 30245, 1374])).
% 11.38/11.68 tff(30273,plain,
% 11.38/11.68 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30248])).
% 11.38/11.68 tff(30274,plain,
% 11.38/11.68 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30273, 30248])).
% 11.38/11.68 tff(30275,plain,
% 11.38/11.68 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30246])).
% 11.38/11.68 tff(30276,plain,
% 11.38/11.68 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 11.38/11.68 inference(symmetry,[status(thm)],[30275])).
% 11.38/11.68 tff(30277,plain,
% 11.38/11.68 (r(s(s(s(elem!1))), s(elem!1))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30199, 30276])).
% 11.38/11.68 tff(30278,plain,
% 11.38/11.68 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30273])).
% 11.38/11.68 tff(30279,plain,
% 11.38/11.68 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30246])).
% 11.38/11.68 tff(30280,plain,
% 11.38/11.68 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 11.38/11.68 inference(symmetry,[status(thm)],[30279])).
% 11.38/11.68 tff(30281,plain,
% 11.38/11.68 (b(s(elem!1), s(s(s(elem!1))))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30270, 30280])).
% 11.38/11.68 tff(30282,plain,
% 11.38/11.68 (z = elem!1),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[5453, 30245])).
% 11.38/11.68 tff(30283,plain,
% 11.38/11.68 (~r(s(s(s(elem!1))), z)),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[9853, 30282, 225])).
% 11.38/11.68 tff(30284,plain,
% 11.38/11.68 (b(s(s(s(elem!1))), z)),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[377, 30283])).
% 11.38/11.68 tff(30285,plain,
% 11.38/11.68 (b(s(elem!1), z) <=> b(s(z), z)),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30246])).
% 11.38/11.68 tff(30286,plain,
% 11.38/11.68 (b(s(z), z) <=> b(s(elem!1), z)),
% 11.38/11.68 inference(symmetry,[status(thm)],[30285])).
% 11.38/11.68 tff(30287,plain,
% 11.38/11.68 (b(s(elem!1), z)),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30200, 30286])).
% 11.38/11.68 tff(30288,plain,
% 11.38/11.68 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30245])).
% 11.38/11.68 tff(30289,plain,
% 11.38/11.68 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 11.38/11.68 inference(symmetry,[status(thm)],[30288])).
% 11.38/11.68 tff(30290,plain,
% 11.38/11.68 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30273])).
% 11.38/11.68 tff(30291,plain,
% 11.38/11.68 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 11.38/11.68 inference(symmetry,[status(thm)],[30290])).
% 11.38/11.68 tff(30292,plain,
% 11.38/11.68 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 11.38/11.68 inference(transitivity,[status(thm)],[30291, 30289])).
% 11.38/11.68 tff(30293,plain,
% 11.38/11.68 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30247])).
% 11.38/11.68 tff(30294,plain,
% 11.38/11.68 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30245])).
% 11.38/11.68 tff(30295,plain,
% 11.38/11.68 (b(s(s(elem!1)), z)),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30194, 30294])).
% 11.38/11.68 tff(30296,plain,
% 11.38/11.68 (b(s(s(z)), z)),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30295, 30293])).
% 11.38/11.68 tff(30297,plain,
% 11.38/11.68 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30247])).
% 11.38/11.68 tff(30298,plain,
% 11.38/11.68 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 11.38/11.68 inference(symmetry,[status(thm)],[30297])).
% 11.38/11.68 tff(30299,plain,
% 11.38/11.68 ((~b(z, s(s(z)))) <=> (~b(z, s(s(elem!1))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30298])).
% 11.38/11.68 tff(30300,plain,
% 11.38/11.68 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30245])).
% 11.38/11.68 tff(30301,plain,
% 11.38/11.68 ((~b(elem!1, s(s(z)))) <=> (~b(z, s(s(z))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30300])).
% 11.38/11.68 tff(30302,plain,
% 11.38/11.68 (~b(z, s(s(z)))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[3583, 30301])).
% 11.38/11.68 tff(30303,plain,
% 11.38/11.68 (~b(z, s(s(elem!1)))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30302, 30299])).
% 11.38/11.68 tff(30304,plain,
% 11.38/11.68 (r(z, s(s(elem!1)))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[324, 30303])).
% 11.38/11.68 tff(30305,plain,
% 11.38/11.68 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30245])).
% 11.38/11.68 tff(30306,plain,
% 11.38/11.68 ((elem!1 = s(s(z))) <=> (z = s(s(z)))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30245])).
% 11.38/11.68 tff(30307,plain,
% 11.38/11.68 ((elem!1 = s(s(z))) <=> (s(s(z)) = z)),
% 11.38/11.68 inference(transitivity,[status(thm)],[30306, 11715])).
% 11.38/11.68 tff(30308,plain,
% 11.38/11.68 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 11.38/11.68 inference(symmetry,[status(thm)],[30307])).
% 11.38/11.68 tff(30309,plain,
% 11.38/11.68 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[30308])).
% 11.38/11.68 tff(30310,plain,
% 11.38/11.68 (~(elem!1 = s(s(z)))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[1207, 30309])).
% 11.38/11.68 tff(30311,plain,
% 11.38/11.68 (r(elem!1, s(s(z)))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[3394, 30310, 3583])).
% 11.38/11.68 tff(30312,plain,
% 11.38/11.68 (r(z, s(s(z)))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30311, 30305])).
% 11.38/11.68 tff(30313,plain,
% 11.38/11.68 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[2980])).
% 11.38/11.68 tff(30314,plain,
% 11.38/11.68 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[29999, 2053, 11, 15510, 1373, 1374, 1035, 326, 1234, 1235, 590])).
% 11.38/11.68 tff(30315,plain,
% 11.38/11.68 (r(s(s(s(s(z)))), s(s(z)))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[1714, 30314])).
% 11.38/11.68 tff(30316,plain,
% 11.38/11.68 (~r(s(s(z)), s(z))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[18433, 30315, 2053, 8505])).
% 11.38/11.68 tff(30317,plain,
% 11.38/11.68 (b(s(s(z)), s(z))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[3778, 30316])).
% 11.38/11.68 tff(30318,plain,
% 11.38/11.68 (b(s(s(elem!1)), s(z))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[30317, 30313])).
% 11.38/11.68 tff(30319,plain,
% 11.38/11.68 (~b(s(z), s(s(elem!1)))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[5321, 30318, 379, 1374])).
% 11.38/11.68 tff(30320,plain,
% 11.38/11.68 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 11.38/11.68 inference(monotonicity,[status(thm)],[2980])).
% 11.38/11.68 tff(30321,plain,
% 11.38/11.68 (b(s(z), s(s(elem!1)))),
% 11.38/11.68 inference(modus_ponens,[status(thm)],[2439, 30320])).
% 11.38/11.68 tff(30322,assumption,(~b(s(z), s(s(elem!1)))), introduced(assumption)).
% 11.38/11.68 tff(30323,plain,
% 11.38/11.68 ($false),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[30322, 30321])).
% 11.38/11.68 tff(30324,plain,((~b(s(z), s(s(z)))) | b(s(z), s(s(elem!1))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.68 tff(30325,plain,
% 11.38/11.68 (~b(s(z), s(s(z)))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[30324, 30319, 11])).
% 11.38/11.68 tff(30326,plain,
% 11.38/11.68 (r(s(z), s(s(z)))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[1788, 30325])).
% 11.38/11.68 tff(30327,plain,
% 11.38/11.68 (r(s(z), s(s(elem!1)))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[23186, 30326, 11])).
% 11.38/11.68 tff(30328,plain,
% 11.38/11.68 (~r(s(s(s(s(z)))), s(z))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[5500, 30327, 722, 2053])).
% 11.38/11.68 tff(30329,plain,
% 11.38/11.68 (b(s(s(s(s(z)))), s(z))),
% 11.38/11.68 inference(unit_resolution,[status(thm)],[749, 30328])).
% 11.38/11.69 tff(30330,plain,
% 11.38/11.69 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[5108, 30329, 30317, 1234])).
% 11.38/11.69 tff(30331,plain,
% 11.38/11.69 (r(s(s(z)), s(s(s(s(z)))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[3652, 30330])).
% 11.38/11.69 tff(30332,plain,
% 11.38/11.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 11.38/11.69 inference(rewrite,[status(thm)],[])).
% 11.38/11.69 tff(30333,plain,
% 11.38/11.69 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 11.38/11.69 inference(rewrite,[status(thm)],[])).
% 11.38/11.69 tff(30334,plain,
% 11.38/11.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 11.38/11.69 inference(monotonicity,[status(thm)],[30333])).
% 11.38/11.69 tff(30335,plain,
% 11.38/11.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 11.38/11.69 inference(transitivity,[status(thm)],[30334, 30332])).
% 11.38/11.69 tff(30336,plain,
% 11.38/11.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 11.38/11.69 inference(quant_inst,[status(thm)],[])).
% 11.38/11.69 tff(30337,plain,
% 11.38/11.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 11.38/11.69 inference(modus_ponens,[status(thm)],[30336, 30335])).
% 11.38/11.69 tff(30338,plain,
% 11.38/11.69 ($false),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[30337, 194, 30331, 722, 30326, 8505])).
% 11.38/11.69 tff(30339,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.69 tff(30340,plain,
% 11.38/11.69 (~r(s(s(s(s(z)))), z)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[30339, 30259, 30312, 1234, 30245, 30270, 1374, 30257, 308, 30195, 30304, 30296, 30200])).
% 11.38/11.69 tff(30341,plain,
% 11.38/11.69 (b(s(s(s(s(z)))), z)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[87, 30340])).
% 11.38/11.69 tff(30342,plain,
% 11.38/11.69 (b(s(s(s(s(elem!1)))), elem!1)),
% 11.38/11.69 inference(modus_ponens,[status(thm)],[30341, 30292])).
% 11.38/11.69 tff(30343,plain,
% 11.38/11.69 (~b(z, s(s(s(s(elem!1)))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[19129, 30342, 30287, 30284, 30281])).
% 11.38/11.69 tff(30344,plain,
% 11.38/11.69 (r(z, s(s(s(s(elem!1)))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[2767, 30343])).
% 11.38/11.69 tff(30345,plain,
% 11.38/11.69 (r(z, s(s(s(s(z)))))),
% 11.38/11.69 inference(modus_ponens,[status(thm)],[30344, 30278])).
% 11.38/11.69 tff(30346,plain,
% 11.38/11.69 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[19836, 30345, 59, 30277])).
% 11.38/11.69 tff(30347,plain,
% 11.38/11.69 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[29931, 30346, 30245])).
% 11.38/11.69 tff(30348,plain,
% 11.38/11.69 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[1095, 30347, 300])).
% 11.38/11.69 tff(30349,plain,
% 11.38/11.69 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.38/11.69 inference(modus_ponens,[status(thm)],[30348, 30274])).
% 11.38/11.69 tff(30350,plain,
% 11.38/11.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.69 inference(rewrite,[status(thm)],[])).
% 11.38/11.69 tff(30351,plain,
% 11.38/11.69 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.69 inference(rewrite,[status(thm)],[])).
% 11.38/11.69 tff(30352,plain,
% 11.38/11.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.38/11.69 inference(monotonicity,[status(thm)],[30351])).
% 11.38/11.69 tff(30353,plain,
% 11.38/11.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.69 inference(transitivity,[status(thm)],[30352, 30350])).
% 11.38/11.69 tff(30354,plain,
% 11.38/11.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.38/11.69 inference(quant_inst,[status(thm)],[])).
% 11.38/11.69 tff(30355,plain,
% 11.38/11.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 11.38/11.69 inference(modus_ponens,[status(thm)],[30354, 30353])).
% 11.38/11.69 tff(30356,plain,
% 11.38/11.69 ($false),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[30355, 391, 30296, 1234, 30349, 30272, 30271])).
% 11.38/11.69 tff(30357,plain,(r(s(s(elem!1)), elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | b(elem!1, s(s(z))) | r(s(s(s(elem!1))), elem!1) | b(elem!1, z) | b(elem!1, s(s(s(elem!1)))) | r(s(z), elem!1) | b(z, s(s(s(elem!1)))) | b(z, elem!1) | b(elem!1, s(z)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.38/11.69 tff(30358,plain,
% 11.38/11.69 (r(s(z), elem!1)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[30357, 30179, 31, 29954, 30151, 30147, 30143, 30129, 10, 30136, 29911, 29692])).
% 11.38/11.69 tff(30359,plain,
% 11.38/11.69 (~b(elem!1, s(s(s(elem!1))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[8846, 11, 10])).
% 11.38/11.69 tff(30360,plain,
% 11.38/11.69 (b(z, elem!1) <=> b(z, z)),
% 11.38/11.69 inference(monotonicity,[status(thm)],[11])).
% 11.38/11.69 tff(30361,plain,
% 11.38/11.69 (b(z, z) <=> b(z, elem!1)),
% 11.38/11.69 inference(symmetry,[status(thm)],[30360])).
% 11.38/11.69 tff(30362,plain,
% 11.38/11.69 ((~b(z, z)) <=> (~b(z, elem!1))),
% 11.38/11.69 inference(monotonicity,[status(thm)],[30361])).
% 11.38/11.69 tff(30363,plain,
% 11.38/11.69 (~b(z, elem!1)),
% 11.38/11.69 inference(modus_ponens,[status(thm)],[30135, 30362])).
% 11.38/11.69 tff(30364,plain,
% 11.38/11.69 (~b(elem!1, s(s(z)))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[3375, 3373, 11])).
% 11.38/11.69 tff(30365,plain,
% 11.38/11.69 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 11.38/11.69 inference(monotonicity,[status(thm)],[11])).
% 11.38/11.69 tff(30366,plain,
% 11.38/11.69 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 11.38/11.69 inference(symmetry,[status(thm)],[30365])).
% 11.38/11.69 tff(30367,plain,
% 11.38/11.69 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 11.38/11.69 inference(transitivity,[status(thm)],[23180, 30366])).
% 11.38/11.69 tff(30368,plain,
% 11.38/11.69 ((~r(s(s(z)), z)) <=> (~r(s(s(elem!1)), elem!1))),
% 11.38/11.69 inference(monotonicity,[status(thm)],[30367])).
% 11.38/11.69 tff(30369,plain,
% 11.38/11.69 (~r(s(s(z)), z)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[30109, 1234, 1233, 2053, 59])).
% 11.38/11.69 tff(30370,plain,
% 11.38/11.69 (~r(s(s(elem!1)), elem!1)),
% 11.38/11.69 inference(modus_ponens,[status(thm)],[30369, 30368])).
% 11.38/11.69 tff(30371,plain,
% 11.38/11.69 (b(elem!1, z) <=> b(z, z)),
% 11.38/11.69 inference(monotonicity,[status(thm)],[11])).
% 11.38/11.69 tff(30372,plain,
% 11.38/11.69 (b(z, z) <=> b(elem!1, z)),
% 11.38/11.69 inference(symmetry,[status(thm)],[30371])).
% 11.38/11.69 tff(30373,plain,
% 11.38/11.69 ((~b(z, z)) <=> (~b(elem!1, z))),
% 11.38/11.69 inference(monotonicity,[status(thm)],[30372])).
% 11.38/11.69 tff(30374,plain,
% 11.38/11.69 (~b(elem!1, z)),
% 11.38/11.69 inference(modus_ponens,[status(thm)],[30135, 30373])).
% 11.38/11.69 tff(30375,plain,
% 11.38/11.69 (~(s(z) = elem!1)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[7796, 30359, 379])).
% 11.38/11.69 tff(30376,plain,
% 11.38/11.69 (~(elem!1 = s(z))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[172, 30375])).
% 11.38/11.69 tff(30377,plain,
% 11.38/11.69 (r(elem!1, s(z))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[837, 30376, 31])).
% 11.38/11.69 tff(30378,plain,
% 11.38/11.69 (r(z, s(z))),
% 11.38/11.69 inference(modus_ponens,[status(thm)],[30377, 8826])).
% 11.38/11.69 tff(30379,plain,
% 11.38/11.69 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[2849, 30375])).
% 11.38/11.69 tff(30380,plain,
% 11.38/11.69 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[10940, 30379])).
% 11.38/11.69 tff(30381,plain,
% 11.38/11.69 (~r(s(s(s(elem!1))), z)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[29942, 1234, 18546, 11, 30380, 30378, 2053, 310, 59])).
% 11.38/11.69 tff(30382,plain,
% 11.38/11.69 (~r(s(s(s(elem!1))), elem!1)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[406, 30381, 11])).
% 11.38/11.69 tff(30383,plain,
% 11.38/11.69 (b(s(s(s(elem!1))), z)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[377, 30381])).
% 11.38/11.69 tff(30384,plain,
% 11.38/11.69 (b(s(s(s(z))), z)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[1680, 30383, 11])).
% 11.38/11.69 tff(30385,plain,
% 11.38/11.69 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[30177, 29960, 1233, 30384, 1234, 11, 310, 2053, 59])).
% 11.38/11.69 tff(30386,plain,
% 11.38/11.69 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[1370, 30385, 297])).
% 11.38/11.69 tff(30387,plain,
% 11.38/11.69 (r(s(z), elem!1)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[30357, 30386, 31, 30382, 30374, 30072, 30370, 30364, 10, 30363, 1234, 30359])).
% 11.38/11.69 tff(30388,plain,
% 11.38/11.69 (r(s(z), z)),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[5433, 30387, 17618])).
% 11.38/11.69 tff(30389,plain,
% 11.38/11.69 (b(s(s(elem!1)), s(z))),
% 11.38/11.69 inference(modus_ponens,[status(thm)],[1233, 30313])).
% 11.38/11.69 tff(30390,plain,
% 11.38/11.69 (~b(s(z), s(s(elem!1)))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[5321, 30386, 379, 30389])).
% 11.38/11.69 tff(30391,plain,
% 11.38/11.69 (~b(s(z), s(s(z)))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[30324, 30390, 11])).
% 11.38/11.69 tff(30392,plain,
% 11.38/11.69 (r(s(z), s(s(z)))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[1788, 30391])).
% 11.38/11.69 tff(30393,plain,
% 11.38/11.69 ($false),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[20331, 30392, 30388, 1749, 29960])).
% 11.38/11.69 tff(30394,plain,(b(z, s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = z)) | b(elem!1, s(z)) | b(z, s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 11.38/11.69 tff(30395,plain,
% 11.38/11.69 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[30394, 30128, 29691, 31, 10, 29911, 379, 26982, 30105, 2053])).
% 11.38/11.69 tff(30396,plain,
% 11.38/11.69 (b(s(s(z)), s(s(s(s(z)))))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[3652, 30395])).
% 11.38/11.69 tff(30397,plain,
% 11.38/11.69 (~b(s(s(s(s(z)))), s(z))),
% 11.38/11.69 inference(unit_resolution,[status(thm)],[5108, 30396, 29911, 30105])).
% 11.38/11.69 tff(30398,plain,
% 11.38/11.69 (r(s(s(s(s(z)))), s(z))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[749, 30397])).
% 11.48/11.70 tff(30399,plain,
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% 11.48/11.70 inference(unit_resolution,[status(thm)],[9117, 30398, 30358, 30130, 29894])).
% 11.48/11.70 tff(30400,plain,(b(z, s(s(s(elem!1)))) | b(elem!1, s(z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.48/11.70 tff(30401,plain,
% 11.48/11.70 (b(z, s(s(s(elem!1))))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[30400, 31, 2053, 379, 183, 1, 80])).
% 11.48/11.70 tff(30402,plain,
% 11.48/11.70 (~(s(z) = elem!1)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[1495, 29890])).
% 11.48/11.70 tff(30403,plain,
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% 11.48/11.70 inference(unit_resolution,[status(thm)],[25009, 30402, 2913, 31, 1, 30401, 15465, 183])).
% 11.48/11.70 tff(30404,plain,
% 11.48/11.70 (z = elem!1),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[141, 30403, 80])).
% 11.48/11.70 tff(30405,plain,
% 11.48/11.70 (~r(elem!1, z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[29452, 30404])).
% 11.48/11.70 tff(30406,plain,
% 11.48/11.70 (elem!1 = z),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[97, 30404])).
% 11.48/11.70 tff(30407,plain,
% 11.48/11.70 (~r(s(s(s(elem!1))), elem!1)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[10856, 29891, 2913, 183])).
% 11.48/11.70 tff(30408,plain,
% 11.48/11.70 (b(s(s(s(elem!1))), elem!1)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[230, 30407, 9])).
% 11.48/11.70 tff(30409,plain,
% 11.48/11.70 (b(s(s(s(elem!1))), z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[28222, 30408, 30406])).
% 11.48/11.70 tff(30410,plain,
% 11.48/11.70 (~r(s(s(s(elem!1))), elem!1)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[10856, 847, 1216, 183])).
% 11.48/11.70 tff(30411,plain,
% 11.48/11.70 (b(s(s(s(elem!1))), elem!1)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[230, 30410, 127])).
% 11.48/11.70 tff(30412,plain,
% 11.48/11.70 (~b(elem!1, z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[17249, 30411, 10682, 380])).
% 11.48/11.70 tff(30413,plain,
% 11.48/11.70 (elem!1 = z),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[526, 30412, 2282])).
% 11.48/11.70 tff(30414,plain,
% 11.48/11.70 (r(elem!1, s(z)) <=> r(z, s(z))),
% 11.48/11.70 inference(monotonicity,[status(thm)],[30413])).
% 11.48/11.70 tff(30415,plain,
% 11.48/11.70 (r(z, s(z)) <=> r(elem!1, s(z))),
% 11.48/11.70 inference(symmetry,[status(thm)],[30414])).
% 11.48/11.70 tff(30416,plain,
% 11.48/11.70 ((~r(z, s(z))) <=> (~r(elem!1, s(z)))),
% 11.48/11.70 inference(monotonicity,[status(thm)],[30415])).
% 11.48/11.70 tff(30417,plain,
% 11.48/11.70 (~r(elem!1, s(z))),
% 11.48/11.70 inference(modus_ponens,[status(thm)],[676, 30416])).
% 11.48/11.70 tff(30418,plain,
% 11.48/11.70 ($false),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[847, 30417])).
% 11.48/11.70 tff(30419,plain,((~r(elem!1, s(z))) | r(z, s(z)) | r(elem!1, z) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.70 tff(30420,plain,
% 11.48/11.70 ($false),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[30419, 30409, 30405, 15464, 2913, 30401, 9, 29891, 183])).
% 11.48/11.70 tff(30421,plain,(b(s(z), s(s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | r(z, elem!1) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.70 tff(30422,plain,
% 11.48/11.70 (b(s(z), s(s(s(s(z)))))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[30421, 31, 80, 11174, 1, 3447, 29889])).
% 11.48/11.70 tff(30423,plain,
% 11.48/11.70 (b(z, s(s(s(elem!1))))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[30400, 31, 3447, 29889, 11174, 1, 80])).
% 11.48/11.70 tff(30424,plain,
% 11.48/11.70 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 11.48/11.70 inference(monotonicity,[status(thm)],[1550])).
% 11.48/11.70 tff(30425,plain,
% 11.48/11.70 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 11.48/11.70 inference(symmetry,[status(thm)],[30424])).
% 11.48/11.70 tff(30426,plain,
% 11.48/11.70 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.70 inference(monotonicity,[status(thm)],[1552])).
% 11.48/11.70 tff(30427,plain,
% 11.48/11.70 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 11.48/11.70 inference(symmetry,[status(thm)],[30426])).
% 11.48/11.70 tff(30428,plain,
% 11.48/11.70 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 11.48/11.70 inference(transitivity,[status(thm)],[30427, 30425])).
% 11.48/11.70 tff(30429,plain,
% 11.48/11.70 (~b(z, s(elem!1))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[8527, 8598, 3373])).
% 11.48/11.70 tff(30430,plain,
% 11.48/11.70 (r(z, s(elem!1))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[566, 30429])).
% 11.48/11.70 tff(30431,plain,
% 11.48/11.70 (b(z, s(s(s(s(z)))))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[11318, 169, 2, 676])).
% 11.48/11.70 tff(30432,plain,
% 11.48/11.70 (~(s(s(s(s(z)))) = elem!1)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[8916, 24160, 1234])).
% 11.48/11.70 tff(30433,plain,
% 11.48/11.70 (r(s(s(s(s(z)))), elem!1)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[762, 29703, 30432])).
% 11.48/11.70 tff(30434,plain,
% 11.48/11.70 (~r(elem!1, z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[6087, 30430, 3447, 30433])).
% 11.48/11.70 tff(30435,plain,
% 11.48/11.70 (b(elem!1, z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[526, 30434, 2])).
% 11.48/11.70 tff(30436,plain,
% 11.48/11.70 (b(s(z), z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[10390, 30435, 8598])).
% 11.48/11.70 tff(30437,plain,
% 11.48/11.70 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.70 inference(transitivity,[status(thm)],[15538, 15540])).
% 11.48/11.70 tff(30438,plain,
% 11.48/11.70 (r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.70 inference(modus_ponens,[status(thm)],[613, 30437])).
% 11.48/11.70 tff(30439,plain,
% 11.48/11.70 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 11.48/11.70 inference(monotonicity,[status(thm)],[1550])).
% 11.48/11.70 tff(30440,plain,
% 11.48/11.70 ((~b(s(elem!1), z)) <=> (~b(s(s(z)), z))),
% 11.48/11.70 inference(monotonicity,[status(thm)],[30439])).
% 11.48/11.70 tff(30441,plain,
% 11.48/11.70 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 11.48/11.70 inference(transitivity,[status(thm)],[15538, 15540, 23973])).
% 11.48/11.70 tff(30442,plain,
% 11.48/11.70 (r(s(s(s(s(z)))), s(elem!1))),
% 11.48/11.70 inference(modus_ponens,[status(thm)],[613, 30441])).
% 11.48/11.70 tff(30443,plain,
% 11.48/11.70 (~r(s(elem!1), elem!1)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[5914, 30442, 2053, 2144])).
% 11.48/11.70 tff(30444,plain,
% 11.48/11.70 (b(s(elem!1), elem!1)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[2168, 30443, 164])).
% 11.48/11.70 tff(30445,plain,
% 11.48/11.70 (~b(s(elem!1), z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[7777, 30444, 665, 133])).
% 11.48/11.70 tff(30446,plain,
% 11.48/11.70 (~b(s(s(z)), z)),
% 11.48/11.70 inference(modus_ponens,[status(thm)],[30445, 30440])).
% 11.48/11.70 tff(30447,plain,
% 11.48/11.70 (r(s(s(z)), z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[1211, 30446])).
% 11.48/11.70 tff(30448,plain,
% 11.48/11.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.48/11.70 inference(rewrite,[status(thm)],[])).
% 11.48/11.70 tff(30449,plain,
% 11.48/11.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.48/11.70 inference(quant_inst,[status(thm)],[])).
% 11.48/11.70 tff(30450,plain,
% 11.48/11.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 11.48/11.70 inference(modus_ponens,[status(thm)],[30449, 30448])).
% 11.48/11.70 tff(30451,plain,
% 11.48/11.70 ($false),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[30450, 194, 2053, 30447, 30438, 8505])).
% 11.48/11.70 tff(30452,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~(elem!1 = s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.70 tff(30453,plain,
% 11.48/11.70 (~r(s(s(s(elem!1))), s(elem!1))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[30452, 169, 29960, 3447, 30435, 133, 164, 30430])).
% 11.48/11.70 tff(30454,plain,
% 11.48/11.70 (b(s(s(s(elem!1))), s(elem!1))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[588, 30453, 15536])).
% 11.48/11.70 tff(30455,plain,
% 11.48/11.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.48/11.70 inference(rewrite,[status(thm)],[])).
% 11.48/11.70 tff(30456,plain,
% 11.48/11.70 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.48/11.70 inference(rewrite,[status(thm)],[])).
% 11.48/11.70 tff(30457,plain,
% 11.48/11.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 11.48/11.70 inference(monotonicity,[status(thm)],[30456])).
% 11.48/11.70 tff(30458,plain,
% 11.48/11.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.48/11.70 inference(transitivity,[status(thm)],[30457, 30455])).
% 11.48/11.70 tff(30459,plain,
% 11.48/11.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 11.48/11.70 inference(quant_inst,[status(thm)],[])).
% 11.48/11.70 tff(30460,plain,
% 11.48/11.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 11.48/11.70 inference(modus_ponens,[status(thm)],[30459, 30458])).
% 11.48/11.70 tff(30461,plain,
% 11.48/11.70 ($false),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[30460, 391, 1101, 10682, 379, 2122, 664])).
% 11.48/11.70 tff(30462,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.70 tff(30463,plain,
% 11.48/11.70 (~b(s(elem!1), elem!1)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[30462, 30454, 379, 10682, 22903])).
% 11.48/11.70 tff(30464,plain,
% 11.48/11.70 (~b(s(s(z)), s(z))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[29583, 30463, 8598])).
% 11.48/11.70 tff(30465,plain,
% 11.48/11.70 (r(s(s(z)), s(z))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[3778, 30464])).
% 11.48/11.70 tff(30466,plain,
% 11.48/11.70 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[18433, 30465, 3447, 29960])).
% 11.48/11.70 tff(30467,plain,
% 11.48/11.70 (b(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[1714, 30466])).
% 11.48/11.70 tff(30468,plain,
% 11.48/11.70 (~b(s(s(z)), z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[17288, 30467, 30436, 30431, 1234])).
% 11.48/11.70 tff(30469,plain,
% 11.48/11.70 (r(s(s(z)), z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[1211, 30468])).
% 11.48/11.70 tff(30470,plain,
% 11.48/11.70 (r(s(elem!1), z)),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[3560, 30469, 8598])).
% 11.48/11.70 tff(30471,plain,
% 11.48/11.70 (~r(s(elem!1), s(s(s(elem!1))))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[7760, 30470, 30430, 29714])).
% 11.48/11.70 tff(30472,plain,
% 11.48/11.70 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[3614, 30471, 8598])).
% 11.48/11.70 tff(30473,plain,
% 11.48/11.70 (b(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[3652, 30472])).
% 11.48/11.70 tff(30474,plain,
% 11.48/11.70 (b(s(elem!1), s(s(s(elem!1))))),
% 11.48/11.70 inference(modus_ponens,[status(thm)],[30473, 30428])).
% 11.48/11.70 tff(30475,plain,
% 11.48/11.70 (b(elem!1, s(s(s(elem!1))))),
% 11.48/11.70 inference(unit_resolution,[status(thm)],[7796, 8598, 379])).
% 11.48/11.71 tff(30476,plain,
% 11.48/11.71 (~b(s(elem!1), s(s(s(elem!1))))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[18098, 30454, 10682, 30475, 30435])).
% 11.48/11.71 tff(30477,plain,
% 11.48/11.71 ($false),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30476, 30474])).
% 11.48/11.71 tff(30478,plain,((~(elem!1 = s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | (elem!1 = z) | b(s(s(s(s(z)))), z) | b(z, s(s(z))) | r(z, s(z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.71 tff(30479,plain,
% 11.48/11.71 (~(elem!1 = s(z))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30478, 676, 379, 10682, 133, 426, 2, 3446, 3373, 1234, 11173])).
% 11.48/11.71 tff(30480,plain,
% 11.48/11.71 (r(elem!1, s(z))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[837, 30479, 31])).
% 11.48/11.71 tff(30481,plain,
% 11.48/11.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))))),
% 11.48/11.71 inference(rewrite,[status(thm)],[])).
% 11.48/11.71 tff(30482,plain,
% 11.48/11.71 (((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))))),
% 11.48/11.71 inference(rewrite,[status(thm)],[])).
% 11.48/11.71 tff(30483,plain,
% 11.48/11.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z))))))),
% 11.48/11.71 inference(monotonicity,[status(thm)],[30482])).
% 11.48/11.71 tff(30484,plain,
% 11.48/11.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))))),
% 11.48/11.71 inference(transitivity,[status(thm)],[30483, 30481])).
% 11.48/11.71 tff(30485,plain,
% 11.48/11.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 11.48/11.71 inference(quant_inst,[status(thm)],[])).
% 11.48/11.71 tff(30486,plain,
% 11.48/11.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z))))),
% 11.48/11.71 inference(modus_ponens,[status(thm)],[30485, 30484])).
% 11.48/11.71 tff(30487,plain,
% 11.48/11.71 (~r(elem!1, s(s(s(elem!1))))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30486, 194, 183, 847, 1747])).
% 11.48/11.71 tff(30488,plain,
% 11.48/11.71 (b(elem!1, s(s(s(elem!1))))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[424, 30487, 1])).
% 11.48/11.71 tff(30489,plain,
% 11.48/11.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(z), s(s(z)))))),
% 11.48/11.71 inference(rewrite,[status(thm)],[])).
% 11.48/11.71 tff(30490,plain,
% 11.48/11.71 (((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(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))) | (~r(s(z), s(s(z)))))),
% 11.48/11.71 inference(rewrite,[status(thm)],[])).
% 11.48/11.71 tff(30491,plain,
% 11.48/11.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(z), s(s(z))))))),
% 11.48/11.71 inference(monotonicity,[status(thm)],[30490])).
% 11.48/11.71 tff(30492,plain,
% 11.48/11.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))) | (~r(s(z), s(s(z)))))),
% 11.48/11.71 inference(transitivity,[status(thm)],[30491, 30489])).
% 11.48/11.71 tff(30493,plain,
% 11.48/11.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 11.48/11.71 inference(quant_inst,[status(thm)],[])).
% 11.48/11.71 tff(30494,plain,
% 11.48/11.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z))))),
% 11.48/11.71 inference(modus_ponens,[status(thm)],[30493, 30492])).
% 11.48/11.71 tff(30495,plain,
% 11.48/11.71 (~r(s(s(s(elem!1))), elem!1)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30494, 194, 183, 847, 1747])).
% 11.48/11.71 tff(30496,plain,
% 11.48/11.71 (b(s(s(s(elem!1))), elem!1)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[230, 30495, 9])).
% 11.48/11.71 tff(30497,plain,
% 11.48/11.71 ($false),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[10845, 30496, 30488, 10682, 133])).
% 11.48/11.71 tff(30498,plain,((~r(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.71 tff(30499,plain,
% 11.48/11.71 (~r(s(z), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30498, 30480, 133, 1, 11174, 10682])).
% 11.48/11.71 tff(30500,plain,
% 11.48/11.71 (b(s(z), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[1788, 30499])).
% 11.48/11.71 tff(30501,plain,
% 11.48/11.71 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[28145, 1235, 133, 1234, 2439])).
% 11.48/11.71 tff(30502,plain,
% 11.48/11.71 (r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[1714, 30501])).
% 11.48/11.71 tff(30503,plain,
% 11.48/11.71 (~r(s(s(z)), s(z))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[18433, 30502, 2053, 8505])).
% 11.48/11.71 tff(30504,plain,
% 11.48/11.71 (b(s(s(z)), s(z))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[3778, 30503])).
% 11.48/11.71 tff(30505,plain,
% 11.48/11.71 ($false),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[16413, 391, 1235, 2439, 30504, 664])).
% 11.48/11.71 tff(30506,plain,((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.71 tff(30507,plain,
% 11.48/11.71 (~b(s(s(z)), z)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30506, 30500, 22903, 3447, 29960, 133, 1234])).
% 11.48/11.71 tff(30508,plain,
% 11.48/11.71 (r(s(s(z)), z)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[1211, 30507])).
% 11.48/11.71 tff(30509,plain,
% 11.48/11.71 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[16255, 194, 3447, 30508, 29960])).
% 11.48/11.71 tff(30510,plain,
% 11.48/11.71 (b(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[3652, 30509])).
% 11.48/11.71 tff(30511,plain,
% 11.48/11.71 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30450, 194, 3447, 30508, 29960])).
% 11.48/11.71 tff(30512,plain,
% 11.48/11.71 (b(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[1714, 30511])).
% 11.48/11.71 tff(30513,plain,
% 11.48/11.71 ($false),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[6275, 30512, 30510, 1234, 30500])).
% 11.48/11.71 tff(30514,plain,(r(z, s(z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(z)) | (~b(s(z), s(s(s(elem!1))))) | (elem!1 = z) | b(s(s(s(s(z)))), z) | b(z, s(s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.71 tff(30515,plain,
% 11.48/11.71 (r(z, s(z))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30514, 3373, 149, 1, 30423, 31, 29889, 2, 3446, 30422, 11173])).
% 11.48/11.71 tff(30516,plain,
% 11.48/11.71 (~(s(z) = elem!1)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[17233, 30515, 80])).
% 11.48/11.71 tff(30517,plain,
% 11.48/11.71 (~(elem!1 = s(z))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[172, 30516])).
% 11.48/11.71 tff(30518,plain,
% 11.48/11.71 (r(elem!1, s(z))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[837, 30517, 31])).
% 11.48/11.71 tff(30519,plain,
% 11.48/11.71 (~r(s(z), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30498, 30518, 149, 1, 11174, 30423])).
% 11.48/11.71 tff(30520,plain,
% 11.48/11.71 (b(s(z), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[1788, 30519])).
% 11.48/11.71 tff(30521,plain,
% 11.48/11.71 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[6275, 26733, 1234, 2439])).
% 11.48/11.71 tff(30522,plain,
% 11.48/11.71 (r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[1714, 30521])).
% 11.48/11.71 tff(30523,plain,
% 11.48/11.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.48/11.71 inference(rewrite,[status(thm)],[])).
% 11.48/11.71 tff(30524,plain,
% 11.48/11.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.48/11.71 inference(quant_inst,[status(thm)],[])).
% 11.48/11.71 tff(30525,plain,
% 11.48/11.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 11.48/11.71 inference(modus_ponens,[status(thm)],[30524, 30523])).
% 11.48/11.71 tff(30526,plain,
% 11.48/11.71 ($false),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30525, 194, 722, 2053, 3557, 30522])).
% 11.48/11.71 tff(30527,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.71 tff(30528,plain,
% 11.48/11.71 (~r(s(s(z)), z)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30527, 30515, 3447, 30422, 30520])).
% 11.48/11.71 tff(30529,plain,
% 11.48/11.71 (b(s(s(z)), z)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[1211, 30528])).
% 11.48/11.71 tff(30530,plain,
% 11.48/11.71 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[28145, 30529, 149, 30422, 30520])).
% 11.48/11.71 tff(30531,plain,
% 11.48/11.71 (r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[1714, 30530])).
% 11.48/11.71 tff(30532,plain,
% 11.48/11.71 (~r(s(s(z)), s(z))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[18433, 30531, 3447, 29960])).
% 11.48/11.71 tff(30533,plain,
% 11.48/11.71 (b(s(s(z)), s(z))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[3778, 30532])).
% 11.48/11.71 tff(30534,plain,
% 11.48/11.71 ($false),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[11759, 194, 1749, 2053, 1697, 8505])).
% 11.48/11.71 tff(30535,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.71 tff(30536,plain,
% 11.48/11.71 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[30535, 30531, 3447, 29960])).
% 11.48/11.71 tff(30537,plain,
% 11.48/11.71 (b(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[3652, 30536])).
% 11.48/11.71 tff(30538,plain,
% 11.48/11.71 (~r(s(z), z)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[5126, 30537, 149, 30515, 30422, 30533])).
% 11.48/11.71 tff(30539,plain,
% 11.48/11.71 (b(s(z), z)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[180, 30538])).
% 11.48/11.71 tff(30540,plain,
% 11.48/11.71 (~b(s(s(s(elem!1))), z)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[11303, 30539, 29889, 30423])).
% 11.48/11.71 tff(30541,plain,
% 11.48/11.71 (r(s(s(s(elem!1))), z)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[377, 30540])).
% 11.48/11.71 tff(30542,plain,
% 11.48/11.71 (~r(s(z), elem!1)),
% 11.48/11.71 inference(unit_resolution,[status(thm)],[17465, 30541, 11174, 30515])).
% 11.48/11.72 tff(30543,plain,
% 11.48/11.72 (b(s(z), elem!1)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[632, 30542, 30516])).
% 11.48/11.72 tff(30544,plain,
% 11.48/11.72 (~b(elem!1, z)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[5231, 30543, 149, 30539])).
% 11.48/11.72 tff(30545,plain,
% 11.48/11.72 (r(elem!1, z)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[526, 30544, 2])).
% 11.48/11.72 tff(30546,plain,
% 11.48/11.72 (~b(elem!1, s(s(s(elem!1))))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[18052, 30545, 31, 30423, 149, 30516, 30515, 9])).
% 11.48/11.72 tff(30547,plain,
% 11.48/11.72 (r(elem!1, s(s(s(elem!1))))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[424, 30546, 1])).
% 11.48/11.72 tff(30548,plain,
% 11.48/11.72 ($false),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[18041, 194, 30545, 30541, 30547, 30515])).
% 11.48/11.72 tff(30549,plain,(b(z, s(s(z))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(z)) | (elem!1 = z) | r(z, elem!1) | b(s(s(s(s(z)))), z) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.72 tff(30550,plain,
% 11.48/11.72 (b(z, s(s(z)))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[30549, 2, 31, 1, 80, 3446, 11173])).
% 11.48/11.72 tff(30551,plain,
% 11.48/11.72 (~(s(z) = elem!1)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[17233, 722, 80])).
% 11.48/11.72 tff(30552,plain,
% 11.48/11.72 (~(elem!1 = s(z))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[172, 30551])).
% 11.48/11.72 tff(30553,plain,
% 11.48/11.72 (r(elem!1, s(z))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[837, 30552, 31])).
% 11.48/11.72 tff(30554,plain,
% 11.48/11.72 (~b(elem!1, s(s(s(elem!1))))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[17700, 2282, 2053, 10682, 133, 2, 150])).
% 11.48/11.72 tff(30555,plain,
% 11.48/11.72 (r(elem!1, s(s(s(elem!1))))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[424, 30554, 1])).
% 11.48/11.72 tff(30556,plain,
% 11.48/11.72 (~b(s(s(s(elem!1))), elem!1)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[10743, 11936, 10682, 133])).
% 11.48/11.72 tff(30557,plain,
% 11.48/11.72 (r(s(s(s(elem!1))), elem!1)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[230, 30556, 9])).
% 11.48/11.72 tff(30558,plain,
% 11.48/11.72 (~r(s(z), elem!1)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[23411, 30557, 183, 30555])).
% 11.48/11.72 tff(30559,plain,
% 11.48/11.72 (b(s(z), elem!1)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[632, 30558, 150])).
% 11.48/11.72 tff(30560,plain,
% 11.48/11.72 (~b(s(z), z)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[5231, 30559, 133, 11936])).
% 11.48/11.72 tff(30561,plain,
% 11.48/11.72 (r(s(z), z)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[180, 30560])).
% 11.48/11.72 tff(30562,plain,
% 11.48/11.72 (b(s(elem!1), elem!1)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[14657, 30556, 10682, 133, 150, 2282, 2])).
% 11.48/11.72 tff(30563,plain,
% 11.48/11.72 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[14662, 30562, 30556])).
% 11.48/11.72 tff(30564,plain,
% 11.48/11.72 (~(s(s(elem!1)) = elem!1)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[451, 30563])).
% 11.48/11.72 tff(30565,plain,
% 11.48/11.72 (~b(s(s(elem!1)), elem!1)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[12771, 30559, 133, 11936])).
% 11.48/11.72 tff(30566,plain,
% 11.48/11.72 (r(s(s(elem!1)), elem!1)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[872, 30565, 30564])).
% 11.48/11.72 tff(30567,plain,
% 11.48/11.72 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[4039, 30566, 9, 30554, 30556])).
% 11.48/11.72 tff(30568,plain,
% 11.48/11.72 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[1370, 30567, 26982])).
% 11.48/11.72 tff(30569,plain,
% 11.48/11.72 (~b(z, s(s(elem!1)))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[15730, 30565, 10682, 30555, 30554, 30556, 9, 30563])).
% 11.48/11.72 tff(30570,plain,
% 11.48/11.72 (r(z, s(s(elem!1)))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[324, 30569])).
% 11.48/11.72 tff(30571,plain,
% 11.48/11.72 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[5875, 30566, 30555, 30557])).
% 11.48/11.72 tff(30572,plain,
% 11.48/11.72 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[1356, 30571, 27044])).
% 11.48/11.72 tff(30573,plain,
% 11.48/11.72 ($false),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[3432, 30572, 30570, 379, 30568, 30561])).
% 11.48/11.72 tff(30574,plain,(r(elem!1, z) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(z) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = z) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.72 tff(30575,plain,
% 11.48/11.72 (r(elem!1, z)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[30574, 30551, 30401, 149, 379, 183, 2, 1, 2053])).
% 11.48/11.72 tff(30576,plain,
% 11.48/11.72 (~r(s(z), z)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[17266, 30575, 722, 30553])).
% 11.48/11.72 tff(30577,plain,
% 11.48/11.72 (b(s(z), z)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[180, 30576])).
% 11.48/11.72 tff(30578,plain,
% 11.48/11.72 (~r(s(z), s(s(z)))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[30498, 30553, 149, 1, 183, 30401])).
% 11.48/11.72 tff(30579,plain,
% 11.48/11.72 (b(s(z), s(s(z)))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[1788, 30578])).
% 11.48/11.72 tff(30580,plain,
% 11.48/11.72 (b(s(z), s(s(s(s(z)))))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[30421, 31, 80, 183, 1, 2053, 379])).
% 11.48/11.72 tff(30581,plain,
% 11.48/11.72 (~r(s(s(z)), z)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[30527, 30579, 2053, 30580, 722])).
% 11.48/11.72 tff(30582,plain,
% 11.48/11.72 (b(s(s(z)), z)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[1211, 30581])).
% 11.48/11.72 tff(30583,plain,
% 11.48/11.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.48/11.72 inference(rewrite,[status(thm)],[])).
% 11.48/11.72 tff(30584,plain,
% 11.48/11.72 (((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.48/11.72 inference(rewrite,[status(thm)],[])).
% 11.48/11.72 tff(30585,plain,
% 11.48/11.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 11.48/11.72 inference(monotonicity,[status(thm)],[30584])).
% 11.48/11.72 tff(30586,plain,
% 11.48/11.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.48/11.72 inference(transitivity,[status(thm)],[30585, 30583])).
% 11.48/11.72 tff(30587,plain,
% 11.48/11.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 11.48/11.72 inference(quant_inst,[status(thm)],[])).
% 11.48/11.72 tff(30588,plain,
% 11.48/11.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 11.48/11.72 inference(modus_ponens,[status(thm)],[30587, 30586])).
% 11.48/11.72 tff(30589,plain,
% 11.48/11.72 ($false),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[30588, 391, 149, 30582, 30579, 30577, 15045])).
% 11.48/11.72 tff(30590,plain,((~r(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | b(elem!1, s(z)) | (~b(s(z), s(s(s(elem!1))))) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.48/11.72 tff(30591,plain,
% 11.48/11.72 (~r(z, s(z))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[30590, 30550, 3447, 1, 11174, 31, 29889, 2, 80])).
% 11.48/11.72 tff(30592,plain,
% 11.48/11.72 (b(z, s(z))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[678, 30591])).
% 11.48/11.72 tff(30593,plain,
% 11.48/11.72 (~r(elem!1, s(z))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[30498, 1747, 133, 1, 11174, 10682])).
% 11.48/11.72 tff(30594,plain,
% 11.48/11.72 (elem!1 = s(z)),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[837, 30593, 31])).
% 11.48/11.72 tff(30595,plain,
% 11.48/11.72 (~b(s(s(s(s(z)))), s(z))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[11177, 30594, 11173])).
% 11.48/11.72 tff(30596,plain,
% 11.48/11.72 (r(s(s(s(s(z)))), s(z))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[749, 30595])).
% 11.48/11.72 tff(30597,plain,
% 11.48/11.72 (s(elem!1) = s(s(z))),
% 11.48/11.72 inference(monotonicity,[status(thm)],[30594])).
% 11.48/11.72 tff(30598,plain,
% 11.48/11.72 (s(s(elem!1)) = s(s(s(z)))),
% 11.48/11.72 inference(monotonicity,[status(thm)],[30597])).
% 11.48/11.72 tff(30599,plain,
% 11.48/11.72 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 11.48/11.72 inference(monotonicity,[status(thm)],[30598])).
% 11.48/11.72 tff(30600,plain,
% 11.48/11.72 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.72 inference(monotonicity,[status(thm)],[30599])).
% 11.48/11.72 tff(30601,plain,
% 11.48/11.72 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 11.48/11.72 inference(monotonicity,[status(thm)],[30597])).
% 11.48/11.72 tff(30602,plain,
% 11.48/11.72 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.72 inference(transitivity,[status(thm)],[30601, 30600])).
% 11.48/11.72 tff(30603,plain,
% 11.48/11.72 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 11.48/11.72 inference(monotonicity,[status(thm)],[30597])).
% 11.48/11.72 tff(30604,plain,
% 11.48/11.72 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(elem!1))))),
% 11.48/11.72 inference(transitivity,[status(thm)],[30603, 10700])).
% 11.48/11.72 tff(30605,plain,
% 11.48/11.72 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 11.48/11.72 inference(symmetry,[status(thm)],[30604])).
% 11.48/11.72 tff(30606,plain,
% 11.48/11.72 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 11.48/11.72 inference(monotonicity,[status(thm)],[30605])).
% 11.48/11.72 tff(30607,plain,
% 11.48/11.72 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.48/11.72 inference(modus_ponens,[status(thm)],[1397, 30606])).
% 11.48/11.72 tff(30608,plain,
% 11.48/11.72 (s(z) = elem!1),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[172, 30594])).
% 11.48/11.72 tff(30609,plain,
% 11.48/11.72 (b(z, s(s(s(s(z)))))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[11318, 30594, 2, 676])).
% 11.48/11.72 tff(30610,plain,
% 11.48/11.72 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[10673, 2405, 723, 1747])).
% 11.48/11.72 tff(30611,plain,
% 11.48/11.72 (b(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[1714, 30610])).
% 11.48/11.72 tff(30612,plain,
% 11.48/11.72 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[15550, 30611, 15045, 1686])).
% 11.48/11.72 tff(30613,plain,
% 11.48/11.72 (r(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.72 inference(unit_resolution,[status(thm)],[3652, 30612])).
% 11.48/11.72 tff(30614,plain,
% 11.48/11.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 11.48/11.72 inference(rewrite,[status(thm)],[])).
% 11.48/11.72 tff(30615,plain,
% 11.48/11.72 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 11.48/11.72 inference(rewrite,[status(thm)],[])).
% 11.48/11.72 tff(30616,plain,
% 11.48/11.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))))),
% 11.48/11.72 inference(monotonicity,[status(thm)],[30615])).
% 11.48/11.72 tff(30617,plain,
% 11.48/11.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 11.48/11.72 inference(transitivity,[status(thm)],[30616, 30614])).
% 11.48/11.72 tff(30618,plain,
% 11.48/11.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 11.48/11.73 inference(quant_inst,[status(thm)],[])).
% 11.48/11.73 tff(30619,plain,
% 11.48/11.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))),
% 11.48/11.73 inference(modus_ponens,[status(thm)],[30618, 30617])).
% 11.48/11.73 tff(30620,plain,
% 11.48/11.73 ($false),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30619, 194, 30613, 723, 1747, 2405])).
% 11.48/11.73 tff(30621,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.73 tff(30622,plain,
% 11.48/11.73 (~r(s(s(z)), s(z))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30621, 30596, 1747, 15045, 30609])).
% 11.48/11.73 tff(30623,plain,
% 11.48/11.73 (b(s(s(z)), s(z))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[3778, 30622])).
% 11.48/11.73 tff(30624,plain,
% 11.48/11.73 (b(s(elem!1), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[29583, 30623, 30608])).
% 11.48/11.73 tff(30625,plain,
% 11.48/11.73 (~b(s(s(s(elem!1))), s(elem!1))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30462, 30624, 379, 10682, 22903])).
% 11.48/11.73 tff(30626,plain,
% 11.48/11.73 (r(s(s(s(elem!1))), s(elem!1))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[588, 30625, 30607])).
% 11.48/11.73 tff(30627,plain,
% 11.48/11.73 (r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.73 inference(modus_ponens,[status(thm)],[30626, 30602])).
% 11.48/11.73 tff(30628,plain,
% 11.48/11.73 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[9076, 30627, 1747, 30596])).
% 11.48/11.73 tff(30629,plain,
% 11.48/11.73 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 11.48/11.73 inference(monotonicity,[status(thm)],[30597])).
% 11.48/11.73 tff(30630,plain,
% 11.48/11.73 ((~r(z, s(elem!1))) <=> (~r(z, s(s(z))))),
% 11.48/11.73 inference(monotonicity,[status(thm)],[30629])).
% 11.48/11.73 tff(30631,plain,
% 11.48/11.73 (~b(s(s(s(s(z)))), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[9614, 30608, 30595])).
% 11.48/11.73 tff(30632,plain,
% 11.48/11.73 (~b(s(z), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[8805, 30594])).
% 11.48/11.73 tff(30633,plain,
% 11.48/11.73 (~(s(s(s(s(z)))) = elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[8916, 30632, 1234])).
% 11.48/11.73 tff(30634,plain,
% 11.48/11.73 (r(s(s(s(s(z)))), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[762, 30633, 30631])).
% 11.48/11.73 tff(30635,plain,
% 11.48/11.73 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 11.48/11.73 inference(monotonicity,[status(thm)],[30597])).
% 11.48/11.73 tff(30636,plain,
% 11.48/11.73 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 11.48/11.73 inference(symmetry,[status(thm)],[30635])).
% 11.48/11.73 tff(30637,plain,
% 11.48/11.73 (b(z, s(elem!1))),
% 11.48/11.73 inference(modus_ponens,[status(thm)],[15045, 30636])).
% 11.48/11.73 tff(30638,plain,
% 11.48/11.73 (~b(elem!1, z)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[6555, 30624, 133, 30637])).
% 11.48/11.73 tff(30639,plain,
% 11.48/11.73 (r(elem!1, z)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[526, 30638, 2])).
% 11.48/11.73 tff(30640,plain,
% 11.48/11.73 (~r(z, s(elem!1))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[6087, 30639, 3447, 30634])).
% 11.48/11.73 tff(30641,plain,
% 11.48/11.73 (~r(z, s(s(z)))),
% 11.48/11.73 inference(modus_ponens,[status(thm)],[30640, 30630])).
% 11.48/11.73 tff(30642,plain,
% 11.48/11.73 (~r(s(z), s(s(z)))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30498, 1810, 133, 1, 183, 10682])).
% 11.48/11.73 tff(30643,plain,
% 11.48/11.73 (b(s(z), s(s(z)))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[1788, 30642])).
% 11.48/11.73 tff(30644,plain,
% 11.48/11.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.48/11.73 inference(rewrite,[status(thm)],[])).
% 11.48/11.73 tff(30645,plain,
% 11.48/11.73 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.48/11.73 inference(rewrite,[status(thm)],[])).
% 11.48/11.73 tff(30646,plain,
% 11.48/11.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 11.48/11.73 inference(monotonicity,[status(thm)],[30645])).
% 11.48/11.73 tff(30647,plain,
% 11.48/11.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.48/11.73 inference(transitivity,[status(thm)],[30646, 30644])).
% 11.48/11.73 tff(30648,plain,
% 11.48/11.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 11.48/11.73 inference(quant_inst,[status(thm)],[])).
% 11.48/11.73 tff(30649,plain,
% 11.48/11.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 11.48/11.73 inference(modus_ponens,[status(thm)],[30648, 30647])).
% 11.48/11.73 tff(30650,plain,
% 11.48/11.73 ($false),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30649, 391, 3823, 1652, 2439, 664, 15045])).
% 11.48/11.73 tff(30651,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.73 tff(30652,plain,
% 11.48/11.73 (~b(s(s(s(s(z)))), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30651, 30643, 3823, 664, 15045])).
% 11.48/11.73 tff(30653,plain,
% 11.48/11.73 (r(elem!1, z)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30574, 1496, 10682, 133, 379, 183, 2, 1, 2053])).
% 11.48/11.73 tff(30654,plain,
% 11.48/11.73 (~b(s(s(s(elem!1))), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[10845, 448, 10682, 133])).
% 11.48/11.73 tff(30655,plain,
% 11.48/11.73 (r(s(s(s(elem!1))), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[230, 30654, 127])).
% 11.48/11.73 tff(30656,plain,
% 11.48/11.73 (~r(s(s(s(elem!1))), z)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[27619, 326, 233, 530])).
% 11.48/11.73 tff(30657,plain,
% 11.48/11.73 (b(s(s(s(elem!1))), z)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[377, 30656])).
% 11.48/11.73 tff(30658,plain,
% 11.48/11.73 (~r(s(z), z)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[855, 326, 847, 530])).
% 11.48/11.73 tff(30659,plain,
% 11.48/11.73 (b(s(z), z)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[180, 30658])).
% 11.48/11.73 tff(30660,plain,
% 11.48/11.73 ($false),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[11303, 30659, 30657, 379, 10682])).
% 11.48/11.73 tff(30661,plain,((~r(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.73 tff(30662,plain,
% 11.48/11.73 (~r(z, s(s(elem!1)))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30661, 30655, 10682, 847, 530, 379])).
% 11.48/11.73 tff(30663,plain,
% 11.48/11.73 (b(z, s(s(elem!1)))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[324, 30662])).
% 11.48/11.73 tff(30664,plain,
% 11.48/11.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 11.48/11.73 inference(rewrite,[status(thm)],[])).
% 11.48/11.73 tff(30665,plain,
% 11.48/11.73 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 11.48/11.73 inference(rewrite,[status(thm)],[])).
% 11.48/11.73 tff(30666,plain,
% 11.48/11.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 11.48/11.73 inference(monotonicity,[status(thm)],[30665])).
% 11.48/11.73 tff(30667,plain,
% 11.48/11.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 11.48/11.73 inference(transitivity,[status(thm)],[30666, 30664])).
% 11.48/11.73 tff(30668,plain,
% 11.48/11.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 11.48/11.73 inference(quant_inst,[status(thm)],[])).
% 11.48/11.73 tff(30669,plain,
% 11.48/11.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 11.48/11.73 inference(modus_ponens,[status(thm)],[30668, 30667])).
% 11.48/11.73 tff(30670,plain,
% 11.48/11.73 ($false),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30669, 391, 448, 2439, 8498, 664, 15045])).
% 11.48/11.73 tff(30671,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.73 tff(30672,plain,
% 11.48/11.73 (~b(s(s(z)), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30671, 448, 2439, 664, 15045])).
% 11.48/11.73 tff(30673,plain,
% 11.48/11.73 (~b(s(s(s(s(z)))), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30651, 2439, 3823, 664, 15045])).
% 11.48/11.73 tff(30674,plain,
% 11.48/11.73 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.73 inference(symmetry,[status(thm)],[14383])).
% 11.48/11.73 tff(30675,plain,
% 11.48/11.73 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 11.48/11.73 inference(monotonicity,[status(thm)],[30674])).
% 11.48/11.73 tff(30676,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 11.48/11.73 tff(30677,plain,
% 11.48/11.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.48/11.73 inference(modus_ponens,[status(thm)],[30676, 30675])).
% 11.48/11.73 tff(30678,plain,
% 11.48/11.73 ($false),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[3823, 30677])).
% 11.48/11.73 tff(30679,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.48/11.73 tff(30680,plain,
% 11.48/11.73 (~(s(s(s(s(z)))) = elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[30679, 30672, 3823])).
% 11.48/11.73 tff(30681,plain,
% 11.48/11.73 (r(s(s(s(s(z)))), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[762, 30680, 30673])).
% 11.48/11.73 tff(30682,plain,
% 11.48/11.73 (~r(s(s(z)), elem!1)),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[20852, 30681, 1697, 530])).
% 11.48/11.73 tff(30683,plain,
% 11.48/11.73 (s(s(z)) = elem!1),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[4730, 30682, 30672])).
% 11.48/11.73 tff(30684,plain,
% 11.48/11.73 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.48/11.73 inference(unit_resolution,[status(thm)],[4584, 30683, 121])).
% 11.48/11.73 tff(30685,plain,
% 11.48/11.73 (s(s(s(z))) = s(elem!1)),
% 11.48/11.73 inference(monotonicity,[status(thm)],[30683])).
% 11.48/11.73 tff(30686,plain,
% 11.48/11.73 (s(s(s(s(z)))) = s(s(elem!1))),
% 11.48/11.73 inference(monotonicity,[status(thm)],[30685])).
% 11.48/11.73 tff(30687,plain,
% 11.48/11.73 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 11.48/11.74 inference(monotonicity,[status(thm)],[30686])).
% 11.48/11.74 tff(30688,plain,
% 11.48/11.74 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 11.48/11.74 inference(monotonicity,[status(thm)],[30687])).
% 11.48/11.74 tff(30689,plain,
% 11.48/11.74 (~b(s(s(elem!1)), elem!1)),
% 11.48/11.74 inference(modus_ponens,[status(thm)],[30673, 30688])).
% 11.48/11.74 tff(30690,plain,
% 11.48/11.74 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 11.48/11.74 inference(monotonicity,[status(thm)],[30686])).
% 11.48/11.74 tff(30691,plain,
% 11.48/11.74 (r(s(s(elem!1)), elem!1)),
% 11.48/11.74 inference(modus_ponens,[status(thm)],[30681, 30690])).
% 11.48/11.74 tff(30692,plain,
% 11.48/11.74 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[4878, 194, 530, 30655, 30691])).
% 11.48/11.74 tff(30693,plain,
% 11.48/11.74 ($false),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[26900, 30692, 30689, 10682, 530, 30655, 30684, 30663])).
% 11.48/11.74 tff(30694,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (s(z) = s(elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.74 tff(30695,plain,
% 11.48/11.74 (~b(elem!1, s(s(s(elem!1))))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[30694, 30653, 10682, 118, 1697, 3823, 30643, 664, 15045, 1810, 379, 9, 133])).
% 11.48/11.74 tff(30696,plain,
% 11.48/11.74 (~r(s(z), s(s(z)))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[30498, 847, 133, 1, 183, 10682])).
% 11.48/11.74 tff(30697,plain,
% 11.48/11.74 (b(s(z), s(s(z)))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[1788, 30696])).
% 11.48/11.74 tff(30698,plain,
% 11.48/11.74 (~r(z, s(s(s(s(z)))))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[17062, 182, 530, 847])).
% 11.48/11.74 tff(30699,plain,
% 11.48/11.74 (b(z, s(s(s(s(z)))))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[800, 30698])).
% 11.48/11.74 tff(30700,plain,
% 11.48/11.74 (~b(s(s(s(s(z)))), s(z))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[10478, 30699, 1234, 664])).
% 11.48/11.74 tff(30701,plain,
% 11.48/11.74 (r(s(s(s(s(z)))), s(z))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[749, 30700])).
% 11.48/11.74 tff(30702,plain,
% 11.48/11.74 (~r(s(s(s(s(z)))), elem!1)),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[15864, 30701, 847, 182])).
% 11.48/11.74 tff(30703,plain,
% 11.48/11.74 (s(s(s(s(z)))) = elem!1),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[762, 30702, 1549])).
% 11.48/11.74 tff(30704,plain,
% 11.48/11.74 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 11.48/11.74 inference(monotonicity,[status(thm)],[30703])).
% 11.48/11.74 tff(30705,plain,
% 11.48/11.74 (b(s(s(z)), elem!1)),
% 11.48/11.74 inference(modus_ponens,[status(thm)],[3823, 30704])).
% 11.48/11.74 tff(30706,plain,
% 11.48/11.74 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[717, 30703])).
% 11.48/11.74 tff(30707,plain,
% 11.48/11.74 (b(s(s(elem!1)), elem!1)),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[15730, 30706, 10682, 410, 4028, 168, 127, 3927])).
% 11.48/11.74 tff(30708,plain,
% 11.48/11.74 (~r(s(s(elem!1)), s(z))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[3996, 30707, 133, 847, 3927, 182])).
% 11.48/11.74 tff(30709,plain,
% 11.48/11.74 (b(s(s(elem!1)), s(z))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[362, 30708])).
% 11.48/11.74 tff(30710,plain,
% 11.48/11.74 ($false),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[26458, 391, 30709, 3927, 2439, 30705, 664])).
% 11.48/11.74 tff(30711,plain,((~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~r(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(s(z)))), elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.74 tff(30712,plain,
% 11.48/11.74 (~r(s(z), z)),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[30711, 3927, 2439, 664, 3823, 133, 847, 10682, 410, 4028, 168, 127, 1549, 1234, 530])).
% 11.48/11.74 tff(30713,plain,
% 11.48/11.74 (b(s(z), z)),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[180, 30712])).
% 11.48/11.74 tff(30714,plain,
% 11.48/11.74 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 11.48/11.74 inference(monotonicity,[status(thm)],[465])).
% 11.48/11.74 tff(30715,plain,
% 11.48/11.74 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.48/11.74 inference(symmetry,[status(thm)],[30714])).
% 11.48/11.74 tff(30716,plain,
% 11.48/11.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 11.48/11.74 inference(rewrite,[status(thm)],[])).
% 11.48/11.74 tff(30717,plain,
% 11.48/11.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 11.48/11.74 inference(quant_inst,[status(thm)],[])).
% 11.48/11.74 tff(30718,plain,
% 11.48/11.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 11.48/11.74 inference(modus_ponens,[status(thm)],[30717, 30716])).
% 11.48/11.74 tff(30719,plain,
% 11.48/11.74 (~r(s(s(s(s(z)))), s(elem!1))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[30718, 194, 530, 27476, 13137])).
% 11.48/11.74 tff(30720,plain,
% 11.48/11.74 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[2136, 42, 30719])).
% 11.48/11.74 tff(30721,plain,
% 11.48/11.74 (b(s(s(s(s(z)))), s(elem!1))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[30720, 13136])).
% 11.48/11.74 tff(30722,plain,
% 11.48/11.74 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.48/11.74 inference(modus_ponens,[status(thm)],[30721, 30715])).
% 11.48/11.74 tff(30723,plain,
% 11.48/11.74 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 11.48/11.74 inference(monotonicity,[status(thm)],[465])).
% 11.48/11.74 tff(30724,plain,
% 11.48/11.74 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.48/11.74 inference(symmetry,[status(thm)],[30723])).
% 11.48/11.74 tff(30725,plain,
% 11.48/11.74 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.48/11.74 inference(monotonicity,[status(thm)],[30724])).
% 11.48/11.74 tff(30726,plain,
% 11.48/11.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 11.48/11.74 inference(rewrite,[status(thm)],[])).
% 11.48/11.74 tff(30727,plain,
% 11.48/11.74 (((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 11.48/11.74 inference(rewrite,[status(thm)],[])).
% 11.48/11.74 tff(30728,plain,
% 11.48/11.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 11.48/11.74 inference(monotonicity,[status(thm)],[30727])).
% 11.48/11.74 tff(30729,plain,
% 11.48/11.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 11.48/11.74 inference(transitivity,[status(thm)],[30728, 30726])).
% 11.48/11.74 tff(30730,plain,
% 11.48/11.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 11.48/11.74 inference(quant_inst,[status(thm)],[])).
% 11.48/11.74 tff(30731,plain,
% 11.48/11.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 11.48/11.74 inference(modus_ponens,[status(thm)],[30730, 30729])).
% 11.48/11.74 tff(30732,plain,
% 11.48/11.74 (~r(s(elem!1), s(s(s(s(z)))))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[30731, 194, 530, 27476, 13137])).
% 11.48/11.74 tff(30733,plain,
% 11.48/11.74 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.48/11.74 inference(modus_ponens,[status(thm)],[30732, 30725])).
% 11.48/11.74 tff(30734,plain,
% 11.48/11.74 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[15351, 30733, 16058])).
% 11.48/11.74 tff(30735,plain,
% 11.48/11.74 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[17481, 30734, 10682, 590, 379])).
% 11.48/11.74 tff(30736,plain,
% 11.48/11.74 ($false),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[30735, 30722])).
% 11.48/11.74 tff(30737,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~r(elem!1, z)) | b(s(s(s(s(z)))), elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.74 tff(30738,plain,
% 11.48/11.74 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[30737, 30713, 10682, 379, 530, 1549, 4486, 3843])).
% 11.48/11.74 tff(30739,plain,
% 11.48/11.74 (~(s(s(elem!1)) = elem!1)),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[451, 30738])).
% 11.48/11.74 tff(30740,plain,
% 11.48/11.74 (~(elem!1 = s(s(elem!1)))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[1292, 30739])).
% 11.48/11.74 tff(30741,plain,
% 11.48/11.74 (b(s(s(elem!1)), elem!1)),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[15730, 30738, 10682, 410, 4028, 168, 127, 3927])).
% 11.48/11.74 tff(30742,plain,
% 11.48/11.74 (~b(elem!1, s(s(elem!1)))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[3979, 30741, 133, 3927])).
% 11.48/11.74 tff(30743,plain,
% 11.48/11.74 (r(elem!1, s(s(elem!1)))),
% 11.48/11.74 inference(unit_resolution,[status(thm)],[1307, 30742, 30740])).
% 11.48/11.74 tff(30744,plain,
% 11.48/11.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.48/11.74 inference(rewrite,[status(thm)],[])).
% 11.48/11.74 tff(30745,plain,
% 11.48/11.74 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.48/11.74 inference(rewrite,[status(thm)],[])).
% 11.48/11.74 tff(30746,plain,
% 11.48/11.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 11.48/11.74 inference(monotonicity,[status(thm)],[30745])).
% 11.48/11.74 tff(30747,plain,
% 11.48/11.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.48/11.74 inference(transitivity,[status(thm)],[30746, 30744])).
% 11.48/11.74 tff(30748,plain,
% 11.48/11.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 11.48/11.75 inference(quant_inst,[status(thm)],[])).
% 11.48/11.75 tff(30749,plain,
% 11.48/11.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 11.48/11.75 inference(modus_ponens,[status(thm)],[30748, 30747])).
% 11.48/11.75 tff(30750,plain,
% 11.48/11.75 ($false),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[30749, 391, 10682, 973, 1374, 379, 590])).
% 11.48/11.75 tff(30751,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.75 tff(30752,plain,
% 11.48/11.75 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[30751, 30741, 10682, 379, 30713])).
% 11.48/11.75 tff(30753,plain,
% 11.48/11.75 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[1370, 30752, 15838])).
% 11.48/11.75 tff(30754,plain,
% 11.48/11.75 (~r(s(s(elem!1)), s(z))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[4159, 30753, 410, 30743])).
% 11.48/11.75 tff(30755,plain,
% 11.48/11.75 (b(s(s(elem!1)), s(z))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[362, 30754])).
% 11.48/11.75 tff(30756,plain,
% 11.48/11.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))))),
% 11.48/11.75 inference(rewrite,[status(thm)],[])).
% 11.48/11.75 tff(30757,plain,
% 11.48/11.75 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))))),
% 11.48/11.75 inference(rewrite,[status(thm)],[])).
% 11.48/11.75 tff(30758,plain,
% 11.48/11.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))))),
% 11.48/11.75 inference(monotonicity,[status(thm)],[30757])).
% 11.48/11.75 tff(30759,plain,
% 11.48/11.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))))),
% 11.48/11.75 inference(transitivity,[status(thm)],[30758, 30756])).
% 11.48/11.75 tff(30760,plain,
% 11.48/11.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 11.48/11.75 inference(quant_inst,[status(thm)],[])).
% 11.48/11.75 tff(30761,plain,
% 11.48/11.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))),
% 11.48/11.75 inference(modus_ponens,[status(thm)],[30760, 30759])).
% 11.48/11.75 tff(30762,plain,
% 11.48/11.75 ($false),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[30761, 391, 30755, 3927, 3823, 2439, 664])).
% 11.48/11.75 tff(30763,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | b(elem!1, s(s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, z)) | b(s(s(s(s(z)))), elem!1) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.75 tff(30764,plain,
% 11.48/11.75 (~b(z, s(s(elem!1)))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[30763, 168, 2439, 664, 410, 10682, 379, 133, 4028, 3823, 127, 530, 1549, 3843, 847, 1234])).
% 11.48/11.75 tff(30765,plain,
% 11.48/11.75 (r(z, s(s(elem!1)))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[324, 30764])).
% 11.48/11.75 tff(30766,plain,
% 11.48/11.75 (~r(s(s(s(elem!1))), z)),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[27619, 30765, 4486, 530])).
% 11.48/11.75 tff(30767,plain,
% 11.48/11.75 (b(s(s(s(elem!1))), z)),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[377, 30766])).
% 11.48/11.75 tff(30768,plain,
% 11.48/11.75 (~r(s(z), z)),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[855, 30765, 847, 530])).
% 11.48/11.75 tff(30769,plain,
% 11.48/11.75 (b(s(z), z)),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[180, 30768])).
% 11.48/11.75 tff(30770,plain,
% 11.48/11.75 ($false),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[11303, 30769, 30767, 379, 10682])).
% 11.48/11.75 tff(30771,plain,(b(s(s(s(elem!1))), elem!1) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(s(z)))), elem!1) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.75 tff(30772,plain,
% 11.48/11.75 (b(s(s(s(elem!1))), elem!1)),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[30771, 6124, 10682, 847, 530, 30697, 664, 379, 133, 4028, 3823, 9, 1549, 3363, 1234])).
% 11.48/11.75 tff(30773,plain,
% 11.48/11.75 (~r(z, s(s(elem!1)))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[855, 182, 847, 530])).
% 11.48/11.75 tff(30774,plain,
% 11.48/11.75 (b(z, s(s(elem!1)))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[324, 30773])).
% 11.48/11.75 tff(30775,plain,
% 11.48/11.75 (~b(s(s(elem!1)), s(z))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[26460, 30705, 2439, 30774, 664])).
% 11.48/11.75 tff(30776,plain,
% 11.48/11.75 (r(s(s(elem!1)), s(z))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[362, 30775])).
% 11.48/11.75 tff(30777,plain,
% 11.48/11.75 (~r(s(z), elem!1)),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[2429, 30701, 1697, 2405])).
% 11.48/11.75 tff(30778,plain,
% 11.48/11.75 (b(s(z), elem!1)),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[632, 30777, 150])).
% 11.48/11.75 tff(30779,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 11.48/11.75 tff(30780,plain,
% 11.48/11.75 (r(s(elem!1), elem!1)),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[2168, 7464, 2163])).
% 11.48/11.75 tff(30781,plain,
% 11.48/11.75 (b(elem!1, s(s(elem!1)))),
% 11.48/11.75 inference(unit_resolution,[status(thm)],[1307, 1293, 30779])).
% 11.48/11.75 tff(30782,plain,
% 11.48/11.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 11.48/11.75 inference(rewrite,[status(thm)],[])).
% 11.48/11.75 tff(30783,plain,
% 11.48/11.75 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 11.48/11.75 inference(rewrite,[status(thm)],[])).
% 11.48/11.75 tff(30784,plain,
% 11.48/11.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 11.48/11.76 inference(monotonicity,[status(thm)],[30783])).
% 11.48/11.76 tff(30785,plain,
% 11.48/11.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 11.48/11.76 inference(transitivity,[status(thm)],[30784, 30782])).
% 11.48/11.76 tff(30786,plain,
% 11.48/11.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 11.48/11.76 inference(quant_inst,[status(thm)],[])).
% 11.48/11.76 tff(30787,plain,
% 11.48/11.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))),
% 11.48/11.76 inference(modus_ponens,[status(thm)],[30786, 30785])).
% 11.48/11.76 tff(30788,plain,
% 11.48/11.76 ($false),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[30787, 391, 133, 644, 1294, 1037, 590])).
% 11.48/11.76 tff(30789,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.76 tff(30790,plain,
% 11.48/11.76 (~b(s(s(elem!1)), s(elem!1))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[30789, 590, 644, 1294, 133])).
% 11.48/11.76 tff(30791,plain,
% 11.48/11.76 (r(s(s(elem!1)), s(elem!1))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[1135, 30790, 265])).
% 11.48/11.76 tff(30792,plain,
% 11.48/11.76 (~r(s(s(elem!1)), elem!1)),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[7930, 30791, 530, 485])).
% 11.48/11.76 tff(30793,plain,
% 11.48/11.76 (b(s(s(elem!1)), elem!1)),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[872, 30792, 249])).
% 11.48/11.76 tff(30794,plain,
% 11.48/11.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 11.48/11.76 inference(rewrite,[status(thm)],[])).
% 11.48/11.76 tff(30795,plain,
% 11.48/11.76 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 11.48/11.76 inference(rewrite,[status(thm)],[])).
% 11.48/11.76 tff(30796,plain,
% 11.48/11.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))))),
% 11.48/11.76 inference(monotonicity,[status(thm)],[30795])).
% 11.48/11.76 tff(30797,plain,
% 11.48/11.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)))),
% 11.48/11.76 inference(transitivity,[status(thm)],[30796, 30794])).
% 11.48/11.76 tff(30798,plain,
% 11.48/11.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 11.48/11.76 inference(quant_inst,[status(thm)],[])).
% 11.48/11.76 tff(30799,plain,
% 11.48/11.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))),
% 11.48/11.76 inference(modus_ponens,[status(thm)],[30798, 30797])).
% 11.48/11.76 tff(30800,plain,
% 11.48/11.76 ($false),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[30799, 391, 133, 30793, 644, 1294, 590])).
% 11.48/11.76 tff(30801,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.76 tff(30802,plain,
% 11.48/11.76 (~b(s(z), z)),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[30801, 30781, 644, 133, 249, 530, 30780])).
% 11.48/11.76 tff(30803,plain,
% 11.48/11.76 (r(s(z), z)),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[180, 30802])).
% 11.48/11.76 tff(30804,plain,
% 11.48/11.76 (~r(z, s(z))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[17266, 30803, 530, 847])).
% 11.48/11.76 tff(30805,plain,
% 11.48/11.76 (b(z, s(z))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[678, 30804])).
% 11.48/11.76 tff(30806,plain,
% 11.48/11.76 (~r(z, s(s(elem!1)))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[855, 30803, 530, 847])).
% 11.48/11.76 tff(30807,plain,
% 11.48/11.76 (b(z, s(s(elem!1)))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[324, 30806])).
% 11.48/11.76 tff(30808,plain,
% 11.48/11.76 (~b(s(s(elem!1)), elem!1)),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[3979, 30807, 133, 30781])).
% 11.48/11.76 tff(30809,plain,
% 11.48/11.76 (r(s(s(elem!1)), elem!1)),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[872, 30808, 249])).
% 11.48/11.76 tff(30810,plain,
% 11.48/11.76 (~r(s(s(elem!1)), s(elem!1))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[7930, 30809, 530, 30780])).
% 11.48/11.76 tff(30811,plain,
% 11.48/11.76 (b(s(s(elem!1)), s(elem!1))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[1135, 30810, 265])).
% 11.48/11.76 tff(30812,plain,
% 11.48/11.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 11.48/11.76 inference(rewrite,[status(thm)],[])).
% 11.48/11.76 tff(30813,plain,
% 11.48/11.76 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 11.48/11.76 inference(rewrite,[status(thm)],[])).
% 11.48/11.76 tff(30814,plain,
% 11.48/11.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 11.48/11.76 inference(monotonicity,[status(thm)],[30813])).
% 11.48/11.76 tff(30815,plain,
% 11.48/11.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 11.48/11.76 inference(transitivity,[status(thm)],[30814, 30812])).
% 11.48/11.76 tff(30816,plain,
% 11.48/11.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 11.48/11.76 inference(quant_inst,[status(thm)],[])).
% 11.48/11.76 tff(30817,plain,
% 11.48/11.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))),
% 11.48/11.76 inference(modus_ponens,[status(thm)],[30816, 30815])).
% 11.48/11.76 tff(30818,plain,
% 11.48/11.76 ($false),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[30817, 391, 133, 644, 30781, 30811, 30805])).
% 11.48/11.76 tff(30819,plain,((s(s(elem!1)) = elem!1) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | r(elem!1, s(s(elem!1))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.48/11.76 tff(30820,plain,
% 11.48/11.76 (b(s(elem!1), elem!1)),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[30819, 30779, 133, 847, 530, 644, 5625])).
% 11.48/11.76 tff(30821,plain,
% 11.48/11.76 (~b(s(s(s(elem!1))), s(elem!1))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[30462, 30820, 379, 10682, 664])).
% 11.48/11.76 tff(30822,plain,
% 11.48/11.76 (b(elem!1, s(s(elem!1)))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[1307, 30779, 6460])).
% 11.48/11.76 tff(30823,plain,
% 11.48/11.76 (~r(s(s(s(elem!1))), s(elem!1))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[15596, 30822, 133, 270, 900, 5625, 3927, 410])).
% 11.48/11.76 tff(30824,plain,
% 11.48/11.76 ($false),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[588, 30823, 30821, 279])).
% 11.48/11.76 tff(30825,plain,(r(elem!1, s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.76 tff(30826,plain,
% 11.48/11.76 (r(elem!1, s(s(elem!1)))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[30825, 30706, 133, 315, 900, 30774, 410, 379, 10682, 664, 847, 530, 30778])).
% 11.48/11.76 tff(30827,plain,
% 11.48/11.76 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[4159, 30826, 410, 30776])).
% 11.48/11.76 tff(30828,plain,
% 11.48/11.76 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[1370, 30827, 297])).
% 11.48/11.76 tff(30829,plain,
% 11.48/11.76 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[12932, 30828, 10682, 30774])).
% 11.48/11.76 tff(30830,plain,
% 11.48/11.76 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[1356, 30829, 315])).
% 11.48/11.76 tff(30831,plain,
% 11.48/11.76 (~(s(s(elem!1)) = elem!1)),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[451, 30706])).
% 11.48/11.76 tff(30832,plain,
% 11.48/11.76 (~b(s(s(elem!1)), elem!1)),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[3996, 30776, 133, 847, 182, 30774])).
% 11.48/11.76 tff(30833,plain,
% 11.48/11.76 (r(s(s(elem!1)), elem!1)),
% 11.48/11.76 inference(unit_resolution,[status(thm)],[872, 30832, 30831])).
% 11.48/11.76 tff(30834,plain,
% 11.48/11.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 11.48/11.76 inference(rewrite,[status(thm)],[])).
% 11.48/11.76 tff(30835,plain,
% 11.48/11.76 (((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 11.48/11.76 inference(rewrite,[status(thm)],[])).
% 11.48/11.76 tff(30836,plain,
% 11.48/11.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 11.48/11.77 inference(monotonicity,[status(thm)],[30835])).
% 11.48/11.77 tff(30837,plain,
% 11.48/11.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 11.48/11.77 inference(transitivity,[status(thm)],[30836, 30834])).
% 11.48/11.77 tff(30838,plain,
% 11.48/11.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 11.48/11.77 inference(quant_inst,[status(thm)],[])).
% 11.48/11.77 tff(30839,plain,
% 11.48/11.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 11.48/11.77 inference(modus_ponens,[status(thm)],[30838, 30837])).
% 11.48/11.77 tff(30840,plain,
% 11.48/11.77 ($false),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[30839, 194, 30833, 410, 183, 30830])).
% 11.48/11.77 tff(30841,plain,((~r(s(z), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(s(s(s(s(z)))), elem!1) | (s(z) = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.77 tff(30842,plain,
% 11.48/11.77 (~r(s(z), z)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[30841, 6124, 183, 10682, 26982, 133, 30772, 379, 664, 847, 530, 30697, 3823, 1549, 150, 1697, 2405, 1234])).
% 11.48/11.77 tff(30843,plain,
% 11.48/11.77 (b(s(z), z)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[180, 30842])).
% 11.48/11.77 tff(30844,plain,
% 11.48/11.77 (~b(s(s(s(elem!1))), z)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[11303, 30843, 379, 10682])).
% 11.48/11.77 tff(30845,plain,
% 11.48/11.77 (r(s(s(s(elem!1))), z)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[377, 30844])).
% 11.48/11.77 tff(30846,plain,
% 11.48/11.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 11.48/11.77 inference(rewrite,[status(thm)],[])).
% 11.48/11.77 tff(30847,plain,
% 11.48/11.77 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 11.48/11.77 inference(rewrite,[status(thm)],[])).
% 11.48/11.77 tff(30848,plain,
% 11.48/11.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))))),
% 11.48/11.77 inference(monotonicity,[status(thm)],[30847])).
% 11.48/11.77 tff(30849,plain,
% 11.48/11.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 11.48/11.77 inference(transitivity,[status(thm)],[30848, 30846])).
% 11.48/11.77 tff(30850,plain,
% 11.48/11.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 11.48/11.77 inference(quant_inst,[status(thm)],[])).
% 11.48/11.77 tff(30851,plain,
% 11.48/11.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))),
% 11.48/11.77 inference(modus_ponens,[status(thm)],[30850, 30849])).
% 11.48/11.77 tff(30852,plain,
% 11.48/11.77 ($false),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[30851, 194, 530, 174, 410, 326])).
% 11.48/11.77 tff(30853,plain,((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.77 tff(30854,plain,
% 11.48/11.77 (~r(z, s(s(elem!1)))),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[30853, 30845, 530, 6124])).
% 11.48/11.77 tff(30855,plain,
% 11.48/11.77 (b(z, s(s(elem!1)))),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[324, 30854])).
% 11.48/11.77 tff(30856,plain,
% 11.48/11.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.48/11.77 inference(rewrite,[status(thm)],[])).
% 11.48/11.77 tff(30857,plain,
% 11.48/11.77 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.48/11.77 inference(rewrite,[status(thm)],[])).
% 11.48/11.77 tff(30858,plain,
% 11.48/11.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 11.48/11.77 inference(monotonicity,[status(thm)],[30857])).
% 11.48/11.77 tff(30859,plain,
% 11.48/11.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.48/11.77 inference(transitivity,[status(thm)],[30858, 30856])).
% 11.48/11.77 tff(30860,plain,
% 11.48/11.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 11.48/11.77 inference(quant_inst,[status(thm)],[])).
% 11.48/11.77 tff(30861,plain,
% 11.48/11.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 11.48/11.77 inference(modus_ponens,[status(thm)],[30860, 30859])).
% 11.48/11.77 tff(30862,plain,
% 11.48/11.77 ($false),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[30861, 391, 381, 900, 3927, 379, 664])).
% 11.48/11.77 tff(30863,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.77 tff(30864,plain,
% 11.48/11.77 (~b(s(s(elem!1)), s(z))),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[30863, 30772, 30855, 379, 664])).
% 11.48/11.77 tff(30865,plain,
% 11.48/11.77 (r(s(s(elem!1)), s(z))),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[362, 30864])).
% 11.48/11.77 tff(30866,plain,
% 11.48/11.77 (~b(s(s(s(elem!1))), z)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[11303, 590, 379, 10682])).
% 11.48/11.77 tff(30867,plain,
% 11.48/11.77 (r(s(s(s(elem!1))), z)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[377, 30866])).
% 11.48/11.77 tff(30868,plain,
% 11.48/11.77 (~r(elem!1, s(s(elem!1)))),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[4159, 327, 410, 340])).
% 11.48/11.77 tff(30869,plain,
% 11.48/11.77 (b(elem!1, s(s(elem!1)))),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[1307, 30868, 1293])).
% 11.48/11.77 tff(30870,plain,
% 11.48/11.77 (~r(s(s(elem!1)), elem!1)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[4178, 327, 174, 133, 21729, 4028, 3927, 340, 127, 1293])).
% 11.48/11.77 tff(30871,plain,
% 11.48/11.77 (b(s(s(elem!1)), elem!1)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[872, 30870, 249])).
% 11.48/11.77 tff(30872,plain,
% 11.48/11.77 ($false),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[3979, 30871, 30869, 133, 3927])).
% 11.48/11.77 tff(30873,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(elem!1))), z)) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.77 tff(30874,plain,
% 11.48/11.77 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[30873, 249, 3927, 133, 30867, 4028, 340, 127, 410])).
% 11.48/11.77 tff(30875,plain,
% 11.48/11.77 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[1370, 30874, 15838])).
% 11.48/11.77 tff(30876,plain,
% 11.48/11.77 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[12932, 30875, 10682, 3927])).
% 11.48/11.77 tff(30877,plain,
% 11.48/11.77 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[1356, 30876, 21729])).
% 11.48/11.77 tff(30878,plain,
% 11.48/11.77 (~b(s(s(elem!1)), elem!1)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[30751, 30875, 10682, 379, 590])).
% 11.48/11.77 tff(30879,plain,
% 11.48/11.77 (r(s(s(elem!1)), elem!1)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[872, 30878, 249])).
% 11.48/11.77 tff(30880,plain,
% 11.48/11.77 ($false),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[4176, 194, 30867, 30879, 410, 30877])).
% 11.48/11.77 tff(30881,plain,((s(s(elem!1)) = elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.48/11.77 tff(30882,plain,
% 11.48/11.77 (s(s(elem!1)) = elem!1),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[30881, 6124, 10682, 379, 30843, 30855, 133, 4028, 30865, 9])).
% 11.48/11.77 tff(30883,plain,
% 11.48/11.77 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 11.48/11.77 inference(monotonicity,[status(thm)],[30882])).
% 11.48/11.77 tff(30884,plain,
% 11.48/11.77 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 11.48/11.77 inference(symmetry,[status(thm)],[30883])).
% 11.48/11.77 tff(30885,plain,
% 11.48/11.77 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 11.48/11.77 inference(monotonicity,[status(thm)],[30882])).
% 11.48/11.77 tff(30886,plain,
% 11.48/11.77 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 11.48/11.77 inference(monotonicity,[status(thm)],[30885])).
% 11.48/11.77 tff(30887,plain,
% 11.48/11.77 (~(elem!1 = s(s(z)))),
% 11.48/11.77 inference(modus_ponens,[status(thm)],[2689, 30886])).
% 11.48/11.77 tff(30888,plain,
% 11.48/11.77 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 11.48/11.77 inference(monotonicity,[status(thm)],[30882])).
% 11.48/11.77 tff(30889,plain,
% 11.48/11.77 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 11.48/11.77 inference(symmetry,[status(thm)],[30888])).
% 11.48/11.77 tff(30890,plain,
% 11.48/11.77 (s(s(s(elem!1))) = s(elem!1)),
% 11.48/11.77 inference(unit_resolution,[status(thm)],[451, 30882])).
% 11.48/11.77 tff(30891,plain,
% 11.48/11.78 (~(s(s(s(s(z)))) = elem!1)),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[717, 30890])).
% 11.48/11.78 tff(30892,plain,
% 11.48/11.78 (r(s(s(s(s(z)))), elem!1)),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[762, 30891, 1549])).
% 11.48/11.78 tff(30893,plain,
% 11.48/11.78 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 11.48/11.78 inference(modus_ponens,[status(thm)],[30892, 30889])).
% 11.48/11.78 tff(30894,plain,
% 11.48/11.78 (~r(s(s(elem!1)), s(s(z)))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[12699, 30893, 1697, 3557])).
% 11.48/11.78 tff(30895,plain,
% 11.48/11.78 (r(s(s(elem!1)), s(s(z))) <=> r(elem!1, s(s(z)))),
% 11.48/11.78 inference(monotonicity,[status(thm)],[445])).
% 11.48/11.78 tff(30896,plain,
% 11.48/11.78 (r(elem!1, s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 11.48/11.78 inference(symmetry,[status(thm)],[30895])).
% 11.48/11.78 tff(30897,plain,
% 11.48/11.78 (r(s(s(elem!1)), s(s(z)))),
% 11.48/11.78 inference(modus_ponens,[status(thm)],[1748, 30896])).
% 11.48/11.78 tff(30898,plain,
% 11.48/11.78 ($false),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[11775, 30897])).
% 11.48/11.78 tff(30899,plain,((~r(elem!1, s(s(z)))) | r(s(s(elem!1)), s(s(z))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.78 tff(30900,plain,
% 11.48/11.78 (~r(elem!1, s(s(z)))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[30899, 30894, 30882])).
% 11.48/11.78 tff(30901,plain,
% 11.48/11.78 (b(elem!1, s(s(z)))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[3394, 30900, 30887])).
% 11.48/11.78 tff(30902,plain,
% 11.48/11.78 (b(s(s(elem!1)), s(s(z)))),
% 11.48/11.78 inference(modus_ponens,[status(thm)],[30901, 30884])).
% 11.48/11.78 tff(30903,plain,
% 11.48/11.78 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 11.48/11.78 inference(monotonicity,[status(thm)],[30882])).
% 11.48/11.78 tff(30904,plain,
% 11.48/11.78 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 11.48/11.78 inference(symmetry,[status(thm)],[30903])).
% 11.48/11.78 tff(30905,plain,
% 11.48/11.78 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 11.48/11.78 inference(monotonicity,[status(thm)],[30882])).
% 11.48/11.78 tff(30906,plain,
% 11.48/11.78 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 11.48/11.78 inference(symmetry,[status(thm)],[30905])).
% 11.48/11.78 tff(30907,plain,
% 11.48/11.78 (r(s(s(elem!1)), z)),
% 11.48/11.78 inference(modus_ponens,[status(thm)],[530, 30906])).
% 11.48/11.78 tff(30908,plain,
% 11.48/11.78 (~r(z, s(s(s(s(z)))))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[7615, 30907, 2053, 30893])).
% 11.48/11.78 tff(30909,plain,
% 11.48/11.78 (b(z, s(s(s(s(z)))))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[800, 30908])).
% 11.48/11.78 tff(30910,plain,
% 11.48/11.78 (~b(s(s(s(s(z)))), s(z))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[10478, 30909, 1234, 664])).
% 11.48/11.78 tff(30911,plain,
% 11.48/11.78 (r(s(s(s(s(z)))), s(z))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[749, 30910])).
% 11.48/11.78 tff(30912,plain,
% 11.48/11.78 (~r(s(z), elem!1)),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[2429, 30911, 1697, 2405])).
% 11.48/11.78 tff(30913,plain,
% 11.48/11.78 (b(s(z), elem!1)),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[632, 30912, 150])).
% 11.48/11.78 tff(30914,plain,
% 11.48/11.78 (b(s(z), s(s(elem!1)))),
% 11.48/11.78 inference(modus_ponens,[status(thm)],[30913, 30904])).
% 11.48/11.78 tff(30915,plain,
% 11.48/11.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 11.48/11.78 inference(rewrite,[status(thm)],[])).
% 11.48/11.78 tff(30916,plain,
% 11.48/11.78 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 11.48/11.78 inference(rewrite,[status(thm)],[])).
% 11.48/11.78 tff(30917,plain,
% 11.48/11.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 11.48/11.78 inference(monotonicity,[status(thm)],[30916])).
% 11.48/11.78 tff(30918,plain,
% 11.48/11.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 11.48/11.78 inference(transitivity,[status(thm)],[30917, 30915])).
% 11.48/11.78 tff(30919,plain,
% 11.48/11.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 11.48/11.78 inference(quant_inst,[status(thm)],[])).
% 11.48/11.78 tff(30920,plain,
% 11.48/11.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 11.48/11.78 inference(modus_ponens,[status(thm)],[30919, 30918])).
% 11.48/11.78 tff(30921,plain,
% 11.48/11.78 ($false),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[30920, 391, 3927, 3823, 590, 5303, 6192])).
% 11.48/11.78 tff(30922,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.78 tff(30923,plain,
% 11.48/11.78 (~b(s(s(elem!1)), s(s(z)))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[30922, 30914, 30855, 3823, 30843])).
% 11.48/11.78 tff(30924,plain,
% 11.48/11.78 ($false),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[30923, 30902])).
% 11.48/11.78 tff(30925,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(z) = elem!1) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (s(s(elem!1)) = s(s(z))) | (~r(elem!1, z)) | b(s(s(s(s(z)))), elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.78 tff(30926,plain,
% 11.48/11.78 (~r(s(s(z)), s(z))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[30925, 30695, 1496, 1697, 3823, 1234, 664, 2053, 3557, 2680, 30653, 30652, 10682, 379, 133, 183, 1810, 1])).
% 11.48/11.78 tff(30927,plain,
% 11.48/11.78 (b(s(s(z)), s(z))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[3778, 30926])).
% 11.48/11.78 tff(30928,plain,
% 11.48/11.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 11.48/11.78 inference(rewrite,[status(thm)],[])).
% 11.48/11.78 tff(30929,plain,
% 11.48/11.78 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 11.48/11.78 inference(rewrite,[status(thm)],[])).
% 11.48/11.78 tff(30930,plain,
% 11.48/11.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 11.48/11.78 inference(monotonicity,[status(thm)],[30929])).
% 11.48/11.78 tff(30931,plain,
% 11.48/11.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 11.48/11.78 inference(transitivity,[status(thm)],[30930, 30928])).
% 11.48/11.78 tff(30932,plain,
% 11.48/11.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 11.48/11.78 inference(quant_inst,[status(thm)],[])).
% 11.48/11.78 tff(30933,plain,
% 11.48/11.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 11.48/11.78 inference(modus_ponens,[status(thm)],[30932, 30931])).
% 11.48/11.78 tff(30934,plain,
% 11.48/11.78 ($false),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[30933, 391, 3823, 30643, 30927, 664, 15045])).
% 11.48/11.78 tff(30935,plain,((elem!1 = s(z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.78 tff(30936,plain,
% 11.48/11.78 (elem!1 = s(z)),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[30935, 3557, 664, 15045, 1697, 1234, 3447, 3823, 10682, 379, 133, 11174, 1, 2, 31])).
% 11.48/11.78 tff(30937,plain,
% 11.48/11.78 (s(z) = elem!1),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[172, 30936])).
% 11.48/11.78 tff(30938,plain,
% 11.48/11.78 (b(elem!1, s(s(s(elem!1))))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[7796, 30937, 379])).
% 11.48/11.78 tff(30939,plain,
% 11.48/11.78 ((elem!1 = s(s(z))) <=> (s(z) = s(s(z)))),
% 11.48/11.78 inference(monotonicity,[status(thm)],[30936])).
% 11.48/11.78 tff(30940,plain,
% 11.48/11.78 ((s(z) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 11.48/11.78 inference(symmetry,[status(thm)],[30939])).
% 11.48/11.78 tff(30941,plain,
% 11.48/11.78 ((s(z) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 11.48/11.78 inference(transitivity,[status(thm)],[30940, 8492])).
% 11.48/11.78 tff(30942,plain,
% 11.48/11.78 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 11.48/11.78 inference(monotonicity,[status(thm)],[30941])).
% 11.48/11.78 tff(30943,plain,
% 11.48/11.78 (~(s(s(z)) = elem!1)),
% 11.48/11.78 inference(modus_ponens,[status(thm)],[1783, 30942])).
% 11.48/11.78 tff(30944,plain,
% 11.48/11.78 (~b(s(s(s(s(z)))), s(z))),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[11177, 30936, 11173])).
% 11.48/11.78 tff(30945,plain,
% 11.48/11.78 (~b(s(s(s(s(z)))), elem!1)),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[9614, 30937, 30944])).
% 11.48/11.78 tff(30946,plain,
% 11.48/11.78 (~b(s(z), elem!1)),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[8805, 30936])).
% 11.48/11.78 tff(30947,plain,
% 11.48/11.78 (~(s(s(s(s(z)))) = elem!1)),
% 11.48/11.78 inference(unit_resolution,[status(thm)],[8916, 30946, 1234])).
% 11.48/11.78 tff(30948,plain,
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% 11.48/11.78 inference(unit_resolution,[status(thm)],[762, 30947, 30945])).
% 11.48/11.78 tff(30949,plain,
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% 11.48/11.78 inference(unit_resolution,[status(thm)],[8520, 30937, 8518])).
% 11.48/11.78 tff(30950,plain,
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% 11.48/11.78 inference(unit_resolution,[status(thm)],[566, 30949])).
% 11.48/11.78 tff(30951,plain,
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% 11.48/11.78 tff(30952,plain,
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% 11.48/11.78 inference(unit_resolution,[status(thm)],[29438, 30936])).
% 11.48/11.78 tff(30953,plain,
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% 11.48/11.78 inference(unit_resolution,[status(thm)],[29435, 30952, 3446])).
% 11.48/11.78 tff(30954,plain,
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% 11.48/11.78 inference(unit_resolution,[status(thm)],[377, 30953])).
% 11.48/11.78 tff(30955,plain,
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% 11.48/11.78 inference(monotonicity,[status(thm)],[30936])).
% 11.48/11.78 tff(30956,plain,
% 11.48/11.78 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 11.48/11.78 inference(monotonicity,[status(thm)],[30955])).
% 11.48/11.78 tff(30957,plain,
% 11.48/11.78 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
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% 11.48/11.79 tff(30958,plain,
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% 11.48/11.79 inference(monotonicity,[status(thm)],[30955])).
% 11.48/11.79 tff(30959,plain,
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% 11.48/11.79 inference(monotonicity,[status(thm)],[30958])).
% 11.48/11.79 tff(30960,plain,
% 11.48/11.79 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 11.48/11.79 inference(monotonicity,[status(thm)],[30959])).
% 11.48/11.79 tff(30961,plain,
% 11.48/11.79 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
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% 11.48/11.79 tff(30962,plain,
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% 11.48/11.79 tff(30963,plain,
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% 11.48/11.79 tff(30964,plain,
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% 11.48/11.79 tff(30965,plain,
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% 11.48/11.79 inference(unit_resolution,[status(thm)],[2767, 30964])).
% 11.48/11.79 tff(30966,plain,
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% 11.48/11.79 inference(symmetry,[status(thm)],[30936])).
% 11.48/11.79 tff(30967,plain,
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% 11.48/11.79 inference(monotonicity,[status(thm)],[30966])).
% 11.48/11.79 tff(30968,plain,
% 11.48/11.79 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 11.48/11.79 inference(monotonicity,[status(thm)],[30967])).
% 11.48/11.79 tff(30969,plain,
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% 11.48/11.79 inference(modus_ponens,[status(thm)],[357, 30968])).
% 11.48/11.79 tff(30970,plain,
% 11.48/11.79 (~b(s(s(s(elem!1))), elem!1)),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[10845, 30938, 10682, 133])).
% 11.48/11.79 tff(30971,plain,
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% 11.48/11.79 inference(unit_resolution,[status(thm)],[230, 30970, 9])).
% 11.48/11.79 tff(30972,plain,
% 11.48/11.79 (~(s(s(s(s(elem!1)))) = elem!1)),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[7472, 30937])).
% 11.48/11.79 tff(30973,plain,
% 11.48/11.79 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 11.48/11.79 inference(monotonicity,[status(thm)],[30958])).
% 11.48/11.79 tff(30974,plain,
% 11.48/11.79 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 11.48/11.79 inference(symmetry,[status(thm)],[30973])).
% 11.48/11.79 tff(30975,plain,
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% 11.48/11.79 inference(monotonicity,[status(thm)],[30974])).
% 11.48/11.79 tff(30976,plain,
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% 11.48/11.79 tff(30977,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.79 tff(30978,plain,
% 11.48/11.79 (~r(z, s(s(s(z))))),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[30977, 3557, 3447, 1697])).
% 11.48/11.79 tff(30979,plain,
% 11.48/11.79 (~r(z, s(s(elem!1)))),
% 11.48/11.79 inference(modus_ponens,[status(thm)],[30978, 30975])).
% 11.48/11.79 tff(30980,plain,
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% 11.48/11.79 inference(unit_resolution,[status(thm)],[324, 30979])).
% 11.48/11.79 tff(30981,plain,
% 11.48/11.79 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 11.48/11.79 inference(monotonicity,[status(thm)],[30959])).
% 11.48/11.79 tff(30982,plain,
% 11.48/11.79 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 11.48/11.79 inference(monotonicity,[status(thm)],[30981, 30958])).
% 11.48/11.79 tff(30983,plain,
% 11.48/11.79 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 11.48/11.79 inference(transitivity,[status(thm)],[30982, 8583])).
% 11.48/11.79 tff(30984,plain,
% 11.48/11.79 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 11.48/11.79 inference(symmetry,[status(thm)],[30983])).
% 11.48/11.79 tff(30985,plain,
% 11.48/11.79 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 11.48/11.79 inference(transitivity,[status(thm)],[30984, 1021])).
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% 11.48/11.79 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 11.48/11.79 inference(monotonicity,[status(thm)],[30985])).
% 11.48/11.79 tff(30987,plain,
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% 11.48/11.79 inference(modus_ponens,[status(thm)],[8593, 30986])).
% 11.48/11.79 tff(30988,plain,
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% 11.48/11.79 tff(30989,plain,
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% 11.48/11.79 tff(30990,plain,
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% 11.48/11.79 tff(30991,plain,
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% 11.48/11.79 tff(30992,plain,
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% 11.48/11.79 inference(unit_resolution,[status(thm)],[15610, 972])).
% 11.48/11.79 tff(30993,plain,
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% 11.48/11.79 tff(30996,plain,
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% 11.48/11.79 tff(30999,plain,
% 11.48/11.79 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[14542, 30998, 30996, 30991])).
% 11.48/11.79 tff(31000,plain,
% 11.48/11.79 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[1164, 30999, 311])).
% 11.48/11.79 tff(31001,plain,
% 11.48/11.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 11.48/11.79 inference(rewrite,[status(thm)],[])).
% 11.48/11.79 tff(31002,plain,
% 11.48/11.79 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 11.48/11.79 inference(rewrite,[status(thm)],[])).
% 11.48/11.79 tff(31003,plain,
% 11.48/11.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 11.48/11.79 inference(monotonicity,[status(thm)],[31002])).
% 11.48/11.79 tff(31004,plain,
% 11.48/11.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 11.48/11.79 inference(transitivity,[status(thm)],[31003, 31001])).
% 11.48/11.79 tff(31005,plain,
% 11.48/11.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 11.48/11.79 inference(quant_inst,[status(thm)],[])).
% 11.48/11.79 tff(31006,plain,
% 11.48/11.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 11.48/11.79 inference(modus_ponens,[status(thm)],[31005, 31004])).
% 11.48/11.79 tff(31007,plain,
% 11.48/11.79 ($false),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[31006, 391, 10682, 379, 1573, 1114, 664])).
% 11.48/11.79 tff(31008,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.79 tff(31009,plain,
% 11.48/11.79 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[31008, 31000, 379, 10682, 664])).
% 11.48/11.79 tff(31010,plain,
% 11.48/11.79 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[1095, 31009, 310])).
% 11.48/11.79 tff(31011,plain,
% 11.48/11.79 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[14564, 31000, 10682, 665, 448])).
% 11.48/11.79 tff(31012,plain,
% 11.48/11.79 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[988, 31011, 957])).
% 11.48/11.79 tff(31013,plain,
% 11.48/11.79 ($false),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[14601, 31012, 31010, 613, 30989])).
% 11.48/11.79 tff(31014,plain,((~b(elem!1, z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = elem!1) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.79 tff(31015,plain,
% 11.48/11.79 (~b(elem!1, z)),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[31014, 30963, 930, 10682, 30938, 379, 664, 30987, 30980, 26982, 30972, 426, 133, 30971, 30969, 30965, 30950])).
% 11.48/11.79 tff(31016,plain,
% 11.48/11.79 (r(elem!1, z)),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[526, 31015, 2])).
% 11.48/11.79 tff(31017,plain,
% 11.48/11.79 (~r(s(s(z)), elem!1)),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[20852, 31016, 1697, 30948])).
% 11.48/11.79 tff(31018,plain,
% 11.48/11.79 (b(s(s(z)), elem!1)),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[4730, 31017, 30943])).
% 11.48/11.79 tff(31019,plain,
% 11.48/11.79 (~b(s(z), s(s(z)))),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[30671, 31018, 30938, 664, 15045])).
% 11.48/11.79 tff(31020,plain,
% 11.48/11.79 (r(s(z), s(s(z)))),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[1788, 31019])).
% 11.48/11.79 tff(31021,plain,
% 11.48/11.79 (r(s(s(s(s(z)))), s(z))),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[749, 30944])).
% 11.48/11.79 tff(31022,plain,
% 11.48/11.79 ($false),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[9185, 194, 3557, 31021, 31020, 1697])).
% 11.48/11.79 tff(31023,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (elem!1 = z) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | b(s(s(s(s(z)))), z) | (~b(s(z), s(s(s(s(z)))))) | r(z, s(s(z))) | b(s(s(s(elem!1))), s(z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.48/11.79 tff(31024,plain,
% 11.48/11.79 (~r(s(s(z)), z)),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[31023, 664, 1697, 15045, 2, 10682, 379, 133, 3446, 1234, 8518, 11173, 3823, 1, 31])).
% 11.48/11.79 tff(31025,plain,
% 11.48/11.79 (b(s(s(z)), z)),
% 11.48/11.79 inference(unit_resolution,[status(thm)],[1211, 31024])).
% 11.48/11.79 tff(31026,plain,
% 11.48/11.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.48/11.79 inference(rewrite,[status(thm)],[])).
% 11.48/11.79 tff(31027,plain,
% 11.48/11.79 (((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.58/11.80 inference(rewrite,[status(thm)],[])).
% 11.58/11.80 tff(31028,plain,
% 11.58/11.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 11.58/11.80 inference(monotonicity,[status(thm)],[31027])).
% 11.58/11.80 tff(31029,plain,
% 11.58/11.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.58/11.80 inference(transitivity,[status(thm)],[31028, 31026])).
% 11.58/11.80 tff(31030,plain,
% 11.58/11.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 11.58/11.80 inference(quant_inst,[status(thm)],[])).
% 11.58/11.80 tff(31031,plain,
% 11.58/11.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 11.58/11.80 inference(modus_ponens,[status(thm)],[31030, 31029])).
% 11.58/11.80 tff(31032,plain,
% 11.58/11.80 ($false),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[31031, 391, 133, 1235, 2439, 664, 15045])).
% 11.58/11.80 tff(31033,plain,((~b(s(z), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.80 tff(31034,plain,
% 11.58/11.80 (~b(s(z), s(s(z)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[31033, 31025, 133, 664, 15045])).
% 11.58/11.80 tff(31035,plain,
% 11.58/11.80 (r(s(z), s(s(z)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[1788, 31034])).
% 11.58/11.80 tff(31036,plain,
% 11.58/11.80 (~r(elem!1, s(z))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[30498, 31035, 133, 1, 11174, 10682])).
% 11.58/11.80 tff(31037,plain,
% 11.58/11.80 (elem!1 = s(z)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[837, 31036, 31])).
% 11.58/11.80 tff(31038,plain,
% 11.58/11.80 (~b(s(s(s(s(z)))), s(z))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[11177, 31037, 11173])).
% 11.58/11.80 tff(31039,plain,
% 11.58/11.80 (r(s(s(s(s(z)))), s(z))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[749, 31038])).
% 11.58/11.80 tff(31040,plain,
% 11.58/11.80 (s(z) = elem!1),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[172, 31037])).
% 11.58/11.80 tff(31041,plain,
% 11.58/11.80 (~r(z, s(elem!1))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[8520, 31040, 8518])).
% 11.58/11.80 tff(31042,plain,
% 11.58/11.80 (b(z, s(elem!1))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[566, 31041])).
% 11.58/11.80 tff(31043,plain,
% 11.58/11.80 (~r(s(s(z)), s(z))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[10673, 31039, 1697, 31035])).
% 11.58/11.80 tff(31044,plain,
% 11.58/11.80 (b(s(s(z)), s(z))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[3778, 31043])).
% 11.58/11.80 tff(31045,plain,
% 11.58/11.80 (b(s(elem!1), elem!1)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[29583, 31044, 31040])).
% 11.58/11.80 tff(31046,plain,
% 11.58/11.80 (~b(elem!1, z)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[6555, 31045, 133, 31042])).
% 11.58/11.80 tff(31047,plain,
% 11.58/11.80 (r(s(z), z)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[7485, 31046, 31040])).
% 11.58/11.80 tff(31048,plain,
% 11.58/11.80 (s(elem!1) = s(s(z))),
% 11.58/11.80 inference(monotonicity,[status(thm)],[31037])).
% 11.58/11.80 tff(31049,plain,
% 11.58/11.80 (s(s(elem!1)) = s(s(s(z)))),
% 11.58/11.80 inference(monotonicity,[status(thm)],[31048])).
% 11.58/11.80 tff(31050,plain,
% 11.58/11.80 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 11.58/11.80 inference(monotonicity,[status(thm)],[31049])).
% 11.58/11.80 tff(31051,plain,
% 11.58/11.80 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 11.58/11.80 inference(monotonicity,[status(thm)],[31050])).
% 11.58/11.80 tff(31052,plain,
% 11.58/11.80 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 11.58/11.80 inference(monotonicity,[status(thm)],[31051])).
% 11.58/11.80 tff(31053,plain,
% 11.58/11.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 11.58/11.80 inference(rewrite,[status(thm)],[])).
% 11.58/11.80 tff(31054,plain,
% 11.58/11.80 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 11.58/11.80 inference(rewrite,[status(thm)],[])).
% 11.58/11.80 tff(31055,plain,
% 11.58/11.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(z)))))))))),
% 11.58/11.80 inference(monotonicity,[status(thm)],[31054])).
% 11.58/11.80 tff(31056,plain,
% 11.58/11.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 11.58/11.80 inference(transitivity,[status(thm)],[31055, 31053])).
% 11.58/11.80 tff(31057,plain,
% 11.58/11.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 11.58/11.80 inference(quant_inst,[status(thm)],[])).
% 11.58/11.80 tff(31058,plain,
% 11.58/11.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(s(z)))))))),
% 11.58/11.80 inference(modus_ponens,[status(thm)],[31057, 31056])).
% 11.58/11.80 tff(31059,plain,
% 11.58/11.80 (~r(z, s(s(s(s(s(z))))))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[31058, 194, 182, 2053, 723])).
% 11.58/11.80 tff(31060,plain,
% 11.58/11.80 ($false),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[31059, 15493])).
% 11.58/11.80 tff(31061,plain,((~r(z, s(s(s(s(elem!1)))))) | (~(elem!1 = s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.80 tff(31062,plain,
% 11.58/11.80 (~r(z, s(s(s(s(elem!1)))))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[31061, 31037, 31047, 3447, 31039])).
% 11.58/11.80 tff(31063,plain,
% 11.58/11.80 (b(z, s(s(s(s(elem!1)))))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[2767, 31062])).
% 11.58/11.80 tff(31064,plain,
% 11.58/11.80 (b(z, s(s(s(s(s(z))))))),
% 11.58/11.80 inference(modus_ponens,[status(thm)],[31063, 31052])).
% 11.58/11.80 tff(31065,plain,
% 11.58/11.80 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 11.58/11.80 inference(monotonicity,[status(thm)],[31050, 31049])).
% 11.58/11.80 tff(31066,plain,
% 11.58/11.80 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[1243, 31044, 1234, 664, 31025])).
% 11.58/11.80 tff(31067,plain,
% 11.58/11.80 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[3482, 31066, 31037])).
% 11.58/11.80 tff(31068,plain,
% 11.58/11.80 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[1370, 31067, 26982])).
% 11.58/11.80 tff(31069,plain,
% 11.58/11.80 (r(s(s(s(s(z)))), s(s(s(z))))),
% 11.58/11.80 inference(modus_ponens,[status(thm)],[31068, 31065])).
% 11.58/11.80 tff(31070,plain,
% 11.58/11.80 (s(s(s(z))) = s(s(elem!1))),
% 11.58/11.80 inference(symmetry,[status(thm)],[31049])).
% 11.58/11.80 tff(31071,plain,
% 11.58/11.80 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 11.58/11.80 inference(monotonicity,[status(thm)],[31070])).
% 11.58/11.80 tff(31072,plain,
% 11.58/11.80 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 11.58/11.80 inference(symmetry,[status(thm)],[31071])).
% 11.58/11.80 tff(31073,plain,
% 11.58/11.80 (b(elem!1, s(s(s(elem!1))))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[7796, 31040, 379])).
% 11.58/11.80 tff(31074,plain,
% 11.58/11.80 (~b(s(s(s(elem!1))), elem!1)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[10845, 31073, 10682, 133])).
% 11.58/11.80 tff(31075,plain,
% 11.58/11.80 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[14662, 31045, 31074])).
% 11.58/11.80 tff(31076,plain,
% 11.58/11.80 (~(s(s(elem!1)) = elem!1)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[451, 31075])).
% 11.58/11.80 tff(31077,plain,
% 11.58/11.80 (~(elem!1 = s(s(elem!1)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[1292, 31076])).
% 11.58/11.80 tff(31078,plain,
% 11.58/11.80 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[29438, 31037])).
% 11.58/11.80 tff(31079,plain,
% 11.58/11.80 (~b(s(s(s(elem!1))), z)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[29435, 31078, 3446])).
% 11.58/11.80 tff(31080,plain,
% 11.58/11.80 (r(s(s(s(elem!1))), z)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[377, 31079])).
% 11.58/11.80 tff(31081,plain,
% 11.58/11.80 (r(s(s(s(elem!1))), elem!1)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[230, 31074, 9])).
% 11.58/11.80 tff(31082,plain,
% 11.58/11.80 (r(elem!1, z)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[526, 31046, 2])).
% 11.58/11.80 tff(31083,plain,
% 11.58/11.80 (~r(z, s(s(elem!1)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[27619, 31082, 31081, 31080])).
% 11.58/11.80 tff(31084,plain,
% 11.58/11.80 (b(z, s(s(elem!1)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[324, 31083])).
% 11.58/11.80 tff(31085,plain,
% 11.58/11.80 (~b(elem!1, s(elem!1))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[24246, 31045, 133, 31042])).
% 11.58/11.80 tff(31086,plain,
% 11.58/11.80 (r(elem!1, s(elem!1))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[443, 31085, 427])).
% 11.58/11.80 tff(31087,plain,
% 11.58/11.80 (b(s(s(elem!1)), elem!1)),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[26917, 31084, 10682, 31082, 31081, 31075, 31086])).
% 11.58/11.80 tff(31088,plain,
% 11.58/11.80 (~b(elem!1, s(s(elem!1)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[3979, 31087, 133, 31084])).
% 11.58/11.80 tff(31089,plain,
% 11.58/11.80 (r(elem!1, s(s(elem!1)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[1307, 31088, 31077])).
% 11.58/11.80 tff(31090,plain,
% 11.58/11.80 (r(s(z), s(s(elem!1)))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[15602, 31089, 31037])).
% 11.58/11.80 tff(31091,plain,
% 11.58/11.80 (r(s(z), s(s(s(z))))),
% 11.58/11.80 inference(modus_ponens,[status(thm)],[31090, 31072])).
% 11.58/11.80 tff(31092,plain,
% 11.58/11.80 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[21877, 31039, 31091, 31069])).
% 11.58/11.80 tff(31093,plain,
% 11.58/11.80 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 11.58/11.80 inference(unit_resolution,[status(thm)],[21879, 31092])).
% 11.58/11.80 tff(31094,plain,
% 11.58/11.80 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 11.58/11.80 inference(monotonicity,[status(thm)],[31049])).
% 11.58/11.80 tff(31095,plain,
% 11.58/11.80 (b(z, s(s(s(z))))),
% 11.58/11.80 inference(modus_ponens,[status(thm)],[31084, 31094])).
% 11.58/11.80 tff(31096,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 11.58/11.80 tff(31097,plain,
% 11.58/11.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 11.58/11.80 inference(rewrite,[status(thm)],[])).
% 11.58/11.80 tff(31098,plain,
% 11.58/11.80 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 11.58/11.80 inference(rewrite,[status(thm)],[])).
% 11.58/11.80 tff(31099,plain,
% 11.58/11.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31098])).
% 11.58/11.81 tff(31100,plain,
% 11.58/11.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 11.58/11.81 inference(transitivity,[status(thm)],[31099, 31097])).
% 11.58/11.81 tff(31101,plain,
% 11.58/11.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 11.58/11.81 inference(quant_inst,[status(thm)],[])).
% 11.58/11.81 tff(31102,plain,
% 11.58/11.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[31101, 31100])).
% 11.58/11.81 tff(31103,plain,
% 11.58/11.81 ($false),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[31102, 391, 1234, 7871, 31096, 15747, 15768])).
% 11.58/11.81 tff(31104,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.81 tff(31105,plain,
% 11.58/11.81 (~b(s(s(s(s(s(z))))), s(z))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[31104, 31095, 1234, 31093, 31064])).
% 11.58/11.81 tff(31106,plain,
% 11.58/11.81 (r(s(s(s(s(s(z))))), s(z))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[20789, 31105])).
% 11.58/11.81 tff(31107,plain,
% 11.58/11.81 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[15757, 31106, 31047, 31039])).
% 11.58/11.81 tff(31108,plain,
% 11.58/11.81 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[8761, 31107])).
% 11.58/11.81 tff(31109,plain,
% 11.58/11.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 11.58/11.81 inference(rewrite,[status(thm)],[])).
% 11.58/11.81 tff(31110,plain,
% 11.58/11.81 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 11.58/11.81 inference(rewrite,[status(thm)],[])).
% 11.58/11.81 tff(31111,plain,
% 11.58/11.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31110])).
% 11.58/11.81 tff(31112,plain,
% 11.58/11.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 11.58/11.81 inference(transitivity,[status(thm)],[31111, 31109])).
% 11.58/11.81 tff(31113,plain,
% 11.58/11.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 11.58/11.81 inference(quant_inst,[status(thm)],[])).
% 11.58/11.81 tff(31114,plain,
% 11.58/11.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[31113, 31112])).
% 11.58/11.81 tff(31115,plain,
% 11.58/11.81 ($false),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[31114, 391, 1234, 31044, 664, 15045, 31108])).
% 11.58/11.81 tff(31116,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (~r(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(s(z)))), z) | r(z, s(s(z))) | (~b(s(z), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z)) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.81 tff(31117,plain,
% 11.58/11.81 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[31116, 30641, 15045, 133, 10682, 2, 1234, 3446, 22903, 379, 11173, 31, 1, 30627])).
% 11.58/11.81 tff(31118,plain,
% 11.58/11.81 ($false),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[3652, 31117, 30628])).
% 11.58/11.81 tff(31119,plain,((~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(s(s(z)))), z) | (~b(s(z), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z)) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.81 tff(31120,plain,
% 11.58/11.81 (~r(s(z), s(s(z)))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[31119, 30550, 149, 30423, 2, 30422, 3446, 29889, 11173, 31, 1, 30591])).
% 11.58/11.81 tff(31121,plain,
% 11.58/11.81 (b(s(z), s(s(z)))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[1788, 31120])).
% 11.58/11.81 tff(31122,plain,
% 11.58/11.81 (s(z) = elem!1),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[30574, 2282, 30423, 149, 29889, 11174, 2, 1, 3447])).
% 11.58/11.81 tff(31123,plain,
% 11.58/11.81 (~b(s(s(z)), z)),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[31033, 31121, 149, 30592, 30550])).
% 11.58/11.81 tff(31124,plain,
% 11.58/11.81 (r(s(s(z)), z)),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[1211, 31123])).
% 11.58/11.81 tff(31125,plain,
% 11.58/11.81 (r(s(elem!1), z)),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[3560, 31122, 31124])).
% 11.58/11.81 tff(31126,plain,
% 11.58/11.81 (b(s(z), z)),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[10390, 11936, 31122])).
% 11.58/11.81 tff(31127,plain,
% 11.58/11.81 (~b(s(s(s(elem!1))), z)),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[11303, 31126, 29889, 30423])).
% 11.58/11.81 tff(31128,plain,
% 11.58/11.81 (r(s(s(s(elem!1))), z)),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[377, 31127])).
% 11.58/11.81 tff(31129,plain,
% 11.58/11.81 (s(s(z)) = s(elem!1)),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31122])).
% 11.58/11.81 tff(31130,plain,
% 11.58/11.81 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31129])).
% 11.58/11.81 tff(31131,plain,
% 11.58/11.81 (b(z, s(elem!1))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[30550, 31130])).
% 11.58/11.81 tff(31132,plain,
% 11.58/11.81 (~(s(s(s(s(elem!1)))) = elem!1)),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[7472, 31122])).
% 11.58/11.81 tff(31133,plain,
% 11.58/11.81 (b(elem!1, s(s(s(elem!1))))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[7796, 31122, 29889])).
% 11.58/11.81 tff(31134,plain,
% 11.58/11.81 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31122])).
% 11.58/11.81 tff(31135,plain,
% 11.58/11.81 (b(elem!1, s(s(z)))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[31121, 31134])).
% 11.58/11.81 tff(31136,assumption,(~b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 11.58/11.81 tff(31137,plain,
% 11.58/11.81 (r(z, s(s(s(s(elem!1)))))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[2767, 31136])).
% 11.58/11.81 tff(31138,plain,
% 11.58/11.81 (s(s(s(elem!1))) = s(elem!1)),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[14456, 31137, 3369, 448, 174, 3557, 1628])).
% 11.58/11.81 tff(31139,plain,
% 11.58/11.81 (s(s(elem!1)) = elem!1),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[6159, 31138])).
% 11.58/11.81 tff(31140,plain,
% 11.58/11.81 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31138])).
% 11.58/11.81 tff(31141,plain,
% 11.58/11.81 (s(s(s(s(elem!1)))) = elem!1),
% 11.58/11.81 inference(transitivity,[status(thm)],[31140, 31139])).
% 11.58/11.81 tff(31142,plain,
% 11.58/11.81 (b(z, s(s(s(s(elem!1))))) <=> b(z, elem!1)),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31141])).
% 11.58/11.81 tff(31143,plain,
% 11.58/11.81 (b(z, elem!1) <=> b(z, s(s(s(s(elem!1)))))),
% 11.58/11.81 inference(symmetry,[status(thm)],[31142])).
% 11.58/11.81 tff(31144,plain,
% 11.58/11.81 (b(z, s(s(s(s(elem!1)))))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[133, 31143])).
% 11.58/11.81 tff(31145,plain,
% 11.58/11.81 ($false),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[31136, 31144])).
% 11.58/11.81 tff(31146,plain,(b(z, s(s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.81 tff(31147,plain,
% 11.58/11.81 (b(z, s(s(s(s(elem!1)))))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[31146, 31135, 149, 31133, 31128, 31124, 31125])).
% 11.58/11.81 tff(31148,plain,
% 11.58/11.81 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31122])).
% 11.58/11.81 tff(31149,plain,
% 11.58/11.81 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31148])).
% 11.58/11.81 tff(31150,plain,
% 11.58/11.81 (~(s(s(elem!1)) = elem!1)),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[357, 31149])).
% 11.58/11.81 tff(31151,plain,
% 11.58/11.81 (~b(s(s(s(elem!1))), elem!1)),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[10743, 11936, 30423, 149])).
% 11.58/11.81 tff(31152,plain,
% 11.58/11.81 (r(s(s(s(elem!1))), elem!1)),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[230, 31151, 9])).
% 11.58/11.81 tff(31153,plain,
% 11.58/11.81 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31129])).
% 11.58/11.81 tff(31154,plain,
% 11.58/11.81 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 11.58/11.81 inference(transitivity,[status(thm)],[31153, 582])).
% 11.58/11.81 tff(31155,plain,
% 11.58/11.81 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31154])).
% 11.58/11.81 tff(31156,plain,
% 11.58/11.81 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[1397, 31155])).
% 11.58/11.81 tff(31157,plain,
% 11.58/11.81 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31129])).
% 11.58/11.81 tff(31158,plain,
% 11.58/11.81 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 11.58/11.81 inference(transitivity,[status(thm)],[31157, 1098])).
% 11.58/11.81 tff(31159,plain,
% 11.58/11.81 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31158])).
% 11.58/11.81 tff(31160,plain,
% 11.58/11.81 (~(s(elem!1) = s(s(elem!1)))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[2680, 31159])).
% 11.58/11.81 tff(31161,plain,
% 11.58/11.81 (s(s(s(z))) = s(s(elem!1))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31129])).
% 11.58/11.81 tff(31162,plain,
% 11.58/11.81 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31161])).
% 11.58/11.81 tff(31163,plain,
% 11.58/11.81 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31162])).
% 11.58/11.81 tff(31164,plain,
% 11.58/11.81 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31163])).
% 11.58/11.81 tff(31165,plain,
% 11.58/11.81 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 11.58/11.81 inference(transitivity,[status(thm)],[31164, 1021])).
% 11.58/11.81 tff(31166,plain,
% 11.58/11.81 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31165])).
% 11.58/11.81 tff(31167,plain,
% 11.58/11.81 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31161])).
% 11.58/11.81 tff(31168,plain,
% 11.58/11.81 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 11.58/11.81 inference(transitivity,[status(thm)],[31167, 19135])).
% 11.58/11.81 tff(31169,plain,
% 11.58/11.81 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(elem!1))))),
% 11.58/11.81 inference(monotonicity,[status(thm)],[31168])).
% 11.58/11.82 tff(31170,plain,
% 11.58/11.82 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 11.58/11.82 inference(modus_ponens,[status(thm)],[8593, 31169])).
% 11.58/11.82 tff(31171,plain,
% 11.58/11.82 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 11.58/11.82 inference(modus_ponens,[status(thm)],[31170, 31166])).
% 11.58/11.82 tff(31172,plain,
% 11.58/11.82 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 11.58/11.82 inference(monotonicity,[status(thm)],[31164])).
% 11.58/11.82 tff(31173,plain,
% 11.58/11.82 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 11.58/11.82 inference(modus_ponens,[status(thm)],[31170, 31172])).
% 11.58/11.82 tff(31174,plain,
% 11.58/11.82 (r(s(s(s(s(elem!1)))), elem!1)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[1004, 14265, 972])).
% 11.58/11.82 tff(31175,plain,
% 11.58/11.82 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[14294, 3927, 133, 665, 10682, 448, 30992, 1035, 233, 297, 315, 249, 2781])).
% 11.58/11.82 tff(31176,plain,
% 11.58/11.82 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[1370, 31175, 297])).
% 11.58/11.82 tff(31177,plain,
% 11.58/11.82 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[12932, 31176, 10682, 3927])).
% 11.58/11.82 tff(31178,plain,
% 11.58/11.82 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[1356, 31177, 315])).
% 11.58/11.82 tff(31179,plain,
% 11.58/11.82 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[14521, 31176, 10682, 448, 665])).
% 11.58/11.82 tff(31180,plain,
% 11.58/11.82 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[1048, 31179, 1035])).
% 11.58/11.82 tff(31181,plain,
% 11.58/11.82 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[14542, 31180, 31178, 31174])).
% 11.58/11.82 tff(31182,plain,
% 11.58/11.82 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[1164, 31181, 311])).
% 11.58/11.82 tff(31183,plain,
% 11.58/11.82 (~r(s(s(s(elem!1))), s(elem!1))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[31014, 3927, 957, 10682, 665, 379, 664, 448, 1035, 297, 972, 164, 133, 233, 249, 2781, 592])).
% 11.58/11.82 tff(31184,plain,
% 11.58/11.82 (b(s(s(s(elem!1))), s(elem!1))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[588, 31183, 279])).
% 11.58/11.82 tff(31185,plain,
% 11.58/11.82 (~b(s(elem!1), s(s(elem!1)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[14314, 31184, 10682, 448, 665])).
% 11.58/11.82 tff(31186,plain,
% 11.58/11.82 (r(s(elem!1), s(s(elem!1)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[8644, 31185, 8611])).
% 11.58/11.82 tff(31187,plain,
% 11.58/11.82 (~b(s(s(elem!1)), s(z))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[14197, 31176, 10682, 665, 448])).
% 11.58/11.82 tff(31188,plain,
% 11.58/11.82 (r(s(s(elem!1)), s(z))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[362, 31187])).
% 11.58/11.82 tff(31189,plain,
% 11.58/11.82 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[14571, 31188, 10682, 448, 957, 665, 31186, 311, 31180, 31178])).
% 11.58/11.82 tff(31190,plain,
% 11.58/11.82 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[1061, 31189, 1050])).
% 11.58/11.82 tff(31191,plain,
% 11.58/11.82 ($false),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[14233, 31190, 31182, 10682, 665, 448])).
% 11.58/11.82 tff(31192,plain,((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (s(elem!1) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = elem!1) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = elem!1) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.82 tff(31193,plain,
% 11.58/11.82 (~b(z, s(s(elem!1)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[31192, 11936, 30423, 31133, 31173, 930, 31171, 31160, 26982, 31156, 149, 31152, 31150, 31147, 29889, 30592, 31132, 426, 31131])).
% 11.58/11.82 tff(31194,plain,
% 11.58/11.82 (r(z, s(s(elem!1)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[324, 31193])).
% 11.58/11.82 tff(31195,plain,
% 11.58/11.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 11.58/11.82 inference(rewrite,[status(thm)],[])).
% 11.58/11.82 tff(31196,plain,
% 11.58/11.82 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 11.58/11.82 inference(rewrite,[status(thm)],[])).
% 11.58/11.82 tff(31197,plain,
% 11.58/11.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 11.58/11.82 inference(monotonicity,[status(thm)],[31196])).
% 11.58/11.82 tff(31198,plain,
% 11.58/11.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 11.58/11.82 inference(transitivity,[status(thm)],[31197, 31195])).
% 11.58/11.82 tff(31199,plain,
% 11.58/11.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 11.58/11.82 inference(quant_inst,[status(thm)],[])).
% 11.58/11.82 tff(31200,plain,
% 11.58/11.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 11.58/11.82 inference(modus_ponens,[status(thm)],[31199, 31198])).
% 11.58/11.82 tff(31201,plain,
% 11.58/11.82 ($false),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[31200, 194, 1628, 174, 326, 604])).
% 11.58/11.82 tff(31202,plain,((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.82 tff(31203,plain,
% 11.58/11.82 (~r(s(elem!1), s(s(s(elem!1))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[31202, 31194, 31128, 31125])).
% 11.58/11.82 tff(31204,plain,
% 11.58/11.82 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[3614, 31203, 31122])).
% 11.58/11.82 tff(31205,plain,
% 11.58/11.82 (b(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[3652, 31204])).
% 11.58/11.82 tff(31206,plain,
% 11.58/11.82 (~b(s(z), s(s(z)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[6275, 3563, 1234, 3823])).
% 11.58/11.82 tff(31207,plain,
% 11.58/11.82 (r(s(z), s(s(z)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[1788, 31206])).
% 11.58/11.82 tff(31208,plain,
% 11.58/11.82 (~r(elem!1, s(z))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[30498, 31207, 149, 1, 183, 10682])).
% 11.58/11.82 tff(31209,plain,
% 11.58/11.82 (elem!1 = s(z)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[837, 31208, 31])).
% 11.58/11.82 tff(31210,plain,
% 11.58/11.82 (s(z) = elem!1),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[172, 31209])).
% 11.58/11.82 tff(31211,plain,
% 11.58/11.82 (~b(z, s(s(s(s(z)))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[15550, 3563, 15045, 3823])).
% 11.58/11.82 tff(31212,plain,
% 11.58/11.82 (r(z, s(z))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[11318, 31209, 2, 31211])).
% 11.58/11.82 tff(31213,plain,
% 11.58/11.82 ($false),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[17233, 31212, 31210, 80])).
% 11.58/11.82 tff(31214,plain,((~b(s(s(s(s(z)))), s(s(z)))) | r(z, elem!1) | (elem!1 = z) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.82 tff(31215,plain,
% 11.58/11.82 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[31214, 31205, 2, 31, 1, 11174, 30423, 30422, 80, 30550])).
% 11.58/11.82 tff(31216,plain,
% 11.58/11.82 (r(s(s(s(s(z)))), s(s(z)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[1714, 31215])).
% 11.58/11.82 tff(31217,plain,
% 11.58/11.82 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 11.58/11.82 inference(monotonicity,[status(thm)],[31122])).
% 11.58/11.82 tff(31218,plain,
% 11.58/11.82 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 11.58/11.82 inference(symmetry,[status(thm)],[31217])).
% 11.58/11.82 tff(31219,plain,
% 11.58/11.82 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(z)))),
% 11.58/11.82 inference(monotonicity,[status(thm)],[31218])).
% 11.58/11.82 tff(31220,plain,
% 11.58/11.82 (~b(s(s(z)), elem!1)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[30671, 31133, 31121, 30592, 30550])).
% 11.58/11.82 tff(31221,plain,
% 11.58/11.82 (~b(s(s(z)), s(z))),
% 11.58/11.82 inference(modus_ponens,[status(thm)],[31220, 31219])).
% 11.58/11.82 tff(31222,plain,
% 11.58/11.82 (r(s(s(z)), s(z))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[3778, 31221])).
% 11.58/11.82 tff(31223,plain,
% 11.58/11.82 (~r(z, s(s(z)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[18433, 31216, 3447, 31222])).
% 11.58/11.82 tff(31224,plain,
% 11.58/11.82 ($false),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[31116, 31223, 31216, 30550, 149, 30423, 2, 30422, 3446, 30592, 29889, 11173, 31, 1, 31205])).
% 11.58/11.82 tff(31225,plain,(r(elem!1, z) | (elem!1 = z) | b(s(s(s(s(z)))), z) | b(s(s(s(elem!1))), s(z)) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.58/11.82 tff(31226,plain,
% 11.58/11.82 (r(elem!1, z)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[31225, 2, 3446, 11173, 31, 1, 80])).
% 11.58/11.82 tff(31227,plain,
% 11.58/11.82 (~b(s(s(s(elem!1))), z)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[22948, 133, 10682, 379, 664])).
% 11.58/11.82 tff(31228,plain,
% 11.58/11.82 (r(s(s(s(elem!1))), z)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[377, 31227])).
% 11.58/11.82 tff(31229,plain,
% 11.58/11.82 (~r(elem!1, s(s(s(elem!1))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[30853, 326, 530, 174])).
% 11.58/11.82 tff(31230,plain,
% 11.58/11.82 (b(elem!1, s(s(s(elem!1))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[424, 31229, 1])).
% 11.58/11.82 tff(31231,plain,
% 11.58/11.82 (~r(s(s(s(elem!1))), elem!1)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[27619, 326, 530, 174])).
% 11.58/11.82 tff(31232,plain,
% 11.58/11.82 (b(s(s(s(elem!1))), elem!1)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[230, 31231, 9])).
% 11.58/11.82 tff(31233,plain,
% 11.58/11.82 ($false),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[10845, 31232, 31230, 10682, 133])).
% 11.58/11.82 tff(31234,plain,((~r(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.82 tff(31235,plain,
% 11.58/11.82 (~r(z, s(s(elem!1)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[31234, 133, 10682, 1, 530, 31228])).
% 11.58/11.82 tff(31236,plain,
% 11.58/11.82 (b(z, s(s(elem!1)))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[324, 31235])).
% 11.58/11.82 tff(31237,plain,
% 11.58/11.82 (~b(s(s(z)), z)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[31033, 2439, 133, 664, 15045])).
% 11.58/11.82 tff(31238,plain,
% 11.58/11.82 (r(s(s(z)), z)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[1211, 31237])).
% 11.58/11.82 tff(31239,plain,
% 11.58/11.82 (~(s(z) = elem!1)),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[7796, 4028, 379])).
% 11.58/11.82 tff(31240,plain,
% 11.58/11.82 (~(elem!1 = s(z))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[172, 31239])).
% 11.58/11.82 tff(31241,plain,
% 11.58/11.82 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[30935, 1697, 664, 15045, 31238, 1234, 2053, 31240, 10682, 379, 133, 183, 1, 2, 31])).
% 11.58/11.82 tff(31242,plain,
% 11.58/11.82 (r(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[3652, 31241])).
% 11.58/11.82 tff(31243,plain,
% 11.58/11.82 (~b(s(s(z)), s(z))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[21530, 2439, 664, 15045])).
% 11.58/11.82 tff(31244,plain,
% 11.58/11.82 (r(s(s(z)), s(z))),
% 11.58/11.82 inference(unit_resolution,[status(thm)],[3778, 31243])).
% 11.58/11.82 tff(31245,plain,
% 11.58/11.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.58/11.82 inference(rewrite,[status(thm)],[])).
% 11.58/11.83 tff(31246,plain,
% 11.58/11.83 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.58/11.83 inference(rewrite,[status(thm)],[])).
% 11.58/11.83 tff(31247,plain,
% 11.58/11.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.58/11.83 inference(monotonicity,[status(thm)],[31246])).
% 11.58/11.83 tff(31248,plain,
% 11.58/11.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.58/11.83 inference(transitivity,[status(thm)],[31247, 31245])).
% 11.58/11.83 tff(31249,plain,
% 11.58/11.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 11.58/11.83 inference(quant_inst,[status(thm)],[])).
% 11.58/11.83 tff(31250,plain,
% 11.58/11.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 11.58/11.83 inference(modus_ponens,[status(thm)],[31249, 31248])).
% 11.58/11.83 tff(31251,plain,
% 11.58/11.83 ($false),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[31250, 391, 381, 3927, 1234, 1759, 664])).
% 11.58/11.83 tff(31252,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.83 tff(31253,plain,
% 11.58/11.83 (~b(s(s(s(s(z)))), s(z))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[31252, 381, 3927, 1234, 664])).
% 11.58/11.83 tff(31254,plain,
% 11.58/11.83 (r(s(s(s(s(z)))), s(z))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[749, 31253])).
% 11.58/11.83 tff(31255,plain,
% 11.58/11.83 (~r(s(z), z)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[20881, 31254, 1749, 2405])).
% 11.58/11.83 tff(31256,plain,
% 11.58/11.83 (b(s(z), z)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[180, 31255])).
% 11.58/11.83 tff(31257,plain,
% 11.58/11.83 ($false),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[6011, 391, 133, 381, 3927, 664, 31256])).
% 11.58/11.83 tff(31258,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.83 tff(31259,plain,
% 11.58/11.83 (~b(s(s(elem!1)), s(z))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[31258, 31242, 31236, 664, 133, 31244, 1234])).
% 11.58/11.83 tff(31260,plain,
% 11.58/11.83 (r(s(s(elem!1)), s(z))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[362, 31259])).
% 11.58/11.83 tff(31261,plain,
% 11.58/11.83 (~b(s(z), z)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[30881, 340, 10682, 379, 4028, 410, 133, 249, 3927, 127])).
% 11.58/11.83 tff(31262,plain,
% 11.58/11.83 (r(s(z), z)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[180, 31261])).
% 11.58/11.83 tff(31263,plain,
% 11.58/11.83 (~r(z, s(s(s(s(z)))))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[10261, 31262, 2053, 3557])).
% 11.58/11.83 tff(31264,plain,
% 11.58/11.83 (b(z, s(s(s(s(z)))))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[800, 31263])).
% 11.58/11.83 tff(31265,plain,
% 11.58/11.83 (~b(s(s(s(s(z)))), s(z))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[10478, 31264, 1234, 664])).
% 11.58/11.83 tff(31266,plain,
% 11.58/11.83 (r(s(s(s(s(z)))), s(z))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[749, 31265])).
% 11.58/11.83 tff(31267,plain,
% 11.58/11.83 (~r(s(s(z)), s(z))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[20881, 31266, 1749, 31262])).
% 11.58/11.83 tff(31268,plain,
% 11.58/11.83 (b(s(s(z)), s(z))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[3778, 31267])).
% 11.58/11.83 tff(31269,plain,
% 11.58/11.83 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[30873, 340, 4028, 133, 3927, 31228, 249, 127, 410])).
% 11.58/11.83 tff(31270,plain,
% 11.58/11.83 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[1370, 31269, 15838])).
% 11.58/11.83 tff(31271,plain,
% 11.58/11.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 11.58/11.83 inference(rewrite,[status(thm)],[])).
% 11.58/11.83 tff(31272,plain,
% 11.58/11.83 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 11.58/11.83 inference(rewrite,[status(thm)],[])).
% 11.58/11.83 tff(31273,plain,
% 11.58/11.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 11.58/11.83 inference(monotonicity,[status(thm)],[31272])).
% 11.58/11.83 tff(31274,plain,
% 11.58/11.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 11.58/11.83 inference(transitivity,[status(thm)],[31273, 31271])).
% 11.58/11.83 tff(31275,plain,
% 11.58/11.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 11.58/11.83 inference(quant_inst,[status(thm)],[])).
% 11.58/11.83 tff(31276,plain,
% 11.58/11.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 11.58/11.83 inference(modus_ponens,[status(thm)],[31275, 31274])).
% 11.58/11.83 tff(31277,plain,
% 11.58/11.83 ($false),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[31276, 391, 31270, 379, 31268, 664, 15045])).
% 11.58/11.83 tff(31278,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | b(elem!1, s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.83 tff(31279,plain,
% 11.58/11.83 (s(s(elem!1)) = elem!1),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[31278, 31260, 664, 15045, 31242, 1234, 2053, 31238, 4028, 133, 31236, 379, 9, 6124, 10682])).
% 11.58/11.83 tff(31280,plain,
% 11.58/11.83 (s(s(s(elem!1))) = s(elem!1)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[451, 31279])).
% 11.58/11.83 tff(31281,plain,
% 11.58/11.83 (~(s(s(z)) = elem!1)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[4584, 31280, 118])).
% 11.58/11.83 tff(31282,plain,
% 11.58/11.83 ($false),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[5608, 194, 1749, 2053, 3557, 719])).
% 11.58/11.83 tff(31283,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.83 tff(31284,plain,
% 11.58/11.83 (~r(z, s(s(s(s(z)))))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[31283, 31242, 2053, 31238])).
% 11.58/11.83 tff(31285,plain,
% 11.58/11.83 (b(z, s(s(s(s(z)))))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[800, 31284])).
% 11.58/11.83 tff(31286,plain,
% 11.58/11.83 (~b(s(s(s(s(z)))), s(z))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[10478, 31285, 1234, 664])).
% 11.58/11.83 tff(31287,plain,
% 11.58/11.83 (r(s(s(s(s(z)))), s(z))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[749, 31286])).
% 11.58/11.83 tff(31288,plain,
% 11.58/11.83 (~r(s(z), elem!1)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[9149, 31287, 31242, 31244])).
% 11.58/11.83 tff(31289,plain,
% 11.58/11.83 (b(s(z), elem!1)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[632, 31288, 31239])).
% 11.58/11.83 tff(31290,plain,
% 11.58/11.83 (~(s(s(s(s(z)))) = elem!1)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[717, 31280])).
% 11.58/11.83 tff(31291,plain,
% 11.58/11.83 (~r(s(s(s(s(z)))), elem!1)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[29085, 6669, 1749, 530])).
% 11.58/11.83 tff(31292,plain,
% 11.58/11.83 (r(elem!1, s(s(s(s(z)))))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[18869, 31291, 720, 1234, 644])).
% 11.58/11.83 tff(31293,plain,
% 11.58/11.83 ($false),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[7111, 194, 1749, 2053, 31292, 6669])).
% 11.58/11.83 tff(31294,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.83 tff(31295,plain,
% 11.58/11.83 (~r(s(s(z)), elem!1)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[31294, 31242, 2053, 31290, 1234, 31289, 530])).
% 11.58/11.83 tff(31296,plain,
% 11.58/11.83 (b(s(s(z)), elem!1)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[4730, 31295, 31281])).
% 11.58/11.83 tff(31297,plain,
% 11.58/11.83 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 11.58/11.83 inference(monotonicity,[status(thm)],[31279])).
% 11.58/11.83 tff(31298,plain,
% 11.58/11.83 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 11.58/11.83 inference(monotonicity,[status(thm)],[31297])).
% 11.58/11.83 tff(31299,plain,
% 11.58/11.83 (~(elem!1 = s(s(z)))),
% 11.58/11.83 inference(modus_ponens,[status(thm)],[2680, 31298])).
% 11.58/11.83 tff(31300,plain,
% 11.58/11.83 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 11.58/11.83 inference(monotonicity,[status(thm)],[31279])).
% 11.58/11.83 tff(31301,plain,
% 11.58/11.83 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 11.58/11.83 inference(symmetry,[status(thm)],[31300])).
% 11.58/11.83 tff(31302,plain,
% 11.58/11.83 (b(s(s(s(s(z)))), elem!1)),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[762, 6221, 720])).
% 11.58/11.83 tff(31303,plain,
% 11.58/11.83 (r(elem!1, s(s(s(s(z)))))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[18869, 6221, 720, 1234, 644])).
% 11.58/11.83 tff(31304,plain,
% 11.58/11.83 (~r(elem!1, s(s(z)))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[18451, 31303, 2405, 1697])).
% 11.58/11.83 tff(31305,plain,
% 11.58/11.83 (b(elem!1, s(s(z)))),
% 11.58/11.83 inference(unit_resolution,[status(thm)],[3394, 31304, 1405])).
% 11.58/11.83 tff(31306,plain,
% 11.58/11.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 11.58/11.83 inference(rewrite,[status(thm)],[])).
% 11.58/11.83 tff(31307,plain,
% 11.58/11.83 (((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 11.58/11.83 inference(rewrite,[status(thm)],[])).
% 11.58/11.83 tff(31308,plain,
% 11.58/11.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 11.58/11.84 inference(monotonicity,[status(thm)],[31307])).
% 11.58/11.84 tff(31309,plain,
% 11.58/11.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 11.58/11.84 inference(transitivity,[status(thm)],[31308, 31306])).
% 11.58/11.84 tff(31310,plain,
% 11.58/11.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 11.58/11.84 inference(quant_inst,[status(thm)],[])).
% 11.58/11.84 tff(31311,plain,
% 11.58/11.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 11.58/11.84 inference(modus_ponens,[status(thm)],[31310, 31309])).
% 11.58/11.84 tff(31312,plain,
% 11.58/11.84 ($false),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[31311, 391, 133, 31305, 31302, 8498, 1686])).
% 11.58/11.84 tff(31313,plain,(r(s(s(s(s(z)))), elem!1) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(z)))))) | (elem!1 = s(s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.84 tff(31314,plain,
% 11.58/11.84 (r(s(s(s(s(z)))), elem!1)),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[31313, 31296, 133, 31285, 31299, 31244, 1697, 31290, 1234, 31289])).
% 11.58/11.84 tff(31315,plain,
% 11.58/11.84 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 11.58/11.84 inference(modus_ponens,[status(thm)],[31314, 31301])).
% 11.58/11.84 tff(31316,plain,
% 11.58/11.84 (~r(s(s(elem!1)), s(s(z)))),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[12699, 31315, 31238, 1697])).
% 11.58/11.84 tff(31317,plain,
% 11.58/11.84 (~r(elem!1, s(s(z)))),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[30899, 31316, 31279])).
% 11.58/11.84 tff(31318,plain,
% 11.58/11.84 (b(elem!1, s(s(z)))),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[3394, 31317, 31299])).
% 11.58/11.84 tff(31319,plain,
% 11.58/11.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 11.58/11.84 inference(rewrite,[status(thm)],[])).
% 11.58/11.84 tff(31320,plain,
% 11.58/11.84 (((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 11.58/11.84 inference(rewrite,[status(thm)],[])).
% 11.58/11.84 tff(31321,plain,
% 11.58/11.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 11.58/11.84 inference(monotonicity,[status(thm)],[31320])).
% 11.58/11.84 tff(31322,plain,
% 11.58/11.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 11.58/11.84 inference(transitivity,[status(thm)],[31321, 31319])).
% 11.58/11.84 tff(31323,plain,
% 11.58/11.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))),
% 11.58/11.84 inference(quant_inst,[status(thm)],[])).
% 11.58/11.84 tff(31324,plain,
% 11.58/11.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 11.58/11.84 inference(modus_ponens,[status(thm)],[31323, 31322])).
% 11.58/11.84 tff(31325,plain,
% 11.58/11.84 ($false),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[31324, 391, 31289, 31318, 2439, 31296])).
% 11.58/11.84 tff(31326,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | b(elem!1, s(s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.84 tff(31327,plain,
% 11.58/11.84 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[31326, 4028, 133, 1234, 2053, 530, 664, 15045, 2439, 379, 10682, 183, 1, 2, 31])).
% 11.58/11.84 tff(31328,plain,
% 11.58/11.84 (b(s(s(s(s(z)))), s(s(z)))),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[1714, 31327])).
% 11.58/11.84 tff(31329,plain,
% 11.58/11.84 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[6275, 31328, 1234, 2439])).
% 11.58/11.84 tff(31330,plain,
% 11.58/11.84 (r(elem!1, s(z))),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[837, 31240, 31])).
% 11.58/11.84 tff(31331,plain,
% 11.58/11.84 (~r(z, s(s(elem!1)))),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[30853, 410, 530, 31228])).
% 11.58/11.84 tff(31332,plain,
% 11.58/11.84 (b(z, s(s(elem!1)))),
% 11.58/11.84 inference(unit_resolution,[status(thm)],[324, 31331])).
% 11.58/11.84 tff(31333,plain,
% 11.58/11.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.58/11.84 inference(rewrite,[status(thm)],[])).
% 11.58/11.84 tff(31334,plain,
% 11.58/11.84 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.58/11.84 inference(rewrite,[status(thm)],[])).
% 11.58/11.84 tff(31335,plain,
% 11.58/11.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.58/11.84 inference(monotonicity,[status(thm)],[31334])).
% 11.58/11.84 tff(31336,plain,
% 11.58/11.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.58/11.84 inference(transitivity,[status(thm)],[31335, 31333])).
% 11.58/11.84 tff(31337,plain,
% 11.58/11.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 11.58/11.84 inference(quant_inst,[status(thm)],[])).
% 11.58/11.84 tff(31338,plain,
% 11.58/11.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 11.58/11.84 inference(modus_ponens,[status(thm)],[31337, 31336])).
% 11.58/11.84 tff(31339,plain,
% 11.58/11.84 ($false),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[31338, 391, 381, 3927, 1234, 3563, 664])).
% 11.58/11.85 tff(31340,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.85 tff(31341,plain,
% 11.58/11.85 (~b(s(s(elem!1)), s(z))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[31340, 3563, 1234, 31332, 664])).
% 11.58/11.85 tff(31342,plain,
% 11.58/11.85 (r(s(s(elem!1)), s(z))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[362, 31341])).
% 11.58/11.85 tff(31343,plain,
% 11.58/11.85 (s(s(elem!1)) = elem!1),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[31278, 31342, 664, 15045, 1749, 1234, 2053, 3557, 4028, 133, 31332, 379, 127, 410, 10682])).
% 11.58/11.85 tff(31344,plain,
% 11.58/11.85 (s(s(s(elem!1))) = s(elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[451, 31343])).
% 11.58/11.85 tff(31345,plain,
% 11.58/11.85 (~(s(s(z)) = elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[4584, 31344, 121])).
% 11.58/11.85 tff(31346,plain,
% 11.58/11.85 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 11.58/11.85 inference(monotonicity,[status(thm)],[31343])).
% 11.58/11.85 tff(31347,plain,
% 11.58/11.85 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 11.58/11.85 inference(monotonicity,[status(thm)],[31346])).
% 11.58/11.85 tff(31348,plain,
% 11.58/11.85 (~(elem!1 = s(s(z)))),
% 11.58/11.85 inference(modus_ponens,[status(thm)],[11940, 31347])).
% 11.58/11.85 tff(31349,plain,
% 11.58/11.85 (~b(s(s(z)), s(z))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[21540, 3563, 1234, 664, 15045])).
% 11.58/11.85 tff(31350,plain,
% 11.58/11.85 (r(s(s(z)), s(z))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[3778, 31349])).
% 11.58/11.85 tff(31351,plain,
% 11.58/11.85 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 11.58/11.85 inference(monotonicity,[status(thm)],[445])).
% 11.58/11.85 tff(31352,plain,
% 11.58/11.85 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 11.58/11.85 inference(symmetry,[status(thm)],[31351])).
% 11.58/11.85 tff(31353,plain,
% 11.58/11.85 (~r(s(s(s(s(z)))), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[22002, 719, 3557, 1749])).
% 11.58/11.85 tff(31354,plain,
% 11.58/11.85 (b(s(s(s(s(z)))), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[762, 31353, 718])).
% 11.58/11.85 tff(31355,plain,
% 11.58/11.85 (~r(elem!1, s(s(z)))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[8570, 719, 3557, 530])).
% 11.58/11.85 tff(31356,plain,
% 11.58/11.85 (b(elem!1, s(s(z)))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[3394, 31355, 1405])).
% 11.58/11.85 tff(31357,plain,
% 11.58/11.85 (~b(s(s(z)), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[11012, 31356, 31354, 3563])).
% 11.58/11.85 tff(31358,plain,
% 11.58/11.85 (r(s(s(z)), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[4730, 31357, 5547])).
% 11.58/11.85 tff(31359,plain,
% 11.58/11.85 (~r(s(z), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[6674, 31358, 2405, 847])).
% 11.58/11.85 tff(31360,plain,
% 11.58/11.85 (b(s(z), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[632, 31359, 150])).
% 11.58/11.85 tff(31361,plain,
% 11.58/11.85 (r(elem!1, s(s(s(s(z)))))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[18869, 31360, 718, 1234, 31353])).
% 11.58/11.85 tff(31362,plain,
% 11.58/11.85 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 11.58/11.85 inference(modus_ponens,[status(thm)],[31361, 31352])).
% 11.58/11.85 tff(31363,plain,
% 11.58/11.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 11.58/11.85 inference(rewrite,[status(thm)],[])).
% 11.58/11.85 tff(31364,plain,
% 11.58/11.85 (((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 11.58/11.85 inference(rewrite,[status(thm)],[])).
% 11.58/11.85 tff(31365,plain,
% 11.58/11.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 11.58/11.85 inference(monotonicity,[status(thm)],[31364])).
% 11.58/11.85 tff(31366,plain,
% 11.58/11.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 11.58/11.85 inference(transitivity,[status(thm)],[31365, 31363])).
% 11.58/11.85 tff(31367,plain,
% 11.58/11.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))),
% 11.58/11.85 inference(quant_inst,[status(thm)],[])).
% 11.58/11.85 tff(31368,plain,
% 11.58/11.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 11.58/11.85 inference(modus_ponens,[status(thm)],[31367, 31366])).
% 11.58/11.85 tff(31369,plain,
% 11.58/11.85 ($false),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[31368, 194, 2053, 719, 2616, 6257])).
% 11.58/11.85 tff(31370,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.85 tff(31371,plain,
% 11.58/11.85 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[31370, 719, 2053, 4782])).
% 11.58/11.85 tff(31372,plain,
% 11.58/11.85 ($false),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[31371, 31362])).
% 11.58/11.85 tff(31373,plain,((~r(z, s(s(s(s(z)))))) | (~(s(s(elem!1)) = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (s(z) = elem!1) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (s(s(z)) = elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (elem!1 = s(s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.85 tff(31374,plain,
% 11.58/11.85 (~r(z, s(s(s(s(z)))))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[31373, 31343, 1234, 31239, 31350, 847, 31345, 3563, 31348, 2053, 3557, 530, 1749])).
% 11.58/11.85 tff(31375,plain,
% 11.58/11.85 (b(z, s(s(s(s(z)))))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[800, 31374])).
% 11.58/11.85 tff(31376,plain,
% 11.58/11.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 11.58/11.85 inference(rewrite,[status(thm)],[])).
% 11.58/11.85 tff(31377,plain,
% 11.58/11.85 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 11.58/11.85 inference(rewrite,[status(thm)],[])).
% 11.58/11.85 tff(31378,plain,
% 11.58/11.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 11.58/11.85 inference(monotonicity,[status(thm)],[31377])).
% 11.58/11.85 tff(31379,plain,
% 11.58/11.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 11.58/11.85 inference(transitivity,[status(thm)],[31378, 31376])).
% 11.58/11.85 tff(31380,plain,
% 11.58/11.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 11.58/11.85 inference(quant_inst,[status(thm)],[])).
% 11.58/11.85 tff(31381,plain,
% 11.58/11.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 11.58/11.85 inference(modus_ponens,[status(thm)],[31380, 31379])).
% 11.58/11.85 tff(31382,plain,
% 11.58/11.85 ($false),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[31381, 391, 1234, 3563, 8498, 1686, 664])).
% 11.58/11.85 tff(31383,plain,((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.85 tff(31384,plain,
% 11.58/11.85 (~b(s(s(z)), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[31383, 3563, 1234, 31375, 664])).
% 11.58/11.85 tff(31385,plain,
% 11.58/11.85 (r(s(s(z)), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[4730, 31384, 31345])).
% 11.58/11.85 tff(31386,plain,
% 11.58/11.85 (~b(s(s(s(s(z)))), s(z))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[10478, 31375, 1234, 664])).
% 11.58/11.85 tff(31387,plain,
% 11.58/11.85 (r(s(s(s(s(z)))), s(z))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[749, 31386])).
% 11.58/11.85 tff(31388,plain,
% 11.58/11.85 (~r(s(z), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[9149, 31387, 1749, 31350])).
% 11.58/11.85 tff(31389,plain,
% 11.58/11.85 (b(s(z), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[632, 31388, 31239])).
% 11.58/11.85 tff(31390,plain,
% 11.58/11.85 (~(s(s(s(s(z)))) = elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[717, 31344])).
% 11.58/11.85 tff(31391,plain,
% 11.58/11.85 (~r(s(s(s(s(z)))), elem!1)),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[29085, 31385, 1749, 530])).
% 11.58/11.85 tff(31392,plain,
% 11.58/11.85 (r(elem!1, s(s(s(s(z)))))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[18869, 31391, 31390, 1234, 31389])).
% 11.58/11.85 tff(31393,plain,
% 11.58/11.85 ($false),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[7111, 194, 1749, 2053, 31392, 31385])).
% 11.58/11.85 tff(31394,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (s(z) = s(elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.85 tff(31395,plain,
% 11.58/11.85 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[31394, 31328, 2053, 1234, 530, 664, 31330, 31238, 15045, 118, 4028, 133, 379, 9, 6124, 10682])).
% 11.58/11.85 tff(31396,plain,
% 11.58/11.85 ($false),
% 11.58/11.85 inference(unit_resolution,[status(thm)],[3652, 31395, 31329])).
% 11.58/11.86 tff(31397,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.86 tff(31398,plain,
% 11.58/11.86 (b(elem!1, s(s(s(elem!1))))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31397, 31226, 30422, 3447, 30592, 30550, 149, 29889, 30423, 31121, 11174, 1, 2, 31])).
% 11.58/11.86 tff(31399,plain,
% 11.58/11.86 (~b(s(s(z)), elem!1)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[30671, 31398, 31121, 30592, 30550])).
% 11.58/11.86 tff(31400,plain,
% 11.58/11.86 (~b(s(s(s(elem!1))), elem!1)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[10845, 31398, 30423, 149])).
% 11.58/11.86 tff(31401,plain,
% 11.58/11.86 (r(s(s(s(elem!1))), elem!1)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[230, 31400, 9])).
% 11.58/11.86 tff(31402,plain,
% 11.58/11.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 11.58/11.86 inference(rewrite,[status(thm)],[])).
% 11.58/11.86 tff(31403,plain,
% 11.58/11.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 11.58/11.86 inference(quant_inst,[status(thm)],[])).
% 11.58/11.86 tff(31404,plain,
% 11.58/11.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 11.58/11.86 inference(modus_ponens,[status(thm)],[31403, 31402])).
% 11.58/11.86 tff(31405,plain,
% 11.58/11.86 (~r(s(s(s(elem!1))), s(s(z)))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31404, 194, 530, 233, 6669])).
% 11.58/11.86 tff(31406,plain,
% 11.58/11.86 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[10713, 42, 31405])).
% 11.58/11.86 tff(31407,plain,
% 11.58/11.86 (b(s(s(s(elem!1))), s(s(z)))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31406, 10703])).
% 11.58/11.86 tff(31408,plain,
% 11.58/11.86 (~r(s(s(z)), s(s(s(elem!1))))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[26812, 194, 530, 233, 6669])).
% 11.58/11.86 tff(31409,plain,
% 11.58/11.86 (b(s(s(z)), s(s(s(elem!1))))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[11041, 31408])).
% 11.58/11.86 tff(31410,plain,
% 11.58/11.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.58/11.86 inference(rewrite,[status(thm)],[])).
% 11.58/11.86 tff(31411,plain,
% 11.58/11.86 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.58/11.86 inference(rewrite,[status(thm)],[])).
% 11.58/11.86 tff(31412,plain,
% 11.58/11.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31411])).
% 11.58/11.86 tff(31413,plain,
% 11.58/11.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.58/11.86 inference(transitivity,[status(thm)],[31412, 31410])).
% 11.58/11.86 tff(31414,plain,
% 11.58/11.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 11.58/11.86 inference(quant_inst,[status(thm)],[])).
% 11.58/11.86 tff(31415,plain,
% 11.58/11.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 11.58/11.86 inference(modus_ponens,[status(thm)],[31414, 31413])).
% 11.58/11.86 tff(31416,plain,
% 11.58/11.86 ($false),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31415, 391, 379, 2439, 31409, 31407])).
% 11.58/11.86 tff(31417,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.86 tff(31418,plain,
% 11.58/11.86 (~r(s(s(z)), elem!1)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31417, 31121, 29889, 31226, 31401])).
% 11.58/11.86 tff(31419,plain,
% 11.58/11.86 (s(s(z)) = elem!1),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[4730, 31418, 31399])).
% 11.58/11.86 tff(31420,plain,
% 11.58/11.86 (s(s(s(z))) = s(elem!1)),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31419])).
% 11.58/11.86 tff(31421,plain,
% 11.58/11.86 (s(s(s(s(z)))) = s(s(elem!1))),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31420])).
% 11.58/11.86 tff(31422,plain,
% 11.58/11.86 (s(s(elem!1)) = s(s(s(s(z))))),
% 11.58/11.86 inference(symmetry,[status(thm)],[31421])).
% 11.58/11.86 tff(31423,plain,
% 11.58/11.86 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31422])).
% 11.58/11.86 tff(31424,plain,
% 11.58/11.86 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 11.58/11.86 inference(symmetry,[status(thm)],[31423])).
% 11.58/11.86 tff(31425,plain,
% 11.58/11.86 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31419])).
% 11.58/11.86 tff(31426,plain,
% 11.58/11.86 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31214, 3823, 2, 31, 1, 11174, 30423, 30422, 80, 30550])).
% 11.58/11.86 tff(31427,plain,
% 11.58/11.86 (r(s(s(s(s(z)))), s(s(z)))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[1714, 31426])).
% 11.58/11.86 tff(31428,plain,
% 11.58/11.86 (~b(s(s(z)), s(z))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[21530, 31121, 30592, 30550])).
% 11.58/11.86 tff(31429,plain,
% 11.58/11.86 (r(s(s(z)), s(z))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[3778, 31428])).
% 11.58/11.86 tff(31430,plain,
% 11.58/11.86 (~r(z, s(s(z)))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[18433, 31427, 3447, 31429])).
% 11.58/11.86 tff(31431,plain,
% 11.58/11.86 ($false),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31116, 31430, 31427, 30550, 149, 30423, 2, 30422, 3446, 30592, 29889, 11173, 31, 1, 3823])).
% 11.58/11.86 tff(31432,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = z) | b(s(s(s(s(z)))), z) | b(s(s(s(elem!1))), s(z)) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.58/11.86 tff(31433,plain,
% 11.58/11.86 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31432, 2, 3446, 11173, 31, 1, 80])).
% 11.58/11.86 tff(31434,plain,
% 11.58/11.86 (r(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[3652, 31433])).
% 11.58/11.86 tff(31435,plain,
% 11.58/11.86 (r(elem!1, s(s(s(s(z)))))),
% 11.58/11.86 inference(modus_ponens,[status(thm)],[31434, 31425])).
% 11.58/11.86 tff(31436,plain,
% 11.58/11.86 (r(elem!1, s(s(elem!1)))),
% 11.58/11.86 inference(modus_ponens,[status(thm)],[31435, 31424])).
% 11.58/11.86 tff(31437,plain,
% 11.58/11.86 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31421])).
% 11.58/11.86 tff(31438,plain,
% 11.58/11.86 (~r(s(z), elem!1)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[23283, 31401, 11174, 31226])).
% 11.58/11.86 tff(31439,plain,
% 11.58/11.86 (~r(z, s(s(s(s(z)))))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31283, 31434, 3447, 31124])).
% 11.58/11.86 tff(31440,plain,
% 11.58/11.86 (b(z, s(s(s(s(z)))))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[800, 31439])).
% 11.58/11.86 tff(31441,plain,
% 11.58/11.86 (~b(s(s(s(s(z)))), s(z))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[10478, 31440, 30422, 30592])).
% 11.58/11.86 tff(31442,plain,
% 11.58/11.86 (r(s(s(s(s(z)))), s(z))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[749, 31441])).
% 11.58/11.86 tff(31443,plain,
% 11.58/11.86 (~r(s(z), z)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[20881, 31442, 31434, 31429])).
% 11.58/11.86 tff(31444,plain,
% 11.58/11.86 (~(s(z) = elem!1)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[7479, 31443, 31226])).
% 11.58/11.86 tff(31445,plain,
% 11.58/11.86 (b(s(z), elem!1)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[632, 31444, 31438])).
% 11.58/11.86 tff(31446,plain,
% 11.58/11.86 (b(s(z), z)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[180, 31443])).
% 11.58/11.86 tff(31447,plain,
% 11.58/11.86 (~b(s(s(s(elem!1))), z)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[22948, 149, 30423, 29889, 30592])).
% 11.58/11.86 tff(31448,plain,
% 11.58/11.86 (r(s(s(s(elem!1))), z)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[377, 31447])).
% 11.58/11.86 tff(31449,plain,
% 11.58/11.86 (~r(z, s(s(elem!1)))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31234, 149, 30423, 1, 31226, 31448])).
% 11.58/11.86 tff(31450,plain,
% 11.58/11.86 (b(z, s(s(elem!1)))),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[324, 31449])).
% 11.58/11.86 tff(31451,plain,
% 11.58/11.86 (~(s(s(s(s(z)))) = elem!1)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[5152, 31418, 31434])).
% 11.58/11.86 tff(31452,plain,
% 11.58/11.86 (~r(s(s(z)), elem!1)),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[31294, 720, 2053, 1749, 1234, 644, 530])).
% 11.58/11.86 tff(31453,plain,
% 11.58/11.86 (s(s(z)) = elem!1),
% 11.58/11.86 inference(unit_resolution,[status(thm)],[4730, 31452, 30676])).
% 11.58/11.86 tff(31454,plain,
% 11.58/11.86 (s(s(s(z))) = s(elem!1)),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31453])).
% 11.58/11.86 tff(31455,plain,
% 11.58/11.86 (s(s(s(s(z)))) = s(s(elem!1))),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31454])).
% 11.58/11.86 tff(31456,plain,
% 11.58/11.86 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31455])).
% 11.58/11.86 tff(31457,plain,
% 11.58/11.86 (b(s(z), s(s(elem!1)))),
% 11.58/11.86 inference(modus_ponens,[status(thm)],[1234, 31456])).
% 11.58/11.86 tff(31458,plain,
% 11.58/11.86 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31455])).
% 11.58/11.86 tff(31459,plain,
% 11.58/11.86 (b(s(s(elem!1)), elem!1)),
% 11.58/11.86 inference(modus_ponens,[status(thm)],[6222, 31458])).
% 11.58/11.86 tff(31460,plain,
% 11.58/11.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 11.58/11.86 inference(rewrite,[status(thm)],[])).
% 11.58/11.86 tff(31461,plain,
% 11.58/11.86 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 11.58/11.86 inference(rewrite,[status(thm)],[])).
% 11.58/11.86 tff(31462,plain,
% 11.58/11.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 11.58/11.86 inference(monotonicity,[status(thm)],[31461])).
% 11.58/11.86 tff(31463,plain,
% 11.58/11.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 11.58/11.87 inference(transitivity,[status(thm)],[31462, 31460])).
% 11.58/11.87 tff(31464,plain,
% 11.58/11.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 11.58/11.87 inference(quant_inst,[status(thm)],[])).
% 11.58/11.87 tff(31465,plain,
% 11.58/11.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31464, 31463])).
% 11.58/11.87 tff(31466,plain,
% 11.58/11.87 ($false),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[31465, 391, 31459, 448, 3927, 590, 31457])).
% 11.58/11.87 tff(31467,plain,((s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(z)), elem!1) | r(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.87 tff(31468,plain,
% 11.58/11.87 (r(s(s(s(s(z)))), elem!1)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[31467, 31451, 31450, 31446, 30422, 31399, 31398, 3447, 31434, 31445, 31226])).
% 11.58/11.87 tff(31469,plain,
% 11.58/11.87 (r(s(s(elem!1)), elem!1)),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31468, 31437])).
% 11.58/11.87 tff(31470,plain,
% 11.58/11.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 11.58/11.87 inference(rewrite,[status(thm)],[])).
% 11.58/11.87 tff(31471,plain,
% 11.58/11.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 11.58/11.87 inference(quant_inst,[status(thm)],[])).
% 11.58/11.87 tff(31472,plain,
% 11.58/11.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31471, 31470])).
% 11.58/11.87 tff(31473,plain,
% 11.58/11.87 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[31472, 194, 31401, 31469, 31436])).
% 11.58/11.87 tff(31474,plain,
% 11.58/11.87 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31421])).
% 11.58/11.87 tff(31475,plain,
% 11.58/11.87 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31419])).
% 11.58/11.87 tff(31476,plain,
% 11.58/11.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[4584, 31453, 121])).
% 11.58/11.87 tff(31477,plain,
% 11.58/11.87 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31458])).
% 11.58/11.87 tff(31478,plain,
% 11.58/11.87 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31453])).
% 11.58/11.87 tff(31479,plain,
% 11.58/11.87 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31478])).
% 11.58/11.87 tff(31480,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 11.58/11.87 tff(31481,plain,
% 11.58/11.87 (~b(s(s(s(s(z)))), elem!1)),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31480, 31479])).
% 11.58/11.87 tff(31482,plain,
% 11.58/11.87 (~b(s(s(elem!1)), elem!1)),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31481, 31477])).
% 11.58/11.87 tff(31483,plain,
% 11.58/11.87 (s(s(elem!1)) = s(s(s(s(z))))),
% 11.58/11.87 inference(symmetry,[status(thm)],[31455])).
% 11.58/11.87 tff(31484,plain,
% 11.58/11.87 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31483])).
% 11.58/11.87 tff(31485,plain,
% 11.58/11.87 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 11.58/11.87 inference(symmetry,[status(thm)],[31484])).
% 11.58/11.87 tff(31486,plain,
% 11.58/11.87 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31453])).
% 11.58/11.87 tff(31487,plain,
% 11.58/11.87 (r(elem!1, s(s(s(s(z)))))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[1749, 31486])).
% 11.58/11.87 tff(31488,plain,
% 11.58/11.87 (r(elem!1, s(s(elem!1)))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31487, 31485])).
% 11.58/11.87 tff(31489,plain,
% 11.58/11.87 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31455])).
% 11.58/11.87 tff(31490,plain,
% 11.58/11.87 (r(s(s(s(s(z)))), elem!1)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[31467, 720, 3927, 590, 1234, 30676, 448, 2053, 1749, 644, 530])).
% 11.58/11.87 tff(31491,plain,
% 11.58/11.87 (r(s(s(elem!1)), elem!1)),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31490, 31489])).
% 11.58/11.87 tff(31492,plain,
% 11.58/11.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[4531, 194, 233, 31491, 31488])).
% 11.58/11.87 tff(31493,plain,
% 11.58/11.87 ($false),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[26900, 31492, 31482, 10682, 530, 233, 31476, 3927])).
% 11.58/11.87 tff(31494,plain,((s(s(s(s(z)))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(z) = s(elem!1)) | b(s(s(z)), elem!1) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.87 tff(31495,plain,
% 11.58/11.87 (b(s(s(s(s(z)))), s(s(z)))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[31494, 31451, 31226, 31401, 31450, 30423, 31434, 118, 31399, 31446, 30422, 31398, 3447, 31445])).
% 11.58/11.87 tff(31496,plain,
% 11.58/11.87 (b(s(s(s(s(z)))), elem!1)),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31495, 31475])).
% 11.58/11.87 tff(31497,plain,
% 11.58/11.87 (b(s(s(elem!1)), elem!1)),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31496, 31474])).
% 11.58/11.87 tff(31498,plain,
% 11.58/11.87 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[30751, 31497, 30423, 29889, 31446])).
% 11.58/11.87 tff(31499,plain,
% 11.58/11.87 ($false),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[1370, 31498, 31473, 26982])).
% 11.58/11.87 tff(31500,plain,((elem!1 = z) | b(s(s(s(s(z)))), z) | b(s(s(s(elem!1))), s(z)) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.58/11.87 tff(31501,plain,
% 11.58/11.87 (elem!1 = z),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[31500, 31, 11173, 3446, 1, 80])).
% 11.58/11.87 tff(31502,plain,
% 11.58/11.87 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), z)),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31501])).
% 11.58/11.87 tff(31503,plain,
% 11.58/11.87 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = z)),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31501])).
% 11.58/11.87 tff(31504,plain,
% 11.58/11.87 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 11.58/11.87 inference(symmetry,[status(thm)],[31503])).
% 11.58/11.87 tff(31505,plain,
% 11.58/11.87 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31504])).
% 11.58/11.87 tff(31506,plain,
% 11.58/11.87 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[6638, 31505])).
% 11.58/11.87 tff(31507,plain,
% 11.58/11.87 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31501])).
% 11.58/11.87 tff(31508,plain,
% 11.58/11.87 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 11.58/11.87 inference(symmetry,[status(thm)],[31507])).
% 11.58/11.87 tff(31509,plain,
% 11.58/11.87 (r(s(s(s(s(z)))), elem!1)),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[3447, 31508])).
% 11.58/11.87 tff(31510,plain,
% 11.58/11.87 (s(elem!1) = s(z)),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31501])).
% 11.58/11.87 tff(31511,plain,
% 11.58/11.87 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31510])).
% 11.58/11.87 tff(31512,plain,
% 11.58/11.87 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 11.58/11.87 inference(symmetry,[status(thm)],[31511])).
% 11.58/11.87 tff(31513,plain,
% 11.58/11.87 (r(s(s(s(elem!1))), s(elem!1))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[11174, 31512])).
% 11.58/11.87 tff(31514,plain,
% 11.58/11.87 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31501])).
% 11.58/11.87 tff(31515,plain,
% 11.58/11.87 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 11.58/11.87 inference(symmetry,[status(thm)],[31514])).
% 11.58/11.87 tff(31516,plain,
% 11.58/11.87 (b(z, s(elem!1)) <=> b(z, s(z))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31510])).
% 11.58/11.87 tff(31517,plain,
% 11.58/11.87 (b(z, s(z)) <=> b(z, s(elem!1))),
% 11.58/11.87 inference(symmetry,[status(thm)],[31516])).
% 11.58/11.87 tff(31518,plain,
% 11.58/11.87 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 11.58/11.87 inference(transitivity,[status(thm)],[31517, 31515])).
% 11.58/11.87 tff(31519,plain,
% 11.58/11.87 ((~b(z, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31518])).
% 11.58/11.87 tff(31520,plain,
% 11.58/11.87 (b(elem!1, s(z)) <=> b(z, s(z))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31501])).
% 11.58/11.87 tff(31521,plain,
% 11.58/11.87 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31520])).
% 11.58/11.87 tff(31522,plain,
% 11.58/11.87 (~b(z, s(z))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31, 31521])).
% 11.58/11.87 tff(31523,plain,
% 11.58/11.87 (~b(elem!1, s(elem!1))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31522, 31519])).
% 11.58/11.87 tff(31524,plain,
% 11.58/11.87 (r(elem!1, s(elem!1))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[443, 31523, 427])).
% 11.58/11.87 tff(31525,plain,
% 11.58/11.87 (r(z, s(z))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[45, 42, 31522, 28])).
% 11.58/11.87 tff(31526,plain,
% 11.58/11.87 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31510])).
% 11.58/11.87 tff(31527,plain,
% 11.58/11.87 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 11.58/11.87 inference(symmetry,[status(thm)],[31526])).
% 11.58/11.87 tff(31528,plain,
% 11.58/11.87 (b(s(elem!1), s(s(s(elem!1))))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[29889, 31527])).
% 11.58/11.87 tff(31529,plain,
% 11.58/11.87 (b(elem!1, s(s(s(elem!1))))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[23154, 31501, 30423])).
% 11.58/11.87 tff(31530,plain,
% 11.58/11.87 (r(s(s(s(elem!1))), elem!1)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[9853, 174, 17618])).
% 11.58/11.87 tff(31531,plain,
% 11.58/11.87 (~r(s(elem!1), elem!1)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[7744, 31530, 2251, 613])).
% 11.58/11.87 tff(31532,plain,
% 11.58/11.87 (b(s(elem!1), elem!1)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[2168, 31531, 164])).
% 11.58/11.87 tff(31533,plain,
% 11.58/11.87 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.58/11.87 inference(symmetry,[status(thm)],[29927])).
% 11.58/11.87 tff(31534,plain,
% 11.58/11.87 ((~r(s(s(s(s(z)))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31533])).
% 11.58/11.87 tff(31535,plain,
% 11.58/11.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 11.58/11.87 inference(rewrite,[status(thm)],[])).
% 11.58/11.87 tff(31536,plain,
% 11.58/11.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 11.58/11.87 inference(quant_inst,[status(thm)],[])).
% 11.58/11.87 tff(31537,plain,
% 11.58/11.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31536, 31535])).
% 11.58/11.87 tff(31538,plain,
% 11.58/11.87 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[31537, 194, 722, 2053, 29913])).
% 11.58/11.87 tff(31539,plain,
% 11.58/11.87 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31538, 31534])).
% 11.58/11.87 tff(31540,plain,
% 11.58/11.87 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[1095, 31539, 305])).
% 11.58/11.87 tff(31541,plain,
% 11.58/11.87 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.58/11.87 inference(symmetry,[status(thm)],[17614])).
% 11.58/11.87 tff(31542,plain,
% 11.58/11.87 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.58/11.87 inference(transitivity,[status(thm)],[17612, 31541])).
% 11.58/11.87 tff(31543,plain,
% 11.58/11.87 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31542])).
% 11.58/11.87 tff(31544,plain,
% 11.58/11.87 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[29920, 31543])).
% 11.58/11.87 tff(31545,plain,
% 11.58/11.87 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[1164, 31544, 1153])).
% 11.58/11.87 tff(31546,plain,
% 11.58/11.87 ($false),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[17954, 31545, 31540, 448, 31532, 1036])).
% 11.58/11.87 tff(31547,plain,((~r(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~(elem!1 = z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (s(elem!1) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.87 tff(31548,plain,
% 11.58/11.87 (~r(s(s(s(elem!1))), z)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[31547, 31529, 31528, 29900, 31501, 31525, 3447, 426, 31524, 31513])).
% 11.58/11.87 tff(31549,plain,
% 11.58/11.87 (b(s(s(s(elem!1))), z)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[377, 31548])).
% 11.58/11.87 tff(31550,plain,
% 11.58/11.87 (~b(s(z), z)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[11303, 31549, 29889, 30423])).
% 11.58/11.87 tff(31551,plain,
% 11.58/11.87 (r(s(z), elem!1)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[3205, 31550, 31501])).
% 11.58/11.87 tff(31552,plain,
% 11.58/11.87 ((s(z) = elem!1) <=> (s(z) = z)),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31501])).
% 11.58/11.87 tff(31553,plain,
% 11.58/11.87 ((s(z) = z) <=> (s(z) = elem!1)),
% 11.58/11.87 inference(symmetry,[status(thm)],[31552])).
% 11.58/11.87 tff(31554,plain,
% 11.58/11.87 ((s(z) = z) <=> (elem!1 = s(z))),
% 11.58/11.87 inference(transitivity,[status(thm)],[31553, 1270])).
% 11.58/11.87 tff(31555,plain,
% 11.58/11.87 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31554])).
% 11.58/11.87 tff(31556,plain,
% 11.58/11.87 (~(elem!1 = s(z))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[23, 31555])).
% 11.58/11.87 tff(31557,plain,
% 11.58/11.87 (r(elem!1, s(z))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[837, 31556, 31])).
% 11.58/11.87 tff(31558,plain,
% 11.58/11.87 (r(s(z), z)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[180, 31550])).
% 11.58/11.87 tff(31559,plain,
% 11.58/11.87 (~r(s(s(s(s(z)))), s(z))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[15864, 31558, 31557, 31509])).
% 11.58/11.87 tff(31560,plain,
% 11.58/11.87 (b(s(s(s(s(z)))), s(z))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[749, 31559])).
% 11.58/11.87 tff(31561,plain,
% 11.58/11.87 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[11865, 31560, 31557, 31551, 31509])).
% 11.58/11.87 tff(31562,plain,
% 11.58/11.87 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[8073, 31561, 31506])).
% 11.58/11.87 tff(31563,plain,
% 11.58/11.87 (b(s(s(s(s(s(s(z)))))), z)),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[31562, 31502])).
% 11.58/11.87 tff(31564,plain,
% 11.58/11.87 (b(s(s(s(z))), z)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[1680, 31549, 31501])).
% 11.58/11.87 tff(31565,plain,
% 11.58/11.87 (s(s(elem!1)) = s(s(z))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31510])).
% 11.58/11.87 tff(31566,plain,
% 11.58/11.87 (s(s(s(elem!1))) = s(s(s(z)))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31565])).
% 11.58/11.87 tff(31567,plain,
% 11.58/11.87 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 11.58/11.87 inference(monotonicity,[status(thm)],[31566])).
% 11.58/11.87 tff(31568,plain,
% 11.58/11.87 (b(z, s(s(s(z))))),
% 11.58/11.87 inference(modus_ponens,[status(thm)],[30423, 31567])).
% 11.58/11.87 tff(31569,plain,
% 11.58/11.87 (~r(s(s(z)), z)),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[26737, 31560, 3447, 31525, 31558, 30422])).
% 11.58/11.87 tff(31570,plain,
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% 11.58/11.87 inference(unit_resolution,[status(thm)],[1211, 31569])).
% 11.58/11.87 tff(31571,plain,
% 11.58/11.87 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[29536, 391, 31570, 31568, 31564, 31563])).
% 11.58/11.87 tff(31572,plain,
% 11.58/11.87 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.58/11.87 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 31571])).
% 11.58/11.87 tff(31573,plain,
% 11.58/11.87 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[29523, 391, 31568, 31564, 31563])).
% 11.58/11.88 tff(31574,plain,
% 11.58/11.88 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[29527, 42, 8094, 31573])).
% 11.58/11.88 tff(31575,plain,
% 11.58/11.88 (~(s(s(z)) = s(s(s(z))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[8879, 31501])).
% 11.58/11.88 tff(31576,plain,
% 11.58/11.88 (~b(s(s(z)), s(s(s(z))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[8632, 391, 31570, 31568, 31564])).
% 11.58/11.88 tff(31577,plain,
% 11.58/11.88 (r(s(s(z)), s(s(s(z))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[24076, 31576, 31575])).
% 11.58/11.88 tff(31578,plain,
% 11.58/11.88 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 11.58/11.88 inference(monotonicity,[status(thm)],[31565])).
% 11.58/11.88 tff(31579,plain,
% 11.58/11.88 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 11.58/11.88 inference(symmetry,[status(thm)],[31578])).
% 11.58/11.88 tff(31580,plain,
% 11.58/11.88 (b(s(s(elem!1)), z)),
% 11.58/11.88 inference(modus_ponens,[status(thm)],[31570, 31579])).
% 11.58/11.88 tff(31581,plain,
% 11.58/11.88 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[13177, 31580, 30423, 31549])).
% 11.58/11.88 tff(31582,plain,
% 11.58/11.88 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[1370, 31581, 26982])).
% 11.58/11.88 tff(31583,plain,
% 11.58/11.88 (r(s(s(s(z))), s(s(z)))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[4385, 31582, 31501])).
% 11.58/11.88 tff(31584,plain,
% 11.58/11.88 ($false),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[29550, 194, 31583, 31577, 31574, 31572])).
% 11.58/11.88 tff(31585,plain,(b(elem!1, s(z)) | b(s(s(s(elem!1))), s(z)) | b(s(s(s(s(z)))), z) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.58/11.88 tff(31586,plain,
% 11.58/11.88 (elem!1 = s(s(s(elem!1)))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[31585, 29430, 3446, 31, 80])).
% 11.58/11.88 tff(31587,plain,
% 11.58/11.88 (s(s(s(elem!1))) = elem!1),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[129, 31586])).
% 11.58/11.88 tff(31588,plain,
% 11.58/11.88 (r(elem!1, s(z))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[837, 26584, 31])).
% 11.58/11.88 tff(31589,plain,
% 11.58/11.88 (~r(elem!1, s(s(s(s(z)))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[11195, 31588, 29426, 1216])).
% 11.58/11.88 tff(31590,plain,
% 11.58/11.88 (~(s(s(s(s(z)))) = elem!1)),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[1436, 31587])).
% 11.58/11.88 tff(31591,plain,
% 11.58/11.88 (~(elem!1 = s(s(s(s(z)))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[769, 31590])).
% 11.58/11.88 tff(31592,plain,
% 11.58/11.88 (b(elem!1, s(s(s(s(z)))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[781, 31591, 31589])).
% 11.58/11.88 tff(31593,plain,
% 11.58/11.88 (~b(s(s(z)), s(z))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[29615, 1749, 1216, 2053])).
% 11.58/11.88 tff(31594,plain,
% 11.58/11.88 ($false),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[3778, 31593, 10581])).
% 11.58/11.88 tff(31595,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.88 tff(31596,plain,
% 11.58/11.88 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[31595, 1216, 29426])).
% 11.58/11.88 tff(31597,plain,
% 11.58/11.88 (b(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[3652, 31596])).
% 11.58/11.88 tff(31598,plain,
% 11.58/11.88 (~b(s(z), s(s(s(elem!1))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[17481, 22855, 10682, 590, 28038])).
% 11.58/11.88 tff(31599,plain,
% 11.58/11.88 (r(s(z), s(s(s(elem!1))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[247, 31598])).
% 11.58/11.88 tff(31600,plain,
% 11.58/11.88 (~b(s(s(z)), s(s(s(elem!1))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[15908, 391, 3823, 22855, 28038])).
% 11.58/11.88 tff(31601,plain,
% 11.58/11.88 (r(s(s(z)), s(s(s(elem!1))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[11041, 31600])).
% 11.58/11.88 tff(31602,plain,
% 11.58/11.88 (~r(s(s(z)), s(z))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[11050, 31601, 16441, 31599])).
% 11.58/11.88 tff(31603,plain,
% 11.58/11.88 (b(s(s(z)), s(z))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[3778, 31602])).
% 11.58/11.88 tff(31604,plain,
% 11.58/11.88 (~r(s(z), s(s(z)))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[25978, 31601, 16441, 31599])).
% 11.58/11.88 tff(31605,plain,
% 11.58/11.88 (b(s(z), s(s(z)))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[1788, 31604])).
% 11.58/11.88 tff(31606,plain,
% 11.58/11.88 (~b(z, s(s(s(s(z)))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[15860, 1652, 133, 2064])).
% 11.58/11.88 tff(31607,plain,
% 11.58/11.88 (r(z, s(s(s(s(z)))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[800, 31606])).
% 11.58/11.88 tff(31608,plain,
% 11.58/11.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.58/11.88 inference(rewrite,[status(thm)],[])).
% 11.58/11.88 tff(31609,plain,
% 11.58/11.88 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.58/11.88 inference(rewrite,[status(thm)],[])).
% 11.58/11.88 tff(31610,plain,
% 11.58/11.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 11.58/11.88 inference(monotonicity,[status(thm)],[31609])).
% 11.58/11.88 tff(31611,plain,
% 11.58/11.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.58/11.88 inference(transitivity,[status(thm)],[31610, 31608])).
% 11.58/11.88 tff(31612,plain,
% 11.58/11.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 11.58/11.88 inference(quant_inst,[status(thm)],[])).
% 11.58/11.88 tff(31613,plain,
% 11.58/11.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 11.58/11.88 inference(modus_ponens,[status(thm)],[31612, 31611])).
% 11.58/11.88 tff(31614,plain,
% 11.58/11.88 (~b(s(s(s(elem!1))), s(s(z)))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[31613, 391, 3823, 22855, 28038])).
% 11.58/11.88 tff(31615,plain,
% 11.58/11.88 (~b(elem!1, s(s(z)))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[16425, 31614, 125])).
% 11.58/11.88 tff(31616,plain,
% 11.58/11.88 (r(elem!1, s(s(z)))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[3394, 31615, 3820])).
% 11.58/11.88 tff(31617,plain,
% 11.58/11.88 (~r(s(s(z)), z)),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[8570, 31616, 530, 31607])).
% 11.58/11.88 tff(31618,plain,
% 11.58/11.88 (b(s(s(z)), z)),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[1211, 31617])).
% 11.58/11.88 tff(31619,plain,
% 11.58/11.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 11.58/11.88 inference(rewrite,[status(thm)],[])).
% 11.58/11.88 tff(31620,plain,
% 11.58/11.88 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 11.58/11.88 inference(rewrite,[status(thm)],[])).
% 11.58/11.88 tff(31621,plain,
% 11.58/11.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 11.58/11.88 inference(monotonicity,[status(thm)],[31620])).
% 11.58/11.88 tff(31622,plain,
% 11.58/11.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 11.58/11.88 inference(transitivity,[status(thm)],[31621, 31619])).
% 11.58/11.88 tff(31623,plain,
% 11.58/11.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 11.58/11.88 inference(quant_inst,[status(thm)],[])).
% 11.58/11.88 tff(31624,plain,
% 11.58/11.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 11.58/11.88 inference(modus_ponens,[status(thm)],[31623, 31622])).
% 11.58/11.88 tff(31625,plain,
% 11.58/11.88 ($false),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[31624, 391, 3823, 31618, 31605, 31603, 664])).
% 11.58/11.88 tff(31626,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(elem!1, z)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.88 tff(31627,plain,
% 11.58/11.88 (~b(s(s(s(s(z)))), elem!1)),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[31626, 31586, 29429, 3618, 31597, 29427, 5450, 22902, 31592])).
% 11.58/11.88 tff(31628,plain,
% 11.58/11.88 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[2694, 31627, 31587])).
% 11.58/11.88 tff(31629,plain,
% 11.58/11.88 (~b(elem!1, s(s(s(elem!1))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[16115, 31588, 22902, 29429, 29427, 31, 1216, 26583])).
% 11.58/11.88 tff(31630,plain,
% 11.58/11.88 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.58/11.88 inference(monotonicity,[status(thm)],[31586])).
% 11.58/11.88 tff(31631,plain,
% 11.58/11.88 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.58/11.88 inference(modus_ponens,[status(thm)],[31592, 31630])).
% 11.58/11.88 tff(31632,plain,
% 11.58/11.88 (r(s(s(s(s(z)))), elem!1)),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[762, 31627, 31590])).
% 11.58/11.88 tff(31633,plain,
% 11.58/11.88 (~r(s(z), elem!1)),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[5396, 31632, 1216, 31588])).
% 11.58/11.88 tff(31634,plain,
% 11.58/11.88 (b(s(z), elem!1)),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[632, 31633, 26583])).
% 11.58/11.88 tff(31635,plain,
% 11.58/11.88 (b(s(z), s(s(s(elem!1))))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[14872, 31634, 31587])).
% 11.58/11.88 tff(31636,plain,
% 11.58/11.88 (~b(s(s(s(s(z)))), s(z))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[15992, 31635, 2, 31597, 31, 31631, 31629, 5450, 1216, 29426])).
% 11.58/11.88 tff(31637,plain,
% 11.58/11.88 (r(s(s(s(s(z)))), s(z))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[749, 31636])).
% 11.58/11.88 tff(31638,plain,
% 11.58/11.88 (r(s(s(s(elem!1))), s(z))),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[223, 29430])).
% 11.58/11.88 tff(31639,plain,
% 11.58/11.88 ($false),
% 11.58/11.88 inference(unit_resolution,[status(thm)],[10698, 194, 31638, 1216, 31637, 31628])).
% 11.58/11.88 tff(31640,plain,(r(s(z), z) | (~r(s(z), s(s(s(s(z)))))) | (elem!1 = z) | b(elem!1, s(z)) | b(s(s(s(s(z)))), z) | r(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 11.58/11.89 tff(31641,plain,
% 11.58/11.89 (r(s(z), z)),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[31640, 484, 2, 31, 3446, 80, 2913])).
% 11.58/11.89 tff(31642,plain,
% 11.58/11.89 (~r(z, s(s(s(s(z)))))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[17062, 838, 530, 182])).
% 11.58/11.89 tff(31643,plain,
% 11.58/11.89 (b(z, s(s(s(s(z)))))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[800, 31642])).
% 11.58/11.89 tff(31644,plain,
% 11.58/11.89 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[31595, 2913, 29426])).
% 11.58/11.89 tff(31645,plain,
% 11.58/11.89 (b(s(s(z)), s(s(s(s(z)))))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[3652, 31644])).
% 11.58/11.89 tff(31646,plain,
% 11.58/11.89 (~r(z, s(s(elem!1)))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[855, 838, 530, 182])).
% 11.58/11.89 tff(31647,plain,
% 11.58/11.89 (b(z, s(s(elem!1)))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[324, 31646])).
% 11.58/11.89 tff(31648,plain,
% 11.58/11.89 (~r(elem!1, s(s(s(s(z)))))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[11195, 838, 29426, 2913])).
% 11.58/11.89 tff(31649,plain,
% 11.58/11.89 (~b(s(s(s(s(z)))), elem!1)),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[15860, 6223, 133, 1686])).
% 11.58/11.89 tff(31650,plain,
% 11.58/11.89 (r(s(s(s(s(z)))), elem!1)),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[762, 31649, 720])).
% 11.58/11.89 tff(31651,plain,
% 11.58/11.89 (~r(s(s(s(s(z)))), s(z))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[15864, 31650, 182, 847])).
% 11.58/11.89 tff(31652,plain,
% 11.58/11.89 (b(s(s(s(s(z)))), s(z))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[749, 31651])).
% 11.58/11.89 tff(31653,plain,
% 11.58/11.89 (~r(s(z), elem!1)),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[5396, 31650, 1216, 847])).
% 11.58/11.89 tff(31654,plain,
% 11.58/11.89 (b(s(z), elem!1)),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[632, 31653, 150])).
% 11.58/11.89 tff(31655,plain,
% 11.58/11.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.58/11.89 inference(rewrite,[status(thm)],[])).
% 11.58/11.89 tff(31656,plain,
% 11.58/11.89 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.58/11.89 inference(rewrite,[status(thm)],[])).
% 11.58/11.89 tff(31657,plain,
% 11.58/11.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 11.58/11.89 inference(monotonicity,[status(thm)],[31656])).
% 11.58/11.89 tff(31658,plain,
% 11.58/11.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.58/11.89 inference(transitivity,[status(thm)],[31657, 31655])).
% 11.58/11.89 tff(31659,plain,
% 11.58/11.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 11.58/11.89 inference(quant_inst,[status(thm)],[])).
% 11.58/11.89 tff(31660,plain,
% 11.58/11.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 11.58/11.89 inference(modus_ponens,[status(thm)],[31659, 31658])).
% 11.58/11.89 tff(31661,plain,
% 11.58/11.89 ($false),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[31660, 391, 133, 31654, 6223, 31652, 1686])).
% 11.58/11.89 tff(31662,plain,((s(s(s(s(z)))) = elem!1) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (s(z) = elem!1) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.89 tff(31663,plain,
% 11.58/11.89 (s(s(s(s(z)))) = elem!1),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[31662, 31643, 22902, 150, 182, 838, 2913, 31648])).
% 11.58/11.89 tff(31664,plain,
% 11.58/11.89 (b(s(s(z)), elem!1)),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[30679, 31663, 31645])).
% 11.58/11.89 tff(31665,plain,
% 11.58/11.89 (~r(z, s(z))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[10620, 2913, 29426])).
% 11.58/11.89 tff(31666,plain,
% 11.58/11.89 (b(z, s(z))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[678, 31665])).
% 11.58/11.89 tff(31667,plain,
% 11.58/11.89 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[717, 31663])).
% 11.58/11.89 tff(31668,plain,
% 11.58/11.89 (~(s(s(elem!1)) = elem!1)),
% 11.58/11.89 inference(unit_resolution,[status(thm)],[451, 31667])).
% 11.58/11.89 tff(31669,plain,
% 11.58/11.89 (s(s(s(s(s(z))))) = s(elem!1)),
% 11.58/11.89 inference(monotonicity,[status(thm)],[31663])).
% 11.58/11.89 tff(31670,plain,
% 11.58/11.89 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 11.58/11.89 inference(monotonicity,[status(thm)],[31669])).
% 11.58/11.89 tff(31671,plain,
% 11.58/11.89 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 11.58/11.89 inference(monotonicity,[status(thm)],[31670])).
% 11.58/11.89 tff(31672,plain,
% 11.58/11.89 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 11.58/11.89 inference(monotonicity,[status(thm)],[31663])).
% 11.58/11.89 tff(31673,plain,
% 11.58/11.89 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 11.58/11.89 inference(transitivity,[status(thm)],[31672, 31671])).
% 11.58/11.89 tff(31674,plain,
% 11.58/11.89 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), elem!1))),
% 11.58/11.89 inference(monotonicity,[status(thm)],[31673])).
% 11.58/11.89 tff(31675,plain,
% 11.58/11.89 (b(z, s(s(s(s(s(s(z))))))) <=> b(z, s(s(elem!1)))),
% 11.58/11.89 inference(monotonicity,[status(thm)],[31670])).
% 11.58/11.89 tff(31676,plain,
% 11.58/11.89 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 11.58/11.89 inference(symmetry,[status(thm)],[31675])).
% 11.58/11.89 tff(31677,plain,
% 11.58/11.89 (b(z, s(s(s(s(s(s(z)))))))),
% 11.58/11.89 inference(modus_ponens,[status(thm)],[31647, 31676])).
% 11.58/11.89 tff(31678,plain,
% 11.58/11.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 11.58/11.89 inference(rewrite,[status(thm)],[])).
% 11.58/11.89 tff(31679,plain,
% 11.58/11.89 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 11.58/11.89 inference(rewrite,[status(thm)],[])).
% 11.58/11.89 tff(31680,plain,
% 11.58/11.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 11.58/11.89 inference(monotonicity,[status(thm)],[31679])).
% 11.58/11.89 tff(31681,plain,
% 11.58/11.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 11.58/11.89 inference(transitivity,[status(thm)],[31680, 31678])).
% 11.58/11.89 tff(31682,plain,
% 11.58/11.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 11.58/11.89 inference(quant_inst,[status(thm)],[])).
% 11.58/11.89 tff(31683,plain,
% 11.58/11.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 11.58/11.89 inference(modus_ponens,[status(thm)],[31682, 31681])).
% 11.58/11.89 tff(31684,plain,
% 11.58/11.90 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[31683, 194, 2053, 1216, 6610])).
% 11.58/11.90 tff(31685,plain,
% 11.58/11.90 ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[11665, 42, 31684])).
% 11.58/11.90 tff(31686,plain,
% 11.58/11.90 (b(s(z), s(s(s(s(s(s(z)))))))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[31685, 11652])).
% 11.58/11.90 tff(31687,plain,
% 11.58/11.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 11.58/11.90 inference(rewrite,[status(thm)],[])).
% 11.58/11.90 tff(31688,plain,
% 11.58/11.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 11.58/11.90 inference(quant_inst,[status(thm)],[])).
% 11.58/11.90 tff(31689,plain,
% 11.58/11.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 11.58/11.90 inference(modus_ponens,[status(thm)],[31688, 31687])).
% 11.58/11.90 tff(31690,plain,
% 11.58/11.90 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[31689, 194, 2053, 1216, 6610])).
% 11.58/11.90 tff(31691,plain,
% 11.58/11.90 (b(s(s(s(s(s(s(z)))))), s(z))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[11674, 42, 5065, 31690])).
% 11.58/11.90 tff(31692,plain,
% 11.58/11.90 ($false),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[14148, 391, 664, 31691, 14101, 31686])).
% 11.58/11.90 tff(31693,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.90 tff(31694,plain,
% 11.58/11.90 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[31693, 31677, 2913, 29426, 31666])).
% 11.58/11.90 tff(31695,plain,
% 11.58/11.90 (~r(s(s(elem!1)), elem!1)),
% 11.58/11.90 inference(modus_ponens,[status(thm)],[31694, 31674])).
% 11.58/11.90 tff(31696,plain,
% 11.58/11.90 (b(s(s(elem!1)), elem!1)),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[872, 31695, 31668])).
% 11.58/11.90 tff(31697,plain,
% 11.58/11.90 (~r(s(s(elem!1)), s(z))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[3996, 31696, 22902, 838, 182, 31647])).
% 11.58/11.90 tff(31698,plain,
% 11.58/11.90 (b(s(s(elem!1)), s(z))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[362, 31697])).
% 11.58/11.90 tff(31699,plain,
% 11.58/11.90 (~b(s(z), s(s(z)))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[26460, 31698, 31666, 31664, 31647])).
% 11.58/11.90 tff(31700,plain,
% 11.58/11.90 (r(s(z), s(s(z)))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[1788, 31699])).
% 11.58/11.90 tff(31701,plain,
% 11.58/11.90 (~b(s(s(s(s(z)))), s(z))),
% 11.58/11.90 inference(unit_resolution,[status(thm)],[11186, 31663, 31])).
% 11.58/11.90 tff(31702,plain,
% 11.58/11.90 (r(s(s(s(s(z)))), s(z))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[749, 31701])).
% 11.69/11.90 tff(31703,plain,
% 11.69/11.90 (~b(s(z), elem!1)),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[6252, 31663, 2881])).
% 11.69/11.90 tff(31704,plain,
% 11.69/11.90 (r(s(z), elem!1)),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[632, 31703, 150])).
% 11.69/11.90 tff(31705,plain,
% 11.69/11.90 (~b(elem!1, s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[16115, 838, 22902, 31666, 29427, 31, 2913, 150])).
% 11.69/11.90 tff(31706,plain,
% 11.69/11.90 (~(s(s(s(elem!1))) = elem!1)),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[1436, 31663])).
% 11.69/11.90 tff(31707,plain,
% 11.69/11.90 (~(elem!1 = s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[129, 31706])).
% 11.69/11.90 tff(31708,plain,
% 11.69/11.90 (r(elem!1, s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[424, 31707, 31705])).
% 11.69/11.90 tff(31709,plain,
% 11.69/11.90 (b(s(s(s(elem!1))), s(z))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[31432, 31707, 2, 3446, 31645, 31, 80])).
% 11.69/11.90 tff(31710,plain,
% 11.69/11.90 (~b(s(z), s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[15561, 31709, 29427, 31666])).
% 11.69/11.90 tff(31711,plain,
% 11.69/11.90 (r(s(z), s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[247, 31710])).
% 11.69/11.90 tff(31712,plain,
% 11.69/11.90 (~r(s(s(s(elem!1))), z)),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[5645, 31711, 31708, 31704])).
% 11.69/11.90 tff(31713,plain,
% 11.69/11.90 (b(s(s(s(elem!1))), z)),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[377, 31712])).
% 11.69/11.90 tff(31714,plain,
% 11.69/11.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 11.69/11.90 inference(rewrite,[status(thm)],[])).
% 11.69/11.90 tff(31715,plain,
% 11.69/11.90 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 11.69/11.90 inference(rewrite,[status(thm)],[])).
% 11.69/11.90 tff(31716,plain,
% 11.69/11.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31715])).
% 11.69/11.90 tff(31717,plain,
% 11.69/11.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 11.69/11.90 inference(transitivity,[status(thm)],[31716, 31714])).
% 11.69/11.90 tff(31718,plain,
% 11.69/11.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 11.69/11.90 inference(quant_inst,[status(thm)],[])).
% 11.69/11.90 tff(31719,plain,
% 11.69/11.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 11.69/11.90 inference(modus_ponens,[status(thm)],[31718, 31717])).
% 11.69/11.90 tff(31720,plain,
% 11.69/11.90 ($false),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[31719, 391, 3823, 1235, 3563, 1686])).
% 11.69/11.90 tff(31721,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.90 tff(31722,plain,
% 11.69/11.90 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[31721, 1235, 1686, 3823])).
% 11.69/11.90 tff(31723,plain,
% 11.69/11.90 (r(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[1714, 31722])).
% 11.69/11.90 tff(31724,plain,
% 11.69/11.90 (~r(s(s(z)), s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[9138, 31723, 723, 1747])).
% 11.69/11.90 tff(31725,plain,
% 11.69/11.90 (b(s(s(z)), s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[11041, 31724])).
% 11.69/11.90 tff(31726,plain,
% 11.69/11.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 11.69/11.90 inference(rewrite,[status(thm)],[])).
% 11.69/11.90 tff(31727,plain,
% 11.69/11.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 11.69/11.90 inference(quant_inst,[status(thm)],[])).
% 11.69/11.90 tff(31728,plain,
% 11.69/11.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 11.69/11.90 inference(modus_ponens,[status(thm)],[31727, 31726])).
% 11.69/11.90 tff(31729,plain,
% 11.69/11.90 ($false),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[31728, 391, 381, 380, 3927, 1235, 31725])).
% 11.69/11.90 tff(31730,plain,((~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.90 tff(31731,plain,
% 11.69/11.90 (~b(s(s(z)), z)),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[31730, 31698, 31713, 31647, 31702, 31700, 31643, 31645])).
% 11.69/11.90 tff(31732,plain,
% 11.69/11.90 (r(s(s(z)), z)),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[1211, 31731])).
% 11.69/11.90 tff(31733,plain,
% 11.69/11.90 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[11508, 31732, 2913, 31700])).
% 11.69/11.90 tff(31734,plain,
% 11.69/11.90 (b(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[1714, 31733])).
% 11.69/11.90 tff(31735,plain,
% 11.69/11.90 (~r(z, s(s(z)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[20649, 31732, 182, 31700])).
% 11.69/11.90 tff(31736,plain,
% 11.69/11.90 (b(z, s(s(z)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[18613, 31735])).
% 11.69/11.90 tff(31737,plain,
% 11.69/11.90 ($false),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[15550, 31736, 31734, 31645, 31643])).
% 11.69/11.90 tff(31738,plain,((s(z) = elem!1) | (~r(s(z), z)) | (elem!1 = z) | b(s(s(s(s(z)))), z) | b(elem!1, s(z)) | r(z, elem!1) | b(s(z), s(s(s(s(z))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.90 tff(31739,plain,
% 11.69/11.90 (s(z) = elem!1),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[31738, 31641, 2, 3446, 31, 80, 2881, 3618])).
% 11.69/11.90 tff(31740,plain,
% 11.69/11.90 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31739])).
% 11.69/11.90 tff(31741,plain,
% 11.69/11.90 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 11.69/11.90 inference(transitivity,[status(thm)],[31740, 2206])).
% 11.69/11.90 tff(31742,plain,
% 11.69/11.90 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31741])).
% 11.69/11.90 tff(31743,plain,
% 11.69/11.90 (~(elem!1 = s(s(elem!1)))),
% 11.69/11.90 inference(modus_ponens,[status(thm)],[357, 31742])).
% 11.69/11.90 tff(31744,plain,
% 11.69/11.90 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[16257, 31, 3446, 98, 2881])).
% 11.69/11.90 tff(31745,plain,
% 11.69/11.90 (elem!1 = s(z)),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[1495, 31739])).
% 11.69/11.90 tff(31746,plain,
% 11.69/11.90 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[29438, 31745])).
% 11.69/11.90 tff(31747,plain,
% 11.69/11.90 (~b(s(s(s(elem!1))), z)),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[29435, 31746, 3446])).
% 11.69/11.90 tff(31748,plain,
% 11.69/11.90 (r(s(s(s(elem!1))), z)),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[377, 31747])).
% 11.69/11.90 tff(31749,plain,
% 11.69/11.90 (~b(s(z), s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[2884, 31745, 2881])).
% 11.69/11.90 tff(31750,plain,
% 11.69/11.90 (r(s(z), s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[247, 31749])).
% 11.69/11.90 tff(31751,plain,
% 11.69/11.90 (r(elem!1, s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[2570, 31750, 31739])).
% 11.69/11.90 tff(31752,plain,
% 11.69/11.90 (~r(z, s(s(elem!1)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[30853, 31751, 3618, 31748])).
% 11.69/11.90 tff(31753,plain,
% 11.69/11.90 (b(z, s(s(elem!1)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[324, 31752])).
% 11.69/11.90 tff(31754,plain,
% 11.69/11.90 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[12932, 31753, 29427, 31744])).
% 11.69/11.90 tff(31755,plain,
% 11.69/11.90 (s(s(z)) = s(elem!1)),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31739])).
% 11.69/11.90 tff(31756,plain,
% 11.69/11.90 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31755])).
% 11.69/11.90 tff(31757,plain,
% 11.69/11.90 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 11.69/11.90 inference(transitivity,[status(thm)],[31756, 582])).
% 11.69/11.90 tff(31758,plain,
% 11.69/11.90 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31757])).
% 11.69/11.90 tff(31759,plain,
% 11.69/11.90 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.69/11.90 inference(modus_ponens,[status(thm)],[1397, 31758])).
% 11.69/11.90 tff(31760,plain,
% 11.69/11.90 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[281, 31759])).
% 11.69/11.90 tff(31761,plain,
% 11.69/11.90 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[1356, 31760, 31754])).
% 11.69/11.90 tff(31762,plain,
% 11.69/11.90 (s(s(s(z))) = s(s(elem!1))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31755])).
% 11.69/11.90 tff(31763,plain,
% 11.69/11.90 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31762])).
% 11.69/11.90 tff(31764,plain,
% 11.69/11.90 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31763])).
% 11.69/11.90 tff(31765,plain,
% 11.69/11.90 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31755])).
% 11.69/11.90 tff(31766,plain,
% 11.69/11.90 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 11.69/11.90 inference(transitivity,[status(thm)],[31765, 31764])).
% 11.69/11.90 tff(31767,plain,
% 11.69/11.90 (b(z, s(s(s(s(z)))))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[27975, 31739, 2, 80])).
% 11.69/11.90 tff(31768,plain,
% 11.69/11.90 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31739])).
% 11.69/11.90 tff(31769,plain,
% 11.69/11.90 (r(elem!1, s(s(s(s(z)))))),
% 11.69/11.90 inference(modus_ponens,[status(thm)],[2913, 31768])).
% 11.69/11.90 tff(31770,plain,
% 11.69/11.90 (~r(z, s(elem!1))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[6444, 31769, 29426, 3618])).
% 11.69/11.90 tff(31771,plain,
% 11.69/11.90 (b(z, s(elem!1))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[566, 31770])).
% 11.69/11.90 tff(31772,plain,
% 11.69/11.90 (b(z, s(s(z)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[8527, 31771, 31739])).
% 11.69/11.90 tff(31773,plain,
% 11.69/11.90 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[15550, 31772, 31645, 31767])).
% 11.69/11.90 tff(31774,plain,
% 11.69/11.90 (r(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[1714, 31773])).
% 11.69/11.90 tff(31775,plain,
% 11.69/11.90 (r(s(s(s(elem!1))), s(elem!1))),
% 11.69/11.90 inference(modus_ponens,[status(thm)],[31774, 31766])).
% 11.69/11.90 tff(31776,plain,
% 11.69/11.90 (~r(elem!1, s(s(elem!1)))),
% 11.69/11.90 inference(unit_resolution,[status(thm)],[24565, 194, 31775, 31751, 31761])).
% 11.69/11.90 tff(31777,plain,
% 11.69/11.90 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31740])).
% 11.69/11.90 tff(31778,plain,
% 11.69/11.90 (~(s(s(elem!1)) = elem!1)),
% 11.69/11.90 inference(modus_ponens,[status(thm)],[357, 31777])).
% 11.69/11.90 tff(31779,plain,
% 11.69/11.90 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 11.69/11.90 inference(monotonicity,[status(thm)],[31739])).
% 11.69/11.91 tff(31780,plain,
% 11.69/11.91 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 11.69/11.91 inference(transitivity,[status(thm)],[31779, 3])).
% 11.69/11.91 tff(31781,plain,
% 11.69/11.91 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 11.69/11.91 inference(transitivity,[status(thm)],[31780, 4])).
% 11.69/11.91 tff(31782,plain,
% 11.69/11.91 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 11.69/11.91 inference(monotonicity,[status(thm)],[31781])).
% 11.69/11.91 tff(31783,plain,
% 11.69/11.91 (~(elem!1 = s(s(s(elem!1))))),
% 11.69/11.91 inference(modus_ponens,[status(thm)],[217, 31782])).
% 11.69/11.91 tff(31784,plain,
% 11.69/11.91 (b(s(s(s(elem!1))), s(z))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[31432, 31783, 2, 3446, 31645, 31, 80])).
% 11.69/11.91 tff(31785,plain,
% 11.69/11.91 (b(s(s(s(elem!1))), elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[3938, 31784, 31739])).
% 11.69/11.91 tff(31786,plain,
% 11.69/11.91 (~b(elem!1, s(s(elem!1)))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[15596, 31775, 22902, 31785, 31760, 31778, 31753, 31751])).
% 11.69/11.91 tff(31787,plain,
% 11.69/11.91 ($false),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[1307, 31786, 31776, 31743])).
% 11.69/11.91 tff(31788,plain,(b(elem!1, z) | (elem!1 = z) | b(s(s(s(s(z)))), z) | b(elem!1, s(z)) | r(z, elem!1) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.91 tff(31789,plain,
% 11.69/11.91 (b(elem!1, z)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[31788, 31, 3446, 2, 80, 2881])).
% 11.69/11.91 tff(31790,plain,
% 11.69/11.91 (~b(s(s(s(elem!1))), s(z))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[10690, 590, 29427, 29429])).
% 11.69/11.91 tff(31791,plain,
% 11.69/11.91 (elem!1 = s(s(s(elem!1)))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[31585, 31790, 3446, 31, 80])).
% 11.69/11.91 tff(31792,plain,
% 11.69/11.91 (s(elem!1) = s(s(s(s(elem!1))))),
% 11.69/11.91 inference(monotonicity,[status(thm)],[31791])).
% 11.69/11.91 tff(31793,plain,
% 11.69/11.91 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 11.69/11.91 inference(monotonicity,[status(thm)],[31792])).
% 11.69/11.91 tff(31794,plain,
% 11.69/11.91 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 11.69/11.91 inference(monotonicity,[status(thm)],[31793])).
% 11.69/11.91 tff(31795,plain,
% 11.69/11.91 (~b(s(z), elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[23575, 590, 29427, 1374, 665])).
% 11.69/11.91 tff(31796,plain,
% 11.69/11.91 (b(s(s(s(elem!1))), z)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[9553, 31791, 665])).
% 11.69/11.91 tff(31797,plain,
% 11.69/11.91 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[29435, 31796, 3446])).
% 11.69/11.91 tff(31798,plain,
% 11.69/11.91 (~(elem!1 = s(z))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[29438, 31797])).
% 11.69/11.91 tff(31799,plain,
% 11.69/11.91 (~(s(z) = elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[1495, 31798])).
% 11.69/11.91 tff(31800,plain,
% 11.69/11.91 (r(s(z), elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[632, 31799, 31795])).
% 11.69/11.91 tff(31801,plain,
% 11.69/11.91 (r(s(s(s(elem!1))), s(z))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[223, 31790])).
% 11.69/11.91 tff(31802,plain,
% 11.69/11.91 (s(s(s(elem!1))) = elem!1),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[129, 31791])).
% 11.69/11.91 tff(31803,plain,
% 11.69/11.91 (r(elem!1, s(z))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[8406, 31802, 31801])).
% 11.69/11.91 tff(31804,plain,
% 11.69/11.91 (~b(s(s(s(elem!1))), elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[10743, 665, 29427, 22902])).
% 11.69/11.91 tff(31805,plain,
% 11.69/11.91 (~(s(s(elem!1)) = elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[1845, 31804, 1374])).
% 11.69/11.91 tff(31806,plain,
% 11.69/11.91 (~(s(s(elem!1)) = s(elem!1))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[264, 31805])).
% 11.69/11.91 tff(31807,plain,
% 11.69/11.91 (~r(elem!1, s(s(s(s(z)))))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[11195, 31803, 29426, 1216])).
% 11.69/11.91 tff(31808,plain,
% 11.69/11.91 (b(elem!1, s(s(s(s(z)))))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[781, 31807, 17538])).
% 11.69/11.91 tff(31809,plain,
% 11.69/11.91 (~r(s(s(s(s(z)))), elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[5396, 31800, 1216, 31803])).
% 11.69/11.91 tff(31810,plain,
% 11.69/11.91 (b(s(s(s(s(z)))), elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[762, 31809, 17534])).
% 11.69/11.91 tff(31811,plain,
% 11.69/11.91 (~r(elem!1, z)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[31626, 31810, 29429, 31791, 31597, 29427, 590, 22902, 31808])).
% 11.69/11.91 tff(31812,plain,
% 11.69/11.91 (b(s(elem!1), elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[14657, 31811, 22902, 29427, 31804, 31799, 2])).
% 11.69/11.91 tff(31813,plain,
% 11.69/11.91 (~b(s(s(elem!1)), elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[5286, 31812, 22902, 665, 31806])).
% 11.69/11.91 tff(31814,plain,
% 11.69/11.91 (r(s(s(elem!1)), elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[872, 31813, 31805])).
% 11.69/11.91 tff(31815,plain,
% 11.69/11.91 (~r(s(s(elem!1)), s(z))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[1899, 31814, 31803, 31800])).
% 11.69/11.91 tff(31816,plain,
% 11.69/11.91 (b(s(s(elem!1)), s(z))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[362, 31815])).
% 11.69/11.91 tff(31817,plain,
% 11.69/11.91 (b(s(s(s(s(s(elem!1))))), s(z))),
% 11.69/11.91 inference(modus_ponens,[status(thm)],[31816, 31794])).
% 11.69/11.91 tff(31818,plain,
% 11.69/11.91 (~b(z, s(s(s(s(z)))))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[15860, 31810, 22902, 31808])).
% 11.69/11.91 tff(31819,plain,
% 11.69/11.91 (r(z, s(s(s(s(z)))))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[800, 31818])).
% 11.69/11.91 tff(31820,plain,
% 11.69/11.91 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[11384, 31802])).
% 11.69/11.91 tff(31821,plain,
% 11.69/11.91 (~b(s(s(s(s(z)))), s(z))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[11707, 31810, 29426, 22902, 665, 31820, 31803, 590, 31800])).
% 11.69/11.91 tff(31822,plain,
% 11.69/11.91 (~b(elem!1, s(s(s(elem!1))))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[15370, 31802])).
% 11.69/11.91 tff(31823,plain,
% 11.69/11.91 (~b(s(s(z)), z)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[17452, 31791, 29427, 665, 590])).
% 11.69/11.91 tff(31824,plain,
% 11.69/11.91 (r(s(s(z)), z)),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[1211, 31823])).
% 11.69/11.91 tff(31825,plain,
% 11.69/11.91 (r(z, s(elem!1)) <=> r(z, s(s(s(s(elem!1)))))),
% 11.69/11.91 inference(monotonicity,[status(thm)],[31792])).
% 11.69/11.91 tff(31826,plain,
% 11.69/11.91 (~b(z, s(elem!1))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[6555, 31812, 22902, 665])).
% 11.69/11.91 tff(31827,plain,
% 11.69/11.91 (r(z, s(elem!1))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[566, 31826])).
% 11.69/11.91 tff(31828,plain,
% 11.69/11.91 (r(z, s(s(s(s(elem!1)))))),
% 11.69/11.91 inference(modus_ponens,[status(thm)],[31827, 31825])).
% 11.69/11.91 tff(31829,plain,
% 11.69/11.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.69/11.91 inference(rewrite,[status(thm)],[])).
% 11.69/11.91 tff(31830,plain,
% 11.69/11.91 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.69/11.91 inference(rewrite,[status(thm)],[])).
% 11.69/11.91 tff(31831,plain,
% 11.69/11.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 11.69/11.91 inference(monotonicity,[status(thm)],[31830])).
% 11.69/11.91 tff(31832,plain,
% 11.69/11.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.69/11.91 inference(transitivity,[status(thm)],[31831, 31829])).
% 11.69/11.91 tff(31833,plain,
% 11.69/11.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.69/11.91 inference(quant_inst,[status(thm)],[])).
% 11.69/11.91 tff(31834,plain,
% 11.69/11.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 11.69/11.91 inference(modus_ponens,[status(thm)],[31833, 31832])).
% 11.69/11.91 tff(31835,plain,
% 11.69/11.91 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[31834, 194, 31828, 29426, 31824])).
% 11.69/11.91 tff(31836,plain,
% 11.69/11.91 (b(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[1714, 31835])).
% 11.69/11.91 tff(31837,plain,
% 11.69/11.91 (~r(s(s(z)), s(z))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[10815, 31836, 1216, 31, 31822, 31821, 31819, 31597, 29426, 98])).
% 11.69/11.91 tff(31838,plain,
% 11.69/11.91 (b(s(s(z)), s(z))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[3778, 31837])).
% 11.69/11.91 tff(31839,plain,
% 11.69/11.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), 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))))))))),
% 11.69/11.91 inference(rewrite,[status(thm)],[])).
% 11.69/11.91 tff(31840,plain,
% 11.69/11.91 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~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)))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), 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))))))))),
% 11.69/11.91 inference(rewrite,[status(thm)],[])).
% 11.69/11.91 tff(31841,plain,
% 11.69/11.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), 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)))))))))),
% 11.69/11.91 inference(monotonicity,[status(thm)],[31840])).
% 11.69/11.91 tff(31842,plain,
% 11.69/11.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), 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))))))))),
% 11.69/11.91 inference(transitivity,[status(thm)],[31841, 31839])).
% 11.69/11.91 tff(31843,plain,
% 11.69/11.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~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))))))))),
% 11.69/11.91 inference(quant_inst,[status(thm)],[])).
% 11.69/11.91 tff(31844,plain,
% 11.69/11.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), 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)))))))),
% 11.69/11.91 inference(modus_ponens,[status(thm)],[31843, 31842])).
% 11.69/11.91 tff(31845,plain,
% 11.69/11.91 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[31844, 391, 29427, 31838, 590, 31817])).
% 11.69/11.91 tff(31846,plain,
% 11.69/11.91 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 11.69/11.91 inference(symmetry,[status(thm)],[31793])).
% 11.69/11.91 tff(31847,plain,
% 11.69/11.91 (r(z, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(elem!1)))),
% 11.69/11.91 inference(monotonicity,[status(thm)],[31846])).
% 11.69/11.91 tff(31848,plain,
% 11.69/11.91 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 11.69/11.91 inference(symmetry,[status(thm)],[31847])).
% 11.69/11.91 tff(31849,plain,
% 11.69/11.91 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[6159, 31805])).
% 11.69/11.91 tff(31850,plain,
% 11.69/11.91 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 11.69/11.91 inference(unit_resolution,[status(thm)],[281, 31849])).
% 11.69/11.92 tff(31851,plain,
% 11.69/11.92 (~b(s(z), s(s(s(elem!1))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[22948, 31796, 29427, 22902, 29429])).
% 11.69/11.92 tff(31852,plain,
% 11.69/11.92 (r(s(z), s(s(s(elem!1))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[247, 31851])).
% 11.69/11.92 tff(31853,plain,
% 11.69/11.92 (~b(z, s(s(elem!1)))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[24044, 31852, 29427, 1374, 590, 31801, 31850])).
% 11.69/11.92 tff(31854,plain,
% 11.69/11.92 (r(z, s(s(elem!1)))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[324, 31853])).
% 11.69/11.92 tff(31855,plain,
% 11.69/11.92 (r(z, s(s(s(s(s(elem!1))))))),
% 11.69/11.92 inference(modus_ponens,[status(thm)],[31854, 31848])).
% 11.69/11.92 tff(31856,plain,
% 11.69/11.92 (r(s(s(elem!1)), z) <=> r(s(s(s(s(s(elem!1))))), z)),
% 11.69/11.92 inference(monotonicity,[status(thm)],[31793])).
% 11.69/11.92 tff(31857,plain,
% 11.69/11.92 (~b(s(s(elem!1)), z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[13177, 31796, 29427, 1374])).
% 11.69/11.92 tff(31858,plain,
% 11.69/11.92 (r(s(s(elem!1)), z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[2629, 31857])).
% 11.69/11.92 tff(31859,plain,
% 11.69/11.92 (r(s(s(s(s(s(elem!1))))), z)),
% 11.69/11.92 inference(modus_ponens,[status(thm)],[31858, 31856])).
% 11.69/11.92 tff(31860,plain,
% 11.69/11.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 11.69/11.92 inference(rewrite,[status(thm)],[])).
% 11.69/11.92 tff(31861,plain,
% 11.69/11.92 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 11.69/11.92 inference(rewrite,[status(thm)],[])).
% 11.69/11.92 tff(31862,plain,
% 11.69/11.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 11.69/11.92 inference(monotonicity,[status(thm)],[31861])).
% 11.69/11.92 tff(31863,plain,
% 11.69/11.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 11.69/11.92 inference(transitivity,[status(thm)],[31862, 31860])).
% 11.69/11.92 tff(31864,plain,
% 11.69/11.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 11.69/11.92 inference(quant_inst,[status(thm)],[])).
% 11.69/11.92 tff(31865,plain,
% 11.69/11.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 11.69/11.92 inference(modus_ponens,[status(thm)],[31864, 31863])).
% 11.69/11.92 tff(31866,plain,
% 11.69/11.92 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31865, 194, 31824, 31859, 31855])).
% 11.69/11.92 tff(31867,plain,
% 11.69/11.92 (~(s(s(z)) = s(s(s(s(s(elem!1))))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[16611, 31791, 2680])).
% 11.69/11.92 tff(31868,plain,
% 11.69/11.92 ($false),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[9497, 42, 31867, 31866, 31845])).
% 11.69/11.92 tff(31869,plain,((~b(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(z)) | (~b(elem!1, z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(s(s(z)))), z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.69/11.92 tff(31870,plain,
% 11.69/11.92 (~b(s(z), z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31869, 31, 2913, 31789, 2, 31744, 3446, 80])).
% 11.69/11.92 tff(31871,plain,
% 11.69/11.92 (~(s(z) = elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[10390, 31870, 31789])).
% 11.69/11.92 tff(31872,plain,
% 11.69/11.92 (~(elem!1 = s(z))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[172, 31871])).
% 11.69/11.92 tff(31873,plain,
% 11.69/11.92 (r(elem!1, s(z))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[837, 31872, 31])).
% 11.69/11.92 tff(31874,plain,
% 11.69/11.92 (~r(elem!1, s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[11195, 31873, 29426, 2913])).
% 11.69/11.92 tff(31875,plain,
% 11.69/11.92 (r(s(z), z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[180, 31870])).
% 11.69/11.92 tff(31876,plain,
% 11.69/11.92 (~(s(s(s(s(z)))) = elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[6966, 31789, 3446])).
% 11.69/11.92 tff(31877,plain,
% 11.69/11.92 (~b(z, s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31662, 31873, 22902, 31876, 31871, 31875, 2913, 31874])).
% 11.69/11.92 tff(31878,plain,
% 11.69/11.92 (r(z, s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[800, 31877])).
% 11.69/11.92 tff(31879,plain,
% 11.69/11.92 ($false),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[10651, 194, 31875, 29426, 2913, 31878])).
% 11.69/11.92 tff(31880,plain,(b(elem!1, s(z)) | (elem!1 = z) | b(s(s(s(s(z)))), z) | r(z, elem!1) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.92 tff(31881,plain,
% 11.69/11.92 (b(elem!1, s(z))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31880, 2881, 3446, 80, 2])).
% 11.69/11.92 tff(31882,plain,
% 11.69/11.92 (~(s(z) = elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[20271, 31881])).
% 11.69/11.92 tff(31883,plain,
% 11.69/11.92 (~b(s(z), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[23112, 31881, 22902, 31666])).
% 11.69/11.92 tff(31884,plain,
% 11.69/11.92 (r(s(z), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[632, 31883, 31882])).
% 11.69/11.92 tff(31885,plain,
% 11.69/11.92 (~r(elem!1, s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[12404, 31884, 29426, 2913])).
% 11.69/11.92 tff(31886,plain,
% 11.69/11.92 (~b(s(z), z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[5970, 31881, 22902, 31666])).
% 11.69/11.92 tff(31887,plain,
% 11.69/11.92 (r(s(z), z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[180, 31886])).
% 11.69/11.92 tff(31888,plain,
% 11.69/11.92 ($false),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[10651, 194, 182, 2053, 1216, 719])).
% 11.69/11.92 tff(31889,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.92 tff(31890,plain,
% 11.69/11.92 (~r(z, s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31889, 31887, 29426, 2913])).
% 11.69/11.92 tff(31891,plain,
% 11.69/11.92 (b(z, s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[800, 31890])).
% 11.69/11.92 tff(31892,plain,
% 11.69/11.92 (~b(s(z), z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[5970, 721, 133, 10679])).
% 11.69/11.92 tff(31893,plain,
% 11.69/11.92 (r(s(z), z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[180, 31892])).
% 11.69/11.92 tff(31894,plain,
% 11.69/11.92 (~r(z, s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31889, 31893, 2053, 1216])).
% 11.69/11.92 tff(31895,plain,
% 11.69/11.92 (b(z, s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[800, 31894])).
% 11.69/11.92 tff(31896,plain,
% 11.69/11.92 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31595, 1216, 2053])).
% 11.69/11.92 tff(31897,plain,
% 11.69/11.92 (b(s(s(z)), s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[3652, 31896])).
% 11.69/11.92 tff(31898,plain,
% 11.69/11.92 (~b(s(z), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[23112, 721, 133, 10679])).
% 11.69/11.92 tff(31899,plain,
% 11.69/11.92 (r(s(z), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[632, 31898, 21435])).
% 11.69/11.92 tff(31900,plain,
% 11.69/11.92 (~r(elem!1, s(s(s(s(z)))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[12404, 31899, 2053, 1216])).
% 11.69/11.92 tff(31901,plain,
% 11.69/11.92 (~r(s(s(s(s(z)))), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[6077, 530, 1216, 31899])).
% 11.69/11.92 tff(31902,plain,
% 11.69/11.92 ($false),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[15860, 6223, 6222, 133, 1686])).
% 11.69/11.92 tff(31903,plain,((s(s(s(s(z)))) = elem!1) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.69/11.92 tff(31904,plain,
% 11.69/11.92 (s(s(s(s(z)))) = elem!1),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31903, 31901, 31895, 31900, 133])).
% 11.69/11.92 tff(31905,plain,
% 11.69/11.92 (~(s(s(s(elem!1))) = elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[1436, 31904])).
% 11.69/11.92 tff(31906,plain,
% 11.69/11.92 (~(elem!1 = s(s(s(elem!1))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[129, 31905])).
% 11.69/11.92 tff(31907,plain,
% 11.69/11.92 (~r(elem!1, s(z))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[10776, 410, 1216, 183])).
% 11.69/11.92 tff(31908,plain,
% 11.69/11.92 (~r(z, s(elem!1))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[8832, 29691, 31907])).
% 11.69/11.92 tff(31909,plain,
% 11.69/11.92 (~r(elem!1, s(elem!1))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[2288, 31908, 29691])).
% 11.69/11.92 tff(31910,plain,
% 11.69/11.92 (b(elem!1, s(elem!1))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[443, 31909, 4598])).
% 11.69/11.92 tff(31911,plain,
% 11.69/11.92 (~r(s(s(s(elem!1))), z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[202, 59, 183, 181])).
% 11.69/11.92 tff(31912,plain,
% 11.69/11.92 (b(s(s(s(elem!1))), z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[377, 31911])).
% 11.69/11.92 tff(31913,plain,
% 11.69/11.92 (b(z, s(s(elem!1)))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[3924, 10, 15838, 91])).
% 11.69/11.92 tff(31914,plain,
% 11.69/11.92 (~r(s(s(s(elem!1))), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[406, 31911, 29691])).
% 11.69/11.92 tff(31915,plain,
% 11.69/11.92 (b(s(s(s(elem!1))), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[230, 31914, 127])).
% 11.69/11.92 tff(31916,plain,
% 11.69/11.92 (~r(s(z), s(s(s(elem!1))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[3499, 59, 183, 181])).
% 11.69/11.92 tff(31917,plain,
% 11.69/11.92 (b(s(z), s(s(s(elem!1))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[247, 31916])).
% 11.69/11.92 tff(31918,plain,
% 11.69/11.92 (~b(s(s(elem!1)), s(z))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[30863, 31917, 664, 31915, 31913])).
% 11.69/11.92 tff(31919,plain,
% 11.69/11.92 (r(s(s(elem!1)), s(z))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[362, 31918])).
% 11.69/11.92 tff(31920,plain,
% 11.69/11.92 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[11169, 31919, 183, 1216])).
% 11.69/11.92 tff(31921,plain,
% 11.69/11.92 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[1370, 31920, 15838])).
% 11.69/11.92 tff(31922,plain,
% 11.69/11.92 (~(s(s(elem!1)) = elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[4206, 31919, 31907])).
% 11.69/11.92 tff(31923,plain,
% 11.69/11.92 (r(s(z), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[3205, 29691, 91])).
% 11.69/11.92 tff(31924,plain,
% 11.69/11.92 (~r(s(s(elem!1)), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[2379, 31919, 410, 31923])).
% 11.69/11.92 tff(31925,plain,
% 11.69/11.92 (b(s(s(elem!1)), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[872, 31924, 31922])).
% 11.69/11.92 tff(31926,plain,
% 11.69/11.92 ($false),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[8469, 31925, 31921, 31913, 31912, 31910])).
% 11.69/11.92 tff(31927,plain,(b(z, s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (s(s(s(elem!1))) = elem!1) | b(s(z), z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.69/11.92 tff(31928,plain,
% 11.69/11.92 (b(z, s(s(s(elem!1))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31927, 6124, 183, 1216, 664, 9, 91, 80])).
% 11.69/11.92 tff(31929,plain,
% 11.69/11.92 (~(elem!1 = z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[23154, 31928, 4028])).
% 11.69/11.92 tff(31930,plain,
% 11.69/11.92 (~(z = elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[97, 31929])).
% 11.69/11.92 tff(31931,plain,
% 11.69/11.92 (b(z, elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[141, 31930, 80])).
% 11.69/11.92 tff(31932,plain,
% 11.69/11.92 (~b(s(z), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[23112, 31931, 721, 664])).
% 11.69/11.92 tff(31933,plain,
% 11.69/11.92 (r(s(z), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[632, 31932, 21435])).
% 11.69/11.92 tff(31934,plain,
% 11.69/11.92 (~r(s(s(s(elem!1))), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[23411, 31933, 183, 6124])).
% 11.69/11.92 tff(31935,plain,
% 11.69/11.92 (b(s(s(s(elem!1))), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[230, 31934, 9])).
% 11.69/11.92 tff(31936,plain,
% 11.69/11.92 (~b(s(z), s(s(s(elem!1))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[23276, 31935, 721, 31928, 31931])).
% 11.69/11.92 tff(31937,plain,
% 11.69/11.92 (r(s(z), s(s(s(elem!1))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[247, 31936])).
% 11.69/11.92 tff(31938,plain,
% 11.69/11.92 ($false),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[17163, 194, 6124, 31933, 31937, 183])).
% 11.69/11.92 tff(31939,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | r(z, elem!1) | (~r(s(z), s(s(s(s(z)))))) | b(s(z), z) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.92 tff(31940,plain,
% 11.69/11.92 (b(elem!1, s(s(s(elem!1))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31939, 91, 721, 10679, 80, 1216, 183, 1])).
% 11.69/11.92 tff(31941,plain,
% 11.69/11.92 ($false),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[8846, 29691, 10, 448])).
% 11.69/11.92 tff(31942,plain,(b(z, s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.69/11.92 tff(31943,plain,
% 11.69/11.92 (b(z, s(s(s(elem!1))))),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[31942, 448, 80])).
% 11.69/11.92 tff(31944,plain,
% 11.69/11.92 (r(elem!1, z)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[17700, 149, 2053, 21435, 448, 31943, 2])).
% 11.69/11.92 tff(31945,plain,
% 11.69/11.92 (~b(s(z), elem!1)),
% 11.69/11.92 inference(unit_resolution,[status(thm)],[23112, 149, 721, 664])).
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% 11.69/11.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 11.69/11.93 inference(monotonicity,[status(thm)],[32024])).
% 11.69/11.93 tff(32026,plain,
% 11.69/11.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 11.69/11.93 inference(transitivity,[status(thm)],[32025, 32023])).
% 11.69/11.93 tff(32027,plain,
% 11.69/11.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 11.69/11.93 inference(quant_inst,[status(thm)],[])).
% 11.69/11.93 tff(32028,plain,
% 11.69/11.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 11.69/11.93 inference(modus_ponens,[status(thm)],[32027, 32026])).
% 11.69/11.93 tff(32029,plain,
% 11.69/11.93 ($false),
% 11.69/11.93 inference(unit_resolution,[status(thm)],[32028, 391, 1686, 7872, 7871, 1684])).
% 11.69/11.93 tff(32030,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.93 tff(32031,plain,
% 11.69/11.93 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 11.69/11.93 inference(unit_resolution,[status(thm)],[32030, 32008, 32022, 31965])).
% 11.69/11.93 tff(32032,plain,
% 11.69/11.93 (r(s(s(s(s(z)))), s(s(s(z))))),
% 11.69/11.93 inference(unit_resolution,[status(thm)],[4426, 42, 32031, 32020])).
% 11.69/11.93 tff(32033,plain,
% 11.69/11.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 11.69/11.93 inference(rewrite,[status(thm)],[])).
% 11.69/11.93 tff(32034,plain,
% 11.69/11.93 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 11.69/11.93 inference(rewrite,[status(thm)],[])).
% 11.69/11.93 tff(32035,plain,
% 11.69/11.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 11.69/11.94 inference(monotonicity,[status(thm)],[32034])).
% 11.69/11.94 tff(32036,plain,
% 11.69/11.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 11.69/11.94 inference(transitivity,[status(thm)],[32035, 32033])).
% 11.69/11.94 tff(32037,plain,
% 11.69/11.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 11.69/11.94 inference(quant_inst,[status(thm)],[])).
% 11.69/11.94 tff(32038,plain,
% 11.69/11.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[32037, 32036])).
% 11.69/11.94 tff(32039,plain,
% 11.69/11.94 ($false),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[32038, 194, 1216, 15705, 30159, 15704])).
% 11.69/11.94 tff(32040,plain,((~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(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.94 tff(32041,plain,
% 11.69/11.94 (~r(s(z), s(s(s(z))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[32040, 32032, 1216, 32019])).
% 11.69/11.94 tff(32042,plain,
% 11.69/11.94 (~r(s(z), s(s(s(elem!1))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[23224, 32041, 31951])).
% 11.69/11.94 tff(32043,plain,
% 11.69/11.94 (b(s(z), s(s(s(elem!1))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[247, 32042])).
% 11.69/11.94 tff(32044,plain,
% 11.69/11.94 (b(s(z), s(s(s(z))))),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[32043, 31971])).
% 11.69/11.94 tff(32045,plain,
% 11.69/11.94 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 11.69/11.94 inference(monotonicity,[status(thm)],[31991, 31966])).
% 11.69/11.94 tff(32046,plain,
% 11.69/11.94 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 11.69/11.94 inference(monotonicity,[status(thm)],[31951])).
% 11.69/11.94 tff(32047,plain,
% 11.69/11.94 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 11.69/11.94 inference(symmetry,[status(thm)],[32046])).
% 11.69/11.94 tff(32048,plain,
% 11.69/11.94 (r(s(elem!1), z)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[27330, 31951, 181])).
% 11.69/11.94 tff(32049,plain,
% 11.69/11.94 (r(s(elem!1), elem!1)),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[32048, 32047])).
% 11.69/11.94 tff(32050,plain,
% 11.69/11.94 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 11.69/11.94 inference(monotonicity,[status(thm)],[31966])).
% 11.69/11.94 tff(32051,plain,
% 11.69/11.94 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 11.69/11.94 inference(symmetry,[status(thm)],[32050])).
% 11.69/11.94 tff(32052,plain,
% 11.69/11.94 (r(s(s(s(elem!1))), s(elem!1))),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[183, 32051])).
% 11.69/11.94 tff(32053,plain,
% 11.69/11.94 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 11.69/11.94 inference(monotonicity,[status(thm)],[31991, 31968])).
% 11.69/11.94 tff(32054,plain,
% 11.69/11.94 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/11.94 inference(symmetry,[status(thm)],[32053])).
% 11.69/11.94 tff(32055,plain,
% 11.69/11.94 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 11.69/11.94 inference(monotonicity,[status(thm)],[32054])).
% 11.69/11.94 tff(32056,plain,
% 11.69/11.94 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[32031, 32055])).
% 11.69/11.94 tff(32057,plain,
% 11.69/11.94 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[1095, 32056, 29900])).
% 11.69/11.94 tff(32058,plain,
% 11.69/11.94 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[14601, 32057, 32052, 32049])).
% 11.69/11.94 tff(32059,plain,
% 11.69/11.94 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[988, 32058, 930])).
% 11.69/11.94 tff(32060,plain,
% 11.69/11.94 (b(s(s(s(s(z)))), s(z))),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[32059, 32045])).
% 11.69/11.94 tff(32061,plain,
% 11.69/11.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.69/11.94 inference(rewrite,[status(thm)],[])).
% 11.69/11.94 tff(32062,plain,
% 11.69/11.94 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.69/11.94 inference(rewrite,[status(thm)],[])).
% 11.69/11.94 tff(32063,plain,
% 11.69/11.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 11.69/11.94 inference(monotonicity,[status(thm)],[32062])).
% 11.69/11.94 tff(32064,plain,
% 11.69/11.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.69/11.94 inference(transitivity,[status(thm)],[32063, 32061])).
% 11.69/11.94 tff(32065,plain,
% 11.69/11.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 11.69/11.94 inference(quant_inst,[status(thm)],[])).
% 11.69/11.94 tff(32066,plain,
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% 11.69/11.94 inference(modus_ponens,[status(thm)],[32065, 32064])).
% 11.69/11.94 tff(32067,plain,
% 11.69/11.94 ($false),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[32066, 391, 31897, 32060, 32011, 32044, 31965])).
% 11.69/11.94 tff(32068,plain,(b(s(z), z) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | r(z, elem!1) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.94 tff(32069,plain,
% 11.69/11.94 (b(s(z), z)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[32068, 1216, 2053, 183, 721, 80, 1])).
% 11.69/11.94 tff(32070,plain,
% 11.69/11.94 (~b(z, elem!1)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[5970, 32069, 721, 10679])).
% 11.69/11.94 tff(32071,plain,
% 11.69/11.94 (z = elem!1),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[141, 32070, 80])).
% 11.69/11.94 tff(32072,plain,
% 11.69/11.94 (b(s(z), z) <=> b(s(z), elem!1)),
% 11.69/11.94 inference(monotonicity,[status(thm)],[32071])).
% 11.69/11.94 tff(32073,plain,
% 11.69/11.94 (b(s(z), elem!1)),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[32069, 32072])).
% 11.69/11.94 tff(32074,plain,
% 11.69/11.94 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 11.69/11.94 inference(monotonicity,[status(thm)],[32071])).
% 11.69/11.94 tff(32075,plain,
% 11.69/11.94 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 11.69/11.94 inference(monotonicity,[status(thm)],[32074])).
% 11.69/11.94 tff(32076,plain,
% 11.69/11.94 (~(s(s(elem!1)) = elem!1)),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[215, 32075])).
% 11.69/11.94 tff(32077,plain,
% 11.69/11.94 (b(s(elem!1), elem!1)),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[644, 23146])).
% 11.69/11.94 tff(32078,plain,
% 11.69/11.94 (r(z, s(s(s(elem!1))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[28273, 6124, 94])).
% 11.69/11.94 tff(32079,plain,
% 11.69/11.94 (~r(s(z), z)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[15518, 501, 2053, 1216])).
% 11.69/11.94 tff(32080,plain,
% 11.69/11.94 (b(s(z), z)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[180, 32079])).
% 11.69/11.94 tff(32081,plain,
% 11.69/11.94 (~r(s(z), elem!1)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[5433, 32079, 17618])).
% 11.69/11.94 tff(32082,plain,
% 11.69/11.94 (b(s(z), elem!1)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[632, 32081, 24])).
% 11.69/11.94 tff(32083,plain,
% 11.69/11.94 (~b(s(s(z)), z)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[9065, 391, 1233, 664, 590])).
% 11.69/11.94 tff(32084,plain,
% 11.69/11.94 (r(s(s(z)), z)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[1211, 32083])).
% 11.69/11.94 tff(32085,plain,
% 11.69/11.94 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[14769, 32084, 2053, 184])).
% 11.69/11.94 tff(32086,plain,
% 11.69/11.94 (b(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[1714, 32085])).
% 11.69/11.94 tff(32087,plain,
% 11.69/11.94 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[32086, 2421])).
% 11.69/11.94 tff(32088,plain,
% 11.69/11.94 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 11.69/11.94 inference(transitivity,[status(thm)],[30313, 1029])).
% 11.69/11.94 tff(32089,plain,
% 11.69/11.94 (b(s(s(elem!1)), s(elem!1))),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[1233, 32088])).
% 11.69/11.94 tff(32090,plain,
% 11.69/11.94 (~b(s(s(elem!1)), elem!1)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[19494, 32089, 802, 2122])).
% 11.69/11.94 tff(32091,plain,
% 11.69/11.94 (r(s(s(elem!1)), elem!1)),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[872, 32090, 249])).
% 11.69/11.94 tff(32092,plain,
% 11.69/11.94 (~b(z, s(s(z)))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[22414, 391, 1233, 664, 590])).
% 11.69/11.94 tff(32093,plain,
% 11.69/11.94 (r(z, s(s(z)))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[18613, 32092])).
% 11.69/11.94 tff(32094,plain,
% 11.69/11.94 (r(z, s(s(elem!1)))),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[32093, 29959])).
% 11.69/11.94 tff(32095,plain,
% 11.69/11.94 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[372, 32094, 184, 32091])).
% 11.69/11.94 tff(32096,plain,
% 11.69/11.94 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[1370, 32095, 297])).
% 11.69/11.94 tff(32097,plain,
% 11.69/11.94 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[18349, 32096, 30389, 644, 32087])).
% 11.69/11.94 tff(32098,plain,
% 11.69/11.94 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[1164, 32097, 311])).
% 11.69/11.94 tff(32099,plain,
% 11.69/11.94 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/11.94 inference(monotonicity,[status(thm)],[934])).
% 11.69/11.94 tff(32100,plain,
% 11.69/11.94 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.69/11.94 inference(symmetry,[status(thm)],[32099])).
% 11.69/11.94 tff(32101,plain,
% 11.69/11.94 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[1538, 32100])).
% 11.69/11.94 tff(32102,plain,
% 11.69/11.94 ($false),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[10970, 32101])).
% 11.69/11.94 tff(32103,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.94 tff(32104,plain,
% 11.69/11.94 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[32103, 32098, 17618])).
% 11.69/11.94 tff(32105,plain,
% 11.69/11.94 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[16851, 32104, 2053, 184])).
% 11.69/11.94 tff(32106,plain,
% 11.69/11.94 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[29931, 32105, 11])).
% 11.69/11.94 tff(32107,plain,
% 11.69/11.94 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[1095, 32106, 310])).
% 11.69/11.94 tff(32108,plain,
% 11.69/11.94 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.69/11.94 inference(modus_ponens,[status(thm)],[32107, 23220])).
% 11.69/11.94 tff(32109,plain,
% 11.69/11.94 (b(s(s(s(z))), s(s(z)))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[2986, 32096, 11])).
% 11.69/11.94 tff(32110,plain,
% 11.69/11.94 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[24809, 32109, 32086, 3823])).
% 11.69/11.94 tff(32111,plain,
% 11.69/11.94 ($false),
% 11.69/11.94 inference(unit_resolution,[status(thm)],[32110, 32108])).
% 11.69/11.94 tff(32112,plain,((~b(s(s(z)), s(z))) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.95 tff(32113,plain,
% 11.69/11.95 (~b(s(s(z)), s(z))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[32112, 3823, 2053, 184, 11, 32082, 297, 249, 802, 2122, 10679, 32080])).
% 11.69/11.95 tff(32114,plain,
% 11.69/11.95 (r(s(s(z)), s(z))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[3778, 32113])).
% 11.69/11.95 tff(32115,plain,
% 11.69/11.95 (r(s(s(elem!1)), s(z))),
% 11.69/11.95 inference(modus_ponens,[status(thm)],[32114, 18396])).
% 11.69/11.95 tff(32116,plain,
% 11.69/11.95 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[11169, 32115, 183, 1216])).
% 11.69/11.95 tff(32117,plain,
% 11.69/11.95 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[1370, 32116, 297])).
% 11.69/11.95 tff(32118,plain,
% 11.69/11.95 (r(s(s(s(z))), s(z))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[29740, 11, 183])).
% 11.69/11.95 tff(32119,plain,
% 11.69/11.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(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))))))),
% 11.69/11.95 inference(rewrite,[status(thm)],[])).
% 11.69/11.95 tff(32120,plain,
% 11.69/11.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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))))))),
% 11.69/11.95 inference(quant_inst,[status(thm)],[])).
% 11.69/11.95 tff(32121,plain,
% 11.69/11.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(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)))))),
% 11.69/11.95 inference(modus_ponens,[status(thm)],[32120, 32119])).
% 11.69/11.95 tff(32122,plain,
% 11.69/11.95 (~r(s(s(z)), s(s(s(z))))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[32121, 194, 1216, 32114, 32118])).
% 11.69/11.95 tff(32123,plain,
% 11.69/11.95 (b(s(s(z)), s(s(s(z))))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[24076, 32122, 8880])).
% 11.69/11.95 tff(32124,plain,
% 11.69/11.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(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)))))),
% 11.69/11.95 inference(rewrite,[status(thm)],[])).
% 11.69/11.95 tff(32125,plain,
% 11.69/11.95 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(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)))))),
% 11.69/11.95 inference(rewrite,[status(thm)],[])).
% 11.69/11.95 tff(32126,plain,
% 11.69/11.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(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))))))),
% 11.69/11.95 inference(monotonicity,[status(thm)],[32125])).
% 11.69/11.95 tff(32127,plain,
% 11.69/11.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(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)))))),
% 11.69/11.95 inference(transitivity,[status(thm)],[32126, 32124])).
% 11.69/11.95 tff(32128,plain,
% 11.69/11.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 11.69/11.95 inference(quant_inst,[status(thm)],[])).
% 11.69/11.95 tff(32129,plain,
% 11.69/11.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(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))))),
% 11.69/11.95 inference(modus_ponens,[status(thm)],[32128, 32127])).
% 11.69/11.95 tff(32130,plain,
% 11.69/11.95 ((~b(s(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))))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[32129, 391, 24129])).
% 11.69/11.95 tff(32131,plain,
% 11.69/11.95 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[32130, 7872, 2983])).
% 11.69/11.95 tff(32132,plain,
% 11.69/11.95 (r(s(s(s(s(z)))), s(s(z)))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[1713, 32131, 1709])).
% 11.69/11.95 tff(32133,plain,
% 11.69/11.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z))), s(s(z)))))),
% 11.69/11.95 inference(rewrite,[status(thm)],[])).
% 11.69/11.95 tff(32134,plain,
% 11.69/11.95 (((~b(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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(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(s(z))), s(s(z)))))),
% 11.69/11.95 inference(rewrite,[status(thm)],[])).
% 11.69/11.95 tff(32135,plain,
% 11.69/11.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(z))), s(s(z))))))),
% 11.69/11.95 inference(monotonicity,[status(thm)],[32134])).
% 11.69/11.95 tff(32136,plain,
% 11.69/11.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z))), s(s(z)))))),
% 11.69/11.95 inference(transitivity,[status(thm)],[32135, 32133])).
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% 11.69/11.95 inference(modus_ponens,[status(thm)],[32137, 32136])).
% 11.69/11.95 tff(32139,plain,
% 11.69/11.95 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[32138, 391, 24129])).
% 11.69/11.95 tff(32140,plain,
% 11.69/11.95 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.69/11.95 inference(unit_resolution,[status(thm)],[32139, 7872, 2983])).
% 11.69/11.95 tff(32141,plain,
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% 11.69/11.95 tff(32142,plain,
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% 11.69/11.95 tff(32144,plain,
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% 11.69/11.95 tff(32148,plain,
% 11.69/11.95 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 11.69/11.95 inference(monotonicity,[status(thm)],[490, 2401])).
% 11.69/11.95 tff(32149,plain,
% 11.69/11.95 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
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% 11.69/11.95 inference(transitivity,[status(thm)],[32149, 32146, 3929])).
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% 11.69/11.95 inference(monotonicity,[status(thm)],[32150])).
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% 11.69/11.95 inference(modus_ponens,[status(thm)],[311, 32151])).
% 11.69/11.95 tff(32153,plain,
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% 11.69/11.95 tff(32156,plain,
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% 11.69/11.95 inference(unit_resolution,[status(thm)],[2201, 32115, 183, 32155])).
% 11.69/11.95 tff(32157,plain,
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% 11.69/11.95 tff(32158,plain,
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% 11.69/11.95 tff(32160,plain,
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% 11.69/11.95 inference(unit_resolution,[status(thm)],[30084, 32159, 11])).
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% 11.69/11.95 tff(32162,plain,
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% 11.69/11.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
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% 11.69/11.95 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
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% 11.69/11.96 inference(monotonicity,[status(thm)],[32164])).
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% 11.69/11.96 tff(32175,plain,
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% 11.69/11.96 tff(32177,plain,
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% 11.69/11.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
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% 11.69/11.96 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
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% 11.69/11.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
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% 11.69/11.96 inference(modus_ponens,[status(thm)],[32188, 32187])).
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% 11.69/11.96 tff(32206,plain,
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% 11.69/11.96 tff(32232,plain,
% 11.69/11.96 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
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% 11.69/11.97 inference(monotonicity,[status(thm)],[32232])).
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% 11.69/11.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
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% 11.69/11.97 tff(32240,plain,
% 11.69/11.97 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
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% 11.69/11.97 inference(monotonicity,[status(thm)],[32240])).
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% 11.69/11.97 tff(32250,plain,
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% 11.69/11.97 tff(32253,plain,
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% 11.69/11.97 inference(unit_resolution,[status(thm)],[24809, 32254, 7872, 24801])).
% 11.69/11.97 tff(32257,plain,
% 11.69/11.97 (r(s(s(z)), s(s(s(s(z)))))),
% 11.69/11.97 inference(unit_resolution,[status(thm)],[3652, 32256])).
% 11.69/11.97 tff(32258,plain,
% 11.69/11.97 (~r(s(s(z)), z)),
% 11.69/11.97 inference(unit_resolution,[status(thm)],[14746, 32257, 184, 2053])).
% 11.69/11.97 tff(32259,plain,
% 11.69/11.97 (b(s(s(z)), z)),
% 11.69/11.97 inference(unit_resolution,[status(thm)],[1211, 32258])).
% 11.69/11.97 tff(32260,plain,
% 11.69/11.97 (~r(s(s(z)), s(z))),
% 11.69/11.97 inference(unit_resolution,[status(thm)],[5585, 32257, 1216, 664, 590])).
% 11.69/11.97 tff(32261,plain,
% 11.69/11.97 (b(s(s(z)), s(z))),
% 11.69/11.97 inference(unit_resolution,[status(thm)],[3778, 32260])).
% 11.69/11.97 tff(32262,plain,
% 11.69/11.97 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 11.69/11.97 inference(unit_resolution,[status(thm)],[20484, 32261, 1686, 590, 32259])).
% 11.69/11.97 tff(32263,plain,
% 11.69/11.97 ($false),
% 11.69/11.97 inference(unit_resolution,[status(thm)],[32262, 32255])).
% 11.69/11.97 tff(32264,plain,((~b(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.97 tff(32265,plain,
% 11.69/11.97 (~b(z, s(s(s(s(z)))))),
% 11.69/11.97 inference(unit_resolution,[status(thm)],[32264, 1216, 32226, 11, 32225, 184, 2053, 32212, 32208])).
% 11.69/11.97 tff(32266,plain,
% 11.69/11.97 (r(z, s(s(s(s(z)))))),
% 11.69/11.97 inference(unit_resolution,[status(thm)],[800, 32265])).
% 11.69/11.97 tff(32267,plain,
% 11.69/11.97 (r(z, s(s(s(s(elem!1)))))),
% 11.69/11.97 inference(modus_ponens,[status(thm)],[32266, 18458])).
% 11.69/11.97 tff(32268,plain,
% 11.69/11.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 11.69/11.97 inference(rewrite,[status(thm)],[])).
% 11.69/11.97 tff(32269,plain,
% 11.69/11.97 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 11.69/11.98 inference(rewrite,[status(thm)],[])).
% 11.69/11.98 tff(32270,plain,
% 11.69/11.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32269])).
% 11.69/11.98 tff(32271,plain,
% 11.69/11.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 11.69/11.98 inference(transitivity,[status(thm)],[32270, 32268])).
% 11.69/11.98 tff(32272,plain,
% 11.69/11.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 11.69/11.98 inference(quant_inst,[status(thm)],[])).
% 11.69/11.98 tff(32273,plain,
% 11.69/11.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 11.69/11.98 inference(modus_ponens,[status(thm)],[32272, 32271])).
% 11.69/11.98 tff(32274,plain,
% 11.69/11.98 ($false),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[32273, 194, 2792, 1749, 2053, 3557])).
% 11.69/11.98 tff(32275,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.98 tff(32276,plain,
% 11.69/11.98 (~r(s(s(z)), z)),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[32275, 1749, 2792, 2053])).
% 11.69/11.98 tff(32277,plain,
% 11.69/11.98 (b(s(s(z)), z)),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[1211, 32276])).
% 11.69/11.98 tff(32278,plain,
% 11.69/11.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 11.69/11.98 inference(rewrite,[status(thm)],[])).
% 11.69/11.98 tff(32279,plain,
% 11.69/11.98 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 11.69/11.98 inference(rewrite,[status(thm)],[])).
% 11.69/11.98 tff(32280,plain,
% 11.69/11.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))))),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32279])).
% 11.69/11.98 tff(32281,plain,
% 11.69/11.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 11.69/11.98 inference(transitivity,[status(thm)],[32280, 32278])).
% 11.69/11.98 tff(32282,plain,
% 11.69/11.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 11.69/11.98 inference(quant_inst,[status(thm)],[])).
% 11.69/11.98 tff(32283,plain,
% 11.69/11.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))),
% 11.69/11.98 inference(modus_ponens,[status(thm)],[32282, 32281])).
% 11.69/11.98 tff(32284,plain,
% 11.69/11.98 (~b(s(s(z)), s(elem!1))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[32283, 391, 592, 591, 32277])).
% 11.69/11.98 tff(32285,assumption,(r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 11.69/11.98 tff(32286,plain,
% 11.69/11.98 (~r(s(s(z)), s(elem!1))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[12123, 194, 1749, 2053, 32285])).
% 11.69/11.98 tff(32287,plain,
% 11.69/11.98 ($false),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[4693, 42, 4690, 32286, 32284])).
% 11.69/11.98 tff(32288,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.98 tff(32289,plain,
% 11.69/11.98 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[32288, 32267, 32223, 592, 2053, 32218, 32215])).
% 11.69/11.98 tff(32290,plain,
% 11.69/11.98 (b(s(s(z)), s(s(s(s(z)))))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[3652, 32289])).
% 11.69/11.98 tff(32291,plain,
% 11.69/11.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 11.69/11.98 inference(rewrite,[status(thm)],[])).
% 11.69/11.98 tff(32292,plain,
% 11.69/11.98 (((~b(s(s(s(z))), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 11.69/11.98 inference(rewrite,[status(thm)],[])).
% 11.69/11.98 tff(32293,plain,
% 11.69/11.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32292])).
% 11.69/11.98 tff(32294,plain,
% 11.69/11.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 11.69/11.98 inference(transitivity,[status(thm)],[32293, 32291])).
% 11.69/11.98 tff(32295,plain,
% 11.69/11.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 11.69/11.98 inference(quant_inst,[status(thm)],[])).
% 11.69/11.98 tff(32296,plain,
% 11.69/11.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 11.69/11.98 inference(modus_ponens,[status(thm)],[32295, 32294])).
% 11.69/11.98 tff(32297,plain,
% 11.69/11.98 ($false),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[32296, 391, 32290, 32212, 32208, 32193])).
% 11.69/11.98 tff(32298,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.98 tff(32299,plain,
% 11.69/11.98 (b(s(s(s(elem!1))), elem!1)),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[32298, 32078, 2053, 1216, 644, 1027, 183, 721, 32181, 9, 4028])).
% 11.69/11.98 tff(32300,plain,
% 11.69/11.98 ($false),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[28222, 32299, 32177, 1027])).
% 11.69/11.98 tff(32301,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~(z = elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.98 tff(32302,plain,
% 11.69/11.98 (b(elem!1, s(s(s(elem!1))))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[32301, 1216, 2053, 32073, 183, 721, 32071, 1])).
% 11.69/11.98 tff(32303,plain,
% 11.69/11.98 (s(z) = s(elem!1)),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32071])).
% 11.69/11.98 tff(32304,plain,
% 11.69/11.98 (s(s(z)) = s(s(elem!1))),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32303])).
% 11.69/11.98 tff(32305,plain,
% 11.69/11.98 (s(s(s(z))) = s(s(s(elem!1)))),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32304])).
% 11.69/11.98 tff(32306,plain,
% 11.69/11.98 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32305])).
% 11.69/11.98 tff(32307,plain,
% 11.69/11.98 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 11.69/11.98 inference(symmetry,[status(thm)],[32306])).
% 11.69/11.98 tff(32308,plain,
% 11.69/11.98 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32307])).
% 11.69/11.98 tff(32309,plain,
% 11.69/11.98 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.69/11.98 inference(symmetry,[status(thm)],[32308])).
% 11.69/11.98 tff(32310,plain,
% 11.69/11.98 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32304])).
% 11.69/11.98 tff(32311,plain,
% 11.69/11.98 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 11.69/11.98 inference(modus_ponens,[status(thm)],[31897, 32310])).
% 11.69/11.98 tff(32312,plain,
% 11.69/11.98 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.69/11.98 inference(modus_ponens,[status(thm)],[32311, 32309])).
% 11.69/11.98 tff(32313,plain,
% 11.69/11.98 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32303])).
% 11.69/11.98 tff(32314,plain,
% 11.69/11.98 (b(s(elem!1), elem!1)),
% 11.69/11.98 inference(modus_ponens,[status(thm)],[32073, 32313])).
% 11.69/11.98 tff(32315,plain,
% 11.69/11.98 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32303])).
% 11.69/11.98 tff(32316,plain,
% 11.69/11.98 (elem!1 = z),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[97, 32071])).
% 11.69/11.98 tff(32317,plain,
% 11.69/11.98 (r(s(s(s(z))), s(z))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[29740, 32316, 183])).
% 11.69/11.98 tff(32318,plain,
% 11.69/11.98 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[31962, 32316, 2053, 1216, 32317])).
% 11.69/11.98 tff(32319,plain,
% 11.69/11.98 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[15351, 32318, 21770])).
% 11.69/11.98 tff(32320,plain,
% 11.69/11.98 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 11.69/11.98 inference(monotonicity,[status(thm)],[32071])).
% 11.69/11.98 tff(32321,plain,
% 11.69/11.98 (r(s(s(s(s(z)))), elem!1)),
% 11.69/11.98 inference(modus_ponens,[status(thm)],[2053, 32320])).
% 11.69/11.98 tff(32322,plain,
% 11.69/11.98 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[307, 29900])).
% 11.69/11.98 tff(32323,plain,
% 11.69/11.98 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[32103, 32318, 32071])).
% 11.69/11.98 tff(32324,plain,
% 11.69/11.98 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[1164, 32323, 32322])).
% 11.69/11.98 tff(32325,plain,
% 11.69/11.98 (b(z, s(s(s(elem!1))))),
% 11.69/11.98 inference(unit_resolution,[status(thm)],[31942, 32302, 80])).
% 11.69/11.98 tff(32326,plain,
% 11.69/11.98 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 11.69/11.99 inference(monotonicity,[status(thm)],[934])).
% 11.69/11.99 tff(32327,plain,
% 11.69/11.99 (r(s(s(s(s(elem!1)))), elem!1)),
% 11.69/11.99 inference(modus_ponens,[status(thm)],[2112, 32326])).
% 11.69/11.99 tff(32328,plain,
% 11.69/11.99 (b(s(z), z) <=> b(s(z), elem!1)),
% 11.69/11.99 inference(monotonicity,[status(thm)],[94])).
% 11.69/11.99 tff(32329,plain,
% 11.69/11.99 (b(s(z), elem!1)),
% 11.69/11.99 inference(modus_ponens,[status(thm)],[590, 32328])).
% 11.69/11.99 tff(32330,plain,
% 11.69/11.99 (r(s(z), s(s(s(z))))),
% 11.69/11.99 inference(unit_resolution,[status(thm)],[23224, 232, 1027])).
% 11.69/11.99 tff(32331,plain,
% 11.69/11.99 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 11.69/11.99 inference(monotonicity,[status(thm)],[931])).
% 11.69/11.99 tff(32332,plain,
% 11.69/11.99 (r(s(s(s(elem!1))), s(elem!1))),
% 11.69/11.99 inference(modus_ponens,[status(thm)],[183, 32331])).
% 11.69/11.99 tff(32333,plain,
% 11.69/11.99 (r(s(elem!1), s(s(s(elem!1))))),
% 11.69/11.99 inference(modus_ponens,[status(thm)],[232, 27399])).
% 11.69/11.99 tff(32334,plain,
% 11.69/11.99 (b(s(s(s(s(s(s(z)))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.69/11.99 inference(monotonicity,[status(thm)],[941])).
% 11.69/11.99 tff(32335,plain,
% 11.69/11.99 (b(s(s(s(s(s(s(z)))))), s(s(z))) <=> b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 11.69/11.99 inference(symmetry,[status(thm)],[32334])).
% 11.69/11.99 tff(32336,plain,
% 11.69/11.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 11.69/11.99 inference(rewrite,[status(thm)],[])).
% 11.69/11.99 tff(32337,plain,
% 11.69/11.99 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 11.69/11.99 inference(rewrite,[status(thm)],[])).
% 11.69/11.99 tff(32338,plain,
% 11.69/11.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 11.69/11.99 inference(monotonicity,[status(thm)],[32337])).
% 11.69/11.99 tff(32339,plain,
% 11.69/11.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 11.69/11.99 inference(transitivity,[status(thm)],[32338, 32336])).
% 11.69/11.99 tff(32340,plain,
% 11.69/11.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 11.69/11.99 inference(quant_inst,[status(thm)],[])).
% 11.69/11.99 tff(32341,plain,
% 11.69/11.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 11.69/11.99 inference(modus_ponens,[status(thm)],[32340, 32339])).
% 11.69/11.99 tff(32342,plain,
% 11.69/11.99 (~b(s(s(elem!1)), elem!1)),
% 11.69/11.99 inference(unit_resolution,[status(thm)],[32341, 391, 448, 23160, 1037, 32077])).
% 11.69/11.99 tff(32343,plain,
% 11.69/11.99 (r(s(s(elem!1)), elem!1)),
% 11.69/11.99 inference(unit_resolution,[status(thm)],[872, 32342, 970])).
% 11.69/11.99 tff(32344,plain,
% 11.69/11.99 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 11.69/11.99 inference(transitivity,[status(thm)],[968, 2206])).
% 11.69/11.99 tff(32345,plain,
% 11.69/11.99 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 11.69/11.99 inference(monotonicity,[status(thm)],[32344])).
% 11.69/11.99 tff(32346,plain,
% 11.69/11.99 (~(elem!1 = s(s(elem!1)))),
% 11.69/11.99 inference(modus_ponens,[status(thm)],[215, 32345])).
% 11.69/11.99 tff(32347,plain,
% 11.69/11.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 11.69/11.99 inference(rewrite,[status(thm)],[])).
% 11.69/11.99 tff(32348,plain,
% 11.69/11.99 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 11.69/11.99 inference(rewrite,[status(thm)],[])).
% 11.69/11.99 tff(32349,plain,
% 11.69/11.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 11.69/11.99 inference(monotonicity,[status(thm)],[32348])).
% 11.69/11.99 tff(32350,plain,
% 11.69/11.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 11.69/11.99 inference(transitivity,[status(thm)],[32349, 32347])).
% 11.69/11.99 tff(32351,plain,
% 11.69/11.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 11.69/11.99 inference(quant_inst,[status(thm)],[])).
% 11.69/11.99 tff(32352,plain,
% 11.69/11.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 11.69/11.99 inference(modus_ponens,[status(thm)],[32351, 32350])).
% 11.69/11.99 tff(32353,plain,
% 11.69/11.99 (~b(elem!1, s(s(elem!1)))),
% 11.69/11.99 inference(unit_resolution,[status(thm)],[32352, 391, 448, 23160, 1037, 32077])).
% 11.69/11.99 tff(32354,plain,
% 11.69/11.99 (r(elem!1, s(s(elem!1)))),
% 11.69/11.99 inference(unit_resolution,[status(thm)],[1307, 32353, 32346])).
% 11.69/11.99 tff(32355,plain,
% 11.69/11.99 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 11.69/11.99 inference(monotonicity,[status(thm)],[94])).
% 11.69/11.99 tff(32356,plain,
% 11.69/11.99 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 11.69/11.99 inference(monotonicity,[status(thm)],[32355])).
% 11.69/11.99 tff(32357,plain,
% 11.69/11.99 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 11.69/11.99 inference(modus_ponens,[status(thm)],[6638, 32356])).
% 11.69/11.99 tff(32358,plain,
% 11.69/11.99 (s(s(s(elem!1))) = s(s(s(z)))),
% 11.69/11.99 inference(symmetry,[status(thm)],[933])).
% 11.69/11.99 tff(32359,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))), introduced(assumption)).
% 11.69/11.99 tff(32360,plain,
% 11.69/11.99 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 11.69/11.99 inference(transitivity,[status(thm)],[32359, 32358])).
% 11.69/11.99 tff(32361,plain,
% 11.69/11.99 ($false),
% 11.69/11.99 inference(unit_resolution,[status(thm)],[8094, 32360])).
% 11.69/11.99 tff(32362,plain,((~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.69/11.99 tff(32363,plain,
% 11.69/11.99 (~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 11.69/11.99 inference(unit_resolution,[status(thm)],[32362, 94])).
% 11.69/11.99 tff(32364,plain,
% 11.69/11.99 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 11.69/11.99 inference(monotonicity,[status(thm)],[931])).
% 11.69/11.99 tff(32365,plain,
% 11.69/11.99 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 11.69/11.99 inference(monotonicity,[status(thm)],[32364])).
% 11.69/11.99 tff(32366,plain,
% 11.69/11.99 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 11.69/11.99 inference(modus_ponens,[status(thm)],[5065, 32365])).
% 11.69/11.99 tff(32367,plain,
% 11.69/11.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 11.69/11.99 inference(rewrite,[status(thm)],[])).
% 11.69/11.99 tff(32368,plain,
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% 11.69/11.99 inference(modus_ponens,[status(thm)],[32368, 32367])).
% 11.69/11.99 tff(32370,plain,
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% 11.69/11.99 tff(32371,plain,
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% 11.69/11.99 tff(32372,plain,
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% 11.69/11.99 tff(32373,plain,
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% 11.69/11.99 tff(32374,plain,
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% 11.69/11.99 inference(unit_resolution,[status(thm)],[1596, 1027])).
% 11.69/11.99 tff(32375,plain,
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% 11.69/11.99 inference(monotonicity,[status(thm)],[94])).
% 11.69/11.99 tff(32376,plain,
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% 11.69/11.99 inference(unit_resolution,[status(thm)],[13828, 327, 364, 174])).
% 11.69/11.99 tff(32377,plain,
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% 11.69/11.99 inference(unit_resolution,[status(thm)],[324, 32376])).
% 11.69/11.99 tff(32378,plain,
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% 11.69/11.99 inference(modus_ponens,[status(thm)],[32377, 32375])).
% 11.69/11.99 tff(32379,plain,
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% 11.69/11.99 tff(32380,plain,
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% 11.69/11.99 inference(unit_resolution,[status(thm)],[2316, 32379, 32374])).
% 11.69/11.99 tff(32381,plain,
% 11.69/11.99 (r(s(s(elem!1)), s(elem!1))),
% 11.69/11.99 inference(unit_resolution,[status(thm)],[1135, 32380, 1081])).
% 11.69/11.99 tff(32382,plain,
% 11.69/11.99 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
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% 11.69/11.99 tff(32383,plain,
% 11.69/11.99 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 11.69/11.99 inference(monotonicity,[status(thm)],[32382])).
% 11.69/11.99 tff(32384,plain,
% 11.69/11.99 (~(s(elem!1) = s(s(s(elem!1))))),
% 11.69/11.99 inference(modus_ponens,[status(thm)],[217, 32383])).
% 11.69/11.99 tff(32385,plain,
% 11.69/11.99 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 11.69/11.99 inference(unit_resolution,[status(thm)],[8883, 1027])).
% 11.69/12.00 tff(32386,plain,
% 11.69/12.00 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[307, 32385])).
% 11.69/12.00 tff(32387,plain,
% 11.69/12.00 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[935])).
% 11.69/12.00 tff(32388,plain,
% 11.69/12.00 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.69/12.00 inference(symmetry,[status(thm)],[32387])).
% 11.69/12.00 tff(32389,plain,
% 11.69/12.00 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[932])).
% 11.69/12.00 tff(32390,plain,
% 11.69/12.00 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.69/12.00 inference(transitivity,[status(thm)],[32389, 32388])).
% 11.69/12.00 tff(32391,plain,
% 11.69/12.00 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[94])).
% 11.69/12.00 tff(32392,plain,
% 11.69/12.00 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 11.69/12.00 inference(symmetry,[status(thm)],[32391])).
% 11.69/12.00 tff(32393,plain,
% 11.69/12.00 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[932])).
% 11.69/12.00 tff(32394,plain,
% 11.69/12.00 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 11.69/12.00 inference(symmetry,[status(thm)],[32393])).
% 11.69/12.00 tff(32395,plain,
% 11.69/12.00 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 11.69/12.00 inference(transitivity,[status(thm)],[32375, 32394, 32392])).
% 11.69/12.00 tff(32396,plain,
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% 11.69/12.00 inference(modus_ponens,[status(thm)],[32377, 32395])).
% 11.69/12.00 tff(32397,plain,
% 11.69/12.00 (r(s(s(s(z))), z)),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[4409, 174, 1027])).
% 11.69/12.00 tff(32398,plain,
% 11.69/12.00 (r(s(s(z)), z)),
% 11.69/12.00 inference(modus_ponens,[status(thm)],[364, 1203])).
% 11.69/12.00 tff(32399,plain,
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% 11.69/12.00 inference(unit_resolution,[status(thm)],[4385, 327, 1027])).
% 11.69/12.00 tff(32400,plain,
% 11.69/12.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 11.69/12.00 inference(rewrite,[status(thm)],[])).
% 11.69/12.00 tff(32401,plain,
% 11.69/12.00 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 11.69/12.00 inference(rewrite,[status(thm)],[])).
% 11.69/12.00 tff(32402,plain,
% 11.69/12.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[32401])).
% 11.69/12.00 tff(32403,plain,
% 11.69/12.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 11.69/12.00 inference(transitivity,[status(thm)],[32402, 32400])).
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% 11.69/12.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 11.69/12.00 inference(quant_inst,[status(thm)],[])).
% 11.69/12.00 tff(32405,plain,
% 11.69/12.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))),
% 11.69/12.00 inference(modus_ponens,[status(thm)],[32404, 32403])).
% 11.69/12.00 tff(32406,plain,
% 11.69/12.00 ($false),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32405, 194, 3557, 719, 4428, 30159])).
% 11.69/12.00 tff(32407,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.00 tff(32408,plain,
% 11.69/12.00 (~r(z, s(s(s(s(z)))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32407, 32399, 32398, 32397])).
% 11.69/12.00 tff(32409,plain,
% 11.69/12.00 (b(z, s(s(s(s(z)))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[800, 32408])).
% 11.69/12.00 tff(32410,plain,
% 11.69/12.00 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[94])).
% 11.69/12.00 tff(32411,plain,
% 11.69/12.00 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 11.69/12.00 inference(symmetry,[status(thm)],[32410])).
% 11.69/12.00 tff(32412,plain,
% 11.69/12.00 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[933])).
% 11.69/12.00 tff(32413,plain,
% 11.69/12.00 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 11.69/12.00 inference(symmetry,[status(thm)],[32412])).
% 11.69/12.00 tff(32414,plain,
% 11.69/12.00 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 11.69/12.00 inference(transitivity,[status(thm)],[32413, 32411])).
% 11.69/12.00 tff(32415,plain,
% 11.69/12.00 (b(z, s(s(s(z))))),
% 11.69/12.00 inference(modus_ponens,[status(thm)],[448, 32414])).
% 11.69/12.00 tff(32416,plain,
% 11.69/12.00 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[933])).
% 11.69/12.00 tff(32417,plain,
% 11.69/12.00 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[32416])).
% 11.69/12.00 tff(32418,plain,
% 11.69/12.00 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[491, 23226])).
% 11.69/12.00 tff(32419,plain,
% 11.69/12.00 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 11.69/12.00 inference(symmetry,[status(thm)],[32418])).
% 11.69/12.00 tff(32420,plain,
% 11.69/12.00 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[301])).
% 11.69/12.00 tff(32421,plain,
% 11.69/12.00 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 11.69/12.00 inference(modus_ponens,[status(thm)],[17615, 32420])).
% 11.69/12.00 tff(32422,plain,
% 11.69/12.00 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[491, 23226])).
% 11.69/12.00 tff(32423,plain,
% 11.69/12.00 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[32422])).
% 11.69/12.00 tff(32424,plain,
% 11.69/12.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.69/12.00 inference(rewrite,[status(thm)],[])).
% 11.69/12.00 tff(32425,plain,
% 11.69/12.00 (((~r(s(s(z)), 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(z))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.69/12.00 inference(rewrite,[status(thm)],[])).
% 11.69/12.00 tff(32426,plain,
% 11.69/12.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[32425])).
% 11.69/12.00 tff(32427,plain,
% 11.69/12.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.69/12.00 inference(transitivity,[status(thm)],[32426, 32424])).
% 11.69/12.00 tff(32428,plain,
% 11.69/12.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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)))))))),
% 11.69/12.00 inference(quant_inst,[status(thm)],[])).
% 11.69/12.00 tff(32429,plain,
% 11.69/12.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 11.69/12.00 inference(modus_ponens,[status(thm)],[32428, 32427])).
% 11.69/12.00 tff(32430,plain,
% 11.69/12.00 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32429, 194, 3557, 1697])).
% 11.69/12.00 tff(32431,plain,
% 11.69/12.00 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32430, 4382])).
% 11.69/12.00 tff(32432,plain,
% 11.69/12.00 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/12.00 inference(modus_ponens,[status(thm)],[32431, 32423])).
% 11.69/12.00 tff(32433,plain,
% 11.69/12.00 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[1164, 32432, 32421])).
% 11.69/12.00 tff(32434,plain,
% 11.69/12.00 (b(s(s(s(z))), s(s(s(s(z)))))),
% 11.69/12.00 inference(modus_ponens,[status(thm)],[32433, 32419])).
% 11.69/12.00 tff(32435,plain,
% 11.69/12.00 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32028, 391, 7872, 7871])).
% 11.69/12.00 tff(32436,plain,
% 11.69/12.00 (~b(z, s(s(s(s(z)))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32435, 32434])).
% 11.69/12.00 tff(32437,plain,
% 11.69/12.00 (r(z, s(s(s(s(z)))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[800, 32436])).
% 11.69/12.00 tff(32438,plain,
% 11.69/12.00 ($false),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32405, 194, 3557, 32437, 4428, 4382])).
% 11.69/12.00 tff(32439,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~(elem!1 = z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.00 tff(32440,plain,
% 11.69/12.00 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32439, 1697, 7871, 4428, 1027, 327, 32398])).
% 11.69/12.00 tff(32441,plain,
% 11.69/12.00 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.69/12.00 inference(modus_ponens,[status(thm)],[32440, 32417])).
% 11.69/12.00 tff(32442,plain,
% 11.69/12.00 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[935])).
% 11.69/12.00 tff(32443,plain,
% 11.69/12.00 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.69/12.00 inference(symmetry,[status(thm)],[32442])).
% 11.69/12.00 tff(32444,plain,
% 11.69/12.00 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 11.69/12.00 inference(monotonicity,[status(thm)],[489])).
% 11.69/12.00 tff(32445,plain,
% 11.69/12.00 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 11.69/12.00 inference(symmetry,[status(thm)],[32444])).
% 11.69/12.00 tff(32446,plain,
% 11.69/12.00 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 11.69/12.00 inference(modus_ponens,[status(thm)],[1697, 32445])).
% 11.69/12.00 tff(32447,plain,
% 11.69/12.00 ($false),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[3950, 32446])).
% 11.69/12.00 tff(32448,plain,((~(elem!1 = z)) | r(s(s(s(s(z)))), s(s(elem!1))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.00 tff(32449,plain,
% 11.69/12.00 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32448, 1697, 1027])).
% 11.69/12.00 tff(32450,plain,
% 11.69/12.00 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.69/12.00 inference(modus_ponens,[status(thm)],[32449, 32443])).
% 11.69/12.00 tff(32451,plain,
% 11.69/12.00 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[14238, 194, 364, 327, 32450])).
% 11.69/12.00 tff(32452,plain,
% 11.69/12.00 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[1095, 32451, 32385])).
% 11.69/12.00 tff(32453,plain,
% 11.69/12.00 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[27316, 32452, 1027])).
% 11.69/12.00 tff(32454,plain,
% 11.69/12.00 ($false),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32453, 32441])).
% 11.69/12.00 tff(32455,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.00 tff(32456,plain,
% 11.69/12.00 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.69/12.00 inference(unit_resolution,[status(thm)],[32455, 327, 364, 94, 32415, 32397])).
% 11.69/12.01 tff(32457,plain,
% 11.69/12.01 (b(s(s(s(s(z)))), s(s(z)))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[1714, 32456])).
% 11.69/12.01 tff(32458,plain,
% 11.69/12.01 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[15550, 32457, 32409, 32396])).
% 11.69/12.01 tff(32459,plain,
% 11.69/12.01 (r(s(s(z)), s(s(s(s(z)))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[3652, 32458])).
% 11.69/12.01 tff(32460,plain,
% 11.69/12.01 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.69/12.01 inference(modus_ponens,[status(thm)],[32459, 32390])).
% 11.69/12.01 tff(32461,plain,
% 11.69/12.01 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[14274, 32460, 991, 327])).
% 11.69/12.01 tff(32462,plain,
% 11.69/12.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[1164, 32461, 32386])).
% 11.69/12.01 tff(32463,plain,
% 11.69/12.01 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.69/12.01 inference(symmetry,[status(thm)],[936])).
% 11.69/12.01 tff(32464,plain,
% 11.69/12.01 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 11.69/12.01 inference(monotonicity,[status(thm)],[932])).
% 11.69/12.01 tff(32465,plain,
% 11.69/12.01 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.69/12.01 inference(transitivity,[status(thm)],[32464, 32463])).
% 11.69/12.01 tff(32466,plain,
% 11.69/12.01 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.69/12.01 inference(modus_ponens,[status(thm)],[32457, 32465])).
% 11.69/12.01 tff(32467,plain,
% 11.69/12.01 (~b(s(elem!1), s(s(s(elem!1))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[19513, 32466, 32077, 448, 32462])).
% 11.69/12.01 tff(32468,plain,
% 11.69/12.01 (r(s(elem!1), s(s(s(elem!1))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[579, 42, 32467, 32384])).
% 11.69/12.01 tff(32469,plain,
% 11.69/12.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 11.69/12.01 inference(rewrite,[status(thm)],[])).
% 11.69/12.01 tff(32470,plain,
% 11.69/12.01 (((~r(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))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 11.69/12.01 inference(rewrite,[status(thm)],[])).
% 11.69/12.01 tff(32471,plain,
% 11.69/12.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 11.69/12.01 inference(monotonicity,[status(thm)],[32470])).
% 11.69/12.01 tff(32472,plain,
% 11.69/12.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 11.69/12.01 inference(transitivity,[status(thm)],[32471, 32469])).
% 11.69/12.01 tff(32473,plain,
% 11.69/12.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 11.69/12.01 inference(quant_inst,[status(thm)],[])).
% 11.69/12.01 tff(32474,plain,
% 11.69/12.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 11.69/12.01 inference(modus_ponens,[status(thm)],[32473, 32472])).
% 11.69/12.01 tff(32475,plain,
% 11.69/12.01 ($false),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[32474, 194, 613, 327, 32468, 32381])).
% 11.69/12.01 tff(32476,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.01 tff(32477,plain,
% 11.69/12.01 (~r(s(s(s(elem!1))), z)),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[32476, 32373, 721, 644, 94, 32327, 448, 32343, 613])).
% 11.69/12.01 tff(32478,plain,
% 11.69/12.01 (~r(s(s(s(elem!1))), elem!1)),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[406, 32477, 1027])).
% 11.69/12.01 tff(32479,plain,
% 11.69/12.01 (b(s(s(s(elem!1))), elem!1)),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[230, 32478, 127])).
% 11.69/12.01 tff(32480,plain,
% 11.69/12.01 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[28695, 32479, 604, 32366, 32363, 613, 448, 32077])).
% 11.69/12.01 tff(32481,plain,
% 11.69/12.01 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[8073, 32480, 32357])).
% 11.69/12.01 tff(32482,assumption,(r(s(s(s(s(s(s(z)))))), s(s(elem!1)))), introduced(assumption)).
% 11.69/12.01 tff(32483,plain,
% 11.69/12.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 11.69/12.01 inference(rewrite,[status(thm)],[])).
% 11.69/12.01 tff(32484,plain,
% 11.69/12.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 11.69/12.01 inference(quant_inst,[status(thm)],[])).
% 11.69/12.01 tff(32485,plain,
% 11.69/12.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 11.69/12.01 inference(modus_ponens,[status(thm)],[32484, 32483])).
% 11.69/12.01 tff(32486,plain,
% 11.69/12.01 ($false),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[32485, 194, 364, 1064, 2741, 32482])).
% 11.69/12.01 tff(32487,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.01 tff(32488,plain,
% 11.69/12.01 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[32487, 32481, 32354, 32343])).
% 11.69/12.01 tff(32489,plain,
% 11.69/12.01 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 11.69/12.01 inference(monotonicity,[status(thm)],[941])).
% 11.69/12.01 tff(32490,plain,
% 11.69/12.01 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 11.69/12.01 inference(symmetry,[status(thm)],[32489])).
% 11.69/12.01 tff(32491,plain,
% 11.69/12.01 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(elem!1))))),
% 11.69/12.01 inference(monotonicity,[status(thm)],[32490])).
% 11.69/12.01 tff(32492,plain,
% 11.69/12.01 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 11.69/12.01 inference(modus_ponens,[status(thm)],[5009, 32491])).
% 11.69/12.01 tff(32493,plain,
% 11.69/12.01 ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) <=> (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 11.69/12.01 inference(monotonicity,[status(thm)],[32335])).
% 11.69/12.01 tff(32494,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 11.69/12.01 tff(32495,plain,
% 11.69/12.01 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 11.69/12.01 inference(modus_ponens,[status(thm)],[32494, 32493])).
% 11.69/12.01 tff(32496,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))), introduced(assumption)).
% 11.69/12.01 tff(32497,plain,
% 11.69/12.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(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(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 11.69/12.01 inference(rewrite,[status(thm)],[])).
% 11.69/12.01 tff(32498,plain,
% 11.69/12.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 11.69/12.01 inference(quant_inst,[status(thm)],[])).
% 11.69/12.01 tff(32499,plain,
% 11.69/12.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 11.69/12.01 inference(modus_ponens,[status(thm)],[32498, 32497])).
% 11.69/12.01 tff(32500,plain,
% 11.69/12.01 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[32499, 42, 32496])).
% 11.69/12.01 tff(32501,plain,
% 11.69/12.01 ($false),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[32500, 32495, 32492])).
% 11.69/12.01 tff(32502,plain,(r(s(s(s(s(s(s(z)))))), s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.01 tff(32503,plain,
% 11.69/12.01 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[32502, 32488, 94])).
% 11.69/12.01 tff(32504,plain,
% 11.69/12.01 (b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 11.69/12.01 inference(modus_ponens,[status(thm)],[32503, 32335])).
% 11.69/12.01 tff(32505,plain,
% 11.69/12.01 (r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 11.69/12.01 inference(monotonicity,[status(thm)],[935])).
% 11.69/12.01 tff(32506,plain,
% 11.69/12.01 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 11.69/12.01 inference(symmetry,[status(thm)],[32505])).
% 11.69/12.01 tff(32507,plain,
% 11.69/12.01 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 11.69/12.01 inference(monotonicity,[status(thm)],[32506])).
% 11.69/12.01 tff(32508,plain,
% 11.69/12.01 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 11.69/12.01 inference(monotonicity,[status(thm)],[94])).
% 11.69/12.01 tff(32509,plain,
% 11.69/12.01 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 11.69/12.01 inference(transitivity,[status(thm)],[32508, 764])).
% 11.69/12.01 tff(32510,plain,
% 11.69/12.01 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 11.69/12.01 inference(monotonicity,[status(thm)],[32509])).
% 11.69/12.01 tff(32511,plain,
% 11.69/12.01 (~(elem!1 = s(s(s(s(z)))))),
% 11.69/12.01 inference(modus_ponens,[status(thm)],[83, 32510])).
% 11.69/12.01 tff(32512,plain,
% 11.69/12.01 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[299, 15838])).
% 11.69/12.01 tff(32513,plain,
% 11.69/12.01 (r(s(s(s(z))), s(s(z)))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[4385, 32373, 1027])).
% 11.69/12.01 tff(32514,plain,
% 11.69/12.01 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[32040, 32513, 1216, 15705])).
% 11.69/12.01 tff(32515,plain,
% 11.69/12.01 (r(s(s(s(s(z)))), s(s(s(z))))),
% 11.69/12.01 inference(modus_ponens,[status(thm)],[1082, 29927])).
% 11.69/12.01 tff(32516,assumption,(~r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 11.69/12.01 tff(32517,plain,
% 11.69/12.01 ($false),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[32516, 32515])).
% 11.69/12.01 tff(32518,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(z)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.01 tff(32519,plain,
% 11.69/12.01 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[32518, 32514, 1027])).
% 11.69/12.01 tff(32520,plain,
% 11.69/12.01 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[1095, 32519, 32512])).
% 11.69/12.01 tff(32521,plain,
% 11.69/12.01 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[27316, 32520, 1027])).
% 11.69/12.01 tff(32522,plain,
% 11.69/12.01 (~b(elem!1, s(s(s(s(z)))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[10959, 32521, 1669, 32479])).
% 11.69/12.01 tff(32523,plain,
% 11.69/12.01 (r(elem!1, s(s(s(s(z)))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[781, 32522, 32511])).
% 11.69/12.01 tff(32524,plain,
% 11.69/12.01 ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 11.69/12.01 inference(unit_resolution,[status(thm)],[12169, 194])).
% 11.69/12.01 tff(32525,plain,
% 11.69/12.01 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[32524, 32481, 32523, 2112])).
% 11.69/12.02 tff(32526,plain,
% 11.69/12.02 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 11.69/12.02 inference(modus_ponens,[status(thm)],[32525, 32507])).
% 11.69/12.02 tff(32527,plain,
% 11.69/12.02 ((s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 11.69/12.02 inference(monotonicity,[status(thm)],[935])).
% 11.69/12.02 tff(32528,plain,
% 11.69/12.02 ((s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 11.69/12.02 inference(transitivity,[status(thm)],[32527, 8179])).
% 11.69/12.02 tff(32529,plain,
% 11.69/12.02 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1)))))),
% 11.69/12.02 inference(symmetry,[status(thm)],[32528])).
% 11.69/12.02 tff(32530,plain,
% 11.69/12.02 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))))),
% 11.69/12.02 inference(monotonicity,[status(thm)],[32529])).
% 11.69/12.02 tff(32531,plain,
% 11.69/12.02 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1)))))),
% 11.69/12.02 inference(modus_ponens,[status(thm)],[4995, 32530])).
% 11.69/12.02 tff(32532,plain,
% 11.69/12.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 11.69/12.02 inference(rewrite,[status(thm)],[])).
% 11.69/12.02 tff(32533,plain,
% 11.69/12.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 11.69/12.02 inference(quant_inst,[status(thm)],[])).
% 11.69/12.02 tff(32534,plain,
% 11.69/12.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 11.69/12.02 inference(modus_ponens,[status(thm)],[32533, 32532])).
% 11.69/12.02 tff(32535,plain,
% 11.69/12.02 ((s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[32534, 42])).
% 11.69/12.02 tff(32536,plain,
% 11.69/12.02 (b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[32535, 32531, 32526])).
% 11.69/12.02 tff(32537,plain,
% 11.69/12.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 11.69/12.02 inference(rewrite,[status(thm)],[])).
% 11.69/12.02 tff(32538,plain,
% 11.69/12.02 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 11.69/12.02 inference(rewrite,[status(thm)],[])).
% 11.69/12.02 tff(32539,plain,
% 11.69/12.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))))),
% 11.69/12.02 inference(monotonicity,[status(thm)],[32538])).
% 11.69/12.02 tff(32540,plain,
% 11.69/12.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 11.69/12.02 inference(transitivity,[status(thm)],[32539, 32537])).
% 11.69/12.02 tff(32541,plain,
% 11.69/12.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 11.69/12.02 inference(quant_inst,[status(thm)],[])).
% 11.69/12.02 tff(32542,plain,
% 11.69/12.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 11.69/12.02 inference(modus_ponens,[status(thm)],[32541, 32540])).
% 11.69/12.02 tff(32543,plain,
% 11.69/12.02 ($false),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[32542, 391, 1037, 32371, 1152, 32536, 32504])).
% 11.69/12.02 tff(32544,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~(z = elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(elem!1))) = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.02 tff(32545,plain,
% 11.69/12.02 (~b(s(s(elem!1)), s(elem!1))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[32544, 32333, 94, 2112, 1152, 32332, 448, 1669, 127, 1216, 32330, 721, 32329, 1573])).
% 11.69/12.02 tff(32546,plain,
% 11.69/12.02 (~b(s(s(elem!1)), s(z))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[1033, 32545, 1027])).
% 11.69/12.02 tff(32547,plain,
% 11.69/12.02 (r(s(s(elem!1)), s(z))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[362, 32546])).
% 11.69/12.02 tff(32548,plain,
% 11.69/12.02 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[11169, 32547, 183, 1216])).
% 11.69/12.02 tff(32549,plain,
% 11.69/12.02 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[1370, 32548, 15838])).
% 11.69/12.02 tff(32550,plain,
% 11.69/12.02 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[1741, 32549, 1573, 1152])).
% 11.69/12.02 tff(32551,plain,
% 11.69/12.02 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[1061, 32550, 947])).
% 11.69/12.02 tff(32552,plain,
% 11.69/12.02 (r(s(s(elem!1)), s(elem!1))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[1135, 32545, 1081])).
% 11.69/12.02 tff(32553,plain,
% 11.69/12.02 (~b(z, s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[24044, 32549, 590, 10682, 183, 232, 21729])).
% 11.69/12.02 tff(32554,plain,
% 11.69/12.02 (r(z, s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[324, 32553])).
% 11.69/12.02 tff(32555,plain,
% 11.69/12.02 (r(elem!1, s(s(elem!1)))),
% 11.69/12.02 inference(modus_ponens,[status(thm)],[32554, 948])).
% 11.69/12.02 tff(32556,plain,
% 11.69/12.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 11.69/12.02 inference(rewrite,[status(thm)],[])).
% 11.69/12.02 tff(32557,plain,
% 11.69/12.02 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 11.69/12.02 inference(rewrite,[status(thm)],[])).
% 11.69/12.02 tff(32558,plain,
% 11.69/12.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 11.69/12.02 inference(monotonicity,[status(thm)],[32557])).
% 11.69/12.02 tff(32559,plain,
% 11.69/12.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 11.69/12.02 inference(transitivity,[status(thm)],[32558, 32556])).
% 11.69/12.02 tff(32560,plain,
% 11.69/12.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 11.69/12.02 inference(quant_inst,[status(thm)],[])).
% 11.69/12.02 tff(32561,plain,
% 11.69/12.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 11.69/12.02 inference(modus_ponens,[status(thm)],[32560, 32559])).
% 11.69/12.02 tff(32562,plain,
% 11.69/12.02 ($false),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[32561, 194, 32555, 32552, 32551, 32327])).
% 11.69/12.02 tff(32563,plain,((~r(s(z), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.02 tff(32564,plain,
% 11.69/12.02 (~r(s(z), s(s(s(elem!1))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[32563, 32071, 32069, 32325, 183, 32324, 32312, 1216, 32321, 32302, 32319, 9, 721])).
% 11.69/12.02 tff(32565,plain,
% 11.69/12.02 (b(s(z), s(s(s(elem!1))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[247, 32564])).
% 11.69/12.02 tff(32566,plain,
% 11.69/12.02 (b(s(elem!1), s(s(s(elem!1))))),
% 11.69/12.02 inference(modus_ponens,[status(thm)],[32565, 32315])).
% 11.69/12.02 tff(32567,plain,
% 11.69/12.02 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[19444, 32566, 32314, 32312, 32302])).
% 11.69/12.02 tff(32568,plain,
% 11.69/12.02 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[1370, 32567, 26982])).
% 11.69/12.02 tff(32569,plain,
% 11.69/12.02 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[31008, 32565, 10679, 32325, 32324])).
% 11.69/12.02 tff(32570,plain,
% 11.69/12.02 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[1095, 32569, 29900])).
% 11.69/12.02 tff(32571,plain,
% 11.69/12.02 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 11.69/12.02 inference(monotonicity,[status(thm)],[32307])).
% 11.69/12.02 tff(32572,plain,
% 11.69/12.02 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 11.69/12.02 inference(symmetry,[status(thm)],[32571])).
% 11.69/12.02 tff(32573,plain,
% 11.69/12.02 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 11.69/12.02 inference(monotonicity,[status(thm)],[32572])).
% 11.69/12.02 tff(32574,plain,
% 11.69/12.02 (s(s(elem!1)) = s(s(z))),
% 11.69/12.02 inference(symmetry,[status(thm)],[32304])).
% 11.69/12.02 tff(32575,plain,
% 11.69/12.02 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 11.69/12.02 inference(monotonicity,[status(thm)],[32574])).
% 11.69/12.02 tff(32576,plain,
% 11.69/12.02 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 11.69/12.02 inference(transitivity,[status(thm)],[32575, 940])).
% 11.69/12.02 tff(32577,plain,
% 11.69/12.02 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 11.69/12.02 inference(symmetry,[status(thm)],[32576])).
% 11.69/12.02 tff(32578,plain,
% 11.69/12.02 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 11.69/12.02 inference(monotonicity,[status(thm)],[32577])).
% 11.69/12.02 tff(32579,plain,
% 11.69/12.02 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 11.69/12.02 inference(modus_ponens,[status(thm)],[714, 32578])).
% 11.69/12.02 tff(32580,plain,
% 11.69/12.02 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 11.69/12.02 inference(modus_ponens,[status(thm)],[32579, 32573])).
% 11.69/12.02 tff(32581,plain,
% 11.69/12.02 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[19513, 32566, 32324, 32314, 32302])).
% 11.69/12.02 tff(32582,plain,
% 11.69/12.02 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[1061, 32581, 32580])).
% 11.69/12.02 tff(32583,plain,
% 11.69/12.02 (~r(s(s(elem!1)), elem!1)),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[14240, 32582, 32570, 32568])).
% 11.69/12.02 tff(32584,plain,
% 11.69/12.02 (b(s(s(elem!1)), elem!1)),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[872, 32583, 32076])).
% 11.69/12.02 tff(32585,plain,
% 11.69/12.02 (~r(s(s(elem!1)), s(z))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[11169, 32568, 183, 1216])).
% 11.69/12.02 tff(32586,plain,
% 11.69/12.02 (b(s(s(elem!1)), s(z))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[362, 32585])).
% 11.69/12.02 tff(32587,plain,
% 11.69/12.02 ($false),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[22561, 32586, 32584, 721, 32073])).
% 11.69/12.02 tff(32588,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | r(z, elem!1) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.69/12.02 tff(32589,plain,
% 11.69/12.02 (~r(s(s(s(elem!1))), s(z))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[32588, 31906, 2053, 80, 1216, 721])).
% 11.69/12.02 tff(32590,plain,
% 11.69/12.02 (b(s(s(s(elem!1))), s(z))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[223, 32589])).
% 11.69/12.02 tff(32591,plain,
% 11.69/12.02 (~b(s(z), s(s(s(elem!1))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[15561, 32590, 10682, 10679])).
% 11.69/12.02 tff(32592,plain,
% 11.69/12.02 (r(s(z), s(s(s(elem!1))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[247, 32591])).
% 11.69/12.02 tff(32593,plain,
% 11.69/12.02 (~b(s(z), s(s(s(elem!1))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[15561, 1526, 10682, 664])).
% 11.69/12.02 tff(32594,plain,
% 11.69/12.02 (r(s(z), s(s(s(elem!1))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[247, 32593])).
% 11.69/12.02 tff(32595,plain,
% 11.69/12.02 (b(elem!1, s(s(s(elem!1))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[5715, 168, 1484, 18873, 32594])).
% 11.69/12.02 tff(32596,plain,
% 11.69/12.02 (r(s(s(s(elem!1))), elem!1)),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[230, 168, 18873])).
% 11.69/12.02 tff(32597,plain,
% 11.69/12.02 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[2865, 32595, 688])).
% 11.69/12.02 tff(32598,plain,
% 11.69/12.02 (~b(s(s(s(elem!1))), z)),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[27078, 32597, 10682, 1686])).
% 11.69/12.02 tff(32599,plain,
% 11.69/12.02 (r(s(s(s(elem!1))), z)),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[377, 32598])).
% 11.69/12.02 tff(32600,plain,
% 11.69/12.02 (~r(z, s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[31234, 32599, 10682, 133, 18874, 530])).
% 11.69/12.02 tff(32601,plain,
% 11.69/12.02 (b(z, s(s(elem!1)))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[324, 32600])).
% 11.69/12.02 tff(32602,plain,
% 11.69/12.02 (~r(z, s(elem!1))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[4255, 32599, 530, 32596])).
% 11.69/12.02 tff(32603,plain,
% 11.69/12.02 (b(z, s(elem!1))),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[566, 32602])).
% 11.69/12.02 tff(32604,plain,
% 11.69/12.02 ($false),
% 11.69/12.02 inference(unit_resolution,[status(thm)],[26924, 32603, 32601, 10682, 133, 168, 1526, 530, 664, 150, 32596, 18875, 32595])).
% 11.69/12.02 tff(32605,plain,(b(s(s(s(elem!1))), elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(elem!1, z)) | (~b(z, s(z))) | (s(z) = elem!1) | (~b(z, s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.03 tff(32606,plain,
% 11.82/12.03 (b(s(s(s(elem!1))), elem!1)),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[32605, 32590, 133, 10682, 530, 10679, 21435, 31895, 31904, 31899])).
% 11.82/12.03 tff(32607,plain,
% 11.82/12.03 (~b(elem!1, s(s(s(elem!1))))),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[10845, 32606, 10682, 133])).
% 11.82/12.03 tff(32608,plain,
% 11.82/12.03 (r(elem!1, s(s(s(elem!1))))),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[424, 32607, 31906])).
% 11.82/12.03 tff(32609,plain,
% 11.82/12.03 (~r(s(s(s(elem!1))), z)),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[5645, 32608, 31899, 32592])).
% 11.82/12.03 tff(32610,plain,
% 11.82/12.03 (b(s(s(s(elem!1))), z)),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[377, 32609])).
% 11.82/12.03 tff(32611,plain,
% 11.82/12.03 (~b(s(s(z)), s(s(s(elem!1))))),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[26759, 391, 133, 380, 1235, 721])).
% 11.82/12.03 tff(32612,plain,
% 11.82/12.03 (r(s(s(z)), s(s(s(elem!1))))),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[11041, 32611])).
% 11.82/12.03 tff(32613,plain,
% 11.82/12.03 (~b(s(s(s(elem!1))), s(s(z)))),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[26790, 391, 133, 380, 1235, 721])).
% 11.82/12.03 tff(32614,plain,
% 11.82/12.03 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[10713, 42, 32613])).
% 11.82/12.03 tff(32615,plain,
% 11.82/12.03 (r(s(s(s(elem!1))), s(s(z)))),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[32614, 10703])).
% 11.82/12.03 tff(32616,plain,
% 11.82/12.03 (r(s(s(s(s(z)))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 11.82/12.03 inference(monotonicity,[status(thm)],[688])).
% 11.82/12.03 tff(32617,plain,
% 11.82/12.03 (r(elem!1, s(s(z)))),
% 11.82/12.03 inference(modus_ponens,[status(thm)],[31723, 32616])).
% 11.82/12.03 tff(32618,plain,
% 11.82/12.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.82/12.03 inference(rewrite,[status(thm)],[])).
% 11.82/12.03 tff(32619,plain,
% 11.82/12.03 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.82/12.03 inference(rewrite,[status(thm)],[])).
% 11.82/12.03 tff(32620,plain,
% 11.82/12.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 11.82/12.03 inference(monotonicity,[status(thm)],[32619])).
% 11.82/12.03 tff(32621,plain,
% 11.82/12.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.82/12.03 inference(transitivity,[status(thm)],[32620, 32618])).
% 11.82/12.03 tff(32622,plain,
% 11.82/12.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 11.82/12.03 inference(quant_inst,[status(thm)],[])).
% 11.82/12.03 tff(32623,plain,
% 11.82/12.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 11.82/12.03 inference(modus_ponens,[status(thm)],[32622, 32621])).
% 11.82/12.03 tff(32624,plain,
% 11.82/12.03 ($false),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[32623, 194, 410, 32617, 32615, 32612])).
% 11.82/12.03 tff(32625,plain,((~b(s(s(z)), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~(s(s(s(s(z)))) = elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.03 tff(32626,plain,
% 11.82/12.03 (~b(s(s(z)), z)),
% 11.82/12.03 inference(unit_resolution,[status(thm)],[32625, 32608, 133, 32610, 721, 31904, 31895, 31897])).
% 11.82/12.03 tff(32627,plain,
% 11.82/12.03 (r(s(s(z)), z)),
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% 11.82/12.04 (r(s(s(z)), z)),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[1211, 32711])).
% 11.82/12.04 tff(32713,plain,
% 11.82/12.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.82/12.04 inference(rewrite,[status(thm)],[])).
% 11.82/12.04 tff(32714,plain,
% 11.82/12.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.82/12.04 inference(quant_inst,[status(thm)],[])).
% 11.82/12.04 tff(32715,plain,
% 11.82/12.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 11.82/12.04 inference(modus_ponens,[status(thm)],[32714, 32713])).
% 11.82/12.04 tff(32716,plain,
% 11.82/12.04 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[32715, 194, 2144, 2053, 32712])).
% 11.82/12.04 tff(32717,plain,
% 11.82/12.04 (b(s(s(s(s(z)))), s(s(z)))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[1714, 32716])).
% 11.82/12.04 tff(32718,plain,
% 11.82/12.04 (~r(s(s(elem!1)), s(z))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[1899, 32692, 847, 364])).
% 11.82/12.04 tff(32719,plain,
% 11.82/12.04 (b(s(s(elem!1)), s(z))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[362, 32718])).
% 11.82/12.04 tff(32720,plain,
% 11.82/12.04 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[31283, 32712, 2053, 719])).
% 11.82/12.04 tff(32721,plain,
% 11.82/12.04 (b(s(s(z)), s(s(s(s(z)))))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[3652, 32720])).
% 11.82/12.04 tff(32722,plain,
% 11.82/12.04 (~b(s(s(z)), s(z))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[9374, 32717, 1234, 32721])).
% 11.82/12.04 tff(32723,plain,
% 11.82/12.04 (r(s(s(z)), s(z))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[3778, 32722])).
% 11.82/12.04 tff(32724,plain,
% 11.82/12.04 (~r(z, s(z))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[4462, 32723, 32692, 32712])).
% 11.82/12.04 tff(32725,plain,
% 11.82/12.04 (b(z, s(z))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[678, 32724])).
% 11.82/12.04 tff(32726,plain,
% 11.82/12.04 (~b(z, s(s(elem!1)))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[31340, 32725, 1234, 32719, 32717])).
% 11.82/12.04 tff(32727,plain,
% 11.82/12.04 (r(z, s(s(elem!1)))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[324, 32726])).
% 11.82/12.04 tff(32728,plain,
% 11.82/12.04 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[9522, 32727, 2053, 32702, 32710])).
% 11.82/12.04 tff(32729,plain,
% 11.82/12.04 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[9445, 32728, 32702, 32701])).
% 11.82/12.04 tff(32730,plain,
% 11.82/12.04 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.82/12.04 inference(transitivity,[status(thm)],[32698, 8492])).
% 11.82/12.04 tff(32731,plain,
% 11.82/12.04 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 11.82/12.04 inference(monotonicity,[status(thm)],[32730])).
% 11.82/12.04 tff(32732,plain,
% 11.82/12.04 (~(s(s(z)) = elem!1)),
% 11.82/12.04 inference(modus_ponens,[status(thm)],[1397, 32731])).
% 11.82/12.04 tff(32733,plain,
% 11.82/12.04 (~r(s(s(z)), elem!1)),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[6674, 32723, 847, 32692])).
% 11.82/12.04 tff(32734,plain,
% 11.82/12.04 (b(s(s(z)), elem!1)),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[4730, 32733, 32732])).
% 11.82/12.04 tff(32735,plain,
% 11.82/12.04 (~b(s(s(s(s(z)))), elem!1)),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[15038, 32734, 1234, 847, 665, 32712, 32700, 32717])).
% 11.82/12.04 tff(32736,plain,
% 11.82/12.04 (r(s(s(s(s(z)))), elem!1)),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[762, 32735, 720])).
% 11.82/12.04 tff(32737,plain,
% 11.82/12.04 (~r(s(s(s(s(z)))), s(z))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[13589, 32736, 133, 1234, 173, 665, 32692, 32700, 770])).
% 11.82/12.04 tff(32738,plain,
% 11.82/12.04 (b(s(s(s(s(z)))), s(z))),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[749, 32737])).
% 11.82/12.04 tff(32739,plain,
% 11.82/12.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.82/12.04 inference(rewrite,[status(thm)],[])).
% 11.82/12.04 tff(32740,plain,
% 11.82/12.04 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.82/12.04 inference(rewrite,[status(thm)],[])).
% 11.82/12.04 tff(32741,plain,
% 11.82/12.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.82/12.04 inference(monotonicity,[status(thm)],[32740])).
% 11.82/12.04 tff(32742,plain,
% 11.82/12.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.82/12.04 inference(transitivity,[status(thm)],[32741, 32739])).
% 11.82/12.04 tff(32743,plain,
% 11.82/12.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 11.82/12.04 inference(quant_inst,[status(thm)],[])).
% 11.82/12.04 tff(32744,plain,
% 11.82/12.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 11.82/12.04 inference(modus_ponens,[status(thm)],[32743, 32742])).
% 11.82/12.04 tff(32745,plain,
% 11.82/12.04 ($false),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[32744, 391, 32719, 1234, 32738, 32717, 32729])).
% 11.82/12.04 tff(32746,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (s(z) = elem!1) | (s(s(elem!1)) = elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.04 tff(32747,plain,
% 11.82/12.04 (~b(s(z), z)),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[32746, 32690, 22902, 11936, 29426, 720, 1234, 32688, 32686, 10645, 29427, 32683, 32679, 32682, 118])).
% 11.82/12.04 tff(32748,plain,
% 11.82/12.04 (r(s(z), z)),
% 11.82/12.04 inference(unit_resolution,[status(thm)],[180, 32747])).
% 11.82/12.05 tff(32749,plain,
% 11.82/12.05 (~r(s(s(z)), z)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[10261, 32748, 29426, 10645])).
% 11.82/12.05 tff(32750,plain,
% 11.82/12.05 (b(s(s(z)), z)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[1211, 32749])).
% 11.82/12.05 tff(32751,plain,
% 11.82/12.05 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[281, 32681])).
% 11.82/12.05 tff(32752,plain,
% 11.82/12.05 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[287, 32684])).
% 11.82/12.05 tff(32753,plain,
% 11.82/12.05 (elem!1 = s(s(s(elem!1)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[26517, 32748, 22902, 29427, 31, 11936, 32686, 32752, 32679, 32751])).
% 11.82/12.05 tff(32754,plain,
% 11.82/12.05 (s(s(s(elem!1))) = elem!1),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[129, 32753])).
% 11.82/12.05 tff(32755,plain,
% 11.82/12.05 (~(s(elem!1) = s(s(s(s(z)))))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[1965, 32754])).
% 11.82/12.05 tff(32756,plain,
% 11.82/12.05 (~r(z, s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[17429, 32755, 29426, 1234, 32748, 124, 32679, 29427, 2, 32753, 32690])).
% 11.82/12.05 tff(32757,plain,
% 11.82/12.05 (b(z, s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[678, 32756])).
% 11.82/12.05 tff(32758,plain,
% 11.82/12.05 (b(s(s(s(elem!1))), z)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[9553, 32753, 11936])).
% 11.82/12.05 tff(32759,plain,
% 11.82/12.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 11.82/12.05 inference(rewrite,[status(thm)],[])).
% 11.82/12.05 tff(32760,plain,
% 11.82/12.05 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 11.82/12.05 inference(rewrite,[status(thm)],[])).
% 11.82/12.05 tff(32761,plain,
% 11.82/12.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 11.82/12.05 inference(monotonicity,[status(thm)],[32760])).
% 11.82/12.05 tff(32762,plain,
% 11.82/12.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 11.82/12.05 inference(transitivity,[status(thm)],[32761, 32759])).
% 11.82/12.05 tff(32763,plain,
% 11.82/12.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 11.82/12.05 inference(quant_inst,[status(thm)],[])).
% 11.82/12.05 tff(32764,plain,
% 11.82/12.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 11.82/12.05 inference(modus_ponens,[status(thm)],[32763, 32762])).
% 11.82/12.05 tff(32765,plain,
% 11.82/12.05 (~b(s(s(z)), s(s(s(elem!1))))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[32764, 391, 32758, 29427, 32750])).
% 11.82/12.05 tff(32766,plain,
% 11.82/12.05 (r(s(s(z)), s(s(s(elem!1))))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[11041, 32765])).
% 11.82/12.05 tff(32767,plain,
% 11.82/12.05 (~b(s(z), s(s(s(elem!1))))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[22948, 32757, 29427, 22902, 32758])).
% 11.82/12.05 tff(32768,plain,
% 11.82/12.05 (~b(s(z), elem!1)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[14872, 32767, 32754])).
% 11.82/12.05 tff(32769,plain,
% 11.82/12.05 (r(s(z), elem!1)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[632, 32768, 32679])).
% 11.82/12.05 tff(32770,plain,
% 11.82/12.05 (~r(s(s(elem!1)), s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[1899, 32769, 32690, 32686])).
% 11.82/12.05 tff(32771,plain,
% 11.82/12.05 (b(s(s(elem!1)), s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[362, 32770])).
% 11.82/12.05 tff(32772,plain,
% 11.82/12.05 (s(elem!1) = s(s(s(s(elem!1))))),
% 11.82/12.05 inference(monotonicity,[status(thm)],[32753])).
% 11.82/12.05 tff(32773,plain,
% 11.82/12.05 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 11.82/12.05 inference(monotonicity,[status(thm)],[32772])).
% 11.82/12.05 tff(32774,plain,
% 11.82/12.05 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 11.82/12.05 inference(monotonicity,[status(thm)],[32773])).
% 11.82/12.05 tff(32775,plain,
% 11.82/12.05 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.82/12.05 inference(monotonicity,[status(thm)],[32753])).
% 11.82/12.05 tff(32776,plain,
% 11.82/12.05 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.82/12.05 inference(modus_ponens,[status(thm)],[32686, 32775])).
% 11.82/12.05 tff(32777,plain,
% 11.82/12.05 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 11.82/12.05 inference(modus_ponens,[status(thm)],[32776, 32774])).
% 11.82/12.05 tff(32778,plain,
% 11.82/12.05 (s(s(s(elem!1))) = elem!1),
% 11.82/12.05 inference(symmetry,[status(thm)],[32753])).
% 11.82/12.05 tff(32779,plain,
% 11.82/12.05 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.82/12.05 inference(monotonicity,[status(thm)],[32778])).
% 11.82/12.05 tff(32780,plain,
% 11.82/12.05 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 11.82/12.05 inference(transitivity,[status(thm)],[32779, 698])).
% 11.82/12.05 tff(32781,plain,
% 11.82/12.05 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 11.82/12.05 inference(monotonicity,[status(thm)],[32780])).
% 11.82/12.05 tff(32782,plain,
% 11.82/12.05 (~(elem!1 = s(s(z)))),
% 11.82/12.05 inference(modus_ponens,[status(thm)],[1397, 32781])).
% 11.82/12.05 tff(32783,plain,
% 11.82/12.05 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[1407, 32782])).
% 11.82/12.05 tff(32784,plain,
% 11.82/12.05 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.82/12.05 inference(transitivity,[status(thm)],[32780, 8492])).
% 11.82/12.05 tff(32785,plain,
% 11.82/12.05 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 11.82/12.05 inference(monotonicity,[status(thm)],[32784])).
% 11.82/12.05 tff(32786,plain,
% 11.82/12.05 (~(s(s(z)) = elem!1)),
% 11.82/12.05 inference(modus_ponens,[status(thm)],[1397, 32785])).
% 11.82/12.05 tff(32787,plain,
% 11.82/12.05 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[14739, 32786, 1234, 32690, 11936, 32750, 32757, 32769])).
% 11.82/12.05 tff(32788,plain,
% 11.82/12.05 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[9445, 32787, 32753, 32783])).
% 11.82/12.05 tff(32789,plain,
% 11.82/12.05 (~r(z, s(s(elem!1)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[9522, 32788, 29426, 32753, 32777])).
% 11.82/12.05 tff(32790,plain,
% 11.82/12.05 (b(z, s(s(elem!1)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[324, 32789])).
% 11.82/12.05 tff(32791,plain,
% 11.82/12.05 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[31340, 32790, 1234, 32757, 32771])).
% 11.82/12.05 tff(32792,plain,
% 11.82/12.05 (r(s(s(s(s(z)))), s(s(z)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[1714, 32791])).
% 11.82/12.05 tff(32793,plain,
% 11.82/12.05 (~b(s(s(s(s(z)))), s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[31252, 32790, 1234, 32757, 32771])).
% 11.82/12.05 tff(32794,plain,
% 11.82/12.05 (r(s(s(s(s(z)))), s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[749, 32793])).
% 11.82/12.05 tff(32795,plain,
% 11.82/12.05 (~r(s(z), s(s(z)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[9138, 32794, 32792, 32766])).
% 11.82/12.05 tff(32796,plain,
% 11.82/12.05 (b(s(z), s(s(z)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[1788, 32795])).
% 11.82/12.05 tff(32797,plain,
% 11.82/12.05 (~r(z, s(s(z)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[30506, 32796, 29426, 1234, 32757, 22902, 32750])).
% 11.82/12.05 tff(32798,plain,
% 11.82/12.05 (~b(z, s(s(z)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[31033, 32796, 22902, 32750, 32757])).
% 11.82/12.05 tff(32799,plain,
% 11.82/12.05 ($false),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[18613, 32798, 32797])).
% 11.82/12.05 tff(32800,plain,(b(z, s(s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = z) | b(elem!1, s(z)) | (s(s(s(s(z)))) = elem!1) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.05 tff(32801,plain,
% 11.82/12.05 (b(z, s(s(s(s(z)))))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[32800, 32677, 2, 31, 32672, 2282, 80])).
% 11.82/12.05 tff(32802,plain,
% 11.82/12.05 (~b(s(s(s(s(z)))), elem!1)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[10865, 32801, 11936, 22902])).
% 11.82/12.05 tff(32803,plain,
% 11.82/12.05 (r(s(s(s(s(z)))), elem!1)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[762, 32802, 32677])).
% 11.82/12.05 tff(32804,plain,
% 11.82/12.05 (b(s(elem!1), elem!1)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[14657, 150, 133, 10682, 2282, 30556, 2])).
% 11.82/12.05 tff(32805,plain,
% 11.82/12.05 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[14662, 32804, 30556])).
% 11.82/12.05 tff(32806,plain,
% 11.82/12.05 (~(s(s(elem!1)) = elem!1)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[451, 32805])).
% 11.82/12.05 tff(32807,plain,
% 11.82/12.05 (~(s(s(elem!1)) = s(elem!1))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[2279, 32805])).
% 11.82/12.05 tff(32808,plain,
% 11.82/12.05 (~b(s(s(elem!1)), elem!1)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[5286, 32807, 133, 11936, 32804])).
% 11.82/12.05 tff(32809,plain,
% 11.82/12.05 (r(s(s(elem!1)), elem!1)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[872, 32808, 32806])).
% 11.82/12.05 tff(32810,plain,
% 11.82/12.05 (~b(s(s(s(s(z)))), s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[17292, 590, 1234, 1686])).
% 11.82/12.05 tff(32811,plain,
% 11.82/12.05 (r(s(s(s(s(z)))), s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[749, 32810])).
% 11.82/12.05 tff(32812,plain,
% 11.82/12.05 (elem!1 = s(s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[13589, 32811, 133, 1234, 2112, 665, 173, 32692, 8922])).
% 11.82/12.05 tff(32813,plain,
% 11.82/12.05 ($false),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[9032, 32719, 32812, 32810])).
% 11.82/12.05 tff(32814,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (s(z) = elem!1) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.05 tff(32815,plain,
% 11.82/12.05 (~b(s(z), z)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[32814, 838, 1234, 2112, 11936, 8922, 133, 32809, 150, 1686])).
% 11.82/12.05 tff(32816,plain,
% 11.82/12.05 (r(s(z), z)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[180, 32815])).
% 11.82/12.05 tff(32817,plain,
% 11.82/12.05 (~r(s(s(s(s(z)))), s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[15864, 32816, 2112, 838])).
% 11.82/12.05 tff(32818,plain,
% 11.82/12.05 (b(s(s(s(s(z)))), s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[749, 32817])).
% 11.82/12.05 tff(32819,plain,
% 11.82/12.05 (~b(z, s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[10478, 32818, 1234, 1686])).
% 11.82/12.05 tff(32820,plain,
% 11.82/12.05 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[281, 32805])).
% 11.82/12.05 tff(32821,plain,
% 11.82/12.05 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[287, 32807])).
% 11.82/12.05 tff(32822,plain,
% 11.82/12.05 (elem!1 = s(s(s(elem!1)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[26517, 32816, 133, 10682, 31, 11936, 32809, 32821, 150, 32820])).
% 11.82/12.05 tff(32823,plain,
% 11.82/12.05 (s(s(s(elem!1))) = elem!1),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[129, 32822])).
% 11.82/12.05 tff(32824,plain,
% 11.82/12.05 (~(s(elem!1) = s(s(s(s(z)))))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[1965, 32823])).
% 11.82/12.05 tff(32825,plain,
% 11.82/12.05 (~r(z, s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[17429, 32824, 29426, 1234, 32816, 124, 150, 10682, 2, 32822, 838])).
% 11.82/12.05 tff(32826,plain,
% 11.82/12.05 ($false),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[678, 32825, 32819])).
% 11.82/12.05 tff(32827,plain,((s(z) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | b(elem!1, s(z)) | (elem!1 = s(s(s(s(z))))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.05 tff(32828,plain,
% 11.82/12.05 (s(z) = elem!1),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[32827, 32801, 29427, 2, 32672, 32803, 22902, 31, 32678, 2282])).
% 11.82/12.05 tff(32829,plain,
% 11.82/12.05 (~b(s(s(s(elem!1))), s(z))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[3938, 32828, 32676])).
% 11.82/12.05 tff(32830,plain,
% 11.82/12.05 (elem!1 = s(s(s(elem!1)))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[31585, 32829, 3446, 31, 80])).
% 11.82/12.05 tff(32831,plain,
% 11.82/12.05 (b(elem!1, s(s(s(elem!1))))),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[8542, 32828, 32672])).
% 11.82/12.05 tff(32832,plain,
% 11.82/12.05 (~(s(s(s(elem!1))) = elem!1)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[15370, 32831])).
% 11.82/12.05 tff(32833,plain,
% 11.82/12.05 ($false),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[129, 32832, 32830])).
% 11.82/12.05 tff(32834,plain,(r(elem!1, z) | b(s(s(s(s(z)))), z) | b(elem!1, s(z)) | r(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.05 tff(32835,plain,
% 11.82/12.05 (r(elem!1, z)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[32834, 31, 3446, 80, 2])).
% 11.82/12.05 tff(32836,plain,
% 11.82/12.05 (~r(s(z), z)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[17062, 719, 32835, 838])).
% 11.82/12.05 tff(32837,plain,
% 11.82/12.05 (b(s(z), z)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[180, 32836])).
% 11.82/12.05 tff(32838,plain,
% 11.82/12.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 11.82/12.05 inference(rewrite,[status(thm)],[])).
% 11.82/12.05 tff(32839,plain,
% 11.82/12.05 (((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 11.82/12.05 inference(rewrite,[status(thm)],[])).
% 11.82/12.05 tff(32840,plain,
% 11.82/12.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))))),
% 11.82/12.05 inference(monotonicity,[status(thm)],[32839])).
% 11.82/12.05 tff(32841,plain,
% 11.82/12.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 11.82/12.05 inference(transitivity,[status(thm)],[32840, 32838])).
% 11.82/12.05 tff(32842,plain,
% 11.82/12.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 11.82/12.05 inference(quant_inst,[status(thm)],[])).
% 11.82/12.05 tff(32843,plain,
% 11.82/12.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))),
% 11.82/12.05 inference(modus_ponens,[status(thm)],[32842, 32841])).
% 11.82/12.05 tff(32844,plain,
% 11.82/12.05 (~r(s(s(s(s(z)))), elem!1)),
% 11.82/12.05 inference(unit_resolution,[status(thm)],[32843, 194, 32835, 29426, 719])).
% 11.82/12.05 tff(32845,plain,
% 11.82/12.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 11.82/12.05 inference(rewrite,[status(thm)],[])).
% 11.82/12.05 tff(32846,plain,
% 11.82/12.05 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 11.82/12.05 inference(rewrite,[status(thm)],[])).
% 11.82/12.05 tff(32847,plain,
% 11.82/12.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 11.82/12.06 inference(monotonicity,[status(thm)],[32846])).
% 11.82/12.06 tff(32848,plain,
% 11.82/12.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 11.82/12.06 inference(transitivity,[status(thm)],[32847, 32845])).
% 11.82/12.06 tff(32849,plain,
% 11.82/12.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 11.82/12.06 inference(quant_inst,[status(thm)],[])).
% 11.82/12.06 tff(32850,plain,
% 11.82/12.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 11.82/12.06 inference(modus_ponens,[status(thm)],[32849, 32848])).
% 11.82/12.06 tff(32851,plain,
% 11.82/12.06 (~r(elem!1, s(s(s(s(z)))))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[32850, 194, 32835, 29426, 719])).
% 11.82/12.06 tff(32852,plain,
% 11.82/12.06 (~b(s(z), elem!1)),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[18869, 720, 32672, 32851, 32844])).
% 11.82/12.06 tff(32853,plain,
% 11.82/12.06 (r(s(z), elem!1)),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[632, 32852, 150])).
% 11.82/12.06 tff(32854,plain,
% 11.82/12.06 (b(elem!1, s(s(s(s(z)))))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[781, 770, 32851])).
% 11.82/12.06 tff(32855,plain,
% 11.82/12.06 (~b(z, s(z))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[10690, 32675, 29427, 590])).
% 11.82/12.06 tff(32856,plain,
% 11.82/12.06 (r(z, s(z))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[678, 32855])).
% 11.82/12.06 tff(32857,plain,
% 11.82/12.06 (~r(s(z), s(s(s(elem!1))))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[16770, 32856, 32835, 838])).
% 11.82/12.06 tff(32858,plain,
% 11.82/12.06 (b(s(z), s(s(s(elem!1))))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[247, 32857])).
% 11.82/12.06 tff(32859,plain,
% 11.82/12.06 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[18274, 32856, 98, 3446, 31])).
% 11.82/12.06 tff(32860,plain,
% 11.82/12.06 (~b(s(s(elem!1)), s(z))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[6169, 32859, 22902, 32675, 590])).
% 11.82/12.06 tff(32861,plain,
% 11.82/12.06 (r(s(s(elem!1)), s(z))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[362, 32860])).
% 11.82/12.06 tff(32862,plain,
% 11.82/12.06 (~b(elem!1, s(s(s(elem!1))))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[18052, 32856, 22902, 29427, 31, 32835, 150, 9])).
% 11.82/12.06 tff(32863,plain,
% 11.82/12.06 (r(elem!1, s(s(s(elem!1))))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[424, 32862, 1])).
% 11.82/12.06 tff(32864,plain,
% 11.82/12.06 (~r(s(s(s(elem!1))), z)),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[30853, 326, 530, 410])).
% 11.82/12.06 tff(32865,plain,
% 11.82/12.06 (b(s(s(s(elem!1))), z)),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[377, 32864])).
% 11.82/12.06 tff(32866,plain,
% 11.82/12.06 ($false),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[11303, 32865, 30659, 379, 10682])).
% 11.82/12.06 tff(32867,plain,((~r(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.06 tff(32868,plain,
% 11.82/12.06 (~r(z, s(s(elem!1)))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[32867, 32863, 29427, 32835, 838, 32858])).
% 11.82/12.06 tff(32869,plain,
% 11.82/12.06 (b(z, s(s(elem!1)))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[324, 32868])).
% 11.82/12.06 tff(32870,plain,
% 11.82/12.06 (s(s(elem!1)) = elem!1),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[30881, 32869, 29427, 22902, 590, 32863, 32862, 32861, 32858, 9])).
% 11.82/12.06 tff(32871,plain,
% 11.82/12.06 (r(s(z), s(s(elem!1)))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[4847, 32870, 1484])).
% 11.82/12.06 tff(32872,plain,
% 11.82/12.06 (~r(s(s(s(s(z)))), s(z))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[5500, 32871, 29426, 32856])).
% 11.82/12.06 tff(32873,plain,
% 11.82/12.06 (b(s(s(s(s(z)))), s(z))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[749, 32872])).
% 11.82/12.06 tff(32874,plain,
% 11.82/12.06 (s(s(s(elem!1))) = s(elem!1)),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[451, 32870])).
% 11.82/12.06 tff(32875,plain,
% 11.82/12.06 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 11.82/12.06 inference(monotonicity,[status(thm)],[32874])).
% 11.82/12.06 tff(32876,plain,
% 11.82/12.06 (b(s(s(s(elem!1))), elem!1)),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[1845, 32870, 32859])).
% 11.82/12.06 tff(32877,plain,
% 11.82/12.06 (b(s(elem!1), elem!1)),
% 11.82/12.06 inference(modus_ponens,[status(thm)],[32876, 32875])).
% 11.82/12.06 tff(32878,plain,
% 11.82/12.06 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 11.82/12.06 inference(monotonicity,[status(thm)],[32874])).
% 11.82/12.06 tff(32879,plain,
% 11.82/12.06 (b(z, s(elem!1))),
% 11.82/12.06 inference(modus_ponens,[status(thm)],[29427, 32878])).
% 11.82/12.06 tff(32880,plain,
% 11.82/12.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.82/12.06 inference(rewrite,[status(thm)],[])).
% 11.82/12.06 tff(32881,plain,
% 11.82/12.06 (((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.82/12.06 inference(rewrite,[status(thm)],[])).
% 11.82/12.06 tff(32882,plain,
% 11.82/12.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 11.82/12.06 inference(monotonicity,[status(thm)],[32881])).
% 11.82/12.06 tff(32883,plain,
% 11.82/12.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.82/12.06 inference(transitivity,[status(thm)],[32882, 32880])).
% 11.82/12.06 tff(32884,plain,
% 11.82/12.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 11.82/12.06 inference(quant_inst,[status(thm)],[])).
% 11.82/12.06 tff(32885,plain,
% 11.82/12.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 11.82/12.06 inference(modus_ponens,[status(thm)],[32884, 32883])).
% 11.82/12.06 tff(32886,plain,
% 11.82/12.06 ($false),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[32885, 391, 22902, 32879, 32877, 2064, 32873])).
% 11.82/12.06 tff(32887,plain,((elem!1 = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~b(s(z), z)) | b(s(s(s(s(z)))), z) | b(elem!1, s(z)) | (s(z) = elem!1) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.06 tff(32888,plain,
% 11.82/12.06 (elem!1 = s(s(s(elem!1)))),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[32887, 32854, 32853, 32837, 3446, 31, 150, 2, 80])).
% 11.82/12.06 tff(32889,plain,
% 11.82/12.06 (s(s(s(elem!1))) = elem!1),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[129, 32888])).
% 11.82/12.06 tff(32890,plain,
% 11.82/12.06 (r(s(s(s(elem!1))), z)),
% 11.82/12.06 inference(unit_resolution,[status(thm)],[533, 32889, 32835])).
% 11.82/12.07 tff(32891,plain,
% 11.82/12.07 (~b(s(z), s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[17484, 32890, 29426, 29427, 719, 16830, 32837, 32889])).
% 11.82/12.07 tff(32892,plain,
% 11.82/12.07 (r(s(z), s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[247, 32891])).
% 11.82/12.07 tff(32893,plain,
% 11.82/12.07 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.82/12.07 inference(monotonicity,[status(thm)],[32888])).
% 11.82/12.07 tff(32894,plain,
% 11.82/12.07 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.82/12.07 inference(modus_ponens,[status(thm)],[32854, 32893])).
% 11.82/12.07 tff(32895,plain,
% 11.82/12.07 (b(s(s(s(s(z)))), elem!1)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[762, 720, 32844])).
% 11.82/12.07 tff(32896,plain,
% 11.82/12.07 (~r(z, s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[18026, 32889, 29426, 29427, 98, 32835, 150, 31])).
% 11.82/12.07 tff(32897,plain,
% 11.82/12.07 (b(z, s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[678, 32896])).
% 11.82/12.07 tff(32898,plain,
% 11.82/12.07 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[31626, 32897, 32835, 32837, 32888, 29427, 32895, 22902, 32854])).
% 11.82/12.07 tff(32899,plain,
% 11.82/12.07 (r(s(s(z)), s(s(s(s(z)))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[3652, 32898])).
% 11.82/12.07 tff(32900,plain,
% 11.82/12.07 (~r(s(s(z)), z)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[31283, 32899, 29426, 719])).
% 11.82/12.07 tff(32901,plain,
% 11.82/12.07 (b(s(s(z)), z)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[1211, 32900])).
% 11.82/12.07 tff(32902,plain,
% 11.82/12.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.07 inference(rewrite,[status(thm)],[])).
% 11.82/12.07 tff(32903,plain,
% 11.82/12.07 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.07 inference(rewrite,[status(thm)],[])).
% 11.82/12.07 tff(32904,plain,
% 11.82/12.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 11.82/12.07 inference(monotonicity,[status(thm)],[32903])).
% 11.82/12.07 tff(32905,plain,
% 11.82/12.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.07 inference(transitivity,[status(thm)],[32904, 32902])).
% 11.82/12.07 tff(32906,plain,
% 11.82/12.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 11.82/12.07 inference(quant_inst,[status(thm)],[])).
% 11.82/12.07 tff(32907,plain,
% 11.82/12.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.82/12.07 inference(modus_ponens,[status(thm)],[32906, 32905])).
% 11.82/12.07 tff(32908,plain,
% 11.82/12.07 (~b(s(s(z)), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[32907, 391, 29427, 32901, 32837, 32894])).
% 11.82/12.07 tff(32909,plain,
% 11.82/12.07 (r(s(s(z)), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[3778, 32908])).
% 11.82/12.07 tff(32910,plain,
% 11.82/12.07 (~r(s(s(z)), s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[11050, 32909, 32890, 32892])).
% 11.82/12.07 tff(32911,plain,
% 11.82/12.07 (b(s(s(z)), s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[11041, 32910])).
% 11.82/12.07 tff(32912,plain,
% 11.82/12.07 (~r(s(s(s(s(z)))), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[9149, 32909, 32853, 32899])).
% 11.82/12.07 tff(32913,plain,
% 11.82/12.07 (b(s(s(s(s(z)))), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[749, 32912])).
% 11.82/12.07 tff(32914,plain,
% 11.82/12.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.07 inference(rewrite,[status(thm)],[])).
% 11.82/12.07 tff(32915,plain,
% 11.82/12.07 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.07 inference(rewrite,[status(thm)],[])).
% 11.82/12.07 tff(32916,plain,
% 11.82/12.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 11.82/12.07 inference(monotonicity,[status(thm)],[32915])).
% 11.82/12.07 tff(32917,plain,
% 11.82/12.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.07 inference(transitivity,[status(thm)],[32916, 32914])).
% 11.82/12.07 tff(32918,plain,
% 11.82/12.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 11.82/12.07 inference(quant_inst,[status(thm)],[])).
% 11.82/12.07 tff(32919,plain,
% 11.82/12.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.82/12.07 inference(modus_ponens,[status(thm)],[32918, 32917])).
% 11.82/12.07 tff(32920,plain,
% 11.82/12.07 ($false),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[32919, 391, 29427, 32901, 32913, 32894, 32911])).
% 11.82/12.07 tff(32921,plain,((s(s(s(s(z)))) = elem!1) | (~r(z, s(s(s(s(z)))))) | (s(z) = elem!1) | b(elem!1, s(z)) | b(s(s(s(s(z)))), z) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.07 tff(32922,plain,
% 11.82/12.07 (s(s(s(s(z)))) = elem!1),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[32921, 719, 150, 31, 3446, 2, 80])).
% 11.82/12.07 tff(32923,plain,
% 11.82/12.07 (~(s(s(s(elem!1))) = elem!1)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[1436, 32922])).
% 11.82/12.07 tff(32924,plain,
% 11.82/12.07 (~(elem!1 = s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[129, 32923])).
% 11.82/12.07 tff(32925,plain,
% 11.82/12.07 (b(s(s(s(elem!1))), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[31500, 32924, 2, 3446, 31, 80])).
% 11.82/12.07 tff(32926,plain,
% 11.82/12.07 (~b(z, s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[10690, 32925, 29427, 32837])).
% 11.82/12.07 tff(32927,plain,
% 11.82/12.07 (r(z, s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[678, 32926])).
% 11.82/12.07 tff(32928,plain,
% 11.82/12.07 (b(s(z), elem!1)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[8916, 32922, 32672])).
% 11.82/12.07 tff(32929,plain,
% 11.82/12.07 (~b(s(z), s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[28322, 32925, 29427, 32837, 32928])).
% 11.82/12.07 tff(32930,plain,
% 11.82/12.07 (r(s(z), s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[247, 32929])).
% 11.82/12.07 tff(32931,plain,
% 11.82/12.07 ($false),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[16770, 32930, 32927, 32835, 838])).
% 11.82/12.07 tff(32932,plain,((~r(z, s(s(s(s(z)))))) | (elem!1 = z) | b(s(s(s(s(z)))), z) | b(elem!1, s(z)) | r(z, elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.07 tff(32933,plain,
% 11.82/12.07 (~r(z, s(s(s(s(z)))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[32932, 150, 3446, 31, 80, 2])).
% 11.82/12.07 tff(32934,plain,
% 11.82/12.07 (b(z, s(s(s(s(z)))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[800, 32933])).
% 11.82/12.07 tff(32935,plain,
% 11.82/12.07 (~r(s(z), z)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[17266, 722, 530, 838])).
% 11.82/12.07 tff(32936,plain,
% 11.82/12.07 (b(s(z), z)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[180, 32935])).
% 11.82/12.07 tff(32937,plain,
% 11.82/12.07 (~r(s(z), s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[16770, 722, 530, 838])).
% 11.82/12.07 tff(32938,plain,
% 11.82/12.07 (b(s(z), s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[247, 32937])).
% 11.82/12.07 tff(32939,plain,
% 11.82/12.07 (~b(s(z), elem!1)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[28322, 32938, 10682, 1526, 32936])).
% 11.82/12.07 tff(32940,plain,
% 11.82/12.07 (r(s(z), elem!1)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[632, 32939, 150])).
% 11.82/12.07 tff(32941,plain,
% 11.82/12.07 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[18274, 722, 115, 3446, 31])).
% 11.82/12.07 tff(32942,plain,
% 11.82/12.07 (~b(s(s(elem!1)), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[6169, 32941, 133, 1526, 32936])).
% 11.82/12.07 tff(32943,plain,
% 11.82/12.07 (r(s(s(elem!1)), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[362, 32942])).
% 11.82/12.07 tff(32944,plain,
% 11.82/12.07 (~b(elem!1, s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[18052, 722, 133, 10682, 31, 530, 150, 9])).
% 11.82/12.07 tff(32945,plain,
% 11.82/12.07 (r(elem!1, s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[424, 32944, 1])).
% 11.82/12.07 tff(32946,plain,
% 11.82/12.07 (~r(z, s(s(elem!1)))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[32867, 32945, 10682, 530, 838, 32938])).
% 11.82/12.07 tff(32947,plain,
% 11.82/12.07 (b(z, s(s(elem!1)))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[324, 32946])).
% 11.82/12.07 tff(32948,plain,
% 11.82/12.07 (s(s(elem!1)) = elem!1),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[30881, 32947, 10682, 133, 32936, 32945, 32944, 32943, 32938, 9])).
% 11.82/12.07 tff(32949,plain,
% 11.82/12.07 (~b(s(s(s(s(z)))), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[17292, 32936, 1234, 1686])).
% 11.82/12.07 tff(32950,plain,
% 11.82/12.07 (r(s(s(s(s(z)))), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[749, 32949])).
% 11.82/12.07 tff(32951,plain,
% 11.82/12.07 (~r(s(z), s(s(elem!1)))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[5500, 32950, 2053, 722])).
% 11.82/12.07 tff(32952,plain,
% 11.82/12.07 ($false),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[4847, 32951, 32948, 32940])).
% 11.82/12.07 tff(32953,plain,((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(z) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (elem!1 = s(s(s(elem!1)))) | (z = elem!1) | b(s(s(s(s(z)))), z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.07 tff(32954,plain,
% 11.82/12.07 (~r(z, s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[32953, 32675, 29427, 22902, 150, 29426, 32672, 32934, 32835, 1, 98, 3446, 31])).
% 11.82/12.07 tff(32955,plain,
% 11.82/12.07 (b(z, s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[678, 32954])).
% 11.82/12.07 tff(32956,plain,
% 11.82/12.07 (~b(s(z), s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[15561, 32955, 29427, 32675])).
% 11.82/12.07 tff(32957,plain,
% 11.82/12.07 (r(s(z), s(s(s(elem!1))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[247, 32956])).
% 11.82/12.07 tff(32958,plain,
% 11.82/12.07 (~b(s(z), z)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[10690, 32955, 29427, 32675])).
% 11.82/12.07 tff(32959,plain,
% 11.82/12.07 (r(s(z), z)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[180, 32958])).
% 11.82/12.07 tff(32960,plain,
% 11.82/12.07 (~b(s(s(s(s(z)))), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[10478, 32955, 32672, 32934])).
% 11.82/12.07 tff(32961,plain,
% 11.82/12.07 (r(s(s(s(s(z)))), s(z))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[749, 32960])).
% 11.82/12.07 tff(32962,plain,
% 11.82/12.07 (~r(s(s(s(s(z)))), elem!1)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[15864, 32961, 32959, 838])).
% 11.82/12.07 tff(32963,plain,
% 11.82/12.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 11.82/12.07 inference(rewrite,[status(thm)],[])).
% 11.82/12.07 tff(32964,plain,
% 11.82/12.07 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 11.82/12.07 inference(rewrite,[status(thm)],[])).
% 11.82/12.07 tff(32965,plain,
% 11.82/12.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 11.82/12.07 inference(monotonicity,[status(thm)],[32964])).
% 11.82/12.07 tff(32966,plain,
% 11.82/12.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 11.82/12.07 inference(transitivity,[status(thm)],[32965, 32963])).
% 11.82/12.07 tff(32967,plain,
% 11.82/12.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 11.82/12.07 inference(quant_inst,[status(thm)],[])).
% 11.82/12.07 tff(32968,plain,
% 11.82/12.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 11.82/12.07 inference(modus_ponens,[status(thm)],[32967, 32966])).
% 11.82/12.07 tff(32969,plain,
% 11.82/12.07 (~r(elem!1, s(s(s(s(z)))))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[32968, 194, 32957, 838, 32961])).
% 11.82/12.07 tff(32970,plain,
% 11.82/12.07 (s(s(s(s(z)))) = elem!1),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[31903, 32969, 32934, 32962, 22902])).
% 11.82/12.07 tff(32971,plain,
% 11.82/12.07 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[717, 32970])).
% 11.82/12.07 tff(32972,plain,
% 11.82/12.07 (~(s(s(elem!1)) = elem!1)),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[451, 32971])).
% 11.82/12.07 tff(32973,plain,
% 11.82/12.07 (~r(z, s(s(elem!1)))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[855, 32959, 32835, 838])).
% 11.82/12.07 tff(32974,plain,
% 11.82/12.07 (b(z, s(s(elem!1)))),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[324, 32973])).
% 11.82/12.07 tff(32975,plain,
% 11.82/12.07 ($false),
% 11.82/12.07 inference(unit_resolution,[status(thm)],[15581, 6124, 4028, 10682, 9, 664, 168, 1526])).
% 11.82/12.07 tff(32976,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | b(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.08 tff(32977,plain,
% 11.82/12.08 (b(elem!1, s(s(s(elem!1))))),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[32976, 168, 664, 10682, 1526, 1])).
% 11.82/12.08 tff(32978,plain,
% 11.82/12.08 (~b(z, s(elem!1))),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[26924, 32977, 10682, 133, 3927, 1526, 530, 664, 150, 4097, 426, 168])).
% 11.82/12.08 tff(32979,plain,
% 11.82/12.08 (r(z, s(elem!1))),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[566, 32978])).
% 11.82/12.08 tff(32980,plain,
% 11.82/12.08 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[2865, 32977, 688])).
% 11.82/12.08 tff(32981,plain,
% 11.82/12.08 (~b(s(s(s(elem!1))), z)),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[27078, 32980, 10682, 1686])).
% 11.82/12.08 tff(32982,plain,
% 11.82/12.08 (r(s(s(s(elem!1))), z)),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[377, 32981])).
% 11.82/12.08 tff(32983,plain,
% 11.82/12.08 ($false),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[4255, 32982, 32979, 530, 4097])).
% 11.82/12.08 tff(32984,plain,(b(s(s(s(elem!1))), elem!1) | (~r(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (s(z) = elem!1) | (~(s(s(s(s(z)))) = elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.08 tff(32985,plain,
% 11.82/12.08 (b(s(s(s(elem!1))), elem!1)),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[32984, 32974, 29427, 32934, 22902, 32835, 32675, 32955, 150, 32970, 1])).
% 11.82/12.08 tff(32986,plain,
% 11.82/12.08 (~b(elem!1, s(s(s(elem!1))))),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[10845, 32985, 29427, 22902])).
% 11.82/12.08 tff(32987,plain,
% 11.82/12.08 (r(elem!1, s(s(s(elem!1))))),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[424, 32986, 1])).
% 11.82/12.08 tff(32988,plain,
% 11.82/12.08 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[18031, 32987, 838, 32957])).
% 11.82/12.08 tff(32989,plain,
% 11.82/12.08 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[1370, 32988, 26982])).
% 11.82/12.08 tff(32990,plain,
% 11.82/12.08 (b(s(z), elem!1)),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[8916, 32970, 32672])).
% 11.82/12.08 tff(32991,plain,
% 11.82/12.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 11.82/12.08 inference(rewrite,[status(thm)],[])).
% 11.82/12.08 tff(32992,plain,
% 11.82/12.08 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 11.82/12.08 inference(rewrite,[status(thm)],[])).
% 11.82/12.08 tff(32993,plain,
% 11.82/12.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))))),
% 11.82/12.08 inference(monotonicity,[status(thm)],[32992])).
% 11.82/12.08 tff(32994,plain,
% 11.82/12.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 11.82/12.08 inference(transitivity,[status(thm)],[32993, 32991])).
% 11.82/12.08 tff(32995,plain,
% 11.82/12.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 11.82/12.08 inference(quant_inst,[status(thm)],[])).
% 11.82/12.08 tff(32996,plain,
% 11.82/12.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))),
% 11.82/12.08 inference(modus_ponens,[status(thm)],[32995, 32994])).
% 11.82/12.08 tff(32997,plain,
% 11.82/12.08 ($false),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[32996, 194, 174, 410, 232, 847])).
% 11.82/12.08 tff(32998,plain,((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.08 tff(32999,plain,
% 11.82/12.08 (~r(s(s(s(elem!1))), z)),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[32998, 32987, 32957, 838])).
% 11.82/12.08 tff(33000,plain,
% 11.82/12.08 (b(s(s(s(elem!1))), z)),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[377, 32999])).
% 11.82/12.08 tff(33001,plain,
% 11.82/12.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 11.82/12.08 inference(rewrite,[status(thm)],[])).
% 11.82/12.08 tff(33002,plain,
% 11.82/12.08 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 11.82/12.08 inference(rewrite,[status(thm)],[])).
% 11.82/12.08 tff(33003,plain,
% 11.82/12.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 11.82/12.08 inference(monotonicity,[status(thm)],[33002])).
% 11.82/12.08 tff(33004,plain,
% 11.82/12.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 11.82/12.08 inference(transitivity,[status(thm)],[33003, 33001])).
% 11.82/12.08 tff(33005,plain,
% 11.82/12.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 11.82/12.08 inference(quant_inst,[status(thm)],[])).
% 11.82/12.08 tff(33006,plain,
% 11.82/12.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1))),
% 11.82/12.08 inference(modus_ponens,[status(thm)],[33005, 33004])).
% 11.82/12.08 tff(33007,plain,
% 11.82/12.08 ($false),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[33006, 391, 381, 380, 1374, 3927, 644])).
% 11.82/12.08 tff(33008,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.08 tff(33009,plain,
% 11.82/12.08 (~b(s(s(elem!1)), s(z))),
% 11.82/12.08 inference(unit_resolution,[status(thm)],[33008, 33000, 32990, 32989, 32974])).
% 11.82/12.08 tff(33010,plain,
% 11.82/12.09 (r(s(s(elem!1)), s(z))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[362, 33009])).
% 11.82/12.09 tff(33011,plain,
% 11.82/12.09 (~b(s(s(elem!1)), elem!1)),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[3996, 33010, 22902, 838, 32959, 32974])).
% 11.82/12.09 tff(33012,plain,
% 11.82/12.09 (r(s(s(elem!1)), elem!1)),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[872, 33011, 32972])).
% 11.82/12.09 tff(33013,plain,
% 11.82/12.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 11.82/12.09 inference(rewrite,[status(thm)],[])).
% 11.82/12.09 tff(33014,plain,
% 11.82/12.09 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 11.82/12.09 inference(rewrite,[status(thm)],[])).
% 11.82/12.09 tff(33015,plain,
% 11.82/12.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 11.82/12.09 inference(monotonicity,[status(thm)],[33014])).
% 11.82/12.09 tff(33016,plain,
% 11.82/12.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 11.82/12.09 inference(transitivity,[status(thm)],[33015, 33013])).
% 11.82/12.09 tff(33017,plain,
% 11.82/12.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 11.82/12.09 inference(quant_inst,[status(thm)],[])).
% 11.82/12.09 tff(33018,plain,
% 11.82/12.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))),
% 11.82/12.09 inference(modus_ponens,[status(thm)],[33017, 33016])).
% 11.82/12.09 tff(33019,plain,
% 11.82/12.09 ($false),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[33018, 194, 33010, 33012, 32957, 838])).
% 11.82/12.09 tff(33020,plain,((elem!1 = s(s(s(elem!1)))) | (s(z) = elem!1) | b(s(s(s(s(z)))), z) | b(elem!1, s(z)) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.09 tff(33021,plain,
% 11.82/12.09 (elem!1 = s(s(s(elem!1)))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[33020, 150, 3446, 31, 2, 80])).
% 11.82/12.09 tff(33022,plain,
% 11.82/12.09 (s(s(s(elem!1))) = elem!1),
% 11.82/12.09 inference(symmetry,[status(thm)],[33021])).
% 11.82/12.09 tff(33023,plain,
% 11.82/12.09 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.82/12.09 inference(monotonicity,[status(thm)],[33022])).
% 11.82/12.09 tff(33024,plain,
% 11.82/12.09 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 11.82/12.09 inference(transitivity,[status(thm)],[33023, 698])).
% 11.82/12.09 tff(33025,plain,
% 11.82/12.09 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 11.82/12.09 inference(monotonicity,[status(thm)],[33024])).
% 11.82/12.09 tff(33026,plain,
% 11.82/12.09 (~(elem!1 = s(s(z)))),
% 11.82/12.09 inference(modus_ponens,[status(thm)],[1397, 33025])).
% 11.82/12.09 tff(33027,plain,
% 11.82/12.09 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.82/12.09 inference(transitivity,[status(thm)],[33024, 8492])).
% 11.82/12.09 tff(33028,plain,
% 11.82/12.09 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 11.82/12.09 inference(monotonicity,[status(thm)],[33027])).
% 11.82/12.09 tff(33029,plain,
% 11.82/12.09 (~(s(s(z)) = elem!1)),
% 11.82/12.09 inference(modus_ponens,[status(thm)],[1397, 33028])).
% 11.82/12.09 tff(33030,plain,
% 11.82/12.09 (s(s(s(elem!1))) = elem!1),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[129, 33021])).
% 11.82/12.09 tff(33031,plain,
% 11.82/12.09 (~b(s(s(s(elem!1))), s(z))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[8400, 33030, 31])).
% 11.82/12.09 tff(33032,plain,
% 11.82/12.09 (r(s(s(s(elem!1))), s(z))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[223, 33031])).
% 11.82/12.09 tff(33033,plain,
% 11.82/12.09 (~r(z, s(z))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[18026, 33030, 29426, 29427, 98, 32835, 150, 31])).
% 11.82/12.09 tff(33034,plain,
% 11.82/12.09 (b(z, s(z))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[678, 33033])).
% 11.82/12.09 tff(33035,plain,
% 11.82/12.09 (~b(s(s(s(s(z)))), s(z))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[10478, 664, 1234, 1686])).
% 11.82/12.09 tff(33036,plain,
% 11.82/12.09 (r(s(s(s(s(z)))), s(z))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[749, 33035])).
% 11.82/12.09 tff(33037,plain,
% 11.82/12.09 (r(elem!1, s(s(s(s(z)))))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[31903, 6221, 1686, 2642, 133])).
% 11.82/12.09 tff(33038,plain,
% 11.82/12.09 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[14788, 33037, 125])).
% 11.82/12.09 tff(33039,plain,
% 11.82/12.09 ($false),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[26348, 194, 232, 183, 723, 4317])).
% 11.82/12.09 tff(33040,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.09 tff(33041,plain,
% 11.82/12.09 (~r(s(z), s(s(s(elem!1))))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[33040, 33038, 33036, 183])).
% 11.82/12.09 tff(33042,plain,
% 11.82/12.09 (b(s(z), s(s(s(elem!1))))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[247, 33041])).
% 11.82/12.09 tff(33043,plain,
% 11.82/12.09 (b(s(z), elem!1)),
% 11.82/12.09 inference(modus_ponens,[status(thm)],[33042, 20978])).
% 11.82/12.09 tff(33044,plain,
% 11.82/12.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.82/12.09 inference(rewrite,[status(thm)],[])).
% 11.82/12.09 tff(33045,plain,
% 11.82/12.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.82/12.09 inference(quant_inst,[status(thm)],[])).
% 11.82/12.09 tff(33046,plain,
% 11.82/12.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 11.82/12.09 inference(modus_ponens,[status(thm)],[33045, 33044])).
% 11.82/12.09 tff(33047,plain,
% 11.82/12.09 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[33046, 194, 183, 723, 1747])).
% 11.82/12.09 tff(33048,plain,
% 11.82/12.09 (~r(s(s(s(s(z)))), elem!1)),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[2116, 33047, 130])).
% 11.82/12.09 tff(33049,plain,
% 11.82/12.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.09 inference(rewrite,[status(thm)],[])).
% 11.82/12.09 tff(33050,plain,
% 11.82/12.09 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.09 inference(rewrite,[status(thm)],[])).
% 11.82/12.09 tff(33051,plain,
% 11.82/12.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 11.82/12.09 inference(monotonicity,[status(thm)],[33050])).
% 11.82/12.09 tff(33052,plain,
% 11.82/12.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.09 inference(transitivity,[status(thm)],[33051, 33049])).
% 11.82/12.09 tff(33053,plain,
% 11.82/12.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.09 inference(quant_inst,[status(thm)],[])).
% 11.82/12.09 tff(33054,plain,
% 11.82/12.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.82/12.09 inference(modus_ponens,[status(thm)],[33053, 33052])).
% 11.82/12.09 tff(33055,plain,
% 11.82/12.09 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[33054, 194, 183, 723, 1747])).
% 11.82/12.09 tff(33056,plain,
% 11.82/12.09 (~r(elem!1, s(s(s(s(z)))))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[14788, 33055, 125])).
% 11.82/12.09 tff(33057,plain,
% 11.82/12.09 ($false),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[31903, 33056, 33048, 1686, 2642, 133])).
% 11.82/12.09 tff(33058,plain,((~r(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.09 tff(33059,plain,
% 11.82/12.09 (~r(s(z), s(s(z)))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[33058, 1686, 133, 125, 183, 33036])).
% 11.82/12.09 tff(33060,plain,
% 11.82/12.09 (b(s(z), s(s(z)))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[1788, 33059])).
% 11.82/12.09 tff(33061,plain,
% 11.82/12.09 (~b(s(s(z)), elem!1)),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[31383, 3563, 1234, 1686, 664])).
% 11.82/12.09 tff(33062,plain,
% 11.82/12.09 (r(s(s(z)), elem!1)),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[4730, 33061, 5547])).
% 11.82/12.09 tff(33063,plain,
% 11.82/12.09 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[6275, 3563, 1234, 2439])).
% 11.82/12.09 tff(33064,plain,
% 11.82/12.09 (r(s(s(z)), s(s(s(s(z)))))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[3652, 33063])).
% 11.82/12.09 tff(33065,plain,
% 11.82/12.09 ($false),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[31294, 33064, 33062, 2053, 1234, 530, 720, 644])).
% 11.82/12.09 tff(33066,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), elem!1)) | (s(s(z)) = elem!1) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.09 tff(33067,plain,
% 11.82/12.09 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[33066, 33043, 1234, 530, 2642, 2053, 18819, 33060, 1686, 664])).
% 11.82/12.09 tff(33068,plain,
% 11.82/12.09 (r(s(s(s(s(z)))), s(s(z)))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[1714, 33067])).
% 11.82/12.09 tff(33069,plain,
% 11.82/12.09 (b(s(s(s(s(z)))), elem!1)),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[762, 6221, 2642])).
% 11.82/12.09 tff(33070,plain,
% 11.82/12.09 (~b(z, s(s(z)))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[31033, 2439, 133, 1235, 664])).
% 11.82/12.09 tff(33071,plain,
% 11.82/12.09 (~r(z, s(s(z)))),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[30506, 2439, 2053, 1234, 664, 133, 1235])).
% 11.82/12.09 tff(33072,plain,
% 11.82/12.09 ($false),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[18613, 33071, 33070])).
% 11.82/12.09 tff(33073,plain,((~b(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.09 tff(33074,plain,
% 11.82/12.09 (~b(s(s(z)), z)),
% 11.82/12.09 inference(unit_resolution,[status(thm)],[33073, 33060, 1234, 664, 133, 2053])).
% 11.82/12.09 tff(33075,plain,
% 11.82/12.10 (r(s(s(z)), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[1211, 33074])).
% 11.82/12.10 tff(33076,plain,
% 11.82/12.10 ($false),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[9185, 194, 3557, 723, 1747, 1697])).
% 11.82/12.10 tff(33077,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.10 tff(33078,plain,
% 11.82/12.10 (~r(s(z), s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33077, 1697, 723, 3557])).
% 11.82/12.10 tff(33079,plain,
% 11.82/12.10 (b(s(z), s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[1788, 33078])).
% 11.82/12.10 tff(33080,plain,
% 11.82/12.10 (~b(z, s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[30651, 33079, 1652, 3823, 664])).
% 11.82/12.10 tff(33081,plain,
% 11.82/12.10 (r(z, s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[18613, 33080])).
% 11.82/12.10 tff(33082,plain,
% 11.82/12.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.82/12.10 inference(rewrite,[status(thm)],[])).
% 11.82/12.10 tff(33083,plain,
% 11.82/12.10 (((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.82/12.10 inference(rewrite,[status(thm)],[])).
% 11.82/12.10 tff(33084,plain,
% 11.82/12.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 11.82/12.10 inference(monotonicity,[status(thm)],[33083])).
% 11.82/12.10 tff(33085,plain,
% 11.82/12.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.82/12.10 inference(transitivity,[status(thm)],[33084, 33082])).
% 11.82/12.10 tff(33086,plain,
% 11.82/12.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 11.82/12.10 inference(quant_inst,[status(thm)],[])).
% 11.82/12.10 tff(33087,plain,
% 11.82/12.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 11.82/12.10 inference(modus_ponens,[status(thm)],[33086, 33085])).
% 11.82/12.10 tff(33088,plain,
% 11.82/12.10 ($false),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33087, 194, 2053, 3557, 1697, 33081])).
% 11.82/12.10 tff(33089,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.10 tff(33090,plain,
% 11.82/12.10 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33089, 33068, 2053, 33075, 33069, 664, 33036])).
% 11.82/12.10 tff(33091,plain,
% 11.82/12.10 (r(s(s(z)), s(s(s(s(z)))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[3652, 33090])).
% 11.82/12.10 tff(33092,plain,
% 11.82/12.10 (~r(s(s(z)), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[31294, 33091, 2053, 1234, 530, 2642, 33043])).
% 11.82/12.10 tff(33093,plain,
% 11.82/12.10 (b(s(s(z)), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[4730, 33092, 18819])).
% 11.82/12.10 tff(33094,plain,
% 11.82/12.10 (~r(s(s(z)), s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[31313, 33093, 133, 1686, 2642, 3820, 6221, 33068, 1234, 33043])).
% 11.82/12.10 tff(33095,plain,
% 11.82/12.10 (~r(z, s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[30535, 33091, 2053, 33068])).
% 11.82/12.10 tff(33096,plain,
% 11.82/12.10 (b(z, s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[18613, 33095])).
% 11.82/12.10 tff(33097,plain,
% 11.82/12.10 (~b(s(s(z)), s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[21530, 33096, 664, 33060])).
% 11.82/12.10 tff(33098,plain,
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% 11.82/12.10 inference(unit_resolution,[status(thm)],[3778, 33097, 33094])).
% 11.82/12.10 tff(33099,plain,(r(s(s(s(s(z)))), elem!1) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~(elem!1 = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.10 tff(33100,plain,
% 11.82/12.10 (r(s(s(s(s(z)))), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33099, 33034, 22902, 32934, 32672, 29426, 32835, 33021, 33032])).
% 11.82/12.10 tff(33101,plain,
% 11.82/12.10 (~b(s(s(s(s(z)))), s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[10478, 33034, 32672, 32934])).
% 11.82/12.10 tff(33102,plain,
% 11.82/12.10 (r(s(s(s(s(z)))), s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[749, 33101])).
% 11.82/12.10 tff(33103,plain,
% 11.82/12.10 (~r(s(z), s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33058, 32934, 22902, 33021, 33032, 33102])).
% 11.82/12.10 tff(33104,plain,
% 11.82/12.10 (b(s(z), s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[1788, 33103])).
% 11.82/12.10 tff(33105,plain,
% 11.82/12.10 (~(s(s(s(s(z)))) = elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[1436, 33030])).
% 11.82/12.10 tff(33106,plain,
% 11.82/12.10 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 11.82/12.10 inference(monotonicity,[status(thm)],[33021])).
% 11.82/12.10 tff(33107,plain,
% 11.82/12.10 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 11.82/12.10 inference(symmetry,[status(thm)],[33106])).
% 11.82/12.10 tff(33108,plain,
% 11.82/12.10 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[2116, 33100, 33030])).
% 11.82/12.10 tff(33109,plain,
% 11.82/12.10 (r(s(s(s(elem!1))), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[533, 33030, 32835])).
% 11.82/12.10 tff(33110,plain,
% 11.82/12.10 ($false),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[28083, 194, 174, 232, 723, 2100])).
% 11.82/12.10 tff(33111,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.10 tff(33112,plain,
% 11.82/12.10 (~r(s(z), s(s(s(elem!1))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33111, 33109, 33102, 33108])).
% 11.82/12.10 tff(33113,plain,
% 11.82/12.10 (b(s(z), s(s(s(elem!1))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[247, 33112])).
% 11.82/12.10 tff(33114,plain,
% 11.82/12.10 (b(s(z), elem!1)),
% 11.82/12.10 inference(modus_ponens,[status(thm)],[33113, 33107])).
% 11.82/12.10 tff(33115,plain,
% 11.82/12.10 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33066, 33114, 32672, 32835, 33105, 29426, 33029, 33104, 32934, 33034])).
% 11.82/12.10 tff(33116,plain,
% 11.82/12.10 (r(s(s(s(s(z)))), s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[1714, 33115])).
% 11.82/12.10 tff(33117,plain,
% 11.82/12.10 (~r(s(s(z)), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[20852, 33116, 32835, 33100])).
% 11.82/12.10 tff(33118,plain,
% 11.82/12.10 (b(s(s(z)), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[4730, 33117, 33029])).
% 11.82/12.10 tff(33119,plain,
% 11.82/12.10 (b(s(s(z)), s(s(s(elem!1))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[20537, 33118, 33021])).
% 11.82/12.10 tff(33120,plain,
% 11.82/12.10 ($false),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[31415, 391, 379, 2439, 8553, 17493])).
% 11.82/12.10 tff(33121,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.82/12.10 tff(33122,plain,
% 11.82/12.10 (~b(s(s(s(elem!1))), s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33121, 33113, 33104, 33119])).
% 11.82/12.10 tff(33123,plain,
% 11.82/12.10 (~b(elem!1, s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[16425, 33122, 33021])).
% 11.82/12.10 tff(33124,plain,
% 11.82/12.10 (r(elem!1, s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[3394, 33123, 33026])).
% 11.82/12.10 tff(33125,plain,
% 11.82/12.10 (r(s(s(s(elem!1))), s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[10022, 33124, 33021])).
% 11.82/12.10 tff(33126,plain,
% 11.82/12.10 (~b(s(s(z)), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33073, 33104, 32672, 33034, 22902, 29426])).
% 11.82/12.10 tff(33127,plain,
% 11.82/12.10 (r(s(s(z)), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[1211, 33126])).
% 11.82/12.10 tff(33128,plain,
% 11.82/12.10 ($false),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[25121, 194, 33127, 33116, 33108, 33125])).
% 11.82/12.10 tff(33129,plain,((s(z) = elem!1) | b(elem!1, s(z)) | b(s(s(s(s(z)))), z) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.10 tff(33130,plain,
% 11.82/12.10 (s(z) = elem!1),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33129, 31, 3446, 2, 80])).
% 11.82/12.10 tff(33131,plain,
% 11.82/12.10 (b(elem!1, s(s(s(elem!1))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[8542, 33130, 32672])).
% 11.82/12.10 tff(33132,plain,
% 11.82/12.10 (~(s(s(s(elem!1))) = elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[15370, 33131])).
% 11.82/12.10 tff(33133,plain,
% 11.82/12.10 (~(elem!1 = s(s(s(elem!1))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[129, 33132])).
% 11.82/12.10 tff(33134,plain,
% 11.82/12.10 (~b(s(s(s(elem!1))), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[10845, 33131, 29427, 22902])).
% 11.82/12.10 tff(33135,plain,
% 11.82/12.10 (~b(s(s(s(elem!1))), s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[3938, 33134, 33130])).
% 11.82/12.10 tff(33136,plain,
% 11.82/12.10 ($false),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[31500, 33135, 33133, 2, 3446, 31, 80])).
% 11.82/12.10 tff(33137,plain,(b(elem!1, s(z)) | (elem!1 = z) | b(s(s(s(s(z)))), z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.10 tff(33138,plain,
% 11.82/12.10 (b(elem!1, s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33137, 3446, 2, 80])).
% 11.82/12.10 tff(33139,plain,
% 11.82/12.10 (b(s(z), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[8916, 688, 32672])).
% 11.82/12.10 tff(33140,plain,
% 11.82/12.10 (~b(s(z), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[4857, 33139, 22902, 33138])).
% 11.82/12.10 tff(33141,plain,
% 11.82/12.10 ($false),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[180, 33140, 32674])).
% 11.82/12.10 tff(33142,plain,((~(s(s(s(s(z)))) = elem!1)) | r(z, elem!1) | b(z, s(z)) | (elem!1 = z) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.10 tff(33143,plain,
% 11.82/12.10 (~(s(s(s(s(z)))) = elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33142, 675, 80, 2, 3446])).
% 11.82/12.10 tff(33144,plain,
% 11.82/12.10 (b(z, s(s(s(elem!1))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[8231, 2, 80])).
% 11.82/12.10 tff(33145,plain,
% 11.82/12.10 (~r(s(z), s(s(s(s(z)))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[32588, 721, 183, 80, 3447, 1])).
% 11.82/12.10 tff(33146,plain,
% 11.82/12.10 (b(s(z), s(s(s(s(z)))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[1230, 33145])).
% 11.82/12.10 tff(33147,plain,
% 11.82/12.10 (~r(s(z), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[26943, 410, 183, 721, 33144, 149, 127])).
% 11.82/12.10 tff(33148,plain,
% 11.82/12.10 (b(s(z), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[632, 33147, 21435])).
% 11.82/12.10 tff(33149,plain,
% 11.82/12.10 (~b(s(z), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[4857, 33148, 721, 149])).
% 11.82/12.10 tff(33150,plain,
% 11.82/12.10 (r(s(z), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[180, 33149])).
% 11.82/12.10 tff(33151,plain,
% 11.82/12.10 (~b(z, s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[23112, 33148, 721, 149])).
% 11.82/12.10 tff(33152,plain,
% 11.82/12.10 (r(z, s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[678, 33151])).
% 11.82/12.10 tff(33153,plain,
% 11.82/12.10 (~r(s(s(s(s(z)))), s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[11989, 194, 33152, 33150, 3447])).
% 11.82/12.10 tff(33154,plain,
% 11.82/12.10 (b(s(s(s(s(z)))), s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[749, 33153])).
% 11.82/12.10 tff(33155,plain,
% 11.82/12.10 (~r(s(s(z)), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[26737, 33154, 3447, 33152, 33150, 1234])).
% 11.82/12.10 tff(33156,plain,
% 11.82/12.10 (b(s(s(z)), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[1211, 33155])).
% 11.82/12.10 tff(33157,plain,
% 11.82/12.10 (~r(s(s(s(elem!1))), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[26128, 194, 183, 33152, 33150])).
% 11.82/12.10 tff(33158,plain,
% 11.82/12.10 (b(s(s(s(elem!1))), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[377, 33157])).
% 11.82/12.10 tff(33159,plain,
% 11.82/12.10 (~b(s(s(z)), s(s(s(elem!1))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[26759, 391, 149, 33158, 33156, 721])).
% 11.82/12.10 tff(33160,plain,
% 11.82/12.10 (r(s(s(z)), s(s(s(elem!1))))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[11041, 33159])).
% 11.82/12.10 tff(33161,plain,
% 11.82/12.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.82/12.10 inference(rewrite,[status(thm)],[])).
% 11.82/12.10 tff(33162,plain,
% 11.82/12.10 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.82/12.10 inference(rewrite,[status(thm)],[])).
% 11.82/12.10 tff(33163,plain,
% 11.82/12.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 11.82/12.10 inference(monotonicity,[status(thm)],[33162])).
% 11.82/12.10 tff(33164,plain,
% 11.82/12.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.82/12.10 inference(transitivity,[status(thm)],[33163, 33161])).
% 11.82/12.10 tff(33165,plain,
% 11.82/12.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(z)))))),
% 11.82/12.10 inference(quant_inst,[status(thm)],[])).
% 11.82/12.10 tff(33166,plain,
% 11.82/12.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 11.82/12.10 inference(modus_ponens,[status(thm)],[33165, 33164])).
% 11.82/12.10 tff(33167,plain,
% 11.82/12.10 (~r(elem!1, s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[33166, 194, 410, 183, 33160])).
% 11.82/12.10 tff(33168,plain,
% 11.82/12.10 (b(elem!1, z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[26824, 33150, 80, 33151, 1234, 2])).
% 11.82/12.10 tff(33169,plain,
% 11.82/12.10 (~b(elem!1, s(s(z)))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[13448, 33168, 33156, 149])).
% 11.82/12.10 tff(33170,plain,
% 11.82/12.10 (elem!1 = s(s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[3394, 33169, 33167])).
% 11.82/12.10 tff(33171,plain,
% 11.82/12.10 (s(elem!1) = s(s(s(z)))),
% 11.82/12.10 inference(monotonicity,[status(thm)],[33170])).
% 11.82/12.10 tff(33172,plain,
% 11.82/12.10 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 11.82/12.10 inference(monotonicity,[status(thm)],[33171])).
% 11.82/12.10 tff(33173,plain,
% 11.82/12.10 (~b(s(s(s(elem!1))), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[10743, 33168, 33144, 149])).
% 11.82/12.10 tff(33174,plain,
% 11.82/12.10 (~(s(s(s(s(z)))) = elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[6966, 33168, 3446])).
% 11.82/12.10 tff(33175,plain,
% 11.82/12.10 (~r(elem!1, z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[26158, 33174, 3447, 33152, 33148, 33150])).
% 11.82/12.10 tff(33176,plain,
% 11.82/12.10 (b(s(elem!1), elem!1)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[14657, 33175, 33144, 149, 21435, 33173, 2])).
% 11.82/12.10 tff(33177,plain,
% 11.82/12.10 (~b(s(elem!1), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[24651, 33176, 33144, 33158, 33168])).
% 11.82/12.10 tff(33178,plain,
% 11.82/12.10 (r(s(elem!1), z)),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[549, 33177])).
% 11.82/12.10 tff(33179,plain,
% 11.82/12.10 (~b(z, s(elem!1))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[6555, 33176, 149, 33168])).
% 11.82/12.10 tff(33180,plain,
% 11.82/12.10 (r(z, s(elem!1))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[566, 33179])).
% 11.82/12.10 tff(33181,plain,
% 11.82/12.10 (~r(s(elem!1), s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[17381, 33180, 33150, 33178])).
% 11.82/12.10 tff(33182,plain,
% 11.82/12.10 (b(s(elem!1), s(z))),
% 11.82/12.10 inference(unit_resolution,[status(thm)],[13479, 33181, 124])).
% 11.82/12.10 tff(33183,plain,
% 11.82/12.10 (b(s(s(s(z))), s(z))),
% 11.82/12.10 inference(modus_ponens,[status(thm)],[33182, 33172])).
% 11.82/12.11 tff(33184,plain,
% 11.82/12.11 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 11.82/12.11 inference(monotonicity,[status(thm)],[33171, 33170])).
% 11.82/12.11 tff(33185,plain,
% 11.82/12.11 (b(s(s(s(z))), s(s(z)))),
% 11.82/12.11 inference(modus_ponens,[status(thm)],[33176, 33184])).
% 11.82/12.11 tff(33186,plain,
% 11.82/12.11 (b(z, elem!1) <=> b(z, s(s(z)))),
% 11.82/12.11 inference(monotonicity,[status(thm)],[33170])).
% 11.82/12.11 tff(33187,plain,
% 11.82/12.11 (b(z, s(s(z)))),
% 11.82/12.11 inference(modus_ponens,[status(thm)],[149, 33186])).
% 11.82/12.11 tff(33188,plain,
% 11.82/12.11 (b(s(z), s(s(z)))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[11253, 33170, 33148])).
% 11.82/12.11 tff(33189,plain,
% 11.82/12.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.82/12.11 inference(rewrite,[status(thm)],[])).
% 11.82/12.11 tff(33190,plain,
% 11.82/12.11 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.82/12.11 inference(rewrite,[status(thm)],[])).
% 11.82/12.11 tff(33191,plain,
% 11.82/12.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))))),
% 11.82/12.11 inference(monotonicity,[status(thm)],[33190])).
% 11.82/12.11 tff(33192,plain,
% 11.82/12.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.82/12.11 inference(transitivity,[status(thm)],[33191, 33189])).
% 11.82/12.11 tff(33193,plain,
% 11.82/12.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 11.82/12.11 inference(quant_inst,[status(thm)],[])).
% 11.82/12.11 tff(33194,plain,
% 11.82/12.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))),
% 11.82/12.11 inference(modus_ponens,[status(thm)],[33193, 33192])).
% 11.82/12.11 tff(33195,plain,
% 11.82/12.11 ($false),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[33194, 391, 33156, 33188, 33187, 33185, 33183])).
% 11.82/12.11 tff(33196,plain,((~r(elem!1, s(s(s(elem!1))))) | (elem!1 = z) | b(s(s(s(s(z)))), z) | r(z, elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.11 tff(33197,plain,
% 11.82/12.11 (~r(elem!1, s(s(s(elem!1))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[33196, 2, 3446, 80, 33146, 183, 721, 9])).
% 11.82/12.11 tff(33198,plain,
% 11.82/12.11 (b(elem!1, s(s(s(elem!1))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[424, 33197, 1])).
% 11.82/12.11 tff(33199,plain,
% 11.82/12.11 (r(elem!1, z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[17700, 33198, 3447, 21435, 2, 33144, 149])).
% 11.82/12.11 tff(33200,plain,
% 11.82/12.11 (~b(z, s(z))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[31950, 33198, 9, 3447, 183, 721, 2, 80])).
% 11.82/12.11 tff(33201,plain,
% 11.82/12.11 (r(z, s(z))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[678, 33200])).
% 11.82/12.11 tff(33202,plain,
% 11.82/12.11 (~b(s(s(s(elem!1))), elem!1)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[10845, 33198, 149, 33144])).
% 11.82/12.11 tff(33203,plain,
% 11.82/12.11 (r(s(s(s(elem!1))), elem!1)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[230, 33202, 9])).
% 11.82/12.11 tff(33204,plain,
% 11.82/12.11 (~r(s(s(s(elem!1))), z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[4113, 33203, 33201, 33199])).
% 11.82/12.11 tff(33205,plain,
% 11.82/12.11 (b(s(s(s(elem!1))), z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[377, 33204])).
% 11.82/12.11 tff(33206,plain,
% 11.82/12.11 (r(elem!1, s(z))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[26814, 33199, 33201, 149, 27211, 33146, 3447])).
% 11.82/12.11 tff(33207,plain,
% 11.82/12.11 (~r(s(z), s(s(s(elem!1))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[22961, 33206, 33144, 1, 149, 183])).
% 11.82/12.11 tff(33208,plain,
% 11.82/12.11 (b(s(z), s(s(s(elem!1))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[247, 33207])).
% 11.82/12.11 tff(33209,plain,
% 11.82/12.11 (~r(s(z), z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[17266, 33206, 33201, 33199])).
% 11.82/12.11 tff(33210,plain,
% 11.82/12.11 (b(s(z), z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[180, 33209])).
% 11.82/12.11 tff(33211,plain,
% 11.82/12.11 ($false),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[11303, 33210, 33208, 33205, 33144])).
% 11.82/12.11 tff(33212,plain,((elem!1 = z) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | r(z, elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.11 tff(33213,plain,
% 11.82/12.11 (~r(s(s(s(elem!1))), s(z))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[33212, 1, 2, 80, 3446, 33138])).
% 11.82/12.11 tff(33214,plain,
% 11.82/12.11 (b(s(s(s(elem!1))), s(z))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[223, 33213])).
% 11.82/12.11 tff(33215,plain,
% 11.82/12.11 (~(s(z) = elem!1)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[20271, 33138])).
% 11.82/12.11 tff(33216,plain,
% 11.82/12.11 (~b(elem!1, z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[13285, 590, 22902, 721])).
% 11.82/12.11 tff(33217,plain,
% 11.82/12.11 (r(elem!1, z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[526, 33216, 2])).
% 11.82/12.11 tff(33218,plain,
% 11.82/12.11 (r(elem!1, s(z))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[26821, 33216, 80, 1234, 675])).
% 11.82/12.11 tff(33219,plain,
% 11.82/12.11 (~r(s(z), s(s(s(elem!1))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[16770, 33217, 26574, 33218])).
% 11.82/12.11 tff(33220,plain,
% 11.82/12.11 (b(s(z), s(s(s(elem!1))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[247, 33219])).
% 11.82/12.11 tff(33221,plain,
% 11.82/12.11 (~b(s(s(s(elem!1))), z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[11303, 33220, 29427, 590])).
% 11.82/12.11 tff(33222,plain,
% 11.82/12.11 (r(s(s(s(elem!1))), z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[377, 33221])).
% 11.82/12.11 tff(33223,plain,
% 11.82/12.11 (~b(s(s(s(elem!1))), elem!1)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[23276, 33220, 29427, 22902, 721])).
% 11.82/12.11 tff(33224,plain,
% 11.82/12.11 (r(s(s(s(elem!1))), elem!1)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[230, 33223, 127])).
% 11.82/12.11 tff(33225,plain,
% 11.82/12.11 ($false),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[4113, 33224, 33222, 26574, 33217])).
% 11.82/12.11 tff(33226,plain,((~b(s(z), z)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | r(z, elem!1) | (~b(s(z), s(s(s(s(z)))))) | b(z, s(z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.11 tff(33227,plain,
% 11.82/12.11 (~b(s(z), z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[33226, 9, 33138, 80, 32672, 675, 2])).
% 11.82/12.11 tff(33228,plain,
% 11.82/12.11 (r(s(z), z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[180, 33227])).
% 11.82/12.11 tff(33229,plain,
% 11.82/12.11 (b(elem!1, z)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[26824, 33228, 80, 32672, 675, 2])).
% 11.82/12.11 tff(33230,plain,
% 11.82/12.11 (~(elem!1 = s(z))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[172, 33215])).
% 11.82/12.11 tff(33231,plain,
% 11.82/12.11 (~b(s(s(s(s(z)))), elem!1)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[2080, 391, 32672, 1759, 33138])).
% 11.82/12.11 tff(33232,plain,
% 11.82/12.11 (r(s(s(s(s(z)))), elem!1)),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[762, 33231, 33143])).
% 11.82/12.11 tff(33233,plain,
% 11.82/12.11 (~(elem!1 = s(s(s(s(z)))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[769, 33143])).
% 11.82/12.11 tff(33234,plain,
% 11.82/12.11 (~b(elem!1, s(s(s(s(z)))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[2088, 391, 32672, 1759, 33138])).
% 11.82/12.11 tff(33235,plain,
% 11.82/12.11 (r(elem!1, s(s(s(s(z)))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[781, 33234, 33233])).
% 11.82/12.11 tff(33236,plain,
% 11.82/12.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.11 inference(rewrite,[status(thm)],[])).
% 11.82/12.11 tff(33237,plain,
% 11.82/12.11 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.11 inference(rewrite,[status(thm)],[])).
% 11.82/12.11 tff(33238,plain,
% 11.82/12.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 11.82/12.11 inference(monotonicity,[status(thm)],[33237])).
% 11.82/12.11 tff(33239,plain,
% 11.82/12.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.11 inference(transitivity,[status(thm)],[33238, 33236])).
% 11.82/12.11 tff(33240,plain,
% 11.82/12.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 11.82/12.11 inference(quant_inst,[status(thm)],[])).
% 11.82/12.11 tff(33241,plain,
% 11.82/12.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 11.82/12.11 inference(modus_ponens,[status(thm)],[33240, 33239])).
% 11.82/12.11 tff(33242,plain,
% 11.82/12.11 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[33241, 391, 33214, 32672, 1759])).
% 11.82/12.11 tff(33243,plain,
% 11.82/12.11 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[2849, 33215])).
% 11.82/12.11 tff(33244,plain,
% 11.82/12.11 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 11.82/12.11 inference(unit_resolution,[status(thm)],[10940, 33243])).
% 11.82/12.11 tff(33245,plain,
% 11.82/12.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.82/12.11 inference(rewrite,[status(thm)],[])).
% 11.82/12.11 tff(33246,plain,
% 11.82/12.11 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.82/12.12 inference(rewrite,[status(thm)],[])).
% 11.82/12.12 tff(33247,plain,
% 11.82/12.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.82/12.12 inference(monotonicity,[status(thm)],[33246])).
% 11.82/12.12 tff(33248,plain,
% 11.82/12.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.82/12.12 inference(transitivity,[status(thm)],[33247, 33245])).
% 11.82/12.12 tff(33249,plain,
% 11.82/12.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 11.82/12.12 inference(quant_inst,[status(thm)],[])).
% 11.82/12.12 tff(33250,plain,
% 11.82/12.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 11.82/12.12 inference(modus_ponens,[status(thm)],[33249, 33248])).
% 11.82/12.12 tff(33251,plain,
% 11.82/12.12 (~b(elem!1, s(s(s(elem!1))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[33250, 391, 33214, 32672, 1759, 33138])).
% 11.82/12.12 tff(33252,plain,
% 11.82/12.12 (r(elem!1, s(s(s(elem!1))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[424, 33251, 1])).
% 11.82/12.12 tff(33253,plain,
% 11.82/12.12 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[25443, 33252, 33244, 2032, 33242])).
% 11.82/12.12 tff(33254,plain,
% 11.82/12.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.82/12.12 inference(rewrite,[status(thm)],[])).
% 11.82/12.12 tff(33255,plain,
% 11.82/12.12 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.82/12.12 inference(rewrite,[status(thm)],[])).
% 11.82/12.12 tff(33256,plain,
% 11.82/12.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 11.82/12.12 inference(monotonicity,[status(thm)],[33255])).
% 11.82/12.12 tff(33257,plain,
% 11.82/12.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.82/12.12 inference(transitivity,[status(thm)],[33256, 33254])).
% 11.82/12.12 tff(33258,plain,
% 11.82/12.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.82/12.12 inference(quant_inst,[status(thm)],[])).
% 11.82/12.12 tff(33259,plain,
% 11.82/12.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 11.82/12.12 inference(modus_ponens,[status(thm)],[33258, 33257])).
% 11.82/12.12 tff(33260,plain,
% 11.82/12.12 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[33259, 391, 33214, 32672, 1759])).
% 11.82/12.12 tff(33261,plain,
% 11.82/12.12 ($false),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[2853, 42, 33243, 33260, 33253])).
% 11.82/12.12 tff(33262,plain,((elem!1 = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = z) | r(z, elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.12 tff(33263,plain,
% 11.82/12.12 (elem!1 = s(s(s(elem!1)))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[33262, 33235, 1759, 2, 80, 3446])).
% 11.82/12.12 tff(33264,plain,
% 11.82/12.12 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[2694, 130, 2081])).
% 11.82/12.12 tff(33265,plain,
% 11.82/12.12 (~r(elem!1, z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[6337, 719, 2032, 33264])).
% 11.82/12.12 tff(33266,plain,
% 11.82/12.12 (b(s(elem!1), elem!1)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[14657, 33265, 133, 10682, 21435, 17368, 2])).
% 11.82/12.12 tff(33267,plain,
% 11.82/12.12 (b(elem!1, z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[526, 33265, 2])).
% 11.82/12.12 tff(33268,plain,
% 11.82/12.12 (~b(s(elem!1), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[7777, 33267, 133, 33266])).
% 11.82/12.12 tff(33269,plain,
% 11.82/12.12 (r(s(elem!1), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[549, 33268])).
% 11.82/12.12 tff(33270,plain,
% 11.82/12.12 (~b(s(z), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[13285, 33267, 133, 721])).
% 11.82/12.12 tff(33271,plain,
% 11.82/12.12 (r(s(z), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[180, 33270])).
% 11.82/12.12 tff(33272,plain,
% 11.82/12.12 (~r(s(elem!1), s(z))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[13489, 33271, 719, 33269])).
% 11.82/12.12 tff(33273,plain,
% 11.82/12.12 (b(s(elem!1), s(z))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[13479, 33272, 124])).
% 11.82/12.12 tff(33274,plain,
% 11.82/12.12 (b(s(s(s(s(elem!1)))), s(z))),
% 11.82/12.12 inference(modus_ponens,[status(thm)],[33273, 17359])).
% 11.82/12.12 tff(33275,plain,
% 11.82/12.12 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[14662, 33266, 17368])).
% 11.82/12.12 tff(33276,plain,
% 11.82/12.12 (~(s(s(elem!1)) = s(elem!1))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[2279, 33275])).
% 11.82/12.12 tff(33277,plain,
% 11.82/12.12 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[287, 33276])).
% 11.82/12.12 tff(33278,plain,
% 11.82/12.12 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[299, 33277])).
% 11.82/12.12 tff(33279,plain,
% 11.82/12.12 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.82/12.12 inference(monotonicity,[status(thm)],[3065])).
% 11.82/12.12 tff(33280,plain,
% 11.82/12.12 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(elem!1))))),
% 11.82/12.12 inference(monotonicity,[status(thm)],[125])).
% 11.82/12.12 tff(33281,plain,
% 11.82/12.12 (r(s(elem!1), elem!1) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.82/12.12 inference(transitivity,[status(thm)],[33280, 33279])).
% 11.82/12.12 tff(33282,plain,
% 11.82/12.12 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 11.82/12.12 inference(monotonicity,[status(thm)],[33281])).
% 11.82/12.12 tff(33283,plain,
% 11.82/12.12 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[2686, 33275])).
% 11.82/12.12 tff(33284,plain,
% 11.82/12.12 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[2711, 33283])).
% 11.82/12.12 tff(33285,plain,
% 11.82/12.12 (~(s(s(elem!1)) = elem!1)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[451, 33275])).
% 11.82/12.12 tff(33286,plain,
% 11.82/12.12 (~b(s(s(elem!1)), elem!1)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[5286, 33276, 133, 33267, 33266])).
% 11.82/12.12 tff(33287,plain,
% 11.82/12.12 (r(s(s(elem!1)), elem!1)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[872, 33286, 33285])).
% 11.82/12.12 tff(33288,plain,
% 11.82/12.12 (~r(s(elem!1), elem!1)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[13245, 33287, 2112, 2032, 130, 33276, 33284])).
% 11.82/12.12 tff(33289,plain,
% 11.82/12.12 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.82/12.12 inference(modus_ponens,[status(thm)],[33288, 33282])).
% 11.82/12.12 tff(33290,plain,
% 11.82/12.12 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[1095, 33289, 33278])).
% 11.82/12.12 tff(33291,plain,
% 11.82/12.12 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[7123, 33267, 29426, 133, 2032, 18819, 719])).
% 11.82/12.12 tff(33292,plain,
% 11.82/12.12 (b(s(s(z)), s(s(s(s(z)))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[3652, 33291])).
% 11.82/12.12 tff(33293,plain,
% 11.82/12.12 (~b(s(s(z)), s(z))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[5126, 33292, 133, 1234, 722, 33271])).
% 11.82/12.12 tff(33294,plain,
% 11.82/12.12 (r(s(s(z)), s(z))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[3778, 33293])).
% 11.82/12.12 tff(33295,plain,
% 11.82/12.12 (~r(s(s(z)), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[26737, 33271, 29426, 722, 1759, 1234])).
% 11.82/12.12 tff(33296,plain,
% 11.82/12.12 (b(s(s(z)), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[1211, 33295])).
% 11.82/12.12 tff(33297,plain,
% 11.82/12.12 (~b(elem!1, s(s(z)))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[13448, 33296, 133, 33267])).
% 11.82/12.12 tff(33298,plain,
% 11.82/12.12 (r(elem!1, s(s(z)))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[3394, 33297, 3820])).
% 11.82/12.12 tff(33299,plain,
% 11.82/12.12 (r(s(s(s(elem!1))), s(s(z)))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[10022, 33298, 125])).
% 11.82/12.12 tff(33300,plain,
% 11.82/12.12 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[18451, 33298, 2032, 33294])).
% 11.82/12.12 tff(33301,plain,
% 11.82/12.12 (b(s(s(s(s(z)))), s(s(z)))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[1714, 33300])).
% 11.82/12.12 tff(33302,plain,
% 11.82/12.12 (~b(s(z), s(s(z)))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[28145, 33301, 133, 1234, 33296])).
% 11.82/12.12 tff(33303,plain,
% 11.82/12.12 (r(s(z), s(s(z)))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[1788, 33302])).
% 11.82/12.12 tff(33304,plain,
% 11.82/12.12 (~r(s(z), s(s(s(elem!1))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[11551, 33303, 33299, 33294])).
% 11.82/12.12 tff(33305,plain,
% 11.82/12.12 (b(s(z), s(s(s(elem!1))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[247, 33304])).
% 11.82/12.12 tff(33306,plain,
% 11.82/12.12 (b(s(s(s(elem!1))), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[9553, 33267, 125])).
% 11.82/12.12 tff(33307,plain,
% 11.82/12.12 (~b(s(s(s(s(elem!1)))), s(z))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[27723, 391, 33306, 10682, 33305, 33290])).
% 11.82/12.12 tff(33308,plain,
% 11.82/12.12 ($false),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[33307, 33274])).
% 11.82/12.12 tff(33309,plain,((~r(z, s(s(s(s(z)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.82/12.12 tff(33310,plain,
% 11.82/12.12 (~r(z, s(s(s(s(z)))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[33309, 33263, 29427, 22902, 32672, 33235, 33232, 26574, 1759, 33138, 2])).
% 11.82/12.12 tff(33311,plain,
% 11.82/12.12 (b(z, s(s(s(s(z)))))),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[800, 33310])).
% 11.82/12.12 tff(33312,plain,
% 11.82/12.12 (~b(s(z), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[17292, 33311, 32672, 1759])).
% 11.82/12.12 tff(33313,plain,
% 11.82/12.12 (r(s(z), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[180, 33312])).
% 11.82/12.12 tff(33314,plain,
% 11.82/12.12 (~r(s(s(z)), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[26737, 33313, 29426, 26574, 1759, 32672])).
% 11.82/12.12 tff(33315,plain,
% 11.82/12.12 (b(s(s(z)), z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[1211, 33314])).
% 11.82/12.12 tff(33316,plain,
% 11.82/12.12 (b(elem!1, z)),
% 11.82/12.12 inference(unit_resolution,[status(thm)],[26824, 33313, 80, 32672, 675, 2])).
% 11.82/12.12 tff(33317,plain,
% 11.92/12.13 (b(s(s(s(elem!1))), z)),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[9553, 33316, 33263])).
% 11.92/12.13 tff(33318,plain,
% 11.92/12.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 11.92/12.13 inference(rewrite,[status(thm)],[])).
% 11.92/12.13 tff(33319,plain,
% 11.92/12.13 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 11.92/12.13 inference(rewrite,[status(thm)],[])).
% 11.92/12.13 tff(33320,plain,
% 11.92/12.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 11.92/12.13 inference(monotonicity,[status(thm)],[33319])).
% 11.92/12.13 tff(33321,plain,
% 11.92/12.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 11.92/12.13 inference(transitivity,[status(thm)],[33320, 33318])).
% 11.92/12.13 tff(33322,plain,
% 11.92/12.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 11.92/12.13 inference(quant_inst,[status(thm)],[])).
% 11.92/12.13 tff(33323,plain,
% 11.92/12.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 11.92/12.13 inference(modus_ponens,[status(thm)],[33322, 33321])).
% 11.92/12.13 tff(33324,plain,
% 11.92/12.13 (~b(s(s(z)), s(s(s(elem!1))))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[33323, 391, 33317, 33315, 1759, 33311])).
% 11.92/12.13 tff(33325,plain,
% 11.92/12.13 (r(s(s(z)), s(s(s(elem!1))))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[11041, 33324])).
% 11.92/12.13 tff(33326,plain,
% 11.92/12.13 (s(s(s(elem!1))) = elem!1),
% 11.92/12.13 inference(symmetry,[status(thm)],[33263])).
% 11.92/12.13 tff(33327,plain,
% 11.92/12.13 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.92/12.13 inference(monotonicity,[status(thm)],[33326])).
% 11.92/12.13 tff(33328,plain,
% 11.92/12.13 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 11.92/12.13 inference(transitivity,[status(thm)],[33327, 698])).
% 11.92/12.13 tff(33329,plain,
% 11.92/12.13 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 11.92/12.13 inference(monotonicity,[status(thm)],[33328])).
% 11.92/12.13 tff(33330,plain,
% 11.92/12.13 (~(elem!1 = s(s(z)))),
% 11.92/12.13 inference(modus_ponens,[status(thm)],[1397, 33329])).
% 11.92/12.13 tff(33331,plain,
% 11.92/12.13 (~b(elem!1, s(s(z)))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[13448, 33315, 22902, 33316])).
% 11.92/12.13 tff(33332,plain,
% 11.92/12.13 (r(elem!1, s(s(z)))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[3394, 33331, 33330])).
% 11.92/12.13 tff(33333,plain,
% 11.92/12.13 (r(s(s(s(elem!1))), s(s(z)))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[10022, 33332, 33263])).
% 11.92/12.13 tff(33334,plain,
% 11.92/12.13 (s(s(s(elem!1))) = elem!1),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[129, 33263])).
% 11.92/12.13 tff(33335,plain,
% 11.92/12.13 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[2694, 33334, 33231])).
% 11.92/12.13 tff(33336,plain,
% 11.92/12.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.92/12.13 inference(rewrite,[status(thm)],[])).
% 11.92/12.13 tff(33337,plain,
% 11.92/12.13 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.92/12.13 inference(rewrite,[status(thm)],[])).
% 11.92/12.13 tff(33338,plain,
% 11.92/12.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 11.92/12.13 inference(monotonicity,[status(thm)],[33337])).
% 11.92/12.13 tff(33339,plain,
% 11.92/12.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.92/12.13 inference(transitivity,[status(thm)],[33338, 33336])).
% 11.92/12.13 tff(33340,plain,
% 11.92/12.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 11.92/12.13 inference(quant_inst,[status(thm)],[])).
% 11.92/12.13 tff(33341,plain,
% 11.92/12.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 11.92/12.13 inference(modus_ponens,[status(thm)],[33340, 33339])).
% 11.92/12.13 tff(33342,plain,
% 11.92/12.13 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[33341, 194, 33335, 33333, 33325])).
% 11.92/12.13 tff(33343,plain,
% 11.92/12.13 (b(s(s(z)), s(s(s(s(z)))))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[3652, 33342])).
% 11.92/12.13 tff(33344,plain,
% 11.92/12.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.92/12.13 inference(rewrite,[status(thm)],[])).
% 11.92/12.13 tff(33345,plain,
% 11.92/12.13 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.92/12.13 inference(rewrite,[status(thm)],[])).
% 11.92/12.13 tff(33346,plain,
% 11.92/12.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 11.92/12.13 inference(monotonicity,[status(thm)],[33345])).
% 11.92/12.13 tff(33347,plain,
% 11.92/12.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 11.92/12.13 inference(transitivity,[status(thm)],[33346, 33344])).
% 11.92/12.13 tff(33348,plain,
% 11.92/12.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.92/12.13 inference(quant_inst,[status(thm)],[])).
% 11.92/12.13 tff(33349,plain,
% 11.92/12.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 11.92/12.13 inference(modus_ponens,[status(thm)],[33348, 33347])).
% 11.92/12.13 tff(33350,plain,
% 11.92/12.13 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[33349, 194, 33335, 33333, 33325])).
% 11.92/12.13 tff(33351,plain,
% 11.92/12.13 (b(s(s(s(s(z)))), s(s(z)))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[1714, 33350])).
% 11.92/12.13 tff(33352,plain,
% 11.92/12.13 ($false),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[31721, 33351, 33343, 33311, 33315])).
% 11.92/12.13 tff(33353,plain,((~b(s(s(s(s(z)))), s(z))) | r(z, elem!1) | b(z, s(z)) | (elem!1 = z) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.13 tff(33354,plain,
% 11.92/12.13 (~b(s(s(s(s(z)))), s(z))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[33353, 675, 80, 2, 3446])).
% 11.92/12.13 tff(33355,plain,
% 11.92/12.13 (r(s(s(s(s(z)))), s(z))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[749, 33354])).
% 11.92/12.13 tff(33356,plain,
% 11.92/12.13 (~r(z, s(s(s(s(z)))))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[731, 33228, 26574, 33355])).
% 11.92/12.13 tff(33357,plain,
% 11.92/12.13 (b(z, s(s(s(s(z)))))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[800, 33356])).
% 11.92/12.13 tff(33358,plain,
% 11.92/12.13 (~b(s(s(s(s(z)))), elem!1)),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[10865, 33357, 33229, 22902])).
% 11.92/12.13 tff(33359,plain,
% 11.92/12.13 (r(s(s(s(s(z)))), elem!1)),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[762, 33358, 33143])).
% 11.92/12.13 tff(33360,plain,
% 11.92/12.13 (~r(elem!1, s(z))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[15864, 33359, 33355, 33228])).
% 11.92/12.13 tff(33361,plain,
% 11.92/12.13 (~r(elem!1, z)),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[26814, 33360, 29426, 22902, 26574, 32672, 33230])).
% 11.92/12.13 tff(33362,plain,
% 11.92/12.13 (~b(elem!1, s(s(s(elem!1))))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[17700, 33361, 2, 29426, 33215, 29427, 22902])).
% 11.92/12.13 tff(33363,plain,
% 11.92/12.13 (~r(s(z), elem!1)),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[27040, 33362, 22902, 29427, 26574, 2, 33215, 1, 33229, 33228])).
% 11.92/12.13 tff(33364,plain,
% 11.92/12.13 (b(s(z), elem!1)),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[632, 33363, 33215])).
% 11.92/12.13 tff(33365,plain,
% 11.92/12.13 (~b(s(s(s(elem!1))), elem!1)),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[10743, 33229, 29427, 22902])).
% 11.92/12.13 tff(33366,plain,
% 11.92/12.13 (b(s(elem!1), elem!1)),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[14657, 33361, 22902, 29427, 33215, 33365, 2])).
% 11.92/12.13 tff(33367,plain,
% 11.92/12.13 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[14662, 33366, 33365])).
% 11.92/12.13 tff(33368,plain,
% 11.92/12.13 (~(s(s(elem!1)) = elem!1)),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[451, 33367])).
% 11.92/12.13 tff(33369,plain,
% 11.92/12.13 (~b(s(s(elem!1)), elem!1)),
% 11.92/12.13 inference(unit_resolution,[status(thm)],[12771, 33364, 22902, 33229])).
% 11.92/12.14 tff(33370,plain,
% 11.92/12.14 (r(s(s(elem!1)), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[872, 33369, 33368])).
% 11.92/12.14 tff(33371,plain,
% 11.92/12.14 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[4039, 33370, 9, 33365, 33362])).
% 11.92/12.14 tff(33372,plain,
% 11.92/12.14 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[1370, 33371, 26982])).
% 11.92/12.14 tff(33373,plain,
% 11.92/12.14 (~r(s(s(s(elem!1))), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[12936, 33370, 29427, 22902, 33229, 1, 33365, 26982, 33364])).
% 11.92/12.14 tff(33374,plain,
% 11.92/12.14 (b(s(s(s(elem!1))), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[377, 33373])).
% 11.92/12.14 tff(33375,plain,
% 11.92/12.14 (~b(s(s(elem!1)), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[13177, 33372, 29427, 33374])).
% 11.92/12.14 tff(33376,plain,
% 11.92/12.14 (r(s(s(elem!1)), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[2629, 33375])).
% 11.92/12.14 tff(33377,plain,
% 11.92/12.14 (~r(s(s(elem!1)), s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[4103, 33376, 26574, 33228])).
% 11.92/12.14 tff(33378,plain,
% 11.92/12.14 (b(s(s(elem!1)), s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[362, 33377])).
% 11.92/12.14 tff(33379,plain,
% 11.92/12.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), 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)))))),
% 11.92/12.14 inference(rewrite,[status(thm)],[])).
% 11.92/12.14 tff(33380,plain,
% 11.92/12.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), 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)))))),
% 11.92/12.14 inference(quant_inst,[status(thm)],[])).
% 11.92/12.14 tff(33381,plain,
% 11.92/12.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 11.92/12.14 inference(modus_ponens,[status(thm)],[33380, 33379])).
% 11.92/12.14 tff(33382,plain,
% 11.92/12.14 ($false),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[33381, 391, 33229, 33378, 33372, 33364, 33214])).
% 11.92/12.14 tff(33383,plain,((elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | r(z, elem!1) | b(z, s(z)) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.14 tff(33384,plain,
% 11.92/12.14 (elem!1 = s(s(s(elem!1)))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[33383, 675, 80, 2, 3446])).
% 11.92/12.14 tff(33385,plain,
% 11.92/12.14 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 11.92/12.14 inference(monotonicity,[status(thm)],[33384])).
% 11.92/12.14 tff(33386,plain,
% 11.92/12.14 (b(s(s(s(elem!1))), s(z))),
% 11.92/12.14 inference(modus_ponens,[status(thm)],[33138, 33385])).
% 11.92/12.14 tff(33387,plain,
% 11.92/12.14 (~b(s(z), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[13285, 11936, 133, 721])).
% 11.92/12.14 tff(33388,plain,
% 11.92/12.14 (r(s(z), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[180, 33387])).
% 11.92/12.14 tff(33389,plain,
% 11.92/12.14 (b(s(elem!1), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[14657, 2282, 133, 10682, 21435, 17368, 2])).
% 11.92/12.14 tff(33390,plain,
% 11.92/12.14 (~b(z, s(elem!1))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[6555, 33389, 133, 11936])).
% 11.92/12.14 tff(33391,plain,
% 11.92/12.14 (r(z, s(elem!1))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[566, 33390])).
% 11.92/12.14 tff(33392,plain,
% 11.92/12.14 (~r(s(elem!1), s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[27002, 33391, 722, 33388])).
% 11.92/12.14 tff(33393,plain,
% 11.92/12.14 (b(s(elem!1), s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[13479, 33392, 124])).
% 11.92/12.14 tff(33394,plain,
% 11.92/12.14 (b(s(s(s(s(elem!1)))), s(z))),
% 11.92/12.14 inference(modus_ponens,[status(thm)],[33393, 17359])).
% 11.92/12.14 tff(33395,plain,
% 11.92/12.14 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[14662, 33389, 17368])).
% 11.92/12.14 tff(33396,plain,
% 11.92/12.14 (~(s(s(elem!1)) = s(elem!1))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[2279, 33395])).
% 11.92/12.14 tff(33397,plain,
% 11.92/12.14 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[287, 33396])).
% 11.92/12.14 tff(33398,plain,
% 11.92/12.14 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[299, 33397])).
% 11.92/12.14 tff(33399,plain,
% 11.92/12.14 (~b(s(elem!1), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[7777, 33389, 133, 11936])).
% 11.92/12.14 tff(33400,plain,
% 11.92/12.14 (r(s(elem!1), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[549, 33399])).
% 11.92/12.14 tff(33401,plain,
% 11.92/12.14 (~(s(s(elem!1)) = elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[451, 33395])).
% 11.92/12.14 tff(33402,plain,
% 11.92/12.14 (~(s(elem!1) = elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[1943, 33401])).
% 11.92/12.14 tff(33403,plain,
% 11.92/12.14 (~(elem!1 = s(elem!1))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[166, 33402])).
% 11.92/12.14 tff(33404,plain,
% 11.92/12.14 (~r(z, s(s(s(s(z)))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[731, 33388, 722, 723])).
% 11.92/12.14 tff(33405,plain,
% 11.92/12.14 (b(z, s(s(s(s(z)))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[800, 33404])).
% 11.92/12.14 tff(33406,plain,
% 11.92/12.14 (~b(s(s(s(s(z)))), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[10865, 33405, 11936, 133])).
% 11.92/12.14 tff(33407,plain,
% 11.92/12.14 (r(s(s(s(s(z)))), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[762, 33406, 720])).
% 11.92/12.14 tff(33408,plain,
% 11.92/12.14 (~r(s(z), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[13589, 33407, 133, 1234, 723, 3820, 27211, 11936, 770])).
% 11.92/12.14 tff(33409,plain,
% 11.92/12.14 (b(s(z), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[632, 33408, 21435])).
% 11.92/12.14 tff(33410,plain,
% 11.92/12.14 (~r(s(elem!1), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[13276, 33409, 133, 11936, 33403, 10682, 17368, 33400, 21769, 118])).
% 11.92/12.14 tff(33411,plain,
% 11.92/12.14 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.92/12.14 inference(modus_ponens,[status(thm)],[33410, 33282])).
% 11.92/12.14 tff(33412,plain,
% 11.92/12.14 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[1095, 33411, 33398])).
% 11.92/12.14 tff(33413,plain,
% 11.92/12.14 (b(s(z), s(s(s(elem!1))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[14872, 33409, 130])).
% 11.92/12.14 tff(33414,plain,
% 11.92/12.14 (b(s(s(s(elem!1))), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[9553, 11936, 125])).
% 11.92/12.14 tff(33415,plain,
% 11.92/12.14 (~b(s(s(s(s(elem!1)))), s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[27723, 391, 33414, 10682, 33413, 33412])).
% 11.92/12.14 tff(33416,plain,
% 11.92/12.14 ($false),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[33415, 33394])).
% 11.92/12.14 tff(33417,plain,(r(elem!1, z) | (~(elem!1 = s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.14 tff(33418,plain,
% 11.92/12.14 (r(elem!1, z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[33417, 33384, 29427, 22902, 32672, 33355, 33143, 26574, 33138, 2])).
% 11.92/12.14 tff(33419,plain,
% 11.92/12.14 (r(elem!1, s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[26814, 33418, 29426, 22902, 26574, 32672, 33230])).
% 11.92/12.14 tff(33420,plain,
% 11.92/12.14 (~r(s(z), s(s(s(elem!1))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[16770, 33418, 26574, 33419])).
% 11.92/12.14 tff(33421,plain,
% 11.92/12.14 (b(s(z), s(s(s(elem!1))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[247, 33420])).
% 11.92/12.14 tff(33422,plain,
% 11.92/12.14 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[20817, 33421, 32672, 33386])).
% 11.92/12.14 tff(33423,plain,
% 11.92/12.14 (~b(s(s(s(s(z)))), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[20820, 33422, 33384])).
% 11.92/12.14 tff(33424,plain,
% 11.92/12.14 (s(s(s(elem!1))) = elem!1),
% 11.92/12.14 inference(symmetry,[status(thm)],[33384])).
% 11.92/12.14 tff(33425,plain,
% 11.92/12.14 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.92/12.14 inference(monotonicity,[status(thm)],[33424])).
% 11.92/12.14 tff(33426,plain,
% 11.92/12.14 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 11.92/12.14 inference(transitivity,[status(thm)],[33425, 698])).
% 11.92/12.14 tff(33427,plain,
% 11.92/12.14 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 11.92/12.14 inference(monotonicity,[status(thm)],[33426])).
% 11.92/12.14 tff(33428,plain,
% 11.92/12.14 (~(elem!1 = s(s(z)))),
% 11.92/12.14 inference(modus_ponens,[status(thm)],[1397, 33427])).
% 11.92/12.14 tff(33429,plain,
% 11.92/12.14 (s(s(s(elem!1))) = elem!1),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[129, 33384])).
% 11.92/12.14 tff(33430,plain,
% 11.92/12.14 (~(s(elem!1) = s(s(s(s(z)))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[1965, 33429])).
% 11.92/12.14 tff(33431,plain,
% 11.92/12.14 (~r(s(z), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[17429, 33419, 29426, 32672, 26574, 124, 33215, 29427, 2, 33384, 33430])).
% 11.92/12.14 tff(33432,plain,
% 11.92/12.14 (b(s(z), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[180, 33431])).
% 11.92/12.14 tff(33433,plain,
% 11.92/12.14 (~b(s(z), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[4857, 33432, 22902, 33138])).
% 11.92/12.14 tff(33434,plain,
% 11.92/12.14 (r(s(z), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[632, 33433, 33215])).
% 11.92/12.14 tff(33435,plain,
% 11.92/12.14 (~b(s(z), s(s(z)))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[9999, 33434, 33138, 33355, 33428, 33423, 32672, 33143])).
% 11.92/12.14 tff(33436,plain,
% 11.92/12.14 (r(s(s(s(s(z)))), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[762, 33423, 33143])).
% 11.92/12.14 tff(33437,plain,
% 11.92/12.14 (r(s(s(s(elem!1))), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[533, 33418, 33429])).
% 11.92/12.14 tff(33438,plain,
% 11.92/12.14 (~r(z, s(s(s(s(z)))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[17484, 33432, 29426, 29427, 33429, 33244, 33437, 33421])).
% 11.92/12.14 tff(33439,plain,
% 11.92/12.14 (b(z, s(s(s(s(z)))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[800, 33438])).
% 11.92/12.14 tff(33440,plain,
% 11.92/12.14 (~r(s(z), s(s(z)))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[10046, 33439, 33355, 33384, 33386, 33432, 33434, 33138, 32672, 33436, 33423, 33233])).
% 11.92/12.14 tff(33441,plain,
% 11.92/12.14 ($false),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[1788, 33440, 33435])).
% 11.92/12.14 tff(33442,plain,(b(z, s(z)) | (elem!1 = z) | r(z, elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.14 tff(33443,plain,
% 11.92/12.14 (b(z, s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[33442, 3446, 80, 2])).
% 11.92/12.14 tff(33444,plain,
% 11.92/12.14 (~b(s(z), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[23112, 33443, 22902, 33138])).
% 11.92/12.14 tff(33445,plain,
% 11.92/12.14 (~(s(s(s(s(z)))) = elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[8916, 33444, 32672])).
% 11.92/12.14 tff(33446,plain,
% 11.92/12.14 (r(s(z), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[632, 33444, 33215])).
% 11.92/12.14 tff(33447,plain,
% 11.92/12.14 (~r(s(s(s(s(z)))), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[32843, 194, 530, 2053, 719])).
% 11.92/12.14 tff(33448,plain,
% 11.92/12.14 (~r(elem!1, s(s(s(s(z)))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[32850, 194, 530, 2053, 719])).
% 11.92/12.14 tff(33449,plain,
% 11.92/12.14 ($false),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[20438, 33448, 33447, 1234, 721, 720])).
% 11.92/12.14 tff(33450,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.14 tff(33451,plain,
% 11.92/12.14 (~r(z, s(s(s(s(z)))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[33450, 530, 721, 720, 1234, 2053])).
% 11.92/12.14 tff(33452,plain,
% 11.92/12.14 (b(z, s(s(s(s(z)))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[800, 33451])).
% 11.92/12.14 tff(33453,plain,
% 11.92/12.14 (~b(s(s(s(s(z)))), s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[10478, 33452, 1234, 664])).
% 11.92/12.14 tff(33454,plain,
% 11.92/12.14 (r(s(s(s(s(z)))), s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[749, 33453])).
% 11.92/12.14 tff(33455,plain,
% 11.92/12.14 (~b(s(s(s(s(z)))), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[9977, 33452, 1234, 721, 664])).
% 11.92/12.14 tff(33456,plain,
% 11.92/12.14 (r(s(s(s(s(z)))), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[762, 33455, 720])).
% 11.92/12.14 tff(33457,plain,
% 11.92/12.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 11.92/12.14 inference(rewrite,[status(thm)],[])).
% 11.92/12.14 tff(33458,plain,
% 11.92/12.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 11.92/12.14 inference(quant_inst,[status(thm)],[])).
% 11.92/12.14 tff(33459,plain,
% 11.92/12.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 11.92/12.14 inference(modus_ponens,[status(thm)],[33458, 33457])).
% 11.92/12.14 tff(33460,plain,
% 11.92/12.14 ($false),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[33459, 194, 530, 1484, 33456, 33454])).
% 11.92/12.14 tff(33461,plain,((~r(elem!1, z)) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.14 tff(33462,plain,
% 11.92/12.14 (~r(elem!1, z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[33461, 33446, 33445, 32672, 33138, 33443, 29426])).
% 11.92/12.14 tff(33463,plain,
% 11.92/12.14 (b(elem!1, z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[526, 33462, 2])).
% 11.92/12.14 tff(33464,plain,
% 11.92/12.14 (~b(s(s(s(elem!1))), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[10743, 33463, 29427, 22902])).
% 11.92/12.14 tff(33465,plain,
% 11.92/12.14 (b(s(elem!1), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[14657, 33464, 22902, 29427, 33215, 33462, 2])).
% 11.92/12.14 tff(33466,plain,
% 11.92/12.14 (~(s(s(s(elem!1))) = s(elem!1))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[14662, 33465, 33464])).
% 11.92/12.14 tff(33467,plain,
% 11.92/12.14 (~(s(s(elem!1)) = s(elem!1))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[2279, 33466])).
% 11.92/12.14 tff(33468,plain,
% 11.92/12.14 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[287, 33467])).
% 11.92/12.14 tff(33469,plain,
% 11.92/12.14 (~b(elem!1, s(s(s(elem!1))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[17700, 33462, 2, 29426, 33215, 29427, 22902])).
% 11.92/12.14 tff(33470,plain,
% 11.92/12.14 (~b(s(z), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[5970, 33443, 22902, 33138])).
% 11.92/12.14 tff(33471,plain,
% 11.92/12.14 (r(s(z), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[180, 33470])).
% 11.92/12.14 tff(33472,plain,
% 11.92/12.14 (~(s(s(elem!1)) = elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[451, 33466])).
% 11.92/12.14 tff(33473,plain,
% 11.92/12.14 (~b(s(s(elem!1)), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[5286, 33467, 22902, 33463, 33465])).
% 11.92/12.14 tff(33474,plain,
% 11.92/12.14 (r(s(s(elem!1)), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[872, 33473, 33472])).
% 11.92/12.14 tff(33475,plain,
% 11.92/12.14 (elem!1 = s(s(s(elem!1)))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[12954, 33474, 29427, 33446, 33471, 33464, 33469, 33468])).
% 11.92/12.14 tff(33476,plain,
% 11.92/12.14 (~(elem!1 = s(s(s(s(z)))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[769, 33445])).
% 11.92/12.14 tff(33477,plain,
% 11.92/12.14 (~b(s(elem!1), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[7777, 33465, 22902, 33463])).
% 11.92/12.14 tff(33478,plain,
% 11.92/12.14 (r(s(elem!1), z)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[549, 33477])).
% 11.92/12.14 tff(33479,plain,
% 11.92/12.14 (~b(z, s(elem!1))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[6555, 33465, 22902, 33463])).
% 11.92/12.14 tff(33480,plain,
% 11.92/12.14 (r(z, s(elem!1))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[566, 33479])).
% 11.92/12.14 tff(33481,plain,
% 11.92/12.14 (~r(s(elem!1), s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[17381, 33480, 33471, 33478])).
% 11.92/12.14 tff(33482,plain,
% 11.92/12.14 (b(s(elem!1), s(z))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[13479, 33481, 124])).
% 11.92/12.14 tff(33483,plain,
% 11.92/12.14 (s(s(s(elem!1))) = elem!1),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[129, 33475])).
% 11.92/12.14 tff(33484,plain,
% 11.92/12.14 (~(s(elem!1) = s(s(s(s(z)))))),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[1965, 33483])).
% 11.92/12.14 tff(33485,plain,
% 11.92/12.14 (s(s(s(elem!1))) = elem!1),
% 11.92/12.14 inference(symmetry,[status(thm)],[33475])).
% 11.92/12.14 tff(33486,plain,
% 11.92/12.14 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.92/12.14 inference(monotonicity,[status(thm)],[33485])).
% 11.92/12.14 tff(33487,plain,
% 11.92/12.14 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 11.92/12.14 inference(transitivity,[status(thm)],[33486, 698])).
% 11.92/12.14 tff(33488,plain,
% 11.92/12.14 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 11.92/12.14 inference(monotonicity,[status(thm)],[33487])).
% 11.92/12.14 tff(33489,plain,
% 11.92/12.14 (~(elem!1 = s(s(z)))),
% 11.92/12.14 inference(modus_ponens,[status(thm)],[1397, 33488])).
% 11.92/12.14 tff(33490,plain,
% 11.92/12.14 (~r(s(s(s(s(z)))), elem!1)),
% 11.92/12.14 inference(unit_resolution,[status(thm)],[13609, 33489, 32672, 33443, 33446, 33230, 33463, 33478, 33484, 22902, 33482, 33476])).
% 11.92/12.14 tff(33491,plain,
% 11.92/12.15 (b(s(s(s(s(z)))), elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[762, 33490, 33445])).
% 11.92/12.15 tff(33492,plain,
% 11.92/12.15 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[20820, 33491, 33475])).
% 11.92/12.15 tff(33493,plain,
% 11.92/12.15 (~b(z, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[9977, 33491, 32672, 33138, 33443])).
% 11.92/12.15 tff(33494,plain,
% 11.92/12.15 (r(z, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[800, 33493])).
% 11.92/12.15 tff(33495,plain,
% 11.92/12.15 (~r(s(s(z)), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[10261, 33494, 29426, 33471])).
% 11.92/12.15 tff(33496,plain,
% 11.92/12.15 (b(s(s(z)), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[1211, 33495])).
% 11.92/12.15 tff(33497,plain,
% 11.92/12.15 (~b(s(z), s(s(z)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33073, 33496, 32672, 33443, 22902, 29426])).
% 11.92/12.15 tff(33498,plain,
% 11.92/12.15 (r(s(z), s(s(z)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[1788, 33497])).
% 11.92/12.15 tff(33499,plain,
% 11.92/12.15 (b(s(s(s(elem!1))), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[9553, 33475, 33463])).
% 11.92/12.15 tff(33500,plain,
% 11.92/12.15 (~b(s(z), s(s(s(elem!1))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[22948, 33499, 29427, 22902, 33443])).
% 11.92/12.15 tff(33501,plain,
% 11.92/12.15 (r(s(z), s(s(s(elem!1))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[247, 33500])).
% 11.92/12.15 tff(33502,plain,
% 11.92/12.15 (~b(elem!1, s(s(z)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[13448, 33496, 22902, 33463])).
% 11.92/12.15 tff(33503,plain,
% 11.92/12.15 (r(elem!1, s(s(z)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[3394, 33502, 33489])).
% 11.92/12.15 tff(33504,plain,
% 11.92/12.15 (r(s(s(s(elem!1))), s(s(z)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[10022, 33503, 33475])).
% 11.92/12.15 tff(33505,plain,
% 11.92/12.15 (~r(s(s(z)), s(z))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[11551, 33504, 33501, 33498])).
% 11.92/12.15 tff(33506,plain,
% 11.92/12.15 (b(s(s(z)), s(z))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[3778, 33505])).
% 11.92/12.15 tff(33507,plain,
% 11.92/12.15 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 11.92/12.15 inference(transitivity,[status(thm)],[33487, 8492])).
% 11.92/12.15 tff(33508,plain,
% 11.92/12.15 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 11.92/12.15 inference(monotonicity,[status(thm)],[33507])).
% 11.92/12.15 tff(33509,plain,
% 11.92/12.15 (~(s(s(z)) = elem!1)),
% 11.92/12.15 inference(modus_ponens,[status(thm)],[1397, 33508])).
% 11.92/12.15 tff(33510,plain,
% 11.92/12.15 (r(elem!1, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[20438, 33490, 32672, 33138, 33445])).
% 11.92/12.15 tff(33511,plain,
% 11.92/12.15 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[7123, 33494, 29426, 22902, 33510, 33509, 33463])).
% 11.92/12.15 tff(33512,plain,
% 11.92/12.15 (b(s(s(z)), s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[3652, 33511])).
% 11.92/12.15 tff(33513,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[18268, 391, 33499, 33512, 32672, 33506, 33492])).
% 11.92/12.15 tff(33514,plain,(b(s(s(s(s(z)))), z) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33515,plain,
% 11.92/12.15 (b(s(s(s(s(z)))), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33514, 80, 2])).
% 11.92/12.15 tff(33516,plain,
% 11.92/12.15 (b(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[25045, 1549, 29427, 22902, 33515, 2881, 31666, 31])).
% 11.92/12.15 tff(33517,plain,
% 11.92/12.15 (~(elem!1 = s(s(s(elem!1))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[28049, 33516, 33515, 2913, 31, 22902, 2])).
% 11.92/12.15 tff(33518,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[27937, 33517, 33516, 80, 33515, 31, 1549, 2881, 2])).
% 11.92/12.15 tff(33519,plain,(b(s(s(s(s(z)))), elem!1) | r(z, elem!1) | b(elem!1, s(z)) | b(s(z), s(s(s(s(z))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33520,plain,
% 11.92/12.15 (b(s(s(s(s(z)))), elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33519, 31, 80, 2881, 2])).
% 11.92/12.15 tff(33521,plain,
% 11.92/12.15 (~b(z, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[10865, 665, 1652, 133])).
% 11.92/12.15 tff(33522,plain,
% 11.92/12.15 (~b(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[14978, 665, 90, 1652, 22903])).
% 11.92/12.15 tff(33523,plain,
% 11.92/12.15 (r(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[180, 33522])).
% 11.92/12.15 tff(33524,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[25072, 33523, 33521, 133, 90, 676, 2, 31, 1652])).
% 11.92/12.15 tff(33525,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | r(z, s(z)) | (elem!1 = z) | b(elem!1, s(z)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33526,plain,
% 11.92/12.15 (~b(elem!1, z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33525, 31, 33515, 31665, 2, 22902, 33520])).
% 11.92/12.15 tff(33527,plain,
% 11.92/12.15 (~(elem!1 = s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[16358, 33526, 33515])).
% 11.92/12.15 tff(33528,plain,
% 11.92/12.15 (r(elem!1, z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[526, 33526, 2])).
% 11.92/12.15 tff(33529,plain,
% 11.92/12.15 (~b(s(s(z)), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[4472, 1686, 90, 31897])).
% 11.92/12.15 tff(33530,plain,
% 11.92/12.15 (r(s(s(z)), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[1211, 33529])).
% 11.92/12.15 tff(33531,plain,
% 11.92/12.15 (~b(elem!1, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[22981, 1686, 90, 133])).
% 11.92/12.15 tff(33532,plain,
% 11.92/12.15 (r(elem!1, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[781, 33531, 8922])).
% 11.92/12.15 tff(33533,plain,
% 11.92/12.15 (~r(z, s(elem!1))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[6444, 33532, 2053, 530])).
% 11.92/12.15 tff(33534,plain,
% 11.92/12.15 (b(z, s(elem!1))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[566, 33533])).
% 11.92/12.15 tff(33535,plain,
% 11.92/12.15 (~r(elem!1, s(z))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[11195, 33532, 2053, 1216])).
% 11.92/12.15 tff(33536,plain,
% 11.92/12.15 (elem!1 = s(z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[837, 33535, 31])).
% 11.92/12.15 tff(33537,plain,
% 11.92/12.15 (s(z) = elem!1),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[172, 33536])).
% 11.92/12.15 tff(33538,plain,
% 11.92/12.15 (b(z, s(s(z)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[8527, 33537, 33534])).
% 11.92/12.15 tff(33539,plain,
% 11.92/12.15 (~b(s(z), s(s(z)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[30651, 33538, 1652, 31897, 10679])).
% 11.92/12.15 tff(33540,plain,
% 11.92/12.15 (r(s(z), s(s(z)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[1788, 33539])).
% 11.92/12.15 tff(33541,plain,
% 11.92/12.15 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[15550, 33538, 1686, 31897])).
% 11.92/12.15 tff(33542,plain,
% 11.92/12.15 (r(s(s(s(s(z)))), s(s(z)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[1714, 33541])).
% 11.92/12.15 tff(33543,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[11508, 33542, 33540, 1216, 33530])).
% 11.92/12.15 tff(33544,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | b(elem!1, s(z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33545,plain,
% 11.92/12.15 (~b(z, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33544, 33520, 2913, 31, 29426, 33528, 33527, 33515, 22902])).
% 11.92/12.15 tff(33546,plain,
% 11.92/12.15 (~(elem!1 = s(z))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[11318, 10644, 2, 29428])).
% 11.92/12.15 tff(33547,plain,
% 11.92/12.15 (~r(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[25072, 10644, 133, 90, 29428, 2, 31, 1652])).
% 11.92/12.15 tff(33548,plain,
% 11.92/12.15 (b(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[180, 33547])).
% 11.92/12.15 tff(33549,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[28307, 33548, 33546, 10682, 90, 1216, 29429, 31, 1])).
% 11.92/12.15 tff(33550,plain,(b(z, s(s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33551,plain,
% 11.92/12.15 (elem!1 = s(s(s(elem!1)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33550, 33545, 33515, 2913, 31, 29427, 2, 22902, 33520])).
% 11.92/12.15 tff(33552,plain,
% 11.92/12.15 (~r(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[25072, 33545, 22902, 33515, 31665, 2, 31, 33520])).
% 11.92/12.15 tff(33553,plain,
% 11.92/12.15 (b(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[180, 33552])).
% 11.92/12.15 tff(33554,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[28049, 33553, 33551, 33515, 2913, 31, 22902, 2])).
% 11.92/12.15 tff(33555,plain,(b(elem!1, s(z)) | (elem!1 = z) | r(z, elem!1) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33556,plain,
% 11.92/12.15 (b(elem!1, s(z))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33555, 2881, 80, 2])).
% 11.92/12.15 tff(33557,plain,
% 11.92/12.15 (~(s(z) = elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[20271, 33556])).
% 11.92/12.15 tff(33558,plain,
% 11.92/12.15 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[2849, 33557])).
% 11.92/12.15 tff(33559,plain,
% 11.92/12.15 (~b(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[5970, 33556, 22902, 31666])).
% 11.92/12.15 tff(33560,plain,
% 11.92/12.15 (r(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[180, 33559])).
% 11.92/12.15 tff(33561,plain,
% 11.92/12.15 (~r(elem!1, z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[32644, 33556, 29427, 22902, 2913, 29426, 80])).
% 11.92/12.15 tff(33562,plain,
% 11.92/12.15 (b(elem!1, z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[526, 33561, 2])).
% 11.92/12.15 tff(33563,plain,
% 11.92/12.15 (~b(elem!1, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[12445, 33562, 33515, 22902])).
% 11.92/12.15 tff(33564,plain,
% 11.92/12.15 (~b(s(z), elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[23112, 33556, 22902, 31666])).
% 11.92/12.15 tff(33565,plain,
% 11.92/12.15 (r(s(z), elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[632, 33564, 33557])).
% 11.92/12.15 tff(33566,plain,
% 11.92/12.15 (~r(elem!1, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[12404, 33565, 29426, 2913])).
% 11.92/12.15 tff(33567,plain,
% 11.92/12.15 (elem!1 = s(s(s(s(z))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[781, 33566, 33563])).
% 11.92/12.15 tff(33568,plain,
% 11.92/12.15 (s(s(s(s(z)))) = elem!1),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[769, 33567])).
% 11.92/12.15 tff(33569,plain,
% 11.92/12.15 (~(s(s(s(elem!1))) = elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[1436, 33568])).
% 11.92/12.15 tff(33570,plain,
% 11.92/12.15 (~(elem!1 = s(s(s(elem!1))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[129, 33569])).
% 11.92/12.15 tff(33571,plain,
% 11.92/12.15 (~b(elem!1, s(s(s(elem!1))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[17700, 2282, 2, 29426, 150, 10682, 133])).
% 11.92/12.15 tff(33572,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[32976, 30556, 33571, 664, 10682, 1526, 1])).
% 11.92/12.15 tff(33573,plain,(r(elem!1, z) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (elem!1 = s(s(s(elem!1)))) | (~b(z, elem!1)) | (elem!1 = z) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33574,plain,
% 11.92/12.15 (~b(s(s(s(elem!1))), s(z))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33573, 33570, 29427, 31666, 33561, 22902, 2, 33557])).
% 11.92/12.15 tff(33575,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[28392, 33574, 33570, 33515, 29427, 2881, 33560, 33558])).
% 11.92/12.15 tff(33576,plain,(b(s(z), s(s(s(s(z))))) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33577,plain,
% 11.92/12.15 (b(s(z), s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33576, 80, 2])).
% 11.92/12.15 tff(33578,plain,
% 11.92/12.15 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[17275, 33571, 2, 133, 722, 150, 118, 838, 9, 30556])).
% 11.92/12.15 tff(33579,plain,
% 11.92/12.15 (~(s(s(elem!1)) = elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[23479, 33578, 427, 30556])).
% 11.92/12.15 tff(33580,plain,
% 11.92/12.15 (b(s(elem!1), elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[14657, 30556, 133, 10682, 150, 2282, 2])).
% 11.92/12.15 tff(33581,plain,
% 11.92/12.15 (~(s(s(elem!1)) = s(elem!1))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[264, 33579])).
% 11.92/12.15 tff(33582,plain,
% 11.92/12.15 (~b(s(s(elem!1)), elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[5286, 33581, 133, 11936, 33580])).
% 11.92/12.15 tff(33583,plain,
% 11.92/12.15 (r(s(s(elem!1)), elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[872, 33582, 33579])).
% 11.92/12.15 tff(33584,plain,
% 11.92/12.15 (~r(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[26517, 33583, 133, 10682, 31, 1, 11936, 26982, 150, 27044])).
% 11.92/12.15 tff(33585,plain,
% 11.92/12.15 (b(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[180, 33584])).
% 11.92/12.15 tff(33586,plain,
% 11.92/12.15 (~b(s(z), elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[5231, 33585, 133, 11936])).
% 11.92/12.15 tff(33587,plain,
% 11.92/12.15 (s(s(s(s(z)))) = elem!1),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[28064, 33585, 90, 133, 150, 11936, 838])).
% 11.92/12.15 tff(33588,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[8916, 33587, 33586, 1234])).
% 11.92/12.15 tff(33589,plain,(r(elem!1, z) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(z)) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33590,plain,
% 11.92/12.15 (r(elem!1, z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33589, 1, 90, 133, 150, 10682, 31, 1234, 2, 722])).
% 11.92/12.15 tff(33591,plain,
% 11.92/12.15 (~r(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[17266, 33590, 722, 838])).
% 11.92/12.15 tff(33592,plain,
% 11.92/12.15 (b(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[180, 33591])).
% 11.92/12.15 tff(33593,plain,
% 11.92/12.15 (b(elem!1, z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[28018, 33592, 133, 90, 1234, 31, 1, 150, 2])).
% 11.92/12.15 tff(33594,plain,
% 11.92/12.15 (s(s(s(s(z)))) = elem!1),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[28064, 33592, 90, 133, 150, 33593, 838])).
% 11.92/12.15 tff(33595,plain,
% 11.92/12.15 (~b(s(z), elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[5231, 33593, 133, 33592])).
% 11.92/12.15 tff(33596,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[8916, 33595, 33594, 1234])).
% 11.92/12.15 tff(33597,plain,((elem!1 = s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (s(z) = elem!1) | b(elem!1, s(z)) | (elem!1 = z) | (~r(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33598,plain,
% 11.92/12.15 (elem!1 = s(s(s(elem!1)))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33597, 30551, 22902, 33515, 33577, 31, 2, 722, 29427])).
% 11.92/12.15 tff(33599,plain,
% 11.92/12.15 (s(s(s(elem!1))) = elem!1),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[129, 33598])).
% 11.92/12.15 tff(33600,plain,
% 11.92/12.15 (~(s(elem!1) = s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[1965, 33599])).
% 11.92/12.15 tff(33601,plain,
% 11.92/12.15 (~r(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[17429, 33600, 29426, 33577, 722, 124, 30551, 29427, 2, 30553, 33598])).
% 11.92/12.15 tff(33602,plain,
% 11.92/12.15 (~r(elem!1, z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[18026, 33599, 29426, 29427, 98, 31, 30551, 722])).
% 11.92/12.15 tff(33603,plain,
% 11.92/12.15 (~(s(s(s(s(z)))) = elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[1436, 33599])).
% 11.92/12.15 tff(33604,plain,
% 11.92/12.15 (b(z, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[32800, 33603, 2, 33577, 31, 33602, 80])).
% 11.92/12.15 tff(33605,plain,
% 11.92/12.15 (~b(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[22664, 33604, 33515, 33577])).
% 11.92/12.15 tff(33606,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[180, 33605, 33601])).
% 11.92/12.15 tff(33607,plain,((~r(z, s(z))) | (elem!1 = z) | b(elem!1, s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33608,plain,
% 11.92/12.15 (~r(z, s(z))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33607, 31, 2, 80])).
% 11.92/12.15 tff(33609,plain,
% 11.92/12.15 (~r(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[22964, 33608, 22902, 33515, 2, 33577, 31])).
% 11.92/12.15 tff(33610,plain,
% 11.92/12.15 (b(z, s(z))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[678, 33608])).
% 11.92/12.15 tff(33611,plain,
% 11.92/12.15 (~b(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[28088, 33610, 33515, 33577])).
% 11.92/12.15 tff(33612,plain,
% 11.92/12.15 ($false),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[180, 33611, 33609])).
% 11.92/12.15 tff(33613,plain,(b(elem!1, s(z)) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.15 tff(33614,plain,
% 11.92/12.15 (b(elem!1, s(z))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33613, 80, 2])).
% 11.92/12.15 tff(33615,plain,
% 11.92/12.15 (~b(s(s(s(s(z)))), elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[27735, 33614, 33515, 22902, 33577])).
% 11.92/12.15 tff(33616,plain,
% 11.92/12.15 (~r(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[27209, 33615, 80, 2, 33515, 33577, 33614])).
% 11.92/12.15 tff(33617,plain,
% 11.92/12.15 (b(s(z), z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[180, 33616])).
% 11.92/12.15 tff(33618,plain,
% 11.92/12.15 (~b(z, s(z))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[28088, 33617, 33515, 33577])).
% 11.92/12.15 tff(33619,plain,
% 11.92/12.15 (s(s(s(elem!1))) = elem!1),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[33226, 33617, 33614, 80, 33577, 33618, 2])).
% 11.92/12.15 tff(33620,plain,
% 11.92/12.15 (~(s(s(s(s(z)))) = elem!1)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[1436, 33619])).
% 11.92/12.15 tff(33621,plain,
% 11.92/12.15 (~b(elem!1, z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[13285, 33617, 22902, 33614])).
% 11.92/12.15 tff(33622,plain,
% 11.92/12.15 (r(elem!1, z)),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[526, 33621, 2])).
% 11.92/12.15 tff(33623,plain,
% 11.92/12.15 (~b(z, s(s(s(s(z)))))),
% 11.92/12.15 inference(unit_resolution,[status(thm)],[22664, 33617, 33515, 33577])).
% 11.92/12.16 tff(33624,plain,
% 11.92/12.16 (r(z, s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[800, 33623])).
% 11.92/12.16 tff(33625,plain,
% 11.92/12.16 ($false),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33450, 33624, 33622, 33614, 33620, 33577, 29426])).
% 11.92/12.16 tff(33626,plain,(r(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 11.92/12.16 tff(33627,plain,
% 11.92/12.16 (elem!1 = z),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33626, 80])).
% 11.92/12.16 tff(33628,plain,
% 11.92/12.16 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 11.92/12.16 inference(monotonicity,[status(thm)],[33627])).
% 11.92/12.16 tff(33629,plain,
% 11.92/12.16 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 11.92/12.16 inference(symmetry,[status(thm)],[33628])).
% 11.92/12.16 tff(33630,plain,
% 11.92/12.16 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(s(s(s(z)))), elem!1))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[33629])).
% 11.92/12.16 tff(33631,plain,
% 11.92/12.16 (~r(s(s(s(s(z)))), elem!1)),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[81, 33630])).
% 11.92/12.16 tff(33632,plain,
% 11.92/12.16 (b(elem!1, s(z)) <=> b(z, s(z))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[33627])).
% 11.92/12.16 tff(33633,plain,
% 11.92/12.16 (~b(elem!1, s(s(s(elem!1))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[31942, 10, 80])).
% 11.92/12.16 tff(33634,plain,
% 11.92/12.16 (r(elem!1, s(s(s(elem!1))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[424, 33633, 1])).
% 11.92/12.16 tff(33635,plain,
% 11.92/12.16 (~r(s(z), s(s(s(elem!1))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[21974, 183, 59, 46])).
% 11.92/12.16 tff(33636,plain,
% 11.92/12.16 (b(s(z), s(s(s(elem!1))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[247, 33635])).
% 11.92/12.16 tff(33637,plain,
% 11.92/12.16 (b(s(z), s(s(s(z))))),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[33636, 18545])).
% 11.92/12.16 tff(33638,plain,
% 11.92/12.16 ((s(z) = z) <=> (elem!1 = s(z))),
% 11.92/12.16 inference(transitivity,[status(thm)],[13, 1270])).
% 11.92/12.16 tff(33639,plain,
% 11.92/12.16 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[33638])).
% 11.92/12.16 tff(33640,plain,
% 11.92/12.16 (~(elem!1 = s(z))),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[23, 33639])).
% 11.92/12.16 tff(33641,plain,
% 11.92/12.16 (r(elem!1, s(z))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[837, 31, 33640])).
% 11.92/12.16 tff(33642,plain,
% 11.92/12.16 (~r(s(z), s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[10776, 183, 410, 33641])).
% 11.92/12.16 tff(33643,plain,
% 11.92/12.16 (b(s(z), s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[1230, 33642])).
% 11.92/12.16 tff(33644,plain,
% 11.92/12.16 (r(s(s(s(z))), s(z))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[29740, 183, 11])).
% 11.92/12.16 tff(33645,plain,
% 11.92/12.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 11.92/12.16 inference(rewrite,[status(thm)],[])).
% 11.92/12.16 tff(33646,plain,
% 11.92/12.16 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 11.92/12.16 inference(rewrite,[status(thm)],[])).
% 11.92/12.16 tff(33647,plain,
% 11.92/12.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[33646])).
% 11.92/12.16 tff(33648,plain,
% 11.92/12.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 11.92/12.16 inference(transitivity,[status(thm)],[33647, 33645])).
% 11.92/12.16 tff(33649,plain,
% 11.92/12.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 11.92/12.16 inference(quant_inst,[status(thm)],[])).
% 11.92/12.16 tff(33650,plain,
% 11.92/12.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[33649, 33648])).
% 11.92/12.16 tff(33651,plain,
% 11.92/12.16 ($false),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33650, 194, 722, 182, 15510, 30260])).
% 11.92/12.16 tff(33652,plain,((~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.16 tff(33653,plain,
% 11.92/12.16 (~r(s(z), z)),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33652, 33644, 29964, 46])).
% 11.92/12.16 tff(33654,plain,
% 11.92/12.16 (b(s(z), z)),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[180, 33653])).
% 11.92/12.16 tff(33655,plain,
% 11.92/12.16 (~b(z, s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[22664, 33654, 90, 33643])).
% 11.92/12.16 tff(33656,plain,
% 11.92/12.16 (r(z, s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[800, 33655])).
% 11.92/12.16 tff(33657,plain,
% 11.92/12.16 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[19836, 33656, 59, 23202])).
% 11.92/12.16 tff(33658,plain,
% 11.92/12.16 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[29931, 33657, 11])).
% 11.92/12.16 tff(33659,plain,
% 11.92/12.16 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[1095, 33658, 310])).
% 11.92/12.16 tff(33660,plain,
% 11.92/12.16 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[33659, 23220])).
% 11.92/12.16 tff(33661,plain,
% 11.92/12.16 ($false),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[29940, 391, 1234, 7872, 4415, 1684])).
% 11.92/12.16 tff(33662,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.16 tff(33663,plain,
% 11.92/12.16 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33662, 33643, 33660, 33637])).
% 11.92/12.16 tff(33664,plain,
% 11.92/12.16 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[1673, 33663, 11])).
% 11.92/12.16 tff(33665,plain,
% 11.92/12.16 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[15351, 33664, 32152])).
% 11.92/12.16 tff(33666,plain,
% 11.92/12.16 (r(s(s(s(z))), s(s(s(s(z)))))),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[33665, 17613])).
% 11.92/12.16 tff(33667,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 11.92/12.16 tff(33668,plain,
% 11.92/12.16 ($false),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[18482, 194, 723, 719, 15510, 33667])).
% 11.92/12.16 tff(33669,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.16 tff(33670,plain,
% 11.92/12.16 (~r(s(s(s(s(z)))), s(z))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33669, 33656, 29964, 33666])).
% 11.92/12.16 tff(33671,plain,
% 11.92/12.16 (b(s(s(s(s(z)))), s(z))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[749, 33670])).
% 11.92/12.16 tff(33672,plain,
% 11.92/12.16 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[27316, 33659, 11])).
% 11.92/12.16 tff(33673,plain,
% 11.92/12.16 (~r(s(z), elem!1)),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[5433, 33653, 17618])).
% 11.92/12.16 tff(33674,plain,
% 11.92/12.16 (b(s(z), elem!1)),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[632, 33673, 24])).
% 11.92/12.16 tff(33675,plain,
% 11.92/12.16 (b(s(s(s(s(z)))), elem!1)),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[90, 17621])).
% 11.92/12.16 tff(33676,plain,
% 11.92/12.16 (~r(s(z), s(s(z)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[22159, 183, 59, 46])).
% 11.92/12.16 tff(33677,plain,
% 11.92/12.16 (b(s(z), s(s(z)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[1788, 33676])).
% 11.92/12.16 tff(33678,plain,
% 11.92/12.16 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[11])).
% 11.92/12.16 tff(33679,plain,
% 11.92/12.16 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 11.92/12.16 inference(transitivity,[status(thm)],[33678, 792])).
% 11.92/12.16 tff(33680,plain,
% 11.92/12.16 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 11.92/12.16 inference(symmetry,[status(thm)],[33679])).
% 11.92/12.16 tff(33681,plain,
% 11.92/12.16 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 11.92/12.16 inference(transitivity,[status(thm)],[33680, 765])).
% 11.92/12.16 tff(33682,plain,
% 11.92/12.16 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[33681])).
% 11.92/12.16 tff(33683,plain,
% 11.92/12.16 (~(s(s(s(s(z)))) = elem!1)),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[83, 33682])).
% 11.92/12.16 tff(33684,plain,
% 11.92/12.16 (r(elem!1, s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[18869, 33674, 6221, 33683, 33643])).
% 11.92/12.16 tff(33685,plain,
% 11.92/12.16 ((elem!1 = s(s(z))) <=> (z = s(s(z)))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[11])).
% 11.92/12.16 tff(33686,plain,
% 11.92/12.16 ((elem!1 = s(s(z))) <=> (s(s(z)) = z)),
% 11.92/12.16 inference(transitivity,[status(thm)],[33685, 11715])).
% 11.92/12.16 tff(33687,plain,
% 11.92/12.16 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 11.92/12.16 inference(symmetry,[status(thm)],[33686])).
% 11.92/12.16 tff(33688,plain,
% 11.92/12.16 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[33687])).
% 11.92/12.16 tff(33689,plain,
% 11.92/12.16 (~(elem!1 = s(s(z)))),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[1207, 33688])).
% 11.92/12.16 tff(33690,plain,
% 11.92/12.16 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33662, 1234, 7872, 18546])).
% 11.92/12.16 tff(33691,plain,
% 11.92/12.16 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[1673, 33690, 11])).
% 11.92/12.16 tff(33692,plain,
% 11.92/12.16 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[15351, 33691, 32152])).
% 11.92/12.16 tff(33693,plain,
% 11.92/12.16 (~r(s(s(s(s(z)))), s(z))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[28132, 174, 719, 33692])).
% 11.92/12.16 tff(33694,plain,
% 11.92/12.16 (b(s(s(s(s(z)))), s(z))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[749, 33693])).
% 11.92/12.16 tff(33695,plain,
% 11.92/12.16 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[491])).
% 11.92/12.16 tff(33696,plain,
% 11.92/12.16 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[33695])).
% 11.92/12.16 tff(33697,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 11.92/12.16 tff(33698,plain,
% 11.92/12.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 11.92/12.16 inference(rewrite,[status(thm)],[])).
% 11.92/12.16 tff(33699,plain,
% 11.92/12.16 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 11.92/12.16 inference(rewrite,[status(thm)],[])).
% 11.92/12.16 tff(33700,plain,
% 11.92/12.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[33699])).
% 11.92/12.16 tff(33701,plain,
% 11.92/12.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 11.92/12.16 inference(transitivity,[status(thm)],[33700, 33698])).
% 11.92/12.16 tff(33702,plain,
% 11.92/12.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 11.92/12.16 inference(quant_inst,[status(thm)],[])).
% 11.92/12.16 tff(33703,plain,
% 11.92/12.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[33702, 33701])).
% 11.92/12.16 tff(33704,plain,
% 11.92/12.16 ($false),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33703, 194, 3557, 719, 4428, 33697])).
% 11.92/12.16 tff(33705,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.16 tff(33706,plain,
% 11.92/12.16 (~r(s(s(z)), s(s(s(z))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33705, 3557, 719, 4428])).
% 11.92/12.16 tff(33707,plain,
% 11.92/12.16 (~r(s(s(z)), s(s(s(elem!1))))),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[33706, 33696])).
% 11.92/12.16 tff(33708,plain,
% 11.92/12.16 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 11.92/12.16 inference(monotonicity,[status(thm)],[489])).
% 11.92/12.16 tff(33709,plain,
% 11.92/12.16 (~r(s(s(s(z))), s(s(z)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[32407, 3557, 719, 4428])).
% 11.92/12.16 tff(33710,plain,
% 11.92/12.16 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[4385, 33709, 11])).
% 11.92/12.16 tff(33711,plain,
% 11.92/12.16 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[1370, 33710, 297])).
% 11.92/12.16 tff(33712,plain,
% 11.92/12.16 (b(s(s(s(elem!1))), s(s(z)))),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[33711, 33708])).
% 11.92/12.16 tff(33713,plain,
% 11.92/12.16 (~b(s(s(z)), s(s(s(elem!1))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33121, 33712, 379, 2439])).
% 11.92/12.16 tff(33714,plain,
% 11.92/12.16 (r(s(s(z)), s(s(s(elem!1))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[11041, 33713])).
% 11.92/12.16 tff(33715,plain,
% 11.92/12.16 ($false),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33714, 33707])).
% 11.92/12.16 tff(33716,plain,((~r(s(s(z)), z)) | (~(elem!1 = z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.16 tff(33717,plain,
% 11.92/12.16 (~r(s(s(z)), z)),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33716, 29913, 379, 2439, 297, 719, 11])).
% 11.92/12.16 tff(33718,plain,
% 11.92/12.16 (b(s(s(z)), z)),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[1211, 33717])).
% 11.92/12.16 tff(33719,plain,
% 11.92/12.16 (~b(elem!1, s(s(z)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[18622, 33718, 1652, 644, 33694])).
% 11.92/12.16 tff(33720,plain,
% 11.92/12.16 (r(elem!1, s(s(z)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[3394, 33719, 33689])).
% 11.92/12.16 tff(33721,plain,
% 11.92/12.16 (r(z, s(s(z)))),
% 11.92/12.16 inference(modus_ponens,[status(thm)],[33720, 18443])).
% 11.92/12.16 tff(33722,plain,
% 11.92/12.16 (~b(s(s(z)), s(z))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[5108, 3823, 1234, 1759])).
% 11.92/12.16 tff(33723,plain,
% 11.92/12.16 (r(s(s(z)), s(z))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[3778, 33722])).
% 11.92/12.16 tff(33724,plain,
% 11.92/12.16 ($false),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[18451, 10126, 33723, 2032, 1748])).
% 11.92/12.16 tff(33725,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.16 tff(33726,plain,
% 11.92/12.16 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33725, 33720, 2032, 1234, 2439, 33694])).
% 11.92/12.16 tff(33727,plain,
% 11.92/12.16 (r(s(s(z)), s(s(s(s(z)))))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[3652, 33726])).
% 11.92/12.16 tff(33728,plain,
% 11.92/12.16 (~r(s(s(s(z))), s(s(z)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[30167, 33727, 15510, 33721])).
% 11.92/12.16 tff(33729,plain,
% 11.92/12.16 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[4385, 33728, 11])).
% 11.92/12.16 tff(33730,plain,
% 11.92/12.16 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[1370, 33729, 297])).
% 11.92/12.16 tff(33731,plain,
% 11.92/12.16 (b(s(s(s(z))), s(s(z)))),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[2986, 33730, 11])).
% 11.92/12.16 tff(33732,plain,
% 11.92/12.16 ($false),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[30355, 391, 33718, 1234, 7872, 33731, 18546])).
% 11.92/12.16 tff(33733,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.16 tff(33734,plain,
% 11.92/12.16 (~r(s(s(s(elem!1))), z)),
% 11.92/12.16 inference(unit_resolution,[status(thm)],[33733, 33643, 33660, 11, 297, 29964, 33684, 33677, 33675, 33674, 33636, 33656])).
% 11.92/12.17 tff(33735,plain,
% 11.92/12.17 (b(s(s(s(elem!1))), z)),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[377, 33734])).
% 11.92/12.17 tff(33736,plain,
% 11.92/12.17 (b(s(s(s(z))), z)),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[1680, 33735, 11])).
% 11.92/12.17 tff(33737,plain,
% 11.92/12.17 (~b(z, s(s(z)))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[30120, 33736, 33643, 33637, 33660])).
% 11.92/12.17 tff(33738,plain,
% 11.92/12.17 (r(z, s(s(z)))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[18613, 33737])).
% 11.92/12.17 tff(33739,plain,
% 11.92/12.17 (~b(elem!1, s(s(z)))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[3375, 33737, 11])).
% 11.92/12.17 tff(33740,plain,
% 11.92/12.17 (r(elem!1, s(s(z)))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[3394, 33739, 33689])).
% 11.92/12.17 tff(33741,plain,
% 11.92/12.17 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[33725, 33671, 33684, 33643, 33677, 33740])).
% 11.92/12.17 tff(33742,plain,
% 11.92/12.17 (r(s(s(z)), s(s(s(s(z)))))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[3652, 33741])).
% 11.92/12.17 tff(33743,plain,
% 11.92/12.17 (~r(s(s(s(z))), s(s(z)))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[30167, 33742, 29964, 33738])).
% 11.92/12.17 tff(33744,plain,
% 11.92/12.17 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[4385, 33743, 11])).
% 11.92/12.17 tff(33745,plain,
% 11.92/12.17 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[1370, 33744, 297])).
% 11.92/12.17 tff(33746,plain,
% 11.92/12.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.92/12.17 inference(rewrite,[status(thm)],[])).
% 11.92/12.17 tff(33747,plain,
% 11.92/12.17 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.92/12.17 inference(rewrite,[status(thm)],[])).
% 11.92/12.17 tff(33748,plain,
% 11.92/12.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 11.92/12.17 inference(monotonicity,[status(thm)],[33747])).
% 11.92/12.17 tff(33749,plain,
% 11.92/12.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.92/12.17 inference(transitivity,[status(thm)],[33748, 33746])).
% 11.92/12.17 tff(33750,plain,
% 11.92/12.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.92/12.17 inference(quant_inst,[status(thm)],[])).
% 11.92/12.17 tff(33751,plain,
% 11.92/12.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 11.92/12.17 inference(modus_ponens,[status(thm)],[33750, 33749])).
% 11.92/12.17 tff(33752,plain,
% 11.92/12.17 ($false),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[33751, 391, 381, 1374, 379, 1759, 3325])).
% 11.92/12.17 tff(33753,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.17 tff(33754,plain,
% 11.92/12.17 (~b(s(s(elem!1)), s(z))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[33753, 33745, 33672, 33636, 33671])).
% 11.92/12.17 tff(33755,plain,
% 11.92/12.17 (r(s(s(elem!1)), s(z))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[362, 33754])).
% 11.92/12.17 tff(33756,plain,
% 11.92/12.17 (r(s(s(z)), s(z))),
% 11.92/12.17 inference(modus_ponens,[status(thm)],[33755, 18397])).
% 11.92/12.17 tff(33757,plain,
% 11.92/12.17 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), z)),
% 11.92/12.17 inference(transitivity,[status(thm)],[30365, 23179])).
% 11.92/12.17 tff(33758,plain,
% 11.92/12.17 (~r(s(s(s(elem!1))), elem!1)),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[406, 33734, 11])).
% 11.92/12.17 tff(33759,plain,
% 11.92/12.17 (r(s(s(elem!1)), elem!1)),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[30357, 33745, 31, 33673, 33758, 30374, 30072, 33739, 10, 30363, 33643, 4028])).
% 11.92/12.17 tff(33760,plain,
% 11.92/12.17 (r(s(s(z)), z)),
% 11.92/12.17 inference(modus_ponens,[status(thm)],[33759, 33757])).
% 11.92/12.17 tff(33761,assumption,(r(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 11.92/12.17 tff(33762,plain,
% 11.92/12.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 11.92/12.17 inference(rewrite,[status(thm)],[])).
% 11.92/12.17 tff(33763,plain,
% 11.92/12.17 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 11.92/12.17 inference(rewrite,[status(thm)],[])).
% 11.92/12.17 tff(33764,plain,
% 11.92/12.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 11.92/12.17 inference(monotonicity,[status(thm)],[33763])).
% 11.92/12.17 tff(33765,plain,
% 11.92/12.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 11.92/12.17 inference(transitivity,[status(thm)],[33764, 33762])).
% 11.92/12.17 tff(33766,plain,
% 11.92/12.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 11.92/12.17 inference(quant_inst,[status(thm)],[])).
% 11.92/12.17 tff(33767,plain,
% 11.92/12.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 11.92/12.17 inference(modus_ponens,[status(thm)],[33766, 33765])).
% 11.92/12.17 tff(33768,plain,
% 11.92/12.17 ($false),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[33767, 194, 722, 3557, 2405, 33761])).
% 11.92/12.17 tff(33769,plain,((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.17 tff(33770,plain,
% 11.92/12.17 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 11.92/12.17 inference(unit_resolution,[status(thm)],[33769, 33760, 46, 33756])).
% 11.92/12.18 tff(33771,assumption,(s(z) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 11.92/12.18 tff(33772,plain,
% 11.92/12.18 (s(s(s(s(s(s(z)))))) = s(z)),
% 11.92/12.18 inference(symmetry,[status(thm)],[33771])).
% 11.92/12.18 tff(33773,plain,
% 11.92/12.18 ($false),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[5065, 33772])).
% 11.92/12.18 tff(33774,plain,(~(s(z) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.18 tff(33775,assumption,(~r(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 11.92/12.18 tff(33776,assumption,(~b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 11.92/12.18 tff(33777,plain,
% 11.92/12.18 ($false),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[11665, 42, 33776, 33775, 33774])).
% 11.92/12.18 tff(33778,plain,(b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.18 tff(33779,plain,
% 11.92/12.18 (b(s(z), s(s(s(s(s(s(z)))))))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[33778, 33770])).
% 11.92/12.18 tff(33780,plain,
% 11.92/12.18 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[18451, 33756, 33684, 33740])).
% 11.92/12.18 tff(33781,plain,
% 11.92/12.18 (b(s(s(s(s(z)))), s(s(z)))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[1714, 33780])).
% 11.92/12.18 tff(33782,plain,
% 11.92/12.18 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = z)),
% 11.92/12.18 inference(monotonicity,[status(thm)],[11])).
% 11.92/12.18 tff(33783,plain,
% 11.92/12.18 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 11.92/12.18 inference(symmetry,[status(thm)],[33782])).
% 11.92/12.18 tff(33784,plain,
% 11.92/12.18 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 11.92/12.18 inference(monotonicity,[status(thm)],[33783])).
% 11.92/12.18 tff(33785,plain,
% 11.92/12.18 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 11.92/12.18 inference(modus_ponens,[status(thm)],[6638, 33784])).
% 11.92/12.18 tff(33786,plain,
% 11.92/12.18 (r(elem!1, s(s(elem!1)))),
% 11.92/12.18 inference(modus_ponens,[status(thm)],[33738, 29971])).
% 11.92/12.18 tff(33787,plain,
% 11.92/12.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 11.92/12.18 inference(rewrite,[status(thm)],[])).
% 11.92/12.18 tff(33788,plain,
% 11.92/12.18 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 11.92/12.18 inference(rewrite,[status(thm)],[])).
% 11.92/12.18 tff(33789,plain,
% 11.92/12.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 11.92/12.18 inference(monotonicity,[status(thm)],[33788])).
% 11.92/12.18 tff(33790,plain,
% 11.92/12.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 11.92/12.18 inference(transitivity,[status(thm)],[33789, 33787])).
% 11.92/12.18 tff(33791,plain,
% 11.92/12.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 11.92/12.18 inference(quant_inst,[status(thm)],[])).
% 11.92/12.18 tff(33792,plain,
% 11.92/12.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 11.92/12.18 inference(modus_ponens,[status(thm)],[33791, 33790])).
% 11.92/12.18 tff(33793,plain,
% 11.92/12.18 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[33792, 194])).
% 11.92/12.18 tff(33794,plain,
% 11.92/12.18 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[33793, 33742, 33684, 33740])).
% 11.92/12.18 tff(33795,plain,
% 11.92/12.18 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[6652, 42, 4995, 33794])).
% 11.92/12.18 tff(33796,plain,
% 11.92/12.18 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[32487, 2741, 1064, 364])).
% 11.92/12.18 tff(33797,plain,
% 11.92/12.18 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[32502, 33796, 17618])).
% 11.92/12.18 tff(33798,plain,
% 11.92/12.18 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 11.92/12.18 inference(symmetry,[status(thm)],[8194])).
% 11.92/12.18 tff(33799,plain,
% 11.92/12.18 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(z))))))))),
% 11.92/12.18 inference(monotonicity,[status(thm)],[33798])).
% 11.92/12.18 tff(33800,plain,
% 11.92/12.18 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 11.92/12.18 inference(modus_ponens,[status(thm)],[5009, 33799])).
% 11.92/12.18 tff(33801,plain,
% 11.92/12.18 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), z)),
% 11.92/12.18 inference(monotonicity,[status(thm)],[11])).
% 11.92/12.18 tff(33802,plain,
% 11.92/12.18 (r(s(s(s(s(s(s(z)))))), z)),
% 11.92/12.18 inference(modus_ponens,[status(thm)],[2741, 33801])).
% 11.92/12.18 tff(33803,plain,
% 11.92/12.18 (r(s(s(z)), z)),
% 11.92/12.18 inference(modus_ponens,[status(thm)],[364, 33757])).
% 11.92/12.18 tff(33804,plain,
% 11.92/12.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 11.92/12.18 inference(rewrite,[status(thm)],[])).
% 11.92/12.18 tff(33805,plain,
% 11.92/12.18 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 11.92/12.18 inference(rewrite,[status(thm)],[])).
% 11.92/12.18 tff(33806,plain,
% 11.92/12.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 11.92/12.18 inference(monotonicity,[status(thm)],[33805])).
% 11.92/12.18 tff(33807,plain,
% 11.92/12.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 11.92/12.18 inference(transitivity,[status(thm)],[33806, 33804])).
% 11.92/12.18 tff(33808,plain,
% 11.92/12.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 11.92/12.18 inference(quant_inst,[status(thm)],[])).
% 11.92/12.18 tff(33809,plain,
% 11.92/12.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 11.92/12.18 inference(modus_ponens,[status(thm)],[33808, 33807])).
% 11.92/12.18 tff(33810,plain,
% 11.92/12.18 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[33809, 194, 722, 33803, 33802])).
% 11.92/12.18 tff(33811,plain,
% 11.92/12.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 11.92/12.18 inference(rewrite,[status(thm)],[])).
% 11.92/12.18 tff(33812,plain,
% 11.92/12.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 11.92/12.18 inference(quant_inst,[status(thm)],[])).
% 11.92/12.18 tff(33813,plain,
% 11.92/12.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 11.92/12.18 inference(modus_ponens,[status(thm)],[33812, 33811])).
% 11.92/12.18 tff(33814,plain,
% 11.92/12.18 ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[33813, 42, 33810])).
% 11.92/12.18 tff(33815,plain,
% 11.92/12.18 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 11.92/12.18 inference(unit_resolution,[status(thm)],[33814, 33800])).
% 11.92/12.18 tff(33816,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 11.92/12.18 tff(33817,plain,
% 11.92/12.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 11.92/12.18 inference(rewrite,[status(thm)],[])).
% 11.92/12.18 tff(33818,plain,
% 11.92/12.18 (((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 11.92/12.18 inference(rewrite,[status(thm)],[])).
% 11.92/12.18 tff(33819,plain,
% 11.92/12.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 11.92/12.18 inference(monotonicity,[status(thm)],[33818])).
% 11.92/12.18 tff(33820,plain,
% 11.92/12.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 11.92/12.18 inference(transitivity,[status(thm)],[33819, 33817])).
% 11.92/12.18 tff(33821,plain,
% 11.92/12.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 11.92/12.18 inference(quant_inst,[status(thm)],[])).
% 11.92/12.18 tff(33822,plain,
% 11.92/12.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 11.92/12.19 inference(modus_ponens,[status(thm)],[33821, 33820])).
% 11.92/12.19 tff(33823,plain,
% 11.92/12.19 ($false),
% 11.92/12.19 inference(unit_resolution,[status(thm)],[33822, 391, 3563, 33816, 33815, 33797])).
% 11.92/12.19 tff(33824,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~(elem!1 = z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.19 tff(33825,plain,
% 11.92/12.19 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 11.92/12.19 inference(unit_resolution,[status(thm)],[33824, 33781, 33795, 46, 11, 33786, 33759])).
% 11.92/12.19 tff(33826,plain,
% 11.92/12.19 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 11.92/12.19 inference(unit_resolution,[status(thm)],[8073, 33825, 33785])).
% 11.92/12.19 tff(33827,plain,
% 11.92/12.19 (r(elem!1, s(s(s(s(s(s(z))))))) <=> r(z, s(s(s(s(s(s(z)))))))),
% 11.92/12.19 inference(monotonicity,[status(thm)],[11])).
% 11.92/12.19 tff(33828,plain,
% 11.92/12.19 (r(z, s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(s(s(s(s(z)))))))),
% 11.92/12.19 inference(symmetry,[status(thm)],[33827])).
% 11.92/12.19 tff(33829,plain,
% 11.92/12.19 (b(elem!1, s(s(s(s(s(s(z))))))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 11.92/12.19 inference(monotonicity,[status(thm)],[11])).
% 11.92/12.19 tff(33830,plain,
% 11.92/12.19 ((~b(elem!1, s(s(s(s(s(s(z)))))))) <=> (~b(z, s(s(s(s(s(s(z))))))))),
% 11.92/12.19 inference(monotonicity,[status(thm)],[33829])).
% 11.92/12.19 tff(33831,assumption,(b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 11.92/12.19 tff(33832,plain,
% 11.92/12.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 11.92/12.19 inference(rewrite,[status(thm)],[])).
% 11.92/12.19 tff(33833,plain,
% 11.92/12.19 (((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 11.92/12.19 inference(rewrite,[status(thm)],[])).
% 11.92/12.19 tff(33834,plain,
% 11.92/12.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 11.92/12.19 inference(monotonicity,[status(thm)],[33833])).
% 11.92/12.19 tff(33835,plain,
% 11.92/12.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 11.92/12.19 inference(transitivity,[status(thm)],[33834, 33832])).
% 11.92/12.19 tff(33836,plain,
% 11.92/12.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 11.92/12.19 inference(quant_inst,[status(thm)],[])).
% 11.92/12.19 tff(33837,plain,
% 11.92/12.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 11.92/12.19 inference(modus_ponens,[status(thm)],[33836, 33835])).
% 11.92/12.19 tff(33838,plain,
% 11.92/12.19 ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 11.92/12.19 inference(unit_resolution,[status(thm)],[33837, 391])).
% 11.92/12.19 tff(33839,plain,
% 11.92/12.19 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 11.92/12.19 inference(unit_resolution,[status(thm)],[33838, 8042, 644, 33831])).
% 11.92/12.19 tff(33840,plain,
% 11.92/12.19 (~b(z, s(s(s(s(s(s(z)))))))),
% 11.92/12.19 inference(modus_ponens,[status(thm)],[33839, 33830])).
% 11.92/12.19 tff(33841,plain,
% 11.92/12.19 ((z = s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 11.92/12.19 inference(unit_resolution,[status(thm)],[11697, 42, 33840])).
% 11.92/12.19 tff(33842,plain,
% 11.92/12.19 (r(z, s(s(s(s(s(s(z)))))))),
% 11.92/12.19 inference(unit_resolution,[status(thm)],[33841, 11645])).
% 11.92/12.19 tff(33843,plain,
% 11.92/12.19 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 11.92/12.19 inference(modus_ponens,[status(thm)],[33842, 33828])).
% 11.92/12.19 tff(33844,plain,
% 11.92/12.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 11.92/12.19 inference(rewrite,[status(thm)],[])).
% 11.92/12.19 tff(33845,plain,
% 11.92/12.19 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 11.92/12.19 inference(rewrite,[status(thm)],[])).
% 11.92/12.19 tff(33846,plain,
% 11.92/12.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 11.92/12.19 inference(monotonicity,[status(thm)],[33845])).
% 11.92/12.19 tff(33847,plain,
% 11.92/12.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 11.92/12.19 inference(transitivity,[status(thm)],[33846, 33844])).
% 11.92/12.19 tff(33848,plain,
% 11.92/12.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(z)))))),
% 11.92/12.19 inference(quant_inst,[status(thm)],[])).
% 11.92/12.19 tff(33849,plain,
% 11.92/12.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 11.92/12.19 inference(modus_ponens,[status(thm)],[33848, 33847])).
% 11.92/12.19 tff(33850,plain,
% 11.92/12.19 ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 11.92/12.19 inference(unit_resolution,[status(thm)],[33849, 194])).
% 11.92/12.19 tff(33851,plain,
% 11.92/12.19 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 11.92/12.19 inference(unit_resolution,[status(thm)],[33850, 33843, 6610, 1748])).
% 11.92/12.20 tff(33852,plain,
% 11.92/12.20 ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 11.92/12.20 inference(unit_resolution,[status(thm)],[33813, 42, 33851])).
% 11.92/12.20 tff(33853,plain,
% 11.92/12.20 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 11.92/12.20 inference(unit_resolution,[status(thm)],[33852, 33800])).
% 11.92/12.20 tff(33854,plain,
% 11.92/12.20 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), z)),
% 11.92/12.20 inference(monotonicity,[status(thm)],[11])).
% 11.92/12.20 tff(33855,plain,
% 11.92/12.20 (b(s(s(s(s(s(s(z)))))), z)),
% 11.92/12.20 inference(modus_ponens,[status(thm)],[8042, 33854])).
% 11.92/12.20 tff(33856,plain,
% 11.92/12.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.92/12.20 inference(rewrite,[status(thm)],[])).
% 11.92/12.20 tff(33857,plain,
% 11.92/12.20 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(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(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.92/12.20 inference(rewrite,[status(thm)],[])).
% 11.92/12.20 tff(33858,plain,
% 11.92/12.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 11.92/12.20 inference(monotonicity,[status(thm)],[33857])).
% 11.92/12.20 tff(33859,plain,
% 11.92/12.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.92/12.20 inference(transitivity,[status(thm)],[33858, 33856])).
% 11.92/12.20 tff(33860,plain,
% 11.92/12.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.92/12.20 inference(quant_inst,[status(thm)],[])).
% 11.92/12.20 tff(33861,plain,
% 11.92/12.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 11.92/12.20 inference(modus_ponens,[status(thm)],[33860, 33859])).
% 11.92/12.20 tff(33862,plain,
% 11.92/12.20 ($false),
% 11.92/12.20 inference(unit_resolution,[status(thm)],[33861, 391, 1759, 2439, 3563, 33855, 33853])).
% 11.92/12.20 tff(33863,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~(elem!1 = z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 11.92/12.20 tff(33864,plain,
% 11.92/12.20 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 11.92/12.20 inference(unit_resolution,[status(thm)],[33863, 33826, 33677, 33781, 33671, 33740, 11, 33674, 33779])).
% 11.99/12.20 tff(33865,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))), introduced(assumption)).
% 11.99/12.20 tff(33866,plain,
% 11.99/12.20 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 11.99/12.20 inference(symmetry,[status(thm)],[33865])).
% 11.99/12.20 tff(33867,plain,
% 11.99/12.20 ($false),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[4995, 33866])).
% 11.99/12.20 tff(33868,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.20 tff(33869,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 11.99/12.20 tff(33870,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 11.99/12.20 tff(33871,plain,
% 11.99/12.20 ($false),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[11685, 42, 33870, 33869, 33868])).
% 11.99/12.20 tff(33872,plain,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.20 tff(33873,plain,
% 11.99/12.20 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[33872, 33864])).
% 11.99/12.20 tff(33874,plain,
% 11.99/12.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(33875,plain,
% 11.99/12.20 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(33876,plain,
% 11.99/12.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 11.99/12.20 inference(monotonicity,[status(thm)],[33875])).
% 11.99/12.20 tff(33877,plain,
% 11.99/12.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 11.99/12.20 inference(transitivity,[status(thm)],[33876, 33874])).
% 11.99/12.20 tff(33878,plain,
% 11.99/12.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 11.99/12.20 inference(quant_inst,[status(thm)],[])).
% 11.99/12.20 tff(33879,plain,
% 11.99/12.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[33878, 33877])).
% 11.99/12.20 tff(33880,plain,
% 11.99/12.20 ($false),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[33879, 391, 33643, 33671, 33873, 33779])).
% 11.99/12.20 tff(33881,plain,((~r(s(s(s(elem!1))), s(z))) | (~(elem!1 = z)) | b(elem!1, s(z)) | b(z, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.20 tff(33882,plain,
% 11.99/12.20 (~r(s(s(s(elem!1))), s(z))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[33881, 31, 11, 10, 4028, 15838, 6221, 90, 410])).
% 11.99/12.20 tff(33883,plain,
% 11.99/12.20 (b(s(s(s(elem!1))), s(z))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[223, 33882])).
% 11.99/12.20 tff(33884,plain,
% 11.99/12.20 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[20748, 1686, 90, 1235])).
% 11.99/12.20 tff(33885,plain,
% 11.99/12.20 (r(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[1714, 33884])).
% 11.99/12.20 tff(33886,plain,
% 11.99/12.20 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[4472, 1686, 90, 1235])).
% 11.99/12.20 tff(33887,plain,
% 11.99/12.20 (r(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[3652, 33886])).
% 11.99/12.20 tff(33888,plain,
% 11.99/12.20 ($false),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[22815, 33887, 33885, 1216, 1747])).
% 11.99/12.20 tff(33889,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.20 tff(33890,plain,
% 11.99/12.20 (~b(z, s(s(s(s(z)))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[33889, 1747, 1216, 90, 1235])).
% 11.99/12.20 tff(33891,plain,
% 11.99/12.20 (r(z, s(s(s(s(z)))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[800, 33890])).
% 11.99/12.20 tff(33892,plain,
% 11.99/12.20 (r(elem!1, s(s(s(s(z)))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[33891, 61])).
% 11.99/12.20 tff(33893,plain,
% 11.99/12.20 (~r(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[14900, 33892, 1216, 33641])).
% 11.99/12.20 tff(33894,plain,
% 11.99/12.20 (b(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[1714, 33893])).
% 11.99/12.20 tff(33895,plain,
% 11.99/12.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(33896,plain,
% 11.99/12.20 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(33897,plain,
% 11.99/12.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 11.99/12.20 inference(monotonicity,[status(thm)],[33896])).
% 11.99/12.20 tff(33898,plain,
% 11.99/12.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 11.99/12.20 inference(transitivity,[status(thm)],[33897, 33895])).
% 11.99/12.20 tff(33899,plain,
% 11.99/12.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 11.99/12.20 inference(quant_inst,[status(thm)],[])).
% 11.99/12.20 tff(33900,plain,
% 11.99/12.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[33899, 33898])).
% 11.99/12.20 tff(33901,plain,
% 11.99/12.20 ($false),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[33900, 194, 722, 1216, 719, 15704])).
% 11.99/12.21 tff(33902,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.21 tff(33903,plain,
% 11.99/12.21 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[33902, 33891, 46, 1216])).
% 11.99/12.21 tff(33904,plain,
% 11.99/12.21 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[32518, 33903, 11])).
% 11.99/12.21 tff(33905,plain,
% 11.99/12.21 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[1095, 33904, 310])).
% 11.99/12.21 tff(33906,plain,
% 11.99/12.21 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[33905, 23220])).
% 11.99/12.21 tff(33907,plain,
% 11.99/12.21 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 11.99/12.21 inference(monotonicity,[status(thm)],[11])).
% 11.99/12.21 tff(33908,plain,
% 11.99/12.21 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 11.99/12.21 inference(monotonicity,[status(thm)],[33680])).
% 11.99/12.21 tff(33909,plain,
% 11.99/12.21 (~(elem!1 = s(s(s(s(z)))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[83, 33908])).
% 11.99/12.21 tff(33910,plain,
% 11.99/12.21 (~r(elem!1, s(s(s(s(z)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[25083, 9024, 33675, 31, 1216])).
% 11.99/12.21 tff(33911,plain,
% 11.99/12.21 (b(elem!1, s(s(s(s(z)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[781, 33910, 33909])).
% 11.99/12.21 tff(33912,plain,
% 11.99/12.21 (b(z, s(s(s(s(z)))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[33911, 33907])).
% 11.99/12.21 tff(33913,plain,
% 11.99/12.21 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[16396, 10646, 1216, 1747])).
% 11.99/12.21 tff(33914,plain,
% 11.99/12.21 (b(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[3652, 33913])).
% 11.99/12.21 tff(33915,plain,
% 11.99/12.21 (~b(z, s(s(s(s(z)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[4472, 33914, 90, 1235])).
% 11.99/12.21 tff(33916,plain,
% 11.99/12.21 ($false),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[33915, 33912])).
% 11.99/12.21 tff(33917,plain,(b(s(s(s(s(z)))), s(z)) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.21 tff(33918,plain,
% 11.99/12.21 (b(s(s(s(s(z)))), s(z))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[33917, 1747, 90, 1235, 1216, 11, 31])).
% 11.99/12.21 tff(33919,plain,
% 11.99/12.21 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 11.99/12.21 inference(monotonicity,[status(thm)],[11])).
% 11.99/12.21 tff(33920,plain,
% 11.99/12.21 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 11.99/12.21 inference(symmetry,[status(thm)],[33919])).
% 11.99/12.21 tff(33921,plain,
% 11.99/12.21 (b(s(s(z)), elem!1)),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[1235, 33920])).
% 11.99/12.21 tff(33922,plain,
% 11.99/12.21 (~b(elem!1, s(s(z)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[11012, 33894, 33675, 33921])).
% 11.99/12.21 tff(33923,plain,
% 11.99/12.21 (r(elem!1, s(s(z)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[3394, 33922, 33689])).
% 11.99/12.21 tff(33924,plain,
% 11.99/12.21 (~r(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[1775, 33923, 33675, 24, 1747, 33918])).
% 11.99/12.21 tff(33925,plain,
% 11.99/12.21 (b(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[3652, 33924])).
% 11.99/12.21 tff(33926,plain,
% 11.99/12.21 (~b(s(s(s(z))), s(s(z)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[24809, 33925, 33906, 33894])).
% 11.99/12.21 tff(33927,plain,
% 11.99/12.21 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[2986, 33926, 11])).
% 11.99/12.21 tff(33928,plain,
% 11.99/12.21 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[1370, 33927, 297])).
% 11.99/12.21 tff(33929,plain,
% 11.99/12.21 (~r(s(z), s(s(s(elem!1))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[18031, 33928, 410, 33641])).
% 11.99/12.21 tff(33930,plain,
% 11.99/12.21 (b(s(z), s(s(s(elem!1))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[247, 33929])).
% 11.99/12.21 tff(33931,plain,
% 11.99/12.21 (b(s(z), s(s(s(z))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[33930, 18545])).
% 11.99/12.21 tff(33932,plain,
% 11.99/12.21 (~b(z, s(s(z)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[15053, 33894, 90, 1235])).
% 11.99/12.21 tff(33933,plain,
% 11.99/12.21 (r(z, s(s(z)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[18613, 33932])).
% 11.99/12.21 tff(33934,plain,
% 11.99/12.21 (~r(s(s(z)), s(z))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[9720, 33933, 46, 1747])).
% 11.99/12.21 tff(33935,plain,
% 11.99/12.21 (b(s(s(z)), s(z))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[3778, 33934])).
% 11.99/12.21 tff(33936,plain,
% 11.99/12.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(33937,plain,
% 11.99/12.21 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(33938,plain,
% 11.99/12.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 11.99/12.21 inference(monotonicity,[status(thm)],[33937])).
% 11.99/12.21 tff(33939,plain,
% 11.99/12.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.99/12.21 inference(transitivity,[status(thm)],[33938, 33936])).
% 11.99/12.21 tff(33940,plain,
% 11.99/12.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 11.99/12.21 inference(quant_inst,[status(thm)],[])).
% 11.99/12.21 tff(33941,plain,
% 11.99/12.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[33940, 33939])).
% 11.99/12.21 tff(33942,plain,
% 11.99/12.21 ($false),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[33941, 391, 33925, 33918, 33935, 4416, 33931])).
% 11.99/12.21 tff(33943,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.21 tff(33944,plain,
% 11.99/12.21 (~r(s(z), s(s(z)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[33943, 1235, 11, 410, 297, 90, 17636, 1216, 31])).
% 11.99/12.21 tff(33945,plain,
% 11.99/12.21 (b(s(z), s(s(z)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[1788, 33944])).
% 11.99/12.21 tff(33946,plain,
% 11.99/12.21 (~b(s(z), z)),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[16487, 33912, 90, 1235, 33945])).
% 11.99/12.21 tff(33947,plain,
% 11.99/12.21 (r(s(z), z)),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[180, 33946])).
% 11.99/12.21 tff(33948,plain,
% 11.99/12.21 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(33949,plain,
% 11.99/12.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))))),
% 11.99/12.21 inference(monotonicity,[status(thm)],[33948])).
% 11.99/12.21 tff(33950,plain,
% 11.99/12.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 11.99/12.21 inference(transitivity,[status(thm)],[33949, 4465])).
% 11.99/12.21 tff(33951,plain,
% 11.99/12.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 11.99/12.21 inference(quant_inst,[status(thm)],[])).
% 11.99/12.21 tff(33952,plain,
% 11.99/12.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[33951, 33950])).
% 11.99/12.21 tff(33953,plain,
% 11.99/12.21 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[33952, 391, 90, 1235, 33912])).
% 11.99/12.21 tff(33954,plain,
% 11.99/12.21 (r(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[3652, 33953])).
% 11.99/12.21 tff(33955,plain,
% 11.99/12.21 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[33954, 2403])).
% 11.99/12.21 tff(33956,plain,
% 11.99/12.21 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.21 inference(monotonicity,[status(thm)],[2401, 489])).
% 11.99/12.21 tff(33957,plain,
% 11.99/12.21 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.99/12.21 inference(symmetry,[status(thm)],[33956])).
% 11.99/12.21 tff(33958,plain,
% 11.99/12.21 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[14891, 391, 90, 1235, 33912])).
% 11.99/12.21 tff(33959,plain,
% 11.99/12.21 (r(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[1714, 33958])).
% 11.99/12.21 tff(33960,plain,
% 11.99/12.21 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[33959, 33957])).
% 11.99/12.21 tff(33961,plain,
% 11.99/12.21 (~r(s(s(z)), s(z))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[14395, 33954, 1216, 33959])).
% 11.99/12.21 tff(33962,plain,
% 11.99/12.21 (b(s(s(z)), s(z))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[3778, 33961])).
% 11.99/12.21 tff(33963,plain,
% 11.99/12.21 (b(s(s(elem!1)), s(z))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[33962, 30313])).
% 11.99/12.21 tff(33964,plain,
% 11.99/12.21 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[22012, 33963, 33945, 1235, 1526])).
% 11.99/12.21 tff(33965,plain,
% 11.99/12.21 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[1370, 33964, 297])).
% 11.99/12.21 tff(33966,plain,
% 11.99/12.21 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[15681, 33965, 33960, 33955])).
% 11.99/12.21 tff(33967,plain,
% 11.99/12.21 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[1164, 33966, 311])).
% 11.99/12.21 tff(33968,plain,
% 11.99/12.21 (b(s(s(s(z))), s(s(s(s(z)))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[33967, 3504])).
% 11.99/12.21 tff(33969,plain,
% 11.99/12.21 (~b(s(s(s(z))), z)),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[1692, 391, 90, 33912, 33968])).
% 11.99/12.21 tff(33970,plain,
% 11.99/12.21 (~b(s(s(s(elem!1))), z)),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[1680, 33969, 11])).
% 11.99/12.21 tff(33971,plain,
% 11.99/12.21 (r(s(s(s(elem!1))), z)),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[377, 33970])).
% 11.99/12.21 tff(33972,plain,
% 11.99/12.21 (r(s(s(s(z))), z)),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[4409, 33971, 11])).
% 11.99/12.21 tff(33973,plain,
% 11.99/12.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(33974,plain,
% 11.99/12.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(33975,plain,
% 11.99/12.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 11.99/12.22 inference(modus_ponens,[status(thm)],[33974, 33973])).
% 11.99/12.22 tff(33976,plain,
% 11.99/12.22 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[33975, 194, 722, 4428, 12178])).
% 11.99/12.22 tff(33977,plain,
% 11.99/12.22 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[29527, 42, 8094, 33976])).
% 11.99/12.22 tff(33978,plain,
% 11.99/12.22 (b(s(s(s(s(s(s(z)))))), s(z))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[14139, 12184])).
% 11.99/12.22 tff(33979,plain,
% 11.99/12.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(33980,plain,
% 11.99/12.22 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(33981,plain,
% 11.99/12.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 11.99/12.22 inference(monotonicity,[status(thm)],[33980])).
% 11.99/12.22 tff(33982,plain,
% 11.99/12.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 11.99/12.22 inference(transitivity,[status(thm)],[33981, 33979])).
% 11.99/12.22 tff(33983,plain,
% 11.99/12.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(33984,plain,
% 11.99/12.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 11.99/12.22 inference(modus_ponens,[status(thm)],[33983, 33982])).
% 11.99/12.22 tff(33985,plain,
% 11.99/12.22 ($false),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[33984, 391, 1235, 2439, 4416, 33978, 33977])).
% 11.99/12.22 tff(33986,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.22 tff(33987,plain,
% 11.99/12.22 (~r(s(s(s(s(s(s(z)))))), z)),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[33986, 33972, 33945, 17636, 46, 1235, 33947])).
% 11.99/12.22 tff(33988,plain,
% 11.99/12.22 (b(s(s(s(s(s(s(z)))))), z)),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[6641, 42, 6638, 33987])).
% 11.99/12.22 tff(33989,plain,
% 11.99/12.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(33990,plain,
% 11.99/12.22 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(33991,plain,
% 11.99/12.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 11.99/12.22 inference(monotonicity,[status(thm)],[33990])).
% 11.99/12.22 tff(33992,plain,
% 11.99/12.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.99/12.22 inference(transitivity,[status(thm)],[33991, 33989])).
% 11.99/12.22 tff(33993,plain,
% 11.99/12.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(33994,plain,
% 11.99/12.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 11.99/12.22 inference(modus_ponens,[status(thm)],[33993, 33992])).
% 11.99/12.22 tff(33995,plain,
% 11.99/12.22 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[33994, 391, 90, 1235, 33912, 33988])).
% 11.99/12.22 tff(33996,plain,
% 11.99/12.22 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 33995])).
% 11.99/12.22 tff(33997,plain,
% 11.99/12.22 (~r(s(z), s(s(s(elem!1))))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[18031, 33965, 410, 33641])).
% 11.99/12.22 tff(33998,plain,
% 11.99/12.22 (b(s(z), s(s(s(elem!1))))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[247, 33997])).
% 11.99/12.22 tff(33999,plain,
% 11.99/12.22 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 11.99/12.23 inference(monotonicity,[status(thm)],[490])).
% 11.99/12.23 tff(34000,plain,
% 11.99/12.23 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 11.99/12.23 inference(transitivity,[status(thm)],[33999, 8583])).
% 11.99/12.23 tff(34001,plain,
% 11.99/12.23 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 11.99/12.23 inference(symmetry,[status(thm)],[34000])).
% 11.99/12.23 tff(34002,plain,
% 11.99/12.23 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 11.99/12.23 inference(monotonicity,[status(thm)],[34001])).
% 11.99/12.23 tff(34003,plain,
% 11.99/12.23 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 11.99/12.23 inference(modus_ponens,[status(thm)],[8593, 34002])).
% 11.99/12.23 tff(34004,plain,
% 11.99/12.23 (r(s(s(s(z))), s(s(z)))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[4385, 33965, 11])).
% 11.99/12.23 tff(34005,plain,
% 11.99/12.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.99/12.23 inference(rewrite,[status(thm)],[])).
% 11.99/12.23 tff(34006,plain,
% 11.99/12.23 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.99/12.23 inference(rewrite,[status(thm)],[])).
% 11.99/12.23 tff(34007,plain,
% 11.99/12.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 11.99/12.23 inference(monotonicity,[status(thm)],[34006])).
% 11.99/12.23 tff(34008,plain,
% 11.99/12.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 11.99/12.23 inference(transitivity,[status(thm)],[34007, 34005])).
% 11.99/12.23 tff(34009,plain,
% 11.99/12.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 11.99/12.23 inference(quant_inst,[status(thm)],[])).
% 11.99/12.23 tff(34010,plain,
% 11.99/12.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 11.99/12.23 inference(modus_ponens,[status(thm)],[34009, 34008])).
% 11.99/12.23 tff(34011,plain,
% 11.99/12.23 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[34010, 194, 33954, 33959, 34004])).
% 11.99/12.23 tff(34012,plain,
% 11.99/12.23 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[32518, 34011, 11])).
% 11.99/12.23 tff(34013,plain,
% 11.99/12.23 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[1095, 34012, 310])).
% 11.99/12.23 tff(34014,plain,
% 11.99/12.23 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[27316, 34013, 11])).
% 11.99/12.23 tff(34015,plain,
% 11.99/12.23 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 11.99/12.23 inference(monotonicity,[status(thm)],[30042])).
% 11.99/12.23 tff(34016,plain,
% 11.99/12.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 11.99/12.23 inference(rewrite,[status(thm)],[])).
% 11.99/12.23 tff(34017,plain,
% 11.99/12.23 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 11.99/12.23 inference(rewrite,[status(thm)],[])).
% 11.99/12.23 tff(34018,plain,
% 11.99/12.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 11.99/12.23 inference(monotonicity,[status(thm)],[34017])).
% 11.99/12.23 tff(34019,plain,
% 11.99/12.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 11.99/12.23 inference(transitivity,[status(thm)],[34018, 34016])).
% 11.99/12.23 tff(34020,plain,
% 11.99/12.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 11.99/12.23 inference(quant_inst,[status(thm)],[])).
% 11.99/12.23 tff(34021,plain,
% 11.99/12.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 11.99/12.23 inference(modus_ponens,[status(thm)],[34020, 34019])).
% 11.99/12.23 tff(34022,plain,
% 11.99/12.23 (~b(s(s(z)), s(s(s(z))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[34021, 391, 1235, 33945, 33962, 17636])).
% 11.99/12.23 tff(34023,plain,
% 11.99/12.23 (~b(s(s(z)), s(s(s(elem!1))))),
% 11.99/12.23 inference(modus_ponens,[status(thm)],[34022, 34015])).
% 11.99/12.23 tff(34024,plain,
% 11.99/12.23 (r(s(s(z)), s(s(s(elem!1))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[11041, 34023])).
% 11.99/12.23 tff(34025,plain,
% 11.99/12.23 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[20773, 33971, 1526, 34024, 33954, 34014, 33998, 33959, 34003])).
% 11.99/12.23 tff(34026,plain,
% 11.99/12.23 (b(s(s(s(s(s(z))))), s(s(z)))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[20778, 34025])).
% 11.99/12.23 tff(34027,plain,
% 11.99/12.23 (~b(s(s(s(s(s(z))))), s(z))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[20784, 34026, 33998, 1526, 33962])).
% 11.99/12.23 tff(34028,plain,
% 11.99/12.23 (r(s(s(s(s(s(z))))), s(z))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[20789, 34027])).
% 11.99/12.23 tff(34029,plain,
% 11.99/12.23 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[15757, 34028, 33947, 10646])).
% 11.99/12.23 tff(34030,plain,
% 11.99/12.23 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[8761, 34029])).
% 11.99/12.23 tff(34031,plain,
% 11.99/12.23 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[20575, 34030, 1526, 34014, 33998])).
% 11.99/12.23 tff(34032,plain,
% 11.99/12.23 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[20797, 34031, 34003])).
% 11.99/12.23 tff(34033,plain,
% 11.99/12.23 (~r(s(s(s(s(s(z))))), z)),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[20558, 34032, 184, 33971])).
% 11.99/12.23 tff(34034,plain,
% 11.99/12.23 (b(s(s(s(s(s(z))))), z)),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[16530, 34033])).
% 11.99/12.23 tff(34035,plain,
% 11.99/12.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 11.99/12.23 inference(rewrite,[status(thm)],[])).
% 11.99/12.23 tff(34036,plain,
% 11.99/12.23 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 11.99/12.23 inference(rewrite,[status(thm)],[])).
% 11.99/12.23 tff(34037,plain,
% 11.99/12.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z))))),
% 11.99/12.23 inference(monotonicity,[status(thm)],[34036])).
% 11.99/12.23 tff(34038,plain,
% 11.99/12.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 11.99/12.23 inference(transitivity,[status(thm)],[34037, 34035])).
% 11.99/12.23 tff(34039,plain,
% 11.99/12.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.99/12.23 inference(quant_inst,[status(thm)],[])).
% 11.99/12.23 tff(34040,plain,
% 11.99/12.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z))),
% 11.99/12.23 inference(modus_ponens,[status(thm)],[34039, 34038])).
% 11.99/12.23 tff(34041,plain,
% 11.99/12.23 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[34040, 391])).
% 11.99/12.23 tff(34042,plain,
% 11.99/12.23 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[34041, 33988, 33912, 34034, 34030])).
% 11.99/12.23 tff(34043,plain,
% 11.99/12.23 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[33872, 34042])).
% 11.99/12.23 tff(34044,plain,
% 11.99/12.23 ($false),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[6696, 194, 33954, 10646, 34043, 33996])).
% 11.99/12.23 tff(34045,plain,(b(s(s(s(s(z)))), s(z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.23 tff(34046,plain,
% 11.99/12.24 (b(s(s(s(s(z)))), s(z))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[34045, 1235, 90, 184, 1526, 11, 410, 297, 1216, 31])).
% 11.99/12.24 tff(34047,plain,
% 11.99/12.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.99/12.24 inference(rewrite,[status(thm)],[])).
% 11.99/12.24 tff(34048,plain,
% 11.99/12.24 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.99/12.24 inference(rewrite,[status(thm)],[])).
% 11.99/12.24 tff(34049,plain,
% 11.99/12.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 11.99/12.24 inference(monotonicity,[status(thm)],[34048])).
% 11.99/12.24 tff(34050,plain,
% 11.99/12.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.99/12.24 inference(transitivity,[status(thm)],[34049, 34047])).
% 11.99/12.24 tff(34051,plain,
% 11.99/12.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 11.99/12.24 inference(quant_inst,[status(thm)],[])).
% 11.99/12.24 tff(34052,plain,
% 11.99/12.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[34051, 34050])).
% 11.99/12.24 tff(34053,plain,
% 11.99/12.24 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[34052, 391, 1235, 34046, 33945, 17636])).
% 11.99/12.24 tff(34054,plain,
% 11.99/12.24 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[34053, 18390])).
% 11.99/12.24 tff(34055,plain,
% 11.99/12.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.99/12.24 inference(rewrite,[status(thm)],[])).
% 11.99/12.24 tff(34056,plain,
% 11.99/12.24 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.99/12.24 inference(rewrite,[status(thm)],[])).
% 11.99/12.24 tff(34057,plain,
% 11.99/12.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 11.99/12.24 inference(monotonicity,[status(thm)],[34056])).
% 11.99/12.24 tff(34058,plain,
% 11.99/12.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.99/12.24 inference(transitivity,[status(thm)],[34057, 34055])).
% 11.99/12.24 tff(34059,plain,
% 11.99/12.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 11.99/12.24 inference(quant_inst,[status(thm)],[])).
% 11.99/12.24 tff(34060,plain,
% 11.99/12.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[34059, 34058])).
% 11.99/12.24 tff(34061,plain,
% 11.99/12.24 ($false),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[34060, 391, 1526, 1235, 1759, 2439, 3325])).
% 11.99/12.24 tff(34062,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.24 tff(34063,plain,
% 11.99/12.24 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[34062, 34046, 1526, 33945, 1235])).
% 11.99/12.24 tff(34064,plain,
% 11.99/12.24 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[27316, 34063, 11])).
% 11.99/12.24 tff(34065,plain,
% 11.99/12.24 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[1095, 34064, 310])).
% 11.99/12.24 tff(34066,plain,
% 11.99/12.24 (r(s(s(s(s(z)))), s(s(s(z))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[32518, 34065, 11])).
% 11.99/12.24 tff(34067,plain,
% 11.99/12.24 (~r(z, s(s(s(s(z)))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[33902, 34066, 46, 1216])).
% 11.99/12.24 tff(34068,plain,
% 11.99/12.24 (b(z, s(s(s(s(z)))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[800, 34067])).
% 11.99/12.24 tff(34069,plain,
% 11.99/12.24 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[4472, 34068, 90, 1235])).
% 11.99/12.24 tff(34070,plain,
% 11.99/12.24 (r(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[3652, 34069])).
% 11.99/12.24 tff(34071,plain,
% 11.99/12.24 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[34070, 2403])).
% 11.99/12.24 tff(34072,plain,
% 11.99/12.24 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[20748, 34068, 90, 1235])).
% 11.99/12.24 tff(34073,plain,
% 11.99/12.24 (r(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[1714, 34072])).
% 11.99/12.24 tff(34074,plain,
% 11.99/12.24 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[34073, 33957])).
% 11.99/12.24 tff(34075,plain,
% 11.99/12.24 (~r(s(s(z)), s(z))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[14395, 34070, 1216, 34073])).
% 11.99/12.24 tff(34076,plain,
% 11.99/12.24 (b(s(s(z)), s(z))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[3778, 34075])).
% 11.99/12.24 tff(34077,plain,
% 11.99/12.24 (b(s(s(elem!1)), s(z))),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[34076, 30313])).
% 11.99/12.24 tff(34078,plain,
% 11.99/12.24 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[22012, 34077, 33945, 1235, 1526])).
% 11.99/12.24 tff(34079,plain,
% 11.99/12.24 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[1370, 34078, 297])).
% 11.99/12.24 tff(34080,plain,
% 11.99/12.24 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[15681, 34079, 34074, 34071])).
% 11.99/12.24 tff(34081,plain,
% 11.99/12.24 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[1164, 34080, 311])).
% 11.99/12.24 tff(34082,plain,
% 11.99/12.24 ($false),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[34081, 34054])).
% 11.99/12.24 tff(34083,plain,((~b(s(s(z)), z)) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.24 tff(34084,plain,
% 11.99/12.24 (~b(s(s(z)), z)),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[34083, 1216, 15838, 1526, 11, 90, 184, 410, 31])).
% 11.99/12.24 tff(34085,plain,
% 11.99/12.24 (r(s(s(z)), z)),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[1211, 34084])).
% 11.99/12.24 tff(34086,plain,
% 11.99/12.24 (~r(s(s(z)), s(z))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[10610, 34085, 46, 1216])).
% 11.99/12.24 tff(34087,plain,
% 11.99/12.24 (b(s(s(z)), s(z))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[3778, 34086])).
% 11.99/12.24 tff(34088,plain,
% 11.99/12.24 (r(s(s(elem!1)), elem!1)),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[34085, 30367])).
% 11.99/12.24 tff(34089,plain,
% 11.99/12.24 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 11.99/12.24 inference(transitivity,[status(thm)],[510, 509])).
% 11.99/12.24 tff(34090,plain,
% 11.99/12.24 ((~r(s(elem!1), elem!1)) <=> (~r(s(z), z))),
% 11.99/12.24 inference(monotonicity,[status(thm)],[34089])).
% 11.99/12.24 tff(34091,plain,
% 11.99/12.24 (r(s(s(elem!1)), elem!1)),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[3557, 30367])).
% 11.99/12.24 tff(34092,plain,
% 11.99/12.24 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 11.99/12.24 inference(monotonicity,[status(thm)],[488])).
% 11.99/12.24 tff(34093,plain,
% 11.99/12.24 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 11.99/12.24 inference(symmetry,[status(thm)],[34092])).
% 11.99/12.24 tff(34094,plain,
% 11.99/12.24 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 11.99/12.24 inference(transitivity,[status(thm)],[23183, 34093])).
% 11.99/12.24 tff(34095,plain,
% 11.99/12.24 (r(s(elem!1), s(s(elem!1)))),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[1747, 34094])).
% 11.99/12.24 tff(34096,plain,
% 11.99/12.24 (~r(s(elem!1), elem!1)),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[7546, 34095, 410, 34091])).
% 11.99/12.24 tff(34097,plain,
% 11.99/12.24 (~r(s(z), z)),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[34096, 34090])).
% 11.99/12.24 tff(34098,plain,
% 11.99/12.24 (b(s(z), z)),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[178, 42, 23, 34097])).
% 11.99/12.24 tff(34099,plain,
% 11.99/12.24 (~b(elem!1, s(s(z)))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[22827, 34098, 1652, 20740, 20654])).
% 11.99/12.24 tff(34100,plain,
% 11.99/12.24 (r(elem!1, s(s(z)))),
% 11.99/12.24 inference(unit_resolution,[status(thm)],[3394, 34099, 33689])).
% 11.99/12.24 tff(34101,plain,
% 11.99/12.24 (r(z, s(s(z)))),
% 11.99/12.24 inference(modus_ponens,[status(thm)],[34100, 18443])).
% 11.99/12.24 tff(34102,plain,
% 11.99/12.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 11.99/12.24 inference(rewrite,[status(thm)],[])).
% 11.99/12.24 tff(34103,plain,
% 11.99/12.24 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 11.99/12.24 inference(rewrite,[status(thm)],[])).
% 11.99/12.24 tff(34104,plain,
% 11.99/12.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))))),
% 11.99/12.24 inference(monotonicity,[status(thm)],[34103])).
% 11.99/12.24 tff(34105,plain,
% 11.99/12.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 11.99/12.25 inference(transitivity,[status(thm)],[34104, 34102])).
% 11.99/12.25 tff(34106,plain,
% 11.99/12.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 11.99/12.25 inference(quant_inst,[status(thm)],[])).
% 11.99/12.25 tff(34107,plain,
% 11.99/12.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))),
% 11.99/12.25 inference(modus_ponens,[status(thm)],[34106, 34105])).
% 11.99/12.25 tff(34108,plain,
% 11.99/12.25 ($false),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[34107, 194, 722, 3557, 1747, 34101])).
% 11.99/12.25 tff(34109,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.25 tff(34110,plain,
% 11.99/12.25 (~r(s(z), s(s(z)))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[34109, 34085, 46, 11, 33675, 410, 1216])).
% 11.99/12.25 tff(34111,plain,
% 11.99/12.25 (b(s(z), s(s(z)))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[1788, 34110])).
% 11.99/12.25 tff(34112,plain,
% 11.99/12.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 11.99/12.25 inference(rewrite,[status(thm)],[])).
% 11.99/12.25 tff(34113,plain,
% 11.99/12.25 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 11.99/12.25 inference(rewrite,[status(thm)],[])).
% 11.99/12.25 tff(34114,plain,
% 11.99/12.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 11.99/12.25 inference(monotonicity,[status(thm)],[34113])).
% 11.99/12.25 tff(34115,plain,
% 11.99/12.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 11.99/12.25 inference(transitivity,[status(thm)],[34114, 34112])).
% 11.99/12.25 tff(34116,plain,
% 11.99/12.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 11.99/12.25 inference(quant_inst,[status(thm)],[])).
% 11.99/12.25 tff(34117,plain,
% 11.99/12.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 11.99/12.25 inference(modus_ponens,[status(thm)],[34116, 34115])).
% 11.99/12.25 tff(34118,plain,
% 11.99/12.25 (~b(s(s(s(z))), s(s(z)))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[34117, 391, 2439, 1233, 4416])).
% 11.99/12.25 tff(34119,plain,
% 11.99/12.25 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[2986, 34118, 11])).
% 11.99/12.25 tff(34120,plain,
% 11.99/12.25 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[1370, 34119, 15838])).
% 11.99/12.25 tff(34121,plain,
% 11.99/12.25 (b(s(s(s(elem!1))), elem!1)),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[4039, 34120, 4028, 127, 364])).
% 11.99/12.25 tff(34122,plain,
% 11.99/12.25 (b(s(s(s(elem!1))), z)),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[28222, 34121, 11])).
% 11.99/12.25 tff(34123,plain,
% 11.99/12.25 (b(s(s(s(z))), z)),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[1680, 34122, 11])).
% 11.99/12.25 tff(34124,plain,
% 11.99/12.25 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[1694, 34123, 90, 1686])).
% 11.99/12.25 tff(34125,plain,
% 11.99/12.25 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.99/12.25 inference(modus_ponens,[status(thm)],[34124, 18390])).
% 11.99/12.25 tff(34126,plain,
% 11.99/12.25 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[307, 32512])).
% 11.99/12.25 tff(34127,plain,
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% 11.99/12.25 inference(rewrite,[status(thm)],[])).
% 11.99/12.25 tff(34128,plain,
% 11.99/12.25 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(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(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 11.99/12.25 inference(rewrite,[status(thm)],[])).
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% 11.99/12.25 inference(monotonicity,[status(thm)],[34128])).
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% 11.99/12.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 11.99/12.25 inference(transitivity,[status(thm)],[34129, 34127])).
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% 11.99/12.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 11.99/12.25 inference(quant_inst,[status(thm)],[])).
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% 11.99/12.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 11.99/12.25 inference(modus_ponens,[status(thm)],[34131, 34130])).
% 11.99/12.25 tff(34133,plain,
% 11.99/12.25 (~b(s(s(z)), s(s(s(z))))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[34132, 391, 2439, 1233, 4416])).
% 11.99/12.25 tff(34134,plain,
% 11.99/12.25 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 11.99/12.25 inference(modus_ponens,[status(thm)],[34133, 30044])).
% 11.99/12.25 tff(34135,plain,
% 11.99/12.25 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[1356, 34134, 21729])).
% 11.99/12.25 tff(34136,plain,
% 11.99/12.25 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[25719, 34135, 410, 364])).
% 11.99/12.25 tff(34137,plain,
% 11.99/12.25 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[1164, 34136, 34126])).
% 11.99/12.25 tff(34138,plain,
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% 11.99/12.25 inference(unit_resolution,[status(thm)],[34137, 34125])).
% 11.99/12.25 tff(34139,plain,((~b(s(z), s(s(z)))) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.25 tff(34140,plain,
% 11.99/12.25 (~b(z, s(s(s(s(z)))))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[34139, 34111, 410, 34088, 90, 11, 4028, 127, 34087, 17636])).
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% 11.99/12.25 (~r(s(s(s(s(z)))), s(s(s(z))))),
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% 11.99/12.25 tff(34143,plain,
% 11.99/12.25 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[32518, 34142, 11])).
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% 11.99/12.25 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 11.99/12.25 tff(34145,plain,
% 11.99/12.25 (b(s(s(s(s(z)))), s(s(s(z))))),
% 11.99/12.25 inference(modus_ponens,[status(thm)],[34144, 23220])).
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% 11.99/12.25 (~r(s(s(z)), s(z))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[10610, 3557, 46, 1216])).
% 11.99/12.25 tff(34147,plain,
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% 11.99/12.25 inference(unit_resolution,[status(thm)],[3778, 34146])).
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% 11.99/12.25 (b(s(s(elem!1)), s(z))),
% 11.99/12.25 inference(modus_ponens,[status(thm)],[34147, 30313])).
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% 11.99/12.25 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 11.99/12.25 inference(monotonicity,[status(thm)],[11])).
% 11.99/12.25 tff(34150,plain,
% 11.99/12.25 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 11.99/12.25 inference(symmetry,[status(thm)],[34149])).
% 11.99/12.25 tff(34151,plain,
% 11.99/12.25 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 11.99/12.25 inference(monotonicity,[status(thm)],[2401])).
% 11.99/12.25 tff(34152,plain,
% 11.99/12.25 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(s(elem!1)))))),
% 11.99/12.25 inference(symmetry,[status(thm)],[34151])).
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% 11.99/12.25 tff(34156,plain,
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% 11.99/12.25 inference(unit_resolution,[status(thm)],[1788, 34155])).
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% 11.99/12.25 tff(34158,plain,
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% 11.99/12.25 tff(34160,plain,
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% 11.99/12.25 inference(unit_resolution,[status(thm)],[1714, 34159])).
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% 11.99/12.25 inference(unit_resolution,[status(thm)],[18613, 34161])).
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% 11.99/12.25 inference(unit_resolution,[status(thm)],[20649, 34162, 3557, 34156])).
% 11.99/12.25 tff(34164,plain,
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% 11.99/12.25 inference(unit_resolution,[status(thm)],[632, 34164, 24])).
% 11.99/12.25 tff(34166,plain,
% 11.99/12.25 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[18333, 34165, 34154, 1526, 34148])).
% 11.99/12.25 tff(34167,plain,
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% 11.99/12.25 inference(unit_resolution,[status(thm)],[180, 34163])).
% 11.99/12.25 tff(34168,plain,
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% 11.99/12.25 inference(unit_resolution,[status(thm)],[6325, 34167, 90, 1526, 33912])).
% 11.99/12.25 tff(34169,plain,
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% 11.99/12.25 inference(unit_resolution,[status(thm)],[28222, 34168, 11])).
% 11.99/12.25 tff(34170,plain,
% 11.99/12.25 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.25 inference(unit_resolution,[status(thm)],[4039, 34169, 4028, 127, 34091])).
% 11.99/12.25 tff(34171,plain,
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% 11.99/12.26 tff(34173,plain,
% 11.99/12.26 (b(s(s(s(s(z)))), s(z))),
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% 11.99/12.26 inference(rewrite,[status(thm)],[])).
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% 11.99/12.26 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 11.99/12.26 inference(rewrite,[status(thm)],[])).
% 11.99/12.26 tff(34176,plain,
% 11.99/12.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 11.99/12.26 inference(monotonicity,[status(thm)],[34175])).
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% 11.99/12.26 inference(transitivity,[status(thm)],[34176, 34174])).
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% 11.99/12.26 inference(quant_inst,[status(thm)],[])).
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% 11.99/12.26 inference(modus_ponens,[status(thm)],[34178, 34177])).
% 11.99/12.26 tff(34180,plain,
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% 11.99/12.26 inference(unit_resolution,[status(thm)],[34179, 391, 34173, 34111, 34087, 34145, 17636])).
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% 11.99/12.26 tff(34182,plain,
% 11.99/12.26 (~r(s(z), s(s(s(s(z)))))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[34181, 33883, 410, 90, 4028, 127, 11, 31, 59])).
% 11.99/12.26 tff(34183,plain,
% 11.99/12.26 (b(s(z), s(s(s(s(z)))))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[1230, 34182])).
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% 11.99/12.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 11.99/12.26 inference(rewrite,[status(thm)],[])).
% 11.99/12.26 tff(34185,plain,
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% 11.99/12.26 inference(monotonicity,[status(thm)],[34185])).
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% 11.99/12.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 11.99/12.26 inference(transitivity,[status(thm)],[34186, 34184])).
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% 11.99/12.26 inference(quant_inst,[status(thm)],[])).
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% 11.99/12.26 inference(modus_ponens,[status(thm)],[34188, 34187])).
% 11.99/12.26 tff(34190,plain,
% 11.99/12.26 (~r(z, s(s(s(s(z)))))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[34189, 194, 722, 723, 1747])).
% 11.99/12.26 tff(34191,plain,
% 11.99/12.26 (b(z, s(s(s(s(z)))))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[800, 34190])).
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% 11.99/12.26 inference(unit_resolution,[status(thm)],[22664, 34191, 90, 1234])).
% 11.99/12.26 tff(34193,plain,
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% 11.99/12.26 inference(unit_resolution,[status(thm)],[180, 34192])).
% 11.99/12.26 tff(34194,plain,
% 11.99/12.26 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[21621, 34193, 90, 184, 1234, 34191])).
% 11.99/12.26 tff(34195,plain,
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% 11.99/12.26 inference(unit_resolution,[status(thm)],[3652, 34194])).
% 11.99/12.26 tff(34196,plain,
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% 11.99/12.26 inference(unit_resolution,[status(thm)],[9076, 34195, 1747, 723])).
% 11.99/12.26 tff(34197,plain,
% 11.99/12.26 (b(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[1714, 34196])).
% 11.99/12.26 tff(34198,plain,
% 11.99/12.26 (~b(s(s(z)), z)),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[20748, 34197, 90, 34191])).
% 11.99/12.26 tff(34199,plain,
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% 11.99/12.26 inference(unit_resolution,[status(thm)],[1211, 34198])).
% 11.99/12.26 tff(34200,plain,
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% 11.99/12.26 inference(unit_resolution,[status(thm)],[12646, 194, 722, 34193, 34199, 1747])).
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% 11.99/12.26 tff(34202,plain,
% 11.99/12.26 (~r(s(s(s(s(z)))), s(z))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[34201, 1747, 722, 90, 184, 1234])).
% 11.99/12.26 tff(34203,plain,
% 11.99/12.26 (b(s(s(s(s(z)))), s(z))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[749, 34202])).
% 11.99/12.26 tff(34204,plain,
% 11.99/12.26 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[18493, 391, 90, 1234, 34203, 17636])).
% 11.99/12.26 tff(34205,plain,
% 11.99/12.26 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[1673, 34204, 11])).
% 11.99/12.26 tff(34206,plain,
% 11.99/12.26 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.99/12.26 inference(unit_resolution,[status(thm)],[15351, 34205, 32152])).
% 11.99/12.26 tff(34207,plain,
% 11.99/12.26 (r(s(s(s(z))), s(s(s(s(z)))))),
% 11.99/12.27 inference(modus_ponens,[status(thm)],[34206, 17613])).
% 11.99/12.27 tff(34208,plain,
% 11.99/12.27 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[6372, 34203, 1526, 1234, 90])).
% 11.99/12.27 tff(34209,plain,
% 11.99/12.27 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[27316, 34208, 11])).
% 11.99/12.27 tff(34210,plain,
% 11.99/12.27 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[1095, 34209, 310])).
% 11.99/12.27 tff(34211,plain,
% 11.99/12.27 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[29931, 34210, 11])).
% 11.99/12.27 tff(34212,plain,
% 11.99/12.27 (~r(elem!1, s(s(s(s(z)))))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[25443, 34205, 32152, 34211, 410])).
% 11.99/12.27 tff(34213,plain,
% 11.99/12.27 (b(elem!1, s(s(s(s(z)))))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[781, 34212, 33909])).
% 11.99/12.27 tff(34214,plain,
% 11.99/12.27 (b(z, s(s(s(s(z)))))),
% 11.99/12.27 inference(modus_ponens,[status(thm)],[34213, 33907])).
% 11.99/12.27 tff(34215,plain,
% 11.99/12.27 (~b(s(z), elem!1)),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[18869, 34212, 6221, 33683, 1234])).
% 11.99/12.27 tff(34216,plain,
% 11.99/12.27 (r(s(z), elem!1)),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[632, 34215, 24])).
% 11.99/12.27 tff(34217,plain,
% 11.99/12.27 (r(s(z), z)),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[5433, 34216, 17618])).
% 11.99/12.27 tff(34218,assumption,(b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 11.99/12.27 tff(34219,plain,
% 11.99/12.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.99/12.27 inference(rewrite,[status(thm)],[])).
% 11.99/12.27 tff(34220,plain,
% 11.99/12.27 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.99/12.27 inference(rewrite,[status(thm)],[])).
% 11.99/12.27 tff(34221,plain,
% 11.99/12.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 11.99/12.27 inference(monotonicity,[status(thm)],[34220])).
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% 11.99/12.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 11.99/12.27 inference(transitivity,[status(thm)],[34221, 34219])).
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% 11.99/12.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 11.99/12.27 inference(quant_inst,[status(thm)],[])).
% 11.99/12.27 tff(34224,plain,
% 11.99/12.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 11.99/12.27 inference(modus_ponens,[status(thm)],[34223, 34222])).
% 11.99/12.27 tff(34225,plain,
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% 11.99/12.27 inference(unit_resolution,[status(thm)],[34224, 391, 90, 1686, 34218, 23676])).
% 11.99/12.27 tff(34226,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.27 tff(34227,plain,
% 11.99/12.27 (~b(s(s(s(s(s(s(z)))))), z)),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[34226, 23676, 1686, 90])).
% 11.99/12.27 tff(34228,assumption,(~b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 11.99/12.27 tff(34229,assumption,(~r(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 11.99/12.27 tff(34230,plain,
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% 11.99/12.27 inference(unit_resolution,[status(thm)],[6641, 42, 6638, 34229, 34228])).
% 11.99/12.27 tff(34231,plain,(b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)), inference(lemma,lemma(discharge,[]))).
% 11.99/12.27 tff(34232,plain,
% 11.99/12.27 (r(s(s(s(s(s(s(z)))))), z)),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[34231, 34227])).
% 11.99/12.27 tff(34233,plain,
% 11.99/12.27 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[12148, 194, 722, 182, 34232])).
% 11.99/12.27 tff(34234,plain,
% 11.99/12.27 (b(s(s(s(s(s(s(z)))))), s(z))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[14139, 34233])).
% 11.99/12.27 tff(34235,plain,
% 11.99/12.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 11.99/12.27 inference(rewrite,[status(thm)],[])).
% 11.99/12.27 tff(34236,plain,
% 11.99/12.27 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 11.99/12.27 inference(rewrite,[status(thm)],[])).
% 11.99/12.27 tff(34237,plain,
% 11.99/12.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 11.99/12.27 inference(monotonicity,[status(thm)],[34236])).
% 11.99/12.27 tff(34238,plain,
% 11.99/12.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 11.99/12.27 inference(transitivity,[status(thm)],[34237, 34235])).
% 11.99/12.27 tff(34239,plain,
% 11.99/12.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 11.99/12.27 inference(quant_inst,[status(thm)],[])).
% 11.99/12.27 tff(34240,plain,
% 11.99/12.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 11.99/12.27 inference(modus_ponens,[status(thm)],[34239, 34238])).
% 11.99/12.27 tff(34241,plain,
% 11.99/12.27 ($false),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[34240, 391, 90, 1234, 1759, 34234, 23676])).
% 11.99/12.27 tff(34242,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.27 tff(34243,plain,
% 11.99/12.27 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[34242, 34203, 1234, 90, 722, 34217, 34214])).
% 11.99/12.27 tff(34244,plain,
% 11.99/12.27 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[33872, 34243])).
% 11.99/12.27 tff(34245,plain,
% 11.99/12.27 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[21621, 34214, 90, 184, 1234, 34217])).
% 11.99/12.27 tff(34246,plain,
% 11.99/12.27 (r(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[3652, 34245])).
% 11.99/12.27 tff(34247,plain,
% 11.99/12.27 (~r(z, s(s(z)))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[20331, 34246, 1747, 34217])).
% 11.99/12.27 tff(34248,plain,
% 11.99/12.27 (b(z, s(s(z)))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[18613, 34247])).
% 11.99/12.27 tff(34249,plain,
% 11.99/12.27 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 11.99/12.27 inference(transitivity,[status(thm)],[18437, 18436])).
% 11.99/12.27 tff(34250,plain,
% 11.99/12.27 (r(s(elem!1), elem!1)),
% 11.99/12.27 inference(modus_ponens,[status(thm)],[34217, 17627])).
% 11.99/12.27 tff(34251,plain,
% 11.99/12.27 (~r(s(s(elem!1)), elem!1)),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[7546, 34250, 410, 34095])).
% 11.99/12.27 tff(34252,plain,
% 11.99/12.27 (b(s(s(elem!1)), elem!1)),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[872, 34251, 30072])).
% 11.99/12.27 tff(34253,plain,
% 11.99/12.27 (b(s(s(z)), z)),
% 11.99/12.27 inference(modus_ponens,[status(thm)],[34252, 34249])).
% 11.99/12.27 tff(34254,plain,
% 11.99/12.27 (((~b(s(s(z)), z)) | (~b(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))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.99/12.27 inference(rewrite,[status(thm)],[])).
% 11.99/12.27 tff(34255,plain,
% 11.99/12.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z))))))),
% 11.99/12.27 inference(monotonicity,[status(thm)],[34254])).
% 11.99/12.27 tff(34256,plain,
% 11.99/12.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))))),
% 11.99/12.27 inference(transitivity,[status(thm)],[34255, 15046])).
% 11.99/12.27 tff(34257,plain,
% 11.99/12.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(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)))))),
% 11.99/12.27 inference(quant_inst,[status(thm)],[])).
% 11.99/12.27 tff(34258,plain,
% 11.99/12.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z))))),
% 11.99/12.27 inference(modus_ponens,[status(thm)],[34257, 34256])).
% 11.99/12.27 tff(34259,plain,
% 11.99/12.27 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[34258, 391, 90, 34253, 34248])).
% 11.99/12.27 tff(34260,plain,
% 11.99/12.27 (r(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.27 inference(unit_resolution,[status(thm)],[1714, 34259])).
% 11.99/12.27 tff(34261,plain,
% 11.99/12.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.99/12.28 inference(rewrite,[status(thm)],[])).
% 11.99/12.28 tff(34262,plain,
% 11.99/12.28 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(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(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.99/12.28 inference(rewrite,[status(thm)],[])).
% 11.99/12.28 tff(34263,plain,
% 11.99/12.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 11.99/12.28 inference(monotonicity,[status(thm)],[34262])).
% 11.99/12.28 tff(34264,plain,
% 11.99/12.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.99/12.28 inference(transitivity,[status(thm)],[34263, 34261])).
% 11.99/12.28 tff(34265,plain,
% 11.99/12.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.99/12.28 inference(quant_inst,[status(thm)],[])).
% 11.99/12.28 tff(34266,plain,
% 11.99/12.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 11.99/12.28 inference(modus_ponens,[status(thm)],[34265, 34264])).
% 11.99/12.28 tff(34267,plain,
% 11.99/12.28 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 11.99/12.28 inference(unit_resolution,[status(thm)],[34266, 194, 34260, 34244, 34207])).
% 11.99/12.28 tff(34268,plain,
% 11.99/12.28 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 11.99/12.28 inference(unit_resolution,[status(thm)],[29527, 42, 8094, 34267])).
% 11.99/12.28 tff(34269,plain,
% 11.99/12.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 11.99/12.28 inference(rewrite,[status(thm)],[])).
% 11.99/12.28 tff(34270,plain,
% 11.99/12.28 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 11.99/12.28 inference(rewrite,[status(thm)],[])).
% 11.99/12.28 tff(34271,plain,
% 11.99/12.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 11.99/12.28 inference(monotonicity,[status(thm)],[34270])).
% 11.99/12.28 tff(34272,plain,
% 11.99/12.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 11.99/12.28 inference(transitivity,[status(thm)],[34271, 34269])).
% 11.99/12.28 tff(34273,plain,
% 11.99/12.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 11.99/12.28 inference(quant_inst,[status(thm)],[])).
% 11.99/12.28 tff(34274,plain,
% 11.99/12.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 11.99/12.28 inference(modus_ponens,[status(thm)],[34273, 34272])).
% 11.99/12.28 tff(34275,plain,
% 11.99/12.28 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.99/12.28 inference(unit_resolution,[status(thm)],[34274, 194, 34246, 34260, 34244])).
% 11.99/12.28 tff(34276,plain,
% 11.99/12.28 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 11.99/12.28 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 34275])).
% 11.99/12.28 tff(34277,plain,
% 11.99/12.28 (r(s(s(s(s(z)))), s(s(s(z))))),
% 11.99/12.28 inference(unit_resolution,[status(thm)],[32518, 34210, 11])).
% 11.99/12.28 tff(34278,plain,
% 11.99/12.28 (~r(s(s(s(z))), s(s(z)))),
% 11.99/12.28 inference(unit_resolution,[status(thm)],[4480, 194, 34246, 34277, 34207])).
% 11.99/12.28 tff(34279,plain,
% 11.99/12.28 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.28 inference(unit_resolution,[status(thm)],[4385, 34278, 11])).
% 11.99/12.28 tff(34280,plain,
% 11.99/12.28 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.28 inference(unit_resolution,[status(thm)],[1370, 34279, 297])).
% 11.99/12.28 tff(34281,plain,
% 11.99/12.28 (b(s(s(s(z))), s(s(z)))),
% 11.99/12.28 inference(unit_resolution,[status(thm)],[2986, 34280, 11])).
% 11.99/12.28 tff(34282,plain,
% 11.99/12.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 11.99/12.28 inference(rewrite,[status(thm)],[])).
% 11.99/12.28 tff(34283,plain,
% 11.99/12.28 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 11.99/12.28 inference(rewrite,[status(thm)],[])).
% 11.99/12.28 tff(34284,plain,
% 11.99/12.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 11.99/12.28 inference(monotonicity,[status(thm)],[34283])).
% 11.99/12.28 tff(34285,plain,
% 11.99/12.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 11.99/12.29 inference(transitivity,[status(thm)],[34284, 34282])).
% 11.99/12.29 tff(34286,plain,
% 11.99/12.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 11.99/12.29 inference(quant_inst,[status(thm)],[])).
% 11.99/12.29 tff(34287,plain,
% 11.99/12.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 11.99/12.29 inference(modus_ponens,[status(thm)],[34286, 34285])).
% 11.99/12.29 tff(34288,plain,
% 11.99/12.29 (~r(s(s(z)), s(s(s(z))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[34287, 194, 34246, 34277, 34207])).
% 11.99/12.29 tff(34289,plain,
% 11.99/12.29 (b(s(s(z)), s(s(s(z))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[24076, 34288, 8880])).
% 11.99/12.29 tff(34290,plain,
% 11.99/12.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.99/12.29 inference(rewrite,[status(thm)],[])).
% 11.99/12.29 tff(34291,plain,
% 11.99/12.29 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.99/12.29 inference(rewrite,[status(thm)],[])).
% 11.99/12.29 tff(34292,plain,
% 11.99/12.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 11.99/12.29 inference(monotonicity,[status(thm)],[34291])).
% 11.99/12.29 tff(34293,plain,
% 11.99/12.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 11.99/12.29 inference(transitivity,[status(thm)],[34292, 34290])).
% 11.99/12.29 tff(34294,plain,
% 11.99/12.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 11.99/12.29 inference(quant_inst,[status(thm)],[])).
% 11.99/12.29 tff(34295,plain,
% 11.99/12.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 11.99/12.29 inference(modus_ponens,[status(thm)],[34294, 34293])).
% 11.99/12.29 tff(34296,plain,
% 11.99/12.29 ($false),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[34295, 391, 34253, 34289, 34281, 34276, 34268])).
% 11.99/12.29 tff(34297,plain,((~r(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.29 tff(34298,plain,
% 11.99/12.29 (~r(s(z), s(s(z)))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[34297, 34183, 90, 46, 11, 15838, 410, 59, 6221, 33883])).
% 11.99/12.29 tff(34299,plain,
% 11.99/12.29 (b(s(z), s(s(z)))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[1788, 34298])).
% 11.99/12.29 tff(34300,plain,
% 11.99/12.29 (r(elem!1, s(s(s(s(z)))))),
% 11.99/12.29 inference(modus_ponens,[status(thm)],[719, 61])).
% 11.99/12.29 tff(34301,plain,
% 11.99/12.29 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 11.99/12.29 inference(modus_ponens,[status(thm)],[1153, 32151])).
% 11.99/12.29 tff(34302,plain,
% 11.99/12.29 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[6372, 1759, 1526, 1234, 90])).
% 11.99/12.29 tff(34303,plain,
% 11.99/12.29 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[27316, 34302, 11])).
% 11.99/12.29 tff(34304,plain,
% 11.99/12.29 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[1095, 34303, 305])).
% 11.99/12.29 tff(34305,plain,
% 11.99/12.29 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[29931, 34304, 11])).
% 11.99/12.29 tff(34306,plain,
% 11.99/12.29 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[25443, 34305, 34301, 2032, 410])).
% 11.99/12.29 tff(34307,plain,
% 11.99/12.29 (b(s(s(s(z))), s(s(s(s(z)))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[1673, 34306, 11])).
% 11.99/12.29 tff(34308,plain,
% 11.99/12.29 ($false),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[18493, 391, 90, 1234, 1759, 17636, 34307])).
% 11.99/12.29 tff(34309,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.29 tff(34310,plain,
% 11.99/12.29 (~b(s(s(s(s(z)))), s(z))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[34309, 34300, 1234, 11, 90, 410, 310, 1526])).
% 11.99/12.29 tff(34311,plain,
% 11.99/12.29 (r(s(s(s(s(z)))), s(z))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[749, 34310])).
% 11.99/12.29 tff(34312,plain,
% 11.99/12.29 (r(elem!1, s(s(s(s(elem!1)))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[23210, 719, 11])).
% 11.99/12.29 tff(34313,plain,
% 11.99/12.29 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[1090, 327, 410, 1063])).
% 11.99/12.29 tff(34314,plain,
% 11.99/12.29 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[1095, 34313, 305])).
% 11.99/12.29 tff(34315,plain,
% 11.99/12.29 (~r(s(z), s(s(s(elem!1))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[18031, 327, 410, 847])).
% 11.99/12.29 tff(34316,plain,
% 11.99/12.29 (b(s(z), s(s(s(elem!1))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[247, 34315])).
% 11.99/12.29 tff(34317,plain,
% 11.99/12.29 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[20817, 34316, 1526, 1234])).
% 11.99/12.29 tff(34318,plain,
% 11.99/12.29 ($false),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[27316, 34317, 34314, 11])).
% 11.99/12.29 tff(34319,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.29 tff(34320,plain,
% 11.99/12.29 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[34319, 34312, 1526, 1234, 310, 410, 11, 847])).
% 11.99/12.29 tff(34321,plain,
% 11.99/12.29 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[1370, 34320, 297])).
% 11.99/12.29 tff(34322,plain,
% 11.99/12.29 (~b(s(s(elem!1)), s(z))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[1660, 34321, 1234, 33675, 1526])).
% 11.99/12.29 tff(34323,plain,
% 11.99/12.29 (r(s(s(elem!1)), s(z))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[362, 34322])).
% 11.99/12.29 tff(34324,plain,
% 11.99/12.29 (r(s(s(z)), s(z))),
% 11.99/12.29 inference(modus_ponens,[status(thm)],[34323, 18397])).
% 11.99/12.29 tff(34325,plain,
% 11.99/12.29 (~r(elem!1, s(s(z)))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[18451, 10126, 2032, 2405])).
% 11.99/12.29 tff(34326,plain,
% 11.99/12.29 (b(elem!1, s(s(z)))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[3394, 34325, 33689])).
% 11.99/12.29 tff(34327,plain,
% 11.99/12.29 (b(z, s(s(z)))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[3375, 34326, 11])).
% 11.99/12.29 tff(34328,plain,
% 11.99/12.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.99/12.29 inference(rewrite,[status(thm)],[])).
% 11.99/12.29 tff(34329,plain,
% 11.99/12.29 (((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.99/12.29 inference(rewrite,[status(thm)],[])).
% 11.99/12.29 tff(34330,plain,
% 11.99/12.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 11.99/12.29 inference(monotonicity,[status(thm)],[34329])).
% 11.99/12.29 tff(34331,plain,
% 11.99/12.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 11.99/12.29 inference(transitivity,[status(thm)],[34330, 34328])).
% 11.99/12.29 tff(34332,plain,
% 11.99/12.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 11.99/12.29 inference(quant_inst,[status(thm)],[])).
% 11.99/12.29 tff(34333,plain,
% 11.99/12.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 11.99/12.29 inference(modus_ponens,[status(thm)],[34332, 34331])).
% 11.99/12.29 tff(34334,plain,
% 11.99/12.29 ($false),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[34333, 391, 3823, 90, 1234, 2439, 34327])).
% 11.99/12.29 tff(34335,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.29 tff(34336,plain,
% 11.99/12.29 (~b(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[34335, 34300, 1234, 2439, 11, 90, 34324])).
% 11.99/12.29 tff(34337,plain,
% 11.99/12.29 (r(s(s(z)), s(s(s(s(z)))))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[3652, 34336])).
% 11.99/12.29 tff(34338,plain,
% 11.99/12.29 (~r(s(z), elem!1)),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[9149, 34311, 34324, 34337])).
% 11.99/12.29 tff(34339,plain,
% 11.99/12.29 (b(s(z), elem!1)),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[632, 34338, 24])).
% 11.99/12.29 tff(34340,plain,
% 11.99/12.29 (~r(s(z), z)),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[731, 34311, 722, 719])).
% 11.99/12.29 tff(34341,plain,
% 11.99/12.29 (b(s(z), z)),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[180, 34340])).
% 11.99/12.29 tff(34342,plain,
% 11.99/12.29 (~r(z, s(s(elem!1)))),
% 11.99/12.29 inference(unit_resolution,[status(thm)],[18485, 723, 11, 15510, 1373, 29975, 719, 2419, 1374])).
% 11.99/12.30 tff(34343,plain,
% 11.99/12.30 (b(z, s(s(elem!1)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[324, 34342])).
% 11.99/12.30 tff(34344,plain,
% 11.99/12.30 (b(elem!1, s(s(z)))),
% 11.99/12.30 inference(modus_ponens,[status(thm)],[34343, 23194])).
% 11.99/12.30 tff(34345,plain,
% 11.99/12.30 (~r(s(s(z)), z)),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[16406, 723, 719, 1749])).
% 11.99/12.30 tff(34346,plain,
% 11.99/12.30 (b(s(s(z)), z)),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[1211, 34345])).
% 11.99/12.30 tff(34347,plain,
% 11.99/12.30 (~b(z, s(s(z)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[15053, 34346, 90, 3563])).
% 11.99/12.30 tff(34348,plain,
% 11.99/12.30 (~b(elem!1, s(s(z)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[3375, 34347, 11])).
% 11.99/12.30 tff(34349,plain,
% 11.99/12.30 ($false),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[34348, 34344])).
% 11.99/12.30 tff(34350,plain,((~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.30 tff(34351,plain,
% 11.99/12.30 (~b(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[34350, 34311, 90, 11, 15510, 311, 719, 34321, 34337])).
% 11.99/12.30 tff(34352,plain,
% 11.99/12.30 (r(s(s(s(s(z)))), s(s(z)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[1714, 34351])).
% 11.99/12.30 tff(34353,plain,
% 11.99/12.30 (~b(z, s(s(z)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[17567, 16408, 847, 590, 6221, 644, 33689, 1749])).
% 11.99/12.30 tff(34354,plain,
% 11.99/12.30 (r(z, s(s(z)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[18613, 34353])).
% 11.99/12.30 tff(34355,plain,
% 11.99/12.30 (~r(s(s(s(z))), s(s(z)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[30167, 34354, 15510, 1749])).
% 11.99/12.30 tff(34356,plain,
% 11.99/12.30 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[4385, 34355, 11])).
% 11.99/12.30 tff(34357,plain,
% 11.99/12.30 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[1370, 34356, 297])).
% 11.99/12.30 tff(34358,plain,
% 11.99/12.30 (b(s(s(s(elem!1))), s(s(z)))),
% 11.99/12.30 inference(modus_ponens,[status(thm)],[34357, 33708])).
% 11.99/12.30 tff(34359,plain,
% 11.99/12.30 (~b(elem!1, s(s(z)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[3375, 34353, 11])).
% 11.99/12.30 tff(34360,plain,
% 11.99/12.30 (r(elem!1, s(s(z)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[3394, 34359, 33689])).
% 11.99/12.30 tff(34361,plain,
% 11.99/12.30 (~r(s(s(z)), s(z))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[18451, 34360, 34300, 1697])).
% 11.99/12.30 tff(34362,plain,
% 11.99/12.30 (b(s(s(z)), s(z))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[3778, 34361])).
% 11.99/12.30 tff(34363,plain,
% 11.99/12.30 (~b(s(s(s(elem!1))), s(s(z)))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[19018, 34362, 1526, 2439])).
% 11.99/12.30 tff(34364,plain,
% 11.99/12.30 ($false),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[34363, 34358])).
% 11.99/12.30 tff(34365,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(z), z)) | r(s(s(s(s(z)))), elem!1) | (~b(s(z), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.30 tff(34366,plain,
% 11.99/12.30 ($false),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[34365, 34352, 34341, 1526, 2439, 297, 11, 15510, 847, 34337, 6221, 34339, 719, 34311])).
% 11.99/12.30 tff(34367,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~(elem!1 = z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(z))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.30 tff(34368,plain,
% 11.99/12.30 (~r(z, s(s(s(s(z)))))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[34367, 33883, 34299, 15838, 11, 29964, 33641, 6221, 90, 46, 34183, 410])).
% 11.99/12.30 tff(34369,plain,
% 11.99/12.30 (b(z, s(s(s(s(z)))))),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[800, 34368])).
% 11.99/12.30 tff(34370,plain,
% 11.99/12.30 (~b(s(z), z)),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[22664, 34369, 90, 34183])).
% 11.99/12.30 tff(34371,plain,
% 11.99/12.30 (r(s(z), z)),
% 11.99/12.30 inference(unit_resolution,[status(thm)],[180, 34370])).
% 12.09/12.30 tff(34372,plain,
% 12.09/12.30 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[21621, 34371, 90, 59, 34183, 34369])).
% 12.09/12.30 tff(34373,plain,
% 12.09/12.30 (r(s(s(z)), s(s(s(s(z)))))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[3652, 34372])).
% 12.09/12.30 tff(34374,plain,
% 12.09/12.30 (r(s(z), elem!1)),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[8411, 34370, 59, 33641, 30374])).
% 12.09/12.30 tff(34375,plain,
% 12.09/12.30 (b(s(s(s(z))), s(s(z)))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[2986, 1374, 11])).
% 12.09/12.30 tff(34376,plain,
% 12.09/12.30 (~b(s(s(elem!1)), s(z))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[1660, 1374, 1234, 1652, 1526])).
% 12.09/12.30 tff(34377,plain,
% 12.09/12.30 (r(s(s(elem!1)), s(z))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[362, 34376])).
% 12.09/12.30 tff(34378,plain,
% 12.09/12.30 (~r(s(s(elem!1)), elem!1)),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[2379, 34377, 410, 1484])).
% 12.09/12.30 tff(34379,plain,
% 12.09/12.30 (b(s(s(elem!1)), elem!1)),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[872, 34378, 30072])).
% 12.09/12.30 tff(34380,plain,
% 12.09/12.30 (b(s(s(z)), z)),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[34379, 34249])).
% 12.09/12.30 tff(34381,plain,
% 12.09/12.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.09/12.30 inference(rewrite,[status(thm)],[])).
% 12.09/12.30 tff(34382,plain,
% 12.09/12.30 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.09/12.30 inference(rewrite,[status(thm)],[])).
% 12.09/12.30 tff(34383,plain,
% 12.09/12.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 12.09/12.30 inference(monotonicity,[status(thm)],[34382])).
% 12.09/12.30 tff(34384,plain,
% 12.09/12.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.09/12.30 inference(transitivity,[status(thm)],[34383, 34381])).
% 12.09/12.30 tff(34385,plain,
% 12.09/12.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 12.09/12.30 inference(quant_inst,[status(thm)],[])).
% 12.09/12.30 tff(34386,plain,
% 12.09/12.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[34385, 34384])).
% 12.09/12.30 tff(34387,plain,
% 12.09/12.30 ($false),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[34386, 391, 34380, 2439, 1686, 34375, 17636])).
% 12.09/12.30 tff(34388,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.30 tff(34389,plain,
% 12.09/12.30 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[34388, 34299, 34369, 11, 410, 34374, 34183, 33675, 33883])).
% 12.09/12.30 tff(34390,plain,
% 12.09/12.30 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[1370, 34389, 15838])).
% 12.09/12.30 tff(34391,plain,
% 12.09/12.30 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[27316, 34317, 11])).
% 12.09/12.30 tff(34392,plain,
% 12.09/12.30 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[1095, 34391, 305])).
% 12.09/12.30 tff(34393,plain,
% 12.09/12.30 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[29931, 34392, 11])).
% 12.09/12.30 tff(34394,plain,
% 12.09/12.30 ($false),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[17519, 194, 1749, 1697, 2100, 11543])).
% 12.09/12.30 tff(34395,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.30 tff(34396,plain,
% 12.09/12.30 (~r(s(s(s(elem!1))), s(s(z)))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[34395, 34393, 1697, 1749])).
% 12.09/12.30 tff(34397,plain,
% 12.09/12.30 ($false),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[34396, 30153])).
% 12.09/12.30 tff(34398,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.30 tff(34399,plain,
% 12.09/12.30 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[34398, 34390, 11, 34373, 32512, 33883, 34183, 410, 33641])).
% 12.09/12.30 tff(34400,plain,
% 12.09/12.30 (b(s(s(s(s(z)))), s(s(z)))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[1714, 34399])).
% 12.09/12.30 tff(34401,plain,
% 12.09/12.30 (~b(s(s(z)), z)),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[20748, 34400, 90, 34369])).
% 12.09/12.30 tff(34402,plain,
% 12.09/12.30 (r(s(s(z)), z)),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[1211, 34401])).
% 12.09/12.30 tff(34403,plain,
% 12.09/12.30 (r(s(s(elem!1)), elem!1)),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[34402, 30367])).
% 12.09/12.30 tff(34404,plain,
% 12.09/12.30 (b(s(s(s(z))), s(z))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[33883, 17635])).
% 12.09/12.30 tff(34405,plain,
% 12.09/12.30 (~r(s(s(z)), s(z))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[4462, 34402, 46, 34374])).
% 12.09/12.30 tff(34406,plain,
% 12.09/12.30 (b(s(s(z)), s(z))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[3778, 34405])).
% 12.09/12.30 tff(34407,plain,
% 12.09/12.30 (~r(s(s(elem!1)), elem!1)),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[34139, 34406, 410, 34299, 90, 11, 4028, 127, 34369, 34404])).
% 12.09/12.30 tff(34408,plain,
% 12.09/12.30 ($false),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[34407, 34403])).
% 12.09/12.30 tff(34409,plain,(b(elem!1, s(z)) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | r(s(s(s(s(z)))), elem!1) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.30 tff(34410,plain,
% 12.09/12.30 (b(elem!1, s(z))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[34409, 33634, 33627, 90, 33633, 9, 6221, 10])).
% 12.09/12.30 tff(34411,plain,
% 12.09/12.30 (b(z, s(z))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[34410, 33632])).
% 12.09/12.30 tff(34412,plain,
% 12.09/12.30 (b(z, s(z))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[721, 33632])).
% 12.09/12.30 tff(34413,plain,
% 12.09/12.30 (b(s(z), z)),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[31939, 183, 1, 80, 721, 1216, 33633, 34412])).
% 12.09/12.30 tff(34414,plain,
% 12.09/12.30 (s(elem!1) = s(z)),
% 12.09/12.30 inference(monotonicity,[status(thm)],[33627])).
% 12.09/12.30 tff(34415,plain,
% 12.09/12.30 (s(s(elem!1)) = s(s(z))),
% 12.09/12.30 inference(monotonicity,[status(thm)],[34414])).
% 12.09/12.30 tff(34416,plain,
% 12.09/12.30 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 12.09/12.30 inference(monotonicity,[status(thm)],[34415])).
% 12.09/12.30 tff(34417,plain,
% 12.09/12.30 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 12.09/12.30 inference(monotonicity,[status(thm)],[33627])).
% 12.09/12.30 tff(34418,plain,
% 12.09/12.30 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), z)),
% 12.09/12.30 inference(transitivity,[status(thm)],[34417, 34416])).
% 12.09/12.30 tff(34419,plain,
% 12.09/12.30 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 12.09/12.30 inference(monotonicity,[status(thm)],[33627])).
% 12.09/12.30 tff(34420,plain,
% 12.09/12.30 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 12.09/12.30 inference(symmetry,[status(thm)],[34419])).
% 12.09/12.30 tff(34421,plain,
% 12.09/12.30 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 12.09/12.30 inference(monotonicity,[status(thm)],[34420])).
% 12.09/12.30 tff(34422,plain,
% 12.09/12.30 (~(s(s(elem!1)) = elem!1)),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[215, 34421])).
% 12.09/12.30 tff(34423,plain,
% 12.09/12.30 (~r(elem!1, s(z))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[10776, 183, 33634, 1216])).
% 12.09/12.30 tff(34424,plain,
% 12.09/12.30 (~r(z, s(elem!1))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[8832, 34423, 33627])).
% 12.09/12.30 tff(34425,plain,
% 12.09/12.30 (~r(elem!1, s(elem!1))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[2288, 34424, 33627])).
% 12.09/12.30 tff(34426,plain,
% 12.09/12.30 (s(s(s(elem!1))) = s(s(s(z)))),
% 12.09/12.30 inference(monotonicity,[status(thm)],[34415])).
% 12.09/12.30 tff(34427,plain,
% 12.09/12.30 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 12.09/12.30 inference(monotonicity,[status(thm)],[34426])).
% 12.09/12.30 tff(34428,plain,
% 12.09/12.30 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 12.09/12.30 inference(monotonicity,[status(thm)],[34426, 34427])).
% 12.09/12.30 tff(34429,plain,
% 12.09/12.30 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 12.09/12.30 inference(transitivity,[status(thm)],[34428, 32147])).
% 12.09/12.30 tff(34430,plain,
% 12.09/12.30 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 12.09/12.30 inference(monotonicity,[status(thm)],[34429])).
% 12.09/12.30 tff(34431,plain,
% 12.09/12.30 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[32322, 34430])).
% 12.09/12.30 tff(34432,plain,
% 12.09/12.30 (~r(s(s(s(elem!1))), elem!1)),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[406, 329, 11])).
% 12.09/12.30 tff(34433,plain,
% 12.09/12.30 (b(s(s(s(elem!1))), elem!1)),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[230, 34432, 127])).
% 12.09/12.30 tff(34434,plain,
% 12.09/12.30 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 12.09/12.30 inference(monotonicity,[status(thm)],[11])).
% 12.09/12.30 tff(34435,plain,
% 12.09/12.30 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 12.09/12.30 inference(symmetry,[status(thm)],[34434])).
% 12.09/12.30 tff(34436,plain,
% 12.09/12.30 (b(z, s(z)) <=> b(z, s(elem!1))),
% 12.09/12.30 inference(symmetry,[status(thm)],[32224])).
% 12.09/12.30 tff(34437,plain,
% 12.09/12.30 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 12.09/12.30 inference(transitivity,[status(thm)],[34436, 34435])).
% 12.09/12.30 tff(34438,plain,
% 12.09/12.30 (b(elem!1, s(elem!1))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[664, 34437])).
% 12.09/12.30 tff(34439,plain,
% 12.09/12.30 (b(z, s(z)) <=> b(elem!1, s(z))),
% 12.09/12.30 inference(symmetry,[status(thm)],[29])).
% 12.09/12.30 tff(34440,plain,
% 12.09/12.30 (b(elem!1, s(z))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[664, 34439])).
% 12.09/12.30 tff(34441,plain,
% 12.09/12.30 (b(s(z), elem!1) <=> b(s(z), z)),
% 12.09/12.30 inference(monotonicity,[status(thm)],[11])).
% 12.09/12.30 tff(34442,plain,
% 12.09/12.30 (b(s(z), z) <=> b(s(z), elem!1)),
% 12.09/12.30 inference(symmetry,[status(thm)],[34441])).
% 12.09/12.30 tff(34443,plain,
% 12.09/12.30 (b(z, s(s(elem!1)))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[3924, 91, 10, 297])).
% 12.09/12.30 tff(34444,plain,
% 12.09/12.30 (b(elem!1, s(s(elem!1)))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[34443, 30009])).
% 12.09/12.30 tff(34445,plain,
% 12.09/12.30 (b(s(s(s(z))), z)),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[1680, 380, 11])).
% 12.09/12.30 tff(34446,plain,
% 12.09/12.30 (b(z, s(s(z)))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[34443, 3367])).
% 12.09/12.30 tff(34447,plain,
% 12.09/12.30 (b(s(z), s(s(s(z))))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[339, 18545])).
% 12.09/12.30 tff(34448,plain,
% 12.09/12.30 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 12.09/12.30 inference(symmetry,[status(thm)],[30313])).
% 12.09/12.30 tff(34449,plain,
% 12.09/12.30 (~b(s(s(s(elem!1))), s(z))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[2907, 339, 34440, 900])).
% 12.09/12.30 tff(34450,plain,
% 12.09/12.30 (r(s(s(s(elem!1))), s(z))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[223, 34449])).
% 12.09/12.30 tff(34451,plain,
% 12.09/12.30 (~r(s(s(elem!1)), s(z))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[11169, 34450, 1216, 327])).
% 12.09/12.30 tff(34452,plain,
% 12.09/12.30 (b(s(s(elem!1)), s(z))),
% 12.09/12.30 inference(unit_resolution,[status(thm)],[362, 34451])).
% 12.09/12.30 tff(34453,plain,
% 12.09/12.30 (b(s(s(z)), s(z))),
% 12.09/12.30 inference(modus_ponens,[status(thm)],[34452, 34448])).
% 12.09/12.30 tff(34454,plain,
% 12.09/12.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 12.09/12.31 inference(rewrite,[status(thm)],[])).
% 12.09/12.31 tff(34455,plain,
% 12.09/12.31 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 12.09/12.31 inference(rewrite,[status(thm)],[])).
% 12.09/12.31 tff(34456,plain,
% 12.09/12.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 12.09/12.31 inference(monotonicity,[status(thm)],[34455])).
% 12.09/12.31 tff(34457,plain,
% 12.09/12.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 12.09/12.31 inference(transitivity,[status(thm)],[34456, 34454])).
% 12.09/12.31 tff(34458,plain,
% 12.09/12.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 12.09/12.31 inference(quant_inst,[status(thm)],[])).
% 12.09/12.31 tff(34459,plain,
% 12.09/12.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 12.09/12.31 inference(modus_ponens,[status(thm)],[34458, 34457])).
% 12.09/12.31 tff(34460,plain,
% 12.09/12.31 ($false),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[34459, 391, 34453, 664, 15045, 34447, 1685])).
% 12.09/12.31 tff(34461,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~(elem!1 = z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.31 tff(34462,plain,
% 12.09/12.31 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[34461, 34446, 664, 34445, 11, 1216, 900, 59, 181])).
% 12.09/12.31 tff(34463,plain,
% 12.09/12.31 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[1370, 34462, 297])).
% 12.09/12.31 tff(34464,plain,
% 12.09/12.31 (~b(s(s(elem!1)), elem!1)),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[1467, 34463, 900, 34444])).
% 12.09/12.31 tff(34465,plain,
% 12.09/12.31 (r(s(s(elem!1)), elem!1)),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[872, 34464, 30072])).
% 12.09/12.31 tff(34466,plain,
% 12.09/12.31 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[4893, 34463, 34443, 380])).
% 12.09/12.31 tff(34467,plain,
% 12.09/12.31 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[1356, 34466, 315])).
% 12.09/12.31 tff(34468,plain,
% 12.09/12.31 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[25719, 34467, 410, 34465])).
% 12.09/12.31 tff(34469,plain,
% 12.09/12.31 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[1164, 34468, 17616])).
% 12.09/12.31 tff(34470,plain,
% 12.09/12.31 (b(s(s(s(z))), s(s(s(s(z)))))),
% 12.09/12.31 inference(modus_ponens,[status(thm)],[34469, 3504])).
% 12.09/12.31 tff(34471,plain,
% 12.09/12.31 (r(s(z), elem!1)),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[3205, 91, 11])).
% 12.09/12.31 tff(34472,plain,
% 12.09/12.31 (~r(s(s(elem!1)), s(z))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[2379, 34465, 410, 34471])).
% 12.09/12.31 tff(34473,plain,
% 12.09/12.31 (b(s(s(elem!1)), s(z))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[362, 34472])).
% 12.09/12.31 tff(34474,plain,
% 12.09/12.31 (b(s(s(z)), s(z))),
% 12.09/12.31 inference(modus_ponens,[status(thm)],[34473, 34448])).
% 12.09/12.31 tff(34475,plain,
% 12.09/12.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 12.09/12.31 inference(rewrite,[status(thm)],[])).
% 12.09/12.31 tff(34476,plain,
% 12.09/12.31 (((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 12.09/12.31 inference(rewrite,[status(thm)],[])).
% 12.09/12.31 tff(34477,plain,
% 12.09/12.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 12.09/12.31 inference(monotonicity,[status(thm)],[34476])).
% 12.09/12.31 tff(34478,plain,
% 12.09/12.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 12.09/12.31 inference(transitivity,[status(thm)],[34477, 34475])).
% 12.09/12.31 tff(34479,plain,
% 12.09/12.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 12.09/12.31 inference(quant_inst,[status(thm)],[])).
% 12.09/12.31 tff(34480,plain,
% 12.09/12.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 12.09/12.31 inference(modus_ponens,[status(thm)],[34479, 34478])).
% 12.09/12.31 tff(34481,plain,
% 12.09/12.31 ($false),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[34480, 391, 90, 34474, 34446, 34445, 34470])).
% 12.09/12.31 tff(34482,plain,(b(s(z), z) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.31 tff(34483,plain,
% 12.09/12.31 (b(s(z), z)),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[34482, 1216, 11, 410, 380, 900, 297, 664, 90, 10])).
% 12.09/12.31 tff(34484,plain,
% 12.09/12.31 (b(s(z), elem!1)),
% 12.09/12.31 inference(modus_ponens,[status(thm)],[34483, 34442])).
% 12.09/12.31 tff(34485,plain,
% 12.09/12.31 (~b(s(s(s(elem!1))), s(z))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[20387, 34484, 34440, 900])).
% 12.09/12.31 tff(34486,plain,
% 12.09/12.31 (r(s(s(s(elem!1))), s(z))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[223, 34485])).
% 12.09/12.31 tff(34487,plain,
% 12.09/12.31 (r(s(s(s(z))), s(z))),
% 12.09/12.31 inference(unit_resolution,[status(thm)],[29740, 34486, 11])).
% 12.09/12.31 tff(34488,plain,
% 12.09/12.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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))))))),
% 12.09/12.32 inference(rewrite,[status(thm)],[])).
% 12.09/12.32 tff(34489,plain,
% 12.09/12.32 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(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))))))),
% 12.09/12.32 inference(rewrite,[status(thm)],[])).
% 12.09/12.32 tff(34490,plain,
% 12.09/12.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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)))))))),
% 12.09/12.32 inference(monotonicity,[status(thm)],[34489])).
% 12.09/12.32 tff(34491,plain,
% 12.09/12.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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))))))),
% 12.09/12.32 inference(transitivity,[status(thm)],[34490, 34488])).
% 12.09/12.32 tff(34492,plain,
% 12.09/12.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 12.09/12.32 inference(quant_inst,[status(thm)],[])).
% 12.09/12.32 tff(34493,plain,
% 12.09/12.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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)))))),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[34492, 34491])).
% 12.09/12.32 tff(34494,plain,
% 12.09/12.32 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[34493, 391, 90, 664, 34483, 34445])).
% 12.09/12.32 tff(34495,plain,
% 12.09/12.32 (r(s(s(s(s(z)))), s(s(s(z))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[4426, 42, 34494, 4414])).
% 12.09/12.32 tff(34496,plain,
% 12.09/12.32 (~b(s(s(s(s(z)))), s(z))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[5575, 391, 90, 664, 34483])).
% 12.09/12.32 tff(34497,plain,
% 12.09/12.32 (r(s(s(s(s(z)))), s(z))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[749, 34496])).
% 12.09/12.32 tff(34498,plain,
% 12.09/12.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 12.09/12.32 inference(rewrite,[status(thm)],[])).
% 12.09/12.32 tff(34499,plain,
% 12.09/12.32 (((~r(s(z), s(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)))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 12.09/12.32 inference(rewrite,[status(thm)],[])).
% 12.09/12.32 tff(34500,plain,
% 12.09/12.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 12.09/12.32 inference(monotonicity,[status(thm)],[34499])).
% 12.09/12.32 tff(34501,plain,
% 12.09/12.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 12.09/12.32 inference(transitivity,[status(thm)],[34500, 34498])).
% 12.09/12.32 tff(34502,plain,
% 12.09/12.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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))))))),
% 12.09/12.32 inference(quant_inst,[status(thm)],[])).
% 12.09/12.32 tff(34503,plain,
% 12.09/12.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[34502, 34501])).
% 12.09/12.32 tff(34504,plain,
% 12.09/12.32 ($false),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[34503, 194, 1216, 34497, 34495, 34487])).
% 12.09/12.32 tff(34505,plain,((~r(s(z), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(z)))) | (~(elem!1 = z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.32 tff(34506,plain,
% 12.09/12.32 (~r(s(z), s(s(s(s(z)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[34505, 34433, 11, 4414, 90, 664, 410, 378, 15838, 10])).
% 12.09/12.32 tff(34507,plain,
% 12.09/12.32 (b(s(z), s(s(s(s(z)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[1230, 34506])).
% 12.09/12.32 tff(34508,plain,
% 12.09/12.32 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 12.09/12.32 inference(monotonicity,[status(thm)],[932])).
% 12.09/12.32 tff(34509,plain,
% 12.09/12.32 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 12.09/12.32 inference(monotonicity,[status(thm)],[94])).
% 12.09/12.32 tff(34510,plain,
% 12.09/12.32 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 12.09/12.32 inference(transitivity,[status(thm)],[34509, 34508])).
% 12.09/12.32 tff(34511,plain,
% 12.09/12.32 ((s(z) = z) <=> (s(z) = elem!1)),
% 12.09/12.32 inference(monotonicity,[status(thm)],[94])).
% 12.09/12.32 tff(34512,plain,
% 12.09/12.32 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 12.09/12.32 inference(monotonicity,[status(thm)],[34511])).
% 12.09/12.32 tff(34513,plain,
% 12.09/12.32 (~(s(z) = elem!1)),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[23, 34512])).
% 12.09/12.32 tff(34514,plain,
% 12.09/12.32 (r(s(z), elem!1)),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[632, 2829, 34513])).
% 12.09/12.32 tff(34515,plain,
% 12.09/12.32 (r(s(z), z)),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[5433, 34514, 94])).
% 12.09/12.32 tff(34516,plain,
% 12.09/12.32 (b(z, s(z)) <=> b(elem!1, s(z))),
% 12.09/12.32 inference(monotonicity,[status(thm)],[94])).
% 12.09/12.32 tff(34517,plain,
% 12.09/12.32 (b(elem!1, s(z))),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[664, 34516])).
% 12.09/12.32 tff(34518,plain,
% 12.09/12.32 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 12.09/12.32 inference(monotonicity,[status(thm)],[94])).
% 12.09/12.32 tff(34519,plain,
% 12.09/12.32 (r(s(s(s(s(z)))), elem!1)),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[3447, 34518])).
% 12.09/12.32 tff(34520,plain,
% 12.09/12.32 (~r(z, s(s(s(s(z)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[10261, 3557, 2053, 182])).
% 12.09/12.32 tff(34521,plain,
% 12.09/12.32 (b(z, s(s(s(s(z)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[800, 34520])).
% 12.09/12.32 tff(34522,plain,
% 12.09/12.32 (~b(s(s(s(s(z)))), s(z))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[10478, 34521, 1234, 664])).
% 12.09/12.32 tff(34523,plain,
% 12.09/12.32 (r(s(s(s(s(z)))), s(z))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[749, 34522])).
% 12.09/12.32 tff(34524,plain,
% 12.09/12.32 (~b(s(s(s(s(z)))), elem!1)),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[9977, 34521, 1234, 664, 721])).
% 12.09/12.32 tff(34525,plain,
% 12.09/12.32 (b(elem!1, s(s(s(s(z)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[9108, 34523, 8922, 1484, 34524])).
% 12.09/12.32 tff(34526,plain,
% 12.09/12.32 (~r(elem!1, s(s(z)))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[9117, 34523, 1484, 2112])).
% 12.09/12.32 tff(34527,plain,
% 12.09/12.32 (b(elem!1, s(s(z)))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[3394, 34526, 1405])).
% 12.09/12.32 tff(34528,plain,
% 12.09/12.32 ($false),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[9187, 34527, 34525, 1484, 1234, 721, 3557, 34523])).
% 12.09/12.32 tff(34529,plain,((~r(s(s(z)), z)) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (elem!1 = s(s(z))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.32 tff(34530,plain,
% 12.09/12.32 (~r(s(s(z)), z)),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[34529, 34519, 1234, 34517, 23151, 32511, 34514, 664, 3447, 34515])).
% 12.09/12.32 tff(34531,plain,
% 12.09/12.32 (b(s(s(z)), z)),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[1211, 34530])).
% 12.09/12.32 tff(34532,plain,
% 12.09/12.32 (b(s(s(elem!1)), elem!1)),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[34531, 34510])).
% 12.09/12.32 tff(34533,plain,
% 12.09/12.32 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 12.09/12.32 inference(transitivity,[status(thm)],[23139, 23138])).
% 12.09/12.32 tff(34534,plain,
% 12.09/12.32 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 12.09/12.32 inference(transitivity,[status(thm)],[34518, 32326])).
% 12.09/12.32 tff(34535,plain,
% 12.09/12.32 (r(s(s(s(s(elem!1)))), elem!1)),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[3447, 34534])).
% 12.09/12.32 tff(34536,plain,
% 12.09/12.32 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 12.09/12.32 inference(monotonicity,[status(thm)],[935])).
% 12.09/12.32 tff(34537,plain,
% 12.09/12.32 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.09/12.32 inference(symmetry,[status(thm)],[34536])).
% 12.09/12.32 tff(34538,plain,
% 12.09/12.32 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 12.09/12.32 inference(monotonicity,[status(thm)],[931])).
% 12.09/12.32 tff(34539,plain,
% 12.09/12.32 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.09/12.32 inference(transitivity,[status(thm)],[34538, 34537])).
% 12.09/12.32 tff(34540,plain,
% 12.09/12.32 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[723, 34539])).
% 12.09/12.32 tff(34541,plain,
% 12.09/12.32 (r(s(elem!1), elem!1)),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[34514, 958])).
% 12.09/12.32 tff(34542,plain,
% 12.09/12.32 (~r(elem!1, s(s(z)))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[9117, 723, 34514, 2112])).
% 12.09/12.32 tff(34543,plain,
% 12.09/12.32 (b(elem!1, s(s(z)))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[3394, 34542, 23151])).
% 12.09/12.32 tff(34544,plain,
% 12.09/12.32 (~r(elem!1, s(s(s(s(z)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[9103, 723, 2112, 34514])).
% 12.09/12.32 tff(34545,plain,
% 12.09/12.32 (b(elem!1, s(s(s(s(z)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[781, 34544, 32511])).
% 12.09/12.32 tff(34546,plain,
% 12.09/12.32 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[9171, 34543, 34514, 1234, 721, 723, 34545])).
% 12.09/12.32 tff(34547,plain,
% 12.09/12.32 (b(s(s(z)), s(s(s(s(z)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[3652, 34546])).
% 12.09/12.32 tff(34548,plain,
% 12.09/12.32 (~b(s(z), s(s(z)))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[10152, 34547, 832, 23151, 34513, 1234, 2829, 723])).
% 12.09/12.32 tff(34549,plain,
% 12.09/12.32 (r(s(z), s(s(z)))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[1788, 34548])).
% 12.09/12.32 tff(34550,plain,
% 12.09/12.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[9127, 34547, 34545, 34543])).
% 12.09/12.32 tff(34551,plain,
% 12.09/12.32 (r(s(s(s(s(z)))), s(s(z)))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[1714, 34550])).
% 12.09/12.32 tff(34552,plain,
% 12.09/12.32 (~r(s(s(z)), s(s(s(elem!1))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[9138, 34551, 723, 34549])).
% 12.09/12.32 tff(34553,plain,
% 12.09/12.32 (b(s(s(z)), s(s(s(elem!1))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[11041, 34552])).
% 12.09/12.32 tff(34554,plain,
% 12.09/12.32 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 12.09/12.32 inference(monotonicity,[status(thm)],[94])).
% 12.09/12.32 tff(34555,plain,
% 12.09/12.32 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 12.09/12.32 inference(transitivity,[status(thm)],[34554, 4])).
% 12.09/12.32 tff(34556,plain,
% 12.09/12.32 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 12.09/12.32 inference(monotonicity,[status(thm)],[34555])).
% 12.09/12.32 tff(34557,plain,
% 12.09/12.32 (~(elem!1 = s(s(s(elem!1))))),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[50, 34556])).
% 12.09/12.32 tff(34558,plain,
% 12.09/12.32 (~r(elem!1, s(s(s(elem!1))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[999, 34540, 34541, 991])).
% 12.09/12.32 tff(34559,plain,
% 12.09/12.32 (b(elem!1, s(s(s(elem!1))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[424, 34558, 34557])).
% 12.09/12.32 tff(34560,plain,
% 12.09/12.32 (~b(s(s(s(elem!1))), s(z))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[8561, 34559, 1234, 34553, 34543])).
% 12.09/12.32 tff(34561,plain,
% 12.09/12.32 (r(s(s(s(elem!1))), s(z))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[223, 34560])).
% 12.09/12.32 tff(34562,plain,
% 12.09/12.32 (r(s(s(s(elem!1))), s(elem!1))),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[34561, 32331])).
% 12.09/12.32 tff(34563,plain,
% 12.09/12.32 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[1149, 194, 34562, 34541, 34540])).
% 12.09/12.32 tff(34564,plain,
% 12.09/12.32 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[1095, 34563, 32385])).
% 12.09/12.32 tff(34565,plain,
% 12.09/12.32 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[1159, 194, 34562, 34541, 34540])).
% 12.09/12.32 tff(34566,plain,
% 12.09/12.32 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[1164, 34565, 32386])).
% 12.09/12.32 tff(34567,plain,
% 12.09/12.32 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 12.09/12.32 inference(monotonicity,[status(thm)],[934])).
% 12.09/12.32 tff(34568,plain,
% 12.09/12.32 (b(elem!1, s(s(s(s(elem!1)))))),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[34545, 34567])).
% 12.09/12.32 tff(34569,plain,
% 12.09/12.32 ($false),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[14248, 391, 34559, 34568, 34566, 34564])).
% 12.09/12.32 tff(34570,plain,((~r(s(s(s(s(z)))), s(z))) | (~(z = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | r(elem!1, s(z)) | b(s(z), elem!1) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.32 tff(34571,plain,
% 12.09/12.32 (~r(s(s(s(s(z)))), s(z))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[34570, 34535, 1234, 94, 832, 2829, 34517, 34519])).
% 12.09/12.32 tff(34572,plain,
% 12.09/12.32 (b(s(s(s(s(z)))), s(z))),
% 12.09/12.32 inference(unit_resolution,[status(thm)],[749, 34571])).
% 12.09/12.32 tff(34573,plain,
% 12.09/12.32 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[34572, 34533])).
% 12.09/12.32 tff(34574,plain,
% 12.09/12.32 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 12.09/12.32 inference(monotonicity,[status(thm)],[935])).
% 12.09/12.32 tff(34575,plain,
% 12.09/12.32 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 12.09/12.32 inference(symmetry,[status(thm)],[34574])).
% 12.09/12.32 tff(34576,plain,
% 12.09/12.32 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 12.09/12.32 inference(monotonicity,[status(thm)],[931])).
% 12.09/12.32 tff(34577,plain,
% 12.09/12.32 (b(s(elem!1), s(s(s(s(z)))))),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[1234, 34576])).
% 12.09/12.32 tff(34578,plain,
% 12.09/12.32 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 12.09/12.32 inference(modus_ponens,[status(thm)],[34577, 34575])).
% 12.09/12.32 tff(34579,plain,
% 12.09/12.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 12.09/12.32 inference(rewrite,[status(thm)],[])).
% 12.09/12.32 tff(34580,plain,
% 12.09/12.32 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 12.09/12.32 inference(rewrite,[status(thm)],[])).
% 12.09/12.32 tff(34581,plain,
% 12.09/12.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 12.09/12.33 inference(monotonicity,[status(thm)],[34580])).
% 12.09/12.33 tff(34582,plain,
% 12.09/12.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 12.09/12.33 inference(transitivity,[status(thm)],[34581, 34579])).
% 12.09/12.33 tff(34583,plain,
% 12.09/12.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 12.09/12.33 inference(quant_inst,[status(thm)],[])).
% 12.09/12.33 tff(34584,plain,
% 12.09/12.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 12.09/12.33 inference(modus_ponens,[status(thm)],[34583, 34582])).
% 12.09/12.33 tff(34585,plain,
% 12.09/12.33 ($false),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[34584, 391, 973, 802, 1037, 17974, 975])).
% 12.09/12.33 tff(34586,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.33 tff(34587,plain,
% 12.09/12.33 (~b(s(s(elem!1)), s(elem!1))),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[34586, 34532, 802, 34578, 34573])).
% 12.09/12.33 tff(34588,plain,
% 12.09/12.33 (r(s(s(elem!1)), s(elem!1))),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[1135, 34587, 1081])).
% 12.09/12.33 tff(34589,plain,
% 12.09/12.33 (~b(elem!1, s(s(s(elem!1))))),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[8846, 10, 1027])).
% 12.09/12.33 tff(34590,plain,
% 12.09/12.33 (b(s(s(s(elem!1))), elem!1)),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[8856, 34589, 34557, 34514, 34513, 3447, 10])).
% 12.09/12.33 tff(34591,plain,
% 12.09/12.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.09/12.33 inference(rewrite,[status(thm)],[])).
% 12.09/12.33 tff(34592,plain,
% 12.09/12.33 (((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.09/12.33 inference(rewrite,[status(thm)],[])).
% 12.09/12.33 tff(34593,plain,
% 12.09/12.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.09/12.33 inference(monotonicity,[status(thm)],[34592])).
% 12.09/12.33 tff(34594,plain,
% 12.09/12.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.09/12.33 inference(transitivity,[status(thm)],[34593, 34591])).
% 12.09/12.33 tff(34595,plain,
% 12.09/12.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 12.09/12.33 inference(quant_inst,[status(thm)],[])).
% 12.09/12.33 tff(34596,plain,
% 12.09/12.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z))))))),
% 12.09/12.33 inference(modus_ponens,[status(thm)],[34595, 34594])).
% 12.09/12.33 tff(34597,plain,
% 12.09/12.33 ($false),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[34596, 391, 900, 973, 1374, 1234, 721])).
% 12.09/12.33 tff(34598,plain,((~b(s(z), s(s(s(s(z)))))) | (~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(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.33 tff(34599,plain,
% 12.09/12.33 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[34598, 34590, 1234, 721, 973])).
% 12.09/12.33 tff(34600,plain,
% 12.09/12.33 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[1370, 34599, 27398])).
% 12.09/12.33 tff(34601,plain,
% 12.09/12.33 (r(s(s(s(elem!1))), s(z))),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[10383, 10, 832, 1234, 2829, 3446])).
% 12.09/12.33 tff(34602,plain,
% 12.09/12.33 (r(s(s(s(elem!1))), s(elem!1))),
% 12.09/12.33 inference(modus_ponens,[status(thm)],[34601, 32331])).
% 12.09/12.33 tff(34603,plain,
% 12.09/12.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 12.09/12.33 inference(rewrite,[status(thm)],[])).
% 12.09/12.33 tff(34604,plain,
% 12.09/12.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 12.09/12.33 inference(quant_inst,[status(thm)],[])).
% 12.09/12.33 tff(34605,plain,
% 12.09/12.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 12.09/12.33 inference(modus_ponens,[status(thm)],[34604, 34603])).
% 12.09/12.33 tff(34606,plain,
% 12.09/12.33 ($false),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[34605, 194, 34602, 34541, 34600, 2170])).
% 12.09/12.33 tff(34607,plain,(b(z, s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | r(elem!1, s(z)) | b(s(z), elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 12.09/12.33 tff(34608,plain,
% 12.09/12.33 (b(z, s(s(s(elem!1))))),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[34607, 34588, 94, 1234, 34517, 34532, 832, 2829, 3446])).
% 12.09/12.33 tff(34609,plain,
% 12.09/12.33 (~b(z, s(s(s(s(z)))))),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[10478, 34572, 1234, 664])).
% 12.09/12.33 tff(34610,plain,
% 12.09/12.33 (r(z, s(s(s(s(z)))))),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[800, 34609])).
% 12.09/12.33 tff(34611,plain,
% 12.09/12.33 (r(elem!1, s(s(s(s(elem!1)))))),
% 12.09/12.33 inference(unit_resolution,[status(thm)],[23210, 34610, 1027])).
% 12.09/12.33 tff(34612,plain,
% 12.09/12.33 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[34554])).
% 12.09/12.34 tff(34613,plain,
% 12.09/12.34 (~(s(s(s(elem!1))) = elem!1)),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[50, 34612])).
% 12.09/12.34 tff(34614,plain,
% 12.09/12.34 (~b(s(z), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[15561, 1526, 664, 10682])).
% 12.09/12.34 tff(34615,plain,
% 12.09/12.34 (r(s(z), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[247, 34614])).
% 12.09/12.34 tff(34616,plain,
% 12.09/12.34 (~r(s(s(s(elem!1))), elem!1)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[14585, 34615, 1484, 1063])).
% 12.09/12.34 tff(34617,plain,
% 12.09/12.34 (b(s(s(s(elem!1))), elem!1)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[230, 34616, 34613])).
% 12.09/12.34 tff(34618,plain,
% 12.09/12.34 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[931])).
% 12.09/12.34 tff(34619,plain,
% 12.09/12.34 (b(s(s(s(elem!1))), s(elem!1))),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[1526, 34618])).
% 12.09/12.34 tff(34620,plain,
% 12.09/12.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 12.09/12.34 inference(rewrite,[status(thm)],[])).
% 12.09/12.34 tff(34621,plain,
% 12.09/12.34 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(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))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 12.09/12.34 inference(rewrite,[status(thm)],[])).
% 12.09/12.34 tff(34622,plain,
% 12.09/12.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[34621])).
% 12.09/12.34 tff(34623,plain,
% 12.09/12.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 12.09/12.34 inference(transitivity,[status(thm)],[34622, 34620])).
% 12.09/12.34 tff(34624,plain,
% 12.09/12.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 12.09/12.34 inference(quant_inst,[status(thm)],[])).
% 12.09/12.34 tff(34625,plain,
% 12.09/12.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34624, 34623])).
% 12.09/12.34 tff(34626,plain,
% 12.09/12.34 ($false),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[34625, 391, 34619, 34617, 802, 17974, 975])).
% 12.09/12.34 tff(34627,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~(z = elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.34 tff(34628,plain,
% 12.09/12.34 (~b(s(s(s(elem!1))), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[34627, 34573, 34578, 802, 94, 34514, 34611, 664, 34608])).
% 12.09/12.34 tff(34629,plain,
% 12.09/12.34 (r(s(s(s(elem!1))), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[223, 34628])).
% 12.09/12.34 tff(34630,plain,
% 12.09/12.34 (~b(s(s(elem!1)), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[1033, 34587, 1027])).
% 12.09/12.34 tff(34631,plain,
% 12.09/12.34 (r(s(s(elem!1)), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[362, 34630])).
% 12.09/12.34 tff(34632,plain,
% 12.09/12.34 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 12.09/12.34 inference(monotonicity,[status(thm)],[94])).
% 12.09/12.34 tff(34633,plain,
% 12.09/12.34 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 12.09/12.34 inference(symmetry,[status(thm)],[34632])).
% 12.09/12.34 tff(34634,plain,
% 12.09/12.34 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 12.09/12.34 inference(transitivity,[status(thm)],[34509, 34508, 34633])).
% 12.09/12.34 tff(34635,plain,
% 12.09/12.34 (b(s(s(elem!1)), z)),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34531, 34634])).
% 12.09/12.34 tff(34636,plain,
% 12.09/12.34 (b(elem!1, s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[23154, 34608, 1027])).
% 12.09/12.34 tff(34637,plain,
% 12.09/12.34 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[932, 931])).
% 12.09/12.34 tff(34638,plain,
% 12.09/12.34 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 12.09/12.34 inference(symmetry,[status(thm)],[34637])).
% 12.09/12.34 tff(34639,plain,
% 12.09/12.34 (r(s(s(z)), s(z))),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34588, 34638])).
% 12.09/12.34 tff(34640,plain,
% 12.09/12.34 (~b(elem!1, s(s(z)))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[10933, 34629, 34639, 34636, 34514])).
% 12.09/12.34 tff(34641,plain,
% 12.09/12.34 (r(elem!1, s(s(z)))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[3394, 34640, 23151])).
% 12.09/12.34 tff(34642,plain,
% 12.09/12.34 (~r(s(s(s(elem!1))), elem!1)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[14370, 34641, 34514, 34517, 34636])).
% 12.09/12.34 tff(34643,plain,
% 12.09/12.34 (b(s(s(s(elem!1))), elem!1)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[230, 34642, 34613])).
% 12.09/12.34 tff(34644,plain,
% 12.09/12.34 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[25637, 34643, 34635, 34608, 802])).
% 12.09/12.34 tff(34645,plain,
% 12.09/12.34 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[1356, 34644, 27414])).
% 12.09/12.34 tff(34646,plain,
% 12.09/12.34 (~r(s(z), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[2201, 34645, 34631, 34629])).
% 12.09/12.34 tff(34647,plain,
% 12.09/12.34 (b(s(z), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[247, 34646])).
% 12.09/12.34 tff(34648,plain,
% 12.09/12.34 (b(s(elem!1), s(s(s(elem!1))))),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34647, 1025])).
% 12.09/12.34 tff(34649,plain,
% 12.09/12.34 (~r(z, s(elem!1))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[8832, 1027, 832])).
% 12.09/12.34 tff(34650,plain,
% 12.09/12.34 (b(z, s(elem!1))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[566, 34649])).
% 12.09/12.34 tff(34651,plain,
% 12.09/12.34 (~b(s(elem!1), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[25659, 34643, 34650, 34608, 802])).
% 12.09/12.34 tff(34652,plain,
% 12.09/12.34 ($false),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[34651, 34648])).
% 12.09/12.34 tff(34653,plain,(b(s(s(s(s(z)))), z) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | r(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.09/12.34 tff(34654,plain,
% 12.09/12.34 (b(s(s(s(s(z)))), z)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[34653, 2829, 802, 664, 1234, 832, 94])).
% 12.09/12.34 tff(34655,plain,
% 12.09/12.34 (b(s(z), elem!1) <=> b(s(z), z)),
% 12.09/12.34 inference(symmetry,[status(thm)],[32328])).
% 12.09/12.34 tff(34656,plain,
% 12.09/12.34 ((~b(s(z), elem!1)) <=> (~b(s(z), z))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[34655])).
% 12.09/12.34 tff(34657,plain,
% 12.09/12.34 (~b(s(z), z)),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[2829, 34656])).
% 12.09/12.34 tff(34658,plain,
% 12.09/12.34 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 12.09/12.34 inference(transitivity,[status(thm)],[23143, 23142])).
% 12.09/12.34 tff(34659,plain,
% 12.09/12.34 (b(s(s(s(s(elem!1)))), elem!1)),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[90, 34658])).
% 12.09/12.34 tff(34660,plain,
% 12.09/12.34 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 12.09/12.34 inference(symmetry,[status(thm)],[32375])).
% 12.09/12.34 tff(34661,plain,
% 12.09/12.34 ((~b(elem!1, s(s(elem!1)))) <=> (~b(z, s(s(elem!1))))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[34660])).
% 12.09/12.34 tff(34662,plain,
% 12.09/12.34 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 12.09/12.34 inference(transitivity,[status(thm)],[32509, 765])).
% 12.09/12.34 tff(34663,plain,
% 12.09/12.34 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[34662])).
% 12.09/12.34 tff(34664,plain,
% 12.09/12.34 (~(s(s(s(s(z)))) = elem!1)),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[83, 34663])).
% 12.09/12.34 tff(34665,plain,
% 12.09/12.34 (~r(s(s(elem!1)), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[2028, 1294, 720, 1484, 1983, 723])).
% 12.09/12.34 tff(34666,plain,
% 12.09/12.34 (~b(s(s(elem!1)), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[3743, 1294, 90, 1234, 721])).
% 12.09/12.34 tff(34667,plain,
% 12.09/12.34 ($false),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[362, 34666, 34665])).
% 12.09/12.34 tff(34668,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.34 tff(34669,plain,
% 12.09/12.34 (~b(elem!1, s(s(elem!1)))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[34668, 723, 1234, 721, 34664, 1484, 946, 90])).
% 12.09/12.34 tff(34670,plain,
% 12.09/12.34 (~b(z, s(s(elem!1)))),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34669, 34661])).
% 12.09/12.34 tff(34671,plain,
% 12.09/12.34 (b(z, s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[3924, 34670, 91, 27398])).
% 12.09/12.34 tff(34672,plain,
% 12.09/12.34 (b(elem!1, s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[23154, 34671, 1027])).
% 12.09/12.34 tff(34673,plain,
% 12.09/12.34 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[932])).
% 12.09/12.34 tff(34674,plain,
% 12.09/12.34 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 12.09/12.34 inference(symmetry,[status(thm)],[34673])).
% 12.09/12.34 tff(34675,plain,
% 12.09/12.34 (r(elem!1, s(s(elem!1)))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[1307, 34669, 32346])).
% 12.09/12.34 tff(34676,plain,
% 12.09/12.34 (r(elem!1, s(s(z)))),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34675, 34674])).
% 12.09/12.34 tff(34677,plain,
% 12.09/12.34 (~r(s(s(s(elem!1))), elem!1)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[14370, 34672, 1484, 721, 34676])).
% 12.09/12.34 tff(34678,plain,
% 12.09/12.34 (b(s(s(s(elem!1))), elem!1)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[230, 34677, 34613])).
% 12.09/12.34 tff(34679,plain,
% 12.09/12.34 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[9883, 391, 34678, 34672, 34659])).
% 12.09/12.34 tff(34680,plain,
% 12.09/12.34 (r(s(elem!1), elem!1)),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[1484, 958])).
% 12.09/12.34 tff(34681,plain,
% 12.09/12.34 (~b(s(s(s(elem!1))), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[8962, 34678, 1234, 721, 23144])).
% 12.09/12.34 tff(34682,plain,
% 12.09/12.34 (r(s(s(s(elem!1))), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[223, 34681])).
% 12.09/12.34 tff(34683,plain,
% 12.09/12.34 (r(s(s(s(elem!1))), s(elem!1))),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34682, 32331])).
% 12.09/12.34 tff(34684,plain,
% 12.09/12.34 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[1149, 194, 34683, 34680, 34540])).
% 12.09/12.34 tff(34685,plain,
% 12.09/12.34 ($false),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[1095, 34684, 34679, 32385])).
% 12.09/12.34 tff(34686,plain,((~r(s(s(s(s(z)))), s(z))) | (~(z = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | b(s(z), z) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.34 tff(34687,plain,
% 12.09/12.34 (~r(s(s(s(s(z)))), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[34686, 34514, 1234, 34517, 94, 34657, 34654])).
% 12.09/12.34 tff(34688,plain,
% 12.09/12.34 (b(s(s(s(s(z)))), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[749, 34687])).
% 12.09/12.34 tff(34689,plain,
% 12.09/12.34 (b(s(s(s(s(z)))), s(elem!1))),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34688, 23139])).
% 12.09/12.34 tff(34690,plain,
% 12.09/12.34 (b(s(s(s(s(z)))), elem!1)),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34654, 23143])).
% 12.09/12.34 tff(34691,plain,
% 12.09/12.34 (~b(s(s(s(s(z)))), s(elem!1))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[15244, 34690, 802, 34577])).
% 12.09/12.34 tff(34692,plain,
% 12.09/12.34 ($false),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[34691, 34689])).
% 12.09/12.34 tff(34693,plain,(b(s(z), elem!1) | (~(z = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(z, s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.34 tff(34694,plain,
% 12.09/12.34 (b(s(z), elem!1)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[34693, 34507, 17618, 34438, 664, 832])).
% 12.09/12.34 tff(34695,plain,
% 12.09/12.34 (~b(s(z), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[18555, 34694, 11, 378, 664])).
% 12.09/12.34 tff(34696,plain,
% 12.09/12.34 (r(s(z), s(s(s(elem!1))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[247, 34695])).
% 12.09/12.34 tff(34697,plain,
% 12.09/12.34 (~b(s(s(s(elem!1))), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[8962, 34507, 34440, 34433, 33675])).
% 12.09/12.34 tff(34698,plain,
% 12.09/12.34 (r(s(s(s(elem!1))), s(z))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[223, 34697])).
% 12.09/12.34 tff(34699,plain,
% 12.09/12.34 (~r(s(z), z)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[3499, 34698, 59, 34696])).
% 12.09/12.34 tff(34700,plain,
% 12.09/12.34 (~r(s(elem!1), elem!1)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[29755, 34699, 11])).
% 12.09/12.34 tff(34701,plain,
% 12.09/12.34 (~b(s(s(s(elem!1))), s(elem!1))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[2340, 34700, 34433, 4598, 438])).
% 12.09/12.34 tff(34702,plain,
% 12.09/12.34 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[935])).
% 12.09/12.34 tff(34703,plain,
% 12.09/12.34 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.09/12.34 inference(symmetry,[status(thm)],[34702])).
% 12.09/12.34 tff(34704,plain,
% 12.09/12.34 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[932])).
% 12.09/12.34 tff(34705,plain,
% 12.09/12.34 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.09/12.34 inference(transitivity,[status(thm)],[34704, 34703])).
% 12.09/12.34 tff(34706,plain,
% 12.09/12.34 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 12.09/12.34 inference(symmetry,[status(thm)],[34518])).
% 12.09/12.34 tff(34707,plain,
% 12.09/12.34 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 12.09/12.34 inference(symmetry,[status(thm)],[32326])).
% 12.09/12.34 tff(34708,plain,
% 12.09/12.34 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 12.09/12.34 inference(transitivity,[status(thm)],[34707, 34706])).
% 12.09/12.34 tff(34709,plain,
% 12.09/12.34 (~b(s(s(s(s(elem!1)))), elem!1)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[17982, 802, 32077, 34578])).
% 12.09/12.34 tff(34710,plain,
% 12.09/12.34 (r(s(s(s(s(elem!1)))), elem!1)),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[1004, 34709, 967])).
% 12.09/12.34 tff(34711,plain,
% 12.09/12.34 (r(s(s(s(s(z)))), z)),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34710, 34708])).
% 12.09/12.34 tff(34712,plain,
% 12.09/12.34 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[14746, 59, 34711, 32398])).
% 12.09/12.34 tff(34713,plain,
% 12.09/12.34 (b(s(s(z)), s(s(s(s(z)))))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[3652, 34712])).
% 12.09/12.34 tff(34714,plain,
% 12.09/12.34 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34713, 34705])).
% 12.09/12.34 tff(34715,plain,
% 12.09/12.34 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[14769, 59, 34711, 32398])).
% 12.09/12.34 tff(34716,plain,
% 12.09/12.34 (b(s(s(s(s(z)))), s(s(z)))),
% 12.09/12.34 inference(unit_resolution,[status(thm)],[1714, 34715])).
% 12.09/12.34 tff(34717,plain,
% 12.09/12.34 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.09/12.34 inference(modus_ponens,[status(thm)],[34716, 32465])).
% 12.09/12.34 tff(34718,plain,
% 12.09/12.34 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 12.09/12.34 inference(symmetry,[status(thm)],[23139])).
% 12.09/12.34 tff(34719,plain,
% 12.09/12.34 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 12.09/12.34 inference(transitivity,[status(thm)],[23137, 34718])).
% 12.09/12.34 tff(34720,plain,
% 12.09/12.34 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 12.09/12.34 inference(monotonicity,[status(thm)],[935])).
% 12.09/12.34 tff(34721,plain,
% 12.09/12.34 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 12.09/12.34 inference(symmetry,[status(thm)],[34720])).
% 12.09/12.34 tff(34722,plain,
% 12.09/12.34 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 12.09/12.34 inference(transitivity,[status(thm)],[34721, 8666])).
% 12.09/12.34 tff(34723,plain,
% 12.09/12.34 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 12.09/12.35 inference(monotonicity,[status(thm)],[34722])).
% 12.09/12.35 tff(34724,plain,
% 12.09/12.35 (s(elem!1) = s(z)),
% 12.09/12.35 inference(symmetry,[status(thm)],[931])).
% 12.09/12.35 tff(34725,plain,
% 12.09/12.35 ((s(elem!1) = s(s(s(s(z))))) <=> (s(z) = s(s(s(s(z)))))),
% 12.09/12.35 inference(monotonicity,[status(thm)],[34724])).
% 12.09/12.35 tff(34726,plain,
% 12.09/12.35 ((s(z) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 12.09/12.35 inference(symmetry,[status(thm)],[34725])).
% 12.09/12.35 tff(34727,plain,
% 12.09/12.35 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 12.09/12.35 inference(monotonicity,[status(thm)],[34726])).
% 12.09/12.35 tff(34728,plain,
% 12.09/12.35 (~(s(elem!1) = s(s(s(s(z)))))),
% 12.09/12.35 inference(modus_ponens,[status(thm)],[743, 34727])).
% 12.09/12.35 tff(34729,plain,
% 12.09/12.35 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 12.09/12.35 inference(modus_ponens,[status(thm)],[34728, 34723])).
% 12.09/12.35 tff(34730,plain,
% 12.09/12.35 (r(elem!1, s(s(s(elem!1))))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[424, 34589, 34557])).
% 12.09/12.35 tff(34731,plain,
% 12.09/12.35 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 12.09/12.35 inference(symmetry,[status(thm)],[32416])).
% 12.09/12.35 tff(34732,plain,
% 12.09/12.35 (r(s(s(s(elem!1))), z)),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[406, 233, 1027])).
% 12.09/12.35 tff(34733,plain,
% 12.09/12.35 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[15335, 34732, 2053, 184])).
% 12.09/12.35 tff(34734,plain,
% 12.09/12.35 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[29931, 34733, 1027])).
% 12.09/12.35 tff(34735,plain,
% 12.09/12.35 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[1095, 34734, 32385])).
% 12.09/12.35 tff(34736,plain,
% 12.09/12.35 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[27316, 34735, 1027])).
% 12.09/12.35 tff(34737,plain,
% 12.09/12.35 (b(s(s(s(s(z)))), s(s(s(z))))),
% 12.09/12.35 inference(modus_ponens,[status(thm)],[34736, 34731])).
% 12.09/12.35 tff(34738,plain,
% 12.09/12.35 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 12.09/12.35 inference(symmetry,[status(thm)],[1025])).
% 12.09/12.35 tff(34739,plain,
% 12.09/12.35 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 12.09/12.35 inference(monotonicity,[status(thm)],[34738])).
% 12.09/12.35 tff(34740,plain,
% 12.09/12.35 (r(s(s(s(s(elem!1)))), elem!1)),
% 12.09/12.35 inference(modus_ponens,[status(thm)],[2053, 34534])).
% 12.09/12.35 tff(34741,plain,
% 12.09/12.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 12.09/12.35 inference(rewrite,[status(thm)],[])).
% 12.09/12.35 tff(34742,plain,
% 12.09/12.35 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 12.09/12.35 inference(rewrite,[status(thm)],[])).
% 12.09/12.35 tff(34743,plain,
% 12.09/12.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 12.09/12.35 inference(monotonicity,[status(thm)],[34742])).
% 12.09/12.35 tff(34744,plain,
% 12.09/12.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 12.09/12.35 inference(transitivity,[status(thm)],[34743, 34741])).
% 12.09/12.35 tff(34745,plain,
% 12.09/12.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 12.09/12.35 inference(quant_inst,[status(thm)],[])).
% 12.09/12.35 tff(34746,plain,
% 12.09/12.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 12.09/12.35 inference(modus_ponens,[status(thm)],[34745, 34744])).
% 12.09/12.35 tff(34747,plain,
% 12.09/12.35 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[34746, 194, 233, 410, 34740])).
% 12.09/12.35 tff(34748,plain,
% 12.09/12.35 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[1164, 34747, 32386])).
% 12.09/12.35 tff(34749,plain,
% 12.09/12.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 12.09/12.35 inference(rewrite,[status(thm)],[])).
% 12.09/12.35 tff(34750,plain,
% 12.09/12.35 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 12.09/12.35 inference(rewrite,[status(thm)],[])).
% 12.09/12.35 tff(34751,plain,
% 12.09/12.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 12.09/12.35 inference(monotonicity,[status(thm)],[34750])).
% 12.09/12.35 tff(34752,plain,
% 12.09/12.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 12.09/12.35 inference(transitivity,[status(thm)],[34751, 34749])).
% 12.09/12.35 tff(34753,plain,
% 12.09/12.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 12.09/12.35 inference(quant_inst,[status(thm)],[])).
% 12.09/12.35 tff(34754,plain,
% 12.09/12.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 12.09/12.35 inference(modus_ponens,[status(thm)],[34753, 34752])).
% 12.09/12.35 tff(34755,plain,
% 12.09/12.35 (~b(s(elem!1), s(s(s(elem!1))))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[34754, 391, 34748, 34735, 34578])).
% 12.09/12.35 tff(34756,plain,
% 12.09/12.35 (~b(s(z), s(s(s(elem!1))))),
% 12.09/12.35 inference(modus_ponens,[status(thm)],[34755, 34739])).
% 12.09/12.35 tff(34757,plain,
% 12.09/12.35 (r(s(z), s(s(s(elem!1))))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[247, 34756])).
% 12.09/12.35 tff(34758,plain,
% 12.09/12.35 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 12.09/12.35 inference(transitivity,[status(thm)],[1199, 1201, 27407])).
% 12.09/12.35 tff(34759,plain,
% 12.09/12.35 (r(s(s(elem!1)), z)),
% 12.09/12.35 inference(modus_ponens,[status(thm)],[3557, 34758])).
% 12.09/12.35 tff(34760,plain,
% 12.09/12.35 (~b(s(s(s(z))), s(s(z)))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[24809, 30107, 7872, 14771])).
% 12.09/12.35 tff(34761,plain,
% 12.09/12.35 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[2986, 34760, 1027])).
% 12.09/12.35 tff(34762,plain,
% 12.09/12.35 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[1370, 34761, 27398])).
% 12.09/12.35 tff(34763,plain,
% 12.09/12.35 (~b(s(z), s(s(z)))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[6275, 30107, 1234, 14771])).
% 12.09/12.35 tff(34764,plain,
% 12.09/12.35 (r(s(z), s(s(z)))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[1788, 34763])).
% 12.09/12.35 tff(34765,plain,
% 12.09/12.35 (r(s(z), s(s(elem!1)))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[23186, 34764, 1027])).
% 12.09/12.35 tff(34766,plain,
% 12.09/12.35 (~r(s(s(elem!1)), z)),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[4840, 34765, 232, 34762])).
% 12.09/12.35 tff(34767,plain,
% 12.09/12.35 ($false),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[34766, 34759])).
% 12.09/12.35 tff(34768,plain,((~r(s(s(z)), z)) | (~(z = elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.35 tff(34769,plain,
% 12.09/12.35 (~r(s(s(z)), z)),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[34768, 34757, 94, 1234, 34737, 2053, 184])).
% 12.09/12.35 tff(34770,plain,
% 12.09/12.35 (b(s(s(z)), z)),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[1211, 34769])).
% 12.09/12.35 tff(34771,plain,
% 12.09/12.35 (b(s(s(elem!1)), elem!1)),
% 12.09/12.35 inference(modus_ponens,[status(thm)],[34770, 34510])).
% 12.09/12.35 tff(34772,plain,
% 12.09/12.35 (~b(s(s(elem!1)), s(elem!1))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[19492, 391, 34771, 802, 2122])).
% 12.09/12.35 tff(34773,plain,
% 12.09/12.35 (r(s(s(elem!1)), s(elem!1))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[1135, 34772, 1081])).
% 12.09/12.35 tff(34774,plain,
% 12.09/12.35 (r(s(elem!1), s(s(s(elem!1))))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[579, 42, 34755, 32384])).
% 12.09/12.35 tff(34775,plain,
% 12.09/12.35 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(s(elem!1)))),
% 12.09/12.35 inference(transitivity,[status(thm)],[1079, 1098])).
% 12.09/12.35 tff(34776,plain,
% 12.09/12.35 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 12.09/12.35 inference(monotonicity,[status(thm)],[34775])).
% 12.09/12.35 tff(34777,plain,
% 12.09/12.35 (~(s(elem!1) = s(s(elem!1)))),
% 12.09/12.35 inference(modus_ponens,[status(thm)],[357, 34776])).
% 12.09/12.35 tff(34778,plain,
% 12.09/12.35 (~b(s(elem!1), s(s(elem!1)))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[24456, 391, 34771, 802, 2122])).
% 12.09/12.35 tff(34779,plain,
% 12.09/12.35 (r(s(elem!1), s(s(elem!1)))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[8644, 34778, 34777])).
% 12.09/12.35 tff(34780,plain,
% 12.09/12.35 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[8653, 34779, 34774, 34773])).
% 12.09/12.35 tff(34781,plain,
% 12.09/12.35 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.35 inference(unit_resolution,[status(thm)],[1370, 34780, 27398])).
% 12.09/12.35 tff(34782,plain,
% 12.09/12.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 12.09/12.35 inference(rewrite,[status(thm)],[])).
% 12.09/12.36 tff(34783,plain,
% 12.09/12.36 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(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(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 12.09/12.36 inference(rewrite,[status(thm)],[])).
% 12.09/12.36 tff(34784,plain,
% 12.09/12.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 12.09/12.36 inference(monotonicity,[status(thm)],[34783])).
% 12.09/12.36 tff(34785,plain,
% 12.09/12.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 12.09/12.36 inference(transitivity,[status(thm)],[34784, 34782])).
% 12.09/12.36 tff(34786,plain,
% 12.09/12.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 12.09/12.36 inference(quant_inst,[status(thm)],[])).
% 12.09/12.36 tff(34787,plain,
% 12.09/12.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 12.09/12.36 inference(modus_ponens,[status(thm)],[34786, 34785])).
% 12.09/12.36 tff(34788,plain,
% 12.09/12.36 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[34787, 194, 34774, 34773, 990])).
% 12.09/12.36 tff(34789,plain,
% 12.09/12.36 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[1048, 34788, 1024])).
% 12.09/12.36 tff(34790,plain,
% 12.09/12.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 12.09/12.36 inference(rewrite,[status(thm)],[])).
% 12.09/12.36 tff(34791,plain,
% 12.09/12.36 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 12.09/12.36 inference(rewrite,[status(thm)],[])).
% 12.09/12.36 tff(34792,plain,
% 12.09/12.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 12.09/12.36 inference(monotonicity,[status(thm)],[34791])).
% 12.09/12.36 tff(34793,plain,
% 12.09/12.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 12.09/12.36 inference(transitivity,[status(thm)],[34792, 34790])).
% 12.09/12.36 tff(34794,plain,
% 12.09/12.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 12.09/12.36 inference(quant_inst,[status(thm)],[])).
% 12.09/12.36 tff(34795,plain,
% 12.09/12.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 12.09/12.36 inference(modus_ponens,[status(thm)],[34794, 34793])).
% 12.09/12.36 tff(34796,plain,
% 12.09/12.36 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[34795, 194, 34774, 34773, 990])).
% 12.09/12.36 tff(34797,plain,
% 12.09/12.36 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[1061, 34796, 947])).
% 12.09/12.36 tff(34798,plain,
% 12.09/12.36 ($false),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[1741, 34797, 34789, 34748, 34781])).
% 12.09/12.36 tff(34799,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~(z = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.36 tff(34800,plain,
% 12.09/12.36 (~r(s(s(s(elem!1))), elem!1)),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[34799, 59, 802, 32077, 94, 1234, 2053, 990, 34730])).
% 12.09/12.36 tff(34801,plain,
% 12.09/12.36 (b(s(s(s(elem!1))), elem!1)),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[230, 34800, 34613])).
% 12.09/12.36 tff(34802,plain,
% 12.09/12.36 (~b(s(s(s(elem!1))), s(z))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[20387, 34801, 34517, 644])).
% 12.09/12.36 tff(34803,plain,
% 12.09/12.36 (r(s(s(s(elem!1))), s(z))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[223, 34802])).
% 12.09/12.36 tff(34804,plain,
% 12.09/12.36 (b(s(s(s(elem!1))), z)),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[28222, 34801, 1027])).
% 12.09/12.36 tff(34805,plain,
% 12.09/12.36 (~b(s(z), s(s(s(elem!1))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[18555, 34804, 1027, 644, 664])).
% 12.09/12.36 tff(34806,plain,
% 12.09/12.36 (r(s(z), s(s(s(elem!1))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[247, 34805])).
% 12.09/12.36 tff(34807,plain,
% 12.09/12.36 (r(s(elem!1), s(s(s(elem!1))))),
% 12.09/12.36 inference(modus_ponens,[status(thm)],[34806, 27399])).
% 12.09/12.36 tff(34808,plain,
% 12.09/12.36 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 12.09/12.36 inference(monotonicity,[status(thm)],[94])).
% 12.09/12.36 tff(34809,plain,
% 12.09/12.36 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 12.09/12.36 inference(symmetry,[status(thm)],[34808])).
% 12.09/12.36 tff(34810,plain,
% 12.09/12.36 (b(s(z), elem!1) <=> b(s(elem!1), z)),
% 12.09/12.36 inference(transitivity,[status(thm)],[23146, 34809])).
% 12.09/12.36 tff(34811,plain,
% 12.09/12.36 (b(s(elem!1), z)),
% 12.09/12.36 inference(modus_ponens,[status(thm)],[644, 34810])).
% 12.09/12.36 tff(34812,plain,
% 12.09/12.36 (r(s(s(s(elem!1))), s(elem!1))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[2614, 34804, 573, 34811, 59])).
% 12.09/12.36 tff(34813,plain,
% 12.09/12.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 12.09/12.36 inference(rewrite,[status(thm)],[])).
% 12.09/12.36 tff(34814,plain,
% 12.09/12.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 12.09/12.36 inference(quant_inst,[status(thm)],[])).
% 12.09/12.36 tff(34815,plain,
% 12.09/12.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 12.09/12.36 inference(modus_ponens,[status(thm)],[34814, 34813])).
% 12.09/12.36 tff(34816,plain,
% 12.09/12.36 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[34815, 194, 34812, 34807, 990])).
% 12.09/12.36 tff(34817,plain,
% 12.09/12.36 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[1095, 34816, 32385])).
% 12.09/12.36 tff(34818,plain,
% 12.09/12.36 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[27316, 34817, 1027])).
% 12.09/12.36 tff(34819,plain,
% 12.09/12.36 (b(s(s(s(s(z)))), s(s(s(z))))),
% 12.09/12.36 inference(modus_ponens,[status(thm)],[34818, 34731])).
% 12.09/12.36 tff(34820,plain,
% 12.09/12.36 (~r(s(s(z)), z)),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[34768, 34819, 94, 1234, 34806, 2053, 59])).
% 12.09/12.36 tff(34821,plain,
% 12.09/12.36 (b(s(s(z)), z)),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[1211, 34820])).
% 12.09/12.36 tff(34822,plain,
% 12.09/12.36 (b(s(s(elem!1)), elem!1)),
% 12.09/12.36 inference(modus_ponens,[status(thm)],[34821, 34510])).
% 12.09/12.36 tff(34823,plain,
% 12.09/12.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(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(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(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(elem!1)), elem!1)))),
% 12.09/12.36 inference(rewrite,[status(thm)],[])).
% 12.09/12.36 tff(34824,plain,
% 12.09/12.36 (((~b(s(elem!1), elem!1)) | (~b(elem!1, 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)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(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(elem!1)), elem!1)))),
% 12.09/12.36 inference(rewrite,[status(thm)],[])).
% 12.09/12.36 tff(34825,plain,
% 12.09/12.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(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(elem!1)), elem!1))))),
% 12.09/12.36 inference(monotonicity,[status(thm)],[34824])).
% 12.09/12.36 tff(34826,plain,
% 12.09/12.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(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(elem!1)), elem!1)))),
% 12.09/12.36 inference(transitivity,[status(thm)],[34825, 34823])).
% 12.09/12.36 tff(34827,plain,
% 12.09/12.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, 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))))))),
% 12.09/12.36 inference(quant_inst,[status(thm)],[])).
% 12.09/12.36 tff(34828,plain,
% 12.09/12.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))),
% 12.09/12.36 inference(modus_ponens,[status(thm)],[34827, 34826])).
% 12.09/12.36 tff(34829,plain,
% 12.09/12.36 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[34828, 391, 34801, 34822, 802, 32077])).
% 12.09/12.36 tff(34830,plain,
% 12.09/12.36 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[1356, 34829, 27414])).
% 12.09/12.36 tff(34831,plain,
% 12.09/12.36 (~b(s(s(elem!1)), s(z))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[22561, 34822, 34517, 644])).
% 12.09/12.36 tff(34832,plain,
% 12.09/12.36 (r(s(s(elem!1)), s(z))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[362, 34831])).
% 12.09/12.36 tff(34833,plain,
% 12.09/12.36 ($false),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[2201, 34832, 34830, 34806, 34803])).
% 12.09/12.36 tff(34834,plain,(b(z, s(s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~(z = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(z))) | r(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.36 tff(34835,plain,
% 12.09/12.36 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[34834, 10, 802, 94, 1234, 34711, 644, 664, 573])).
% 12.09/12.36 tff(34836,plain,
% 12.09/12.36 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[988, 34835, 34729])).
% 12.09/12.36 tff(34837,plain,
% 12.09/12.36 (b(s(s(s(s(z)))), s(z))),
% 12.09/12.36 inference(modus_ponens,[status(thm)],[34836, 34719])).
% 12.09/12.36 tff(34838,plain,
% 12.09/12.36 (~b(z, s(s(s(s(z)))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[10478, 34837, 1234, 664])).
% 12.09/12.36 tff(34839,plain,
% 12.09/12.36 (r(z, s(s(s(s(z)))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[800, 34838])).
% 12.09/12.36 tff(34840,plain,
% 12.09/12.36 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[10090, 34839, 34711, 59])).
% 12.09/12.36 tff(34841,plain,
% 12.09/12.36 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[32103, 34840, 94])).
% 12.09/12.36 tff(34842,plain,
% 12.09/12.36 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[1164, 34841, 32386])).
% 12.09/12.36 tff(34843,plain,
% 12.09/12.36 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[1741, 34842, 34717, 34714])).
% 12.09/12.36 tff(34844,plain,
% 12.09/12.36 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[1370, 34843, 27398])).
% 12.09/12.36 tff(34845,plain,
% 12.09/12.36 (b(s(s(s(elem!1))), elem!1)),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[4039, 34844, 364, 34613, 34589])).
% 12.09/12.36 tff(34846,plain,
% 12.09/12.36 (b(s(s(s(elem!1))), z)),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[28222, 34845, 1027])).
% 12.09/12.36 tff(34847,plain,
% 12.09/12.36 (~b(s(z), s(s(z)))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[6275, 34713, 1234, 34716])).
% 12.09/12.36 tff(34848,plain,
% 12.09/12.36 (r(s(z), s(s(z)))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[1788, 34847])).
% 12.09/12.36 tff(34849,plain,
% 12.09/12.36 (r(s(z), s(s(elem!1)))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[23186, 34848, 1027])).
% 12.09/12.36 tff(34850,plain,
% 12.09/12.36 (r(s(s(elem!1)), z)),
% 12.09/12.36 inference(modus_ponens,[status(thm)],[364, 27407])).
% 12.09/12.36 tff(34851,plain,
% 12.09/12.36 (~r(s(z), s(s(s(elem!1))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[4840, 34844, 34850, 34849])).
% 12.09/12.36 tff(34852,plain,
% 12.09/12.36 (b(s(z), s(s(s(elem!1))))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[247, 34851])).
% 12.09/12.36 tff(34853,plain,
% 12.09/12.36 ($false),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[18555, 34852, 34846, 1027, 644, 664])).
% 12.09/12.36 tff(34854,plain,(b(z, s(s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | r(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.36 tff(34855,plain,
% 12.09/12.36 (~r(s(s(elem!1)), elem!1)),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[34854, 34507, 664, 10, 17618, 34694, 34438, 573])).
% 12.09/12.36 tff(34856,plain,
% 12.09/12.36 (b(s(s(elem!1)), elem!1)),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[872, 34855, 30072])).
% 12.09/12.36 tff(34857,plain,
% 12.09/12.36 (~b(s(s(s(s(z)))), s(z))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[26707, 34507, 34440, 33675, 34694])).
% 12.09/12.36 tff(34858,plain,
% 12.09/12.36 (r(s(s(s(s(z)))), s(z))),
% 12.09/12.36 inference(unit_resolution,[status(thm)],[749, 34857])).
% 12.09/12.36 tff(34859,plain,
% 12.09/12.37 (b(s(elem!1), elem!1)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[2168, 34700, 4597])).
% 12.09/12.37 tff(34860,plain,
% 12.09/12.37 (~b(s(elem!1), s(s(elem!1)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[24456, 391, 973, 802, 2122])).
% 12.09/12.37 tff(34861,plain,
% 12.09/12.37 (r(s(elem!1), s(s(elem!1)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[8644, 34860, 34777])).
% 12.09/12.37 tff(34862,plain,
% 12.09/12.37 (~b(s(s(elem!1)), s(elem!1))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[19492, 391, 973, 802, 2122])).
% 12.09/12.37 tff(34863,plain,
% 12.09/12.37 (r(s(s(elem!1)), s(elem!1))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[1135, 34862, 1081])).
% 12.09/12.37 tff(34864,plain,
% 12.09/12.37 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[18194, 194, 613, 34863, 34861])).
% 12.09/12.37 tff(34865,plain,
% 12.09/12.37 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[1370, 34864, 27398])).
% 12.09/12.37 tff(34866,plain,
% 12.09/12.37 (r(s(s(z)), s(z))),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[34863, 34638])).
% 12.09/12.37 tff(34867,plain,
% 12.09/12.37 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[931, 932])).
% 12.09/12.37 tff(34868,plain,
% 12.09/12.37 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 12.09/12.37 inference(symmetry,[status(thm)],[34867])).
% 12.09/12.37 tff(34869,plain,
% 12.09/12.37 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(z), s(s(z))))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[34868])).
% 12.09/12.37 tff(34870,plain,
% 12.09/12.37 (~b(s(z), s(s(z)))),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[34860, 34869])).
% 12.09/12.37 tff(34871,plain,
% 12.09/12.37 (r(s(z), s(s(z)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[1788, 34870])).
% 12.09/12.37 tff(34872,plain,
% 12.09/12.37 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[10673, 34871, 723, 34866])).
% 12.09/12.37 tff(34873,plain,
% 12.09/12.37 (b(s(s(s(s(z)))), s(s(z)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[1714, 34872])).
% 12.09/12.37 tff(34874,plain,
% 12.09/12.37 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[34873, 32465])).
% 12.09/12.37 tff(34875,plain,
% 12.09/12.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 12.09/12.37 inference(rewrite,[status(thm)],[])).
% 12.09/12.37 tff(34876,plain,
% 12.09/12.37 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 12.09/12.37 inference(rewrite,[status(thm)],[])).
% 12.09/12.37 tff(34877,plain,
% 12.09/12.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[34876])).
% 12.09/12.37 tff(34878,plain,
% 12.09/12.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 12.09/12.37 inference(transitivity,[status(thm)],[34877, 34875])).
% 12.09/12.37 tff(34879,plain,
% 12.09/12.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 12.09/12.37 inference(quant_inst,[status(thm)],[])).
% 12.09/12.37 tff(34880,plain,
% 12.09/12.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[34879, 34878])).
% 12.09/12.37 tff(34881,plain,
% 12.09/12.37 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[34880, 194, 613, 34540, 34861])).
% 12.09/12.37 tff(34882,plain,
% 12.09/12.37 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[1164, 34881, 32386])).
% 12.09/12.37 tff(34883,plain,
% 12.09/12.37 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[1142, 194, 34863, 34540, 34861])).
% 12.09/12.37 tff(34884,plain,
% 12.09/12.37 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[1048, 34883, 1024])).
% 12.09/12.37 tff(34885,plain,
% 12.09/12.37 ($false),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[1741, 34884, 34882, 34874, 34865])).
% 12.09/12.37 tff(34886,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.37 tff(34887,plain,
% 12.09/12.37 (~r(s(s(s(elem!1))), s(elem!1))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[34886, 34859, 17618, 34858, 34438, 34856])).
% 12.09/12.37 tff(34888,plain,
% 12.09/12.37 ($false),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[588, 34887, 34701, 8876])).
% 12.09/12.37 tff(34889,plain,(r(s(s(s(elem!1))), z) | r(elem!1, s(elem!1)) | (~(elem!1 = z)) | (~b(z, s(z))) | b(z, s(s(s(elem!1)))) | r(z, s(elem!1)) | r(elem!1, s(z)) | (s(s(s(s(z)))) = s(s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.09/12.37 tff(34890,plain,
% 12.09/12.37 (r(s(s(s(elem!1))), z)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[34889, 34424, 33627, 90, 10, 34412, 34423, 34431, 34425, 33634, 9])).
% 12.09/12.37 tff(34891,plain,
% 12.09/12.37 (~r(s(z), z)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[202, 34890, 59, 183])).
% 12.09/12.37 tff(34892,plain,
% 12.09/12.37 (~r(s(elem!1), elem!1)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[29755, 34891, 33627])).
% 12.09/12.37 tff(34893,plain,
% 12.09/12.37 (b(s(elem!1), elem!1)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[2168, 34892, 426])).
% 12.09/12.37 tff(34894,plain,
% 12.09/12.37 ((s(z) = elem!1) <=> (s(z) = z)),
% 12.09/12.37 inference(monotonicity,[status(thm)],[33627])).
% 12.09/12.37 tff(34895,plain,
% 12.09/12.37 ((s(z) = z) <=> (s(z) = elem!1)),
% 12.09/12.37 inference(symmetry,[status(thm)],[34894])).
% 12.09/12.37 tff(34896,plain,
% 12.09/12.37 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[34895])).
% 12.09/12.37 tff(34897,plain,
% 12.09/12.37 (~(s(z) = elem!1)),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[23, 34896])).
% 12.09/12.37 tff(34898,plain,
% 12.09/12.37 (z = elem!1),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[5453, 33627])).
% 12.09/12.37 tff(34899,plain,
% 12.09/12.37 (r(s(s(s(elem!1))), elem!1)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[9853, 34890, 34898])).
% 12.09/12.37 tff(34900,plain,
% 12.09/12.37 (~r(s(z), elem!1)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[23411, 34899, 33634, 183])).
% 12.09/12.37 tff(34901,plain,
% 12.09/12.37 (b(s(z), elem!1)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[632, 34900, 34897])).
% 12.09/12.37 tff(34902,plain,
% 12.09/12.37 (~b(s(s(s(s(z)))), s(z))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[20920, 34901, 90, 34412, 721])).
% 12.09/12.37 tff(34903,plain,
% 12.09/12.37 (r(s(s(s(s(z)))), s(z))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[749, 34902])).
% 12.09/12.37 tff(34904,plain,
% 12.09/12.37 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[33627])).
% 12.09/12.37 tff(34905,plain,
% 12.09/12.37 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 12.09/12.37 inference(symmetry,[status(thm)],[34904])).
% 12.09/12.37 tff(34906,plain,
% 12.09/12.37 (b(z, s(elem!1)) <=> b(z, s(z))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[34414])).
% 12.09/12.37 tff(34907,plain,
% 12.09/12.37 (b(z, s(z)) <=> b(z, s(elem!1))),
% 12.09/12.37 inference(symmetry,[status(thm)],[34906])).
% 12.09/12.37 tff(34908,plain,
% 12.09/12.37 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 12.09/12.37 inference(transitivity,[status(thm)],[33632, 34907, 34905])).
% 12.09/12.37 tff(34909,plain,
% 12.09/12.37 (b(elem!1, s(elem!1))),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[721, 34908])).
% 12.09/12.37 tff(34910,plain,
% 12.09/12.37 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[34414])).
% 12.09/12.37 tff(34911,plain,
% 12.09/12.37 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 12.09/12.37 inference(symmetry,[status(thm)],[34910])).
% 12.09/12.37 tff(34912,plain,
% 12.09/12.37 (r(s(s(s(elem!1))), s(elem!1))),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[183, 34911])).
% 12.09/12.37 tff(34913,plain,
% 12.09/12.37 (~b(s(s(elem!1)), elem!1)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[34886, 34912, 34898, 34909, 34903, 34893])).
% 12.09/12.37 tff(34914,plain,
% 12.09/12.37 (r(s(s(elem!1)), elem!1)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[872, 34913, 34422])).
% 12.09/12.37 tff(34915,plain,
% 12.09/12.37 (r(s(s(z)), z)),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[34914, 34418])).
% 12.09/12.37 tff(34916,plain,
% 12.09/12.37 (r(s(s(s(z))), z)),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[4409, 34890, 33627])).
% 12.09/12.37 tff(34917,plain,
% 12.09/12.37 (s(s(s(z))) = s(s(s(elem!1)))),
% 12.09/12.37 inference(symmetry,[status(thm)],[34426])).
% 12.09/12.37 tff(34918,plain,
% 12.09/12.37 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[34917])).
% 12.09/12.37 tff(34919,plain,
% 12.09/12.37 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 12.09/12.37 inference(symmetry,[status(thm)],[34918])).
% 12.09/12.37 tff(34920,plain,
% 12.09/12.37 (r(z, s(s(s(z))))),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[59, 34919])).
% 12.09/12.37 tff(34921,plain,
% 12.09/12.37 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[34427, 34426])).
% 12.09/12.37 tff(34922,plain,
% 12.09/12.37 (r(s(s(s(z))), s(z))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[29740, 183, 33627])).
% 12.09/12.37 tff(34923,plain,
% 12.09/12.37 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[34503, 194, 1216, 34903, 34922])).
% 12.09/12.37 tff(34924,plain,
% 12.09/12.37 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[32518, 34923, 33627])).
% 12.09/12.37 tff(34925,plain,
% 12.09/12.37 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[1095, 34924, 29900])).
% 12.09/12.37 tff(34926,plain,
% 12.09/12.37 (b(s(s(s(s(z)))), s(s(s(z))))),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[34925, 34921])).
% 12.09/12.37 tff(34927,plain,
% 12.09/12.37 (~r(s(s(z)), s(s(s(z))))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[24069, 194, 3557, 4428, 15510])).
% 12.09/12.37 tff(34928,plain,
% 12.09/12.37 (b(s(s(z)), s(s(s(z))))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[24074, 42, 8880, 34927])).
% 12.09/12.37 tff(34929,plain,
% 12.09/12.37 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[4380])).
% 12.09/12.37 tff(34930,plain,
% 12.09/12.37 (~r(s(s(s(z))), s(s(z)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[24836, 194, 3557, 4428, 15510])).
% 12.09/12.37 tff(34931,plain,
% 12.09/12.37 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.37 inference(modus_ponens,[status(thm)],[34930, 34929])).
% 12.09/12.37 tff(34932,plain,
% 12.09/12.37 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[1370, 34931, 8881])).
% 12.09/12.37 tff(34933,plain,
% 12.09/12.37 ($false),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[32143, 34932, 34928, 2405, 7872, 1216, 11])).
% 12.09/12.37 tff(34934,plain,((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.37 tff(34935,plain,
% 12.09/12.37 (~r(s(s(z)), s(z))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[34934, 34926, 34920, 33627, 1216, 34916, 34915])).
% 12.09/12.37 tff(34936,plain,
% 12.09/12.37 (b(s(s(z)), s(z))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[3778, 34935])).
% 12.09/12.37 tff(34937,plain,
% 12.09/12.37 (~b(z, s(s(z)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[22414, 391, 34936, 34412, 34413])).
% 12.09/12.37 tff(34938,plain,
% 12.09/12.37 (r(z, s(s(z)))),
% 12.09/12.37 inference(unit_resolution,[status(thm)],[18613, 34937])).
% 12.09/12.37 tff(34939,plain,
% 12.09/12.37 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[34427, 34415])).
% 12.09/12.37 tff(34940,plain,
% 12.09/12.37 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 12.09/12.37 inference(monotonicity,[status(thm)],[34427, 34415])).
% 12.09/12.37 tff(34941,plain,
% 12.09/12.37 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 12.09/12.38 inference(transitivity,[status(thm)],[34940, 940])).
% 12.09/12.38 tff(34942,plain,
% 12.09/12.38 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 12.09/12.38 inference(symmetry,[status(thm)],[34941])).
% 12.09/12.38 tff(34943,plain,
% 12.09/12.38 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 12.09/12.38 inference(monotonicity,[status(thm)],[34942])).
% 12.09/12.38 tff(34944,plain,
% 12.09/12.38 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 12.09/12.38 inference(modus_ponens,[status(thm)],[714, 34943])).
% 12.09/12.38 tff(34945,plain,
% 12.09/12.38 (~r(s(s(s(z))), s(s(z)))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[24836, 194, 34915, 34916, 34920])).
% 12.09/12.38 tff(34946,plain,
% 12.09/12.38 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[4385, 34945, 33627])).
% 12.09/12.38 tff(34947,plain,
% 12.09/12.38 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[1370, 34946, 26982])).
% 12.09/12.38 tff(34948,plain,
% 12.09/12.38 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.09/12.38 inference(monotonicity,[status(thm)],[34427])).
% 12.09/12.38 tff(34949,plain,
% 12.09/12.38 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.38 inference(symmetry,[status(thm)],[34948])).
% 12.09/12.38 tff(34950,plain,
% 12.09/12.38 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.09/12.38 inference(monotonicity,[status(thm)],[34917])).
% 12.09/12.38 tff(34951,plain,
% 12.09/12.38 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.38 inference(transitivity,[status(thm)],[34950, 34949])).
% 12.09/12.38 tff(34952,plain,
% 12.09/12.38 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 12.09/12.38 inference(monotonicity,[status(thm)],[34951])).
% 12.09/12.38 tff(34953,plain,
% 12.09/12.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 12.09/12.38 inference(rewrite,[status(thm)],[])).
% 12.09/12.38 tff(34954,plain,
% 12.09/12.38 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 12.09/12.38 inference(rewrite,[status(thm)],[])).
% 12.09/12.38 tff(34955,plain,
% 12.09/12.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))))),
% 12.09/12.38 inference(monotonicity,[status(thm)],[34954])).
% 12.09/12.38 tff(34956,plain,
% 12.09/12.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 12.09/12.38 inference(transitivity,[status(thm)],[34955, 34953])).
% 12.09/12.38 tff(34957,plain,
% 12.09/12.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 12.09/12.38 inference(quant_inst,[status(thm)],[])).
% 12.09/12.38 tff(34958,plain,
% 12.09/12.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 12.09/12.38 inference(modus_ponens,[status(thm)],[34957, 34956])).
% 12.09/12.38 tff(34959,plain,
% 12.09/12.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[34958, 194, 1216, 34903, 34922])).
% 12.09/12.38 tff(34960,plain,
% 12.09/12.38 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.38 inference(modus_ponens,[status(thm)],[34959, 34952])).
% 12.09/12.38 tff(34961,plain,
% 12.09/12.38 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[1164, 34960, 32322])).
% 12.09/12.38 tff(34962,plain,
% 12.09/12.38 (s(s(z)) = s(s(elem!1))),
% 12.09/12.38 inference(symmetry,[status(thm)],[34415])).
% 12.09/12.38 tff(34963,plain,
% 12.09/12.38 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 12.09/12.38 inference(monotonicity,[status(thm)],[34962])).
% 12.09/12.38 tff(34964,plain,
% 12.09/12.38 (b(s(s(elem!1)), s(z))),
% 12.09/12.38 inference(modus_ponens,[status(thm)],[34936, 34963])).
% 12.09/12.38 tff(34965,plain,
% 12.09/12.38 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[18349, 34964, 34961, 34947, 34901])).
% 12.09/12.38 tff(34966,plain,
% 12.09/12.38 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[1061, 34965, 34944])).
% 12.09/12.38 tff(34967,plain,
% 12.09/12.38 (r(s(s(s(s(z)))), s(s(z)))),
% 12.09/12.38 inference(modus_ponens,[status(thm)],[34966, 34939])).
% 12.09/12.38 tff(34968,plain,
% 12.09/12.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 12.09/12.38 inference(rewrite,[status(thm)],[])).
% 12.09/12.38 tff(34969,plain,
% 12.09/12.38 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 12.09/12.38 inference(rewrite,[status(thm)],[])).
% 12.09/12.38 tff(34970,plain,
% 12.09/12.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 12.09/12.38 inference(monotonicity,[status(thm)],[34969])).
% 12.09/12.38 tff(34971,plain,
% 12.09/12.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 12.09/12.38 inference(transitivity,[status(thm)],[34970, 34968])).
% 12.09/12.38 tff(34972,plain,
% 12.09/12.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 12.09/12.38 inference(quant_inst,[status(thm)],[])).
% 12.09/12.38 tff(34973,plain,
% 12.09/12.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 12.09/12.38 inference(modus_ponens,[status(thm)],[34972, 34971])).
% 12.09/12.38 tff(34974,plain,
% 12.09/12.38 (~r(z, s(s(s(s(z)))))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[34973, 194, 34915, 34967, 34938])).
% 12.09/12.38 tff(34975,plain,
% 12.09/12.38 (b(z, s(s(s(s(z)))))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[800, 34974])).
% 12.09/12.38 tff(34976,plain,
% 12.09/12.38 (b(s(s(s(z))), s(s(z)))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[2986, 34947, 33627])).
% 12.09/12.38 tff(34977,plain,
% 12.09/12.38 (~(s(s(z)) = s(s(s(z))))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[8879, 33627])).
% 12.09/12.38 tff(34978,plain,
% 12.09/12.38 (~r(s(s(z)), s(s(s(z))))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[24069, 194, 34915, 34916, 34920])).
% 12.09/12.38 tff(34979,plain,
% 12.09/12.38 (b(s(s(z)), s(s(s(z))))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[24076, 34978, 34977])).
% 12.09/12.38 tff(34980,plain,
% 12.09/12.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.09/12.38 inference(rewrite,[status(thm)],[])).
% 12.09/12.38 tff(34981,plain,
% 12.09/12.38 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.09/12.38 inference(rewrite,[status(thm)],[])).
% 12.09/12.38 tff(34982,plain,
% 12.09/12.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 12.09/12.38 inference(monotonicity,[status(thm)],[34981])).
% 12.09/12.38 tff(34983,plain,
% 12.09/12.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.09/12.38 inference(transitivity,[status(thm)],[34982, 34980])).
% 12.09/12.38 tff(34984,plain,
% 12.09/12.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 12.09/12.38 inference(quant_inst,[status(thm)],[])).
% 12.09/12.38 tff(34985,plain,
% 12.09/12.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 12.09/12.38 inference(modus_ponens,[status(thm)],[34984, 34983])).
% 12.09/12.38 tff(34986,plain,
% 12.09/12.38 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[34985, 391, 34936, 34926, 34979, 34976])).
% 12.09/12.38 tff(34987,plain,
% 12.09/12.38 (r(s(s(z)), s(s(s(s(z)))))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[3652, 34986])).
% 12.09/12.38 tff(34988,plain,
% 12.09/12.38 (~r(s(z), s(s(z)))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[11508, 34967, 1216, 34915])).
% 12.09/12.38 tff(34989,plain,
% 12.09/12.38 (b(s(z), s(s(z)))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[1788, 34988])).
% 12.09/12.38 tff(34990,plain,
% 12.09/12.38 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.09/12.38 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 6697])).
% 12.09/12.38 tff(34991,plain,
% 12.09/12.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 12.09/12.38 inference(rewrite,[status(thm)],[])).
% 12.09/12.38 tff(34992,plain,
% 12.09/12.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 12.09/12.39 inference(quant_inst,[status(thm)],[])).
% 12.09/12.39 tff(34993,plain,
% 12.09/12.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[34992, 34991])).
% 12.09/12.39 tff(34994,plain,
% 12.09/12.39 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[34993, 194, 1216, 723, 6610])).
% 12.09/12.39 tff(34995,plain,
% 12.09/12.39 (b(s(s(s(s(s(s(z)))))), s(z))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[14139, 34994])).
% 12.09/12.39 tff(34996,plain,
% 12.09/12.39 ($false),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[6692, 391, 2439, 1233, 34995, 34990])).
% 12.09/12.39 tff(34997,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.09/12.39 tff(34998,plain,
% 12.09/12.39 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[34997, 34989, 34936, 1216, 34903, 34987])).
% 12.09/12.39 tff(34999,plain,
% 12.09/12.39 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[33872, 34998])).
% 12.09/12.39 tff(35000,plain,
% 12.09/12.39 (~b(s(s(s(s(s(s(z)))))), z)),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[34226, 34999, 34975, 90])).
% 12.09/12.39 tff(35001,plain,
% 12.09/12.39 (r(s(s(s(s(s(s(z)))))), z)),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[34231, 35000])).
% 12.09/12.39 tff(35002,plain,
% 12.09/12.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.09/12.39 inference(rewrite,[status(thm)],[])).
% 12.09/12.39 tff(35003,plain,
% 12.09/12.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.09/12.39 inference(quant_inst,[status(thm)],[])).
% 12.09/12.39 tff(35004,plain,
% 12.09/12.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[35003, 35002])).
% 12.09/12.39 tff(35005,plain,
% 12.09/12.39 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[35004, 194, 34916, 34920, 35001])).
% 12.09/12.39 tff(35006,plain,
% 12.09/12.39 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.09/12.39 inference(monotonicity,[status(thm)],[34917])).
% 12.09/12.39 tff(35007,plain,
% 12.09/12.39 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.09/12.39 inference(transitivity,[status(thm)],[34429, 35006, 3929])).
% 12.09/12.39 tff(35008,plain,
% 12.09/12.39 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 12.09/12.39 inference(monotonicity,[status(thm)],[35007])).
% 12.09/12.39 tff(35009,plain,
% 12.09/12.39 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[32322, 35008])).
% 12.09/12.39 tff(35010,plain,
% 12.09/12.39 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 12.09/12.39 inference(monotonicity,[status(thm)],[34950])).
% 12.09/12.39 tff(35011,plain,
% 12.09/12.39 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[34959, 35010])).
% 12.09/12.39 tff(35012,plain,
% 12.09/12.39 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[15351, 35011, 35009])).
% 12.09/12.39 tff(35013,plain,
% 12.09/12.39 (b(s(s(s(z))), s(s(s(s(z)))))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[1673, 35012, 33627])).
% 12.09/12.39 tff(35014,plain,
% 12.09/12.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.09/12.39 inference(rewrite,[status(thm)],[])).
% 12.09/12.39 tff(35015,plain,
% 12.09/12.39 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.09/12.39 inference(rewrite,[status(thm)],[])).
% 12.09/12.39 tff(35016,plain,
% 12.09/12.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 12.09/12.39 inference(monotonicity,[status(thm)],[35015])).
% 12.09/12.39 tff(35017,plain,
% 12.09/12.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.09/12.39 inference(transitivity,[status(thm)],[35016, 35014])).
% 12.09/12.39 tff(35018,plain,
% 12.09/12.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.09/12.39 inference(quant_inst,[status(thm)],[])).
% 12.09/12.39 tff(35019,plain,
% 12.09/12.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[35018, 35017])).
% 12.09/12.39 tff(35020,plain,
% 12.09/12.39 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[35019, 391, 90, 34975, 35013, 34999])).
% 12.09/12.39 tff(35021,plain,
% 12.09/12.39 ($false),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[29527, 42, 8094, 35020, 35005])).
% 12.09/12.39 tff(35022,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | b(z, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.09/12.39 tff(35023,plain,
% 12.09/12.39 (~r(s(s(s(elem!1))), s(z))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[35022, 1216, 90, 721, 10, 1, 80])).
% 12.09/12.39 tff(35024,plain,
% 12.09/12.39 (b(s(s(s(elem!1))), s(z))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[223, 35023])).
% 12.09/12.39 tff(35025,plain,
% 12.09/12.39 (b(z, s(z))),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[721, 29])).
% 12.09/12.39 tff(35026,plain,
% 12.09/12.39 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[34126, 32151])).
% 12.09/12.39 tff(35027,plain,
% 12.09/12.39 (~b(z, s(s(z)))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[22399, 1686, 721, 33675, 3823])).
% 12.09/12.39 tff(35028,plain,
% 12.09/12.39 (r(z, s(s(z)))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[18613, 35027])).
% 12.09/12.39 tff(35029,plain,
% 12.09/12.39 (~r(s(z), z)),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[20649, 20941, 35028, 1747])).
% 12.09/12.39 tff(35030,plain,
% 12.09/12.39 (b(s(z), z)),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[180, 35029])).
% 12.09/12.39 tff(35031,plain,
% 12.09/12.39 (~b(s(s(s(elem!1))), z)),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[6325, 35030, 90, 1526, 1686])).
% 12.09/12.39 tff(35032,plain,
% 12.09/12.39 (r(s(s(s(elem!1))), z)),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[377, 35031])).
% 12.09/12.39 tff(35033,plain,
% 12.09/12.39 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[16453, 35032, 90, 35025, 184, 3823, 1686, 35030])).
% 12.09/12.39 tff(35034,plain,
% 12.09/12.39 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[15351, 35033, 15348])).
% 12.09/12.39 tff(35035,plain,
% 12.09/12.39 (r(s(s(s(z))), s(s(s(s(z)))))),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[35034, 17613])).
% 12.09/12.39 tff(35036,plain,
% 12.09/12.39 (r(elem!1, s(s(elem!1)))),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[35028, 29971])).
% 12.09/12.39 tff(35037,plain,
% 12.09/12.39 (r(s(s(elem!1)), elem!1)),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[20941, 30367])).
% 12.09/12.39 tff(35038,plain,
% 12.09/12.39 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 12.09/12.39 inference(symmetry,[status(thm)],[33854])).
% 12.09/12.39 tff(35039,plain,
% 12.09/12.39 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 12.09/12.39 inference(monotonicity,[status(thm)],[35038])).
% 12.09/12.39 tff(35040,plain,
% 12.09/12.39 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 12.09/12.39 inference(modus_ponens,[status(thm)],[34227, 35039])).
% 12.09/12.39 tff(35041,plain,
% 12.09/12.39 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[8073, 35040, 33785])).
% 12.09/12.39 tff(35042,plain,
% 12.09/12.39 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[32487, 35041, 1064, 35037])).
% 12.09/12.39 tff(35043,plain,
% 12.09/12.39 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.09/12.39 inference(unit_resolution,[status(thm)],[32502, 35042, 17618])).
% 12.09/12.39 tff(35044,plain,
% 12.09/12.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 12.09/12.39 inference(rewrite,[status(thm)],[])).
% 12.09/12.39 tff(35045,plain,
% 12.09/12.39 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 12.09/12.39 inference(rewrite,[status(thm)],[])).
% 12.09/12.39 tff(35046,plain,
% 12.09/12.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 12.09/12.39 inference(monotonicity,[status(thm)],[35045])).
% 12.09/12.39 tff(35047,plain,
% 12.09/12.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 12.09/12.39 inference(transitivity,[status(thm)],[35046, 35044])).
% 12.19/12.40 tff(35048,plain,
% 12.19/12.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 12.19/12.40 inference(quant_inst,[status(thm)],[])).
% 12.19/12.40 tff(35049,plain,
% 12.19/12.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 12.19/12.40 inference(modus_ponens,[status(thm)],[35048, 35047])).
% 12.19/12.40 tff(35050,plain,
% 12.19/12.40 ($false),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[35049, 391, 3823, 90, 1686, 23676, 35043])).
% 12.19/12.40 tff(35051,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.40 tff(35052,plain,
% 12.19/12.40 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[35051, 1686, 90, 3823, 35036, 11])).
% 12.19/12.40 tff(35053,plain,
% 12.19/12.40 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[33872, 35052])).
% 12.19/12.40 tff(35054,plain,
% 12.19/12.40 (~r(s(z), elem!1)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[5433, 35029, 17618])).
% 12.19/12.40 tff(35055,plain,
% 12.19/12.40 (b(s(z), elem!1)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[632, 35054, 24])).
% 12.19/12.40 tff(35056,plain,
% 12.19/12.40 (~b(s(s(s(s(z)))), s(z))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[20920, 35055, 90, 35025, 721])).
% 12.19/12.40 tff(35057,plain,
% 12.19/12.40 (r(s(s(s(s(z)))), s(z))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[749, 35056])).
% 12.19/12.40 tff(35058,plain,
% 12.19/12.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.19/12.40 inference(rewrite,[status(thm)],[])).
% 12.19/12.40 tff(35059,plain,
% 12.19/12.40 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.19/12.40 inference(rewrite,[status(thm)],[])).
% 12.19/12.40 tff(35060,plain,
% 12.19/12.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 12.19/12.40 inference(monotonicity,[status(thm)],[35059])).
% 12.19/12.40 tff(35061,plain,
% 12.19/12.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.19/12.40 inference(transitivity,[status(thm)],[35060, 35058])).
% 12.19/12.40 tff(35062,plain,
% 12.19/12.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.19/12.40 inference(quant_inst,[status(thm)],[])).
% 12.19/12.40 tff(35063,plain,
% 12.19/12.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 12.19/12.40 inference(modus_ponens,[status(thm)],[35062, 35061])).
% 12.19/12.40 tff(35064,plain,
% 12.19/12.40 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[35063, 194, 35057, 35053, 35035])).
% 12.19/12.40 tff(35065,plain,
% 12.19/12.40 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[29527, 42, 8094, 35064])).
% 12.19/12.40 tff(35066,plain,
% 12.19/12.40 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[34993, 194, 1216, 35057, 35053])).
% 12.19/12.40 tff(35067,plain,
% 12.19/12.40 (b(s(s(s(s(s(s(z)))))), s(z))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[14139, 35066])).
% 12.19/12.40 tff(35068,plain,
% 12.19/12.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.19/12.40 inference(rewrite,[status(thm)],[])).
% 12.19/12.40 tff(35069,plain,
% 12.19/12.40 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.19/12.40 inference(rewrite,[status(thm)],[])).
% 12.19/12.40 tff(35070,plain,
% 12.19/12.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 12.19/12.40 inference(monotonicity,[status(thm)],[35069])).
% 12.19/12.40 tff(35071,plain,
% 12.19/12.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.19/12.40 inference(transitivity,[status(thm)],[35070, 35068])).
% 12.19/12.40 tff(35072,plain,
% 12.19/12.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.19/12.40 inference(quant_inst,[status(thm)],[])).
% 12.19/12.40 tff(35073,plain,
% 12.19/12.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 12.19/12.40 inference(modus_ponens,[status(thm)],[35072, 35071])).
% 12.19/12.40 tff(35074,plain,
% 12.19/12.40 ($false),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[35073, 391, 1686, 35030, 17636, 35067, 35065])).
% 12.19/12.40 tff(35075,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.40 tff(35076,plain,
% 12.19/12.40 (~b(z, s(s(s(s(z)))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[35075, 1747, 90, 3823, 11, 35026, 59, 721, 1526, 1216])).
% 12.19/12.40 tff(35077,plain,
% 12.19/12.40 (r(z, s(s(s(s(z)))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[800, 35076])).
% 12.19/12.40 tff(35078,plain,
% 12.19/12.40 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[1090, 327, 410, 34312])).
% 12.19/12.40 tff(35079,plain,
% 12.19/12.40 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[1095, 35078, 32512])).
% 12.19/12.40 tff(35080,plain,
% 12.19/12.40 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[27316, 35079, 11])).
% 12.19/12.40 tff(35081,plain,
% 12.19/12.40 (~r(s(z), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[1224, 723, 1216, 719])).
% 12.19/12.40 tff(35082,plain,
% 12.19/12.40 (b(s(z), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[180, 35081])).
% 12.19/12.40 tff(35083,plain,
% 12.19/12.40 (~b(s(s(z)), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[7203, 35082, 90, 664, 3823])).
% 12.19/12.40 tff(35084,plain,
% 12.19/12.40 (r(s(s(z)), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[1211, 35083])).
% 12.19/12.40 tff(35085,plain,
% 12.19/12.40 (~r(elem!1, s(z))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[6347, 723, 1216, 34300])).
% 12.19/12.40 tff(35086,plain,
% 12.19/12.40 (~r(z, s(elem!1))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[8832, 35085, 11])).
% 12.19/12.40 tff(35087,plain,
% 12.19/12.40 (~r(elem!1, s(elem!1))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[2288, 35086, 11])).
% 12.19/12.40 tff(35088,plain,
% 12.19/12.40 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 12.19/12.40 inference(monotonicity,[status(thm)],[32149])).
% 12.19/12.40 tff(35089,plain,
% 12.19/12.40 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 12.19/12.40 inference(modus_ponens,[status(thm)],[34126, 35088])).
% 12.19/12.40 tff(35090,plain,
% 12.19/12.40 (r(s(s(s(elem!1))), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[34889, 35086, 11, 90, 10, 664, 35085, 35089, 35087, 410, 127])).
% 12.19/12.40 tff(35091,plain,
% 12.19/12.40 (r(s(s(s(z))), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[4409, 35090, 11])).
% 12.19/12.40 tff(35092,plain,
% 12.19/12.40 ($false),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[32407, 35091, 35084, 719, 30159])).
% 12.19/12.40 tff(35093,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), z)) | b(z, s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.40 tff(35094,plain,
% 12.19/12.40 (~r(s(s(s(s(z)))), s(z))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[35093, 30158, 719, 11, 90, 10, 35025, 410, 127, 3823, 1216])).
% 12.19/12.40 tff(35095,plain,
% 12.19/12.40 (b(s(s(s(s(z)))), s(z))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[749, 35094])).
% 12.19/12.40 tff(35096,plain,
% 12.19/12.40 (~b(s(z), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[20495, 35095, 35025, 1526, 35080])).
% 12.19/12.40 tff(35097,plain,
% 12.19/12.40 (r(s(z), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[180, 35096])).
% 12.19/12.40 tff(35098,plain,
% 12.19/12.40 (~r(s(z), s(s(s(elem!1))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[337, 35097, 59, 327])).
% 12.19/12.40 tff(35099,plain,
% 12.19/12.40 (b(s(z), s(s(s(elem!1))))),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[247, 35098])).
% 12.19/12.40 tff(35100,plain,
% 12.19/12.40 (~b(s(s(s(elem!1))), elem!1)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[2907, 35099, 721, 1526])).
% 12.19/12.40 tff(35101,plain,
% 12.19/12.40 (r(s(s(s(elem!1))), elem!1)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[230, 35100, 127])).
% 12.19/12.40 tff(35102,plain,
% 12.19/12.40 (r(s(s(s(elem!1))), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[406, 35101, 11])).
% 12.19/12.40 tff(35103,plain,
% 12.19/12.40 (~b(s(s(z)), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[14992, 35099, 90, 35025, 3563])).
% 12.19/12.40 tff(35104,plain,
% 12.19/12.40 (r(s(s(z)), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[1211, 35103])).
% 12.19/12.40 tff(35105,plain,
% 12.19/12.40 (~r(s(s(s(z))), z)),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[32407, 35104, 719, 30158])).
% 12.19/12.40 tff(35106,plain,
% 12.19/12.40 ($false),
% 12.19/12.40 inference(unit_resolution,[status(thm)],[4409, 35105, 35102, 11])).
% 12.19/12.40 tff(35107,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = z)) | (~r(z, s(s(s(s(z)))))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.41 tff(35108,plain,
% 12.19/12.41 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[35107, 719, 11, 127, 90, 3563, 721, 1526, 10, 410, 3823, 1216])).
% 12.19/12.41 tff(35109,plain,
% 12.19/12.41 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[1370, 35108, 15838])).
% 12.19/12.41 tff(35110,plain,
% 12.19/12.41 (b(s(s(s(z))), s(s(z)))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[2986, 35109, 11])).
% 12.19/12.41 tff(35111,plain,
% 12.19/12.41 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[24809, 35110, 3823, 3563])).
% 12.19/12.41 tff(35112,plain,
% 12.19/12.41 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.41 inference(modus_ponens,[status(thm)],[35111, 30118])).
% 12.19/12.41 tff(35113,plain,
% 12.19/12.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.19/12.41 inference(rewrite,[status(thm)],[])).
% 12.19/12.41 tff(35114,plain,
% 12.19/12.41 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.19/12.41 inference(rewrite,[status(thm)],[])).
% 12.19/12.41 tff(35115,plain,
% 12.19/12.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 12.19/12.41 inference(monotonicity,[status(thm)],[35114])).
% 12.19/12.41 tff(35116,plain,
% 12.19/12.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.19/12.41 inference(transitivity,[status(thm)],[35115, 35113])).
% 12.19/12.41 tff(35117,plain,
% 12.19/12.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 12.19/12.41 inference(quant_inst,[status(thm)],[])).
% 12.19/12.41 tff(35118,plain,
% 12.19/12.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 12.19/12.41 inference(modus_ponens,[status(thm)],[35117, 35116])).
% 12.19/12.41 tff(35119,plain,
% 12.19/12.41 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[35118, 391, 3823, 90, 3563, 35110])).
% 12.19/12.41 tff(35120,plain,
% 12.19/12.41 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[1673, 35119, 11])).
% 12.19/12.41 tff(35121,plain,
% 12.19/12.41 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[25443, 35120, 35026, 34300, 410])).
% 12.19/12.41 tff(35122,plain,
% 12.19/12.41 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[29931, 35121, 11])).
% 12.19/12.41 tff(35123,plain,
% 12.19/12.41 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[1095, 35122, 32512])).
% 12.19/12.41 tff(35124,plain,
% 12.19/12.41 ($false),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[35123, 35112])).
% 12.19/12.41 tff(35125,plain,((~r(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(s(s(elem!1)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.41 tff(35126,plain,
% 12.19/12.41 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[35125, 35077, 410, 3823, 90, 11, 127, 721, 1526, 10, 1216])).
% 12.19/12.41 tff(35127,plain,
% 12.19/12.41 (r(s(s(s(s(z)))), s(s(z)))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[1714, 35126])).
% 12.19/12.41 tff(35128,plain,
% 12.19/12.41 (~r(s(s(z)), z)),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[11508, 35127, 1216, 1747])).
% 12.19/12.41 tff(35129,plain,
% 12.19/12.41 (~b(s(s(z)), z)),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[22034, 35127, 90, 35025, 1216, 3823])).
% 12.19/12.41 tff(35130,plain,
% 12.19/12.41 ($false),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[1211, 35129, 35128])).
% 12.19/12.41 tff(35131,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = z)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.41 tff(35132,plain,
% 12.19/12.41 (~r(s(z), s(s(z)))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[35131, 3823, 1216, 90, 410, 11, 127, 721, 1526, 10])).
% 12.19/12.41 tff(35133,plain,
% 12.19/12.41 (b(s(z), s(s(z)))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[1788, 35132])).
% 12.19/12.41 tff(35134,plain,
% 12.19/12.41 (~b(z, s(s(z)))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[30651, 35133, 33675, 35025, 3823])).
% 12.19/12.41 tff(35135,plain,
% 12.19/12.41 (~b(z, s(s(elem!1)))),
% 12.19/12.41 inference(modus_ponens,[status(thm)],[35134, 29965])).
% 12.19/12.41 tff(35136,plain,
% 12.19/12.41 (b(s(z), z)),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[3924, 35135, 10, 15838])).
% 12.19/12.41 tff(35137,plain,
% 12.19/12.41 (~b(s(s(z)), z)),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[7203, 35136, 90, 35025, 3823])).
% 12.19/12.41 tff(35138,plain,
% 12.19/12.41 (r(s(s(z)), z)),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[1211, 35137])).
% 12.19/12.41 tff(35139,plain,
% 12.19/12.41 (r(z, s(s(z)))),
% 12.19/12.41 inference(unit_resolution,[status(thm)],[18613, 35134])).
% 12.19/12.41 tff(35140,plain,
% 12.19/12.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))))),
% 12.19/12.41 inference(rewrite,[status(thm)],[])).
% 12.19/12.41 tff(35141,plain,
% 12.19/12.41 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))))),
% 12.19/12.41 inference(rewrite,[status(thm)],[])).
% 12.19/12.41 tff(35142,plain,
% 12.19/12.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z))))))),
% 12.19/12.41 inference(monotonicity,[status(thm)],[35141])).
% 12.19/12.42 tff(35143,plain,
% 12.19/12.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))))),
% 12.19/12.42 inference(transitivity,[status(thm)],[35142, 35140])).
% 12.19/12.42 tff(35144,plain,
% 12.19/12.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 12.19/12.42 inference(quant_inst,[status(thm)],[])).
% 12.19/12.42 tff(35145,plain,
% 12.19/12.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z))))),
% 12.19/12.42 inference(modus_ponens,[status(thm)],[35144, 35143])).
% 12.19/12.42 tff(35146,plain,
% 12.19/12.42 (~b(s(s(s(z))), z)),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[35145, 391, 3823, 35133, 35025, 17636])).
% 12.19/12.42 tff(35147,plain,
% 12.19/12.42 (~b(s(s(s(elem!1))), z)),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[1680, 35146, 11])).
% 12.19/12.42 tff(35148,plain,
% 12.19/12.42 (r(s(s(s(elem!1))), z)),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[377, 35147])).
% 12.19/12.42 tff(35149,plain,
% 12.19/12.42 (r(s(s(s(z))), z)),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[4409, 35148, 11])).
% 12.19/12.42 tff(35150,plain,
% 12.19/12.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 12.19/12.42 inference(rewrite,[status(thm)],[])).
% 12.19/12.42 tff(35151,plain,
% 12.19/12.42 (((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 12.19/12.42 inference(rewrite,[status(thm)],[])).
% 12.19/12.42 tff(35152,plain,
% 12.19/12.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))))),
% 12.19/12.42 inference(monotonicity,[status(thm)],[35151])).
% 12.19/12.42 tff(35153,plain,
% 12.19/12.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 12.19/12.42 inference(transitivity,[status(thm)],[35152, 35150])).
% 12.19/12.42 tff(35154,plain,
% 12.19/12.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 12.19/12.42 inference(quant_inst,[status(thm)],[])).
% 12.19/12.42 tff(35155,plain,
% 12.19/12.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))),
% 12.19/12.42 inference(modus_ponens,[status(thm)],[35154, 35153])).
% 12.19/12.42 tff(35156,plain,
% 12.19/12.42 ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[35155, 194, 3557, 4428])).
% 12.19/12.42 tff(35157,plain,
% 12.19/12.42 ($false),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[35156, 4382, 8505])).
% 12.19/12.42 tff(35158,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.42 tff(35159,plain,
% 12.19/12.42 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[35158, 35149, 11, 35139, 35138])).
% 12.19/12.42 tff(35160,plain,
% 12.19/12.42 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[1370, 35159, 15838])).
% 12.19/12.42 tff(35161,plain,
% 12.19/12.42 (b(s(s(s(z))), s(s(z)))),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[2986, 35160, 11])).
% 12.19/12.42 tff(35162,plain,
% 12.19/12.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.19/12.42 inference(rewrite,[status(thm)],[])).
% 12.19/12.42 tff(35163,plain,
% 12.19/12.42 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.19/12.42 inference(rewrite,[status(thm)],[])).
% 12.19/12.42 tff(35164,plain,
% 12.19/12.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 12.19/12.42 inference(monotonicity,[status(thm)],[35163])).
% 12.19/12.42 tff(35165,plain,
% 12.19/12.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.19/12.42 inference(transitivity,[status(thm)],[35164, 35162])).
% 12.19/12.42 tff(35166,plain,
% 12.19/12.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 12.19/12.42 inference(quant_inst,[status(thm)],[])).
% 12.19/12.42 tff(35167,plain,
% 12.19/12.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 12.19/12.42 inference(modus_ponens,[status(thm)],[35166, 35165])).
% 12.19/12.42 tff(35168,plain,
% 12.19/12.42 ($false),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[35167, 391, 3823, 90, 35133, 35161, 17636])).
% 12.19/12.42 tff(35169,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | b(z, s(s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.42 tff(35170,plain,
% 12.19/12.42 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[35169, 1216, 33627, 10, 90, 33634, 9, 721, 35024])).
% 12.19/12.42 tff(35171,plain,
% 12.19/12.42 (r(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[3652, 35170])).
% 12.19/12.42 tff(35172,plain,
% 12.19/12.42 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 12.19/12.42 inference(monotonicity,[status(thm)],[34917])).
% 12.19/12.42 tff(35173,plain,
% 12.19/12.42 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 12.19/12.42 inference(symmetry,[status(thm)],[35172])).
% 12.19/12.42 tff(35174,plain,
% 12.19/12.42 (b(s(s(s(z))), s(z))),
% 12.19/12.42 inference(modus_ponens,[status(thm)],[35024, 35173])).
% 12.19/12.42 tff(35175,plain,
% 12.19/12.42 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 12.19/12.42 inference(monotonicity,[status(thm)],[11])).
% 12.19/12.42 tff(35176,plain,
% 12.19/12.42 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 12.19/12.42 inference(symmetry,[status(thm)],[35175])).
% 12.19/12.42 tff(35177,plain,
% 12.19/12.42 (r(s(s(z)), elem!1)),
% 12.19/12.42 inference(modus_ponens,[status(thm)],[3557, 35176])).
% 12.19/12.42 tff(35178,plain,
% 12.19/12.42 (~r(s(s(s(s(z)))), s(z))),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[16406, 719, 1749, 3557])).
% 12.19/12.42 tff(35179,plain,
% 12.19/12.42 (b(s(s(s(s(z)))), s(z))),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[749, 35178])).
% 12.19/12.42 tff(35180,plain,
% 12.19/12.42 (~b(s(z), elem!1)),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[20920, 35179, 90, 664, 721])).
% 12.19/12.42 tff(35181,plain,
% 12.19/12.42 (r(s(z), elem!1)),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[632, 35180, 150])).
% 12.19/12.42 tff(35182,plain,
% 12.19/12.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 12.19/12.42 inference(rewrite,[status(thm)],[])).
% 12.19/12.42 tff(35183,plain,
% 12.19/12.42 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 12.19/12.42 inference(rewrite,[status(thm)],[])).
% 12.19/12.42 tff(35184,plain,
% 12.19/12.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))))),
% 12.19/12.42 inference(monotonicity,[status(thm)],[35183])).
% 12.19/12.42 tff(35185,plain,
% 12.19/12.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 12.19/12.42 inference(transitivity,[status(thm)],[35184, 35182])).
% 12.19/12.42 tff(35186,plain,
% 12.19/12.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 12.19/12.42 inference(quant_inst,[status(thm)],[])).
% 12.19/12.42 tff(35187,plain,
% 12.19/12.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 12.19/12.42 inference(modus_ponens,[status(thm)],[35186, 35185])).
% 12.19/12.42 tff(35188,plain,
% 12.19/12.42 ($false),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[35187, 194, 410, 1484, 6669, 2405])).
% 12.19/12.42 tff(35189,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.42 tff(35190,plain,
% 12.19/12.42 (~r(s(s(z)), s(z))),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[35189, 35181, 410, 6669])).
% 12.19/12.42 tff(35191,plain,
% 12.19/12.42 (b(s(s(z)), s(z))),
% 12.19/12.42 inference(unit_resolution,[status(thm)],[3778, 35190])).
% 12.19/12.42 tff(35192,plain,
% 12.19/12.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 12.19/12.43 inference(rewrite,[status(thm)],[])).
% 12.19/12.43 tff(35193,plain,
% 12.19/12.43 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 12.19/12.43 inference(rewrite,[status(thm)],[])).
% 12.19/12.43 tff(35194,plain,
% 12.19/12.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 12.19/12.43 inference(monotonicity,[status(thm)],[35193])).
% 12.19/12.43 tff(35195,plain,
% 12.19/12.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 12.19/12.43 inference(transitivity,[status(thm)],[35194, 35192])).
% 12.19/12.43 tff(35196,plain,
% 12.19/12.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 12.19/12.43 inference(quant_inst,[status(thm)],[])).
% 12.19/12.43 tff(35197,plain,
% 12.19/12.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 12.19/12.43 inference(modus_ponens,[status(thm)],[35196, 35195])).
% 12.19/12.43 tff(35198,plain,
% 12.19/12.43 ($false),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[35197, 391, 90, 1759, 2439, 1233, 664])).
% 12.19/12.43 tff(35199,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.43 tff(35200,plain,
% 12.19/12.43 (~b(s(z), s(s(z)))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[35199, 35191, 90, 664, 35179])).
% 12.19/12.43 tff(35201,plain,
% 12.19/12.43 (r(s(z), s(s(z)))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[1788, 35200])).
% 12.19/12.43 tff(35202,plain,
% 12.19/12.43 (r(s(z), z)),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[5433, 35181, 94])).
% 12.19/12.43 tff(35203,plain,
% 12.19/12.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 12.19/12.43 inference(rewrite,[status(thm)],[])).
% 12.19/12.43 tff(35204,plain,
% 12.19/12.43 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 12.19/12.43 inference(rewrite,[status(thm)],[])).
% 12.19/12.43 tff(35205,plain,
% 12.19/12.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))))),
% 12.19/12.43 inference(monotonicity,[status(thm)],[35204])).
% 12.19/12.43 tff(35206,plain,
% 12.19/12.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 12.19/12.43 inference(transitivity,[status(thm)],[35205, 35203])).
% 12.19/12.43 tff(35207,plain,
% 12.19/12.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 12.19/12.43 inference(quant_inst,[status(thm)],[])).
% 12.19/12.43 tff(35208,plain,
% 12.19/12.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))),
% 12.19/12.43 inference(modus_ponens,[status(thm)],[35207, 35206])).
% 12.19/12.43 tff(35209,plain,
% 12.19/12.43 ($false),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[35208, 194, 35202, 3557, 35201, 719])).
% 12.19/12.43 tff(35210,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~(z = elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.43 tff(35211,plain,
% 12.19/12.43 (~r(z, s(s(s(s(z)))))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[35210, 3557, 90, 35025, 410, 35177, 17618, 24, 721, 1749])).
% 12.19/12.43 tff(35212,plain,
% 12.19/12.43 (b(z, s(s(s(s(z)))))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[800, 35211])).
% 12.19/12.43 tff(35213,plain,
% 12.19/12.43 (~r(s(s(s(s(z)))), s(z))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[16396, 1747, 1216, 1749])).
% 12.19/12.43 tff(35214,plain,
% 12.19/12.43 (b(s(s(s(s(z)))), s(z))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[749, 35213])).
% 12.19/12.43 tff(35215,plain,
% 12.19/12.43 (~b(s(z), elem!1)),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[20920, 35214, 90, 664, 721])).
% 12.19/12.43 tff(35216,plain,
% 12.19/12.43 (r(s(z), elem!1)),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[632, 35215, 150])).
% 12.19/12.43 tff(35217,plain,
% 12.19/12.43 (r(s(z), z)),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[5433, 35216, 94])).
% 12.19/12.43 tff(35218,plain,
% 12.19/12.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 12.19/12.43 inference(rewrite,[status(thm)],[])).
% 12.19/12.43 tff(35219,plain,
% 12.19/12.43 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 12.19/12.43 inference(rewrite,[status(thm)],[])).
% 12.19/12.43 tff(35220,plain,
% 12.19/12.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(z))))))),
% 12.19/12.43 inference(monotonicity,[status(thm)],[35219])).
% 12.19/12.43 tff(35221,plain,
% 12.19/12.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 12.19/12.43 inference(transitivity,[status(thm)],[35220, 35218])).
% 12.19/12.43 tff(35222,plain,
% 12.19/12.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 12.19/12.43 inference(quant_inst,[status(thm)],[])).
% 12.19/12.43 tff(35223,plain,
% 12.19/12.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(z))))),
% 12.19/12.43 inference(modus_ponens,[status(thm)],[35222, 35221])).
% 12.19/12.43 tff(35224,plain,
% 12.19/12.43 ($false),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[35223, 194, 35217, 3557, 1747, 15510])).
% 12.19/12.43 tff(35225,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~(z = elem!1)) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.43 tff(35226,plain,
% 12.19/12.43 (~r(s(z), s(s(z)))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[35225, 3557, 15510, 17618, 24, 90, 35025, 721, 1216, 1749])).
% 12.19/12.43 tff(35227,plain,
% 12.19/12.43 (b(s(z), s(s(z)))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[1788, 35226])).
% 12.19/12.43 tff(35228,plain,
% 12.19/12.43 (~b(s(s(z)), s(z))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[34139, 35227, 410, 4416, 90, 11, 4028, 127, 34091, 35212])).
% 12.19/12.43 tff(35229,plain,
% 12.19/12.43 (r(s(s(z)), s(z))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[3778, 35228])).
% 12.19/12.43 tff(35230,plain,
% 12.19/12.43 (~b(s(z), z)),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[5585, 35229, 1216, 35025, 1749])).
% 12.19/12.43 tff(35231,plain,
% 12.19/12.43 (~r(s(z), elem!1)),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[35189, 35229, 410, 35177])).
% 12.19/12.43 tff(35232,plain,
% 12.19/12.43 ($false),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[3205, 35231, 35230, 11])).
% 12.19/12.43 tff(35233,plain,((~r(s(s(z)), z)) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | b(elem!1, s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(s(z))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.43 tff(35234,plain,
% 12.19/12.43 (~r(s(s(z)), z)),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[35233, 1216, 33634, 33627, 35171, 35174, 90, 33633, 9, 34920, 721])).
% 12.19/12.43 tff(35235,plain,
% 12.19/12.43 (b(s(s(z)), z)),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[1211, 35234])).
% 12.19/12.43 tff(35236,plain,
% 12.19/12.43 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 12.19/12.43 inference(monotonicity,[status(thm)],[33627])).
% 12.19/12.43 tff(35237,plain,
% 12.19/12.43 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 12.19/12.43 inference(symmetry,[status(thm)],[35236])).
% 12.19/12.43 tff(35238,plain,
% 12.19/12.43 (b(s(s(s(s(z)))), elem!1)),
% 12.19/12.43 inference(modus_ponens,[status(thm)],[90, 35237])).
% 12.19/12.43 tff(35239,plain,
% 12.19/12.43 (~r(s(z), s(s(z)))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[33889, 1686, 1216, 90, 1235])).
% 12.19/12.43 tff(35240,plain,
% 12.19/12.43 (b(s(z), s(s(z)))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[1788, 35239])).
% 12.19/12.43 tff(35241,plain,
% 12.19/12.43 (~b(s(z), z)),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[16487, 35240, 90, 1235, 1686])).
% 12.19/12.43 tff(35242,plain,
% 12.19/12.43 (b(z, s(s(elem!1)))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[3924, 35241, 10, 15838])).
% 12.19/12.43 tff(35243,plain,
% 12.19/12.43 (~b(s(s(elem!1)), s(z))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[26460, 35242, 664, 35240, 33921])).
% 12.19/12.43 tff(35244,plain,
% 12.19/12.43 (r(s(s(elem!1)), s(z))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[362, 35243])).
% 12.19/12.43 tff(35245,plain,
% 12.19/12.43 (~b(s(s(s(s(z)))), s(z))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[23366, 35240, 90, 664, 1235])).
% 12.19/12.43 tff(35246,plain,
% 12.19/12.43 (r(s(s(s(s(z)))), s(z))),
% 12.19/12.43 inference(unit_resolution,[status(thm)],[749, 35245])).
% 12.19/12.44 tff(35247,plain,
% 12.19/12.44 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 12.19/12.44 inference(monotonicity,[status(thm)],[489])).
% 12.19/12.44 tff(35248,plain,
% 12.19/12.44 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 12.19/12.44 inference(transitivity,[status(thm)],[35247, 940])).
% 12.19/12.44 tff(35249,plain,
% 12.19/12.44 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 12.19/12.44 inference(symmetry,[status(thm)],[35248])).
% 12.19/12.44 tff(35250,plain,
% 12.19/12.44 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 12.19/12.44 inference(monotonicity,[status(thm)],[35249])).
% 12.19/12.44 tff(35251,plain,
% 12.19/12.44 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 12.19/12.44 inference(modus_ponens,[status(thm)],[714, 35250])).
% 12.19/12.44 tff(35252,plain,
% 12.19/12.44 (r(s(z), elem!1)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[3205, 35241, 11])).
% 12.19/12.44 tff(35253,plain,
% 12.19/12.44 (~b(elem!1, s(s(elem!1)))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[2028, 35244, 35252, 35251, 33683, 35246])).
% 12.19/12.44 tff(35254,plain,
% 12.19/12.44 (r(elem!1, s(s(elem!1)))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[1307, 35253, 30031])).
% 12.19/12.44 tff(35255,plain,
% 12.19/12.44 (~r(elem!1, s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[6408, 35254, 1216, 35244])).
% 12.19/12.44 tff(35256,plain,
% 12.19/12.44 (~r(z, s(elem!1))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[8832, 35255, 11])).
% 12.19/12.44 tff(35257,plain,
% 12.19/12.44 (~r(elem!1, s(elem!1))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[2288, 35256, 11])).
% 12.19/12.44 tff(35258,plain,
% 12.19/12.44 (b(elem!1, s(s(z)))),
% 12.19/12.44 inference(modus_ponens,[status(thm)],[34443, 23194])).
% 12.19/12.44 tff(35259,plain,
% 12.19/12.44 (b(s(s(s(z))), s(z))),
% 12.19/12.44 inference(modus_ponens,[status(thm)],[224, 17635])).
% 12.19/12.44 tff(35260,plain,
% 12.19/12.44 (b(s(z), s(s(s(z))))),
% 12.19/12.44 inference(modus_ponens,[status(thm)],[20924, 18545])).
% 12.19/12.44 tff(35261,plain,
% 12.19/12.44 (~b(s(s(s(s(z)))), s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[4452, 35260, 664, 4414, 35259, 29913])).
% 12.19/12.44 tff(35262,plain,
% 12.19/12.44 (r(s(s(s(s(z)))), s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[749, 35261])).
% 12.19/12.44 tff(35263,plain,
% 12.19/12.44 (~b(s(z), elem!1)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[3200, 91, 11])).
% 12.19/12.44 tff(35264,plain,
% 12.19/12.44 (~b(s(z), s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[34693, 35263, 17618, 34438, 664, 832])).
% 12.19/12.44 tff(35265,plain,
% 12.19/12.44 (r(s(z), s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[1230, 35264])).
% 12.19/12.44 tff(35266,plain,
% 12.19/12.44 (~r(z, s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[1224, 35262, 181, 35265])).
% 12.19/12.44 tff(35267,plain,
% 12.19/12.44 (b(z, s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[800, 35266])).
% 12.19/12.44 tff(35268,plain,
% 12.19/12.44 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[22399, 35267, 34440, 1652, 34446])).
% 12.19/12.44 tff(35269,plain,
% 12.19/12.44 (r(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[3652, 35268])).
% 12.19/12.44 tff(35270,plain,
% 12.19/12.44 (~r(s(z), s(s(z)))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[16396, 35269, 35265, 35262])).
% 12.19/12.44 tff(35271,plain,
% 12.19/12.44 (b(s(z), s(s(z)))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[1788, 35270])).
% 12.19/12.44 tff(35272,plain,
% 12.19/12.44 (~r(s(s(z)), s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[9149, 35269, 34471, 35262])).
% 12.19/12.44 tff(35273,plain,
% 12.19/12.44 (b(s(s(z)), s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[3778, 35272])).
% 12.19/12.44 tff(35274,plain,
% 12.19/12.44 ($false),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[10150, 35273, 35271, 34440, 35258])).
% 12.19/12.44 tff(35275,plain,(b(s(z), z) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(z))) | (s(s(s(s(z)))) = s(s(s(z)))) | (~(elem!1 = z)) | r(elem!1, s(z)) | (~r(s(s(s(elem!1))), z)) | b(z, s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.44 tff(35276,plain,
% 12.19/12.44 (~r(s(s(s(elem!1))), z)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[35275, 35255, 11, 33675, 664, 35241, 35089, 10, 15838])).
% 12.19/12.44 tff(35277,plain,
% 12.19/12.44 ($false),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[34889, 35276, 35256, 11, 90, 10, 664, 35255, 35089, 35257, 410, 127])).
% 12.19/12.44 tff(35278,plain,((~b(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), z)) | b(z, s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.44 tff(35279,plain,
% 12.19/12.44 (~b(z, s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[35278, 1216, 90, 10, 34412, 33634, 9, 33627, 35235])).
% 12.19/12.44 tff(35280,plain,
% 12.19/12.44 (r(z, s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[800, 35279])).
% 12.19/12.44 tff(35281,plain,
% 12.19/12.44 (~b(s(z), z)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[16415, 723, 664, 1216, 1749, 719])).
% 12.19/12.44 tff(35282,plain,
% 12.19/12.44 ($false),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[180, 35081, 35281])).
% 12.19/12.44 tff(35283,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.44 tff(35284,plain,
% 12.19/12.44 (~r(s(s(s(s(z)))), s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[35283, 1216, 35280, 34412, 35171])).
% 12.19/12.44 tff(35285,plain,
% 12.19/12.44 (b(s(s(s(s(z)))), s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[749, 35284])).
% 12.19/12.44 tff(35286,plain,
% 12.19/12.44 (~b(s(z), s(s(z)))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[2447, 35285, 35238, 721, 35235])).
% 12.19/12.44 tff(35287,plain,
% 12.19/12.44 (r(s(z), s(s(z)))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[1788, 35286])).
% 12.19/12.44 tff(35288,plain,
% 12.19/12.44 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[22815, 35287, 1216, 35171])).
% 12.19/12.44 tff(35289,plain,
% 12.19/12.44 (~b(s(z), elem!1)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[20920, 35285, 90, 34412, 721])).
% 12.19/12.44 tff(35290,plain,
% 12.19/12.44 (r(s(z), elem!1)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[632, 35289, 34897])).
% 12.19/12.44 tff(35291,plain,
% 12.19/12.44 (r(s(z), z)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[5433, 35290, 34898])).
% 12.19/12.44 tff(35292,plain,
% 12.19/12.44 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[20333, 35291, 35238, 721, 35171, 35235, 90, 35285])).
% 12.19/12.44 tff(35293,plain,
% 12.19/12.44 ($false),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[1714, 35292, 35288])).
% 12.19/12.44 tff(35294,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)) | b(z, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.19/12.44 tff(35295,plain,
% 12.19/12.44 (~r(s(z), s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[35294, 34410, 90, 10, 1, 80])).
% 12.19/12.44 tff(35296,plain,
% 12.19/12.44 (b(s(z), s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[1230, 35295])).
% 12.19/12.44 tff(35297,plain,
% 12.19/12.44 (~b(s(z), z)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[28088, 35296, 90, 34411])).
% 12.19/12.44 tff(35298,plain,
% 12.19/12.44 (r(s(z), elem!1)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[3205, 35297, 33627])).
% 12.19/12.44 tff(35299,plain,
% 12.19/12.44 (~b(s(s(s(s(z)))), s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[22918, 35296, 90, 34411])).
% 12.19/12.44 tff(35300,plain,
% 12.19/12.44 (r(s(s(s(s(z)))), s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[749, 35299])).
% 12.19/12.44 tff(35301,plain,
% 12.19/12.44 ($false),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[34686, 35300, 35297, 34898, 90, 34410, 35296, 35298])).
% 12.19/12.44 tff(35302,plain,(b(z, s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.19/12.44 tff(35303,plain,
% 12.19/12.44 (b(z, s(s(s(elem!1))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[35302, 88, 1, 80, 33631])).
% 12.19/12.44 tff(35304,plain,
% 12.19/12.44 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 12.19/12.44 inference(symmetry,[status(thm)],[34417])).
% 12.19/12.44 tff(35305,plain,
% 12.19/12.44 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 12.19/12.44 inference(symmetry,[status(thm)],[34416])).
% 12.19/12.44 tff(35306,plain,
% 12.19/12.44 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 12.19/12.44 inference(transitivity,[status(thm)],[35305, 35304])).
% 12.19/12.44 tff(35307,plain,
% 12.19/12.44 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.19/12.44 inference(transitivity,[status(thm)],[34429, 35006])).
% 12.19/12.44 tff(35308,plain,
% 12.19/12.44 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 12.19/12.44 inference(monotonicity,[status(thm)],[35307])).
% 12.19/12.44 tff(35309,plain,
% 12.19/12.44 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.19/12.44 inference(modus_ponens,[status(thm)],[32322, 35308])).
% 12.19/12.44 tff(35310,plain,
% 12.19/12.44 (b(z, s(s(s(elem!1))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[35302, 90, 1, 80, 6221])).
% 12.19/12.44 tff(35311,plain,
% 12.19/12.44 ((elem!1 = s(s(z))) <=> (z = s(s(z)))),
% 12.19/12.44 inference(monotonicity,[status(thm)],[33627])).
% 12.19/12.44 tff(35312,plain,
% 12.19/12.44 ((elem!1 = s(s(z))) <=> (s(s(z)) = z)),
% 12.19/12.44 inference(transitivity,[status(thm)],[35311, 11715])).
% 12.19/12.44 tff(35313,plain,
% 12.19/12.44 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 12.19/12.44 inference(symmetry,[status(thm)],[35312])).
% 12.19/12.44 tff(35314,plain,
% 12.19/12.44 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 12.19/12.44 inference(monotonicity,[status(thm)],[35313])).
% 12.19/12.44 tff(35315,plain,
% 12.19/12.44 (~(elem!1 = s(s(z)))),
% 12.19/12.44 inference(modus_ponens,[status(thm)],[1207, 35314])).
% 12.19/12.44 tff(35316,plain,
% 12.19/12.44 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 12.19/12.44 inference(transitivity,[status(thm)],[34152, 34150])).
% 12.19/12.44 tff(35317,plain,
% 12.19/12.44 (b(elem!1, s(s(s(s(elem!1)))))),
% 12.19/12.44 inference(modus_ponens,[status(thm)],[1686, 35316])).
% 12.19/12.44 tff(35318,plain,
% 12.19/12.44 (b(s(s(elem!1)), elem!1)),
% 12.19/12.44 inference(modus_ponens,[status(thm)],[1235, 30006])).
% 12.19/12.44 tff(35319,plain,
% 12.19/12.44 (~b(z, s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[22918, 1759, 90, 1234])).
% 12.19/12.44 tff(35320,plain,
% 12.19/12.44 (r(z, s(z))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[678, 35319])).
% 12.19/12.44 tff(35321,plain,
% 12.19/12.44 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[34242, 29072, 1234, 90, 1759, 35320, 1686])).
% 12.19/12.44 tff(35322,plain,
% 12.19/12.44 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[33872, 35321])).
% 12.19/12.44 tff(35323,plain,
% 12.19/12.44 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[34274, 194, 33887, 33885, 35322])).
% 12.19/12.44 tff(35324,plain,
% 12.19/12.44 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 35323])).
% 12.19/12.44 tff(35325,assumption,(b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 12.19/12.44 tff(35326,plain,
% 12.19/12.44 ($false),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[33994, 391, 90, 1235, 1686, 34218, 35325])).
% 12.19/12.44 tff(35327,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.44 tff(35328,plain,
% 12.19/12.44 (~b(s(s(s(s(s(s(z)))))), z)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[35327, 1686, 1235, 90, 35324])).
% 12.19/12.44 tff(35329,plain,
% 12.19/12.44 (r(s(s(s(s(s(s(z)))))), z)),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[34231, 35328])).
% 12.19/12.44 tff(35330,plain,
% 12.19/12.44 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[12232, 194, 35320, 29072, 35329])).
% 12.19/12.44 tff(35331,plain,
% 12.19/12.44 (b(s(z), s(s(s(s(s(s(z)))))))),
% 12.19/12.44 inference(unit_resolution,[status(thm)],[33778, 35330])).
% 12.19/12.44 tff(35332,plain,
% 12.19/12.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 12.19/12.44 inference(rewrite,[status(thm)],[])).
% 12.19/12.44 tff(35333,plain,
% 12.19/12.44 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 12.19/12.44 inference(rewrite,[status(thm)],[])).
% 12.19/12.44 tff(35334,plain,
% 12.19/12.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 12.19/12.44 inference(monotonicity,[status(thm)],[35333])).
% 12.19/12.44 tff(35335,plain,
% 12.19/12.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 12.19/12.44 inference(transitivity,[status(thm)],[35334, 35332])).
% 12.19/12.44 tff(35336,plain,
% 12.19/12.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 12.19/12.44 inference(quant_inst,[status(thm)],[])).
% 12.19/12.44 tff(35337,plain,
% 12.19/12.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 12.19/12.45 inference(modus_ponens,[status(thm)],[35336, 35335])).
% 12.19/12.45 tff(35338,plain,
% 12.19/12.45 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[35337, 194, 33887, 33885, 35322])).
% 12.19/12.45 tff(35339,plain,
% 12.19/12.45 ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[33813, 42, 35338])).
% 12.19/12.45 tff(35340,plain,
% 12.19/12.45 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[35339, 33800])).
% 12.19/12.45 tff(35341,plain,
% 12.19/12.45 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[12148, 194, 35320, 29072, 35329])).
% 12.19/12.45 tff(35342,plain,
% 12.19/12.45 (b(s(s(s(s(s(s(z)))))), s(z))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[14139, 35341])).
% 12.19/12.45 tff(35343,plain,
% 12.19/12.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 12.19/12.45 inference(rewrite,[status(thm)],[])).
% 12.19/12.45 tff(35344,plain,
% 12.19/12.45 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 12.19/12.45 inference(rewrite,[status(thm)],[])).
% 12.19/12.45 tff(35345,plain,
% 12.19/12.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 12.19/12.45 inference(monotonicity,[status(thm)],[35344])).
% 12.19/12.45 tff(35346,plain,
% 12.19/12.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 12.19/12.45 inference(transitivity,[status(thm)],[35345, 35343])).
% 12.19/12.45 tff(35347,plain,
% 12.19/12.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))),
% 12.19/12.45 inference(quant_inst,[status(thm)],[])).
% 12.19/12.45 tff(35348,plain,
% 12.19/12.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 12.19/12.45 inference(modus_ponens,[status(thm)],[35347, 35346])).
% 12.19/12.45 tff(35349,plain,
% 12.19/12.45 (~b(s(z), s(s(z)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[35348, 391, 1234, 35342, 35340, 35331])).
% 12.19/12.45 tff(35350,plain,
% 12.19/12.45 (r(s(z), s(s(z)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[1788, 35349])).
% 12.19/12.45 tff(35351,plain,
% 12.19/12.45 (~r(z, s(s(z)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[20331, 35350, 33887, 29072])).
% 12.19/12.45 tff(35352,plain,
% 12.19/12.45 (~r(z, s(s(elem!1)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[30084, 35351, 11])).
% 12.19/12.45 tff(35353,plain,
% 12.19/12.45 (b(z, s(s(elem!1)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[324, 35352])).
% 12.19/12.45 tff(35354,plain,
% 12.19/12.45 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[25778, 35353, 10682, 35318, 35317])).
% 12.19/12.45 tff(35355,plain,
% 12.19/12.45 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[1370, 35354, 297])).
% 12.19/12.45 tff(35356,plain,
% 12.19/12.45 (r(s(s(s(elem!1))), s(s(z)))),
% 12.19/12.45 inference(modus_ponens,[status(thm)],[35355, 30003])).
% 12.19/12.45 tff(35357,plain,
% 12.19/12.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 12.19/12.45 inference(rewrite,[status(thm)],[])).
% 12.19/12.45 tff(35358,plain,
% 12.19/12.45 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 12.19/12.45 inference(rewrite,[status(thm)],[])).
% 12.19/12.45 tff(35359,plain,
% 12.19/12.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 12.19/12.45 inference(monotonicity,[status(thm)],[35358])).
% 12.19/12.45 tff(35360,plain,
% 12.19/12.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 12.19/12.45 inference(transitivity,[status(thm)],[35359, 35357])).
% 12.19/12.45 tff(35361,plain,
% 12.19/12.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))),
% 12.19/12.45 inference(quant_inst,[status(thm)],[])).
% 12.19/12.45 tff(35362,plain,
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% 12.19/12.45 inference(modus_ponens,[status(thm)],[35361, 35360])).
% 12.19/12.45 tff(35363,plain,
% 12.19/12.45 (~b(s(s(z)), s(z))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[35362, 391, 1234, 35342, 35340, 35331])).
% 12.19/12.45 tff(35364,plain,
% 12.19/12.45 (r(s(s(z)), s(z))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[3778, 35363])).
% 12.19/12.45 tff(35365,plain,
% 12.19/12.45 (r(s(z), elem!1)),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[3205, 29071, 11])).
% 12.19/12.45 tff(35366,plain,
% 12.19/12.45 (b(elem!1, s(s(s(elem!1))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[23154, 10682, 11])).
% 12.19/12.45 tff(35367,plain,
% 12.19/12.45 (~r(elem!1, s(s(z)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[1775, 35350, 33675, 24, 33887, 1759])).
% 12.19/12.45 tff(35368,plain,
% 12.19/12.45 (b(elem!1, s(s(z)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[3394, 35367, 33689])).
% 12.19/12.45 tff(35369,plain,
% 12.19/12.45 (~r(s(s(s(elem!1))), s(z))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[10933, 35368, 35366, 35365, 35364])).
% 12.19/12.45 tff(35370,plain,
% 12.19/12.45 (b(s(s(s(elem!1))), s(z))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[223, 35369])).
% 12.19/12.45 tff(35371,plain,
% 12.19/12.45 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[6372, 35370, 1234, 1759, 90])).
% 12.19/12.45 tff(35372,plain,
% 12.19/12.45 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[27316, 35371, 11])).
% 12.19/12.45 tff(35373,plain,
% 12.19/12.45 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[1095, 35372, 310])).
% 12.19/12.45 tff(35374,plain,
% 12.19/12.45 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[29931, 35373, 11])).
% 12.19/12.45 tff(35375,plain,
% 12.19/12.45 (~r(s(s(s(elem!1))), s(s(z)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[34395, 35374, 33885, 33887])).
% 12.19/12.45 tff(35376,plain,
% 12.19/12.45 ($false),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[35375, 35356])).
% 12.19/12.45 tff(35377,plain,((~b(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.45 tff(35378,plain,
% 12.19/12.45 (~b(z, s(s(s(s(z)))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[35377, 1235, 1234, 1759, 90, 26982, 35310, 33627])).
% 12.19/12.45 tff(35379,plain,
% 12.19/12.45 (r(z, s(s(s(s(z)))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[800, 35378])).
% 12.19/12.45 tff(35380,plain,
% 12.19/12.45 (b(s(s(s(z))), z)),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[1680, 378, 11])).
% 12.19/12.45 tff(35381,plain,
% 12.19/12.45 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.45 inference(monotonicity,[status(thm)],[489, 2401])).
% 12.19/12.45 tff(35382,plain,
% 12.19/12.45 (b(s(s(elem!1)), z)),
% 12.19/12.45 inference(modus_ponens,[status(thm)],[1235, 30005])).
% 12.19/12.45 tff(35383,plain,
% 12.19/12.45 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[13177, 378, 10682, 2641])).
% 12.19/12.45 tff(35384,plain,
% 12.19/12.45 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[1370, 35383, 15838])).
% 12.19/12.45 tff(35385,plain,
% 12.19/12.45 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 12.19/12.45 inference(monotonicity,[status(thm)],[2416])).
% 12.19/12.45 tff(35386,plain,
% 12.19/12.45 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 12.19/12.45 inference(modus_ponens,[status(thm)],[714, 35385])).
% 12.19/12.45 tff(35387,plain,
% 12.19/12.45 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 12.19/12.45 inference(monotonicity,[status(thm)],[2401])).
% 12.19/12.45 tff(35388,plain,
% 12.19/12.45 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 12.19/12.45 inference(symmetry,[status(thm)],[35387])).
% 12.19/12.45 tff(35389,plain,
% 12.19/12.45 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 12.19/12.45 inference(transitivity,[status(thm)],[35388, 1593])).
% 12.19/12.45 tff(35390,plain,
% 12.19/12.45 (b(s(s(s(s(elem!1)))), elem!1)),
% 12.19/12.45 inference(modus_ponens,[status(thm)],[90, 35389])).
% 12.19/12.45 tff(35391,plain,
% 12.19/12.45 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[8729, 34433, 35390, 35366, 973])).
% 12.19/12.45 tff(35392,plain,
% 12.19/12.45 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[1061, 35391, 35386])).
% 12.19/12.45 tff(35393,plain,
% 12.19/12.45 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[15681, 35392, 1176, 35384])).
% 12.19/12.45 tff(35394,plain,
% 12.19/12.45 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.19/12.45 inference(unit_resolution,[status(thm)],[1164, 35393, 34126])).
% 12.19/12.45 tff(35395,plain,
% 12.19/12.45 (b(s(s(s(z))), s(s(s(s(z)))))),
% 12.19/12.45 inference(modus_ponens,[status(thm)],[35394, 3504])).
% 12.19/12.45 tff(35396,plain,
% 12.19/12.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 12.19/12.46 inference(rewrite,[status(thm)],[])).
% 12.19/12.46 tff(35397,plain,
% 12.19/12.46 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 12.19/12.46 inference(rewrite,[status(thm)],[])).
% 12.19/12.46 tff(35398,plain,
% 12.19/12.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))))),
% 12.19/12.46 inference(monotonicity,[status(thm)],[35397])).
% 12.19/12.46 tff(35399,plain,
% 12.19/12.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 12.19/12.46 inference(transitivity,[status(thm)],[35398, 35396])).
% 12.19/12.46 tff(35400,plain,
% 12.19/12.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 12.19/12.46 inference(quant_inst,[status(thm)],[])).
% 12.19/12.46 tff(35401,plain,
% 12.19/12.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 12.19/12.46 inference(modus_ponens,[status(thm)],[35400, 35399])).
% 12.19/12.46 tff(35402,plain,
% 12.19/12.46 ($false),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[35401, 391, 90, 23190, 35380, 35395])).
% 12.19/12.46 tff(35403,plain,(r(s(s(s(elem!1))), z) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.46 tff(35404,plain,
% 12.19/12.46 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[35403, 329, 11, 90, 35318, 127, 10682, 35382])).
% 12.19/12.46 tff(35405,plain,
% 12.19/12.46 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[1048, 35404, 2419])).
% 12.19/12.46 tff(35406,plain,
% 12.19/12.46 (b(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.46 inference(modus_ponens,[status(thm)],[35405, 35381])).
% 12.19/12.46 tff(35407,plain,
% 12.19/12.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 12.19/12.46 inference(rewrite,[status(thm)],[])).
% 12.19/12.46 tff(35408,plain,
% 12.19/12.46 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 12.19/12.46 inference(rewrite,[status(thm)],[])).
% 12.19/12.46 tff(35409,plain,
% 12.19/12.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 12.19/12.46 inference(monotonicity,[status(thm)],[35408])).
% 12.19/12.46 tff(35410,plain,
% 12.19/12.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 12.19/12.46 inference(transitivity,[status(thm)],[35409, 35407])).
% 12.19/12.46 tff(35411,plain,
% 12.19/12.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 12.19/12.46 inference(quant_inst,[status(thm)],[])).
% 12.19/12.46 tff(35412,plain,
% 12.19/12.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 12.19/12.46 inference(modus_ponens,[status(thm)],[35411, 35410])).
% 12.19/12.46 tff(35413,plain,
% 12.19/12.46 ($false),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[35412, 391, 35406, 90, 1235, 23190, 35380])).
% 12.19/12.46 tff(35414,plain,(r(s(s(s(elem!1))), z) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~(elem!1 = z)) | (s(s(s(elem!1))) = elem!1) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.46 tff(35415,plain,
% 12.19/12.46 (r(s(s(s(elem!1))), z)),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[35414, 1235, 90, 33627, 9, 35310])).
% 12.19/12.46 tff(35416,plain,
% 12.19/12.46 (r(s(z), z)),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[5433, 1484, 17618])).
% 12.19/12.46 tff(35417,plain,
% 12.19/12.46 (~r(s(s(s(elem!1))), s(z))),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[17465, 174, 35320, 1484])).
% 12.19/12.46 tff(35418,plain,
% 12.19/12.46 (b(s(s(s(elem!1))), s(z))),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[223, 35417])).
% 12.19/12.46 tff(35419,plain,
% 12.19/12.46 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[6372, 35418, 1234, 1759, 90])).
% 12.19/12.46 tff(35420,plain,
% 12.19/12.46 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[27316, 35419, 11])).
% 12.19/12.46 tff(35421,plain,
% 12.19/12.46 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.46 inference(unit_resolution,[status(thm)],[1095, 35420, 305])).
% 12.19/12.46 tff(35422,plain,
% 12.19/12.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 12.19/12.46 inference(rewrite,[status(thm)],[])).
% 12.19/12.46 tff(35423,plain,
% 12.19/12.46 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 12.19/12.46 inference(rewrite,[status(thm)],[])).
% 12.19/12.46 tff(35424,plain,
% 12.19/12.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[35423])).
% 12.19/12.47 tff(35425,plain,
% 12.19/12.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 12.19/12.47 inference(transitivity,[status(thm)],[35424, 35422])).
% 12.19/12.47 tff(35426,plain,
% 12.19/12.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 12.19/12.47 inference(quant_inst,[status(thm)],[])).
% 12.19/12.47 tff(35427,plain,
% 12.19/12.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35426, 35425])).
% 12.19/12.47 tff(35428,plain,
% 12.19/12.47 ($false),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[35427, 194, 174, 2792, 1538, 1082])).
% 12.19/12.47 tff(35429,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.47 tff(35430,plain,
% 12.19/12.47 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[35429, 35421, 18459, 174])).
% 12.19/12.47 tff(35431,plain,
% 12.19/12.47 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[1164, 35430, 1153])).
% 12.19/12.47 tff(35432,plain,
% 12.19/12.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35431, 3504])).
% 12.19/12.47 tff(35433,plain,
% 12.19/12.47 (~r(s(z), s(s(s(elem!1))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[27817, 174, 182, 719])).
% 12.19/12.47 tff(35434,plain,
% 12.19/12.47 (b(s(z), s(s(s(elem!1))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[247, 35433])).
% 12.19/12.47 tff(35435,plain,
% 12.19/12.47 (b(s(z), s(s(s(z))))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35434, 18545])).
% 12.19/12.47 tff(35436,plain,
% 12.19/12.47 (b(s(s(s(z))), s(z))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35418, 17635])).
% 12.19/12.47 tff(35437,plain,
% 12.19/12.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 12.19/12.47 inference(rewrite,[status(thm)],[])).
% 12.19/12.47 tff(35438,plain,
% 12.19/12.47 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 12.19/12.47 inference(rewrite,[status(thm)],[])).
% 12.19/12.47 tff(35439,plain,
% 12.19/12.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[35438])).
% 12.19/12.47 tff(35440,plain,
% 12.19/12.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 12.19/12.47 inference(transitivity,[status(thm)],[35439, 35437])).
% 12.19/12.47 tff(35441,plain,
% 12.19/12.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 12.19/12.47 inference(quant_inst,[status(thm)],[])).
% 12.19/12.47 tff(35442,plain,
% 12.19/12.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35441, 35440])).
% 12.19/12.47 tff(35443,plain,
% 12.19/12.47 ($false),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[35442, 391, 1759, 35436, 35435, 35432])).
% 12.19/12.47 tff(35444,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.47 tff(35445,plain,
% 12.19/12.47 ($false),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[35444, 35416, 1484, 11, 305, 1234, 90, 1759, 174, 719])).
% 12.19/12.47 tff(35446,plain,((~r(s(z), elem!1)) | (~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.47 tff(35447,plain,
% 12.19/12.47 (~r(s(z), elem!1)),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[35446, 35415, 29900, 1234, 90, 1759, 33627, 35379])).
% 12.19/12.47 tff(35448,plain,
% 12.19/12.47 (b(s(z), elem!1)),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[632, 35447, 34897])).
% 12.19/12.47 tff(35449,plain,
% 12.19/12.47 (~b(elem!1, s(s(z)))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[18622, 35448, 35238, 1759, 1235])).
% 12.19/12.47 tff(35450,plain,
% 12.19/12.47 (r(elem!1, s(s(z)))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[3394, 35449, 35315])).
% 12.19/12.47 tff(35451,plain,
% 12.19/12.47 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[33627])).
% 12.19/12.47 tff(35452,plain,
% 12.19/12.47 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 12.19/12.47 inference(symmetry,[status(thm)],[35451])).
% 12.19/12.47 tff(35453,plain,
% 12.19/12.47 (r(elem!1, s(s(s(s(z)))))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35379, 35452])).
% 12.19/12.47 tff(35454,plain,
% 12.19/12.47 (~r(s(s(z)), s(z))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[34335, 3823, 1234, 2032, 11, 90, 2439])).
% 12.19/12.47 tff(35455,plain,
% 12.19/12.47 ($false),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[3778, 35454, 33722])).
% 12.19/12.47 tff(35456,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.47 tff(35457,plain,
% 12.19/12.47 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[35456, 2439, 35453, 33627, 90, 1234, 1759])).
% 12.19/12.47 tff(35458,plain,
% 12.19/12.47 (r(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[3652, 35457])).
% 12.19/12.47 tff(35459,plain,
% 12.19/12.47 (b(s(z), elem!1) <=> b(s(z), z)),
% 12.19/12.47 inference(monotonicity,[status(thm)],[33627])).
% 12.19/12.47 tff(35460,plain,
% 12.19/12.47 (b(s(z), z) <=> b(s(z), elem!1)),
% 12.19/12.47 inference(symmetry,[status(thm)],[35459])).
% 12.19/12.47 tff(35461,plain,
% 12.19/12.47 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[34414])).
% 12.19/12.47 tff(35462,plain,
% 12.19/12.47 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 12.19/12.47 inference(symmetry,[status(thm)],[35461])).
% 12.19/12.47 tff(35463,plain,
% 12.19/12.47 (b(s(z), s(s(elem!1)))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[30324, 2439, 33627])).
% 12.19/12.47 tff(35464,plain,
% 12.19/12.47 (b(s(elem!1), s(s(elem!1)))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35463, 35462])).
% 12.19/12.47 tff(35465,plain,
% 12.19/12.47 (b(elem!1, s(s(s(elem!1))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[23154, 35310, 33627])).
% 12.19/12.47 tff(35466,plain,
% 12.19/12.47 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 12.19/12.47 inference(monotonicity,[status(thm)],[33627])).
% 12.19/12.47 tff(35467,plain,
% 12.19/12.47 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 12.19/12.47 inference(symmetry,[status(thm)],[35466])).
% 12.19/12.47 tff(35468,plain,
% 12.19/12.47 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 12.19/12.47 inference(monotonicity,[status(thm)],[34427])).
% 12.19/12.47 tff(35469,plain,
% 12.19/12.47 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 12.19/12.47 inference(symmetry,[status(thm)],[35468])).
% 12.19/12.47 tff(35470,plain,
% 12.19/12.47 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 12.19/12.47 inference(transitivity,[status(thm)],[35469, 35467])).
% 12.19/12.47 tff(35471,plain,
% 12.19/12.47 (b(s(s(s(s(elem!1)))), elem!1)),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[90, 35470])).
% 12.19/12.47 tff(35472,plain,
% 12.19/12.47 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 12.19/12.47 inference(monotonicity,[status(thm)],[34415])).
% 12.19/12.47 tff(35473,plain,
% 12.19/12.47 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 12.19/12.47 inference(symmetry,[status(thm)],[35472])).
% 12.19/12.47 tff(35474,plain,
% 12.19/12.47 (b(s(s(elem!1)), z)),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[1235, 35473])).
% 12.19/12.47 tff(35475,plain,
% 12.19/12.47 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 12.19/12.47 inference(monotonicity,[status(thm)],[33627])).
% 12.19/12.47 tff(35476,plain,
% 12.19/12.47 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 12.19/12.47 inference(symmetry,[status(thm)],[35475])).
% 12.19/12.47 tff(35477,plain,
% 12.19/12.47 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 12.19/12.47 inference(transitivity,[status(thm)],[35473, 35476])).
% 12.19/12.47 tff(35478,plain,
% 12.19/12.47 (b(s(s(elem!1)), elem!1)),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[1235, 35477])).
% 12.19/12.47 tff(35479,plain,
% 12.19/12.47 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[34415, 34427])).
% 12.19/12.47 tff(35480,plain,
% 12.19/12.47 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.19/12.47 inference(symmetry,[status(thm)],[35479])).
% 12.19/12.47 tff(35481,plain,
% 12.19/12.47 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35458, 35480])).
% 12.19/12.47 tff(35482,plain,
% 12.19/12.47 (r(s(s(s(elem!1))), z)),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[35403, 35481, 33627, 90, 35478, 9, 35310, 35474])).
% 12.19/12.47 tff(35483,plain,
% 12.19/12.47 (r(s(elem!1), z)),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[27330, 181, 11])).
% 12.19/12.47 tff(35484,plain,
% 12.19/12.47 (~r(s(s(s(elem!1))), s(elem!1))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[14304, 35483, 18459, 174])).
% 12.19/12.47 tff(35485,plain,
% 12.19/12.47 (b(s(s(s(elem!1))), s(elem!1))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[588, 35484, 8876])).
% 12.19/12.47 tff(35486,plain,
% 12.19/12.47 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[27546, 35485, 2698, 448, 7625])).
% 12.19/12.47 tff(35487,plain,
% 12.19/12.47 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[1095, 35486, 305])).
% 12.19/12.47 tff(35488,plain,
% 12.19/12.47 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[35429, 35487, 18459, 174])).
% 12.19/12.47 tff(35489,plain,
% 12.19/12.47 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[1164, 35488, 1153])).
% 12.19/12.47 tff(35490,plain,
% 12.19/12.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35489, 3504])).
% 12.19/12.47 tff(35491,plain,
% 12.19/12.47 (~r(s(z), s(s(s(elem!1))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[27817, 181, 174, 719])).
% 12.19/12.47 tff(35492,plain,
% 12.19/12.47 (b(s(z), s(s(s(elem!1))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[247, 35491])).
% 12.19/12.47 tff(35493,plain,
% 12.19/12.47 (b(s(z), s(s(s(z))))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35492, 18545])).
% 12.19/12.47 tff(35494,plain,
% 12.19/12.47 (~r(s(s(s(elem!1))), s(z))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[17465, 34471, 722, 174])).
% 12.19/12.47 tff(35495,plain,
% 12.19/12.47 (b(s(s(s(elem!1))), s(z))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[223, 35494])).
% 12.19/12.47 tff(35496,plain,
% 12.19/12.47 (b(s(s(s(z))), s(z))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35495, 17635])).
% 12.19/12.47 tff(35497,plain,
% 12.19/12.47 ($false),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[35442, 391, 1759, 35496, 35493, 35490])).
% 12.19/12.47 tff(35498,plain,(b(s(z), z) | (~b(s(s(s(s(z)))), s(z))) | (~(elem!1 = z)) | (~r(s(s(s(elem!1))), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.19/12.47 tff(35499,plain,
% 12.19/12.47 (b(s(z), z)),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[35498, 35482, 33627, 1759, 29900, 35471, 35465, 35464, 35320, 35379])).
% 12.19/12.47 tff(35500,plain,
% 12.19/12.47 (b(s(z), elem!1)),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35499, 35460])).
% 12.19/12.47 tff(35501,plain,
% 12.19/12.47 (~b(elem!1, s(s(z)))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[18622, 35500, 35238, 1759, 1235])).
% 12.19/12.47 tff(35502,plain,
% 12.19/12.47 (r(elem!1, s(s(z)))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[3394, 35501, 35315])).
% 12.19/12.47 tff(35503,plain,
% 12.19/12.47 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[33793, 35502, 35453, 35458])).
% 12.19/12.47 tff(35504,plain,
% 12.19/12.47 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[6652, 42, 4995, 35503])).
% 12.19/12.47 tff(35505,plain,
% 12.19/12.47 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 12.19/12.47 inference(symmetry,[status(thm)],[34963])).
% 12.19/12.47 tff(35506,plain,
% 12.19/12.47 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[34415])).
% 12.19/12.47 tff(35507,plain,
% 12.19/12.47 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 12.19/12.47 inference(symmetry,[status(thm)],[35506])).
% 12.19/12.47 tff(35508,plain,
% 12.19/12.47 (b(elem!1, z) <=> b(z, z)),
% 12.19/12.47 inference(monotonicity,[status(thm)],[33627])).
% 12.19/12.47 tff(35509,plain,
% 12.19/12.47 (b(z, z) <=> b(elem!1, z)),
% 12.19/12.47 inference(symmetry,[status(thm)],[35508])).
% 12.19/12.47 tff(35510,plain,
% 12.19/12.47 ((~b(z, z)) <=> (~b(elem!1, z))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[35509])).
% 12.19/12.47 tff(35511,plain,
% 12.19/12.47 (~b(elem!1, z)),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[30135, 35510])).
% 12.19/12.47 tff(35512,plain,
% 12.19/12.47 (r(elem!1, s(z))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[26821, 35319, 80, 35511, 1234])).
% 12.19/12.47 tff(35513,plain,
% 12.19/12.47 (~b(z, s(s(z)))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[17567, 35500, 35512, 1235, 6221, 35499, 35315, 35458])).
% 12.19/12.47 tff(35514,plain,
% 12.19/12.47 (r(z, s(s(z)))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[18613, 35513])).
% 12.19/12.47 tff(35515,plain,
% 12.19/12.47 (r(z, s(s(elem!1)))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35514, 35507])).
% 12.19/12.47 tff(35516,plain,
% 12.19/12.47 (~r(elem!1, z)),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[29452, 34898])).
% 12.19/12.47 tff(35517,plain,
% 12.19/12.47 (r(s(elem!1), z) <=> r(s(z), z)),
% 12.19/12.47 inference(monotonicity,[status(thm)],[34414])).
% 12.19/12.47 tff(35518,plain,
% 12.19/12.47 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 12.19/12.47 inference(monotonicity,[status(thm)],[33627])).
% 12.19/12.47 tff(35519,plain,
% 12.19/12.47 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 12.19/12.47 inference(transitivity,[status(thm)],[35518, 35517])).
% 12.19/12.47 tff(35520,plain,
% 12.19/12.47 ((~r(s(elem!1), elem!1)) <=> (~r(s(z), z))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[35519])).
% 12.19/12.47 tff(35521,plain,
% 12.19/12.47 (r(s(s(s(elem!1))), elem!1)),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[9853, 35482, 34898])).
% 12.19/12.47 tff(35522,plain,
% 12.19/12.47 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(z))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[34414])).
% 12.19/12.47 tff(35523,plain,
% 12.19/12.47 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 12.19/12.47 inference(transitivity,[status(thm)],[35522, 204])).
% 12.19/12.47 tff(35524,plain,
% 12.19/12.47 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 12.19/12.47 inference(symmetry,[status(thm)],[35523])).
% 12.19/12.47 tff(35525,plain,
% 12.19/12.47 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[35524])).
% 12.19/12.47 tff(35526,plain,
% 12.19/12.47 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[217, 35525])).
% 12.19/12.47 tff(35527,plain,
% 12.19/12.47 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 12.19/12.47 inference(transitivity,[status(thm)],[34907, 34905])).
% 12.19/12.47 tff(35528,plain,
% 12.19/12.47 ((~b(z, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 12.19/12.47 inference(monotonicity,[status(thm)],[35527])).
% 12.19/12.47 tff(35529,plain,
% 12.19/12.47 (~b(elem!1, s(elem!1))),
% 12.19/12.47 inference(modus_ponens,[status(thm)],[35319, 35528])).
% 12.19/12.47 tff(35530,plain,
% 12.19/12.47 (r(elem!1, s(elem!1))),
% 12.19/12.47 inference(unit_resolution,[status(thm)],[443, 35529, 427])).
% 12.19/12.47 tff(35531,plain,
% 12.19/12.47 (b(s(elem!1), z) <=> b(s(z), z)),
% 12.19/12.47 inference(monotonicity,[status(thm)],[34414])).
% 12.19/12.47 tff(35532,plain,
% 12.19/12.47 (b(s(z), z) <=> b(s(elem!1), z)),
% 12.19/12.48 inference(symmetry,[status(thm)],[35531])).
% 12.19/12.48 tff(35533,plain,
% 12.19/12.48 (b(s(elem!1), z)),
% 12.19/12.48 inference(modus_ponens,[status(thm)],[35499, 35532])).
% 12.19/12.48 tff(35534,plain,
% 12.19/12.48 (~r(s(elem!1), elem!1)),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[12962, 35533, 35310, 35530, 35526, 35521])).
% 12.19/12.48 tff(35535,plain,
% 12.19/12.48 (~r(s(z), z)),
% 12.19/12.48 inference(modus_ponens,[status(thm)],[35534, 35520])).
% 12.19/12.48 tff(35536,plain,
% 12.19/12.48 (~b(s(s(s(elem!1))), s(z))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[27326, 35535, 35310, 35465, 34897, 35516, 35482, 90])).
% 12.19/12.48 tff(35537,plain,
% 12.19/12.48 (r(s(s(s(elem!1))), s(z))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[223, 35536])).
% 12.19/12.48 tff(35538,plain,
% 12.19/12.48 (~r(s(z), s(s(s(elem!1))))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[29577, 35537, 80, 35310, 35512, 1, 35482])).
% 12.19/12.48 tff(35539,plain,
% 12.19/12.48 (b(s(z), s(s(s(elem!1))))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[247, 35538])).
% 12.19/12.48 tff(35540,plain,
% 12.19/12.48 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[30751, 35539, 35310, 35478, 35499])).
% 12.19/12.48 tff(35541,plain,
% 12.19/12.48 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[1370, 35540, 26982])).
% 12.19/12.48 tff(35542,plain,
% 12.19/12.48 (~r(s(s(elem!1)), s(z))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[7327, 35541, 35515, 35482])).
% 12.19/12.48 tff(35543,plain,
% 12.19/12.48 (b(s(s(elem!1)), s(z))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[362, 35542])).
% 12.19/12.48 tff(35544,plain,
% 12.19/12.48 (b(s(s(z)), s(z))),
% 12.19/12.48 inference(modus_ponens,[status(thm)],[35543, 35505])).
% 12.19/12.48 tff(35545,plain,
% 12.19/12.48 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 12.19/12.48 inference(monotonicity,[status(thm)],[34427, 34415])).
% 12.19/12.48 tff(35546,plain,
% 12.19/12.48 (r(elem!1, s(s(s(s(elem!1)))))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[23210, 35379, 33627])).
% 12.19/12.48 tff(35547,plain,
% 12.19/12.48 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 12.19/12.48 inference(monotonicity,[status(thm)],[33627])).
% 12.19/12.48 tff(35548,plain,
% 12.19/12.48 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 12.19/12.48 inference(symmetry,[status(thm)],[35547])).
% 12.19/12.48 tff(35549,plain,
% 12.19/12.48 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 12.19/12.48 inference(transitivity,[status(thm)],[35507, 35548])).
% 12.19/12.48 tff(35550,plain,
% 12.19/12.48 (r(elem!1, s(s(elem!1)))),
% 12.19/12.48 inference(modus_ponens,[status(thm)],[35514, 35549])).
% 12.19/12.48 tff(35551,plain,
% 12.19/12.48 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[1184, 35550, 35546, 35481])).
% 12.19/12.48 tff(35552,plain,
% 12.19/12.48 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[1061, 35551, 34944])).
% 12.19/12.48 tff(35553,plain,
% 12.19/12.48 (b(s(s(s(s(z)))), s(s(z)))),
% 12.19/12.48 inference(modus_ponens,[status(thm)],[35552, 35545])).
% 12.19/12.48 tff(35554,plain,
% 12.19/12.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 12.19/12.48 inference(rewrite,[status(thm)],[])).
% 12.19/12.48 tff(35555,plain,
% 12.19/12.48 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 12.19/12.48 inference(rewrite,[status(thm)],[])).
% 12.19/12.48 tff(35556,plain,
% 12.19/12.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 12.19/12.48 inference(monotonicity,[status(thm)],[35555])).
% 12.19/12.48 tff(35557,plain,
% 12.19/12.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 12.19/12.48 inference(transitivity,[status(thm)],[35556, 35554])).
% 12.19/12.48 tff(35558,plain,
% 12.19/12.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 12.19/12.48 inference(quant_inst,[status(thm)],[])).
% 12.19/12.48 tff(35559,plain,
% 12.19/12.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 12.19/12.48 inference(modus_ponens,[status(thm)],[35558, 35557])).
% 12.19/12.48 tff(35560,plain,
% 12.19/12.48 ($false),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[35559, 391, 1234, 1759, 35553, 35544, 35504])).
% 12.19/12.48 tff(35561,plain,((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | r(z, elem!1) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.19/12.48 tff(35562,plain,
% 12.19/12.48 (~b(s(z), s(s(z)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[35561, 1235, 1759, 80, 1, 90, 1234, 6221])).
% 12.19/12.48 tff(35563,plain,
% 12.19/12.48 (r(s(z), s(s(z)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[1788, 35562])).
% 12.19/12.48 tff(35564,plain,
% 12.19/12.48 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[1775, 35450, 35238, 34897, 35563, 1759])).
% 12.19/12.48 tff(35565,plain,
% 12.19/12.48 (b(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[3652, 35564])).
% 12.19/12.48 tff(35566,plain,
% 12.19/12.48 (~b(s(s(z)), s(z))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[5108, 35565, 1234, 1759])).
% 12.19/12.48 tff(35567,plain,
% 12.19/12.48 (r(s(s(z)), s(z))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[3778, 35566])).
% 12.19/12.48 tff(35568,plain,
% 12.19/12.48 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[18451, 35567, 35453, 35450])).
% 12.19/12.48 tff(35569,plain,
% 12.19/12.48 (b(s(s(s(s(z)))), s(s(z)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[1714, 35568])).
% 12.19/12.48 tff(35570,plain,
% 12.19/12.48 (~r(z, s(s(z)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[9720, 35567, 35320, 35563])).
% 12.19/12.48 tff(35571,plain,
% 12.19/12.48 (b(z, s(s(z)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[18613, 35570])).
% 12.19/12.48 tff(35572,plain,
% 12.19/12.48 ($false),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[15053, 35571, 35569, 90, 1235])).
% 12.19/12.48 tff(35573,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | r(z, elem!1) | (elem!1 = s(s(s(elem!1)))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.19/12.48 tff(35574,plain,
% 12.19/12.48 (~b(s(s(z)), z)),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[35573, 1759, 1234, 90, 80, 1, 6221])).
% 12.19/12.48 tff(35575,plain,
% 12.19/12.48 (r(s(s(z)), z)),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[1211, 35574])).
% 12.19/12.48 tff(35576,plain,
% 12.19/12.48 ((~b(z, s(z))) <=> (~b(z, s(elem!1)))),
% 12.19/12.48 inference(monotonicity,[status(thm)],[34436])).
% 12.19/12.48 tff(35577,plain,
% 12.19/12.48 (~b(z, s(elem!1))),
% 12.19/12.48 inference(modus_ponens,[status(thm)],[35319, 35576])).
% 12.19/12.48 tff(35578,plain,
% 12.19/12.48 (r(z, s(elem!1))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[566, 35577])).
% 12.19/12.48 tff(35579,plain,
% 12.19/12.48 (~r(s(s(elem!1)), s(z))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[2621, 29072, 35578, 23181])).
% 12.19/12.48 tff(35580,plain,
% 12.19/12.48 (b(s(s(elem!1)), s(z))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[362, 35579])).
% 12.19/12.48 tff(35581,plain,
% 12.19/12.48 (~r(s(s(z)), s(z))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[4462, 35365, 35320, 3557])).
% 12.19/12.48 tff(35582,plain,
% 12.19/12.48 (b(s(s(z)), s(z))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[3778, 35581])).
% 12.19/12.48 tff(35583,plain,
% 12.19/12.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.19/12.48 inference(rewrite,[status(thm)],[])).
% 12.19/12.48 tff(35584,plain,
% 12.19/12.48 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.19/12.48 inference(rewrite,[status(thm)],[])).
% 12.19/12.48 tff(35585,plain,
% 12.19/12.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.19/12.48 inference(monotonicity,[status(thm)],[35584])).
% 12.19/12.48 tff(35586,plain,
% 12.19/12.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.19/12.48 inference(transitivity,[status(thm)],[35585, 35583])).
% 12.19/12.48 tff(35587,plain,
% 12.19/12.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 12.19/12.48 inference(quant_inst,[status(thm)],[])).
% 12.19/12.48 tff(35588,plain,
% 12.19/12.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 12.19/12.48 inference(modus_ponens,[status(thm)],[35587, 35586])).
% 12.19/12.48 tff(35589,plain,
% 12.19/12.48 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[35588, 391, 90, 1234, 1759, 35582])).
% 12.19/12.48 tff(35590,plain,
% 12.19/12.48 (r(s(s(s(s(z)))), s(s(z)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[1714, 35589])).
% 12.19/12.48 tff(35591,plain,
% 12.19/12.48 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.19/12.48 inference(modus_ponens,[status(thm)],[35590, 33957])).
% 12.19/12.48 tff(35592,plain,
% 12.19/12.48 (~r(s(z), s(s(z)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[12646, 194, 35320, 29072, 3557])).
% 12.19/12.48 tff(35593,plain,
% 12.19/12.48 (b(s(z), s(s(z)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[1788, 35592])).
% 12.19/12.48 tff(35594,plain,
% 12.19/12.48 (b(s(z), s(s(elem!1)))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[30324, 35593, 11])).
% 12.19/12.48 tff(35595,plain,
% 12.19/12.48 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[5108, 35582, 1234, 1759])).
% 12.19/12.48 tff(35596,plain,
% 12.19/12.48 (r(s(s(z)), s(s(s(s(z)))))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[3652, 35595])).
% 12.19/12.48 tff(35597,plain,
% 12.19/12.48 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 12.19/12.48 inference(unit_resolution,[status(thm)],[35337, 194, 35596, 35590, 35322])).
% 12.19/12.49 tff(35598,plain,
% 12.19/12.49 ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[33813, 42, 35597])).
% 12.19/12.49 tff(35599,plain,
% 12.19/12.49 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[35598, 33800])).
% 12.19/12.49 tff(35600,plain,
% 12.19/12.49 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[34274, 194, 35596, 35590, 35322])).
% 12.19/12.49 tff(35601,plain,
% 12.19/12.49 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 35600])).
% 12.19/12.49 tff(35602,plain,
% 12.19/12.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.19/12.49 inference(rewrite,[status(thm)],[])).
% 12.19/12.49 tff(35603,plain,
% 12.19/12.49 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.19/12.49 inference(rewrite,[status(thm)],[])).
% 12.19/12.49 tff(35604,plain,
% 12.19/12.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 12.19/12.49 inference(monotonicity,[status(thm)],[35603])).
% 12.19/12.49 tff(35605,plain,
% 12.19/12.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.19/12.49 inference(transitivity,[status(thm)],[35604, 35602])).
% 12.19/12.49 tff(35606,plain,
% 12.19/12.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.19/12.49 inference(quant_inst,[status(thm)],[])).
% 12.19/12.49 tff(35607,plain,
% 12.19/12.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 12.19/12.49 inference(modus_ponens,[status(thm)],[35606, 35605])).
% 12.19/12.49 tff(35608,plain,
% 12.19/12.49 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[35607, 391, 1234, 35593, 35582, 35601])).
% 12.19/12.49 tff(35609,plain,
% 12.19/12.49 (r(s(s(s(s(s(s(z)))))), s(z))),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[14139, 35608])).
% 12.19/12.49 tff(35610,plain,
% 12.19/12.49 (~r(s(s(s(s(s(s(z)))))), z)),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[12319, 194, 35320, 29072, 35609])).
% 12.19/12.49 tff(35611,plain,
% 12.19/12.49 (b(s(s(s(s(s(s(z)))))), z)),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[34231, 35610])).
% 12.19/12.49 tff(35612,plain,
% 12.19/12.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 12.19/12.49 inference(rewrite,[status(thm)],[])).
% 12.19/12.49 tff(35613,plain,
% 12.19/12.49 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 12.19/12.49 inference(rewrite,[status(thm)],[])).
% 12.19/12.49 tff(35614,plain,
% 12.19/12.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 12.19/12.49 inference(monotonicity,[status(thm)],[35613])).
% 12.19/12.49 tff(35615,plain,
% 12.19/12.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 12.19/12.49 inference(transitivity,[status(thm)],[35614, 35612])).
% 12.19/12.49 tff(35616,plain,
% 12.19/12.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 12.19/12.49 inference(quant_inst,[status(thm)],[])).
% 12.19/12.49 tff(35617,plain,
% 12.19/12.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 12.19/12.49 inference(modus_ponens,[status(thm)],[35616, 35615])).
% 12.19/12.49 tff(35618,plain,
% 12.19/12.49 (~r(z, s(s(s(s(s(s(z)))))))),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[35617, 194, 35320, 29072, 35609])).
% 12.19/12.49 tff(35619,plain,
% 12.19/12.49 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[11697, 42, 35618])).
% 12.19/12.49 tff(35620,plain,
% 12.19/12.49 (b(z, s(s(s(s(s(s(z)))))))),
% 12.19/12.49 inference(unit_resolution,[status(thm)],[35619, 11645])).
% 12.19/12.49 tff(35621,plain,
% 12.19/12.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.19/12.49 inference(rewrite,[status(thm)],[])).
% 12.19/12.49 tff(35622,plain,
% 12.19/12.49 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.19/12.49 inference(rewrite,[status(thm)],[])).
% 12.19/12.49 tff(35623,plain,
% 12.19/12.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 12.19/12.49 inference(monotonicity,[status(thm)],[35622])).
% 12.19/12.49 tff(35624,plain,
% 12.19/12.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.29/12.50 inference(transitivity,[status(thm)],[35623, 35621])).
% 12.29/12.50 tff(35625,plain,
% 12.29/12.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))))),
% 12.29/12.50 inference(quant_inst,[status(thm)],[])).
% 12.29/12.50 tff(35626,plain,
% 12.29/12.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 12.29/12.50 inference(modus_ponens,[status(thm)],[35625, 35624])).
% 12.29/12.50 tff(35627,plain,
% 12.29/12.50 (~b(z, s(s(z)))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[35626, 391, 1686, 35620, 35611, 35599])).
% 12.29/12.50 tff(35628,plain,
% 12.29/12.50 (r(z, s(s(z)))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[18613, 35627])).
% 12.29/12.50 tff(35629,plain,
% 12.29/12.50 (r(z, s(s(elem!1)))),
% 12.29/12.50 inference(modus_ponens,[status(thm)],[35628, 29959])).
% 12.29/12.50 tff(35630,plain,
% 12.29/12.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 12.29/12.50 inference(rewrite,[status(thm)],[])).
% 12.29/12.50 tff(35631,plain,
% 12.29/12.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 12.29/12.50 inference(quant_inst,[status(thm)],[])).
% 12.29/12.50 tff(35632,plain,
% 12.29/12.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 12.29/12.50 inference(modus_ponens,[status(thm)],[35631, 35630])).
% 12.29/12.50 tff(35633,plain,
% 12.29/12.50 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[35632, 194, 174, 326, 2616])).
% 12.29/12.50 tff(35634,plain,
% 12.29/12.50 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[1370, 35633, 297])).
% 12.29/12.50 tff(35635,plain,
% 12.29/12.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 12.29/12.50 inference(rewrite,[status(thm)],[])).
% 12.29/12.50 tff(35636,plain,
% 12.29/12.50 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 12.29/12.50 inference(rewrite,[status(thm)],[])).
% 12.29/12.50 tff(35637,plain,
% 12.29/12.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))))),
% 12.29/12.50 inference(monotonicity,[status(thm)],[35636])).
% 12.29/12.50 tff(35638,plain,
% 12.29/12.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 12.29/12.50 inference(transitivity,[status(thm)],[35637, 35635])).
% 12.29/12.50 tff(35639,plain,
% 12.29/12.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 12.29/12.50 inference(quant_inst,[status(thm)],[])).
% 12.29/12.50 tff(35640,plain,
% 12.29/12.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))),
% 12.29/12.50 inference(modus_ponens,[status(thm)],[35639, 35638])).
% 12.29/12.50 tff(35641,plain,
% 12.29/12.50 (~r(s(z), s(s(s(elem!1))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[35640, 194, 174, 326, 182])).
% 12.29/12.50 tff(35642,plain,
% 12.29/12.50 (b(s(z), s(s(s(elem!1))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[247, 35641])).
% 12.29/12.50 tff(35643,plain,
% 12.29/12.50 ($false),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[5321, 35642, 35634, 5303, 381])).
% 12.29/12.50 tff(35644,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.50 tff(35645,plain,
% 12.29/12.50 (~r(s(s(s(elem!1))), z)),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[35644, 35629, 23181, 29072, 297, 35580, 35594])).
% 12.29/12.50 tff(35646,plain,
% 12.29/12.50 (b(s(s(s(elem!1))), z)),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[377, 35645])).
% 12.29/12.50 tff(35647,plain,
% 12.29/12.50 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[27078, 35646, 10682, 1686])).
% 12.29/12.50 tff(35648,plain,
% 12.29/12.50 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[27316, 35647, 11])).
% 12.29/12.50 tff(35649,plain,
% 12.29/12.50 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[1095, 35648, 310])).
% 12.29/12.50 tff(35650,plain,
% 12.29/12.50 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[14240, 35649, 34091, 35591])).
% 12.29/12.50 tff(35651,plain,
% 12.29/12.50 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[1370, 35650, 297])).
% 12.29/12.50 tff(35652,plain,
% 12.29/12.50 (~b(s(s(s(elem!1))), s(z))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[1660, 35651, 1234, 33675, 35580])).
% 12.29/12.50 tff(35653,plain,
% 12.29/12.50 (r(s(s(s(elem!1))), s(z))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[223, 35652])).
% 12.29/12.50 tff(35654,plain,
% 12.29/12.50 (r(s(s(s(z))), s(z))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[29740, 35653, 11])).
% 12.29/12.50 tff(35655,plain,
% 12.29/12.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.29/12.50 inference(rewrite,[status(thm)],[])).
% 12.29/12.50 tff(35656,plain,
% 12.29/12.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.29/12.50 inference(quant_inst,[status(thm)],[])).
% 12.29/12.50 tff(35657,plain,
% 12.29/12.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 12.29/12.50 inference(modus_ponens,[status(thm)],[35656, 35655])).
% 12.29/12.50 tff(35658,plain,
% 12.29/12.50 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[35657, 194, 29072, 35609, 35654])).
% 12.29/12.50 tff(35659,plain,
% 12.29/12.50 (b(s(s(s(z))), z)),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[1680, 35646, 11])).
% 12.29/12.50 tff(35660,plain,
% 12.29/12.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.29/12.50 inference(rewrite,[status(thm)],[])).
% 12.29/12.50 tff(35661,plain,
% 12.29/12.50 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.29/12.50 inference(rewrite,[status(thm)],[])).
% 12.29/12.50 tff(35662,plain,
% 12.29/12.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 12.29/12.50 inference(monotonicity,[status(thm)],[35661])).
% 12.29/12.50 tff(35663,plain,
% 12.29/12.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.29/12.50 inference(transitivity,[status(thm)],[35662, 35660])).
% 12.29/12.50 tff(35664,plain,
% 12.29/12.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.29/12.50 inference(quant_inst,[status(thm)],[])).
% 12.29/12.50 tff(35665,plain,
% 12.29/12.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 12.29/12.50 inference(modus_ponens,[status(thm)],[35664, 35663])).
% 12.29/12.50 tff(35666,plain,
% 12.29/12.50 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[35665, 391, 90, 1686, 35659, 35611])).
% 12.29/12.50 tff(35667,plain,
% 12.29/12.50 ($false),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[29527, 42, 8094, 35666, 35658])).
% 12.29/12.50 tff(35668,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.50 tff(35669,plain,
% 12.29/12.50 (~b(z, s(s(s(s(z)))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[35668, 3557, 33627, 1234, 26982, 10682, 90, 1759])).
% 12.29/12.50 tff(35670,plain,
% 12.29/12.50 (r(z, s(s(s(s(z)))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[800, 35669])).
% 12.29/12.50 tff(35671,plain,
% 12.29/12.50 (b(elem!1, s(s(s(elem!1))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[23154, 10682, 33627])).
% 12.29/12.50 tff(35672,plain,
% 12.29/12.50 (r(s(s(s(z))), z)),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[4409, 174, 33627])).
% 12.29/12.50 tff(35673,plain,
% 12.29/12.50 (r(elem!1, s(s(s(s(elem!1)))))),
% 12.29/12.50 inference(unit_resolution,[status(thm)],[23210, 719, 33627])).
% 12.29/12.51 tff(35674,plain,
% 12.29/12.51 (r(s(s(elem!1)), elem!1)),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[3557, 35306])).
% 12.29/12.51 tff(35675,plain,
% 12.29/12.51 (r(s(s(s(elem!1))), elem!1)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[9853, 174, 34898])).
% 12.29/12.51 tff(35676,plain,
% 12.29/12.51 (~b(z, s(s(elem!1)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[14223, 35675, 10682, 35674, 35673, 26982, 27044])).
% 12.29/12.51 tff(35677,plain,
% 12.29/12.51 (~b(elem!1, s(s(z)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[3379, 35676, 33627])).
% 12.29/12.51 tff(35678,plain,
% 12.29/12.51 (r(elem!1, s(s(z)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[3394, 35677, 35315])).
% 12.29/12.51 tff(35679,plain,
% 12.29/12.51 (~r(s(z), s(s(z)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[1775, 35678, 35238, 34897, 1749, 1759])).
% 12.29/12.51 tff(35680,plain,
% 12.29/12.51 (b(s(z), s(s(z)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[1788, 35679])).
% 12.29/12.51 tff(35681,plain,
% 12.29/12.51 (~b(s(z), s(s(s(elem!1))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[33716, 35680, 3557, 719, 26982, 35672, 33627])).
% 12.29/12.51 tff(35682,plain,
% 12.29/12.51 (r(s(z), s(s(s(elem!1))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[247, 35681])).
% 12.29/12.51 tff(35683,plain,
% 12.29/12.51 (~r(s(z), z)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[27817, 35682, 174, 719])).
% 12.29/12.51 tff(35684,plain,
% 12.29/12.51 (~r(s(s(s(elem!1))), s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[29577, 35682, 80, 10682, 847, 1, 174])).
% 12.29/12.51 tff(35685,plain,
% 12.29/12.51 (b(s(s(s(elem!1))), s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[223, 35684])).
% 12.29/12.51 tff(35686,plain,
% 12.29/12.51 ($false),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[27326, 35685, 35683, 10682, 35671, 34897, 35516, 174, 90])).
% 12.29/12.51 tff(35687,plain,((~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | r(z, elem!1) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.51 tff(35688,plain,
% 12.29/12.51 (~r(s(s(s(elem!1))), z)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35687, 1749, 90, 35670, 80, 35512, 1, 3557, 10682, 1759])).
% 12.29/12.51 tff(35689,plain,
% 12.29/12.51 (b(s(s(s(elem!1))), z)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[377, 35688])).
% 12.29/12.51 tff(35690,plain,
% 12.29/12.51 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 12.29/12.51 inference(monotonicity,[status(thm)],[491])).
% 12.29/12.51 tff(35691,plain,
% 12.29/12.51 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 12.29/12.51 inference(symmetry,[status(thm)],[35690])).
% 12.29/12.51 tff(35692,plain,
% 12.29/12.51 (b(z, s(s(s(z))))),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[10682, 35691])).
% 12.29/12.51 tff(35693,plain,
% 12.29/12.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.51 inference(rewrite,[status(thm)],[])).
% 12.29/12.51 tff(35694,plain,
% 12.29/12.51 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.51 inference(rewrite,[status(thm)],[])).
% 12.29/12.51 tff(35695,plain,
% 12.29/12.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.29/12.51 inference(monotonicity,[status(thm)],[35694])).
% 12.29/12.51 tff(35696,plain,
% 12.29/12.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.51 inference(transitivity,[status(thm)],[35695, 35693])).
% 12.29/12.51 tff(35697,plain,
% 12.29/12.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.51 inference(quant_inst,[status(thm)],[])).
% 12.29/12.51 tff(35698,plain,
% 12.29/12.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[35697, 35696])).
% 12.29/12.51 tff(35699,plain,
% 12.29/12.51 ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35698, 391, 90, 1234])).
% 12.29/12.51 tff(35700,plain,
% 12.29/12.51 ($false),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35699, 35692, 1677, 3198])).
% 12.29/12.51 tff(35701,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~(elem!1 = z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.51 tff(35702,plain,
% 12.29/12.51 (~b(s(z), elem!1)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35701, 35689, 33627, 90, 10682, 1234])).
% 12.29/12.51 tff(35703,plain,
% 12.29/12.51 (r(s(z), elem!1)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[632, 35702, 34897])).
% 12.29/12.51 tff(35704,plain,
% 12.29/12.51 (~r(s(s(z)), s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[4462, 35703, 35320, 3557])).
% 12.29/12.51 tff(35705,plain,
% 12.29/12.51 (b(s(s(z)), s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[3778, 35704])).
% 12.29/12.51 tff(35706,plain,
% 12.29/12.51 (r(elem!1, s(s(s(s(elem!1)))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[23210, 35670, 33627])).
% 12.29/12.51 tff(35707,plain,
% 12.29/12.51 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[1749, 35480])).
% 12.29/12.51 tff(35708,plain,
% 12.29/12.51 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[20086, 35707, 35674, 35706])).
% 12.29/12.51 tff(35709,plain,
% 12.29/12.51 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[1061, 35708, 34944])).
% 12.29/12.51 tff(35710,plain,
% 12.29/12.51 (b(s(s(s(s(z)))), s(s(z)))),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[35709, 35545])).
% 12.29/12.51 tff(35711,plain,
% 12.29/12.51 ($false),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35588, 391, 90, 1234, 1759, 35710, 35705])).
% 12.29/12.51 tff(35712,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | r(z, elem!1) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.51 tff(35713,plain,
% 12.29/12.51 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35712, 1759, 1234, 90, 35575, 35310, 80, 1])).
% 12.29/12.51 tff(35714,plain,
% 12.29/12.51 (b(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[3652, 35713])).
% 12.29/12.51 tff(35715,plain,
% 12.29/12.51 (~b(s(s(z)), s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[5108, 35714, 1234, 1759])).
% 12.29/12.51 tff(35716,plain,
% 12.29/12.51 (r(s(s(z)), s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[3778, 35715])).
% 12.29/12.51 tff(35717,plain,
% 12.29/12.51 (~r(s(z), elem!1)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[4462, 35716, 35320, 35575])).
% 12.29/12.51 tff(35718,plain,
% 12.29/12.51 (b(s(z), elem!1)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[632, 35717, 34897])).
% 12.29/12.51 tff(35719,plain,
% 12.29/12.51 (~b(s(s(s(elem!1))), z)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35701, 35718, 33627, 90, 35310, 1234])).
% 12.29/12.51 tff(35720,plain,
% 12.29/12.51 (r(s(s(s(elem!1))), z)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[377, 35719])).
% 12.29/12.51 tff(35721,plain,
% 12.29/12.51 (~b(z, s(s(s(s(z)))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35668, 35575, 33627, 1234, 26982, 35310, 90, 1759])).
% 12.29/12.51 tff(35722,plain,
% 12.29/12.51 (r(z, s(s(s(s(z)))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[800, 35721])).
% 12.29/12.51 tff(35723,plain,
% 12.29/12.51 (r(elem!1, s(s(s(s(elem!1)))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[23210, 35722, 33627])).
% 12.29/12.51 tff(35724,plain,
% 12.29/12.51 (r(s(s(elem!1)), elem!1)),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[35575, 35306])).
% 12.29/12.51 tff(35725,plain,
% 12.29/12.51 (r(elem!1, s(s(s(s(z)))))),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[35722, 35452])).
% 12.29/12.51 tff(35726,plain,
% 12.29/12.51 (~b(s(z), s(s(z)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35456, 35714, 35725, 33627, 90, 1234, 1759])).
% 12.29/12.51 tff(35727,plain,
% 12.29/12.51 (r(s(z), s(s(z)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[1788, 35726])).
% 12.29/12.51 tff(35728,plain,
% 12.29/12.51 (~r(z, s(s(z)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[9720, 35727, 35320, 35716])).
% 12.29/12.51 tff(35729,plain,
% 12.29/12.51 (~r(z, s(s(elem!1)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[30084, 35728, 33627])).
% 12.29/12.51 tff(35730,plain,
% 12.29/12.51 (b(z, s(s(elem!1)))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[324, 35729])).
% 12.29/12.51 tff(35731,plain,
% 12.29/12.51 (~r(s(s(s(elem!1))), elem!1)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[14223, 35730, 35310, 35724, 35723, 26982, 27044])).
% 12.29/12.51 tff(35732,plain,
% 12.29/12.51 ($false),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[9853, 35731, 35720, 34898])).
% 12.29/12.51 tff(35733,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | r(z, elem!1) | (elem!1 = s(s(s(elem!1)))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.51 tff(35734,plain,
% 12.29/12.51 (~b(s(s(s(s(z)))), s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35733, 1234, 90, 80, 1, 6221])).
% 12.29/12.51 tff(35735,plain,
% 12.29/12.51 (r(s(s(s(s(z)))), s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[749, 35734])).
% 12.29/12.51 tff(35736,plain,
% 12.29/12.51 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 12.29/12.51 inference(monotonicity,[status(thm)],[488])).
% 12.29/12.51 tff(35737,plain,
% 12.29/12.51 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.29/12.51 inference(symmetry,[status(thm)],[35736])).
% 12.29/12.51 tff(35738,plain,
% 12.29/12.51 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 12.29/12.51 inference(monotonicity,[status(thm)],[2401])).
% 12.29/12.51 tff(35739,plain,
% 12.29/12.51 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 12.29/12.51 inference(symmetry,[status(thm)],[35738])).
% 12.29/12.51 tff(35740,plain,
% 12.29/12.51 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.29/12.51 inference(transitivity,[status(thm)],[35739, 35737])).
% 12.29/12.51 tff(35741,plain,
% 12.29/12.51 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[723, 35740])).
% 12.29/12.51 tff(35742,plain,
% 12.29/12.51 (~b(elem!1, s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[34686, 29071, 17618, 90, 723, 1234, 35365])).
% 12.29/12.51 tff(35743,plain,
% 12.29/12.51 (~b(z, s(z))),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[35742, 30])).
% 12.29/12.51 tff(35744,plain,
% 12.29/12.51 (r(z, s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[45, 42, 35743, 28])).
% 12.29/12.51 tff(35745,plain,
% 12.29/12.51 (~b(s(s(z)), z)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[35414, 329, 90, 11, 127, 10682])).
% 12.29/12.51 tff(35746,plain,
% 12.29/12.51 (r(s(s(z)), z)),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[1211, 35745])).
% 12.29/12.51 tff(35747,plain,
% 12.29/12.51 (~r(s(s(z)), s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[4462, 35746, 35365, 722])).
% 12.29/12.51 tff(35748,plain,
% 12.29/12.51 (b(s(s(z)), s(z))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[3778, 35747])).
% 12.29/12.51 tff(35749,plain,
% 12.29/12.51 (r(s(s(elem!1)), elem!1)),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[35746, 30367])).
% 12.29/12.51 tff(35750,plain,
% 12.29/12.51 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[27078, 378, 10682, 1686])).
% 12.29/12.51 tff(35751,plain,
% 12.29/12.51 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[27316, 35750, 11])).
% 12.29/12.51 tff(35752,plain,
% 12.29/12.51 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[1095, 35751, 32512])).
% 12.29/12.51 tff(35753,plain,
% 12.29/12.51 (b(s(s(elem!1)), s(z))),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[35748, 30313])).
% 12.29/12.51 tff(35754,plain,
% 12.29/12.51 (r(s(elem!1), elem!1)),
% 12.29/12.51 inference(modus_ponens,[status(thm)],[29072, 17627])).
% 12.29/12.51 tff(35755,plain,
% 12.29/12.51 (~r(s(s(s(elem!1))), s(elem!1))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[14601, 35752, 990, 35754])).
% 12.29/12.51 tff(35756,plain,
% 12.29/12.51 (b(s(s(s(elem!1))), s(elem!1))),
% 12.29/12.51 inference(unit_resolution,[status(thm)],[588, 35755, 8876])).
% 12.29/12.52 tff(35757,plain,
% 12.29/12.52 (b(s(s(s(elem!1))), s(z))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35756, 494])).
% 12.29/12.52 tff(35758,plain,
% 12.29/12.52 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1660, 35757, 1234, 33675, 35753])).
% 12.29/12.52 tff(35759,plain,
% 12.29/12.52 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1370, 35758, 15838])).
% 12.29/12.52 tff(35760,plain,
% 12.29/12.52 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[14240, 35759, 35752, 35749])).
% 12.29/12.52 tff(35761,plain,
% 12.29/12.52 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1061, 35760, 35386])).
% 12.29/12.52 tff(35762,plain,
% 12.29/12.52 (b(s(s(s(s(z)))), s(s(z)))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35761, 2420])).
% 12.29/12.52 tff(35763,plain,
% 12.29/12.52 (~r(s(z), s(s(z)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[12646, 194, 722, 29072, 35746])).
% 12.29/12.52 tff(35764,plain,
% 12.29/12.52 (b(s(z), s(s(z)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1788, 35763])).
% 12.29/12.52 tff(35765,plain,
% 12.29/12.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.52 inference(rewrite,[status(thm)],[])).
% 12.29/12.52 tff(35766,plain,
% 12.29/12.52 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.52 inference(rewrite,[status(thm)],[])).
% 12.29/12.52 tff(35767,plain,
% 12.29/12.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.29/12.52 inference(monotonicity,[status(thm)],[35766])).
% 12.29/12.52 tff(35768,plain,
% 12.29/12.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.52 inference(transitivity,[status(thm)],[35767, 35765])).
% 12.29/12.52 tff(35769,plain,
% 12.29/12.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.52 inference(quant_inst,[status(thm)],[])).
% 12.29/12.52 tff(35770,plain,
% 12.29/12.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35769, 35768])).
% 12.29/12.52 tff(35771,plain,
% 12.29/12.52 ($false),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[35770, 391, 1234, 35764, 35762, 35748])).
% 12.29/12.52 tff(35772,plain,(r(s(s(s(elem!1))), z) | (~b(s(z), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.52 tff(35773,plain,
% 12.29/12.52 (r(s(s(s(elem!1))), z)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[35772, 35744, 11, 1234, 35741, 10682, 1686, 90, 127])).
% 12.29/12.52 tff(35774,plain,
% 12.29/12.52 (~r(s(s(s(elem!1))), s(z))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[17465, 174, 35744, 35365])).
% 12.29/12.52 tff(35775,plain,
% 12.29/12.52 (b(s(s(s(elem!1))), s(z))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[223, 35774])).
% 12.29/12.52 tff(35776,plain,
% 12.29/12.52 (~r(s(s(z)), s(z))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[20881, 1749, 723, 29072])).
% 12.29/12.52 tff(35777,plain,
% 12.29/12.52 (b(s(s(z)), s(z))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[3778, 35776])).
% 12.29/12.52 tff(35778,plain,
% 12.29/12.52 (b(s(s(elem!1)), s(z))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35777, 30313])).
% 12.29/12.52 tff(35779,plain,
% 12.29/12.52 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1660, 35778, 1234, 33675, 35775])).
% 12.29/12.52 tff(35780,plain,
% 12.29/12.52 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1370, 35779, 297])).
% 12.29/12.52 tff(35781,plain,
% 12.29/12.52 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[1749, 2403])).
% 12.29/12.52 tff(35782,plain,
% 12.29/12.52 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 12.29/12.52 inference(transitivity,[status(thm)],[29, 34436, 34435])).
% 12.29/12.52 tff(35783,plain,
% 12.29/12.52 ((~b(elem!1, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 12.29/12.52 inference(monotonicity,[status(thm)],[35782])).
% 12.29/12.52 tff(35784,plain,
% 12.29/12.52 (~b(elem!1, s(elem!1))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35742, 35783])).
% 12.29/12.52 tff(35785,plain,
% 12.29/12.52 (r(elem!1, s(elem!1))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[443, 35784, 7437])).
% 12.29/12.52 tff(35786,plain,
% 12.29/12.52 (~r(s(s(s(elem!1))), s(elem!1))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[7744, 31530, 35754, 35785])).
% 12.29/12.52 tff(35787,plain,
% 12.29/12.52 (b(s(s(s(elem!1))), s(elem!1))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[588, 35786, 8876])).
% 12.29/12.52 tff(35788,plain,
% 12.29/12.52 (r(s(elem!1), z)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[27330, 29072, 11])).
% 12.29/12.52 tff(35789,plain,
% 12.29/12.52 (~r(elem!1, z)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[29452, 17618])).
% 12.29/12.52 tff(35790,plain,
% 12.29/12.52 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 12.29/12.52 inference(symmetry,[status(thm)],[32216])).
% 12.29/12.52 tff(35791,plain,
% 12.29/12.52 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 12.29/12.52 inference(transitivity,[status(thm)],[18406, 35790])).
% 12.29/12.52 tff(35792,plain,
% 12.29/12.52 ((~b(s(z), z)) <=> (~b(s(elem!1), elem!1))),
% 12.29/12.52 inference(monotonicity,[status(thm)],[35791])).
% 12.29/12.52 tff(35793,plain,
% 12.29/12.52 (~b(s(elem!1), elem!1)),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[29071, 35792])).
% 12.29/12.52 tff(35794,plain,
% 12.29/12.52 (~b(s(z), elem!1)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[3200, 29071, 11])).
% 12.29/12.52 tff(35795,plain,
% 12.29/12.52 (~r(s(z), s(s(s(elem!1))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[5246, 31530, 24, 35742, 35794])).
% 12.29/12.52 tff(35796,plain,
% 12.29/12.52 (b(s(z), s(s(s(elem!1))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[247, 35795])).
% 12.29/12.52 tff(35797,plain,
% 12.29/12.52 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[20817, 35775, 1234, 35796])).
% 12.29/12.52 tff(35798,plain,
% 12.29/12.52 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[27316, 35797, 11])).
% 12.29/12.52 tff(35799,plain,
% 12.29/12.52 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1095, 35798, 310])).
% 12.29/12.52 tff(35800,plain,
% 12.29/12.52 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[29931, 35799, 11])).
% 12.29/12.52 tff(35801,plain,
% 12.29/12.52 (r(s(s(s(elem!1))), s(s(z)))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35780, 30003])).
% 12.29/12.52 tff(35802,plain,
% 12.29/12.52 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[34395, 35801, 35800, 1749])).
% 12.29/12.52 tff(35803,plain,
% 12.29/12.52 (b(s(s(s(s(z)))), s(s(z)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1714, 35802])).
% 12.29/12.52 tff(35804,plain,
% 12.29/12.52 (~b(s(s(z)), z)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[20748, 35803, 90, 1686])).
% 12.29/12.52 tff(35805,plain,
% 12.29/12.52 (r(s(s(z)), z)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1211, 35804])).
% 12.29/12.52 tff(35806,plain,
% 12.29/12.52 (b(s(s(s(elem!1))), elem!1)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[27431, 35805, 10682, 35793, 35366, 35785, 29072, 174, 24, 35789, 35775, 31530, 35788, 164])).
% 12.29/12.52 tff(35807,plain,
% 12.29/12.52 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[2706, 35806, 35390, 35366, 35787])).
% 12.29/12.52 tff(35808,plain,
% 12.29/12.52 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1164, 35807, 311])).
% 12.29/12.52 tff(35809,plain,
% 12.29/12.52 (b(s(s(s(z))), s(z))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35775, 17635])).
% 12.29/12.52 tff(35810,plain,
% 12.29/12.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.52 inference(rewrite,[status(thm)],[])).
% 12.29/12.52 tff(35811,plain,
% 12.29/12.52 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(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)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.52 inference(rewrite,[status(thm)],[])).
% 12.29/12.52 tff(35812,plain,
% 12.29/12.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.29/12.52 inference(monotonicity,[status(thm)],[35811])).
% 12.29/12.52 tff(35813,plain,
% 12.29/12.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.52 inference(transitivity,[status(thm)],[35812, 35810])).
% 12.29/12.52 tff(35814,plain,
% 12.29/12.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(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))))))),
% 12.29/12.52 inference(quant_inst,[status(thm)],[])).
% 12.29/12.52 tff(35815,plain,
% 12.29/12.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35814, 35813])).
% 12.29/12.52 tff(35816,plain,
% 12.29/12.52 (~b(s(s(z)), s(s(s(z))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[35815, 391, 90, 1234, 35777, 35809])).
% 12.29/12.52 tff(35817,plain,
% 12.29/12.52 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35816, 30044])).
% 12.29/12.52 tff(35818,plain,
% 12.29/12.52 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1356, 35817, 315])).
% 12.29/12.52 tff(35819,plain,
% 12.29/12.52 (~r(s(s(elem!1)), elem!1)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[26915, 35818, 35785, 31530])).
% 12.29/12.52 tff(35820,plain,
% 12.29/12.52 (b(s(s(elem!1)), elem!1)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[872, 35819, 30072])).
% 12.29/12.52 tff(35821,plain,
% 12.29/12.52 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[8729, 35806, 35390, 35366, 35820])).
% 12.29/12.52 tff(35822,plain,
% 12.29/12.52 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1061, 35821, 35386])).
% 12.29/12.52 tff(35823,plain,
% 12.29/12.52 ($false),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[15681, 35822, 35808, 35781, 35780])).
% 12.29/12.52 tff(35824,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (s(elem!1) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.52 tff(35825,plain,
% 12.29/12.52 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[35824, 35773, 10682, 4597, 90, 1686, 11, 15838, 1234, 723])).
% 12.29/12.52 tff(35826,plain,
% 12.29/12.52 (b(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[3652, 35825])).
% 12.29/12.52 tff(35827,plain,
% 12.29/12.52 (~b(s(s(z)), z)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[4472, 35826, 90, 1686])).
% 12.29/12.52 tff(35828,plain,
% 12.29/12.52 (r(s(s(z)), z)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[1211, 35827])).
% 12.29/12.52 tff(35829,plain,
% 12.29/12.52 (r(s(s(elem!1)), elem!1)),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35828, 30367])).
% 12.29/12.52 tff(35830,plain,
% 12.29/12.52 (r(s(s(s(elem!1))), elem!1)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[9853, 35773, 17618])).
% 12.29/12.52 tff(35831,plain,
% 12.29/12.52 (r(elem!1, s(elem!1))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[443, 35784, 4598])).
% 12.29/12.52 tff(35832,plain,
% 12.29/12.52 (b(elem!1, s(z)) <=> b(z, s(elem!1))),
% 12.29/12.52 inference(transitivity,[status(thm)],[29, 34436])).
% 12.29/12.52 tff(35833,plain,
% 12.29/12.52 ((~b(elem!1, s(z))) <=> (~b(z, s(elem!1)))),
% 12.29/12.52 inference(monotonicity,[status(thm)],[35832])).
% 12.29/12.52 tff(35834,plain,
% 12.29/12.52 (~b(z, s(elem!1))),
% 12.29/12.52 inference(modus_ponens,[status(thm)],[35742, 35833])).
% 12.29/12.52 tff(35835,plain,
% 12.29/12.52 (r(z, s(elem!1))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[566, 35834])).
% 12.29/12.52 tff(35836,plain,
% 12.29/12.52 (~r(s(elem!1), s(s(s(elem!1))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[7760, 35773, 35788, 35835])).
% 12.29/12.52 tff(35837,plain,
% 12.29/12.52 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[27422, 35828, 17618, 10682, 35773, 29072, 35830, 35831, 35836])).
% 12.29/12.52 tff(35838,plain,
% 12.29/12.52 (~r(s(s(elem!1)), elem!1)),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[26915, 35837, 35831, 35830])).
% 12.29/12.52 tff(35839,plain,
% 12.29/12.52 ($false),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[35838, 35829])).
% 12.29/12.52 tff(35840,plain,((~b(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.52 tff(35841,plain,
% 12.29/12.52 (~b(z, s(s(s(s(z)))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[35840, 1234, 35310, 90, 33627, 35735, 9])).
% 12.29/12.52 tff(35842,plain,
% 12.29/12.52 (r(z, s(s(s(s(z)))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[800, 35841])).
% 12.29/12.52 tff(35843,plain,
% 12.29/12.52 (~b(z, s(s(s(s(z)))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[35840, 1234, 10682, 90, 11, 723, 127])).
% 12.29/12.52 tff(35844,plain,
% 12.29/12.52 (r(z, s(s(s(s(z)))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[800, 35843])).
% 12.29/12.52 tff(35845,plain,
% 12.29/12.52 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[16406, 35746, 723, 35844])).
% 12.29/12.52 tff(35846,plain,
% 12.29/12.52 (b(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.52 inference(unit_resolution,[status(thm)],[3652, 35845])).
% 12.29/12.52 tff(35847,plain,
% 12.29/12.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.53 inference(rewrite,[status(thm)],[])).
% 12.29/12.53 tff(35848,plain,
% 12.29/12.53 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.53 inference(rewrite,[status(thm)],[])).
% 12.29/12.53 tff(35849,plain,
% 12.29/12.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.29/12.53 inference(monotonicity,[status(thm)],[35848])).
% 12.29/12.53 tff(35850,plain,
% 12.29/12.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.53 inference(transitivity,[status(thm)],[35849, 35847])).
% 12.29/12.53 tff(35851,plain,
% 12.29/12.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 12.29/12.53 inference(quant_inst,[status(thm)],[])).
% 12.29/12.53 tff(35852,plain,
% 12.29/12.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 12.29/12.53 inference(modus_ponens,[status(thm)],[35851, 35850])).
% 12.29/12.53 tff(35853,plain,
% 12.29/12.53 (~b(s(s(z)), s(z))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[35852, 391, 35846, 90, 1234, 23190])).
% 12.29/12.53 tff(35854,plain,
% 12.29/12.53 (~b(s(z), elem!1)),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[35701, 378, 11, 90, 10682, 1234])).
% 12.29/12.53 tff(35855,plain,
% 12.29/12.53 (r(s(z), elem!1)),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[632, 35854, 24])).
% 12.29/12.53 tff(35856,plain,
% 12.29/12.53 (r(s(z), z)),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[5433, 35855, 17618])).
% 12.29/12.53 tff(35857,plain,
% 12.29/12.53 (~r(s(s(z)), s(z))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[10250, 194, 35856, 35746, 35844])).
% 12.29/12.53 tff(35858,plain,
% 12.29/12.53 ($false),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[3778, 35857, 35853])).
% 12.29/12.53 tff(35859,plain,(r(s(s(s(elem!1))), z) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.53 tff(35860,plain,
% 12.29/12.53 (r(s(s(s(elem!1))), z)),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[35859, 1234, 90, 35735, 33627, 35310, 9])).
% 12.29/12.53 tff(35861,plain,
% 12.29/12.53 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[28132, 35860, 35735, 35842])).
% 12.29/12.53 tff(35862,plain,
% 12.29/12.53 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[15351, 35861, 35009])).
% 12.29/12.53 tff(35863,plain,
% 12.29/12.53 (b(s(s(s(z))), s(s(s(s(z)))))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[1673, 35862, 33627])).
% 12.29/12.53 tff(35864,plain,
% 12.29/12.53 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 12.29/12.53 inference(monotonicity,[status(thm)],[34917])).
% 12.29/12.53 tff(35865,plain,
% 12.29/12.53 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 12.29/12.53 inference(symmetry,[status(thm)],[35864])).
% 12.29/12.53 tff(35866,plain,
% 12.29/12.53 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[23863, 35861, 90, 35310, 35309])).
% 12.29/12.53 tff(35867,plain,
% 12.29/12.53 (~r(s(z), s(s(s(elem!1))))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[33111, 35866, 35735, 35860])).
% 12.29/12.53 tff(35868,plain,
% 12.29/12.53 (b(s(z), s(s(s(elem!1))))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[247, 35867])).
% 12.29/12.53 tff(35869,plain,
% 12.29/12.53 (b(s(z), s(s(s(z))))),
% 12.29/12.53 inference(modus_ponens,[status(thm)],[35868, 35865])).
% 12.29/12.53 tff(35870,plain,
% 12.29/12.53 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 12.29/12.53 inference(monotonicity,[status(thm)],[34426])).
% 12.29/12.53 tff(35871,plain,
% 12.29/12.53 (b(z, s(s(s(z))))),
% 12.29/12.53 inference(modus_ponens,[status(thm)],[35310, 35870])).
% 12.29/12.53 tff(35872,plain,
% 12.29/12.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.53 inference(rewrite,[status(thm)],[])).
% 12.29/12.53 tff(35873,plain,
% 12.29/12.53 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.53 inference(rewrite,[status(thm)],[])).
% 12.29/12.53 tff(35874,plain,
% 12.29/12.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.29/12.53 inference(monotonicity,[status(thm)],[35873])).
% 12.29/12.53 tff(35875,plain,
% 12.29/12.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.53 inference(transitivity,[status(thm)],[35874, 35872])).
% 12.29/12.53 tff(35876,plain,
% 12.29/12.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 12.29/12.53 inference(quant_inst,[status(thm)],[])).
% 12.29/12.53 tff(35877,plain,
% 12.29/12.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 12.29/12.53 inference(modus_ponens,[status(thm)],[35876, 35875])).
% 12.29/12.53 tff(35878,plain,
% 12.29/12.53 ($false),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[35877, 391, 90, 1234, 35871, 35869, 35863])).
% 12.29/12.53 tff(35879,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | r(z, elem!1) | (elem!1 = s(s(s(elem!1)))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.53 tff(35880,plain,
% 12.29/12.53 (~b(s(z), s(s(s(s(z)))))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[35879, 88, 80, 1, 33631])).
% 12.29/12.53 tff(35881,plain,
% 12.29/12.53 (b(s(z), elem!1)),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[632, 1492, 24])).
% 12.29/12.53 tff(35882,plain,
% 12.29/12.53 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.29/12.53 inference(transitivity,[status(thm)],[32149, 32146])).
% 12.29/12.53 tff(35883,plain,
% 12.29/12.53 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 12.29/12.53 inference(monotonicity,[status(thm)],[35882])).
% 12.29/12.53 tff(35884,plain,
% 12.29/12.53 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.29/12.53 inference(modus_ponens,[status(thm)],[34126, 35883])).
% 12.29/12.53 tff(35885,plain,
% 12.29/12.53 (~r(s(s(s(elem!1))), s(z))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[23013, 378, 90, 10682, 35884, 1216])).
% 12.29/12.53 tff(35886,plain,
% 12.29/12.53 (b(s(s(s(elem!1))), s(z))),
% 12.29/12.53 inference(unit_resolution,[status(thm)],[223, 35885])).
% 12.29/12.53 tff(35887,plain,
% 12.29/12.53 (b(s(s(s(z))), s(z))),
% 12.29/12.53 inference(modus_ponens,[status(thm)],[35886, 17635])).
% 12.29/12.53 tff(35888,plain,
% 12.29/12.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 12.29/12.54 inference(rewrite,[status(thm)],[])).
% 12.29/12.54 tff(35889,plain,
% 12.29/12.54 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 12.29/12.54 inference(rewrite,[status(thm)],[])).
% 12.29/12.54 tff(35890,plain,
% 12.29/12.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))))),
% 12.29/12.54 inference(monotonicity,[status(thm)],[35889])).
% 12.29/12.54 tff(35891,plain,
% 12.29/12.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 12.29/12.54 inference(transitivity,[status(thm)],[35890, 35888])).
% 12.29/12.54 tff(35892,plain,
% 12.29/12.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 12.29/12.54 inference(quant_inst,[status(thm)],[])).
% 12.29/12.54 tff(35893,plain,
% 12.29/12.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 12.29/12.54 inference(modus_ponens,[status(thm)],[35892, 35891])).
% 12.29/12.54 tff(35894,plain,
% 12.29/12.54 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[35893, 391, 90, 23190, 35887, 35380])).
% 12.29/12.54 tff(35895,plain,
% 12.29/12.54 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[1673, 35894, 11])).
% 12.29/12.54 tff(35896,plain,
% 12.29/12.54 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[15351, 35895, 35026])).
% 12.29/12.54 tff(35897,plain,
% 12.29/12.54 (r(s(s(s(z))), s(s(s(s(z)))))),
% 12.29/12.54 inference(modus_ponens,[status(thm)],[35896, 17613])).
% 12.29/12.54 tff(35898,plain,
% 12.29/12.54 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[7880, 35380, 90, 23190])).
% 12.29/12.54 tff(35899,plain,
% 12.29/12.54 (r(s(s(s(s(z)))), s(s(s(z))))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[4426, 42, 35898, 35089])).
% 12.29/12.54 tff(35900,plain,
% 12.29/12.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 12.29/12.54 inference(rewrite,[status(thm)],[])).
% 12.29/12.54 tff(35901,plain,
% 12.29/12.54 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 12.29/12.54 inference(rewrite,[status(thm)],[])).
% 12.29/12.54 tff(35902,plain,
% 12.29/12.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 12.29/12.54 inference(monotonicity,[status(thm)],[35901])).
% 12.29/12.54 tff(35903,plain,
% 12.29/12.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 12.29/12.54 inference(transitivity,[status(thm)],[35902, 35900])).
% 12.29/12.54 tff(35904,plain,
% 12.29/12.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 12.29/12.54 inference(quant_inst,[status(thm)],[])).
% 12.29/12.54 tff(35905,plain,
% 12.29/12.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 12.29/12.54 inference(modus_ponens,[status(thm)],[35904, 35903])).
% 12.29/12.54 tff(35906,plain,
% 12.29/12.54 (~r(s(z), s(s(s(z))))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[35905, 194, 1216, 35899, 35897])).
% 12.29/12.54 tff(35907,plain,
% 12.29/12.54 (~r(s(z), s(s(s(elem!1))))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[23224, 35906, 11])).
% 12.29/12.54 tff(35908,plain,
% 12.29/12.54 (b(s(z), s(s(s(elem!1))))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[247, 35907])).
% 12.29/12.54 tff(35909,plain,
% 12.29/12.54 (b(s(z), s(s(s(z))))),
% 12.29/12.54 inference(modus_ponens,[status(thm)],[35908, 18545])).
% 12.29/12.54 tff(35910,plain,
% 12.29/12.54 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 12.29/12.54 inference(transitivity,[status(thm)],[32216, 18405, 34442])).
% 12.29/12.54 tff(35911,plain,
% 12.29/12.54 ((~b(s(elem!1), elem!1)) <=> (~b(s(z), elem!1))),
% 12.29/12.54 inference(monotonicity,[status(thm)],[35910])).
% 12.29/12.54 tff(35912,plain,
% 12.29/12.54 (b(s(s(s(elem!1))), s(elem!1))),
% 12.29/12.54 inference(modus_ponens,[status(thm)],[35886, 17624])).
% 12.29/12.54 tff(35913,plain,
% 12.29/12.54 (~b(s(elem!1), elem!1)),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[6869, 35912, 35366, 34433])).
% 12.29/12.54 tff(35914,plain,
% 12.29/12.54 (~b(s(z), elem!1)),
% 12.29/12.54 inference(modus_ponens,[status(thm)],[35913, 35911])).
% 12.29/12.54 tff(35915,plain,
% 12.29/12.54 (r(s(z), elem!1)),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[632, 35914, 24])).
% 12.29/12.54 tff(35916,plain,
% 12.29/12.54 (r(s(s(z)), elem!1)),
% 12.29/12.54 inference(modus_ponens,[status(thm)],[35746, 35176])).
% 12.29/12.54 tff(35917,plain,
% 12.29/12.54 (~b(elem!1, s(z))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[2907, 35908, 34433, 35886])).
% 12.29/12.54 tff(35918,plain,
% 12.29/12.54 (r(elem!1, s(z))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[837, 35917, 33640])).
% 12.29/12.54 tff(35919,plain,
% 12.29/12.54 (~r(s(s(z)), s(z))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[6674, 35918, 35916, 35915])).
% 12.29/12.54 tff(35920,plain,
% 12.29/12.54 (b(s(s(z)), s(z))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[3778, 35919])).
% 12.29/12.54 tff(35921,plain,
% 12.29/12.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 12.29/12.54 inference(rewrite,[status(thm)],[])).
% 12.29/12.54 tff(35922,plain,
% 12.29/12.54 (((~b(s(s(s(z))), s(z))) | (~b(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)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 12.29/12.54 inference(rewrite,[status(thm)],[])).
% 12.29/12.54 tff(35923,plain,
% 12.29/12.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 12.29/12.54 inference(monotonicity,[status(thm)],[35922])).
% 12.29/12.54 tff(35924,plain,
% 12.29/12.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 12.29/12.54 inference(transitivity,[status(thm)],[35923, 35921])).
% 12.29/12.54 tff(35925,plain,
% 12.29/12.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(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))))))),
% 12.29/12.54 inference(quant_inst,[status(thm)],[])).
% 12.29/12.54 tff(35926,plain,
% 12.29/12.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 12.29/12.54 inference(modus_ponens,[status(thm)],[35925, 35924])).
% 12.29/12.54 tff(35927,plain,
% 12.29/12.54 (~b(s(s(z)), s(s(s(z))))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[35926, 391, 35920, 35887, 35909])).
% 12.29/12.54 tff(35928,plain,
% 12.29/12.54 (r(s(s(z)), s(s(s(z))))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[24076, 35927, 8880])).
% 12.29/12.54 tff(35929,plain,
% 12.29/12.54 (~r(s(s(elem!1)), s(z))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[4958, 35908, 24, 35366, 35886, 35749])).
% 12.29/12.54 tff(35930,plain,
% 12.29/12.54 (b(s(s(elem!1)), s(z))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[362, 35929])).
% 12.29/12.54 tff(35931,plain,
% 12.29/12.54 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[4762, 35930, 35886, 35908])).
% 12.29/12.54 tff(35932,plain,
% 12.29/12.54 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[1370, 35931, 15838])).
% 12.29/12.54 tff(35933,plain,
% 12.29/12.54 (r(s(s(s(z))), s(s(z)))),
% 12.29/12.54 inference(unit_resolution,[status(thm)],[4385, 35932, 11])).
% 12.29/12.54 tff(35934,plain,
% 12.29/12.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 12.29/12.54 inference(rewrite,[status(thm)],[])).
% 12.29/12.54 tff(35935,plain,
% 12.29/12.54 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 12.29/12.54 inference(rewrite,[status(thm)],[])).
% 12.29/12.54 tff(35936,plain,
% 12.29/12.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 12.29/12.54 inference(monotonicity,[status(thm)],[35935])).
% 12.29/12.54 tff(35937,plain,
% 12.29/12.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 12.29/12.55 inference(transitivity,[status(thm)],[35936, 35934])).
% 12.29/12.55 tff(35938,plain,
% 12.29/12.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 12.29/12.55 inference(quant_inst,[status(thm)],[])).
% 12.29/12.55 tff(35939,plain,
% 12.29/12.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 12.29/12.55 inference(modus_ponens,[status(thm)],[35938, 35937])).
% 12.29/12.55 tff(35940,plain,
% 12.29/12.55 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[35939, 194, 35933, 35928, 35899])).
% 12.29/12.55 tff(35941,plain,
% 12.29/12.55 (b(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[3652, 35940])).
% 12.29/12.55 tff(35942,plain,
% 12.29/12.55 (r(s(elem!1), elem!1)),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[2168, 35913, 4597])).
% 12.29/12.55 tff(35943,plain,
% 12.29/12.55 (r(s(z), z)),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[29755, 35942, 11])).
% 12.29/12.55 tff(35944,plain,
% 12.29/12.55 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.55 inference(modus_ponens,[status(thm)],[35898, 30118])).
% 12.29/12.55 tff(35945,plain,
% 12.29/12.55 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[1095, 35944, 32512])).
% 12.29/12.55 tff(35946,plain,
% 12.29/12.55 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[29931, 35945, 11])).
% 12.29/12.55 tff(35947,plain,
% 12.29/12.55 (~r(z, s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[2108, 35946, 1216, 35943])).
% 12.29/12.55 tff(35948,plain,
% 12.29/12.55 (b(z, s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[800, 35947])).
% 12.29/12.55 tff(35949,plain,
% 12.29/12.55 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[25141, 35886, 90, 10682, 1216, 35884])).
% 12.29/12.55 tff(35950,plain,
% 12.29/12.55 (b(s(s(s(s(z)))), s(s(z)))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[1714, 35949])).
% 12.29/12.55 tff(35951,plain,
% 12.29/12.55 (~b(z, s(s(z)))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[15550, 35941, 35950, 35948])).
% 12.29/12.55 tff(35952,plain,
% 12.29/12.55 (r(z, s(s(z)))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[18613, 35951])).
% 12.29/12.55 tff(35953,plain,
% 12.29/12.55 (r(elem!1, s(s(elem!1)))),
% 12.29/12.55 inference(modus_ponens,[status(thm)],[35952, 29971])).
% 12.29/12.55 tff(35954,plain,
% 12.29/12.55 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[35051, 35953, 90, 35948, 35941, 11])).
% 12.29/12.55 tff(35955,plain,
% 12.29/12.55 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[33872, 35954])).
% 12.29/12.55 tff(35956,plain,
% 12.29/12.55 (~b(z, s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[15561, 35908, 10682, 35886])).
% 12.29/12.55 tff(35957,plain,
% 12.29/12.55 (r(z, s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[678, 35956])).
% 12.29/12.55 tff(35958,plain,
% 12.29/12.55 (~r(s(z), s(s(z)))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[12646, 194, 35957, 35943, 35746])).
% 12.29/12.55 tff(35959,plain,
% 12.29/12.55 (b(s(z), s(s(z)))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[1788, 35958])).
% 12.29/12.55 tff(35960,plain,
% 12.29/12.55 (~b(s(s(s(s(z)))), s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[1795, 391, 35959, 35950, 35920])).
% 12.29/12.55 tff(35961,plain,
% 12.29/12.55 (r(s(s(s(s(z)))), s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[749, 35960])).
% 12.29/12.55 tff(35962,plain,
% 12.29/12.55 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[35063, 194, 35961, 35955, 35897])).
% 12.29/12.55 tff(35963,plain,
% 12.29/12.55 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[29527, 42, 8094, 35962])).
% 12.29/12.55 tff(35964,plain,
% 12.29/12.55 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[34993, 194, 1216, 35961, 35955])).
% 12.29/12.55 tff(35965,plain,
% 12.29/12.55 (b(s(s(s(s(s(s(z)))))), s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[14139, 35964])).
% 12.29/12.55 tff(35966,plain,
% 12.29/12.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.29/12.55 inference(rewrite,[status(thm)],[])).
% 12.29/12.55 tff(35967,plain,
% 12.29/12.55 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.29/12.55 inference(rewrite,[status(thm)],[])).
% 12.29/12.55 tff(35968,plain,
% 12.29/12.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 12.29/12.55 inference(monotonicity,[status(thm)],[35967])).
% 12.29/12.55 tff(35969,plain,
% 12.29/12.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.29/12.55 inference(transitivity,[status(thm)],[35968, 35966])).
% 12.29/12.55 tff(35970,plain,
% 12.29/12.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.29/12.55 inference(quant_inst,[status(thm)],[])).
% 12.29/12.55 tff(35971,plain,
% 12.29/12.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 12.29/12.55 inference(modus_ponens,[status(thm)],[35970, 35969])).
% 12.29/12.55 tff(35972,plain,
% 12.29/12.55 ($false),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[35971, 391, 35941, 35959, 35887, 35965, 35963])).
% 12.29/12.55 tff(35973,plain,(r(s(s(s(elem!1))), z) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.55 tff(35974,plain,
% 12.29/12.55 (r(s(s(s(elem!1))), z)),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[35973, 2913, 90, 11, 10682, 9])).
% 12.29/12.55 tff(35975,plain,
% 12.29/12.55 (r(s(s(s(elem!1))), elem!1)),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[9853, 35974, 17618])).
% 12.29/12.55 tff(35976,plain,
% 12.29/12.55 (b(s(z), z)),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[3205, 1492, 11])).
% 12.29/12.55 tff(35977,plain,
% 12.29/12.55 (r(s(z), z)),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[27326, 1526, 10682, 448, 150, 2282, 174, 90])).
% 12.29/12.55 tff(35978,plain,
% 12.29/12.55 (~b(s(z), s(s(s(elem!1))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[28322, 1526, 10682, 590, 644])).
% 12.29/12.55 tff(35979,plain,
% 12.29/12.55 (r(s(z), s(s(s(elem!1))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[247, 35978])).
% 12.29/12.55 tff(35980,plain,
% 12.29/12.55 (~r(z, s(s(s(elem!1))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[241, 35979, 233, 35977])).
% 12.29/12.55 tff(35981,plain,
% 12.29/12.55 (b(s(s(s(elem!1))), z)),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[28285, 35980, 90, 2881, 1526, 448, 127])).
% 12.29/12.55 tff(35982,plain,
% 12.29/12.55 (~r(z, s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[27817, 35979, 35977, 174])).
% 12.29/12.55 tff(35983,plain,
% 12.29/12.55 (b(z, s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[800, 35982])).
% 12.29/12.55 tff(35984,plain,
% 12.29/12.55 ($false),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[6325, 35983, 35981, 90, 590, 1526])).
% 12.29/12.55 tff(35985,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | b(s(z), s(s(s(s(z))))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (s(z) = elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.55 tff(35986,plain,
% 12.29/12.55 (~b(s(s(s(elem!1))), s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[35985, 35976, 90, 2881, 35366, 9, 35974, 35975, 10682, 35881, 24, 35789])).
% 12.29/12.55 tff(35987,plain,
% 12.29/12.55 (r(s(s(s(elem!1))), s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[223, 35986])).
% 12.29/12.55 tff(35988,plain,
% 12.29/12.55 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.29/12.55 inference(modus_ponens,[status(thm)],[32322, 35883])).
% 12.29/12.55 tff(35989,plain,
% 12.29/12.55 (~b(s(s(s(s(z)))), s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[23356, 183, 33640, 90, 1, 10682, 1216, 3557])).
% 12.29/12.55 tff(35990,plain,
% 12.29/12.55 (r(s(s(s(s(z)))), s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[749, 35989])).
% 12.29/12.55 tff(35991,plain,
% 12.29/12.55 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[34958, 194, 1216, 35990, 33644])).
% 12.29/12.55 tff(35992,plain,
% 12.29/12.55 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.29/12.55 inference(modus_ponens,[status(thm)],[35991, 29912])).
% 12.29/12.55 tff(35993,plain,
% 12.29/12.55 ((~r(s(s(s(s(z)))), s(s(s(z))))) <=> (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 12.29/12.55 inference(monotonicity,[status(thm)],[29926])).
% 12.29/12.55 tff(35994,plain,
% 12.29/12.55 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[34503, 194, 1216, 35990, 33644])).
% 12.29/12.55 tff(35995,plain,
% 12.29/12.55 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.55 inference(modus_ponens,[status(thm)],[35994, 35993])).
% 12.29/12.55 tff(35996,plain,
% 12.29/12.55 ($false),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[23863, 35995, 35992, 90, 10682, 35988])).
% 12.29/12.55 tff(35997,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~(elem!1 = z)) | (~r(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.55 tff(35998,plain,
% 12.29/12.55 (~r(s(s(z)), z)),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[35997, 35987, 10682, 11, 2913, 1, 90])).
% 12.29/12.55 tff(35999,plain,
% 12.29/12.55 (b(s(s(z)), z)),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[1211, 35998])).
% 12.29/12.55 tff(36000,plain,
% 12.29/12.55 (~r(elem!1, s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[10856, 35987, 2913, 35975])).
% 12.29/12.55 tff(36001,plain,
% 12.29/12.55 (b(elem!1, s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[837, 36000, 33640])).
% 12.29/12.55 tff(36002,plain,
% 12.29/12.55 (~r(z, s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[16377, 35987, 2913, 35974])).
% 12.29/12.55 tff(36003,plain,
% 12.29/12.55 (b(z, s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[678, 36002])).
% 12.29/12.55 tff(36004,plain,
% 12.29/12.55 (~b(s(s(s(s(z)))), s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[20920, 36003, 90, 35881, 36001])).
% 12.29/12.55 tff(36005,plain,
% 12.29/12.55 (r(s(s(s(s(z)))), s(z))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[749, 36004])).
% 12.29/12.55 tff(36006,plain,
% 12.29/12.55 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[7203, 35999, 90, 35976, 36003])).
% 12.29/12.55 tff(36007,plain,
% 12.29/12.55 (r(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[3652, 36006])).
% 12.29/12.55 tff(36008,plain,
% 12.29/12.55 (~r(z, s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[16415, 36007, 35976, 2913, 36003, 36005])).
% 12.29/12.55 tff(36009,plain,
% 12.29/12.55 (b(z, s(s(s(s(z)))))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[800, 36008])).
% 12.29/12.55 tff(36010,plain,
% 12.29/12.55 (~r(s(z), s(s(z)))),
% 12.29/12.55 inference(unit_resolution,[status(thm)],[16396, 36007, 2913, 36005])).
% 12.29/12.55 tff(36011,plain,
% 12.29/12.56 (b(s(z), s(s(z)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1788, 36010])).
% 12.29/12.56 tff(36012,plain,
% 12.29/12.56 ($false),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[16487, 36011, 36009, 90, 35976, 35999])).
% 12.29/12.56 tff(36013,plain,(r(s(z), elem!1) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~(elem!1 = z)) | (elem!1 = s(s(s(elem!1)))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.56 tff(36014,plain,
% 12.29/12.56 (r(s(z), elem!1)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[36013, 88, 35303, 33627, 1, 35880])).
% 12.29/12.56 tff(36015,plain,
% 12.29/12.56 (r(s(z), z)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[5433, 36014, 34898])).
% 12.29/12.56 tff(36016,plain,
% 12.29/12.56 (b(s(s(s(elem!1))), s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[28392, 36015, 88, 35303, 1, 35880, 35309])).
% 12.29/12.56 tff(36017,plain,
% 12.29/12.56 (r(s(z), s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1230, 35880])).
% 12.29/12.56 tff(36018,plain,
% 12.29/12.56 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[25141, 36016, 88, 35303, 36017, 35309])).
% 12.29/12.56 tff(36019,plain,
% 12.29/12.56 (b(s(s(s(s(z)))), s(s(z)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1714, 36018])).
% 12.29/12.56 tff(36020,plain,
% 12.29/12.56 (~b(s(s(z)), z)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[25151, 36019, 88, 35303, 36016])).
% 12.29/12.56 tff(36021,plain,
% 12.29/12.56 (r(s(s(z)), z)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1211, 36020])).
% 12.29/12.56 tff(36022,plain,
% 12.29/12.56 (r(s(s(elem!1)), elem!1)),
% 12.29/12.56 inference(modus_ponens,[status(thm)],[36021, 35306])).
% 12.29/12.56 tff(36023,plain,
% 12.29/12.56 (r(s(s(elem!1)), z)),
% 12.29/12.56 inference(modus_ponens,[status(thm)],[36021, 35305])).
% 12.29/12.56 tff(36024,plain,
% 12.29/12.56 (r(s(s(s(elem!1))), z)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[35973, 36017, 88, 33627, 35303, 9])).
% 12.29/12.56 tff(36025,plain,
% 12.29/12.56 (~r(s(z), s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[27817, 719, 182, 174])).
% 12.29/12.56 tff(36026,plain,
% 12.29/12.56 (b(s(z), s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[247, 36025])).
% 12.29/12.56 tff(36027,plain,
% 12.29/12.56 (~b(z, s(s(elem!1)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[14223, 34312, 10682, 364, 31530, 297, 315])).
% 12.29/12.56 tff(36028,plain,
% 12.29/12.56 (r(z, s(s(elem!1)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[324, 36027])).
% 12.29/12.56 tff(36029,plain,
% 12.29/12.56 ($false),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[13840, 36028, 36026, 174, 182, 2616, 297, 364])).
% 12.29/12.56 tff(36030,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.56 tff(36031,plain,
% 12.29/12.56 (~r(z, s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[36030, 36024, 36015, 36023, 26982, 36022, 35303, 33627])).
% 12.29/12.56 tff(36032,plain,
% 12.29/12.56 (b(z, s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[800, 36031])).
% 12.29/12.56 tff(36033,plain,
% 12.29/12.56 (b(elem!1, s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[23154, 35303, 33627])).
% 12.29/12.56 tff(36034,plain,
% 12.29/12.56 (r(s(s(s(elem!1))), elem!1)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[9853, 36024, 34898])).
% 12.29/12.56 tff(36035,plain,
% 12.29/12.56 (r(s(s(s(z))), z)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[4409, 36024, 33627])).
% 12.29/12.56 tff(36036,plain,
% 12.29/12.56 (~r(s(s(elem!1)), s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[4958, 379, 24, 35366, 1526, 34091])).
% 12.29/12.56 tff(36037,plain,
% 12.29/12.56 (b(s(s(elem!1)), s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[362, 36036])).
% 12.29/12.56 tff(36038,plain,
% 12.29/12.56 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[4762, 36037, 1526, 379])).
% 12.29/12.56 tff(36039,plain,
% 12.29/12.56 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1370, 36038, 297])).
% 12.29/12.56 tff(36040,plain,
% 12.29/12.56 (~r(z, s(s(z)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[35158, 36039, 11, 4428, 3557])).
% 12.29/12.56 tff(36041,plain,
% 12.29/12.56 (b(z, s(s(z)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[18613, 36040])).
% 12.29/12.56 tff(36042,plain,
% 12.29/12.56 (~b(z, s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[15561, 379, 10682, 1526])).
% 12.29/12.56 tff(36043,plain,
% 12.29/12.56 (r(z, s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[678, 36042])).
% 12.29/12.56 tff(36044,plain,
% 12.29/12.56 (~r(s(s(z)), s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[10610, 36043, 1216, 3557])).
% 12.29/12.56 tff(36045,plain,
% 12.29/12.56 (b(s(s(z)), s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[3778, 36044])).
% 12.29/12.56 tff(36046,plain,
% 12.29/12.56 ($false),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[23259, 391, 3563, 1686, 36045, 36041, 18546])).
% 12.29/12.56 tff(36047,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.56 tff(36048,plain,
% 12.29/12.56 (~b(s(z), s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[36047, 36019, 36032, 33627, 36035, 36021, 26982, 36016, 36017, 35303])).
% 12.29/12.56 tff(36049,plain,
% 12.29/12.56 (r(s(z), s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[247, 36048])).
% 12.29/12.56 tff(36050,plain,
% 12.29/12.56 (~r(z, s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[241, 36049, 36034, 36015])).
% 12.29/12.56 tff(36051,plain,
% 12.29/12.56 (b(s(s(s(elem!1))), z)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[28285, 36050, 88, 35880, 36016, 36033, 9])).
% 12.29/12.56 tff(36052,plain,
% 12.29/12.56 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[27078, 36051, 35303, 36032])).
% 12.29/12.56 tff(36053,plain,
% 12.29/12.56 (r(s(z), s(s(s(z))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[23224, 36049, 33627])).
% 12.29/12.56 tff(36054,plain,
% 12.29/12.56 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[23238, 36053, 33627, 36017, 36035])).
% 12.29/12.56 tff(36055,plain,
% 12.29/12.56 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1095, 36054, 29900])).
% 12.29/12.56 tff(36056,plain,
% 12.29/12.56 ($false),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[27316, 36055, 36052, 33627])).
% 12.29/12.56 tff(36057,plain,(r(s(s(s(s(z)))), z) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.56 tff(36058,plain,
% 12.29/12.56 (r(s(s(s(s(z)))), z)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[36057, 79, 66])).
% 12.29/12.56 tff(36059,plain,
% 12.29/12.56 (~r(s(z), s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[10620, 46, 36058])).
% 12.29/12.56 tff(36060,plain,
% 12.29/12.56 (b(s(z), s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1230, 36059])).
% 12.29/12.56 tff(36061,plain,
% 12.29/12.56 (r(s(s(s(s(z)))), z)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[36057, 80, 1])).
% 12.29/12.56 tff(36062,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 12.29/12.56 tff(36063,plain,
% 12.29/12.56 (~r(s(s(s(elem!1))), elem!1)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[406, 329, 33627])).
% 12.29/12.56 tff(36064,plain,
% 12.29/12.56 (b(s(s(z)), z)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1211, 36062])).
% 12.29/12.56 tff(36065,plain,
% 12.29/12.56 (b(s(s(elem!1)), elem!1)),
% 12.29/12.56 inference(modus_ponens,[status(thm)],[36064, 35477])).
% 12.29/12.56 tff(36066,plain,
% 12.29/12.56 (b(s(s(s(elem!1))), elem!1)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[230, 225, 9])).
% 12.29/12.56 tff(36067,plain,
% 12.29/12.56 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 12.29/12.56 inference(monotonicity,[status(thm)],[33627])).
% 12.29/12.56 tff(36068,plain,
% 12.29/12.56 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 12.29/12.56 inference(symmetry,[status(thm)],[36067])).
% 12.29/12.56 tff(36069,plain,
% 12.29/12.56 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 12.29/12.56 inference(monotonicity,[status(thm)],[34427])).
% 12.29/12.56 tff(36070,plain,
% 12.29/12.56 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(s(elem!1)))))),
% 12.29/12.56 inference(symmetry,[status(thm)],[36069])).
% 12.29/12.56 tff(36071,plain,
% 12.29/12.56 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 12.29/12.56 inference(transitivity,[status(thm)],[36070, 36068])).
% 12.29/12.56 tff(36072,plain,
% 12.29/12.56 (r(elem!1, s(s(s(s(z)))))),
% 12.29/12.56 inference(modus_ponens,[status(thm)],[719, 35452])).
% 12.29/12.56 tff(36073,plain,
% 12.29/12.56 (r(s(s(s(s(z)))), elem!1)),
% 12.29/12.56 inference(modus_ponens,[status(thm)],[36061, 33629])).
% 12.29/12.56 tff(36074,plain,
% 12.29/12.56 (~r(s(z), elem!1)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[14627, 1216, 36073, 2032])).
% 12.29/12.56 tff(36075,plain,
% 12.29/12.56 (b(s(z), elem!1)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[632, 36074, 34897])).
% 12.29/12.56 tff(36076,plain,
% 12.29/12.56 ((s(z) = z) <=> (elem!1 = s(z))),
% 12.29/12.56 inference(transitivity,[status(thm)],[34895, 1270])).
% 12.29/12.56 tff(36077,plain,
% 12.29/12.56 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 12.29/12.56 inference(monotonicity,[status(thm)],[36076])).
% 12.29/12.56 tff(36078,plain,
% 12.29/12.56 (~(elem!1 = s(z))),
% 12.29/12.56 inference(modus_ponens,[status(thm)],[23, 36077])).
% 12.29/12.56 tff(36079,plain,
% 12.29/12.56 (~r(elem!1, s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[11195, 1216, 36061, 2032])).
% 12.29/12.56 tff(36080,plain,
% 12.29/12.56 (b(elem!1, s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[837, 36079, 36078])).
% 12.29/12.56 tff(36081,plain,
% 12.29/12.56 (~b(s(s(s(elem!1))), s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[20387, 36080, 900, 36075])).
% 12.29/12.56 tff(36082,plain,
% 12.29/12.56 (~r(s(s(s(elem!1))), s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[32588, 36080, 80, 36061, 1, 1216])).
% 12.29/12.56 tff(36083,plain,
% 12.29/12.56 ($false),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[223, 36082, 36081])).
% 12.29/12.56 tff(36084,plain,((~r(s(z), s(s(s(s(z)))))) | r(z, elem!1) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.56 tff(36085,plain,
% 12.29/12.56 (~r(s(z), s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[36084, 36072, 1, 36066, 80])).
% 12.29/12.56 tff(36086,plain,
% 12.29/12.56 (b(s(z), s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1230, 36085])).
% 12.29/12.56 tff(36087,plain,
% 12.29/12.56 (b(elem!1, s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[31585, 11173, 80, 1, 3446])).
% 12.29/12.56 tff(36088,plain,
% 12.29/12.56 (~b(z, s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[23154, 4028, 11])).
% 12.29/12.56 tff(36089,plain,
% 12.29/12.56 (b(s(s(s(elem!1))), elem!1)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[8856, 34471, 1, 21435, 4028, 36088, 2053])).
% 12.29/12.56 tff(36090,plain,
% 12.29/12.56 (b(elem!1, s(elem!1))),
% 12.29/12.56 inference(modus_ponens,[status(thm)],[35025, 34437])).
% 12.29/12.56 tff(36091,plain,
% 12.29/12.56 (r(elem!1, s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[34693, 35263, 1234, 17618, 35025, 36090])).
% 12.29/12.56 tff(36092,plain,
% 12.29/12.56 (b(z, s(s(elem!1)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[3924, 91, 26982, 36088])).
% 12.29/12.56 tff(36093,plain,
% 12.29/12.56 (r(z, s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[28273, 6124, 17618])).
% 12.29/12.56 tff(36094,plain,
% 12.29/12.56 (~r(s(z), s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[3499, 181, 183, 36093])).
% 12.29/12.56 tff(36095,plain,
% 12.29/12.56 (b(s(z), s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[247, 36094])).
% 12.29/12.56 tff(36096,plain,
% 12.29/12.56 (~b(s(s(elem!1)), s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[30863, 36095, 36089, 35025, 36092])).
% 12.29/12.56 tff(36097,plain,
% 12.29/12.56 (r(s(s(elem!1)), s(z))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[362, 36096])).
% 12.29/12.56 tff(36098,plain,
% 12.29/12.56 (~r(s(s(elem!1)), elem!1)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1899, 36097, 36091, 34471])).
% 12.29/12.56 tff(36099,plain,
% 12.29/12.56 (b(s(s(elem!1)), elem!1)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[872, 36098, 30072])).
% 12.29/12.56 tff(36100,plain,
% 12.29/12.56 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[34598, 36099, 721, 1234, 36089])).
% 12.29/12.56 tff(36101,plain,
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% 12.29/12.56 inference(unit_resolution,[status(thm)],[1370, 36100, 26982])).
% 12.29/12.56 tff(36102,plain,
% 12.29/12.56 (r(s(s(s(z))), s(s(z)))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[4385, 36101, 11])).
% 12.29/12.56 tff(36103,plain,
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% 12.29/12.56 inference(modus_ponens,[status(thm)],[36097, 18397])).
% 12.29/12.56 tff(36104,plain,
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% 12.29/12.56 tff(36105,plain,
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% 12.29/12.56 inference(quant_inst,[status(thm)],[])).
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% 12.29/12.56 inference(modus_ponens,[status(thm)],[36105, 36104])).
% 12.29/12.56 tff(36107,plain,
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% 12.29/12.56 inference(unit_resolution,[status(thm)],[36106, 194, 181, 36103, 36102, 32118])).
% 12.29/12.56 tff(36108,plain,(b(s(z), z) | (~(elem!1 = z)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.56 tff(36109,plain,
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% 12.29/12.56 inference(unit_resolution,[status(thm)],[36108, 4028, 721, 1234, 1, 11, 2053, 183])).
% 12.29/12.56 tff(36110,plain,
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% 12.29/12.56 inference(modus_ponens,[status(thm)],[36109, 34442])).
% 12.29/12.56 tff(36111,plain,
% 12.29/12.56 ((~r(z, s(z))) <=> (~r(z, s(elem!1)))),
% 12.29/12.56 inference(monotonicity,[status(thm)],[30073])).
% 12.29/12.56 tff(36112,plain,
% 12.29/12.56 (r(z, s(s(s(z))))),
% 12.29/12.56 inference(modus_ponens,[status(thm)],[36093, 500])).
% 12.29/12.56 tff(36113,plain,
% 12.29/12.56 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 12.29/12.56 inference(monotonicity,[status(thm)],[11])).
% 12.29/12.56 tff(36114,plain,
% 12.29/12.56 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 12.29/12.56 inference(symmetry,[status(thm)],[36113])).
% 12.29/12.56 tff(36115,plain,
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% 12.29/12.56 inference(modus_ponens,[status(thm)],[2053, 36114])).
% 12.29/12.56 tff(36116,plain,
% 12.29/12.56 (r(s(s(s(elem!1))), z)),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[406, 233, 11])).
% 12.29/12.56 tff(36117,plain,
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% 12.29/12.56 inference(unit_resolution,[status(thm)],[4409, 36116, 11])).
% 12.29/12.56 tff(36118,plain,
% 12.29/12.56 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 12.29/12.56 inference(monotonicity,[status(thm)],[2401, 488])).
% 12.29/12.56 tff(36119,plain,
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% 12.29/12.56 inference(modus_ponens,[status(thm)],[590, 35791])).
% 12.29/12.56 tff(36120,plain,
% 12.29/12.56 (r(z, s(s(s(elem!1))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[28273, 410, 17618])).
% 12.29/12.56 tff(36121,plain,
% 12.29/12.56 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[34799, 233, 1234, 2053, 17618, 410, 34438, 36120, 36119])).
% 12.29/12.56 tff(36122,plain,
% 12.29/12.56 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[988, 36121, 957])).
% 12.29/12.56 tff(36123,plain,
% 12.29/12.56 (b(s(s(s(s(z)))), s(z))),
% 12.29/12.56 inference(modus_ponens,[status(thm)],[36122, 36118])).
% 12.29/12.56 tff(36124,plain,
% 12.29/12.56 (~b(z, s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[7102, 391, 1234, 36123, 664])).
% 12.29/12.56 tff(36125,plain,
% 12.29/12.56 (r(z, s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[800, 36124])).
% 12.29/12.56 tff(36126,plain,
% 12.29/12.56 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[10090, 36125, 2053, 36120])).
% 12.29/12.56 tff(36127,plain,
% 12.29/12.56 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[15351, 36126, 15348])).
% 12.29/12.56 tff(36128,plain,
% 12.29/12.56 (b(s(s(s(z))), s(s(s(s(z)))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[1673, 36127, 11])).
% 12.29/12.56 tff(36129,plain,
% 12.29/12.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.29/12.56 inference(rewrite,[status(thm)],[])).
% 12.29/12.56 tff(36130,plain,
% 12.29/12.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.29/12.56 inference(quant_inst,[status(thm)],[])).
% 12.29/12.56 tff(36131,plain,
% 12.29/12.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 12.29/12.56 inference(modus_ponens,[status(thm)],[36130, 36129])).
% 12.29/12.56 tff(36132,plain,
% 12.29/12.56 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[36131, 194, 719, 4428, 33802])).
% 12.29/12.56 tff(36133,plain,
% 12.29/12.56 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.29/12.56 inference(unit_resolution,[status(thm)],[29527, 42, 8094, 36132])).
% 12.29/12.57 tff(36134,plain,
% 12.29/12.57 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[32524, 2741, 34300, 2112])).
% 12.29/12.57 tff(36135,plain,
% 12.29/12.57 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[11685, 42, 36134, 33868])).
% 12.29/12.57 tff(36136,plain,
% 12.29/12.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.29/12.57 inference(rewrite,[status(thm)],[])).
% 12.29/12.57 tff(36137,plain,
% 12.29/12.57 (((~b(s(z), s(s(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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.29/12.57 inference(rewrite,[status(thm)],[])).
% 12.29/12.57 tff(36138,plain,
% 12.29/12.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 12.29/12.57 inference(monotonicity,[status(thm)],[36137])).
% 12.29/12.57 tff(36139,plain,
% 12.29/12.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.29/12.57 inference(transitivity,[status(thm)],[36138, 36136])).
% 12.29/12.57 tff(36140,plain,
% 12.29/12.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.29/12.57 inference(quant_inst,[status(thm)],[])).
% 12.29/12.57 tff(36141,plain,
% 12.29/12.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 12.29/12.57 inference(modus_ponens,[status(thm)],[36140, 36139])).
% 12.29/12.57 tff(36142,plain,
% 12.29/12.57 ($false),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[36141, 391, 1234, 1759, 1684, 36135, 36133])).
% 12.29/12.57 tff(36143,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.57 tff(36144,plain,
% 12.29/12.57 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[36143, 36123, 1234, 36128, 36125, 36117, 11, 36115])).
% 12.29/12.57 tff(36145,plain,
% 12.29/12.57 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[8073, 36144, 33785])).
% 12.29/12.57 tff(36146,plain,
% 12.29/12.57 (b(s(s(s(s(s(s(z)))))), z)),
% 12.29/12.57 inference(modus_ponens,[status(thm)],[36145, 33854])).
% 12.29/12.57 tff(36147,plain,
% 12.29/12.57 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[15335, 36116, 2053, 36120])).
% 12.29/12.57 tff(36148,plain,
% 12.29/12.57 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[29931, 36147, 11])).
% 12.29/12.57 tff(36149,plain,
% 12.29/12.57 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[1095, 36148, 305])).
% 12.29/12.57 tff(36150,plain,
% 12.29/12.57 (b(s(s(s(s(z)))), s(s(s(z))))),
% 12.29/12.57 inference(modus_ponens,[status(thm)],[36149, 23220])).
% 12.29/12.57 tff(36151,plain,
% 12.29/12.57 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 12.29/12.57 inference(monotonicity,[status(thm)],[18544])).
% 12.29/12.57 tff(36152,plain,
% 12.29/12.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.57 inference(rewrite,[status(thm)],[])).
% 12.29/12.57 tff(36153,plain,
% 12.29/12.57 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.57 inference(rewrite,[status(thm)],[])).
% 12.29/12.57 tff(36154,plain,
% 12.29/12.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.29/12.57 inference(monotonicity,[status(thm)],[36153])).
% 12.29/12.57 tff(36155,plain,
% 12.29/12.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.29/12.57 inference(transitivity,[status(thm)],[36154, 36152])).
% 12.29/12.57 tff(36156,plain,
% 12.29/12.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 12.29/12.57 inference(quant_inst,[status(thm)],[])).
% 12.29/12.57 tff(36157,plain,
% 12.29/12.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 12.29/12.57 inference(modus_ponens,[status(thm)],[36156, 36155])).
% 12.29/12.57 tff(36158,plain,
% 12.29/12.57 (~b(s(z), s(s(s(z))))),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[36157, 391, 1234, 36123, 36128])).
% 12.29/12.57 tff(36159,plain,
% 12.29/12.57 (~b(s(z), s(s(s(elem!1))))),
% 12.29/12.57 inference(modus_ponens,[status(thm)],[36158, 36151])).
% 12.29/12.57 tff(36160,plain,
% 12.29/12.57 (r(s(z), s(s(s(elem!1))))),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[247, 36159])).
% 12.29/12.57 tff(36161,plain,
% 12.29/12.57 (~r(s(s(z)), z)),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[34768, 36160, 1234, 17618, 36120, 2053, 36150])).
% 12.29/12.57 tff(36162,plain,
% 12.29/12.57 (b(s(s(z)), z)),
% 12.29/12.57 inference(unit_resolution,[status(thm)],[1211, 36161])).
% 12.29/12.58 tff(36163,plain,
% 12.29/12.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.29/12.58 inference(rewrite,[status(thm)],[])).
% 12.29/12.58 tff(36164,plain,
% 12.29/12.58 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.29/12.58 inference(rewrite,[status(thm)],[])).
% 12.29/12.58 tff(36165,plain,
% 12.29/12.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 12.29/12.58 inference(monotonicity,[status(thm)],[36164])).
% 12.29/12.58 tff(36166,plain,
% 12.29/12.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.29/12.58 inference(transitivity,[status(thm)],[36165, 36163])).
% 12.29/12.58 tff(36167,plain,
% 12.29/12.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 12.29/12.58 inference(quant_inst,[status(thm)],[])).
% 12.29/12.58 tff(36168,plain,
% 12.29/12.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 12.29/12.58 inference(modus_ponens,[status(thm)],[36167, 36166])).
% 12.29/12.58 tff(36169,plain,
% 12.29/12.58 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[36168, 391, 36162, 1234, 664, 36146])).
% 12.29/12.58 tff(36170,plain,
% 12.29/12.58 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 36169])).
% 12.29/12.58 tff(36171,plain,
% 12.29/12.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.29/12.58 inference(rewrite,[status(thm)],[])).
% 12.29/12.58 tff(36172,plain,
% 12.29/12.58 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.29/12.58 inference(rewrite,[status(thm)],[])).
% 12.29/12.58 tff(36173,plain,
% 12.29/12.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 12.29/12.58 inference(monotonicity,[status(thm)],[36172])).
% 12.29/12.58 tff(36174,plain,
% 12.29/12.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.29/12.58 inference(transitivity,[status(thm)],[36173, 36171])).
% 12.29/12.58 tff(36175,plain,
% 12.29/12.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 12.29/12.58 inference(quant_inst,[status(thm)],[])).
% 12.29/12.58 tff(36176,plain,
% 12.29/12.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 12.29/12.58 inference(modus_ponens,[status(thm)],[36175, 36174])).
% 12.29/12.58 tff(36177,plain,
% 12.29/12.58 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[36176, 391, 1234, 664, 590, 36146])).
% 12.29/12.58 tff(36178,plain,
% 12.29/12.58 (r(s(s(s(s(s(s(z)))))), s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[14139, 36177])).
% 12.29/12.58 tff(36179,plain,
% 12.29/12.58 (~b(s(s(z)), s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[18720, 391, 36162, 1234, 664, 590])).
% 12.29/12.58 tff(36180,plain,
% 12.29/12.58 (r(s(s(z)), s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[3778, 36179])).
% 12.29/12.58 tff(36181,plain,
% 12.29/12.58 (~b(s(z), s(s(z)))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[18728, 391, 36162, 1234, 664, 590])).
% 12.29/12.58 tff(36182,plain,
% 12.29/12.58 (r(s(z), s(s(z)))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[1788, 36181])).
% 12.29/12.58 tff(36183,plain,
% 12.29/12.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 12.29/12.58 inference(rewrite,[status(thm)],[])).
% 12.29/12.58 tff(36184,plain,
% 12.29/12.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 12.29/12.58 inference(quant_inst,[status(thm)],[])).
% 12.29/12.58 tff(36185,plain,
% 12.29/12.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 12.29/12.58 inference(modus_ponens,[status(thm)],[36184, 36183])).
% 12.29/12.58 tff(36186,plain,
% 12.29/12.58 ($false),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[36185, 194, 36182, 36180, 36178, 36170])).
% 12.29/12.58 tff(36187,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.58 tff(36188,plain,
% 12.29/12.58 (~r(s(s(s(elem!1))), elem!1)),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[36187, 36109, 35025, 1234, 11, 2053, 21770, 29900, 930, 6124])).
% 12.29/12.58 tff(36189,plain,
% 12.29/12.58 (b(s(s(s(elem!1))), elem!1)),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[230, 36188, 9])).
% 12.29/12.58 tff(36190,plain,
% 12.29/12.58 (b(s(s(s(elem!1))), z)),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[28222, 36189, 11])).
% 12.29/12.58 tff(36191,plain,
% 12.29/12.58 (~b(s(z), s(s(s(elem!1))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[18555, 36190, 35025, 11, 36110])).
% 12.29/12.58 tff(36192,plain,
% 12.29/12.58 (r(s(z), s(s(s(elem!1))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[247, 36191])).
% 12.29/12.58 tff(36193,plain,
% 12.29/12.58 (r(s(z), s(s(s(z))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[23224, 36192, 11])).
% 12.29/12.58 tff(36194,plain,
% 12.29/12.58 (~r(z, s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[30267, 36193, 32118, 36112])).
% 12.29/12.58 tff(36195,plain,
% 12.29/12.58 (~r(z, s(elem!1))),
% 12.29/12.58 inference(modus_ponens,[status(thm)],[36194, 36111])).
% 12.29/12.58 tff(36196,plain,
% 12.29/12.58 (~r(s(s(elem!1)), elem!1)),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[34854, 36195, 1234, 35025, 17618, 36088, 36090, 36110])).
% 12.29/12.58 tff(36197,plain,
% 12.29/12.58 (b(s(s(elem!1)), elem!1)),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[872, 36196, 30072])).
% 12.29/12.58 tff(36198,plain,
% 12.29/12.58 (b(s(elem!1), elem!1)),
% 12.29/12.58 inference(modus_ponens,[status(thm)],[36109, 35791])).
% 12.29/12.58 tff(36199,plain,
% 12.29/12.58 (~b(s(s(elem!1)), s(elem!1))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[19494, 36197, 36090, 36198])).
% 12.29/12.58 tff(36200,plain,
% 12.29/12.58 (r(s(s(elem!1)), s(elem!1))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[1135, 36199, 30039])).
% 12.29/12.58 tff(36201,plain,
% 12.29/12.58 (b(s(elem!1), z)),
% 12.29/12.58 inference(modus_ponens,[status(thm)],[36109, 18406])).
% 12.29/12.58 tff(36202,plain,
% 12.29/12.58 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[3903, 36197, 36090, 36201, 36189])).
% 12.29/12.58 tff(36203,plain,
% 12.29/12.58 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[1356, 36202, 27044])).
% 12.29/12.58 tff(36204,plain,
% 12.29/12.58 ($false),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[24584, 36203, 36200, 23202, 6124, 30039, 36198, 30031, 36197])).
% 12.29/12.58 tff(36205,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), z)) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.58 tff(36206,plain,
% 12.29/12.58 ($false),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[36205, 36087, 11174, 33627, 36061, 4028, 1, 1234])).
% 12.29/12.58 tff(36207,plain,(b(s(s(s(elem!1))), s(z)) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | r(z, elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.58 tff(36208,plain,
% 12.29/12.58 (b(s(s(s(elem!1))), s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[36207, 36086, 1, 33633, 80, 3446])).
% 12.29/12.58 tff(36209,plain,
% 12.29/12.58 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[10090, 719, 36061, 59])).
% 12.29/12.58 tff(36210,plain,
% 12.29/12.58 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[15351, 36209, 35009])).
% 12.29/12.58 tff(36211,plain,
% 12.29/12.58 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[10108, 36208, 36086, 36210])).
% 12.29/12.58 tff(36212,plain,
% 12.29/12.58 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[27316, 36211, 33627])).
% 12.29/12.58 tff(36213,plain,
% 12.29/12.58 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[1095, 36212, 29900])).
% 12.29/12.58 tff(36214,plain,
% 12.29/12.58 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[1090, 36213, 33634, 35673])).
% 12.29/12.58 tff(36215,plain,
% 12.29/12.58 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[1370, 36214, 26982])).
% 12.29/12.58 tff(36216,plain,
% 12.29/12.58 (~b(elem!1, s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[34598, 36215, 36066, 973, 36086])).
% 12.29/12.58 tff(36217,plain,
% 12.29/12.58 (r(elem!1, s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[837, 36216, 36078])).
% 12.29/12.58 tff(36218,plain,
% 12.29/12.58 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 12.29/12.58 inference(transitivity,[status(thm)],[34420, 2206])).
% 12.29/12.58 tff(36219,plain,
% 12.29/12.58 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 12.29/12.58 inference(monotonicity,[status(thm)],[36218])).
% 12.29/12.58 tff(36220,plain,
% 12.29/12.58 (~(elem!1 = s(s(elem!1)))),
% 12.29/12.58 inference(modus_ponens,[status(thm)],[215, 36219])).
% 12.29/12.58 tff(36221,plain,
% 12.29/12.58 (b(z, elem!1) <=> b(z, z)),
% 12.29/12.58 inference(monotonicity,[status(thm)],[33627])).
% 12.29/12.58 tff(36222,plain,
% 12.29/12.58 (b(z, z) <=> b(z, elem!1)),
% 12.29/12.58 inference(symmetry,[status(thm)],[36221])).
% 12.29/12.58 tff(36223,plain,
% 12.29/12.58 ((~b(z, z)) <=> (~b(z, elem!1))),
% 12.29/12.58 inference(monotonicity,[status(thm)],[36222])).
% 12.29/12.58 tff(36224,plain,
% 12.29/12.58 (~b(z, elem!1)),
% 12.29/12.58 inference(modus_ponens,[status(thm)],[30135, 36223])).
% 12.29/12.58 tff(36225,plain,
% 12.29/12.58 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 12.29/12.58 inference(transitivity,[status(thm)],[34942, 1021])).
% 12.29/12.58 tff(36226,plain,
% 12.29/12.58 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 12.29/12.58 inference(monotonicity,[status(thm)],[36225])).
% 12.29/12.58 tff(36227,plain,
% 12.29/12.58 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 12.29/12.58 inference(modus_ponens,[status(thm)],[714, 36226])).
% 12.29/12.58 tff(36228,plain,
% 12.29/12.58 (~b(s(z), elem!1)),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[18559, 36217, 225, 36208, 36086, 36227, 35511, 973, 32322, 35309, 36215, 10, 36224, 36220, 33633, 36216])).
% 12.29/12.58 tff(36229,plain,
% 12.29/12.58 ($false),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[17659, 36228, 36217, 3446, 10, 36208, 34897, 36086])).
% 12.29/12.58 tff(36230,plain,((~r(z, s(s(s(s(z)))))) | b(s(s(s(s(z)))), z) | b(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.58 tff(36231,plain,
% 12.29/12.58 (~r(z, s(s(s(s(z)))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[36230, 36065, 10, 225, 3446, 1, 80])).
% 12.29/12.58 tff(36232,plain,
% 12.29/12.58 (b(z, s(s(s(s(z)))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[800, 36231])).
% 12.29/12.58 tff(36233,plain,
% 12.29/12.58 (b(elem!1, s(s(s(s(elem!1)))))),
% 12.29/12.58 inference(modus_ponens,[status(thm)],[36232, 36071])).
% 12.29/12.58 tff(36234,plain,
% 12.29/12.58 (~r(s(z), z)),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[15518, 1216, 36061, 15510])).
% 12.29/12.58 tff(36235,plain,
% 12.29/12.58 (~r(s(z), elem!1)),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[5433, 36234, 34898])).
% 12.29/12.58 tff(36236,plain,
% 12.29/12.58 (b(s(z), elem!1)),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[632, 36235, 34897])).
% 12.29/12.58 tff(36237,plain,
% 12.29/12.58 ($false),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[32588, 36087, 11174, 80, 36061, 1, 1216])).
% 12.29/12.58 tff(36238,plain,(b(s(s(s(elem!1))), s(z)) | r(z, elem!1) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 12.29/12.58 tff(36239,plain,
% 12.29/12.58 (b(s(s(s(elem!1))), s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[36238, 1216, 1, 80, 3446])).
% 12.29/12.58 tff(36240,plain,
% 12.29/12.58 (~b(elem!1, s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[20387, 36239, 900, 36236])).
% 12.29/12.58 tff(36241,plain,
% 12.29/12.58 (r(elem!1, s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[837, 36240, 36078])).
% 12.29/12.58 tff(36242,plain,
% 12.29/12.58 (~r(z, s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[10620, 1216, 36061])).
% 12.29/12.58 tff(36243,plain,
% 12.29/12.58 (b(z, s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[678, 36242])).
% 12.29/12.58 tff(36244,plain,
% 12.29/12.58 (~b(s(z), s(s(s(elem!1))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[18555, 36236, 33627, 380, 36243])).
% 12.29/12.58 tff(36245,plain,
% 12.29/12.58 (r(s(z), s(s(s(elem!1))))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[247, 36244])).
% 12.29/12.58 tff(36246,plain,
% 12.29/12.58 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[18031, 36241, 410, 36245])).
% 12.29/12.58 tff(36247,plain,
% 12.29/12.58 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[1370, 36246, 26982])).
% 12.29/12.58 tff(36248,plain,
% 12.29/12.58 (~b(elem!1, s(s(elem!1)))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[1467, 36247, 900, 973])).
% 12.29/12.58 tff(36249,plain,
% 12.29/12.58 (r(elem!1, s(s(elem!1)))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[1307, 36248, 36220])).
% 12.29/12.58 tff(36250,plain,
% 12.29/12.58 (~b(s(s(elem!1)), s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[18333, 36247, 974, 36236, 36239])).
% 12.29/12.58 tff(36251,plain,
% 12.29/12.58 (r(s(s(elem!1)), s(z))),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[362, 36250])).
% 12.29/12.58 tff(36252,plain,
% 12.29/12.58 ($false),
% 12.29/12.58 inference(unit_resolution,[status(thm)],[6408, 36251, 36249, 1216, 36241])).
% 12.29/12.58 tff(36253,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1) | b(s(s(s(s(z)))), z) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.59 tff(36254,plain,
% 12.29/12.59 (~r(s(z), s(s(s(s(z)))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[36253, 36233, 36066, 36065, 33634, 1, 80, 3446, 380, 34920])).
% 12.29/12.59 tff(36255,plain,
% 12.29/12.59 (b(s(z), s(s(s(s(z)))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1230, 36254])).
% 12.29/12.59 tff(36256,plain,
% 12.29/12.59 (b(s(s(s(elem!1))), s(z))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[36207, 36255, 1, 33633, 80, 3446])).
% 12.29/12.59 tff(36257,plain,
% 12.29/12.59 ((~r(s(s(z)), z)) <=> (~r(s(s(elem!1)), elem!1))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[35306])).
% 12.29/12.59 tff(36258,plain,
% 12.29/12.59 (~r(s(s(elem!1)), elem!1)),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[36062, 36257])).
% 12.29/12.59 tff(36259,plain,
% 12.29/12.59 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[17288, 35976, 1686, 1234, 1235])).
% 12.29/12.59 tff(36260,plain,
% 12.29/12.59 (r(s(s(s(s(z)))), s(s(z)))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1714, 36259])).
% 12.29/12.59 tff(36261,plain,
% 12.29/12.59 (~b(z, s(s(elem!1)))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[6210, 35976, 380, 35318, 1526])).
% 12.29/12.59 tff(36262,plain,
% 12.29/12.59 (r(z, s(s(elem!1)))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[324, 36261])).
% 12.29/12.59 tff(36263,plain,
% 12.29/12.59 (r(z, s(s(z)))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[30084, 36262, 11])).
% 12.29/12.59 tff(36264,plain,
% 12.29/12.59 (~r(s(s(z)), s(z))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[18433, 36263, 2053, 36260])).
% 12.29/12.59 tff(36265,plain,
% 12.29/12.59 (~b(elem!1, s(s(z)))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[3379, 36261, 11])).
% 12.29/12.59 tff(36266,plain,
% 12.29/12.59 (~b(elem!1, s(z))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[20387, 35881, 900, 1526])).
% 12.29/12.59 tff(36267,plain,
% 12.29/12.59 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[30357, 36266, 888, 225, 1234, 30374, 30072, 1492, 10, 30363, 36265, 4028])).
% 12.29/12.59 tff(36268,plain,
% 12.29/12.59 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1370, 36267, 297])).
% 12.29/12.59 tff(36269,plain,
% 12.29/12.59 (~b(s(s(z)), s(z))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[30177, 36263, 11, 2053, 59, 34445, 310, 1234, 36268])).
% 12.29/12.59 tff(36270,plain,
% 12.29/12.59 ($false),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[3778, 36269, 36264])).
% 12.29/12.59 tff(36271,plain,(r(s(z), elem!1) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(elem!1)), elem!1) | r(s(s(s(elem!1))), elem!1) | b(z, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.59 tff(36272,plain,
% 12.29/12.59 (r(s(z), elem!1)),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[36271, 36255, 36061, 33627, 26982, 36258, 225, 10, 33633, 36066, 36256, 380, 36232, 36064])).
% 12.29/12.59 tff(36273,plain,
% 12.29/12.59 (~r(elem!1, s(z))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[17656, 36272, 33627, 3446, 59, 36256, 36255, 930, 35309])).
% 12.29/12.59 tff(36274,plain,
% 12.29/12.59 (b(elem!1, s(z))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[837, 36273, 36078])).
% 12.29/12.59 tff(36275,plain,
% 12.29/12.59 (b(s(z), elem!1)),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[8907, 36273, 80, 3446, 10, 36256])).
% 12.29/12.59 tff(36276,plain,
% 12.29/12.59 ($false),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[20387, 36275, 36274, 36066, 36256])).
% 12.29/12.59 tff(36277,plain,(r(s(s(z)), z) | r(z, elem!1) | b(s(s(s(s(z)))), z) | b(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), z)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.59 tff(36278,plain,
% 12.29/12.59 ($false),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[36277, 36063, 378, 3446, 10, 80, 36062, 1])).
% 12.29/12.59 tff(36279,plain,(r(s(s(s(elem!1))), z) | b(s(s(s(s(z)))), z) | b(z, s(s(s(elem!1)))) | r(z, elem!1) | r(s(s(z)), z) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.59 tff(36280,plain,
% 12.29/12.59 (r(s(s(s(elem!1))), z)),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[36279, 36062, 10, 80, 3446, 1])).
% 12.29/12.59 tff(36281,plain,
% 12.29/12.59 (~b(s(z), s(s(s(s(z)))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[36207, 11173, 1, 4028, 80, 3446])).
% 12.29/12.59 tff(36282,plain,
% 12.29/12.59 (~r(s(z), s(s(s(s(z)))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[36238, 11173, 1, 80, 3446])).
% 12.29/12.59 tff(36283,plain,
% 12.29/12.59 ($false),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1230, 36282, 36281])).
% 12.29/12.59 tff(36284,plain,(b(s(s(s(elem!1))), s(z)) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1) | b(s(s(s(s(z)))), z) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.59 tff(36285,plain,
% 12.29/12.59 (b(s(s(s(elem!1))), s(z))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[36284, 33633, 80, 3446, 1])).
% 12.29/12.59 tff(36286,plain,
% 12.29/12.59 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[15335, 36280, 36061, 59])).
% 12.29/12.59 tff(36287,plain,
% 12.29/12.59 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[29931, 36286, 33627])).
% 12.29/12.59 tff(36288,plain,
% 12.29/12.59 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1095, 36287, 29900])).
% 12.29/12.59 tff(36289,plain,
% 12.29/12.59 (b(s(s(s(s(z)))), s(s(s(z))))),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[36288, 34921])).
% 12.29/12.59 tff(36290,plain,
% 12.29/12.59 (~r(s(z), z)),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[15518, 1216, 36061, 34920])).
% 12.29/12.59 tff(36291,plain,
% 12.29/12.59 (b(s(z), z)),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[180, 36290])).
% 12.29/12.59 tff(36292,plain,
% 12.29/12.59 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[31283, 3557, 2053, 719])).
% 12.29/12.59 tff(36293,plain,
% 12.29/12.59 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[18886, 3557, 2053, 184, 664, 3843, 590, 719])).
% 12.29/12.59 tff(36294,plain,
% 12.29/12.59 ($false),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[3652, 36293, 36292])).
% 12.29/12.59 tff(36295,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.29/12.59 tff(36296,plain,
% 12.29/12.59 (~r(s(s(z)), z)),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[36295, 719, 36061, 59, 35309, 36243, 36291])).
% 12.29/12.59 tff(36297,plain,
% 12.29/12.59 (b(s(s(z)), z)),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1211, 36296])).
% 12.29/12.59 tff(36298,plain,
% 12.29/12.59 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[34415])).
% 12.29/12.59 tff(36299,plain,
% 12.29/12.59 (b(s(s(elem!1)), elem!1)),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[36297, 35477])).
% 12.29/12.59 tff(36300,plain,
% 12.29/12.59 (r(s(s(s(elem!1))), elem!1)),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[36230, 36299, 10, 719, 3446, 1, 80])).
% 12.29/12.59 tff(36301,plain,
% 12.29/12.59 (r(s(s(s(elem!1))), z)),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[406, 36300, 33627])).
% 12.29/12.59 tff(36302,plain,
% 12.29/12.59 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[34414])).
% 12.29/12.59 tff(36303,plain,
% 12.29/12.59 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 12.29/12.59 inference(symmetry,[status(thm)],[36302])).
% 12.29/12.59 tff(36304,plain,
% 12.29/12.59 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[15335, 36301, 36061, 59])).
% 12.29/12.59 tff(36305,plain,
% 12.29/12.59 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[29931, 36304, 33627])).
% 12.29/12.59 tff(36306,plain,
% 12.29/12.59 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1095, 36305, 29900])).
% 12.29/12.59 tff(36307,plain,
% 12.29/12.59 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[27316, 36306, 33627])).
% 12.29/12.59 tff(36308,plain,
% 12.29/12.59 (~r(s(z), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[20513, 36307, 36061, 36285, 36301, 36210, 35309, 719, 59, 1216])).
% 12.29/12.59 tff(36309,plain,
% 12.29/12.59 (b(s(z), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[247, 36308])).
% 12.29/12.59 tff(36310,plain,
% 12.29/12.59 (b(s(elem!1), s(s(s(elem!1))))),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[36309, 36303])).
% 12.29/12.59 tff(36311,plain,
% 12.29/12.59 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[34414])).
% 12.29/12.59 tff(36312,plain,
% 12.29/12.59 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 12.29/12.59 inference(symmetry,[status(thm)],[36311])).
% 12.29/12.59 tff(36313,plain,
% 12.29/12.59 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[36312])).
% 12.29/12.59 tff(36314,plain,
% 12.29/12.59 (~(s(s(elem!1)) = s(elem!1))),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[357, 36313])).
% 12.29/12.59 tff(36315,plain,
% 12.29/12.59 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[34414])).
% 12.29/12.59 tff(36316,plain,
% 12.29/12.59 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 12.29/12.59 inference(symmetry,[status(thm)],[36315])).
% 12.29/12.59 tff(36317,plain,
% 12.29/12.59 (b(s(s(s(elem!1))), s(elem!1))),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[36285, 36316])).
% 12.29/12.59 tff(36318,plain,
% 12.29/12.59 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[34414])).
% 12.29/12.59 tff(36319,plain,
% 12.29/12.59 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.29/12.59 inference(symmetry,[status(thm)],[36318])).
% 12.29/12.59 tff(36320,plain,
% 12.29/12.59 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[34427])).
% 12.29/12.59 tff(36321,plain,
% 12.29/12.59 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 12.29/12.59 inference(symmetry,[status(thm)],[36320])).
% 12.29/12.59 tff(36322,plain,
% 12.29/12.59 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.29/12.59 inference(transitivity,[status(thm)],[36321, 36319])).
% 12.29/12.59 tff(36323,plain,
% 12.29/12.59 (~b(s(s(s(s(z)))), s(z))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[20495, 36307, 36291, 36243, 36285])).
% 12.29/12.59 tff(36324,plain,
% 12.29/12.59 (r(s(s(s(s(z)))), s(z))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[749, 36323])).
% 12.29/12.59 tff(36325,plain,
% 12.29/12.59 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[36324, 36322])).
% 12.29/12.59 tff(36326,plain,
% 12.29/12.59 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1144, 36325, 36317, 36314, 36306, 36227, 36310])).
% 12.29/12.59 tff(36327,plain,
% 12.29/12.59 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1356, 36326, 27044])).
% 12.29/12.59 tff(36328,plain,
% 12.29/12.59 (~r(z, s(s(elem!1)))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1450, 36327, 36301, 59])).
% 12.29/12.59 tff(36329,plain,
% 12.29/12.59 (b(z, s(s(elem!1)))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[324, 36328])).
% 12.29/12.59 tff(36330,plain,
% 12.29/12.59 (b(z, s(s(z)))),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[36329, 36298])).
% 12.29/12.59 tff(36331,plain,
% 12.29/12.59 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[34426])).
% 12.29/12.59 tff(36332,plain,
% 12.29/12.59 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 12.29/12.59 inference(transitivity,[status(thm)],[36331, 8583])).
% 12.29/12.59 tff(36333,plain,
% 12.29/12.59 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 12.29/12.59 inference(symmetry,[status(thm)],[36332])).
% 12.29/12.59 tff(36334,plain,
% 12.29/12.59 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[36333])).
% 12.29/12.59 tff(36335,plain,
% 12.29/12.59 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[8593, 36334])).
% 12.29/12.59 tff(36336,plain,
% 12.29/12.59 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[34917])).
% 12.29/12.59 tff(36337,plain,
% 12.29/12.59 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 12.29/12.59 inference(monotonicity,[status(thm)],[36336])).
% 12.29/12.59 tff(36338,plain,
% 12.29/12.59 (b(s(s(s(z))), s(s(s(s(z)))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[1673, 36210, 33627])).
% 12.29/12.59 tff(36339,plain,
% 12.29/12.59 (b(s(s(s(z))), s(z))),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[36285, 35173])).
% 12.29/12.59 tff(36340,plain,
% 12.29/12.59 (b(s(s(s(s(z)))), s(s(s(z))))),
% 12.29/12.59 inference(modus_ponens,[status(thm)],[36306, 34921])).
% 12.29/12.59 tff(36341,plain,
% 12.29/12.59 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[31595, 1216, 36061])).
% 12.29/12.59 tff(36342,plain,
% 12.29/12.59 (b(s(s(z)), s(s(s(s(z)))))),
% 12.29/12.59 inference(unit_resolution,[status(thm)],[3652, 36341])).
% 12.29/12.59 tff(36343,plain,
% 12.29/12.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 12.29/12.60 inference(rewrite,[status(thm)],[])).
% 12.29/12.60 tff(36344,plain,
% 12.29/12.60 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 12.29/12.60 inference(rewrite,[status(thm)],[])).
% 12.29/12.60 tff(36345,plain,
% 12.29/12.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 12.29/12.60 inference(monotonicity,[status(thm)],[36344])).
% 12.29/12.60 tff(36346,plain,
% 12.29/12.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 12.29/12.60 inference(transitivity,[status(thm)],[36345, 36343])).
% 12.29/12.60 tff(36347,plain,
% 12.29/12.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 12.39/12.60 inference(quant_inst,[status(thm)],[])).
% 12.39/12.60 tff(36348,plain,
% 12.39/12.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 12.39/12.60 inference(modus_ponens,[status(thm)],[36347, 36346])).
% 12.39/12.60 tff(36349,plain,
% 12.39/12.60 (~b(s(s(z)), s(s(s(z))))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[36348, 391, 36342, 36340, 36339, 36338])).
% 12.39/12.60 tff(36350,plain,
% 12.39/12.60 (~b(s(s(z)), s(s(s(elem!1))))),
% 12.39/12.60 inference(modus_ponens,[status(thm)],[36349, 36337])).
% 12.39/12.60 tff(36351,plain,
% 12.39/12.60 (r(s(s(z)), s(s(s(elem!1))))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[11041, 36350])).
% 12.39/12.60 tff(36352,plain,
% 12.39/12.60 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[20563, 36351, 59, 36243, 36301, 36297, 36330])).
% 12.39/12.60 tff(36353,plain,
% 12.39/12.60 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[20797, 36352, 36335])).
% 12.39/12.60 tff(36354,plain,
% 12.39/12.60 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[20575, 36353, 36285, 36307, 36309])).
% 12.39/12.60 tff(36355,plain,
% 12.39/12.60 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[8761, 36354])).
% 12.39/12.60 tff(36356,plain,
% 12.39/12.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 12.39/12.60 inference(rewrite,[status(thm)],[])).
% 12.39/12.60 tff(36357,plain,
% 12.39/12.60 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 12.39/12.60 inference(rewrite,[status(thm)],[])).
% 12.39/12.60 tff(36358,plain,
% 12.39/12.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 12.39/12.60 inference(monotonicity,[status(thm)],[36357])).
% 12.39/12.60 tff(36359,plain,
% 12.39/12.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 12.39/12.60 inference(transitivity,[status(thm)],[36358, 36356])).
% 12.39/12.60 tff(36360,plain,
% 12.39/12.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 12.39/12.60 inference(quant_inst,[status(thm)],[])).
% 12.39/12.60 tff(36361,plain,
% 12.39/12.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 12.39/12.60 inference(modus_ponens,[status(thm)],[36360, 36359])).
% 12.39/12.60 tff(36362,plain,
% 12.39/12.60 ($false),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[36361, 194, 184, 2053, 16500, 15748])).
% 12.39/12.60 tff(36363,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.60 tff(36364,plain,
% 12.39/12.60 (~r(s(s(s(s(s(z))))), z)),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[36363, 36355, 36061, 59])).
% 12.39/12.60 tff(36365,plain,
% 12.39/12.60 (b(s(s(s(s(s(z))))), z)),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[16530, 36364])).
% 12.39/12.60 tff(36366,plain,
% 12.39/12.60 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[18792, 36365, 36243, 36330, 36297])).
% 12.39/12.60 tff(36367,plain,
% 12.39/12.60 (r(s(s(s(s(s(z))))), s(s(z)))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[20778, 36366])).
% 12.39/12.60 tff(36368,plain,
% 12.39/12.60 (~r(s(elem!1), elem!1)),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[29755, 36290, 33627])).
% 12.39/12.60 tff(36369,plain,
% 12.39/12.60 (b(s(elem!1), elem!1)),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[2168, 36368, 426])).
% 12.39/12.60 tff(36370,plain,
% 12.39/12.60 (~r(s(z), elem!1)),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[5433, 36290, 34898])).
% 12.39/12.60 tff(36371,plain,
% 12.39/12.60 (b(s(z), elem!1)),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[632, 36370, 34897])).
% 12.39/12.60 tff(36372,plain,
% 12.39/12.60 (~r(elem!1, s(z))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[11195, 36072, 36061, 1216])).
% 12.39/12.60 tff(36373,plain,
% 12.39/12.60 (~r(z, s(elem!1))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[8832, 36372, 33627])).
% 12.39/12.60 tff(36374,plain,
% 12.39/12.60 (~r(elem!1, s(elem!1))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[2288, 36373, 33627])).
% 12.39/12.60 tff(36375,plain,
% 12.39/12.60 (b(elem!1, s(elem!1))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[443, 36374, 427])).
% 12.39/12.60 tff(36376,plain,
% 12.39/12.60 (~b(s(s(z)), s(z))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[32112, 36375, 33627, 36061, 59, 36371, 26982, 34422, 36342, 36369, 36243, 36291])).
% 12.39/12.60 tff(36377,plain,
% 12.39/12.60 (r(s(s(z)), s(z))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[3778, 36376])).
% 12.39/12.60 tff(36378,plain,
% 12.39/12.60 (~b(s(z), s(s(z)))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[10666, 391, 36297, 36243, 36291])).
% 12.39/12.60 tff(36379,plain,
% 12.39/12.60 (r(s(z), s(s(z)))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[1788, 36378])).
% 12.39/12.60 tff(36380,plain,
% 12.39/12.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 12.39/12.60 inference(rewrite,[status(thm)],[])).
% 12.39/12.60 tff(36381,plain,
% 12.39/12.60 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 12.39/12.60 inference(rewrite,[status(thm)],[])).
% 12.39/12.60 tff(36382,plain,
% 12.39/12.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 12.39/12.60 inference(monotonicity,[status(thm)],[36381])).
% 12.39/12.60 tff(36383,plain,
% 12.39/12.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 12.39/12.60 inference(transitivity,[status(thm)],[36382, 36380])).
% 12.39/12.60 tff(36384,plain,
% 12.39/12.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 12.39/12.60 inference(quant_inst,[status(thm)],[])).
% 12.39/12.60 tff(36385,plain,
% 12.39/12.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 12.39/12.60 inference(modus_ponens,[status(thm)],[36384, 36383])).
% 12.39/12.60 tff(36386,plain,
% 12.39/12.60 (~r(s(s(s(s(s(z))))), s(z))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[36385, 194, 36379, 36377, 36367])).
% 12.39/12.60 tff(36387,plain,
% 12.39/12.60 (b(s(s(s(s(s(z))))), s(z))),
% 12.39/12.60 inference(unit_resolution,[status(thm)],[20789, 36386])).
% 12.39/12.60 tff(36388,plain,
% 12.39/12.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 12.39/12.60 inference(rewrite,[status(thm)],[])).
% 12.39/12.60 tff(36389,plain,
% 12.39/12.60 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 12.39/12.60 inference(rewrite,[status(thm)],[])).
% 12.39/12.60 tff(36390,plain,
% 12.39/12.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 12.39/12.60 inference(monotonicity,[status(thm)],[36389])).
% 12.39/12.60 tff(36391,plain,
% 12.39/12.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 12.39/12.61 inference(transitivity,[status(thm)],[36390, 36388])).
% 12.39/12.61 tff(36392,plain,
% 12.39/12.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 12.39/12.61 inference(quant_inst,[status(thm)],[])).
% 12.39/12.61 tff(36393,plain,
% 12.39/12.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36392, 36391])).
% 12.39/12.61 tff(36394,plain,
% 12.39/12.61 ($false),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36393, 391, 36243, 36291, 36365, 36387])).
% 12.39/12.61 tff(36395,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | b(z, s(s(s(elem!1)))) | b(s(s(s(s(z)))), z) | (elem!1 = s(s(s(elem!1)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.61 tff(36396,plain,
% 12.39/12.61 (~r(z, s(s(s(s(z)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36395, 1216, 10, 3446, 1, 80])).
% 12.39/12.61 tff(36397,plain,
% 12.39/12.61 (b(z, s(s(s(s(z)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[800, 36396])).
% 12.39/12.61 tff(36398,plain,
% 12.39/12.61 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[31721, 36064, 36397, 36342])).
% 12.39/12.61 tff(36399,plain,
% 12.39/12.61 (r(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[1714, 36398])).
% 12.39/12.61 tff(36400,plain,
% 12.39/12.61 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[32252, 36399, 36061, 1216, 59, 36397, 36291])).
% 12.39/12.61 tff(36401,plain,
% 12.39/12.61 ($false),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36400, 36289])).
% 12.39/12.61 tff(36402,plain,(r(s(s(z)), z) | b(z, s(s(s(elem!1)))) | r(z, elem!1) | b(s(s(s(s(z)))), z) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.61 tff(36403,plain,
% 12.39/12.61 (r(s(s(z)), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36402, 1216, 80, 3446, 1, 10])).
% 12.39/12.61 tff(36404,plain,
% 12.39/12.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[30977, 36403, 36061, 34920])).
% 12.39/12.61 tff(36405,plain,
% 12.39/12.61 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[15345, 36403, 36061, 36285, 35309, 36291, 36243])).
% 12.39/12.61 tff(36406,plain,
% 12.39/12.61 ($false),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[1714, 36405, 36404])).
% 12.39/12.61 tff(36407,plain,((~r(s(z), s(s(s(s(z)))))) | r(z, elem!1) | b(s(s(s(s(z)))), z) | (elem!1 = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.61 tff(36408,plain,
% 12.39/12.61 (~r(s(z), s(s(s(s(z)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36407, 10, 3446, 1, 80])).
% 12.39/12.61 tff(36409,plain,
% 12.39/12.61 (b(s(z), s(s(s(s(z)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[1230, 36408])).
% 12.39/12.61 tff(36410,plain,
% 12.39/12.61 (s(s(elem!1)) = s(s(z))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[8823])).
% 12.39/12.61 tff(36411,plain,
% 12.39/12.61 (s(s(s(elem!1))) = s(s(s(z)))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36410])).
% 12.39/12.61 tff(36412,plain,
% 12.39/12.61 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36411])).
% 12.39/12.61 tff(36413,plain,
% 12.39/12.61 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.61 inference(symmetry,[status(thm)],[36412])).
% 12.39/12.61 tff(36414,plain,
% 12.39/12.61 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36411])).
% 12.39/12.61 tff(36415,plain,
% 12.39/12.61 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36411, 36414])).
% 12.39/12.61 tff(36416,plain,
% 12.39/12.61 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.61 inference(transitivity,[status(thm)],[36415, 36413])).
% 12.39/12.61 tff(36417,plain,
% 12.39/12.61 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36414])).
% 12.39/12.61 tff(36418,plain,
% 12.39/12.61 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.39/12.61 inference(symmetry,[status(thm)],[36417])).
% 12.39/12.61 tff(36419,plain,
% 12.39/12.61 (s(s(s(z))) = s(s(s(elem!1)))),
% 12.39/12.61 inference(symmetry,[status(thm)],[36411])).
% 12.39/12.61 tff(36420,plain,
% 12.39/12.61 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36419])).
% 12.39/12.61 tff(36421,plain,
% 12.39/12.61 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.39/12.61 inference(transitivity,[status(thm)],[36420, 36418])).
% 12.39/12.61 tff(36422,plain,
% 12.39/12.61 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36421])).
% 12.39/12.61 tff(36423,plain,
% 12.39/12.61 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36419])).
% 12.39/12.61 tff(36424,plain,
% 12.39/12.61 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 12.39/12.61 inference(symmetry,[status(thm)],[36423])).
% 12.39/12.61 tff(36425,plain,
% 12.39/12.61 (r(z, s(s(s(z))))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[59, 36424])).
% 12.39/12.61 tff(36426,plain,
% 12.39/12.61 (r(s(s(s(elem!1))), elem!1)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[230, 1440, 168])).
% 12.39/12.61 tff(36427,plain,
% 12.39/12.61 (r(s(s(s(elem!1))), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[406, 36426, 8816])).
% 12.39/12.61 tff(36428,plain,
% 12.39/12.61 (r(s(s(s(z))), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[4409, 36427, 8816])).
% 12.39/12.61 tff(36429,plain,
% 12.39/12.61 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[32189, 194, 2053, 36428, 36425])).
% 12.39/12.61 tff(36430,plain,
% 12.39/12.61 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36429, 36422])).
% 12.39/12.61 tff(36431,plain,
% 12.39/12.61 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[1164, 36430, 8885])).
% 12.39/12.61 tff(36432,plain,
% 12.39/12.61 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36431, 36416])).
% 12.39/12.61 tff(36433,plain,
% 12.39/12.61 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36414, 36411])).
% 12.39/12.61 tff(36434,plain,
% 12.39/12.61 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.39/12.61 inference(symmetry,[status(thm)],[36433])).
% 12.39/12.61 tff(36435,plain,
% 12.39/12.61 ((~r(s(s(s(s(z)))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36434])).
% 12.39/12.61 tff(36436,plain,
% 12.39/12.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 12.39/12.61 inference(rewrite,[status(thm)],[])).
% 12.39/12.61 tff(36437,plain,
% 12.39/12.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 12.39/12.61 inference(quant_inst,[status(thm)],[])).
% 12.39/12.61 tff(36438,plain,
% 12.39/12.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36437, 36436])).
% 12.39/12.61 tff(36439,plain,
% 12.39/12.61 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36438, 194, 2053, 36428, 36425])).
% 12.39/12.61 tff(36440,plain,
% 12.39/12.61 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36439, 36435])).
% 12.39/12.61 tff(36441,plain,
% 12.39/12.61 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[1095, 36440, 8884])).
% 12.39/12.61 tff(36442,plain,
% 12.39/12.61 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[27316, 36441, 8816])).
% 12.39/12.61 tff(36443,plain,
% 12.39/12.61 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[10108, 36442, 1234, 1526])).
% 12.39/12.61 tff(36444,plain,
% 12.39/12.61 ($false),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36443, 36432])).
% 12.39/12.61 tff(36445,plain,(r(z, elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), z)) | b(s(s(s(elem!1))), elem!1) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.61 tff(36446,plain,
% 12.39/12.61 (b(s(s(s(elem!1))), elem!1)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36445, 36409, 80, 36061, 10, 36285])).
% 12.39/12.61 tff(36447,plain,
% 12.39/12.61 (b(s(s(s(elem!1))), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[28222, 36446, 33627])).
% 12.39/12.61 tff(36448,plain,
% 12.39/12.61 (r(s(s(s(elem!1))), elem!1)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36277, 36062, 3446, 10, 80, 36447, 1])).
% 12.39/12.61 tff(36449,plain,
% 12.39/12.61 (~r(s(z), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[3969, 36280, 36061, 59, 35309])).
% 12.39/12.61 tff(36450,plain,
% 12.39/12.61 (b(s(z), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[180, 36449])).
% 12.39/12.61 tff(36451,plain,
% 12.39/12.61 (~b(z, s(z))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36187, 36450, 33627, 36061, 33634, 36409, 35009, 29900, 930, 36448])).
% 12.39/12.61 tff(36452,plain,
% 12.39/12.61 (r(z, s(z))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[678, 36451])).
% 12.39/12.61 tff(36453,plain,
% 12.39/12.61 (~r(s(z), s(s(s(elem!1))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[5980, 36452, 59, 36280])).
% 12.39/12.61 tff(36454,plain,
% 12.39/12.61 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[27316, 36288, 33627])).
% 12.39/12.61 tff(36455,plain,
% 12.39/12.61 (~b(s(z), s(s(s(elem!1))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[20817, 36454, 36409, 36285])).
% 12.39/12.61 tff(36456,plain,
% 12.39/12.61 ($false),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[247, 36455, 36453])).
% 12.39/12.61 tff(36457,plain,(r(s(s(z)), z) | b(s(s(s(s(z)))), z) | b(z, s(s(s(elem!1)))) | r(z, elem!1) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.61 tff(36458,plain,
% 12.39/12.61 (r(s(s(z)), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36457, 10, 3446, 80, 1])).
% 12.39/12.61 tff(36459,plain,
% 12.39/12.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[30977, 36458, 36061, 34920])).
% 12.39/12.61 tff(36460,plain,
% 12.39/12.61 (b(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[1714, 36459])).
% 12.39/12.61 tff(36461,plain,
% 12.39/12.61 (~b(s(s(z)), s(z))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[30109, 36458, 36061, 36409, 59])).
% 12.39/12.61 tff(36462,plain,
% 12.39/12.61 (r(s(s(z)), s(z))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[3778, 36461])).
% 12.39/12.61 tff(36463,plain,
% 12.39/12.61 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 12.39/12.61 inference(monotonicity,[status(thm)],[33627])).
% 12.39/12.61 tff(36464,plain,
% 12.39/12.61 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 12.39/12.61 inference(symmetry,[status(thm)],[36463])).
% 12.39/12.61 tff(36465,plain,
% 12.39/12.61 (r(s(s(z)), elem!1)),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36458, 36464])).
% 12.39/12.61 tff(36466,plain,
% 12.39/12.61 (~r(s(z), elem!1)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[35189, 36465, 33634, 36462])).
% 12.39/12.61 tff(36467,plain,
% 12.39/12.61 (b(s(z), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[3205, 36466, 33627])).
% 12.39/12.61 tff(36468,plain,
% 12.39/12.61 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[14746, 36458, 36061, 59])).
% 12.39/12.61 tff(36469,plain,
% 12.39/12.61 (b(s(s(z)), s(s(s(s(z)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[3652, 36468])).
% 12.39/12.61 tff(36470,plain,
% 12.39/12.61 (~b(s(z), s(s(z)))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[6275, 36460, 36409, 36469])).
% 12.39/12.61 tff(36471,plain,
% 12.39/12.61 (r(s(z), s(s(z)))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[1788, 36470])).
% 12.39/12.61 tff(36472,plain,
% 12.39/12.61 (r(s(s(elem!1)), z)),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36458, 35305])).
% 12.39/12.61 tff(36473,plain,
% 12.39/12.61 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[34962])).
% 12.39/12.61 tff(36474,plain,
% 12.39/12.61 (r(s(s(elem!1)), s(z))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36462, 36473])).
% 12.39/12.61 tff(36475,plain,
% 12.39/12.61 (~r(z, s(z))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[9045, 36474, 36472, 36471])).
% 12.39/12.61 tff(36476,plain,
% 12.39/12.61 (b(z, s(z))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[678, 36475])).
% 12.39/12.61 tff(36477,plain,
% 12.39/12.61 ($false),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[15345, 36476, 36467, 36061, 36285, 35309, 36458, 36460])).
% 12.39/12.61 tff(36478,plain,(b(z, s(s(s(elem!1)))) | b(s(s(s(s(z)))), z) | r(z, elem!1) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.61 tff(36479,plain,
% 12.39/12.61 (b(s(s(s(s(z)))), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[36478, 10, 79, 66])).
% 12.39/12.61 tff(36480,plain,
% 12.39/12.61 ((elem!1 = s(elem!1)) <=> (z = s(elem!1))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[11])).
% 12.39/12.61 tff(36481,plain,
% 12.39/12.61 ((elem!1 = s(elem!1)) <=> (s(elem!1) = z)),
% 12.39/12.61 inference(transitivity,[status(thm)],[36480, 558])).
% 12.39/12.61 tff(36482,plain,
% 12.39/12.61 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 12.39/12.61 inference(symmetry,[status(thm)],[36481])).
% 12.39/12.61 tff(36483,plain,
% 12.39/12.61 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36482])).
% 12.39/12.61 tff(36484,plain,
% 12.39/12.61 (~(elem!1 = s(elem!1))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[355, 36483])).
% 12.39/12.61 tff(36485,plain,
% 12.39/12.61 (~b(elem!1, s(elem!1))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[31, 35783])).
% 12.39/12.61 tff(36486,plain,
% 12.39/12.61 (r(elem!1, s(elem!1))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[443, 36485, 36484])).
% 12.39/12.61 tff(36487,plain,
% 12.39/12.61 (~b(elem!1, s(s(s(elem!1))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[8846, 10, 11])).
% 12.39/12.61 tff(36488,plain,
% 12.39/12.61 (b(s(s(s(elem!1))), elem!1)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[8856, 34471, 24, 66, 36058, 36487, 10])).
% 12.39/12.61 tff(36489,plain,
% 12.39/12.61 (~r(s(s(s(z))), s(z))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[33652, 181, 29964, 722])).
% 12.39/12.61 tff(36490,plain,
% 12.39/12.61 (~r(s(s(s(elem!1))), s(z))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[29740, 36489, 11])).
% 12.39/12.61 tff(36491,plain,
% 12.39/12.61 (b(s(s(s(elem!1))), s(z))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[223, 36490])).
% 12.39/12.61 tff(36492,plain,
% 12.39/12.61 (~r(s(z), s(s(s(s(z)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[10620, 722, 36058])).
% 12.39/12.61 tff(36493,plain,
% 12.39/12.61 (b(s(z), s(s(s(s(z)))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[1230, 36492])).
% 12.39/12.61 tff(36494,plain,
% 12.39/12.61 (r(elem!1, s(s(s(elem!1))))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[424, 36487, 66])).
% 12.39/12.61 tff(36495,plain,
% 12.39/12.61 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[490])).
% 12.39/12.61 tff(36496,plain,
% 12.39/12.61 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.39/12.61 inference(symmetry,[status(thm)],[36495])).
% 12.39/12.61 tff(36497,plain,
% 12.39/12.61 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36496])).
% 12.39/12.61 tff(36498,plain,
% 12.39/12.61 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[32147])).
% 12.39/12.61 tff(36499,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 12.39/12.61 tff(36500,plain,
% 12.39/12.61 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36499])).
% 12.39/12.61 tff(36501,plain,
% 12.39/12.61 (s(s(z)) = s(s(s(s(z))))),
% 12.39/12.61 inference(transitivity,[status(thm)],[710, 36500, 692, 36499])).
% 12.39/12.61 tff(36502,plain,
% 12.39/12.61 ($false),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[714, 36501])).
% 12.39/12.61 tff(36503,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.61 tff(36504,plain,
% 12.39/12.61 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36503, 36498])).
% 12.39/12.61 tff(36505,plain,
% 12.39/12.61 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36504, 36497])).
% 12.39/12.61 tff(36506,plain,
% 12.39/12.61 (~r(s(s(s(elem!1))), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[3969, 181, 36058, 59, 36505])).
% 12.39/12.61 tff(36507,plain,
% 12.39/12.61 (b(s(s(s(elem!1))), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[377, 36506])).
% 12.39/12.61 tff(36508,plain,
% 12.39/12.61 (b(s(s(s(z))), z)),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[1680, 36507, 11])).
% 12.39/12.61 tff(36509,plain,
% 12.39/12.61 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.39/12.61 inference(transitivity,[status(thm)],[36496, 3929])).
% 12.39/12.61 tff(36510,plain,
% 12.39/12.61 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 12.39/12.61 inference(monotonicity,[status(thm)],[36509])).
% 12.39/12.61 tff(36511,plain,
% 12.39/12.61 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36504, 36510])).
% 12.39/12.61 tff(36512,plain,
% 12.39/12.61 (r(s(s(s(s(z)))), elem!1)),
% 12.39/12.61 inference(modus_ponens,[status(thm)],[36058, 36114])).
% 12.39/12.61 tff(36513,plain,
% 12.39/12.61 (~r(s(s(s(s(z)))), s(z))),
% 12.39/12.61 inference(unit_resolution,[status(thm)],[15864, 181, 36512, 847])).
% 12.39/12.61 tff(36514,plain,
% 12.39/12.61 (b(s(s(s(s(z)))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[749, 36513])).
% 12.39/12.62 tff(36515,plain,
% 12.39/12.62 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[6372, 36491, 36479, 36493, 36514])).
% 12.39/12.62 tff(36516,plain,
% 12.39/12.62 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[27316, 36515, 11])).
% 12.39/12.62 tff(36517,plain,
% 12.39/12.62 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1095, 36516, 17615])).
% 12.39/12.62 tff(36518,plain,
% 12.39/12.62 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[29931, 36517, 11])).
% 12.39/12.62 tff(36519,plain,
% 12.39/12.62 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[16851, 36518, 36058, 59])).
% 12.39/12.62 tff(36520,plain,
% 12.39/12.62 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[15351, 36519, 36511])).
% 12.39/12.62 tff(36521,plain,
% 12.39/12.62 (b(s(s(s(z))), s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1673, 36520, 11])).
% 12.39/12.62 tff(36522,plain,
% 12.39/12.62 (~b(z, s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1694, 36521, 36479, 36508])).
% 12.39/12.62 tff(36523,plain,
% 12.39/12.62 (r(z, s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[800, 36522])).
% 12.39/12.62 tff(36524,plain,
% 12.39/12.62 (r(elem!1, s(s(s(s(elem!1)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[23210, 36523, 11])).
% 12.39/12.62 tff(36525,plain,
% 12.39/12.62 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[34319, 36524, 36494, 847, 17615, 36493, 11, 36491])).
% 12.39/12.62 tff(36526,plain,
% 12.39/12.62 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1370, 36525, 23216])).
% 12.39/12.62 tff(36527,plain,
% 12.39/12.62 (~r(s(s(elem!1)), s(elem!1))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[19037, 36526, 2251, 30072, 35483, 30031, 36488])).
% 12.39/12.62 tff(36528,plain,
% 12.39/12.62 (~b(s(s(elem!1)), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[3263, 36526, 36493, 36514, 36491])).
% 12.39/12.62 tff(36529,plain,
% 12.39/12.62 (~b(s(s(elem!1)), s(elem!1))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[2316, 36528, 1597])).
% 12.39/12.62 tff(36530,plain,
% 12.39/12.62 ($false),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1135, 36529, 36527, 30039])).
% 12.39/12.62 tff(36531,plain,(b(s(z), z) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~(elem!1 = z)) | b(z, s(s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.62 tff(36532,plain,
% 12.39/12.62 (b(s(z), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[36531, 36486, 33641, 11, 10, 46])).
% 12.39/12.62 tff(36533,plain,
% 12.39/12.62 (~b(z, s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[22664, 36532, 36479, 36060])).
% 12.39/12.62 tff(36534,plain,
% 12.39/12.62 (r(z, s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[800, 36533])).
% 12.39/12.62 tff(36535,plain,
% 12.39/12.62 (r(elem!1, s(s(s(s(z)))))),
% 12.39/12.62 inference(modus_ponens,[status(thm)],[36534, 61])).
% 12.39/12.62 tff(36536,plain,
% 12.39/12.62 (~r(s(z), s(s(z)))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[34201, 723, 36479, 46, 59, 36060])).
% 12.39/12.62 tff(36537,plain,
% 12.39/12.62 (b(s(z), s(s(z)))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1788, 36536])).
% 12.39/12.62 tff(36538,plain,
% 12.39/12.62 (~r(s(s(z)), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[30527, 36537, 36058, 36060, 46])).
% 12.39/12.62 tff(36539,plain,
% 12.39/12.62 (b(s(s(z)), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1211, 36538])).
% 12.39/12.62 tff(36540,plain,
% 12.39/12.62 (b(s(s(elem!1)), elem!1)),
% 12.39/12.62 inference(modus_ponens,[status(thm)],[36539, 30006])).
% 12.39/12.62 tff(36541,plain,
% 12.39/12.62 (b(s(z), s(s(elem!1)))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[30324, 36537, 11])).
% 12.39/12.62 tff(36542,plain,
% 12.39/12.62 (~r(s(z), s(s(s(z))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[18419, 723, 36058, 46])).
% 12.39/12.62 tff(36543,plain,
% 12.39/12.62 (~r(s(z), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[23224, 36542, 11])).
% 12.39/12.62 tff(36544,plain,
% 12.39/12.62 (b(s(z), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[247, 36543])).
% 12.39/12.62 tff(36545,plain,
% 12.39/12.62 (r(elem!1, s(s(s(s(elem!1)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[23210, 36534, 11])).
% 12.39/12.62 tff(36546,plain,
% 12.39/12.62 (~r(s(s(s(elem!1))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[30400, 36544, 36058, 10, 31, 66, 79])).
% 12.39/12.62 tff(36547,plain,
% 12.39/12.62 (b(s(s(s(elem!1))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[223, 36546])).
% 12.39/12.62 tff(36548,plain,
% 12.39/12.62 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[34319, 36547, 36494, 33641, 17615, 36060, 11, 36545])).
% 12.39/12.62 tff(36549,plain,
% 12.39/12.62 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1370, 36548, 23216])).
% 12.39/12.62 tff(36550,plain,
% 12.39/12.62 (~b(s(s(elem!1)), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[5321, 36549, 36544, 36541])).
% 12.39/12.62 tff(36551,plain,
% 12.39/12.62 (r(s(s(elem!1)), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[362, 36550])).
% 12.39/12.62 tff(36552,plain,
% 12.39/12.62 (~r(s(s(s(z))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[33652, 35416, 15510, 722])).
% 12.39/12.62 tff(36553,plain,
% 12.39/12.62 (~r(s(s(s(elem!1))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[29740, 36552, 11])).
% 12.39/12.62 tff(36554,plain,
% 12.39/12.62 (~r(s(s(s(s(z)))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[9103, 1484, 36512, 2032])).
% 12.39/12.62 tff(36555,plain,
% 12.39/12.62 (b(s(s(s(s(z)))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[749, 36554])).
% 12.39/12.62 tff(36556,plain,
% 12.39/12.62 (~b(s(s(s(elem!1))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[34309, 36555, 11, 90, 410, 36493, 17615, 2032])).
% 12.39/12.62 tff(36557,plain,
% 12.39/12.62 ($false),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[223, 36556, 36553])).
% 12.39/12.62 tff(36558,plain,((~r(s(z), elem!1)) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.62 tff(36559,plain,
% 12.39/12.62 (~r(s(z), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[36558, 36535, 36479, 36494, 11, 29964, 46])).
% 12.39/12.62 tff(36560,plain,
% 12.39/12.62 (b(s(z), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[632, 36559, 24])).
% 12.39/12.62 tff(36561,plain,
% 12.39/12.62 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[20817, 36547, 36060, 36544])).
% 12.39/12.62 tff(36562,plain,
% 12.39/12.62 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[27316, 36561, 11])).
% 12.39/12.62 tff(36563,plain,
% 12.39/12.62 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1095, 36562, 17615])).
% 12.39/12.62 tff(36564,plain,
% 12.39/12.62 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[29931, 36563, 11])).
% 12.39/12.62 tff(36565,plain,
% 12.39/12.62 (~r(s(s(s(elem!1))), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[15335, 36564, 36058, 59])).
% 12.39/12.62 tff(36566,plain,
% 12.39/12.62 (~r(s(s(s(elem!1))), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[406, 36565, 11])).
% 12.39/12.62 tff(36567,plain,
% 12.39/12.62 (~b(s(s(elem!1)), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[18514, 36566, 11, 59, 17616, 2419, 36479, 36060, 36560, 33641, 36547, 36549, 36505, 36551])).
% 12.39/12.62 tff(36568,plain,
% 12.39/12.62 ($false),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[36567, 36540])).
% 12.39/12.62 tff(36569,plain,((~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = z)) | b(z, s(s(s(elem!1)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.62 tff(36570,plain,
% 12.39/12.62 (~r(s(s(s(s(z)))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[36569, 31, 10, 11])).
% 12.39/12.62 tff(36571,plain,
% 12.39/12.62 (b(s(s(s(s(z)))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[749, 36570])).
% 12.39/12.62 tff(36572,plain,
% 12.39/12.62 (~b(s(s(s(elem!1))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[34309, 36571, 11, 36479, 36494, 36060, 17615, 36535])).
% 12.39/12.62 tff(36573,plain,
% 12.39/12.62 (r(s(s(s(elem!1))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[223, 36572])).
% 12.39/12.62 tff(36574,plain,
% 12.39/12.62 (~r(s(z), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[21974, 36573, 59, 46])).
% 12.39/12.62 tff(36575,plain,
% 12.39/12.62 (~b(s(z), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[30400, 36573, 36058, 10, 31, 66, 79])).
% 12.39/12.62 tff(36576,plain,
% 12.39/12.62 ($false),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[247, 36575, 36574])).
% 12.39/12.62 tff(36577,plain,(b(elem!1, s(z)) | b(z, s(s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.62 tff(36578,plain,
% 12.39/12.62 (b(elem!1, s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[36577, 10, 11])).
% 12.39/12.62 tff(36579,plain,
% 12.39/12.62 (~r(s(z), s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[35294, 36578, 10, 36479, 66, 79])).
% 12.39/12.62 tff(36580,plain,
% 12.39/12.62 (b(s(z), s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1230, 36579])).
% 12.39/12.62 tff(36581,plain,
% 12.39/12.62 (~r(s(s(s(elem!1))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[36205, 36580, 11, 36058, 36487, 66, 36578])).
% 12.39/12.62 tff(36582,plain,
% 12.39/12.62 (b(s(s(s(elem!1))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[223, 36581])).
% 12.39/12.62 tff(36583,plain,
% 12.39/12.62 (b(s(s(s(elem!1))), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[36445, 36582, 79, 36058, 10, 36580])).
% 12.39/12.62 tff(36584,plain,
% 12.39/12.62 (~b(s(z), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[20387, 36583, 36578, 36582])).
% 12.39/12.62 tff(36585,plain,
% 12.39/12.62 (r(s(z), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[632, 36584, 24])).
% 12.39/12.62 tff(36586,plain,
% 12.39/12.62 (r(s(s(s(s(elem!1)))), elem!1)),
% 12.39/12.62 inference(modus_ponens,[status(thm)],[36058, 29980])).
% 12.39/12.62 tff(36587,plain,
% 12.39/12.62 (r(elem!1, s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[34570, 2829, 94, 991, 1234, 2112, 721, 723])).
% 12.39/12.62 tff(36588,plain,
% 12.39/12.62 (r(s(z), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[5433, 5429, 94])).
% 12.39/12.62 tff(36589,plain,
% 12.39/12.62 ($false),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[15864, 36588, 36587, 2112, 723])).
% 12.39/12.62 tff(36590,plain,(b(s(z), elem!1) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~(z = elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.62 tff(36591,plain,
% 12.39/12.62 (~r(s(s(s(s(z)))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[36590, 36584, 17618, 36512, 36586, 36578, 36580, 24])).
% 12.39/12.62 tff(36592,plain,
% 12.39/12.62 (b(s(s(s(s(z)))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[749, 36591])).
% 12.39/12.62 tff(36593,plain,
% 12.39/12.62 (r(s(z), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[5433, 36585, 17618])).
% 12.39/12.62 tff(36594,plain,
% 12.39/12.62 (~b(s(z), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[2907, 36583, 36578, 36582])).
% 12.39/12.62 tff(36595,plain,
% 12.39/12.62 (r(s(z), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[247, 36594])).
% 12.39/12.62 tff(36596,plain,
% 12.39/12.62 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[337, 36595, 59, 36593])).
% 12.39/12.62 tff(36597,plain,
% 12.39/12.62 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1370, 36596, 23216])).
% 12.39/12.62 tff(36598,plain,
% 12.39/12.62 (~b(s(s(elem!1)), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[3263, 36597, 36580, 36592, 36582])).
% 12.39/12.62 tff(36599,plain,
% 12.39/12.62 (r(s(s(elem!1)), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[362, 36598])).
% 12.39/12.62 tff(36600,plain,
% 12.39/12.62 (~b(s(s(elem!1)), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[34598, 36597, 36578, 36583, 36580])).
% 12.39/12.62 tff(36601,plain,
% 12.39/12.62 (r(s(s(elem!1)), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[872, 36600, 30072])).
% 12.39/12.62 tff(36602,plain,
% 12.39/12.62 ($false),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[2379, 36601, 36599, 36494, 36585])).
% 12.39/12.62 tff(36603,plain,(b(z, s(s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.62 tff(36604,plain,
% 12.39/12.62 (~(elem!1 = z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[36603, 10])).
% 12.39/12.62 tff(36605,plain,
% 12.39/12.62 (~b(s(s(s(s(z)))), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[22897, 36604, 10])).
% 12.39/12.62 tff(36606,plain,
% 12.39/12.62 (r(z, elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[33626, 2])).
% 12.39/12.62 tff(36607,plain,
% 12.39/12.62 (~r(s(z), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[2061, 2913, 29426, 36606])).
% 12.39/12.62 tff(36608,plain,
% 12.39/12.62 (b(s(z), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[180, 36607])).
% 12.39/12.62 tff(36609,plain,
% 12.39/12.62 (~r(s(s(s(elem!1))), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[3969, 59, 29426, 181, 21769])).
% 12.39/12.62 tff(36610,plain,
% 12.39/12.62 (~b(s(s(s(s(z)))), z)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[21727, 10, 2, 91])).
% 12.39/12.62 tff(36611,plain,
% 12.39/12.62 (~r(s(z), s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[2061, 181, 2053, 411])).
% 12.39/12.62 tff(36612,plain,
% 12.39/12.62 (b(s(z), s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[1230, 36611])).
% 12.39/12.62 tff(36613,plain,
% 12.39/12.62 (~r(s(z), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[8931, 17538, 2053, 411, 721, 181, 36612])).
% 12.39/12.62 tff(36614,plain,
% 12.39/12.62 (b(s(z), elem!1)),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[632, 36613, 21435])).
% 12.39/12.62 tff(36615,plain,
% 12.39/12.62 (~r(s(s(s(s(z)))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[3243, 181, 2053, 411])).
% 12.39/12.62 tff(36616,plain,
% 12.39/12.62 (b(s(s(s(s(z)))), s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[749, 36615])).
% 12.39/12.62 tff(36617,plain,
% 12.39/12.62 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 12.39/12.62 inference(monotonicity,[status(thm)],[125])).
% 12.39/12.62 tff(36618,plain,
% 12.39/12.62 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 12.39/12.62 inference(transitivity,[status(thm)],[36617, 3042])).
% 12.39/12.62 tff(36619,plain,
% 12.39/12.62 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 12.39/12.62 inference(symmetry,[status(thm)],[36618])).
% 12.39/12.62 tff(36620,plain,
% 12.39/12.62 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 12.39/12.62 inference(transitivity,[status(thm)],[36619, 93])).
% 12.39/12.62 tff(36621,plain,
% 12.39/12.62 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = z))),
% 12.39/12.62 inference(monotonicity,[status(thm)],[36620])).
% 12.39/12.62 tff(36622,plain,
% 12.39/12.62 (~(elem!1 = z)),
% 12.39/12.62 inference(modus_ponens,[status(thm)],[50, 36621])).
% 12.39/12.62 tff(36623,plain,
% 12.39/12.62 (~r(z, s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[2097, 1759, 1234, 721, 2642, 411])).
% 12.39/12.62 tff(36624,plain,
% 12.39/12.62 (b(z, s(s(s(s(z)))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[800, 36623])).
% 12.39/12.62 tff(36625,plain,
% 12.39/12.62 (~b(z, s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[10478, 36624, 1234, 1759])).
% 12.39/12.62 tff(36626,plain,
% 12.39/12.62 (r(z, s(z))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[678, 36625])).
% 12.39/12.62 tff(36627,plain,
% 12.39/12.62 (b(s(z), s(s(s(elem!1))))),
% 12.39/12.62 inference(unit_resolution,[status(thm)],[14872, 130, 644])).
% 12.39/12.62 tff(36628,plain,
% 12.39/12.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.39/12.62 inference(rewrite,[status(thm)],[])).
% 12.39/12.62 tff(36629,plain,
% 12.39/12.62 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.39/12.62 inference(rewrite,[status(thm)],[])).
% 12.39/12.62 tff(36630,plain,
% 12.39/12.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.39/12.62 inference(monotonicity,[status(thm)],[36629])).
% 12.39/12.62 tff(36631,plain,
% 12.39/12.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.39/12.62 inference(transitivity,[status(thm)],[36630, 36628])).
% 12.39/12.62 tff(36632,plain,
% 12.39/12.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 12.39/12.62 inference(quant_inst,[status(thm)],[])).
% 12.39/12.62 tff(36633,plain,
% 12.39/12.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 12.39/12.63 inference(modus_ponens,[status(thm)],[36632, 36631])).
% 12.39/12.63 tff(36634,plain,
% 12.39/12.63 (~b(s(z), z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[36633, 391, 36627, 1234, 1759, 36624])).
% 12.39/12.63 tff(36635,plain,
% 12.39/12.63 (r(s(z), z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[180, 36634])).
% 12.39/12.63 tff(36636,plain,
% 12.39/12.63 (~r(elem!1, z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[26158, 36635, 2053, 644, 2642, 36626])).
% 12.39/12.63 tff(36637,plain,
% 12.39/12.63 (b(elem!1, z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[526, 36636, 36622])).
% 12.39/12.63 tff(36638,plain,
% 12.39/12.63 (~b(elem!1, s(s(s(s(z)))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[3150, 36637, 644, 721, 1759])).
% 12.39/12.63 tff(36639,plain,
% 12.39/12.63 (r(elem!1, s(s(s(s(z)))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[781, 36638, 3810])).
% 12.39/12.63 tff(36640,plain,
% 12.39/12.63 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.63 inference(modus_ponens,[status(thm)],[36639, 14785])).
% 12.39/12.63 tff(36641,plain,
% 12.39/12.63 (~b(s(s(s(s(z)))), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[26707, 1759, 1234, 644, 721])).
% 12.39/12.63 tff(36642,plain,
% 12.39/12.63 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[2694, 36641, 130])).
% 12.39/12.63 tff(36643,plain,
% 12.39/12.63 ($false),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[16849, 194, 184, 2053, 36642, 36640])).
% 12.39/12.63 tff(36644,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.63 tff(36645,plain,
% 12.39/12.63 (~(elem!1 = s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[36644, 36614, 2053, 721, 36612, 59, 36616, 411])).
% 12.39/12.63 tff(36646,plain,
% 12.39/12.63 (b(elem!1, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[10532, 36645, 411, 59, 27211, 665, 181, 36614])).
% 12.39/12.63 tff(36647,plain,
% 12.39/12.63 (~r(s(s(s(elem!1))), z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[3969, 59, 2053, 181, 21769])).
% 12.39/12.63 tff(36648,plain,
% 12.39/12.63 (b(s(s(s(elem!1))), z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[377, 36647])).
% 12.39/12.63 tff(36649,plain,
% 12.39/12.63 (~(s(s(s(elem!1))) = elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[8, 36645])).
% 12.39/12.63 tff(36650,plain,
% 12.39/12.63 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[8251, 36649])).
% 12.39/12.63 tff(36651,plain,
% 12.39/12.63 (b(z, s(s(elem!1)))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[3924, 36650, 91, 10])).
% 12.39/12.63 tff(36652,plain,
% 12.39/12.63 (~b(s(z), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[22283, 36651, 36648, 36646, 36614])).
% 12.39/12.63 tff(36653,plain,
% 12.39/12.63 (r(s(z), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[247, 36652])).
% 12.39/12.63 tff(36654,plain,
% 12.39/12.63 (~r(s(s(s(elem!1))), s(z))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[3499, 36653, 181, 59])).
% 12.39/12.63 tff(36655,plain,
% 12.39/12.63 (~b(s(s(s(elem!1))), s(z))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[21704, 36653, 411, 181, 59, 665, 36646, 721, 36651, 121])).
% 12.39/12.63 tff(36656,plain,
% 12.39/12.63 ($false),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[223, 36655, 36654])).
% 12.39/12.63 tff(36657,plain,((~b(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | b(s(z), z) | b(z, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.63 tff(36658,plain,
% 12.39/12.63 (~b(elem!1, z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[36657, 10, 721, 118, 91, 36606, 29426, 36610])).
% 12.39/12.63 tff(36659,plain,
% 12.39/12.63 (r(elem!1, z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[526, 36658, 2])).
% 12.39/12.63 tff(36660,plain,
% 12.39/12.63 (~(s(s(s(elem!1))) = elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[533, 36659, 36609])).
% 12.39/12.63 tff(36661,plain,
% 12.39/12.63 (b(s(s(s(elem!1))), z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[377, 36609])).
% 12.39/12.63 tff(36662,plain,
% 12.39/12.63 (~b(s(s(s(elem!1))), s(z))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[21676, 36659, 36606, 721, 59, 36660, 181])).
% 12.39/12.63 tff(36663,plain,
% 12.39/12.63 (r(s(s(s(elem!1))), s(z))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[223, 36662])).
% 12.39/12.63 tff(36664,plain,
% 12.39/12.63 (~r(elem!1, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[19887, 36663, 36606, 59])).
% 12.39/12.63 tff(36665,plain,
% 12.39/12.63 (~r(s(z), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[3499, 36663, 181, 59])).
% 12.39/12.63 tff(36666,plain,
% 12.39/12.63 (b(s(z), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[247, 36665])).
% 12.39/12.63 tff(36667,plain,
% 12.39/12.63 ($false),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[21723, 36666, 36664, 91, 721, 10, 36661, 36660])).
% 12.39/12.63 tff(36668,plain,(b(z, s(s(s(elem!1)))) | b(s(z), z) | (~b(elem!1, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.63 tff(36669,plain,
% 12.39/12.63 (b(s(z), z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[36668, 10, 2, 20263])).
% 12.39/12.63 tff(36670,plain,
% 12.39/12.63 (b(z, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[20262, 31, 2])).
% 12.39/12.63 tff(36671,plain,
% 12.39/12.63 (~(elem!1 = s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[22900, 36670, 89])).
% 12.39/12.63 tff(36672,plain,
% 12.39/12.63 (~b(s(s(s(elem!1))), s(z))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[10690, 31666, 36670, 36608])).
% 12.39/12.63 tff(36673,plain,
% 12.39/12.63 (~b(s(s(s(s(z)))), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[9614, 29702, 8598])).
% 12.39/12.63 tff(36674,plain,
% 12.39/12.63 (~b(s(s(s(elem!1))), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[1563, 36673, 169])).
% 12.39/12.63 tff(36675,plain,
% 12.39/12.63 (~b(elem!1, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[8314, 169, 2881])).
% 12.39/12.63 tff(36676,plain,
% 12.39/12.63 (r(elem!1, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[424, 36675, 1])).
% 12.39/12.63 tff(36677,plain,
% 12.39/12.63 (~r(s(s(s(elem!1))), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[29125, 36676, 411, 29714])).
% 12.39/12.63 tff(36678,plain,
% 12.39/12.63 ($false),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[230, 36677, 36674, 9])).
% 12.39/12.63 tff(36679,plain,((~(elem!1 = s(z))) | (~r(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | b(s(s(s(s(z)))), z) | b(s(z), s(s(s(s(z))))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.63 tff(36680,plain,
% 12.39/12.63 (~(elem!1 = s(z))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[36679, 3446, 36671, 36606, 2881, 36672])).
% 12.39/12.63 tff(36681,plain,
% 12.39/12.63 (r(elem!1, s(z))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[837, 36680, 31])).
% 12.39/12.63 tff(36682,plain,
% 12.39/12.63 (~r(s(s(s(s(z)))), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[10408, 36681, 29426, 36606])).
% 12.39/12.63 tff(36683,plain,
% 12.39/12.63 (r(s(s(s(elem!1))), s(z))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[223, 36672])).
% 12.39/12.63 tff(36684,plain,
% 12.39/12.63 (~r(elem!1, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[10776, 36681, 2913, 36683])).
% 12.39/12.63 tff(36685,plain,
% 12.39/12.63 (b(elem!1, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[424, 36684, 36671])).
% 12.39/12.63 tff(36686,plain,
% 12.39/12.63 (~(s(s(s(elem!1))) = elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[8, 36671])).
% 12.39/12.63 tff(36687,plain,
% 12.39/12.63 (~r(s(s(s(elem!1))), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[10856, 36681, 2913, 36683])).
% 12.39/12.63 tff(36688,plain,
% 12.39/12.63 (b(s(s(s(elem!1))), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[230, 36687, 36686])).
% 12.39/12.63 tff(36689,plain,
% 12.39/12.63 (~(s(z) = elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[1495, 36680])).
% 12.39/12.63 tff(36690,plain,
% 12.39/12.63 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[2849, 36689])).
% 12.39/12.63 tff(36691,plain,
% 12.39/12.63 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[2853, 42, 3843, 16859])).
% 12.39/12.63 tff(36692,plain,
% 12.39/12.63 ($false),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[16936, 194, 183, 1216, 36691, 16843])).
% 12.39/12.63 tff(36693,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.63 tff(36694,plain,
% 12.39/12.63 (~b(s(s(s(s(z)))), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[36693, 36690, 2913, 36683, 36688, 36685])).
% 12.39/12.63 tff(36695,plain,
% 12.39/12.63 (s(s(s(s(z)))) = elem!1),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[762, 36694, 36682])).
% 12.39/12.63 tff(36696,plain,
% 12.39/12.63 (b(s(s(z)), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[30679, 36695, 31645])).
% 12.39/12.63 tff(36697,plain,
% 12.39/12.63 (~r(elem!1, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[10776, 847, 1216, 183])).
% 12.39/12.63 tff(36698,plain,
% 12.39/12.63 (~b(elem!1, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[28909, 847, 411, 10682, 9, 665])).
% 12.39/12.63 tff(36699,plain,
% 12.39/12.63 ($false),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[424, 36698, 36697, 1])).
% 12.39/12.63 tff(36700,plain,((~r(elem!1, s(z))) | (elem!1 = s(s(s(elem!1)))) | (~r(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.63 tff(36701,plain,
% 12.39/12.63 (~b(elem!1, z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[36700, 36681, 36606, 36670, 36671, 2913, 36683])).
% 12.39/12.63 tff(36702,plain,
% 12.39/12.63 (r(elem!1, z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[526, 36701, 2])).
% 12.39/12.63 tff(36703,plain,
% 12.39/12.63 (~b(z, s(s(s(s(z)))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[16124, 36695, 89])).
% 12.39/12.63 tff(36704,plain,
% 12.39/12.63 (r(z, s(s(s(s(z)))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[800, 36703])).
% 12.39/12.63 tff(36705,plain,
% 12.39/12.63 (~r(z, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[16904, 36685, 2, 36606, 2881, 89, 36608, 3446, 36688, 36689, 31666, 31])).
% 12.39/12.63 tff(36706,plain,
% 12.39/12.63 (~b(s(s(s(s(z)))), s(z))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[11186, 36695, 31])).
% 12.39/12.63 tff(36707,plain,
% 12.39/12.63 (r(s(s(s(s(z)))), s(z))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[749, 36706])).
% 12.39/12.63 tff(36708,plain,
% 12.39/12.63 (~b(s(s(z)), z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[10965, 36707, 2881, 36681, 36705, 36608, 31666, 36685, 36606])).
% 12.39/12.63 tff(36709,plain,
% 12.39/12.63 (r(s(s(z)), z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[1211, 36708])).
% 12.39/12.63 tff(36710,plain,
% 12.39/12.63 (~r(elem!1, s(s(z)))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[8570, 36709, 36704, 36702])).
% 12.39/12.63 tff(36711,plain,
% 12.39/12.63 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 12.39/12.63 inference(monotonicity,[status(thm)],[36695])).
% 12.39/12.63 tff(36712,plain,
% 12.39/12.63 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 12.39/12.63 inference(transitivity,[status(thm)],[36711, 698])).
% 12.39/12.63 tff(36713,plain,
% 12.39/12.63 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(z))))),
% 12.39/12.63 inference(monotonicity,[status(thm)],[36712])).
% 12.39/12.63 tff(36714,plain,
% 12.39/12.63 (~(elem!1 = s(s(z)))),
% 12.39/12.63 inference(modus_ponens,[status(thm)],[714, 36713])).
% 12.39/12.63 tff(36715,plain,
% 12.39/12.63 (b(elem!1, s(s(z)))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[3394, 36714, 36710])).
% 12.39/12.63 tff(36716,plain,
% 12.39/12.63 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[16257, 3446, 2881, 98, 31])).
% 12.39/12.63 tff(36717,plain,
% 12.39/12.63 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[717, 36695])).
% 12.39/12.63 tff(36718,plain,
% 12.39/12.63 (~(s(s(elem!1)) = elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[451, 36717])).
% 12.39/12.63 tff(36719,plain,
% 12.39/12.63 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[8251, 36686])).
% 12.39/12.63 tff(36720,plain,
% 12.39/12.63 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[314, 36719])).
% 12.39/12.63 tff(36721,plain,
% 12.39/12.63 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[2865, 36695, 36685])).
% 12.39/12.63 tff(36722,plain,
% 12.39/12.63 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 12.39/12.63 inference(monotonicity,[status(thm)],[36695])).
% 12.39/12.63 tff(36723,plain,
% 12.39/12.63 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.63 inference(symmetry,[status(thm)],[36722])).
% 12.39/12.63 tff(36724,plain,
% 12.39/12.63 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.63 inference(modus_ponens,[status(thm)],[36688, 36723])).
% 12.39/12.63 tff(36725,plain,
% 12.39/12.63 (~b(s(z), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[17481, 36724, 36670, 36608, 36721])).
% 12.39/12.63 tff(36726,plain,
% 12.39/12.63 (r(s(z), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[247, 36725])).
% 12.39/12.63 tff(36727,plain,
% 12.39/12.63 (~b(z, s(s(elem!1)))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[24044, 36726, 36670, 36608, 36716, 36683, 36720])).
% 12.39/12.63 tff(36728,plain,
% 12.39/12.63 (r(z, s(s(elem!1)))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[324, 36727])).
% 12.39/12.63 tff(36729,plain,
% 12.39/12.63 (~r(s(s(elem!1)), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[867, 36728, 36606, 36702])).
% 12.39/12.63 tff(36730,plain,
% 12.39/12.63 (b(s(s(elem!1)), elem!1)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[872, 36729, 36718])).
% 12.39/12.63 tff(36731,plain,
% 12.39/12.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 12.39/12.63 inference(rewrite,[status(thm)],[])).
% 12.39/12.63 tff(36732,plain,
% 12.39/12.63 (((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(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)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 12.39/12.63 inference(rewrite,[status(thm)],[])).
% 12.39/12.63 tff(36733,plain,
% 12.39/12.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 12.39/12.63 inference(monotonicity,[status(thm)],[36732])).
% 12.39/12.63 tff(36734,plain,
% 12.39/12.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 12.39/12.63 inference(transitivity,[status(thm)],[36733, 36731])).
% 12.39/12.63 tff(36735,plain,
% 12.39/12.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 12.39/12.63 inference(quant_inst,[status(thm)],[])).
% 12.39/12.63 tff(36736,plain,
% 12.39/12.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 12.39/12.63 inference(modus_ponens,[status(thm)],[36735, 36734])).
% 12.39/12.63 tff(36737,plain,
% 12.39/12.63 ($false),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[36736, 391, 36688, 36730, 36716, 36715, 36696])).
% 12.39/12.63 tff(36738,plain,(b(s(s(s(s(z)))), z) | b(s(z), s(s(s(s(z))))) | b(elem!1, s(z)) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.63 tff(36739,plain,
% 12.39/12.63 (b(s(s(s(s(z)))), z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[36738, 2881, 31, 89, 2])).
% 12.39/12.63 tff(36740,plain,
% 12.39/12.63 (elem!1 = s(z)),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[28307, 36739, 36670, 36671, 2913, 31666, 31, 36608])).
% 12.39/12.63 tff(36741,plain,
% 12.39/12.63 (~b(s(z), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[2884, 36740, 2881])).
% 12.39/12.63 tff(36742,plain,
% 12.39/12.63 (r(z, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[24987, 36739, 2881, 36672, 36671])).
% 12.39/12.63 tff(36743,plain,
% 12.39/12.63 (~r(elem!1, s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[19887, 36742, 36606, 36683])).
% 12.39/12.63 tff(36744,plain,
% 12.39/12.63 (s(z) = elem!1),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[172, 36740])).
% 12.39/12.63 tff(36745,plain,
% 12.39/12.63 (~r(s(z), s(s(s(elem!1))))),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[2570, 36744, 36743])).
% 12.39/12.63 tff(36746,plain,
% 12.39/12.63 ($false),
% 12.39/12.63 inference(unit_resolution,[status(thm)],[247, 36745, 36741])).
% 12.39/12.64 tff(36747,plain,(b(s(z), s(s(s(s(z))))) | b(elem!1, s(z)) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.64 tff(36748,plain,
% 12.39/12.64 (b(s(z), s(s(s(s(z)))))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[36747, 31, 89, 2])).
% 12.39/12.64 tff(36749,plain,
% 12.39/12.64 (~r(elem!1, s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[845, 722, 36606, 181])).
% 12.39/12.64 tff(36750,plain,
% 12.39/12.64 (elem!1 = s(z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[837, 36749, 31])).
% 12.39/12.64 tff(36751,plain,
% 12.39/12.64 (s(z) = elem!1),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[172, 36750])).
% 12.39/12.64 tff(36752,plain,
% 12.39/12.64 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[18274, 722, 98, 31, 3446])).
% 12.39/12.64 tff(36753,plain,
% 12.39/12.64 (~r(s(s(s(s(z)))), s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[3243, 181, 29426, 36606])).
% 12.39/12.64 tff(36754,plain,
% 12.39/12.64 (b(s(s(s(s(z)))), s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[749, 36753])).
% 12.39/12.64 tff(36755,plain,
% 12.39/12.64 (b(s(s(s(elem!1))), s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[11177, 36750, 36754])).
% 12.39/12.64 tff(36756,plain,
% 12.39/12.64 (~b(s(s(elem!1)), s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[3263, 36755, 1234, 36754, 36752])).
% 12.39/12.64 tff(36757,plain,
% 12.39/12.64 (r(s(s(elem!1)), s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[362, 36756])).
% 12.39/12.64 tff(36758,plain,
% 12.39/12.64 (~r(s(s(elem!1)), z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[4103, 36757, 722, 181])).
% 12.39/12.64 tff(36759,plain,
% 12.39/12.64 (b(s(s(elem!1)), z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[2629, 36758])).
% 12.39/12.64 tff(36760,plain,
% 12.39/12.64 (b(s(s(s(z))), z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[7886, 36759, 36751])).
% 12.39/12.64 tff(36761,plain,
% 12.39/12.64 (s(elem!1) = s(s(z))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36750])).
% 12.39/12.64 tff(36762,plain,
% 12.39/12.64 (s(s(elem!1)) = s(s(s(z)))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36761])).
% 12.39/12.64 tff(36763,plain,
% 12.39/12.64 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36762])).
% 12.39/12.64 tff(36764,plain,
% 12.39/12.64 (~b(elem!1, z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[10390, 36751, 91])).
% 12.39/12.64 tff(36765,plain,
% 12.39/12.64 (r(elem!1, z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[526, 36764, 2])).
% 12.39/12.64 tff(36766,plain,
% 12.39/12.64 (r(s(s(elem!1)), elem!1)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[2220, 36757, 36751])).
% 12.39/12.64 tff(36767,plain,
% 12.39/12.64 (~r(z, s(s(elem!1)))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[867, 36766, 36606, 36765])).
% 12.39/12.64 tff(36768,plain,
% 12.39/12.64 (b(z, s(s(elem!1)))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[324, 36767])).
% 12.39/12.64 tff(36769,plain,
% 12.39/12.64 (b(z, s(s(s(z))))),
% 12.39/12.64 inference(modus_ponens,[status(thm)],[36768, 36763])).
% 12.39/12.64 tff(36770,plain,
% 12.39/12.64 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36762])).
% 12.39/12.64 tff(36771,plain,
% 12.39/12.64 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[3482, 36752, 36750])).
% 12.39/12.64 tff(36772,plain,
% 12.39/12.64 (b(s(s(s(s(z)))), s(s(s(z))))),
% 12.39/12.64 inference(modus_ponens,[status(thm)],[36771, 36770])).
% 12.39/12.64 tff(36773,plain,
% 12.39/12.64 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36762])).
% 12.39/12.64 tff(36774,plain,
% 12.39/12.64 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36773])).
% 12.39/12.64 tff(36775,plain,
% 12.39/12.64 (b(z, s(s(s(s(z)))))),
% 12.39/12.64 inference(modus_ponens,[status(thm)],[36670, 36774])).
% 12.39/12.64 tff(36776,plain,
% 12.39/12.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 12.39/12.64 inference(rewrite,[status(thm)],[])).
% 12.39/12.64 tff(36777,plain,
% 12.39/12.64 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 12.39/12.64 inference(rewrite,[status(thm)],[])).
% 12.39/12.64 tff(36778,plain,
% 12.39/12.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36777])).
% 12.39/12.64 tff(36779,plain,
% 12.39/12.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 12.39/12.64 inference(transitivity,[status(thm)],[36778, 36776])).
% 12.39/12.64 tff(36780,plain,
% 12.39/12.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 12.39/12.64 inference(quant_inst,[status(thm)],[])).
% 12.39/12.64 tff(36781,plain,
% 12.39/12.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 12.39/12.64 inference(modus_ponens,[status(thm)],[36780, 36779])).
% 12.39/12.64 tff(36782,plain,
% 12.39/12.64 ($false),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[36781, 391, 36775, 36772, 36769, 36760])).
% 12.39/12.64 tff(36783,plain,((~r(z, s(z))) | (elem!1 = z) | (~b(s(z), s(s(s(s(z)))))) | b(s(z), z) | b(elem!1, s(z)) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.64 tff(36784,plain,
% 12.39/12.64 (~r(z, s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[36783, 91, 1234, 2, 31, 3446])).
% 12.39/12.64 tff(36785,plain,
% 12.39/12.64 (b(z, s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[678, 36784])).
% 12.39/12.64 tff(36786,plain,
% 12.39/12.64 (~b(z, s(s(s(s(z)))))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[10478, 36785, 1234, 36754])).
% 12.39/12.64 tff(36787,plain,
% 12.39/12.64 (~(elem!1 = s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[11318, 36786, 2, 36784])).
% 12.39/12.64 tff(36788,plain,
% 12.39/12.64 (r(elem!1, s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[837, 36787, 31])).
% 12.39/12.64 tff(36789,plain,
% 12.39/12.64 (r(z, s(s(s(s(z)))))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[800, 36786])).
% 12.39/12.64 tff(36790,plain,
% 12.39/12.64 (~r(elem!1, z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[17062, 36788, 181, 36789])).
% 12.39/12.64 tff(36791,plain,
% 12.39/12.64 (b(elem!1, z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[526, 36790, 2])).
% 12.39/12.64 tff(36792,plain,
% 12.39/12.64 (~(s(z) = elem!1)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[1495, 36787])).
% 12.39/12.64 tff(36793,plain,
% 12.39/12.64 (~r(s(z), elem!1)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[2475, 36788, 36606, 181])).
% 12.39/12.64 tff(36794,plain,
% 12.39/12.64 (b(s(z), elem!1)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[632, 36793, 36792])).
% 12.39/12.64 tff(36795,plain,
% 12.39/12.64 ($false),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[10501, 36794, 36791, 36606, 3446, 1234, 181, 36788])).
% 12.39/12.64 tff(36796,plain,(b(s(z), z) | b(s(s(s(s(z)))), z) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.64 tff(36797,plain,
% 12.39/12.64 (b(s(z), z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[36796, 3446, 1234, 2, 31])).
% 12.39/12.64 tff(36798,plain,
% 12.39/12.64 (b(s(z), elem!1)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[19761, 150, 36606, 31, 722])).
% 12.39/12.64 tff(36799,plain,
% 12.39/12.64 (~b(elem!1, z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[23575, 36798, 36670, 590, 1374])).
% 12.39/12.64 tff(36800,plain,
% 12.39/12.64 (r(elem!1, z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[526, 36799, 2])).
% 12.39/12.64 tff(36801,plain,
% 12.39/12.64 (~r(s(z), s(s(s(elem!1))))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[16770, 36800, 722, 838])).
% 12.39/12.64 tff(36802,plain,
% 12.39/12.64 (b(s(z), s(s(s(elem!1))))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[247, 36801])).
% 12.39/12.64 tff(36803,plain,
% 12.39/12.64 (~b(s(s(s(elem!1))), z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[11303, 36802, 36670, 590])).
% 12.39/12.64 tff(36804,plain,
% 12.39/12.64 (~r(s(s(s(elem!1))), z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[11294, 36802, 29426, 36606, 36670, 3363, 590])).
% 12.39/12.64 tff(36805,plain,
% 12.39/12.64 ($false),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[377, 36804, 36803])).
% 12.39/12.64 tff(36806,plain,((s(z) = elem!1) | (~b(s(z), z)) | (~r(z, s(z))) | (elem!1 = z) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.64 tff(36807,plain,
% 12.39/12.64 (s(z) = elem!1),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[36806, 722, 36797, 2, 36752, 31])).
% 12.39/12.64 tff(36808,plain,
% 12.39/12.64 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36807])).
% 12.39/12.64 tff(36809,plain,
% 12.39/12.64 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 12.39/12.64 inference(symmetry,[status(thm)],[36808])).
% 12.39/12.64 tff(36810,plain,
% 12.39/12.64 (b(elem!1, s(s(s(elem!1))))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[8542, 36807, 1234])).
% 12.39/12.64 tff(36811,plain,
% 12.39/12.64 (b(s(z), s(s(s(elem!1))))),
% 12.39/12.64 inference(modus_ponens,[status(thm)],[36810, 36809])).
% 12.39/12.64 tff(36812,plain,
% 12.39/12.64 (~b(s(s(elem!1)), elem!1)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[30751, 36811, 36670, 36752, 36797])).
% 12.39/12.64 tff(36813,plain,
% 12.39/12.64 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36807])).
% 12.39/12.64 tff(36814,plain,
% 12.39/12.64 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36813])).
% 12.39/12.64 tff(36815,plain,
% 12.39/12.64 (~(s(s(elem!1)) = elem!1)),
% 12.39/12.64 inference(modus_ponens,[status(thm)],[357, 36814])).
% 12.39/12.64 tff(36816,plain,
% 12.39/12.64 (r(s(s(elem!1)), elem!1)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[872, 36812, 36815])).
% 12.39/12.64 tff(36817,plain,
% 12.39/12.64 (b(s(z), z) <=> b(elem!1, z)),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36807])).
% 12.39/12.64 tff(36818,plain,
% 12.39/12.64 (b(elem!1, z)),
% 12.39/12.64 inference(modus_ponens,[status(thm)],[36797, 36817])).
% 12.39/12.64 tff(36819,plain,
% 12.39/12.64 (~b(s(s(s(elem!1))), elem!1)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[28903, 36818, 36670, 36810])).
% 12.39/12.64 tff(36820,plain,
% 12.39/12.64 (~b(s(s(s(elem!1))), s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[3938, 36819, 36807])).
% 12.39/12.64 tff(36821,plain,
% 12.39/12.64 (r(s(s(s(elem!1))), s(z))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[223, 36820])).
% 12.39/12.64 tff(36822,plain,
% 12.39/12.64 (elem!1 = s(z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[1495, 36807])).
% 12.39/12.64 tff(36823,plain,
% 12.39/12.64 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[29438, 36822])).
% 12.39/12.64 tff(36824,plain,
% 12.39/12.64 (~b(s(s(s(elem!1))), z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[29435, 36823, 3446])).
% 12.39/12.64 tff(36825,plain,
% 12.39/12.64 (r(s(s(s(elem!1))), z)),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[377, 36824])).
% 12.39/12.64 tff(36826,plain,
% 12.39/12.64 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 12.39/12.64 inference(unit_resolution,[status(thm)],[3482, 36822, 36752])).
% 12.39/12.64 tff(36827,plain,
% 12.39/12.64 (s(s(z)) = s(elem!1)),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36807])).
% 12.39/12.64 tff(36828,plain,
% 12.39/12.64 (s(s(s(z))) = s(s(elem!1))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36827])).
% 12.39/12.64 tff(36829,plain,
% 12.39/12.64 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36828])).
% 12.39/12.64 tff(36830,plain,
% 12.39/12.64 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36829])).
% 12.39/12.64 tff(36831,plain,
% 12.39/12.64 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 12.39/12.64 inference(symmetry,[status(thm)],[36830])).
% 12.39/12.64 tff(36832,plain,
% 12.39/12.64 (b(z, s(s(s(s(z)))))),
% 12.39/12.64 inference(modus_ponens,[status(thm)],[36670, 36831])).
% 12.39/12.64 tff(36833,plain,
% 12.39/12.64 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[820, 818])).
% 12.39/12.64 tff(36834,plain,
% 12.39/12.64 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.64 inference(symmetry,[status(thm)],[36833])).
% 12.39/12.64 tff(36835,plain,
% 12.39/12.64 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 12.39/12.64 inference(monotonicity,[status(thm)],[36834])).
% 12.39/12.64 tff(36836,plain,
% 12.39/12.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 12.39/12.65 inference(rewrite,[status(thm)],[])).
% 12.39/12.65 tff(36837,plain,
% 12.39/12.65 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 12.39/12.65 inference(rewrite,[status(thm)],[])).
% 12.39/12.65 tff(36838,plain,
% 12.39/12.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(z))))))),
% 12.39/12.65 inference(monotonicity,[status(thm)],[36837])).
% 12.39/12.65 tff(36839,plain,
% 12.39/12.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 12.39/12.65 inference(transitivity,[status(thm)],[36838, 36836])).
% 12.39/12.65 tff(36840,plain,
% 12.39/12.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 12.39/12.65 inference(quant_inst,[status(thm)],[])).
% 12.39/12.65 tff(36841,plain,
% 12.39/12.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(z))))),
% 12.39/12.65 inference(modus_ponens,[status(thm)],[36840, 36839])).
% 12.39/12.65 tff(36842,plain,
% 12.39/12.65 ($false),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[36841, 391, 1235, 2439, 1686, 590, 1232])).
% 12.39/12.65 tff(36843,plain,((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.65 tff(36844,plain,
% 12.39/12.65 (~b(s(s(z)), z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[36843, 2439, 590, 1232, 1686])).
% 12.39/12.65 tff(36845,plain,
% 12.39/12.65 (r(s(s(z)), z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[1211, 36844])).
% 12.39/12.65 tff(36846,plain,
% 12.39/12.65 (r(s(elem!1), z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[3560, 36845, 812])).
% 12.39/12.65 tff(36847,plain,
% 12.39/12.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[18118, 194, 411, 36846, 174])).
% 12.39/12.65 tff(36848,plain,
% 12.39/12.65 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.65 inference(modus_ponens,[status(thm)],[36847, 36835])).
% 12.39/12.65 tff(36849,plain,
% 12.39/12.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 12.39/12.65 inference(rewrite,[status(thm)],[])).
% 12.39/12.65 tff(36850,plain,
% 12.39/12.65 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 12.39/12.65 inference(rewrite,[status(thm)],[])).
% 12.39/12.65 tff(36851,plain,
% 12.39/12.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 12.39/12.65 inference(monotonicity,[status(thm)],[36850])).
% 12.39/12.65 tff(36852,plain,
% 12.39/12.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 12.39/12.65 inference(transitivity,[status(thm)],[36851, 36849])).
% 12.39/12.65 tff(36853,plain,
% 12.39/12.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 12.39/12.65 inference(quant_inst,[status(thm)],[])).
% 12.39/12.65 tff(36854,plain,
% 12.39/12.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 12.39/12.65 inference(modus_ponens,[status(thm)],[36853, 36852])).
% 12.39/12.65 tff(36855,plain,
% 12.39/12.65 (~r(s(elem!1), s(s(s(elem!1))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[36854, 194, 411, 36846, 174])).
% 12.39/12.65 tff(36856,plain,
% 12.39/12.65 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[3614, 36855, 812])).
% 12.39/12.65 tff(36857,plain,
% 12.39/12.65 (b(s(s(z)), s(s(s(s(z)))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[3652, 36856])).
% 12.39/12.65 tff(36858,plain,
% 12.39/12.65 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[6275, 36857, 1234, 2439])).
% 12.39/12.65 tff(36859,plain,
% 12.39/12.65 (r(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[1714, 36858])).
% 12.39/12.65 tff(36860,plain,
% 12.39/12.65 ($false),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[36859, 36848])).
% 12.39/12.65 tff(36861,plain,((~b(s(z), s(s(z)))) | (~(s(z) = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.65 tff(36862,plain,
% 12.39/12.65 (~b(s(z), s(s(z)))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[36861, 36832, 36606, 1234, 36797, 36807, 36826, 36825])).
% 12.39/12.65 tff(36863,plain,
% 12.39/12.65 (r(s(z), s(s(z)))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[1788, 36862])).
% 12.39/12.65 tff(36864,plain,
% 12.39/12.65 (~r(z, s(s(s(elem!1))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[22159, 36821, 722, 36863])).
% 12.39/12.65 tff(36865,plain,
% 12.39/12.65 (~(s(s(s(elem!1))) = elem!1)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[10792, 411, 53])).
% 12.39/12.65 tff(36866,plain,
% 12.39/12.65 (~r(s(z), s(s(s(elem!1))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[23631, 168, 183, 270, 10782, 1374, 411, 364, 590, 2, 36865, 4017])).
% 12.39/12.65 tff(36867,plain,
% 12.39/12.65 (b(s(z), s(s(s(elem!1))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[247, 36866])).
% 12.39/12.65 tff(36868,plain,
% 12.39/12.65 (~b(s(s(s(elem!1))), z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[11303, 36867, 10782, 590])).
% 12.39/12.65 tff(36869,plain,
% 12.39/12.65 (r(s(s(s(elem!1))), z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[377, 36868])).
% 12.39/12.65 tff(36870,plain,
% 12.39/12.65 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[11294, 36869, 590, 10782, 411, 2053, 36867])).
% 12.39/12.65 tff(36871,plain,
% 12.39/12.65 (s(z) = elem!1),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[2849, 36870])).
% 12.39/12.65 tff(36872,plain,
% 12.39/12.65 (s(s(z)) = s(elem!1)),
% 12.39/12.65 inference(monotonicity,[status(thm)],[36871])).
% 12.39/12.65 tff(36873,plain,
% 12.39/12.65 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 12.39/12.65 inference(monotonicity,[status(thm)],[36872])).
% 12.39/12.65 tff(36874,plain,
% 12.39/12.65 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 12.39/12.65 inference(monotonicity,[status(thm)],[36871])).
% 12.39/12.65 tff(36875,plain,
% 12.39/12.65 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 12.39/12.65 inference(transitivity,[status(thm)],[36874, 36873])).
% 12.39/12.65 tff(36876,plain,
% 12.39/12.65 (~r(z, s(s(s(s(z)))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[10733, 36871, 53])).
% 12.39/12.65 tff(36877,plain,
% 12.39/12.65 (b(z, s(s(s(s(z)))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[800, 36876])).
% 12.39/12.65 tff(36878,plain,
% 12.39/12.65 (elem!1 = s(z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[1495, 36871])).
% 12.39/12.65 tff(36879,plain,
% 12.39/12.65 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[3482, 36878, 1374])).
% 12.39/12.65 tff(36880,plain,
% 12.39/12.65 (b(s(z), s(s(s(s(z)))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[2884, 36878, 36867])).
% 12.39/12.65 tff(36881,plain,
% 12.39/12.65 (~b(s(z), s(s(z)))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[36861, 36871, 36880, 411, 36869, 590, 36879, 36877])).
% 12.39/12.65 tff(36882,plain,
% 12.39/12.65 (r(s(z), s(s(z)))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[1788, 36881])).
% 12.39/12.65 tff(36883,plain,
% 12.39/12.65 (r(elem!1, s(elem!1))),
% 12.39/12.65 inference(modus_ponens,[status(thm)],[36882, 36875])).
% 12.39/12.65 tff(36884,plain,
% 12.39/12.65 (r(s(s(s(elem!1))), elem!1)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[230, 168, 36865])).
% 12.39/12.65 tff(36885,plain,
% 12.39/12.65 ($false),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[18136, 194, 411, 36869, 36884, 36883])).
% 12.39/12.65 tff(36886,plain,(b(s(s(s(elem!1))), elem!1) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | r(z, s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.65 tff(36887,plain,
% 12.39/12.65 ($false),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[36886, 36864, 36821, 29426, 36606, 36752, 36797, 36819, 270, 36816, 2, 36812])).
% 12.39/12.65 tff(36888,plain,((~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = z) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(s(s(z)))), z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.65 tff(36889,plain,
% 12.39/12.65 (~r(z, s(z))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[36888, 3446, 2, 36748, 36720, 31])).
% 12.39/12.65 tff(36890,plain,
% 12.39/12.65 (b(z, s(z))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[678, 36889])).
% 12.39/12.65 tff(36891,plain,
% 12.39/12.65 (b(s(z), z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[36796, 3446, 36748, 2, 31])).
% 12.39/12.65 tff(36892,plain,
% 12.39/12.65 (~r(s(s(s(s(z)))), elem!1)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[10408, 838, 29426, 36606])).
% 12.39/12.65 tff(36893,plain,
% 12.39/12.65 (~b(s(s(s(elem!1))), s(z))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[10690, 664, 36670, 590])).
% 12.39/12.65 tff(36894,plain,
% 12.39/12.65 (r(s(s(s(elem!1))), s(z))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[223, 36893])).
% 12.39/12.65 tff(36895,plain,
% 12.39/12.65 (~b(s(s(s(elem!1))), z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[11303, 379, 10682, 590])).
% 12.39/12.65 tff(36896,plain,
% 12.39/12.65 (~r(s(s(s(elem!1))), z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[11294, 379, 2053, 411, 10682, 3843, 590])).
% 12.39/12.65 tff(36897,plain,
% 12.39/12.65 ($false),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[377, 36896, 36895])).
% 12.39/12.65 tff(36898,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.65 tff(36899,plain,
% 12.39/12.65 (~b(s(z), s(s(s(elem!1))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[36898, 3363, 36606, 36670, 29426, 590])).
% 12.39/12.65 tff(36900,plain,
% 12.39/12.65 (r(s(z), s(s(s(elem!1))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[247, 36899])).
% 12.39/12.65 tff(36901,plain,
% 12.39/12.65 (~r(elem!1, s(s(s(elem!1))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[22955, 194, 36900, 36894, 838])).
% 12.39/12.65 tff(36902,plain,
% 12.39/12.65 (b(elem!1, s(s(s(elem!1))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[424, 36901, 36671])).
% 12.39/12.65 tff(36903,plain,
% 12.39/12.65 (~b(elem!1, z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[28909, 36902, 36606, 36670, 36686, 838])).
% 12.39/12.65 tff(36904,plain,
% 12.39/12.65 (r(elem!1, z)),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[526, 36903, 2])).
% 12.39/12.65 tff(36905,plain,
% 12.39/12.65 (~r(elem!1, s(s(s(s(z)))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[17579, 194, 36606, 36904, 29426])).
% 12.39/12.65 tff(36906,plain,
% 12.39/12.65 (~b(z, s(s(s(s(z)))))),
% 12.39/12.65 inference(unit_resolution,[status(thm)],[18671, 36905, 89, 36748, 590, 36892])).
% 12.39/12.66 tff(36907,plain,
% 12.39/12.66 (r(z, s(s(s(s(z)))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[800, 36906])).
% 12.39/12.66 tff(36908,plain,
% 12.39/12.66 (~r(s(s(s(elem!1))), elem!1)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[5762, 194, 36900, 36894, 838])).
% 12.39/12.66 tff(36909,plain,
% 12.39/12.66 (b(s(s(s(elem!1))), elem!1)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[230, 36908, 36686])).
% 12.39/12.66 tff(36910,plain,
% 12.39/12.66 (~(s(elem!1) = elem!1)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[158, 36686])).
% 12.39/12.66 tff(36911,plain,
% 12.39/12.66 (~r(s(s(s(s(z)))), elem!1)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[10408, 847, 2053, 411])).
% 12.39/12.66 tff(36912,plain,
% 12.39/12.66 (~r(elem!1, s(s(s(s(z)))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[17579, 194, 411, 530, 2053])).
% 12.39/12.66 tff(36913,plain,
% 12.39/12.66 (~b(s(z), elem!1)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[18869, 720, 1234, 36912, 36911])).
% 12.39/12.66 tff(36914,plain,
% 12.39/12.66 (r(s(z), elem!1)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[632, 36913, 150])).
% 12.39/12.66 tff(36915,plain,
% 12.39/12.66 (~b(s(z), s(s(s(elem!1))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[36898, 3363, 411, 10682, 2053, 590])).
% 12.39/12.66 tff(36916,plain,
% 12.39/12.66 (r(s(z), s(s(s(elem!1))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[247, 36915])).
% 12.39/12.66 tff(36917,plain,
% 12.39/12.66 (b(s(s(s(s(z)))), elem!1)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[762, 720, 36911])).
% 12.39/12.66 tff(36918,plain,
% 12.39/12.66 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[16841, 391, 900, 448, 36917])).
% 12.39/12.66 tff(36919,plain,
% 12.39/12.66 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[15351, 36918, 16830])).
% 12.39/12.66 tff(36920,plain,
% 12.39/12.66 (~r(s(s(s(s(z)))), s(z))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[33040, 36919, 28299, 36916])).
% 12.39/12.66 tff(36921,plain,
% 12.39/12.66 (b(s(s(s(s(z)))), s(z))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[749, 36920])).
% 12.39/12.66 tff(36922,plain,
% 12.39/12.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 12.39/12.66 inference(rewrite,[status(thm)],[])).
% 12.39/12.66 tff(36923,plain,
% 12.39/12.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 12.39/12.66 inference(quant_inst,[status(thm)],[])).
% 12.39/12.66 tff(36924,plain,
% 12.39/12.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 12.39/12.66 inference(modus_ponens,[status(thm)],[36923, 36922])).
% 12.39/12.66 tff(36925,plain,
% 12.39/12.66 (~b(s(s(z)), s(z))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[36924, 391, 900, 10682, 1235, 590])).
% 12.39/12.66 tff(36926,plain,
% 12.39/12.66 (r(s(s(z)), s(z))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[3778, 36925])).
% 12.39/12.66 tff(36927,plain,
% 12.39/12.66 (~r(s(s(z)), elem!1)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[6674, 36926, 847, 1484])).
% 12.39/12.66 tff(36928,plain,
% 12.39/12.66 (b(s(s(z)), elem!1)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[4730, 36927, 26332])).
% 12.39/12.66 tff(36929,plain,
% 12.39/12.66 (~b(s(z), s(s(z)))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[17302, 391, 900, 10682, 1235, 590])).
% 12.39/12.66 tff(36930,plain,
% 12.39/12.66 (r(s(z), s(s(z)))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[1788, 36929])).
% 12.39/12.66 tff(36931,plain,
% 12.39/12.66 (~b(elem!1, s(s(z)))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[10933, 36926, 448, 183, 1484])).
% 12.39/12.66 tff(36932,plain,
% 12.39/12.66 (r(elem!1, s(s(z)))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[3394, 36931, 20632])).
% 12.39/12.66 tff(36933,plain,
% 12.39/12.66 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[1775, 36932, 1759, 150, 1652, 36930])).
% 12.39/12.66 tff(36934,plain,
% 12.39/12.66 (b(s(s(z)), s(s(s(s(z)))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[3652, 36933])).
% 12.39/12.66 tff(36935,plain,
% 12.39/12.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 12.39/12.66 inference(rewrite,[status(thm)],[])).
% 12.39/12.66 tff(36936,plain,
% 12.39/12.66 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 12.39/12.66 inference(rewrite,[status(thm)],[])).
% 12.39/12.66 tff(36937,plain,
% 12.39/12.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 12.39/12.66 inference(monotonicity,[status(thm)],[36936])).
% 12.39/12.66 tff(36938,plain,
% 12.39/12.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 12.39/12.66 inference(transitivity,[status(thm)],[36937, 36935])).
% 12.39/12.66 tff(36939,plain,
% 12.39/12.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 12.39/12.66 inference(quant_inst,[status(thm)],[])).
% 12.39/12.66 tff(36940,plain,
% 12.39/12.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))),
% 12.39/12.66 inference(modus_ponens,[status(thm)],[36939, 36938])).
% 12.39/12.66 tff(36941,plain,
% 12.39/12.66 ($false),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[36940, 391, 900, 448, 36934, 1652, 36928])).
% 12.39/12.66 tff(36942,plain,((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (s(z) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.66 tff(36943,plain,
% 12.39/12.66 (~b(s(s(z)), z)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[36942, 36917, 448, 900, 36921, 150, 28299, 36914, 847, 10682, 590, 484])).
% 12.39/12.66 tff(36944,plain,
% 12.39/12.66 (r(s(s(z)), z)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[1211, 36943])).
% 12.39/12.66 tff(36945,plain,
% 12.39/12.66 (~r(elem!1, s(s(z)))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[8570, 36944, 719, 530])).
% 12.39/12.66 tff(36946,plain,
% 12.39/12.66 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[31283, 36944, 2053, 719])).
% 12.39/12.66 tff(36947,plain,
% 12.39/12.66 (b(s(s(z)), s(s(s(s(z)))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[3652, 36946])).
% 12.39/12.66 tff(36948,plain,
% 12.39/12.66 (~b(s(s(z)), s(z))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[5108, 36947, 1234, 36921])).
% 12.39/12.66 tff(36949,plain,
% 12.39/12.66 (r(s(s(z)), s(z))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[3778, 36948])).
% 12.39/12.66 tff(36950,plain,
% 12.39/12.66 (~b(elem!1, s(s(z)))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[10933, 36949, 448, 28299, 36914])).
% 12.39/12.66 tff(36951,plain,
% 12.39/12.66 (elem!1 = s(s(z))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[3394, 36950, 36945])).
% 12.39/12.66 tff(36952,plain,
% 12.39/12.66 (s(elem!1) = s(s(s(z)))),
% 12.39/12.66 inference(monotonicity,[status(thm)],[36951])).
% 12.39/12.66 tff(36953,plain,
% 12.39/12.66 (s(s(elem!1)) = s(s(s(s(z))))),
% 12.39/12.66 inference(monotonicity,[status(thm)],[36952])).
% 12.39/12.66 tff(36954,plain,
% 12.39/12.66 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 12.39/12.66 inference(monotonicity,[status(thm)],[36953])).
% 12.39/12.66 tff(36955,plain,
% 12.39/12.66 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 12.39/12.66 inference(monotonicity,[status(thm)],[36952, 36954])).
% 12.39/12.66 tff(36956,plain,
% 12.39/12.66 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 12.39/12.66 inference(symmetry,[status(thm)],[36955])).
% 12.39/12.66 tff(36957,plain,
% 12.39/12.66 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(z))))), z)),
% 12.39/12.66 inference(monotonicity,[status(thm)],[36954])).
% 12.39/12.66 tff(36958,plain,
% 12.39/12.66 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[16858, 391, 900, 448, 36917])).
% 12.39/12.66 tff(36959,plain,
% 12.39/12.66 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[2853, 42, 3363, 36958])).
% 12.39/12.66 tff(36960,plain,
% 12.39/12.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.39/12.66 inference(rewrite,[status(thm)],[])).
% 12.39/12.66 tff(36961,plain,
% 12.39/12.66 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.39/12.66 inference(rewrite,[status(thm)],[])).
% 12.39/12.66 tff(36962,plain,
% 12.39/12.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 12.39/12.66 inference(monotonicity,[status(thm)],[36961])).
% 12.39/12.66 tff(36963,plain,
% 12.39/12.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.39/12.66 inference(transitivity,[status(thm)],[36962, 36960])).
% 12.39/12.66 tff(36964,plain,
% 12.39/12.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))),
% 12.39/12.66 inference(quant_inst,[status(thm)],[])).
% 12.39/12.66 tff(36965,plain,
% 12.39/12.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 12.39/12.66 inference(modus_ponens,[status(thm)],[36964, 36963])).
% 12.39/12.66 tff(36966,plain,
% 12.39/12.66 (~r(s(s(s(elem!1))), z)),
% 12.39/12.66 inference(unit_resolution,[status(thm)],[36965, 194, 719, 36959, 36919])).
% 12.39/12.67 tff(36967,plain,
% 12.39/12.67 (b(s(s(s(elem!1))), z)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[377, 36966])).
% 12.39/12.67 tff(36968,plain,
% 12.39/12.67 (b(s(s(s(s(s(z))))), z)),
% 12.39/12.67 inference(modus_ponens,[status(thm)],[36967, 36957])).
% 12.39/12.67 tff(36969,plain,
% 12.39/12.67 (r(s(elem!1), z) <=> r(s(s(s(z))), z)),
% 12.39/12.67 inference(monotonicity,[status(thm)],[36952])).
% 12.39/12.67 tff(36970,plain,
% 12.39/12.67 ((~r(s(elem!1), z)) <=> (~r(s(s(s(z))), z))),
% 12.39/12.67 inference(monotonicity,[status(thm)],[36969])).
% 12.39/12.67 tff(36971,plain,
% 12.39/12.67 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(z)))),
% 12.39/12.67 inference(monotonicity,[status(thm)],[36951])).
% 12.39/12.67 tff(36972,plain,
% 12.39/12.67 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 12.39/12.67 inference(symmetry,[status(thm)],[36971])).
% 12.39/12.67 tff(36973,plain,
% 12.39/12.67 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = elem!1))),
% 12.39/12.67 inference(monotonicity,[status(thm)],[36972])).
% 12.39/12.67 tff(36974,plain,
% 12.39/12.67 (~(s(s(elem!1)) = elem!1)),
% 12.39/12.67 inference(modus_ponens,[status(thm)],[11940, 36973])).
% 12.39/12.67 tff(36975,plain,
% 12.39/12.67 (~(s(s(elem!1)) = s(elem!1))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[264, 36974])).
% 12.39/12.67 tff(36976,plain,
% 12.39/12.67 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(z)))),
% 12.39/12.67 inference(monotonicity,[status(thm)],[36951])).
% 12.39/12.67 tff(36977,plain,
% 12.39/12.67 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 12.39/12.67 inference(symmetry,[status(thm)],[36976])).
% 12.39/12.67 tff(36978,plain,
% 12.39/12.67 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.67 inference(monotonicity,[status(thm)],[36953])).
% 12.39/12.67 tff(36979,plain,
% 12.39/12.67 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 12.39/12.67 inference(symmetry,[status(thm)],[36978])).
% 12.39/12.67 tff(36980,plain,
% 12.39/12.67 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 12.39/12.67 inference(transitivity,[status(thm)],[36979, 36977])).
% 12.39/12.67 tff(36981,plain,
% 12.39/12.67 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.67 inference(monotonicity,[status(thm)],[36951])).
% 12.39/12.67 tff(36982,plain,
% 12.39/12.67 (b(s(s(s(s(z)))), s(s(z)))),
% 12.39/12.67 inference(modus_ponens,[status(thm)],[36917, 36981])).
% 12.39/12.67 tff(36983,plain,
% 12.39/12.67 (b(s(s(elem!1)), elem!1)),
% 12.39/12.67 inference(modus_ponens,[status(thm)],[36982, 36980])).
% 12.39/12.67 tff(36984,plain,
% 12.39/12.67 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 12.39/12.67 inference(symmetry,[status(thm)],[36954])).
% 12.39/12.67 tff(36985,plain,
% 12.39/12.67 (s(s(s(z))) = s(elem!1)),
% 12.39/12.67 inference(symmetry,[status(thm)],[36952])).
% 12.39/12.67 tff(36986,plain,
% 12.39/12.67 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 12.39/12.67 inference(monotonicity,[status(thm)],[36985, 36984])).
% 12.39/12.67 tff(36987,plain,
% 12.39/12.67 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 12.39/12.67 inference(transitivity,[status(thm)],[36986, 582])).
% 12.39/12.67 tff(36988,plain,
% 12.39/12.67 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 12.39/12.67 inference(monotonicity,[status(thm)],[36987])).
% 12.39/12.67 tff(36989,plain,
% 12.39/12.67 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.39/12.67 inference(modus_ponens,[status(thm)],[8593, 36988])).
% 12.39/12.67 tff(36990,plain,
% 12.39/12.67 (~(s(elem!1) = s(s(elem!1)))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[9802, 36975])).
% 12.39/12.67 tff(36991,plain,
% 12.39/12.67 (~r(s(elem!1), z)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[28613, 36990, 448, 36989, 36967, 36983, 36975, 297, 10682, 411, 164, 530])).
% 12.39/12.67 tff(36992,plain,
% 12.39/12.67 (~r(s(s(s(z))), z)),
% 12.39/12.67 inference(modus_ponens,[status(thm)],[36991, 36970])).
% 12.39/12.67 tff(36993,plain,
% 12.39/12.67 (b(s(s(s(z))), z)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[8765, 42, 741, 36992])).
% 12.39/12.67 tff(36994,plain,
% 12.39/12.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 12.39/12.67 inference(rewrite,[status(thm)],[])).
% 12.39/12.67 tff(36995,plain,
% 12.39/12.67 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 12.39/12.67 inference(rewrite,[status(thm)],[])).
% 12.39/12.67 tff(36996,plain,
% 12.39/12.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 12.39/12.67 inference(monotonicity,[status(thm)],[36995])).
% 12.39/12.67 tff(36997,plain,
% 12.39/12.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 12.39/12.67 inference(transitivity,[status(thm)],[36996, 36994])).
% 12.39/12.67 tff(36998,plain,
% 12.39/12.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 12.39/12.67 inference(quant_inst,[status(thm)],[])).
% 12.39/12.67 tff(36999,plain,
% 12.39/12.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 12.39/12.67 inference(modus_ponens,[status(thm)],[36998, 36997])).
% 12.39/12.67 tff(37000,plain,
% 12.39/12.67 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[36999, 391, 1234, 664, 36993, 36968])).
% 12.39/12.67 tff(37001,plain,
% 12.39/12.67 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[21879, 37000])).
% 12.39/12.67 tff(37002,plain,
% 12.39/12.67 (r(s(elem!1), s(s(s(elem!1))))),
% 12.39/12.67 inference(modus_ponens,[status(thm)],[37001, 36956])).
% 12.39/12.67 tff(37003,plain,
% 12.39/12.67 (~b(s(elem!1), z)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[12799, 1101, 10682, 380])).
% 12.39/12.67 tff(37004,plain,
% 12.39/12.67 (r(s(elem!1), z)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[549, 37003])).
% 12.39/12.67 tff(37005,plain,
% 12.39/12.67 (~b(s(elem!1), elem!1)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[6869, 1101, 448, 900])).
% 12.39/12.67 tff(37006,plain,
% 12.39/12.67 (r(s(elem!1), elem!1)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[2168, 37005, 164])).
% 12.39/12.67 tff(37007,plain,
% 12.39/12.67 ($false),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[541, 37006, 37004, 411, 530])).
% 12.39/12.67 tff(37008,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(elem!1) = elem!1) | (~b(elem!1, s(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))), z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.67 tff(37009,plain,
% 12.39/12.67 (~b(s(s(s(elem!1))), s(elem!1))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[37008, 36967, 411, 164, 448, 900, 10682, 530])).
% 12.39/12.67 tff(37010,plain,
% 12.39/12.67 (r(s(s(s(elem!1))), s(elem!1))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[588, 36989, 37009])).
% 12.39/12.67 tff(37011,plain,
% 12.39/12.67 (b(s(elem!1), z)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[549, 36991])).
% 12.39/12.67 tff(37012,plain,
% 12.39/12.67 (~r(s(elem!1), s(s(s(elem!1))))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[12813, 37011, 121, 10682, 590, 36967, 37010])).
% 12.39/12.67 tff(37013,plain,
% 12.39/12.67 ($false),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[37012, 37002])).
% 12.39/12.67 tff(37014,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(z))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.67 tff(37015,plain,
% 12.39/12.67 (s(s(s(s(z)))) = elem!1),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[37014, 36902, 664, 118, 36670, 590, 36748, 36719, 36606, 36910, 36904, 36907, 29426, 36909, 150, 838, 36903])).
% 12.39/12.67 tff(37016,plain,
% 12.39/12.67 (b(s(z), elem!1)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[8916, 37015, 36748])).
% 12.39/12.67 tff(37017,plain,
% 12.39/12.67 (~r(z, s(s(z)))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[8513, 6668, 411, 530])).
% 12.39/12.67 tff(37018,plain,
% 12.39/12.67 (~r(s(s(z)), z)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[31283, 1749, 2053, 719])).
% 12.39/12.67 tff(37019,plain,
% 12.39/12.67 (b(s(s(z)), z)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[1211, 37018])).
% 12.39/12.67 tff(37020,plain,
% 12.39/12.67 (~b(z, s(s(z)))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[17567, 37019, 590, 847, 36911, 644, 715, 1749])).
% 12.39/12.67 tff(37021,plain,
% 12.39/12.67 ($false),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[18613, 37020, 37017])).
% 12.39/12.67 tff(37022,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.67 tff(37023,plain,
% 12.39/12.67 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[37022, 37016, 838, 590, 36606, 36904, 37015, 29426, 36907])).
% 12.39/12.67 tff(37024,plain,
% 12.39/12.67 (~b(s(s(s(s(z)))), s(z))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[11186, 37015, 31])).
% 12.39/12.67 tff(37025,plain,
% 12.39/12.67 (r(s(s(s(s(z)))), s(z))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[749, 37024])).
% 12.39/12.67 tff(37026,plain,
% 12.39/12.67 (b(s(s(z)), elem!1)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[30679, 3823, 688])).
% 12.39/12.67 tff(37027,plain,
% 12.39/12.67 (~b(s(s(z)), s(s(s(elem!1))))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[16878, 391, 900, 22957, 37026])).
% 12.39/12.67 tff(37028,plain,
% 12.39/12.67 (b(s(z), elem!1)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[8916, 688, 1234])).
% 12.39/12.67 tff(37029,plain,
% 12.39/12.67 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[33040, 232, 183, 723])).
% 12.39/12.67 tff(37030,plain,
% 12.39/12.67 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[15351, 37029, 15348])).
% 12.39/12.67 tff(37031,plain,
% 12.39/12.67 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[2865, 22957, 688])).
% 12.39/12.67 tff(37032,plain,
% 12.39/12.67 (~r(s(s(s(elem!1))), z)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[18687, 37031, 1234, 3823, 232, 37030])).
% 12.39/12.67 tff(37033,plain,
% 12.39/12.67 (b(s(s(s(elem!1))), z)),
% 12.39/12.67 inference(unit_resolution,[status(thm)],[377, 37032])).
% 12.39/12.67 tff(37034,plain,
% 12.39/12.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 12.39/12.67 inference(rewrite,[status(thm)],[])).
% 12.39/12.67 tff(37035,plain,
% 12.39/12.67 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 12.39/12.67 inference(rewrite,[status(thm)],[])).
% 12.39/12.67 tff(37036,plain,
% 12.39/12.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 12.39/12.67 inference(monotonicity,[status(thm)],[37035])).
% 12.39/12.68 tff(37037,plain,
% 12.39/12.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 12.39/12.68 inference(transitivity,[status(thm)],[37036, 37034])).
% 12.39/12.68 tff(37038,plain,
% 12.39/12.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 12.39/12.68 inference(quant_inst,[status(thm)],[])).
% 12.39/12.68 tff(37039,plain,
% 12.39/12.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 12.39/12.68 inference(modus_ponens,[status(thm)],[37038, 37037])).
% 12.39/12.68 tff(37040,plain,
% 12.39/12.68 (~b(s(s(z)), s(z))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[37039, 391, 37033, 22957, 37028, 37026])).
% 12.39/12.68 tff(37041,plain,
% 12.39/12.68 (r(s(s(z)), s(z))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[3778, 37040])).
% 12.39/12.68 tff(37042,plain,
% 12.39/12.68 (~r(s(s(z)), s(s(s(elem!1))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[18934, 194, 232, 183, 37041])).
% 12.39/12.68 tff(37043,plain,
% 12.39/12.68 ($false),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[11041, 37042, 37027])).
% 12.39/12.68 tff(37044,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.68 tff(37045,plain,
% 12.39/12.68 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[37044, 37025, 36894, 36748, 36900, 36909, 36671, 838, 16830, 37015])).
% 12.39/12.68 tff(37046,plain,
% 12.39/12.68 ($false),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[3652, 37045, 37023])).
% 12.39/12.68 tff(37047,plain,((s(z) = elem!1) | (~b(s(z), z)) | b(elem!1, s(z)) | (~b(z, s(z))) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.68 tff(37048,plain,
% 12.39/12.68 (s(z) = elem!1),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[37047, 36891, 31, 36890, 89, 2])).
% 12.39/12.68 tff(37049,plain,
% 12.39/12.68 (r(z, s(z)) <=> r(z, elem!1)),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37048])).
% 12.39/12.68 tff(37050,plain,
% 12.39/12.68 (r(z, elem!1) <=> r(z, s(z))),
% 12.39/12.68 inference(symmetry,[status(thm)],[37049])).
% 12.39/12.68 tff(37051,plain,
% 12.39/12.68 (r(z, s(z))),
% 12.39/12.68 inference(modus_ponens,[status(thm)],[36606, 37050])).
% 12.39/12.68 tff(37052,plain,
% 12.39/12.68 ($false),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[36889, 37051])).
% 12.39/12.68 tff(37053,plain,(b(s(s(s(s(z)))), z) | b(elem!1, s(z)) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.68 tff(37054,plain,
% 12.39/12.68 (b(s(s(s(s(z)))), z)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[37053, 31, 89, 2])).
% 12.39/12.68 tff(37055,plain,
% 12.39/12.68 (s(z) = elem!1),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[28962, 37054, 36606, 31, 36671, 36748, 2])).
% 12.39/12.68 tff(37056,plain,
% 12.39/12.68 ($false),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[28819, 37055, 37054, 2, 36606, 36686, 36748])).
% 12.39/12.68 tff(37057,plain,(b(elem!1, s(z)) | (elem!1 = z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.68 tff(37058,plain,
% 12.39/12.68 (b(elem!1, s(z))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[37057, 89, 2])).
% 12.39/12.68 tff(37059,plain,
% 12.39/12.68 (~r(s(z), s(s(s(s(z)))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[2061, 181, 29426, 36606])).
% 12.39/12.68 tff(37060,plain,
% 12.39/12.68 (b(s(z), s(s(s(s(z)))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[1230, 37059])).
% 12.39/12.68 tff(37061,plain,
% 12.39/12.68 (~b(s(s(s(s(z)))), elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[2080, 391, 37060, 36754, 37058])).
% 12.39/12.68 tff(37062,plain,
% 12.39/12.68 (b(z, s(s(s(elem!1))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[36668, 91, 37058, 2])).
% 12.39/12.68 tff(37063,plain,
% 12.39/12.68 (~r(s(s(s(s(z)))), s(z))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[3243, 182, 29426, 36606])).
% 12.39/12.68 tff(37064,plain,
% 12.39/12.68 (b(s(s(s(s(z)))), s(z))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[749, 37063])).
% 12.39/12.68 tff(37065,plain,
% 12.39/12.68 (~r(s(z), s(s(s(s(z)))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[2061, 182, 29426, 36606])).
% 12.39/12.68 tff(37066,plain,
% 12.39/12.68 (b(s(z), s(s(s(s(z)))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[1230, 37065])).
% 12.39/12.68 tff(37067,plain,
% 12.39/12.68 (~b(elem!1, s(s(s(s(z)))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[2088, 391, 37066, 37064, 37058])).
% 12.39/12.68 tff(37068,plain,
% 12.39/12.68 (~r(elem!1, s(s(s(s(z)))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[17579, 194, 36606, 3618, 29426])).
% 12.39/12.68 tff(37069,plain,
% 12.39/12.68 (elem!1 = s(s(s(s(z))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[781, 37068, 37067])).
% 12.39/12.68 tff(37070,plain,
% 12.39/12.68 (s(elem!1) = s(s(s(s(s(z)))))),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37069])).
% 12.39/12.68 tff(37071,plain,
% 12.39/12.68 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37070])).
% 12.39/12.68 tff(37072,plain,
% 12.39/12.68 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37071])).
% 12.39/12.68 tff(37073,plain,
% 12.39/12.68 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 12.39/12.68 inference(symmetry,[status(thm)],[37072])).
% 12.39/12.68 tff(37074,plain,
% 12.39/12.68 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37073])).
% 12.39/12.68 tff(37075,plain,
% 12.39/12.68 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 12.39/12.68 inference(symmetry,[status(thm)],[37074])).
% 12.39/12.68 tff(37076,plain,
% 12.39/12.68 (s(s(s(s(s(z))))) = s(elem!1)),
% 12.39/12.68 inference(symmetry,[status(thm)],[37070])).
% 12.39/12.68 tff(37077,plain,
% 12.39/12.68 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37076])).
% 12.39/12.68 tff(37078,plain,
% 12.39/12.68 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 12.39/12.68 inference(transitivity,[status(thm)],[37077, 582])).
% 12.39/12.68 tff(37079,plain,
% 12.39/12.68 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 12.39/12.68 inference(symmetry,[status(thm)],[37078])).
% 12.39/12.68 tff(37080,plain,
% 12.39/12.68 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37079])).
% 12.39/12.68 tff(37081,plain,
% 12.39/12.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 12.39/12.68 inference(rewrite,[status(thm)],[])).
% 12.39/12.68 tff(37082,plain,
% 12.39/12.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 12.39/12.68 inference(quant_inst,[status(thm)],[])).
% 12.39/12.68 tff(37083,plain,
% 12.39/12.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 12.39/12.68 inference(modus_ponens,[status(thm)],[37082, 37081])).
% 12.39/12.68 tff(37084,plain,
% 12.39/12.68 (~r(s(s(s(s(z)))), elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[37083, 194, 36606, 3618, 29426])).
% 12.39/12.68 tff(37085,plain,
% 12.39/12.68 (~(s(z) = elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[20271, 37058])).
% 12.39/12.68 tff(37086,plain,
% 12.39/12.68 (~r(s(z), elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[627, 3618, 36606, 182])).
% 12.39/12.68 tff(37087,plain,
% 12.39/12.68 (b(s(z), elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[632, 37086, 37085])).
% 12.39/12.68 tff(37088,plain,
% 12.39/12.68 (s(s(s(s(z)))) = elem!1),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[18869, 37068, 37066, 37087, 37084])).
% 12.39/12.68 tff(37089,plain,
% 12.39/12.68 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[717, 37088])).
% 12.39/12.68 tff(37090,plain,
% 12.39/12.68 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 12.39/12.68 inference(modus_ponens,[status(thm)],[37089, 37080])).
% 12.39/12.68 tff(37091,plain,
% 12.39/12.68 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37073])).
% 12.39/12.68 tff(37092,plain,
% 12.39/12.68 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37091])).
% 12.39/12.68 tff(37093,plain,
% 12.39/12.68 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(s(elem!1))), z)),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37073])).
% 12.39/12.68 tff(37094,plain,
% 12.39/12.68 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 12.39/12.68 inference(symmetry,[status(thm)],[37093])).
% 12.39/12.68 tff(37095,plain,
% 12.39/12.68 (~b(z, s(s(s(s(z)))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[16124, 37088, 89])).
% 12.39/12.68 tff(37096,plain,
% 12.39/12.68 (r(z, s(s(s(s(z)))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[800, 37095])).
% 12.39/12.68 tff(37097,plain,
% 12.39/12.68 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[2849, 37085])).
% 12.39/12.68 tff(37098,plain,
% 12.39/12.68 (~(elem!1 = s(s(s(elem!1))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[22900, 10682, 89])).
% 12.39/12.68 tff(37099,plain,
% 12.39/12.68 (~(s(s(s(elem!1))) = elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[8, 37098])).
% 12.39/12.68 tff(37100,plain,
% 12.39/12.68 (~(s(elem!1) = elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[158, 37099])).
% 12.39/12.68 tff(37101,plain,
% 12.39/12.68 (~(elem!1 = s(elem!1))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[166, 37100])).
% 12.39/12.68 tff(37102,plain,
% 12.39/12.68 (~r(s(elem!1), z)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[29050, 3618, 36606, 37058, 118, 37101, 182])).
% 12.39/12.68 tff(37103,plain,
% 12.39/12.68 (b(s(elem!1), z)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[549, 37102])).
% 12.39/12.68 tff(37104,plain,
% 12.39/12.68 (~b(elem!1, s(s(s(s(z)))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[2088, 391, 1234, 1759, 37058])).
% 12.39/12.68 tff(37105,plain,
% 12.39/12.68 (elem!1 = s(s(s(s(z))))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[781, 37068, 37104])).
% 12.39/12.68 tff(37106,plain,
% 12.39/12.68 (s(s(s(s(z)))) = elem!1),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[18869, 37068, 1234, 644, 37084])).
% 12.39/12.68 tff(37107,plain,
% 12.39/12.68 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 12.39/12.68 inference(monotonicity,[status(thm)],[23648])).
% 12.39/12.68 tff(37108,plain,
% 12.39/12.68 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 12.39/12.68 inference(symmetry,[status(thm)],[37107])).
% 12.39/12.68 tff(37109,plain,
% 12.39/12.68 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 12.39/12.68 inference(modus_ponens,[status(thm)],[1526, 37108])).
% 12.39/12.68 tff(37110,plain,
% 12.39/12.68 (~b(s(s(s(elem!1))), elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[20387, 1526, 721, 644])).
% 12.39/12.68 tff(37111,plain,
% 12.39/12.68 (r(s(s(s(elem!1))), elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[230, 37110, 37099])).
% 12.39/12.68 tff(37112,plain,
% 12.39/12.68 (~r(s(s(s(elem!1))), z)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[23607, 37111, 411, 530])).
% 12.39/12.68 tff(37113,plain,
% 12.39/12.68 (~r(s(elem!1), elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[28617, 37111, 591, 530, 10682, 14410])).
% 12.39/12.68 tff(37114,plain,
% 12.39/12.68 (b(s(s(s(elem!1))), z)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[377, 37112])).
% 12.39/12.68 tff(37115,plain,
% 12.39/12.68 (~b(s(s(s(elem!1))), s(elem!1))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[12799, 37114, 10682, 591])).
% 12.39/12.68 tff(37116,plain,
% 12.39/12.68 (r(elem!1, z)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[526, 24022, 484])).
% 12.39/12.68 tff(37117,plain,
% 12.39/12.68 (~(s(s(s(elem!1))) = elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[533, 37116, 329])).
% 12.39/12.68 tff(37118,plain,
% 12.39/12.68 (~(s(elem!1) = elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[158, 37117])).
% 12.39/12.68 tff(37119,plain,
% 12.39/12.68 (~(elem!1 = s(elem!1))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[166, 37118])).
% 12.39/12.68 tff(37120,plain,
% 12.39/12.68 (b(s(elem!1), elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[2168, 37118, 469])).
% 12.39/12.68 tff(37121,plain,
% 12.39/12.68 (r(z, elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[141, 24023, 89])).
% 12.39/12.68 tff(37122,plain,
% 12.39/12.68 (~r(s(z), elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[627, 182, 530, 411])).
% 12.39/12.68 tff(37123,plain,
% 12.39/12.68 (b(s(z), elem!1)),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[632, 37122, 150])).
% 12.39/12.68 tff(37124,plain,
% 12.39/12.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 12.39/12.68 inference(rewrite,[status(thm)],[])).
% 12.39/12.68 tff(37125,plain,
% 12.39/12.68 (((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 12.39/12.68 inference(rewrite,[status(thm)],[])).
% 12.39/12.68 tff(37126,plain,
% 12.39/12.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(elem!1)))))),
% 12.39/12.68 inference(monotonicity,[status(thm)],[37125])).
% 12.39/12.68 tff(37127,plain,
% 12.39/12.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 12.39/12.68 inference(transitivity,[status(thm)],[37126, 37124])).
% 12.39/12.68 tff(37128,plain,
% 12.39/12.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 12.39/12.68 inference(quant_inst,[status(thm)],[])).
% 12.39/12.68 tff(37129,plain,
% 12.39/12.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(z, s(elem!1)))),
% 12.39/12.68 inference(modus_ponens,[status(thm)],[37128, 37127])).
% 12.39/12.68 tff(37130,plain,
% 12.39/12.68 (~b(z, s(z))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[37129, 391, 592, 591, 751])).
% 12.39/12.68 tff(37131,plain,
% 12.39/12.68 (r(z, s(z))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[678, 37130])).
% 12.39/12.68 tff(37132,plain,
% 12.39/12.68 (~r(s(s(elem!1)), s(z))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[4103, 37131, 2616, 182])).
% 12.39/12.68 tff(37133,plain,
% 12.39/12.68 (b(s(s(elem!1)), s(z))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[362, 37132])).
% 12.39/12.68 tff(37134,plain,
% 12.39/12.68 (b(elem!1, s(z))),
% 12.39/12.68 inference(modus_ponens,[status(thm)],[37133, 446])).
% 12.39/12.68 tff(37135,plain,
% 12.39/12.68 ($false),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[17171, 391, 644, 2122, 751, 37134])).
% 12.39/12.68 tff(37136,plain,((~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.68 tff(37137,plain,
% 12.39/12.68 (~b(s(z), s(elem!1))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[37136, 37123, 2122, 445, 4782, 182, 592, 24435])).
% 12.39/12.68 tff(37138,plain,
% 12.39/12.68 (r(s(z), s(elem!1))),
% 12.39/12.68 inference(unit_resolution,[status(thm)],[602, 42, 121, 37137])).
% 12.39/12.68 tff(37139,plain,
% 12.39/12.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 12.39/12.68 inference(rewrite,[status(thm)],[])).
% 12.39/12.68 tff(37140,plain,
% 12.39/12.68 (((~b(s(elem!1), z)) | (~b(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)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 12.39/12.69 inference(rewrite,[status(thm)],[])).
% 12.39/12.69 tff(37141,plain,
% 12.39/12.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 12.39/12.69 inference(monotonicity,[status(thm)],[37140])).
% 12.39/12.69 tff(37142,plain,
% 12.39/12.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 12.39/12.69 inference(transitivity,[status(thm)],[37141, 37139])).
% 12.39/12.69 tff(37143,plain,
% 12.39/12.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(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))))),
% 12.39/12.69 inference(quant_inst,[status(thm)],[])).
% 12.39/12.69 tff(37144,plain,
% 12.39/12.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 12.39/12.69 inference(modus_ponens,[status(thm)],[37143, 37142])).
% 12.39/12.69 tff(37145,plain,
% 12.39/12.69 (~b(s(s(s(s(z)))), s(elem!1))),
% 12.39/12.69 inference(unit_resolution,[status(thm)],[37144, 391, 592, 591, 90])).
% 12.39/12.69 tff(37146,plain,
% 12.39/12.69 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 12.39/12.69 inference(unit_resolution,[status(thm)],[2136, 42, 37145])).
% 12.39/12.69 tff(37147,plain,
% 12.39/12.69 (r(s(s(s(s(z)))), s(elem!1))),
% 12.39/12.69 inference(unit_resolution,[status(thm)],[37146, 5479])).
% 12.39/12.69 tff(37148,plain,
% 12.39/12.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 12.39/12.69 inference(rewrite,[status(thm)],[])).
% 12.39/12.69 tff(37149,plain,
% 12.39/12.69 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 12.39/12.69 inference(rewrite,[status(thm)],[])).
% 12.39/12.69 tff(37150,plain,
% 12.39/12.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 12.39/12.69 inference(monotonicity,[status(thm)],[37149])).
% 12.39/12.69 tff(37151,plain,
% 12.39/12.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 12.39/12.69 inference(transitivity,[status(thm)],[37150, 37148])).
% 12.39/12.69 tff(37152,plain,
% 12.39/12.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 12.39/12.69 inference(quant_inst,[status(thm)],[])).
% 12.39/12.69 tff(37153,plain,
% 12.39/12.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 12.39/12.69 inference(modus_ponens,[status(thm)],[37152, 37151])).
% 12.39/12.69 tff(37154,plain,
% 12.39/12.69 (~b(s(elem!1), s(s(s(s(z)))))),
% 12.39/12.69 inference(unit_resolution,[status(thm)],[37153, 391, 592, 591, 90])).
% 12.39/12.69 tff(37155,plain,
% 12.39/12.69 ((s(elem!1) = s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 12.39/12.69 inference(unit_resolution,[status(thm)],[2142, 42, 37154])).
% 12.39/12.69 tff(37156,plain,
% 12.39/12.69 (r(s(elem!1), s(s(s(s(z)))))),
% 12.39/12.69 inference(unit_resolution,[status(thm)],[37155, 5524])).
% 12.39/12.69 tff(37157,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 12.39/12.69 tff(37158,plain,
% 12.39/12.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 12.39/12.69 inference(rewrite,[status(thm)],[])).
% 12.39/12.69 tff(37159,plain,
% 12.39/12.69 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 12.39/12.69 inference(rewrite,[status(thm)],[])).
% 12.39/12.69 tff(37160,plain,
% 12.39/12.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 12.39/12.69 inference(monotonicity,[status(thm)],[37159])).
% 12.39/12.69 tff(37161,plain,
% 12.39/12.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 12.39/12.69 inference(transitivity,[status(thm)],[37160, 37158])).
% 12.39/12.69 tff(37162,plain,
% 12.39/12.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))),
% 12.39/12.69 inference(quant_inst,[status(thm)],[])).
% 12.39/12.69 tff(37163,plain,
% 12.39/12.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 12.39/12.69 inference(modus_ponens,[status(thm)],[37162, 37161])).
% 12.39/12.69 tff(37164,plain,
% 12.39/12.69 (~r(s(s(s(s(z)))), s(z))),
% 12.39/12.69 inference(unit_resolution,[status(thm)],[37163, 194, 37157, 37156, 37147])).
% 12.39/12.69 tff(37165,plain,
% 12.39/12.69 (b(s(s(s(s(z)))), s(z))),
% 12.39/12.69 inference(unit_resolution,[status(thm)],[749, 37164])).
% 12.39/12.69 tff(37166,plain,
% 12.39/12.69 (~r(s(s(s(s(z)))), elem!1)),
% 12.39/12.69 inference(unit_resolution,[status(thm)],[26191, 194, 2251, 37156, 37147])).
% 12.39/12.69 tff(37167,plain,
% 12.39/12.69 (b(s(s(s(s(z)))), elem!1)),
% 12.39/12.69 inference(unit_resolution,[status(thm)],[762, 37166, 5470])).
% 12.39/12.70 tff(37168,plain,
% 12.39/12.70 (~r(elem!1, s(s(s(s(z)))))),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[26200, 194, 2251, 37156, 37147])).
% 12.39/12.70 tff(37169,plain,
% 12.39/12.70 (b(elem!1, s(s(s(s(z)))))),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[781, 37168, 5511])).
% 12.39/12.70 tff(37170,plain,
% 12.39/12.70 ($false),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[14958, 391, 644, 90, 37169, 37167, 37165])).
% 12.39/12.70 tff(37171,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 12.39/12.70 tff(37172,plain,
% 12.39/12.70 (~b(s(s(s(s(z)))), z)),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[37171, 37123, 2251, 37138, 3363, 452, 592, 24435])).
% 12.39/12.70 tff(37173,plain,
% 12.39/12.70 (r(s(s(s(s(z)))), z)),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[87, 37172])).
% 12.39/12.70 tff(37174,plain,
% 12.39/12.70 (~r(s(s(s(s(z)))), s(z))),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[3241, 194, 411, 182, 37173])).
% 12.39/12.70 tff(37175,plain,
% 12.39/12.70 (b(s(s(s(s(z)))), s(z))),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[749, 37174])).
% 12.39/12.70 tff(37176,plain,
% 12.39/12.70 (~r(s(s(s(s(z)))), elem!1)),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[37083, 194, 411, 530, 37173])).
% 12.39/12.70 tff(37177,plain,
% 12.39/12.70 (b(s(s(s(s(z)))), elem!1)),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[762, 37176, 718])).
% 12.39/12.70 tff(37178,plain,
% 12.39/12.70 (~r(elem!1, s(s(s(s(z)))))),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[17579, 194, 411, 530, 37173])).
% 12.39/12.70 tff(37179,plain,
% 12.39/12.70 (b(elem!1, s(s(s(s(z)))))),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[781, 37178, 12003])).
% 12.39/12.70 tff(37180,plain,
% 12.39/12.70 ($false),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[17129, 391, 37123, 37179, 37177, 37175])).
% 12.39/12.70 tff(37181,plain,((~r(s(z), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (s(z) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.39/12.70 tff(37182,plain,
% 12.39/12.70 (~r(s(z), z)),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[37181, 11958, 530, 2251, 411, 121, 2122, 445, 150])).
% 12.39/12.70 tff(37183,plain,
% 12.39/12.70 (b(s(z), z)),
% 12.39/12.70 inference(unit_resolution,[status(thm)],[180, 37182])).
% 12.39/12.70 tff(37184,plain,
% 12.39/12.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 12.39/12.70 inference(rewrite,[status(thm)],[])).
% 12.39/12.70 tff(37185,plain,
% 12.39/12.70 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 12.39/12.70 inference(rewrite,[status(thm)],[])).
% 12.39/12.70 tff(37186,plain,
% 12.39/12.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z)))))),
% 12.39/12.70 inference(monotonicity,[status(thm)],[37185])).
% 12.39/12.70 tff(37187,plain,
% 12.39/12.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 12.39/12.70 inference(transitivity,[status(thm)],[37186, 37184])).
% 12.39/12.70 tff(37188,plain,
% 12.39/12.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 12.49/12.70 inference(quant_inst,[status(thm)],[])).
% 12.49/12.70 tff(37189,plain,
% 12.49/12.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z)))),
% 12.49/12.70 inference(modus_ponens,[status(thm)],[37188, 37187])).
% 12.49/12.70 tff(37190,plain,
% 12.49/12.70 (~b(s(elem!1), s(z))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[37189, 391, 11958, 24435, 37183])).
% 12.49/12.70 tff(37191,plain,
% 12.49/12.70 (~b(s(s(s(elem!1))), s(z))),
% 12.49/12.70 inference(modus_ponens,[status(thm)],[37190, 4779])).
% 12.49/12.70 tff(37192,plain,
% 12.49/12.70 (r(s(s(s(elem!1))), s(z))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[223, 37191])).
% 12.49/12.70 tff(37193,plain,
% 12.49/12.70 (r(s(elem!1), s(z))),
% 12.49/12.70 inference(modus_ponens,[status(thm)],[37192, 4776])).
% 12.49/12.70 tff(37194,plain,
% 12.49/12.70 (~b(s(z), s(elem!1))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[598, 391, 11958, 24435, 37183])).
% 12.49/12.70 tff(37195,plain,
% 12.49/12.70 (r(s(z), s(elem!1))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[602, 42, 121, 37194])).
% 12.49/12.70 tff(37196,plain,
% 12.49/12.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 12.49/12.70 inference(rewrite,[status(thm)],[])).
% 12.49/12.70 tff(37197,plain,
% 12.49/12.70 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 12.49/12.70 inference(rewrite,[status(thm)],[])).
% 12.49/12.70 tff(37198,plain,
% 12.49/12.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 12.49/12.70 inference(monotonicity,[status(thm)],[37197])).
% 12.49/12.70 tff(37199,plain,
% 12.49/12.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 12.49/12.70 inference(transitivity,[status(thm)],[37198, 37196])).
% 12.49/12.70 tff(37200,plain,
% 12.49/12.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 12.49/12.70 inference(quant_inst,[status(thm)],[])).
% 12.49/12.70 tff(37201,plain,
% 12.49/12.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 12.49/12.70 inference(modus_ponens,[status(thm)],[37200, 37199])).
% 12.49/12.70 tff(37202,plain,
% 12.49/12.70 (~r(s(z), elem!1)),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[37201, 194, 2251, 37195, 37193])).
% 12.49/12.70 tff(37203,plain,
% 12.49/12.70 (b(s(z), elem!1)),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[632, 37202, 150])).
% 12.49/12.70 tff(37204,plain,
% 12.49/12.70 (~b(s(s(s(s(z)))), z)),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[37171, 37203, 2251, 37195, 3363, 452, 11958, 24435])).
% 12.49/12.70 tff(37205,plain,
% 12.49/12.70 (r(s(s(s(s(z)))), z)),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[87, 37204])).
% 12.49/12.70 tff(37206,plain,
% 12.49/12.70 (~r(s(s(s(s(z)))), elem!1)),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[37083, 194, 411, 530, 37205])).
% 12.49/12.70 tff(37207,plain,
% 12.49/12.70 (b(s(s(s(s(z)))), elem!1)),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[762, 37206, 718])).
% 12.49/12.70 tff(37208,plain,
% 12.49/12.70 (~r(elem!1, s(s(s(s(z)))))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[17579, 194, 411, 530, 37205])).
% 12.49/12.70 tff(37209,plain,
% 12.49/12.70 (b(elem!1, s(s(s(s(z)))))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[781, 37208, 12003])).
% 12.49/12.70 tff(37210,plain,
% 12.49/12.70 (~b(s(s(s(s(z)))), s(z))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[17129, 391, 37203, 37209, 37207])).
% 12.49/12.70 tff(37211,plain,
% 12.49/12.70 (r(s(s(s(s(z)))), s(z))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[749, 37210])).
% 12.49/12.70 tff(37212,plain,
% 12.49/12.70 (~b(s(z), s(s(s(s(z)))))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[17588, 391, 37203, 37209, 37207])).
% 12.49/12.70 tff(37213,plain,
% 12.49/12.70 (r(s(z), s(s(s(s(z)))))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[1230, 37212])).
% 12.49/12.70 tff(37214,plain,
% 12.49/12.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 12.49/12.70 inference(rewrite,[status(thm)],[])).
% 12.49/12.70 tff(37215,plain,
% 12.49/12.70 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 12.49/12.70 inference(rewrite,[status(thm)],[])).
% 12.49/12.70 tff(37216,plain,
% 12.49/12.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 12.49/12.70 inference(monotonicity,[status(thm)],[37215])).
% 12.49/12.70 tff(37217,plain,
% 12.49/12.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 12.49/12.70 inference(transitivity,[status(thm)],[37216, 37214])).
% 12.49/12.70 tff(37218,plain,
% 12.49/12.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 12.49/12.70 inference(quant_inst,[status(thm)],[])).
% 12.49/12.70 tff(37219,plain,
% 12.49/12.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 12.49/12.70 inference(modus_ponens,[status(thm)],[37218, 37217])).
% 12.49/12.70 tff(37220,plain,
% 12.49/12.70 (~r(s(s(s(s(z)))), s(elem!1))),
% 12.49/12.70 inference(unit_resolution,[status(thm)],[37219, 194, 37213, 37211, 37193])).
% 12.49/12.70 tff(37221,plain,
% 12.49/12.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 12.49/12.70 inference(rewrite,[status(thm)],[])).
% 12.49/12.70 tff(37222,plain,
% 12.49/12.70 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 12.49/12.70 inference(rewrite,[status(thm)],[])).
% 12.49/12.71 tff(37223,plain,
% 12.49/12.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 12.49/12.71 inference(monotonicity,[status(thm)],[37222])).
% 12.49/12.71 tff(37224,plain,
% 12.49/12.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 12.49/12.71 inference(transitivity,[status(thm)],[37223, 37221])).
% 12.49/12.71 tff(37225,plain,
% 12.49/12.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 12.49/12.71 inference(quant_inst,[status(thm)],[])).
% 12.49/12.71 tff(37226,plain,
% 12.49/12.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 12.49/12.71 inference(modus_ponens,[status(thm)],[37225, 37224])).
% 12.49/12.71 tff(37227,plain,
% 12.49/12.71 (~b(s(s(s(s(z)))), s(elem!1))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37226, 391, 2122, 37209, 37207])).
% 12.49/12.71 tff(37228,plain,
% 12.49/12.71 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[2136, 42, 37227])).
% 12.49/12.71 tff(37229,plain,
% 12.49/12.71 (s(s(s(s(z)))) = s(elem!1)),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37228, 37220])).
% 12.49/12.71 tff(37230,plain,
% 12.49/12.71 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 12.49/12.71 inference(transitivity,[status(thm)],[37229, 479])).
% 12.49/12.71 tff(37231,plain,
% 12.49/12.71 ($false),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[3363, 37230])).
% 12.49/12.71 tff(37232,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (s(z) = elem!1) | (s(z) = s(elem!1)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.71 tff(37233,plain,
% 12.49/12.71 (~(s(s(elem!1)) = elem!1)),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37232, 5538, 411, 530, 2122, 150, 24024, 10682])).
% 12.49/12.71 tff(37234,plain,
% 12.49/12.71 ($false),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37233, 2459])).
% 12.49/12.71 tff(37235,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(elem!1), elem!1)) | (s(z) = elem!1) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.71 tff(37236,plain,
% 12.49/12.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37235, 37121, 37116, 37120, 150, 10682, 37119, 4028])).
% 12.49/12.71 tff(37237,plain,
% 12.49/12.71 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[281, 37236])).
% 12.49/12.71 tff(37238,plain,
% 12.49/12.71 (~(elem!1 = s(s(s(elem!1))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[129, 37117])).
% 12.49/12.71 tff(37239,plain,
% 12.49/12.71 (r(elem!1, s(s(s(elem!1))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[424, 37238, 4028])).
% 12.49/12.71 tff(37240,plain,
% 12.49/12.71 (~b(s(s(elem!1)), elem!1)),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[25235, 24024, 285, 37120, 150, 37121, 37116, 37239, 378, 10682])).
% 12.49/12.71 tff(37241,plain,
% 12.49/12.71 (~(s(s(elem!1)) = elem!1)),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[451, 37236])).
% 12.49/12.71 tff(37242,plain,
% 12.49/12.71 (r(s(s(elem!1)), elem!1)),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[872, 37241, 37240])).
% 12.49/12.71 tff(37243,plain,
% 12.49/12.71 (~r(s(s(elem!1)), z)),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[8360, 37242, 37116, 37121])).
% 12.49/12.71 tff(37244,plain,
% 12.49/12.71 (b(s(s(elem!1)), z)),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[2629, 37243])).
% 12.49/12.71 tff(37245,plain,
% 12.49/12.71 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[24681, 391, 378, 10682, 37244])).
% 12.49/12.71 tff(37246,plain,
% 12.49/12.71 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[1354, 42, 37245, 37237])).
% 12.49/12.71 tff(37247,plain,
% 12.49/12.71 (r(s(s(s(elem!1))), s(elem!1))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[588, 37236, 486])).
% 12.49/12.71 tff(37248,plain,
% 12.49/12.71 ($false),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[15592, 194, 37247, 37242, 37239, 37246])).
% 12.49/12.71 tff(37249,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(elem!1)) | (s(z) = elem!1) | (s(s(elem!1)) = s(elem!1)) | r(s(elem!1), elem!1) | b(z, elem!1) | r(s(s(s(elem!1))), z) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.71 tff(37250,plain,
% 12.49/12.71 (b(elem!1, s(s(s(elem!1))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37249, 37115, 89, 10682, 21435, 37113, 14413, 37112, 484])).
% 12.49/12.71 tff(37251,plain,
% 12.49/12.71 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[2865, 37250, 688])).
% 12.49/12.71 tff(37252,plain,
% 12.49/12.71 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 12.49/12.71 inference(modus_ponens,[status(thm)],[37251, 23714])).
% 12.49/12.71 tff(37253,plain,
% 12.49/12.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.71 inference(rewrite,[status(thm)],[])).
% 12.49/12.71 tff(37254,plain,
% 12.49/12.71 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.71 inference(rewrite,[status(thm)],[])).
% 12.49/12.71 tff(37255,plain,
% 12.49/12.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 12.49/12.71 inference(monotonicity,[status(thm)],[37254])).
% 12.49/12.71 tff(37256,plain,
% 12.49/12.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.71 inference(transitivity,[status(thm)],[37255, 37253])).
% 12.49/12.71 tff(37257,plain,
% 12.49/12.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.71 inference(quant_inst,[status(thm)],[])).
% 12.49/12.71 tff(37258,plain,
% 12.49/12.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.71 inference(modus_ponens,[status(thm)],[37257, 37256])).
% 12.49/12.71 tff(37259,plain,
% 12.49/12.71 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37258, 391, 1234, 1759])).
% 12.49/12.71 tff(37260,plain,
% 12.49/12.71 ($false),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37259, 37252, 37109])).
% 12.49/12.71 tff(37261,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = elem!1)) | b(z, elem!1) | (~b(z, s(s(s(elem!1))))) | b(elem!1, z) | (~b(s(elem!1), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.71 tff(37262,plain,
% 12.49/12.71 (~b(s(s(s(elem!1))), s(z))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37261, 37105, 1759, 1234, 37106, 89, 10682, 484, 591, 3618, 36606, 37058, 644])).
% 12.49/12.71 tff(37263,plain,
% 12.49/12.71 (r(s(s(s(elem!1))), s(z))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[223, 37262])).
% 12.49/12.71 tff(37264,plain,
% 12.49/12.71 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 12.49/12.71 inference(monotonicity,[status(thm)],[23648])).
% 12.49/12.71 tff(37265,plain,
% 12.49/12.71 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 12.49/12.71 inference(symmetry,[status(thm)],[37264])).
% 12.49/12.71 tff(37266,plain,
% 12.49/12.71 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 12.49/12.71 inference(modus_ponens,[status(thm)],[183, 37265])).
% 12.49/12.71 tff(37267,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 12.49/12.71 tff(37268,plain,
% 12.49/12.71 ($false),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37267, 37266])).
% 12.49/12.71 tff(37269,plain,(r(s(s(s(s(s(s(s(z))))))), s(z)) | (~r(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.71 tff(37270,plain,
% 12.49/12.71 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[37269, 37263, 37105])).
% 12.49/12.71 tff(37271,plain,
% 12.49/12.71 (s(elem!1) = s(s(s(s(s(z)))))),
% 12.49/12.71 inference(monotonicity,[status(thm)],[37105])).
% 12.49/12.71 tff(37272,plain,
% 12.49/12.71 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 12.49/12.71 inference(monotonicity,[status(thm)],[37271])).
% 12.49/12.71 tff(37273,plain,
% 12.49/12.71 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 12.49/12.71 inference(monotonicity,[status(thm)],[37272])).
% 12.49/12.71 tff(37274,plain,
% 12.49/12.71 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 12.49/12.71 inference(monotonicity,[status(thm)],[37273, 37272])).
% 12.49/12.71 tff(37275,plain,
% 12.49/12.71 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[8251, 37099])).
% 12.49/12.71 tff(37276,plain,
% 12.49/12.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[717, 37106])).
% 12.49/12.71 tff(37277,plain,
% 12.49/12.71 (~b(z, s(s(s(s(z)))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[16124, 37106, 89])).
% 12.49/12.71 tff(37278,plain,
% 12.49/12.71 (r(z, s(s(s(s(z)))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[800, 37277])).
% 12.49/12.71 tff(37279,plain,
% 12.49/12.71 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 12.49/12.71 inference(symmetry,[status(thm)],[37273])).
% 12.49/12.71 tff(37280,plain,
% 12.49/12.71 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.49/12.71 inference(monotonicity,[status(thm)],[37105, 37279])).
% 12.49/12.71 tff(37281,plain,
% 12.49/12.71 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 12.49/12.71 inference(symmetry,[status(thm)],[37280])).
% 12.49/12.71 tff(37282,plain,
% 12.49/12.71 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.49/12.71 inference(monotonicity,[status(thm)],[37105])).
% 12.49/12.71 tff(37283,plain,
% 12.49/12.71 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 12.49/12.71 inference(transitivity,[status(thm)],[37282, 37281])).
% 12.49/12.71 tff(37284,plain,
% 12.49/12.71 (r(elem!1, s(s(s(elem!1))))),
% 12.49/12.71 inference(unit_resolution,[status(thm)],[424, 4028, 37098])).
% 12.49/12.71 tff(37285,plain,
% 12.49/12.71 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 12.49/12.71 inference(modus_ponens,[status(thm)],[37284, 37283])).
% 12.49/12.71 tff(37286,assumption,(r(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 12.49/12.71 tff(37287,plain,
% 12.49/12.71 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 12.49/12.72 inference(monotonicity,[status(thm)],[2738])).
% 12.49/12.72 tff(37288,plain,
% 12.49/12.72 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 12.49/12.72 inference(symmetry,[status(thm)],[37287])).
% 12.49/12.72 tff(37289,assumption,(r(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 12.49/12.72 tff(37290,plain,
% 12.49/12.72 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 12.49/12.72 inference(modus_ponens,[status(thm)],[37289, 37288])).
% 12.49/12.72 tff(37291,plain,
% 12.49/12.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.72 inference(rewrite,[status(thm)],[])).
% 12.49/12.72 tff(37292,plain,
% 12.49/12.72 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.72 inference(rewrite,[status(thm)],[])).
% 12.49/12.72 tff(37293,plain,
% 12.49/12.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 12.49/12.72 inference(monotonicity,[status(thm)],[37292])).
% 12.49/12.72 tff(37294,plain,
% 12.49/12.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.72 inference(transitivity,[status(thm)],[37293, 37291])).
% 12.49/12.72 tff(37295,plain,
% 12.49/12.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.72 inference(quant_inst,[status(thm)],[])).
% 12.49/12.72 tff(37296,plain,
% 12.49/12.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.72 inference(modus_ponens,[status(thm)],[37295, 37294])).
% 12.49/12.72 tff(37297,plain,
% 12.49/12.72 ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[37296, 194, 2053, 719])).
% 12.49/12.72 tff(37298,plain,
% 12.49/12.72 ($false),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[37297, 37290, 37286])).
% 12.49/12.72 tff(37299,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.72 tff(37300,plain,
% 12.49/12.72 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[37299, 37285, 37278, 29426, 37105])).
% 12.49/12.72 tff(37301,assumption,(~r(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 12.49/12.72 tff(37302,plain,
% 12.49/12.72 ($false),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[37301, 23651])).
% 12.49/12.72 tff(37303,plain,((~r(s(s(s(elem!1))), z)) | r(s(s(s(s(s(s(s(z))))))), z) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.72 tff(37304,plain,
% 12.49/12.72 (~r(s(s(s(elem!1))), z)),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[37303, 37300, 37105])).
% 12.49/12.72 tff(37305,plain,
% 12.49/12.72 (b(s(s(s(elem!1))), z)),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[377, 37304])).
% 12.49/12.72 tff(37306,plain,
% 12.49/12.72 (~b(s(s(s(elem!1))), s(elem!1))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[12799, 37305, 10682, 591])).
% 12.49/12.72 tff(37307,plain,
% 12.49/12.72 (r(s(s(s(elem!1))), s(elem!1))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[588, 37306, 37276])).
% 12.49/12.72 tff(37308,plain,
% 12.49/12.72 (~(s(s(elem!1)) = s(elem!1))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[2279, 37276])).
% 12.49/12.72 tff(37309,plain,
% 12.49/12.72 (r(s(elem!1), elem!1)),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[37249, 37306, 89, 10682, 37085, 4028, 37308, 37304, 484])).
% 12.49/12.72 tff(37310,plain,
% 12.49/12.72 (b(s(s(s(elem!1))), elem!1)),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[13054, 37309, 37099, 37307, 4028])).
% 12.49/12.72 tff(37311,plain,
% 12.49/12.72 (b(s(s(elem!1)), elem!1)),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[29114, 37310, 36606, 591, 37275, 37276, 3618, 2, 37305, 10682])).
% 12.49/12.72 tff(37312,plain,
% 12.49/12.72 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[34598, 37311, 37058, 1234, 37310])).
% 12.49/12.72 tff(37313,plain,
% 12.49/12.72 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[1370, 37312, 37275])).
% 12.49/12.72 tff(37314,plain,
% 12.49/12.72 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 12.49/12.72 inference(modus_ponens,[status(thm)],[37313, 37274])).
% 12.49/12.72 tff(37315,plain,
% 12.49/12.72 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.49/12.72 inference(monotonicity,[status(thm)],[37272])).
% 12.49/12.72 tff(37316,plain,
% 12.49/12.72 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 12.49/12.72 inference(monotonicity,[status(thm)],[37105])).
% 12.49/12.72 tff(37317,plain,
% 12.49/12.72 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.49/12.72 inference(transitivity,[status(thm)],[37316, 37315])).
% 12.49/12.72 tff(37318,plain,
% 12.49/12.72 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.49/12.72 inference(modus_ponens,[status(thm)],[37311, 37317])).
% 12.49/12.72 tff(37319,plain,
% 12.49/12.72 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[33879, 391, 1234, 1759, 37318])).
% 12.49/12.72 tff(37320,plain,
% 12.49/12.72 (r(s(z), s(s(s(s(s(s(z)))))))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[11665, 42, 37319, 33774])).
% 12.49/12.72 tff(37321,plain,
% 12.49/12.72 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 12.49/12.72 inference(monotonicity,[status(thm)],[37272])).
% 12.49/12.72 tff(37322,plain,
% 12.49/12.72 (~b(s(s(elem!1)), s(z))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[22561, 37311, 37058, 644])).
% 12.49/12.72 tff(37323,plain,
% 12.49/12.72 (r(s(s(elem!1)), s(z))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[362, 37322])).
% 12.49/12.72 tff(37324,plain,
% 12.49/12.72 (r(s(s(s(s(s(s(z)))))), s(z))),
% 12.49/12.72 inference(modus_ponens,[status(thm)],[37323, 37321])).
% 12.49/12.72 tff(37325,plain,
% 12.49/12.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 12.49/12.72 inference(rewrite,[status(thm)],[])).
% 12.49/12.72 tff(37326,plain,
% 12.49/12.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 12.49/12.72 inference(quant_inst,[status(thm)],[])).
% 12.49/12.72 tff(37327,plain,
% 12.49/12.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 12.49/12.72 inference(modus_ponens,[status(thm)],[37326, 37325])).
% 12.49/12.72 tff(37328,plain,
% 12.49/12.72 ($false),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[37327, 194, 37324, 37320, 37314, 37270])).
% 12.49/12.72 tff(37329,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (elem!1 = z) | (~b(z, s(s(s(elem!1))))) | b(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.72 tff(37330,plain,
% 12.49/12.72 (b(elem!1, s(s(s(elem!1))))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[37329, 37087, 37064, 37066, 37103, 2, 10682, 89, 484])).
% 12.49/12.72 tff(37331,plain,
% 12.49/12.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.72 inference(rewrite,[status(thm)],[])).
% 12.49/12.72 tff(37332,plain,
% 12.49/12.72 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.72 inference(rewrite,[status(thm)],[])).
% 12.49/12.72 tff(37333,plain,
% 12.49/12.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 12.49/12.72 inference(monotonicity,[status(thm)],[37332])).
% 12.49/12.72 tff(37334,plain,
% 12.49/12.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.72 inference(transitivity,[status(thm)],[37333, 37331])).
% 12.49/12.72 tff(37335,plain,
% 12.49/12.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 12.49/12.72 inference(quant_inst,[status(thm)],[])).
% 12.49/12.72 tff(37336,plain,
% 12.49/12.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 12.49/12.72 inference(modus_ponens,[status(thm)],[37335, 37334])).
% 12.49/12.72 tff(37337,plain,
% 12.49/12.72 ($false),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[37336, 391, 448, 644, 379, 11286, 11284])).
% 12.49/12.72 tff(37338,plain,((~r(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.72 tff(37339,plain,
% 12.49/12.72 (~b(s(z), s(s(s(elem!1))))),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[37338, 174, 2053, 411, 644, 448, 3843])).
% 12.49/12.72 tff(37340,plain,
% 12.49/12.72 ($false),
% 12.49/12.72 inference(unit_resolution,[status(thm)],[247, 37339, 35433])).
% 12.49/12.72 tff(37341,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.73 tff(37342,plain,
% 12.49/12.73 (~r(s(s(s(elem!1))), z)),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[37341, 37087, 36606, 29426, 37330, 37097, 182, 37096])).
% 12.49/12.73 tff(37343,plain,
% 12.49/12.73 (b(s(s(s(elem!1))), z)),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[377, 37342])).
% 12.49/12.73 tff(37344,plain,
% 12.49/12.73 (b(s(s(s(s(s(s(s(z))))))), z)),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[37343, 37094])).
% 12.49/12.73 tff(37345,plain,
% 12.49/12.73 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(s(elem!1))))),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37073])).
% 12.49/12.73 tff(37346,plain,
% 12.49/12.73 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 12.49/12.73 inference(symmetry,[status(thm)],[37345])).
% 12.49/12.73 tff(37347,plain,
% 12.49/12.73 (b(z, s(s(s(s(s(s(s(z))))))))),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[10682, 37346])).
% 12.49/12.73 tff(37348,plain,
% 12.49/12.73 (b(s(elem!1), z) <=> b(s(s(s(s(s(z))))), z)),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37070])).
% 12.49/12.73 tff(37349,plain,
% 12.49/12.73 (b(s(s(s(s(s(z))))), z)),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[37103, 37348])).
% 12.49/12.73 tff(37350,plain,
% 12.49/12.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.73 inference(rewrite,[status(thm)],[])).
% 12.49/12.73 tff(37351,plain,
% 12.49/12.73 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.73 inference(rewrite,[status(thm)],[])).
% 12.49/12.73 tff(37352,plain,
% 12.49/12.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37351])).
% 12.49/12.73 tff(37353,plain,
% 12.49/12.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.73 inference(transitivity,[status(thm)],[37352, 37350])).
% 12.49/12.73 tff(37354,plain,
% 12.49/12.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.73 inference(quant_inst,[status(thm)],[])).
% 12.49/12.73 tff(37355,plain,
% 12.49/12.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[37354, 37353])).
% 12.49/12.73 tff(37356,plain,
% 12.49/12.73 ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[37355, 391, 37349])).
% 12.49/12.73 tff(37357,plain,
% 12.49/12.73 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[37356, 37347, 37344])).
% 12.49/12.73 tff(37358,plain,
% 12.49/12.73 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[37357, 37092])).
% 12.49/12.73 tff(37359,plain,
% 12.49/12.73 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[20797, 37358, 37090])).
% 12.49/12.73 tff(37360,plain,
% 12.49/12.73 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[37359, 37075])).
% 12.49/12.73 tff(37361,plain,
% 12.49/12.73 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37073])).
% 12.49/12.73 tff(37362,plain,
% 12.49/12.73 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 12.49/12.73 inference(symmetry,[status(thm)],[37361])).
% 12.49/12.73 tff(37363,plain,
% 12.49/12.73 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37073])).
% 12.49/12.73 tff(37364,plain,
% 12.49/12.73 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37363])).
% 12.49/12.73 tff(37365,plain,
% 12.49/12.73 (~r(s(s(z)), z)),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[10261, 37096, 29426, 182])).
% 12.49/12.73 tff(37366,plain,
% 12.49/12.73 (b(s(s(z)), z)),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[1211, 37365])).
% 12.49/12.73 tff(37367,plain,
% 12.49/12.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.73 inference(rewrite,[status(thm)],[])).
% 12.49/12.73 tff(37368,plain,
% 12.49/12.73 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.73 inference(rewrite,[status(thm)],[])).
% 12.49/12.73 tff(37369,plain,
% 12.49/12.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37368])).
% 12.49/12.73 tff(37370,plain,
% 12.49/12.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.73 inference(transitivity,[status(thm)],[37369, 37367])).
% 12.49/12.73 tff(37371,plain,
% 12.49/12.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.73 inference(quant_inst,[status(thm)],[])).
% 12.49/12.73 tff(37372,plain,
% 12.49/12.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[37371, 37370])).
% 12.49/12.73 tff(37373,plain,
% 12.49/12.73 ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[37372, 391, 37366])).
% 12.49/12.73 tff(37374,plain,
% 12.49/12.73 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[37373, 37347, 37344])).
% 12.49/12.73 tff(37375,plain,
% 12.49/12.73 (~b(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[37374, 37364])).
% 12.49/12.73 tff(37376,plain,
% 12.49/12.73 (r(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[11041, 37375])).
% 12.49/12.73 tff(37377,plain,
% 12.49/12.73 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[37376, 37362])).
% 12.49/12.73 tff(37378,plain,
% 12.49/12.73 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37073])).
% 12.49/12.73 tff(37379,plain,
% 12.49/12.73 (r(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 12.49/12.73 inference(symmetry,[status(thm)],[37378])).
% 12.49/12.73 tff(37380,plain,
% 12.49/12.73 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37070])).
% 12.49/12.73 tff(37381,plain,
% 12.49/12.73 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 12.49/12.73 inference(transitivity,[status(thm)],[37380, 37379])).
% 12.49/12.73 tff(37382,plain,
% 12.49/12.73 (~b(s(s(s(elem!1))), s(elem!1))),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[12799, 37343, 10682, 37103])).
% 12.49/12.73 tff(37383,plain,
% 12.49/12.73 (r(s(s(s(elem!1))), s(elem!1))),
% 12.49/12.73 inference(unit_resolution,[status(thm)],[588, 37382, 37089])).
% 12.49/12.73 tff(37384,plain,
% 12.49/12.73 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[37383, 37381])).
% 12.49/12.73 tff(37385,plain,
% 12.49/12.73 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 12.49/12.73 inference(commutativity,[status(thm)],[])).
% 12.49/12.73 tff(37386,plain,
% 12.49/12.73 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 12.49/12.73 inference(symmetry,[status(thm)],[37385])).
% 12.49/12.73 tff(37387,plain,
% 12.49/12.73 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37386])).
% 12.49/12.73 tff(37388,plain,
% 12.49/12.73 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 12.49/12.73 inference(modus_ponens,[status(thm)],[8678, 37387])).
% 12.49/12.73 tff(37389,plain,
% 12.49/12.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.73 inference(rewrite,[status(thm)],[])).
% 12.49/12.73 tff(37390,plain,
% 12.49/12.73 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.73 inference(rewrite,[status(thm)],[])).
% 12.49/12.73 tff(37391,plain,
% 12.49/12.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 12.49/12.73 inference(monotonicity,[status(thm)],[37390])).
% 12.49/12.73 tff(37392,plain,
% 12.49/12.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.74 inference(transitivity,[status(thm)],[37391, 37389])).
% 12.49/12.74 tff(37393,plain,
% 12.49/12.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 12.49/12.74 inference(quant_inst,[status(thm)],[])).
% 12.49/12.74 tff(37394,plain,
% 12.49/12.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.74 inference(modus_ponens,[status(thm)],[37393, 37392])).
% 12.49/12.74 tff(37395,plain,
% 12.49/12.74 ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37394, 391, 37366, 37349])).
% 12.49/12.74 tff(37396,plain,
% 12.49/12.74 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37395, 37344, 37347])).
% 12.49/12.74 tff(37397,plain,
% 12.49/12.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 12.49/12.74 inference(rewrite,[status(thm)],[])).
% 12.49/12.74 tff(37398,plain,
% 12.49/12.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 12.49/12.74 inference(quant_inst,[status(thm)],[])).
% 12.49/12.74 tff(37399,plain,
% 12.49/12.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 12.49/12.74 inference(modus_ponens,[status(thm)],[37398, 37397])).
% 12.49/12.74 tff(37400,plain,
% 12.49/12.74 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37399, 42, 37396])).
% 12.49/12.74 tff(37401,plain,
% 12.49/12.74 (r(s(s(z)), s(s(s(s(s(z))))))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37400, 37388])).
% 12.49/12.74 tff(37402,plain,
% 12.49/12.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.74 inference(rewrite,[status(thm)],[])).
% 12.49/12.74 tff(37403,plain,
% 12.49/12.74 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.74 inference(rewrite,[status(thm)],[])).
% 12.49/12.74 tff(37404,plain,
% 12.49/12.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 12.49/12.74 inference(monotonicity,[status(thm)],[37403])).
% 12.49/12.74 tff(37405,plain,
% 12.49/12.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 12.49/12.74 inference(transitivity,[status(thm)],[37404, 37402])).
% 12.49/12.74 tff(37406,plain,
% 12.49/12.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 12.49/12.74 inference(quant_inst,[status(thm)],[])).
% 12.49/12.74 tff(37407,plain,
% 12.49/12.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 12.49/12.74 inference(modus_ponens,[status(thm)],[37406, 37405])).
% 12.49/12.74 tff(37408,plain,
% 12.49/12.74 ($false),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37407, 194, 37401, 37384, 37377, 37360])).
% 12.49/12.74 tff(37409,plain,(b(elem!1, z) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (elem!1 = z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.74 tff(37410,plain,
% 12.49/12.74 (b(elem!1, z)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37409, 37062, 181, 2, 89])).
% 12.49/12.74 tff(37411,plain,
% 12.49/12.74 (b(s(s(s(elem!1))), elem!1)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[29228, 90, 411, 721, 37098, 1234, 10682, 665, 121, 21435])).
% 12.49/12.74 tff(37412,plain,
% 12.49/12.74 (~b(z, s(z))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[22918, 90, 1234, 1759])).
% 12.49/12.74 tff(37413,plain,
% 12.49/12.74 (r(z, s(z))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[678, 37412])).
% 12.49/12.74 tff(37414,plain,
% 12.49/12.74 ($false),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[29285, 37413, 37411, 721, 10682, 665, 21435, 411, 89, 1234, 90])).
% 12.49/12.74 tff(37415,plain,((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~r(z, elem!1)) | b(z, elem!1) | (~b(s(z), s(s(s(s(z)))))) | (s(z) = s(elem!1)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.74 tff(37416,plain,
% 12.49/12.74 (~b(s(s(s(s(z)))), z)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37415, 37062, 37058, 37410, 36606, 89, 37060, 118, 36754])).
% 12.49/12.74 tff(37417,plain,
% 12.49/12.74 (~(s(s(s(s(z)))) = elem!1)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[6966, 37416, 37410])).
% 12.49/12.74 tff(37418,plain,
% 12.49/12.74 (r(s(s(s(s(z)))), elem!1)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[762, 37417, 37061])).
% 12.49/12.74 tff(37419,plain,
% 12.49/12.74 (~b(elem!1, s(s(s(s(z)))))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[2088, 391, 37060, 36754, 37058])).
% 12.49/12.74 tff(37420,plain,
% 12.49/12.74 (~(elem!1 = s(s(s(s(z)))))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[769, 37417])).
% 12.49/12.74 tff(37421,plain,
% 12.49/12.74 (r(elem!1, s(s(s(s(z)))))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[781, 37420, 37419])).
% 12.49/12.74 tff(37422,plain,
% 12.49/12.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 12.49/12.74 inference(rewrite,[status(thm)],[])).
% 12.49/12.74 tff(37423,plain,
% 12.49/12.74 (((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 12.49/12.74 inference(rewrite,[status(thm)],[])).
% 12.49/12.74 tff(37424,plain,
% 12.49/12.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z))))))))),
% 12.49/12.74 inference(monotonicity,[status(thm)],[37423])).
% 12.49/12.74 tff(37425,plain,
% 12.49/12.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 12.49/12.74 inference(transitivity,[status(thm)],[37424, 37422])).
% 12.49/12.74 tff(37426,plain,
% 12.49/12.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 12.49/12.74 inference(quant_inst,[status(thm)],[])).
% 12.49/12.74 tff(37427,plain,
% 12.49/12.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 12.49/12.74 inference(modus_ponens,[status(thm)],[37426, 37425])).
% 12.49/12.74 tff(37428,plain,
% 12.49/12.74 ($false),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37427, 194, 36606, 29426, 37421, 37418])).
% 12.49/12.74 tff(37429,plain,(b(s(z), z) | b(z, elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.74 tff(37430,plain,
% 12.49/12.74 (b(s(z), z)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37429, 89, 2])).
% 12.49/12.74 tff(37431,plain,
% 12.49/12.74 (~b(elem!1, z)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[21922, 31666, 37058, 37430])).
% 12.49/12.74 tff(37432,plain,
% 12.49/12.74 (r(elem!1, z)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[526, 37431, 2])).
% 12.49/12.74 tff(37433,plain,
% 12.49/12.74 (~r(s(s(s(s(z)))), elem!1)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37083, 194, 36606, 37432, 29426])).
% 12.49/12.74 tff(37434,plain,
% 12.49/12.74 (~r(s(s(s(elem!1))), elem!1)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[8289, 37432, 36606, 59])).
% 12.49/12.74 tff(37435,plain,
% 12.49/12.74 (~b(z, s(s(elem!1)))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[21335, 3807, 411, 121, 721, 10, 530])).
% 12.49/12.74 tff(37436,plain,
% 12.49/12.74 (r(z, s(s(elem!1)))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[324, 37435])).
% 12.49/12.74 tff(37437,plain,
% 12.49/12.74 (~r(s(s(elem!1)), elem!1)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[867, 37436, 411, 530])).
% 12.49/12.74 tff(37438,plain,
% 12.49/12.74 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[1450, 37436, 59, 18016])).
% 12.49/12.74 tff(37439,plain,
% 12.49/12.74 ($false),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[20595, 37438, 37437, 2053, 411, 59, 530, 721, 3807, 18016])).
% 12.49/12.74 tff(37440,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.74 tff(37441,plain,
% 12.49/12.74 (~(s(s(s(elem!1))) = elem!1)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[37440, 37432, 36606, 29426, 37058, 118, 10])).
% 12.49/12.74 tff(37442,plain,
% 12.49/12.74 (b(s(s(s(elem!1))), elem!1)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[230, 37441, 37434])).
% 12.49/12.74 tff(37443,plain,
% 12.49/12.74 (~r(s(s(s(elem!1))), elem!1)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[8289, 530, 411, 184])).
% 12.49/12.74 tff(37444,plain,
% 12.49/12.74 (b(s(s(s(elem!1))), elem!1)),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[230, 127, 37443])).
% 12.49/12.74 tff(37445,plain,
% 12.49/12.74 ($false),
% 12.49/12.74 inference(unit_resolution,[status(thm)],[21740, 4030, 37444, 411, 721, 590, 530, 184])).
% 12.49/12.74 tff(37446,plain,((s(s(s(elem!1))) = elem!1) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.75 tff(37447,plain,
% 12.49/12.75 (b(elem!1, s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37446, 37441, 37058, 37430, 37432, 59, 36606])).
% 12.49/12.75 tff(37448,plain,
% 12.49/12.75 (~b(s(s(s(s(z)))), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[16861, 37447, 29426, 37097, 59, 37442])).
% 12.49/12.75 tff(37449,plain,
% 12.49/12.75 (s(s(s(s(z)))) = elem!1),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[762, 37448, 37433])).
% 12.49/12.75 tff(37450,plain,
% 12.49/12.75 (b(s(s(z)), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[30679, 37449, 31645])).
% 12.49/12.75 tff(37451,plain,
% 12.49/12.75 (~b(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[16878, 391, 37442, 37447, 37450])).
% 12.49/12.75 tff(37452,plain,
% 12.49/12.75 (r(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[11041, 37451])).
% 12.49/12.75 tff(37453,plain,
% 12.49/12.75 (~b(s(s(s(elem!1))), s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[21754, 37442, 36606, 37058, 37430, 37432, 37447])).
% 12.49/12.75 tff(37454,plain,
% 12.49/12.75 (r(s(s(s(elem!1))), s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[223, 37453])).
% 12.49/12.75 tff(37455,plain,
% 12.49/12.75 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[10940, 37097])).
% 12.49/12.75 tff(37456,plain,
% 12.49/12.75 (~b(z, s(s(s(s(z)))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[16124, 37449, 89])).
% 12.49/12.75 tff(37457,plain,
% 12.49/12.75 (r(z, s(s(s(s(z)))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[800, 37456])).
% 12.49/12.75 tff(37458,plain,
% 12.49/12.75 (~r(s(s(z)), z)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[15362, 37457, 29426, 59, 37455, 31645, 37454])).
% 12.49/12.75 tff(37459,plain,
% 12.49/12.75 (b(s(s(z)), z)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[1211, 37458])).
% 12.49/12.75 tff(37460,plain,
% 12.49/12.75 (~b(s(s(z)), s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[10658, 391, 37459, 31666, 37430])).
% 12.49/12.75 tff(37461,plain,
% 12.49/12.75 (r(s(s(z)), s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[3778, 37460])).
% 12.49/12.75 tff(37462,plain,
% 12.49/12.75 (~b(s(z), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[6252, 37449, 2881])).
% 12.49/12.75 tff(37463,plain,
% 12.49/12.75 (r(s(z), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[632, 37462, 37085])).
% 12.49/12.75 tff(37464,plain,
% 12.49/12.75 ($false),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[10923, 194, 37463, 37454, 37461, 37452])).
% 12.49/12.75 tff(37465,plain,(b(s(z), s(s(s(s(z))))) | b(z, elem!1) | b(z, s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.75 tff(37466,plain,
% 12.49/12.75 (b(z, elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37465, 2881, 2, 10])).
% 12.49/12.75 tff(37467,plain,
% 12.49/12.75 (~b(z, s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[5970, 37466, 36669, 20263])).
% 12.49/12.75 tff(37468,plain,
% 12.49/12.75 ($false),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[678, 37467, 31665])).
% 12.49/12.75 tff(37469,plain,(b(s(z), s(s(s(s(z))))) | (elem!1 = z) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.75 tff(37470,plain,
% 12.49/12.75 (b(z, s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37469, 2881, 2])).
% 12.49/12.75 tff(37471,plain,
% 12.49/12.75 (~b(s(s(s(elem!1))), s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[10690, 31666, 37470, 36608])).
% 12.49/12.75 tff(37472,plain,
% 12.49/12.75 (b(z, elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37053, 31, 2, 3446])).
% 12.49/12.75 tff(37473,plain,
% 12.49/12.75 (~(elem!1 = s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[36679, 1, 2881, 411, 3446, 11173])).
% 12.49/12.75 tff(37474,plain,
% 12.49/12.75 (s(z) = elem!1),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[25009, 1, 11174, 2913, 31, 10682, 664, 133])).
% 12.49/12.75 tff(37475,plain,
% 12.49/12.75 ($false),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[1495, 37474, 37473])).
% 12.49/12.75 tff(37476,plain,((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, elem!1)) | b(s(z), s(s(s(s(z))))) | (~r(z, elem!1)) | b(s(s(s(s(z)))), z) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.75 tff(37477,plain,
% 12.49/12.75 (elem!1 = s(s(s(elem!1)))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37476, 31, 37470, 31666, 37472, 2881, 36606, 3446, 37471])).
% 12.49/12.75 tff(37478,plain,
% 12.49/12.75 (s(s(s(elem!1))) = elem!1),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[129, 37477])).
% 12.49/12.75 tff(37479,plain,
% 12.49/12.75 (~(s(s(s(s(z)))) = elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[1436, 37478])).
% 12.49/12.75 tff(37480,plain,
% 12.49/12.75 (~(elem!1 = s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[11318, 10644, 2, 31665])).
% 12.49/12.75 tff(37481,plain,
% 12.49/12.75 (r(elem!1, s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[837, 37480, 31])).
% 12.49/12.75 tff(37482,plain,
% 12.49/12.75 (~r(elem!1, s(s(s(s(z)))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[11195, 37481, 29426, 2913])).
% 12.49/12.75 tff(37483,plain,
% 12.49/12.75 (r(s(s(s(elem!1))), s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[223, 37471])).
% 12.49/12.75 tff(37484,plain,
% 12.49/12.75 (~(s(z) = elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[1495, 37480])).
% 12.49/12.75 tff(37485,plain,
% 12.49/12.75 (elem!1 = s(s(s(elem!1)))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[25009, 37484, 37483, 2913, 31, 37470, 31666, 133])).
% 12.49/12.75 tff(37486,plain,
% 12.49/12.75 (s(s(s(elem!1))) = elem!1),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[129, 37485])).
% 12.49/12.75 tff(37487,plain,
% 12.49/12.75 (~(s(s(s(s(z)))) = elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[1436, 37486])).
% 12.49/12.75 tff(37488,plain,
% 12.49/12.75 (~(elem!1 = s(s(s(s(z)))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[769, 37487])).
% 12.49/12.75 tff(37489,plain,
% 12.49/12.75 (b(elem!1, s(s(s(s(z)))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[781, 37488, 37482])).
% 12.49/12.75 tff(37490,plain,
% 12.49/12.75 (~r(s(s(s(s(z)))), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[10408, 37481, 29426, 36606])).
% 12.49/12.75 tff(37491,plain,
% 12.49/12.75 (b(s(s(s(s(z)))), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[762, 37487, 37490])).
% 12.49/12.75 tff(37492,plain,
% 12.49/12.75 (~b(elem!1, s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[16115, 37481, 2913, 133, 37470, 31, 31666, 37484])).
% 12.49/12.75 tff(37493,plain,
% 12.49/12.75 (r(z, s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[10797, 37492, 36606, 2913, 31, 36608, 31666, 10645])).
% 12.49/12.75 tff(37494,plain,
% 12.49/12.75 (~b(elem!1, z)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[19321, 37493, 36606, 2881, 31, 31666, 36608, 2, 37484])).
% 12.49/12.75 tff(37495,plain,
% 12.49/12.75 (r(elem!1, z)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[526, 37494, 2])).
% 12.49/12.75 tff(37496,plain,
% 12.49/12.75 ($false),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[31626, 37495, 37491, 37470, 31666, 37485, 37489, 36608, 133, 31645])).
% 12.49/12.75 tff(37497,plain,(b(z, s(s(s(s(z))))) | (~b(z, elem!1)) | (elem!1 = z) | b(s(z), s(s(s(s(z))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.75 tff(37498,plain,
% 12.49/12.75 (b(z, s(s(s(s(z)))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37497, 37472, 2, 2881, 31])).
% 12.49/12.75 tff(37499,plain,
% 12.49/12.75 (r(elem!1, s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[8406, 37478, 37483])).
% 12.49/12.75 tff(37500,plain,
% 12.49/12.75 (~r(s(s(s(s(z)))), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[10408, 37499, 29426, 36606])).
% 12.49/12.75 tff(37501,plain,
% 12.49/12.75 (~r(elem!1, s(s(s(s(z)))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[11195, 37499, 29426, 2913])).
% 12.49/12.75 tff(37502,plain,
% 12.49/12.75 ($false),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[31903, 37501, 37500, 37472, 37498, 37479])).
% 12.49/12.75 tff(37503,plain,(b(elem!1, s(z)) | b(s(z), s(s(s(s(z))))) | b(s(s(s(s(z)))), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.75 tff(37504,plain,
% 12.49/12.75 (b(elem!1, s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37503, 2881, 3446, 2])).
% 12.49/12.75 tff(37505,plain,
% 12.49/12.75 (~(s(z) = elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[20271, 37504])).
% 12.49/12.75 tff(37506,plain,
% 12.49/12.75 (r(s(z), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[632, 37505, 2829])).
% 12.49/12.75 tff(37507,plain,
% 12.49/12.75 (~b(elem!1, z)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[21922, 37504, 31666, 36608])).
% 12.49/12.75 tff(37508,plain,
% 12.49/12.75 (r(elem!1, z)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[526, 37507, 2])).
% 12.49/12.75 tff(37509,plain,
% 12.49/12.75 (~r(s(s(s(s(z)))), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[6077, 37508, 37506, 2913])).
% 12.49/12.75 tff(37510,plain,
% 12.49/12.75 (~r(s(s(s(elem!1))), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[23283, 37508, 37506, 37483])).
% 12.49/12.75 tff(37511,plain,
% 12.49/12.75 (~b(z, elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[5970, 37504, 36608, 31666])).
% 12.49/12.75 tff(37512,plain,
% 12.49/12.75 (~(elem!1 = s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[22900, 37511, 37470])).
% 12.49/12.75 tff(37513,plain,
% 12.49/12.75 (~(s(s(s(elem!1))) = elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[8, 37512])).
% 12.49/12.75 tff(37514,plain,
% 12.49/12.75 (b(s(s(s(elem!1))), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[230, 37513, 37510])).
% 12.49/12.75 tff(37515,plain,
% 12.49/12.75 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[2849, 37505])).
% 12.49/12.75 tff(37516,plain,
% 12.49/12.75 (~b(s(z), s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[36898, 37515, 36606, 37470, 29426, 36608])).
% 12.49/12.75 tff(37517,plain,
% 12.49/12.75 (r(s(z), s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[247, 37516])).
% 12.49/12.75 tff(37518,plain,
% 12.49/12.75 (~r(s(s(s(elem!1))), z)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[5645, 5429, 410, 232])).
% 12.49/12.75 tff(37519,plain,
% 12.49/12.75 ($false),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[377, 37518, 25419])).
% 12.49/12.75 tff(37520,plain,(b(s(z), elem!1) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (s(z) = elem!1) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.75 tff(37521,plain,
% 12.49/12.75 ($false),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37520, 6124, 4028, 411, 2829, 10682, 150, 530, 232])).
% 12.49/12.75 tff(37522,plain,(b(elem!1, s(s(s(elem!1)))) | (~r(z, elem!1)) | b(s(z), elem!1) | (~b(z, s(s(s(elem!1))))) | (s(z) = elem!1) | (~r(elem!1, z)) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.75 tff(37523,plain,
% 12.49/12.75 (b(elem!1, s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37522, 37470, 2829, 36606, 37505, 37508, 37517, 37512])).
% 12.49/12.75 tff(37524,plain,
% 12.49/12.75 (~b(s(s(s(s(z)))), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[36693, 37523, 37515, 37514, 37483, 2913])).
% 12.49/12.75 tff(37525,plain,
% 12.49/12.75 (s(s(s(s(z)))) = elem!1),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[762, 37524, 37509])).
% 12.49/12.75 tff(37526,plain,
% 12.49/12.75 (b(s(s(z)), elem!1)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[30679, 37525, 31645])).
% 12.49/12.75 tff(37527,plain,
% 12.49/12.75 (~b(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[16878, 391, 37514, 37523, 37526])).
% 12.49/12.75 tff(37528,plain,
% 12.49/12.75 (r(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[11041, 37527])).
% 12.49/12.75 tff(37529,plain,
% 12.49/12.75 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 12.49/12.75 inference(rewrite,[status(thm)],[])).
% 12.49/12.75 tff(37530,plain,
% 12.49/12.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 12.49/12.75 inference(monotonicity,[status(thm)],[37529])).
% 12.49/12.75 tff(37531,plain,
% 12.49/12.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 12.49/12.75 inference(transitivity,[status(thm)],[37530, 18932])).
% 12.49/12.75 tff(37532,plain,
% 12.49/12.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 12.49/12.75 inference(quant_inst,[status(thm)],[])).
% 12.49/12.75 tff(37533,plain,
% 12.49/12.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 12.49/12.75 inference(modus_ponens,[status(thm)],[37532, 37531])).
% 12.49/12.75 tff(37534,plain,
% 12.49/12.75 (~r(s(s(z)), s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37533, 194, 37517, 37483, 37528])).
% 12.49/12.75 tff(37535,plain,
% 12.49/12.75 (b(s(s(z)), s(z))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[3778, 37534])).
% 12.49/12.75 tff(37536,plain,
% 12.49/12.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 12.49/12.75 inference(rewrite,[status(thm)],[])).
% 12.49/12.75 tff(37537,plain,
% 12.49/12.75 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 12.49/12.75 inference(rewrite,[status(thm)],[])).
% 12.49/12.75 tff(37538,plain,
% 12.49/12.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 12.49/12.75 inference(monotonicity,[status(thm)],[37537])).
% 12.49/12.75 tff(37539,plain,
% 12.49/12.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 12.49/12.75 inference(transitivity,[status(thm)],[37538, 37536])).
% 12.49/12.75 tff(37540,plain,
% 12.49/12.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 12.49/12.75 inference(quant_inst,[status(thm)],[])).
% 12.49/12.75 tff(37541,plain,
% 12.49/12.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 12.49/12.75 inference(modus_ponens,[status(thm)],[37540, 37539])).
% 12.49/12.75 tff(37542,plain,
% 12.49/12.75 (~r(s(z), s(s(z)))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[37541, 194, 37517, 37483, 37528])).
% 12.49/12.75 tff(37543,plain,
% 12.49/12.75 (b(s(z), s(s(z)))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[1788, 37542])).
% 12.49/12.75 tff(37544,plain,
% 12.49/12.75 (~b(z, s(s(s(s(z)))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[16124, 37525, 37511])).
% 12.49/12.75 tff(37545,plain,
% 12.49/12.75 (r(z, s(s(s(s(z)))))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[800, 37544])).
% 12.49/12.75 tff(37546,plain,
% 12.49/12.75 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 12.49/12.75 inference(monotonicity,[status(thm)],[37525])).
% 12.49/12.75 tff(37547,plain,
% 12.49/12.75 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 12.49/12.75 inference(transitivity,[status(thm)],[37546, 698])).
% 12.49/12.75 tff(37548,plain,
% 12.49/12.75 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(z))))),
% 12.49/12.75 inference(monotonicity,[status(thm)],[37547])).
% 12.49/12.75 tff(37549,plain,
% 12.49/12.75 (~(elem!1 = s(s(z)))),
% 12.49/12.75 inference(modus_ponens,[status(thm)],[714, 37548])).
% 12.49/12.75 tff(37550,plain,
% 12.49/12.75 (~b(elem!1, s(s(z)))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[10150, 37543, 37504, 37535])).
% 12.49/12.75 tff(37551,plain,
% 12.49/12.75 (r(elem!1, s(s(z)))),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[3394, 37550, 37549])).
% 12.49/12.75 tff(37552,plain,
% 12.49/12.75 (~r(s(s(z)), z)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[8570, 37551, 37508, 37545])).
% 12.49/12.75 tff(37553,plain,
% 12.49/12.75 (b(s(s(z)), z)),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[1211, 37552])).
% 12.49/12.75 tff(37554,plain,
% 12.49/12.75 ($false),
% 12.49/12.75 inference(unit_resolution,[status(thm)],[16413, 391, 37553, 37543, 37535, 31666])).
% 12.49/12.75 tff(37555,plain,(b(s(z), s(s(s(s(z))))) | b(s(z), elem!1) | (elem!1 = z) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.76 tff(37556,plain,
% 12.49/12.76 (b(s(z), s(s(s(s(z)))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[37555, 3446, 2, 2829])).
% 12.49/12.76 tff(37557,plain,
% 12.49/12.76 (~(s(s(s(s(z)))) = elem!1)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[8916, 37556, 2829])).
% 12.49/12.76 tff(37558,plain,
% 12.49/12.76 (b(s(z), s(s(s(s(z)))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[37469, 10, 2])).
% 12.49/12.76 tff(37559,plain,
% 12.49/12.76 (~r(elem!1, z)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[33450, 719, 721, 1234, 8917, 29426])).
% 12.49/12.76 tff(37560,plain,
% 12.49/12.76 (b(elem!1, z)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[526, 37559, 2])).
% 12.49/12.76 tff(37561,plain,
% 12.49/12.76 (~b(z, s(z))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[21922, 37560, 721, 590])).
% 12.49/12.76 tff(37562,plain,
% 12.49/12.76 (r(z, s(z))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[678, 37561])).
% 12.49/12.76 tff(37563,plain,
% 12.49/12.76 (~r(s(z), s(s(z)))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[22159, 37562, 184, 183])).
% 12.49/12.76 tff(37564,plain,
% 12.49/12.76 (b(s(z), s(s(z)))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[1788, 37563])).
% 12.49/12.76 tff(37565,plain,
% 12.49/12.76 (~r(elem!1, s(z))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[18234, 37562, 36606, 3446, 1234, 37560, 21435])).
% 12.49/12.76 tff(37566,plain,
% 12.49/12.76 (~b(s(s(s(s(z)))), s(z))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[2097, 719, 36606, 721, 8917, 1234])).
% 12.49/12.76 tff(37567,plain,
% 12.49/12.76 (r(s(s(s(s(z)))), s(z))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[749, 37566])).
% 12.49/12.76 tff(37568,plain,
% 12.49/12.76 (~r(elem!1, s(s(s(s(z)))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[15063, 37567, 36606, 719])).
% 12.49/12.76 tff(37569,plain,
% 12.49/12.76 (r(s(s(s(s(z)))), elem!1)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[20438, 37568, 1234, 721, 8917])).
% 12.49/12.76 tff(37570,plain,
% 12.49/12.76 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[22263, 37564, 719, 590, 37569])).
% 12.49/12.76 tff(37571,plain,
% 12.49/12.76 (b(s(s(z)), s(s(s(s(z)))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[3652, 37570])).
% 12.49/12.76 tff(37572,plain,
% 12.49/12.76 (elem!1 = s(s(z))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[10152, 37571, 21435, 1234, 2829, 37567, 37565, 37564])).
% 12.49/12.76 tff(37573,plain,
% 12.49/12.76 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 12.49/12.76 inference(monotonicity,[status(thm)],[37572])).
% 12.49/12.76 tff(37574,plain,
% 12.49/12.76 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 12.49/12.76 inference(symmetry,[status(thm)],[37573])).
% 12.49/12.76 tff(37575,plain,
% 12.49/12.76 (b(s(z), elem!1)),
% 12.49/12.76 inference(modus_ponens,[status(thm)],[37564, 37574])).
% 12.49/12.76 tff(37576,plain,
% 12.49/12.76 ($false),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[2829, 37575])).
% 12.49/12.76 tff(37577,plain,((~r(z, s(s(s(s(z)))))) | b(s(z), elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(s(z)))), z) | (~b(elem!1, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.76 tff(37578,plain,
% 12.49/12.76 (~r(z, s(s(s(s(z)))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[37577, 2829, 1234, 590, 184, 183, 3446, 721, 2])).
% 12.49/12.76 tff(37579,plain,
% 12.49/12.76 (b(z, s(s(s(s(z)))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[800, 37578])).
% 12.49/12.76 tff(37580,plain,
% 12.49/12.76 (~b(s(s(s(s(z)))), s(z))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[17292, 37579, 1234, 590])).
% 12.49/12.76 tff(37581,plain,
% 12.49/12.76 (r(s(s(s(s(z)))), s(z))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[749, 37580])).
% 12.49/12.76 tff(37582,plain,
% 12.49/12.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.76 inference(rewrite,[status(thm)],[])).
% 12.49/12.76 tff(37583,plain,
% 12.49/12.76 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.76 inference(rewrite,[status(thm)],[])).
% 12.49/12.76 tff(37584,plain,
% 12.49/12.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 12.49/12.76 inference(monotonicity,[status(thm)],[37583])).
% 12.49/12.76 tff(37585,plain,
% 12.49/12.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.76 inference(transitivity,[status(thm)],[37584, 37582])).
% 12.49/12.76 tff(37586,plain,
% 12.49/12.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.76 inference(quant_inst,[status(thm)],[])).
% 12.49/12.76 tff(37587,plain,
% 12.49/12.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 12.49/12.76 inference(modus_ponens,[status(thm)],[37586, 37585])).
% 12.49/12.76 tff(37588,plain,
% 12.49/12.76 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[37587, 194, 26933, 183, 37581])).
% 12.49/12.76 tff(37589,plain,
% 12.49/12.76 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[15351, 37588, 21770])).
% 12.49/12.76 tff(37590,plain,
% 12.49/12.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 12.49/12.76 inference(rewrite,[status(thm)],[])).
% 12.49/12.76 tff(37591,plain,
% 12.49/12.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 12.49/12.76 inference(quant_inst,[status(thm)],[])).
% 12.49/12.76 tff(37592,plain,
% 12.49/12.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 12.49/12.76 inference(modus_ponens,[status(thm)],[37591, 37590])).
% 12.49/12.76 tff(37593,plain,
% 12.49/12.76 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[37592, 194, 26933, 183, 37581])).
% 12.49/12.76 tff(37594,plain,
% 12.49/12.76 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[2853, 42, 21769, 37593])).
% 12.49/12.76 tff(37595,plain,
% 12.49/12.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.76 inference(rewrite,[status(thm)],[])).
% 12.49/12.76 tff(37596,plain,
% 12.49/12.76 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.76 inference(rewrite,[status(thm)],[])).
% 12.49/12.76 tff(37597,plain,
% 12.49/12.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 12.49/12.76 inference(monotonicity,[status(thm)],[37596])).
% 12.49/12.76 tff(37598,plain,
% 12.49/12.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.76 inference(transitivity,[status(thm)],[37597, 37595])).
% 12.49/12.76 tff(37599,plain,
% 12.49/12.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 12.49/12.76 inference(quant_inst,[status(thm)],[])).
% 12.49/12.76 tff(37600,plain,
% 12.49/12.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 12.49/12.76 inference(modus_ponens,[status(thm)],[37599, 37598])).
% 12.49/12.76 tff(37601,plain,
% 12.49/12.76 ($false),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[37600, 391, 1234, 37579, 590, 37594, 37589])).
% 12.49/12.76 tff(37602,plain,(b(s(z), elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(s(z)))), z) | (~b(elem!1, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.76 tff(37603,plain,
% 12.49/12.76 (b(s(z), elem!1)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[37602, 183, 36669, 37558, 59, 3446, 20263, 2])).
% 12.49/12.76 tff(37604,plain,
% 12.49/12.76 (~b(z, elem!1)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[4857, 37603, 36669, 20263])).
% 12.49/12.76 tff(37605,plain,
% 12.49/12.76 (~r(s(s(s(s(z)))), elem!1)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[37083, 194, 411, 530, 2053])).
% 12.49/12.76 tff(37606,plain,
% 12.49/12.76 (s(s(s(s(z)))) = elem!1),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[20438, 37605, 721, 1234, 36912])).
% 12.49/12.76 tff(37607,plain,
% 12.49/12.76 (s(s(s(s(s(z))))) = s(elem!1)),
% 12.49/12.76 inference(monotonicity,[status(thm)],[37606])).
% 12.49/12.76 tff(37608,plain,
% 12.49/12.76 (r(s(s(s(s(s(z))))), z) <=> r(s(elem!1), z)),
% 12.49/12.76 inference(monotonicity,[status(thm)],[37607])).
% 12.49/12.76 tff(37609,plain,
% 12.49/12.76 (r(s(elem!1), z) <=> r(s(s(s(s(s(z))))), z)),
% 12.49/12.76 inference(symmetry,[status(thm)],[37608])).
% 12.49/12.76 tff(37610,plain,
% 12.49/12.76 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(s(z))))), z))),
% 12.49/12.76 inference(monotonicity,[status(thm)],[37609])).
% 12.49/12.76 tff(37611,plain,
% 12.49/12.76 (~r(s(s(s(elem!1))), elem!1)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[8289, 530, 411, 59])).
% 12.49/12.76 tff(37612,plain,
% 12.49/12.76 (~(s(s(s(elem!1))) = elem!1)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[37440, 530, 411, 2053, 721, 121, 10])).
% 12.49/12.76 tff(37613,plain,
% 12.49/12.76 (b(s(s(s(elem!1))), elem!1)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[230, 37612, 37611])).
% 12.49/12.76 tff(37614,plain,
% 12.49/12.76 (~(s(elem!1) = elem!1)),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[158, 37612])).
% 12.49/12.76 tff(37615,plain,
% 12.49/12.76 (~(elem!1 = s(elem!1))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[166, 37614])).
% 12.49/12.76 tff(37616,plain,
% 12.49/12.76 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[717, 37606])).
% 12.49/12.76 tff(37617,plain,
% 12.49/12.76 (~b(z, s(s(s(s(z)))))),
% 12.49/12.76 inference(unit_resolution,[status(thm)],[18671, 37605, 89, 590, 1234, 36912])).
% 12.49/12.77 tff(37618,plain,
% 12.49/12.77 (r(z, s(s(s(s(z)))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[800, 37617])).
% 12.49/12.77 tff(37619,plain,
% 12.49/12.77 (~b(s(z), s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[22138, 37612, 411, 721, 590, 530, 59])).
% 12.49/12.77 tff(37620,plain,
% 12.49/12.77 (r(s(z), s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[247, 37619])).
% 12.49/12.77 tff(37621,plain,
% 12.49/12.77 (b(elem!1, s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[37446, 37612, 721, 590, 530, 59, 411])).
% 12.49/12.77 tff(37622,plain,
% 12.49/12.77 (~b(s(s(s(elem!1))), s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[21754, 37613, 411, 721, 590, 530, 37621])).
% 12.49/12.77 tff(37623,plain,
% 12.49/12.77 (r(s(s(s(elem!1))), s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[223, 37622])).
% 12.49/12.77 tff(37624,plain,
% 12.49/12.77 (~r(z, s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[21974, 37623, 59, 37620])).
% 12.49/12.77 tff(37625,plain,
% 12.49/12.77 (b(z, s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[678, 37624])).
% 12.49/12.77 tff(37626,plain,
% 12.49/12.77 (~r(s(s(z)), z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[36295, 37625, 59, 2053, 21769, 590, 37618])).
% 12.49/12.77 tff(37627,plain,
% 12.49/12.77 (b(s(s(z)), z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[1211, 37626])).
% 12.49/12.77 tff(37628,plain,
% 12.49/12.77 (b(s(z), elem!1)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[8916, 37606, 1234])).
% 12.49/12.77 tff(37629,plain,
% 12.49/12.77 (~b(s(z), s(s(z)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[18902, 391, 37628, 37627, 37625, 590])).
% 12.49/12.77 tff(37630,plain,
% 12.49/12.77 (r(s(z), s(s(z)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[1788, 37629])).
% 12.49/12.77 tff(37631,plain,
% 12.49/12.77 (~b(s(s(z)), s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[18894, 391, 37628, 37627, 37625, 590])).
% 12.49/12.77 tff(37632,plain,
% 12.49/12.77 (r(s(s(z)), s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[3778, 37631])).
% 12.49/12.77 tff(37633,plain,
% 12.49/12.77 (~r(s(s(s(elem!1))), s(s(z)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[11551, 37632, 37620, 37630])).
% 12.49/12.77 tff(37634,plain,
% 12.49/12.77 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[10713, 42, 37633])).
% 12.49/12.77 tff(37635,plain,
% 12.49/12.77 (b(s(s(s(elem!1))), s(s(z)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[37634, 10703])).
% 12.49/12.77 tff(37636,plain,
% 12.49/12.77 (~r(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[18934, 194, 37620, 37623, 37632])).
% 12.49/12.77 tff(37637,plain,
% 12.49/12.77 (b(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[11041, 37636])).
% 12.49/12.77 tff(37638,plain,
% 12.49/12.77 (~b(s(s(z)), elem!1)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[15437, 391, 37613, 37621, 37637])).
% 12.49/12.77 tff(37639,plain,
% 12.49/12.77 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[30679, 37638, 37606])).
% 12.49/12.77 tff(37640,plain,
% 12.49/12.77 (r(s(s(z)), s(s(s(s(z)))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[3652, 37639])).
% 12.49/12.77 tff(37641,plain,
% 12.49/12.77 (~b(s(s(s(elem!1))), z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[19720, 37640, 2053, 59, 37635, 37618])).
% 12.49/12.77 tff(37642,plain,
% 12.49/12.77 (r(s(s(s(elem!1))), z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[377, 37641])).
% 12.49/12.77 tff(37643,plain,
% 12.49/12.77 (elem!1 = s(s(s(s(z))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[16908, 37606])).
% 12.49/12.77 tff(37644,plain,
% 12.49/12.77 (b(s(s(s(s(z)))), s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[13738, 37643, 721])).
% 12.49/12.77 tff(37645,plain,
% 12.49/12.77 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 12.49/12.77 inference(monotonicity,[status(thm)],[37606])).
% 12.49/12.77 tff(37646,plain,
% 12.49/12.77 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 12.49/12.77 inference(transitivity,[status(thm)],[37645, 698])).
% 12.49/12.77 tff(37647,plain,
% 12.49/12.77 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 12.49/12.77 inference(transitivity,[status(thm)],[37646, 8492])).
% 12.49/12.77 tff(37648,plain,
% 12.49/12.77 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 12.49/12.77 inference(monotonicity,[status(thm)],[37647])).
% 12.49/12.77 tff(37649,plain,
% 12.49/12.77 (~(s(s(z)) = elem!1)),
% 12.49/12.77 inference(modus_ponens,[status(thm)],[714, 37648])).
% 12.49/12.77 tff(37650,plain,
% 12.49/12.77 (r(s(s(z)), elem!1)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[4730, 37638, 37649])).
% 12.49/12.77 tff(37651,plain,
% 12.49/12.77 (~r(z, s(s(z)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[8513, 37650, 411, 530])).
% 12.49/12.77 tff(37652,plain,
% 12.49/12.77 (b(z, s(s(z)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[18613, 37651])).
% 12.49/12.77 tff(37653,plain,
% 12.49/12.77 (~b(s(s(s(s(s(z))))), z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[18810, 37652, 1234, 37625, 37644, 37630, 37640, 37627])).
% 12.49/12.77 tff(37654,plain,
% 12.49/12.77 (r(s(s(s(s(s(z))))), z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[16530, 37653])).
% 12.49/12.77 tff(37655,plain,
% 12.49/12.77 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 12.49/12.77 inference(monotonicity,[status(thm)],[23648, 6534])).
% 12.49/12.77 tff(37656,plain,
% 12.49/12.77 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 12.49/12.77 inference(symmetry,[status(thm)],[37655])).
% 12.49/12.77 tff(37657,plain,
% 12.49/12.77 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 12.49/12.77 inference(modus_ponens,[status(thm)],[613, 37656])).
% 12.49/12.77 tff(37658,plain,
% 12.49/12.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 12.49/12.77 inference(rewrite,[status(thm)],[])).
% 12.49/12.77 tff(37659,plain,
% 12.49/12.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 12.49/12.77 inference(quant_inst,[status(thm)],[])).
% 12.49/12.77 tff(37660,plain,
% 12.49/12.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 12.49/12.77 inference(modus_ponens,[status(thm)],[37659, 37658])).
% 12.49/12.77 tff(37661,plain,
% 12.49/12.77 ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[37660, 194, 719, 16500])).
% 12.49/12.77 tff(37662,plain,
% 12.49/12.77 ($false),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[37661, 37657, 23651])).
% 12.49/12.77 tff(37663,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.77 tff(37664,plain,
% 12.49/12.77 (~r(s(s(s(elem!1))), s(elem!1))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[37663, 37654, 37643, 37618, 37642])).
% 12.49/12.77 tff(37665,plain,
% 12.49/12.77 (b(s(s(s(elem!1))), s(elem!1))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[588, 37664, 37616])).
% 12.49/12.77 tff(37666,plain,
% 12.49/12.77 (~r(s(elem!1), z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[3554, 37665, 37615, 59, 530, 37613])).
% 12.49/12.77 tff(37667,plain,
% 12.49/12.77 (~r(s(s(s(s(s(z))))), z)),
% 12.49/12.77 inference(modus_ponens,[status(thm)],[37666, 37610])).
% 12.49/12.77 tff(37668,plain,
% 12.49/12.77 ($false),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[37654, 37667])).
% 12.49/12.77 tff(37669,plain,((~r(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | b(z, elem!1) | (s(z) = s(elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.77 tff(37670,plain,
% 12.49/12.77 (~r(elem!1, z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[37669, 37604, 29426, 36606, 36669, 20263, 37558, 118, 10])).
% 12.49/12.77 tff(37671,plain,
% 12.49/12.77 (b(elem!1, z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[526, 37670, 2])).
% 12.49/12.77 tff(37672,plain,
% 12.49/12.77 (~b(z, s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[21922, 37671, 20263, 36669])).
% 12.49/12.77 tff(37673,plain,
% 12.49/12.77 (r(z, s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[678, 37672])).
% 12.49/12.77 tff(37674,plain,
% 12.49/12.77 (~r(s(z), s(s(z)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[22159, 37673, 59, 183])).
% 12.49/12.77 tff(37675,plain,
% 12.49/12.77 (b(s(z), s(s(z)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[1788, 37674])).
% 12.49/12.77 tff(37676,plain,
% 12.49/12.77 (r(s(s(s(s(z)))), elem!1)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[17542, 37671, 36606, 36669, 3446, 37558, 37603])).
% 12.49/12.77 tff(37677,plain,
% 12.49/12.77 (~r(s(z), s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[21974, 37673, 59, 183])).
% 12.49/12.77 tff(37678,plain,
% 12.49/12.77 (b(s(z), s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[247, 37677])).
% 12.49/12.77 tff(37679,plain,
% 12.49/12.77 (~r(elem!1, s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[19887, 183, 36606, 59])).
% 12.49/12.77 tff(37680,plain,
% 12.49/12.77 (~(s(s(s(elem!1))) = elem!1)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[15970, 37670, 10, 183])).
% 12.49/12.77 tff(37681,plain,
% 12.49/12.77 (~(elem!1 = s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[129, 37680])).
% 12.49/12.77 tff(37682,plain,
% 12.49/12.77 (b(elem!1, s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[424, 37681, 37679])).
% 12.49/12.77 tff(37683,plain,
% 12.49/12.77 (~r(s(s(s(elem!1))), z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[37338, 37678, 29426, 36606, 37603, 37682, 20304])).
% 12.49/12.77 tff(37684,plain,
% 12.49/12.77 (b(s(s(s(elem!1))), z)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[377, 37683])).
% 12.49/12.77 tff(37685,plain,
% 12.49/12.77 (~b(z, s(s(elem!1)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[22283, 37684, 37603, 37682, 37678])).
% 12.49/12.77 tff(37686,plain,
% 12.49/12.77 (r(z, s(s(elem!1)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[324, 37685])).
% 12.49/12.77 tff(37687,plain,
% 12.49/12.77 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[8251, 37680])).
% 12.49/12.77 tff(37688,plain,
% 12.49/12.77 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[314, 37687])).
% 12.49/12.77 tff(37689,plain,
% 12.49/12.77 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[1418, 37686, 59, 183])).
% 12.49/12.77 tff(37690,plain,
% 12.49/12.77 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[1356, 37689, 37688])).
% 12.49/12.77 tff(37691,plain,
% 12.49/12.77 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[22188, 37690, 37682, 20263, 37678])).
% 12.49/12.77 tff(37692,plain,
% 12.49/12.77 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[1370, 37691, 37687])).
% 12.49/12.77 tff(37693,plain,
% 12.49/12.77 (~r(s(s(elem!1)), s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[348, 37692, 59, 37686])).
% 12.49/12.77 tff(37694,plain,
% 12.49/12.77 (b(s(s(elem!1)), s(z))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[362, 37693])).
% 12.49/12.77 tff(37695,plain,
% 12.49/12.77 (s(s(elem!1)) = elem!1),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[1324, 37694, 36606, 20263, 37603, 37671, 37686])).
% 12.49/12.77 tff(37696,plain,
% 12.49/12.77 (s(s(s(elem!1))) = s(elem!1)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[451, 37695])).
% 12.49/12.77 tff(37697,plain,
% 12.49/12.77 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 12.49/12.77 inference(monotonicity,[status(thm)],[37696])).
% 12.49/12.77 tff(37698,plain,
% 12.49/12.77 (b(s(z), s(elem!1))),
% 12.49/12.77 inference(modus_ponens,[status(thm)],[37678, 37697])).
% 12.49/12.77 tff(37699,plain,
% 12.49/12.77 (~(s(elem!1) = elem!1)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[158, 37680])).
% 12.49/12.77 tff(37700,plain,
% 12.49/12.77 (~(elem!1 = s(elem!1))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[166, 37699])).
% 12.49/12.77 tff(37701,plain,
% 12.49/12.77 (~b(s(s(s(elem!1))), elem!1)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[22149, 37678, 20263, 37682, 37671])).
% 12.49/12.77 tff(37702,plain,
% 12.49/12.77 (r(s(s(s(elem!1))), elem!1)),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[230, 37701, 37680])).
% 12.49/12.77 tff(37703,plain,
% 12.49/12.77 (~r(elem!1, s(elem!1))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[434, 37702, 36606, 59])).
% 12.49/12.77 tff(37704,plain,
% 12.49/12.77 (b(elem!1, s(elem!1))),
% 12.49/12.77 inference(unit_resolution,[status(thm)],[443, 37703, 37700])).
% 12.49/12.77 tff(37705,plain,
% 12.49/12.77 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 12.49/12.77 inference(monotonicity,[status(thm)],[37696])).
% 12.49/12.77 tff(37706,plain,
% 12.49/12.77 (b(s(elem!1), z)),
% 12.49/12.77 inference(modus_ponens,[status(thm)],[37684, 37705])).
% 12.49/12.77 tff(37707,plain,
% 12.49/12.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 12.49/12.77 inference(rewrite,[status(thm)],[])).
% 12.49/12.77 tff(37708,plain,
% 12.49/12.77 (((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 12.49/12.78 inference(rewrite,[status(thm)],[])).
% 12.49/12.78 tff(37709,plain,
% 12.49/12.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 12.49/12.78 inference(monotonicity,[status(thm)],[37708])).
% 12.49/12.78 tff(37710,plain,
% 12.49/12.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 12.49/12.78 inference(transitivity,[status(thm)],[37709, 37707])).
% 12.49/12.78 tff(37711,plain,
% 12.49/12.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 12.49/12.78 inference(quant_inst,[status(thm)],[])).
% 12.49/12.78 tff(37712,plain,
% 12.49/12.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 12.49/12.78 inference(modus_ponens,[status(thm)],[37711, 37710])).
% 12.49/12.78 tff(37713,plain,
% 12.49/12.78 ($false),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37712, 391, 644, 591, 802, 751, 1686])).
% 12.49/12.78 tff(37714,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.78 tff(37715,plain,
% 12.49/12.78 (~b(z, s(s(s(s(z)))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37714, 37603, 37706, 37704, 37698])).
% 12.49/12.78 tff(37716,plain,
% 12.49/12.78 (r(z, s(s(s(s(z)))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[800, 37715])).
% 12.49/12.78 tff(37717,plain,
% 12.49/12.78 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[22263, 37716, 37675, 36669, 37676])).
% 12.49/12.78 tff(37718,plain,
% 12.49/12.78 (b(s(s(z)), s(s(s(s(z)))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[3652, 37717])).
% 12.49/12.78 tff(37719,plain,
% 12.49/12.78 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[6275, 37718, 37558, 37675])).
% 12.49/12.78 tff(37720,plain,
% 12.49/12.78 (r(s(s(s(s(z)))), s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[1714, 37719])).
% 12.49/12.78 tff(37721,plain,
% 12.49/12.78 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 12.49/12.78 inference(monotonicity,[status(thm)],[37695])).
% 12.49/12.78 tff(37722,plain,
% 12.49/12.78 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 12.49/12.78 inference(monotonicity,[status(thm)],[37721])).
% 12.49/12.78 tff(37723,plain,
% 12.49/12.78 (~(elem!1 = s(s(z)))),
% 12.49/12.78 inference(modus_ponens,[status(thm)],[2680, 37722])).
% 12.49/12.78 tff(37724,plain,
% 12.49/12.78 (~r(elem!1, s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[22641, 37716, 36606, 37676])).
% 12.49/12.78 tff(37725,plain,
% 12.49/12.78 (b(elem!1, s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[3394, 37724, 37723])).
% 12.49/12.78 tff(37726,plain,
% 12.49/12.78 (~b(s(s(z)), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[9159, 37725, 20263, 37675, 37558])).
% 12.49/12.78 tff(37727,plain,
% 12.49/12.78 (r(s(s(z)), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[3778, 37726])).
% 12.49/12.78 tff(37728,plain,
% 12.49/12.78 (~r(z, s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[18433, 37727, 29426, 37720])).
% 12.49/12.78 tff(37729,plain,
% 12.49/12.78 (b(z, s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[18613, 37728])).
% 12.49/12.78 tff(37730,plain,
% 12.49/12.78 (~r(s(s(z)), z)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[30527, 37675, 29426, 37558, 37673])).
% 12.49/12.78 tff(37731,plain,
% 12.49/12.78 (b(s(s(z)), z)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[1211, 37730])).
% 12.49/12.78 tff(37732,plain,
% 12.49/12.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 12.49/12.78 inference(rewrite,[status(thm)],[])).
% 12.49/12.78 tff(37733,plain,
% 12.49/12.78 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 12.49/12.78 inference(rewrite,[status(thm)],[])).
% 12.49/12.78 tff(37734,plain,
% 12.49/12.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))))),
% 12.49/12.78 inference(monotonicity,[status(thm)],[37733])).
% 12.49/12.78 tff(37735,plain,
% 12.49/12.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 12.49/12.78 inference(transitivity,[status(thm)],[37734, 37732])).
% 12.49/12.78 tff(37736,plain,
% 12.49/12.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))),
% 12.49/12.78 inference(quant_inst,[status(thm)],[])).
% 12.49/12.78 tff(37737,plain,
% 12.49/12.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))),
% 12.49/12.78 inference(modus_ponens,[status(thm)],[37736, 37735])).
% 12.49/12.78 tff(37738,plain,
% 12.49/12.78 ($false),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37737, 391, 37671, 37731, 37725, 37729])).
% 12.49/12.78 tff(37739,plain,((~r(s(s(s(elem!1))), s(z))) | b(s(s(s(s(z)))), z) | b(z, s(s(s(elem!1)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.78 tff(37740,plain,
% 12.49/12.78 (~r(s(s(s(elem!1))), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37739, 10, 3446, 2])).
% 12.49/12.78 tff(37741,plain,
% 12.49/12.78 ($false),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[17668, 37740, 10, 2829, 3446, 37556])).
% 12.49/12.78 tff(37742,plain,(b(z, s(s(s(elem!1)))) | b(s(z), elem!1) | b(s(s(s(s(z)))), z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.78 tff(37743,plain,
% 12.49/12.78 (b(z, s(s(s(elem!1))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37742, 3446, 2829, 2])).
% 12.49/12.78 tff(37744,plain,
% 12.49/12.78 (b(s(z), z)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[36796, 31, 2, 3446, 1234])).
% 12.49/12.78 tff(37745,plain,
% 12.49/12.78 (~r(z, s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[36888, 31, 2, 1234, 3446, 27044])).
% 12.49/12.78 tff(37746,plain,
% 12.49/12.78 (b(z, s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[678, 37745])).
% 12.49/12.78 tff(37747,plain,
% 12.49/12.78 (~b(s(s(s(elem!1))), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[10690, 37746, 10682, 37744])).
% 12.49/12.78 tff(37748,plain,
% 12.49/12.78 (r(s(s(s(elem!1))), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[223, 37747])).
% 12.49/12.78 tff(37749,plain,
% 12.49/12.78 (~r(s(z), s(s(s(elem!1))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[22961, 1810, 10682, 133, 1, 183])).
% 12.49/12.78 tff(37750,plain,
% 12.49/12.78 (~b(s(z), s(s(s(elem!1))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[36898, 23018, 411, 10682, 2053, 590])).
% 12.49/12.78 tff(37751,plain,
% 12.49/12.78 ($false),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[247, 37750, 37749])).
% 12.49/12.78 tff(37752,plain,((elem!1 = s(z)) | (~r(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.78 tff(37753,plain,
% 12.49/12.78 (elem!1 = s(z)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37752, 37744, 10682, 29426, 36606, 37472, 1, 37748, 31])).
% 12.49/12.78 tff(37754,plain,
% 12.49/12.78 (r(z, elem!1) <=> r(z, s(z))),
% 12.49/12.78 inference(monotonicity,[status(thm)],[37753])).
% 12.49/12.78 tff(37755,plain,
% 12.49/12.78 (r(z, s(z)) <=> r(z, elem!1)),
% 12.49/12.78 inference(symmetry,[status(thm)],[37754])).
% 12.49/12.78 tff(37756,plain,
% 12.49/12.78 ((~r(z, s(z))) <=> (~r(z, elem!1))),
% 12.49/12.78 inference(monotonicity,[status(thm)],[37755])).
% 12.49/12.78 tff(37757,plain,
% 12.49/12.78 (~r(z, elem!1)),
% 12.49/12.78 inference(modus_ponens,[status(thm)],[37745, 37756])).
% 12.49/12.78 tff(37758,plain,
% 12.49/12.78 ($false),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[36606, 37757])).
% 12.49/12.78 tff(37759,plain,(b(elem!1, s(z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.78 tff(37760,plain,
% 12.49/12.78 (b(elem!1, s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37759, 1, 37743, 2, 37556, 3446])).
% 12.49/12.78 tff(37761,plain,
% 12.49/12.78 (~(elem!1 = s(s(s(s(z)))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[769, 37557])).
% 12.49/12.78 tff(37762,plain,
% 12.49/12.78 (~(s(z) = elem!1)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[20271, 37760])).
% 12.49/12.78 tff(37763,plain,
% 12.49/12.78 (r(s(z), elem!1)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[632, 37762, 2829])).
% 12.49/12.78 tff(37764,plain,
% 12.49/12.78 (~r(s(z), z)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[8931, 37763, 29426, 36606, 37760, 37761, 37556])).
% 12.49/12.78 tff(37765,plain,
% 12.49/12.78 (b(s(z), z)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[180, 37764])).
% 12.49/12.78 tff(37766,plain,
% 12.49/12.78 (~r(z, s(s(s(s(z)))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[2097, 1759, 411, 721, 720, 1234])).
% 12.49/12.78 tff(37767,plain,
% 12.49/12.78 (~b(z, s(s(s(s(z)))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[17292, 1759, 1234, 590])).
% 12.49/12.78 tff(37768,plain,
% 12.49/12.78 ($false),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[800, 37767, 37766])).
% 12.49/12.78 tff(37769,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.78 tff(37770,plain,
% 12.49/12.78 (~b(s(s(s(s(z)))), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37769, 37765, 37557, 36606, 37760, 37556])).
% 12.49/12.78 tff(37771,plain,
% 12.49/12.78 (r(s(s(s(s(z)))), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[749, 37770])).
% 12.49/12.78 tff(37772,plain,
% 12.49/12.78 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[2849, 37762])).
% 12.49/12.78 tff(37773,plain,
% 12.49/12.78 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[10940, 37772])).
% 12.49/12.78 tff(37774,plain,
% 12.49/12.78 (~b(s(z), s(s(s(elem!1))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[36898, 37765, 36606, 37743, 29426, 37772])).
% 12.49/12.78 tff(37775,plain,
% 12.49/12.78 (r(s(z), s(s(s(elem!1))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[247, 37774])).
% 12.49/12.78 tff(37776,plain,
% 12.49/12.78 (~r(s(z), z)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[8931, 1484, 29426, 36606, 721, 770, 1234])).
% 12.49/12.78 tff(37777,plain,
% 12.49/12.78 (b(s(z), z)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[180, 37776])).
% 12.49/12.78 tff(37778,plain,
% 12.49/12.78 (~b(z, s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[10690, 1526, 10682, 37777])).
% 12.49/12.78 tff(37779,plain,
% 12.49/12.78 (r(z, s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[678, 37778])).
% 12.49/12.78 tff(37780,plain,
% 12.49/12.78 (~r(elem!1, s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[22623, 37779, 36606, 1484])).
% 12.49/12.78 tff(37781,plain,
% 12.49/12.78 (~b(s(s(s(s(z)))), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37769, 37777, 720, 36606, 721, 1234])).
% 12.49/12.78 tff(37782,plain,
% 12.49/12.78 (~r(elem!1, s(s(s(s(z)))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[21996, 37779, 36606, 1484])).
% 12.49/12.78 tff(37783,plain,
% 12.49/12.78 (r(s(s(s(s(z)))), elem!1)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[20438, 37782, 1234, 721, 720])).
% 12.49/12.78 tff(37784,plain,
% 12.49/12.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 12.49/12.78 inference(rewrite,[status(thm)],[])).
% 12.49/12.78 tff(37785,plain,
% 12.49/12.78 (((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 12.49/12.78 inference(rewrite,[status(thm)],[])).
% 12.49/12.78 tff(37786,plain,
% 12.49/12.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 12.49/12.78 inference(monotonicity,[status(thm)],[37785])).
% 12.49/12.78 tff(37787,plain,
% 12.49/12.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 12.49/12.78 inference(transitivity,[status(thm)],[37786, 37784])).
% 12.49/12.78 tff(37788,plain,
% 12.49/12.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 12.49/12.78 inference(quant_inst,[status(thm)],[])).
% 12.49/12.78 tff(37789,plain,
% 12.49/12.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 12.49/12.78 inference(modus_ponens,[status(thm)],[37788, 37787])).
% 12.49/12.78 tff(37790,plain,
% 12.49/12.78 ($false),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37789, 194, 411, 410, 2053, 2112])).
% 12.49/12.78 tff(37791,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.78 tff(37792,plain,
% 12.49/12.78 (~r(elem!1, s(s(s(elem!1))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[37791, 37783, 36606, 29426])).
% 12.49/12.78 tff(37793,plain,
% 12.49/12.78 (b(elem!1, s(s(s(elem!1))))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[424, 37792, 1])).
% 12.49/12.78 tff(37794,plain,
% 12.49/12.78 (~b(z, s(s(elem!1)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[9087, 37793, 37777, 721, 1526])).
% 12.49/12.78 tff(37795,plain,
% 12.49/12.78 (r(z, s(s(elem!1)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[324, 37794])).
% 12.49/12.78 tff(37796,plain,
% 12.49/12.78 (~r(s(s(elem!1)), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[22122, 37795, 1484, 37779])).
% 12.49/12.78 tff(37797,plain,
% 12.49/12.78 (b(s(s(elem!1)), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[362, 37796])).
% 12.49/12.78 tff(37798,plain,
% 12.49/12.78 (~(elem!1 = s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[9032, 37797, 37781])).
% 12.49/12.78 tff(37799,plain,
% 12.49/12.78 (r(s(s(s(s(z)))), s(z))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[749, 37781])).
% 12.49/12.78 tff(37800,plain,
% 12.49/12.78 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[9010, 37793, 1526, 721, 1234])).
% 12.49/12.78 tff(37801,plain,
% 12.49/12.78 (r(s(s(s(s(z)))), s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[1714, 37800])).
% 12.49/12.78 tff(37802,plain,
% 12.49/12.78 (~r(elem!1, z)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[16803, 37779, 36606, 1484])).
% 12.49/12.78 tff(37803,plain,
% 12.49/12.78 (b(elem!1, z)),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[526, 37802, 2])).
% 12.49/12.78 tff(37804,plain,
% 12.49/12.78 (~b(s(z), s(s(z)))),
% 12.49/12.78 inference(unit_resolution,[status(thm)],[14507, 37793, 10682, 1526, 37803])).
% 12.49/12.78 tff(37805,plain,
% 12.49/12.78 (r(s(z), s(s(z)))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[1788, 37804])).
% 12.49/12.79 tff(37806,plain,
% 12.49/12.79 (~r(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[9138, 37805, 37801, 37799])).
% 12.49/12.79 tff(37807,plain,
% 12.49/12.79 (b(s(s(z)), s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[11041, 37806])).
% 12.49/12.79 tff(37808,plain,
% 12.49/12.79 (~b(elem!1, s(s(z)))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[8561, 37807, 1526, 1234, 37793])).
% 12.49/12.79 tff(37809,plain,
% 12.49/12.79 ($false),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[3394, 37808, 37798, 37780])).
% 12.49/12.79 tff(37810,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(elem!1)))) | (s(s(s(s(z)))) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.79 tff(37811,plain,
% 12.49/12.79 (~b(s(s(s(elem!1))), s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37810, 37763, 37556, 37743, 37760, 1, 37557, 2])).
% 12.49/12.79 tff(37812,plain,
% 12.49/12.79 (r(s(s(s(elem!1))), s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[223, 37811])).
% 12.49/12.79 tff(37813,plain,
% 12.49/12.79 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[33040, 37812, 37775, 37771])).
% 12.49/12.79 tff(37814,plain,
% 12.49/12.79 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[15351, 37813, 37773])).
% 12.49/12.79 tff(37815,plain,
% 12.49/12.79 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37592, 194, 37763, 37812, 37771])).
% 12.49/12.79 tff(37816,plain,
% 12.49/12.79 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[2853, 42, 37772, 37815])).
% 12.49/12.79 tff(37817,plain,
% 12.49/12.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.79 inference(rewrite,[status(thm)],[])).
% 12.49/12.79 tff(37818,plain,
% 12.49/12.79 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.79 inference(rewrite,[status(thm)],[])).
% 12.49/12.79 tff(37819,plain,
% 12.49/12.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 12.49/12.79 inference(monotonicity,[status(thm)],[37818])).
% 12.49/12.79 tff(37820,plain,
% 12.49/12.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.49/12.79 inference(transitivity,[status(thm)],[37819, 37817])).
% 12.49/12.79 tff(37821,plain,
% 12.49/12.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))),
% 12.49/12.79 inference(quant_inst,[status(thm)],[])).
% 12.49/12.79 tff(37822,plain,
% 12.49/12.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 12.49/12.79 inference(modus_ponens,[status(thm)],[37821, 37820])).
% 12.49/12.79 tff(37823,plain,
% 12.49/12.79 (~b(z, s(s(s(s(z)))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37822, 391, 37743, 37816, 37814])).
% 12.49/12.79 tff(37824,plain,
% 12.49/12.79 (r(z, s(s(s(s(z)))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[800, 37823])).
% 12.49/12.79 tff(37825,plain,
% 12.49/12.79 (~r(elem!1, s(s(s(s(z)))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[15063, 37824, 36606, 37771])).
% 12.49/12.79 tff(37826,plain,
% 12.49/12.79 (r(s(s(s(s(z)))), elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[20438, 37825, 37556, 37760, 37557])).
% 12.49/12.79 tff(37827,plain,
% 12.49/12.79 (~r(elem!1, s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37791, 37826, 36606, 29426])).
% 12.49/12.79 tff(37828,plain,
% 12.49/12.79 (b(elem!1, s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[424, 37827, 1])).
% 12.49/12.79 tff(37829,plain,
% 12.49/12.79 (~r(elem!1, z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[33450, 37824, 37556, 37760, 37557, 29426])).
% 12.49/12.79 tff(37830,plain,
% 12.49/12.79 (b(elem!1, z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[526, 37829, 2])).
% 12.49/12.79 tff(37831,plain,
% 12.49/12.79 (~b(z, s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[21922, 37830, 37760, 37765])).
% 12.49/12.79 tff(37832,plain,
% 12.49/12.79 (r(z, s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[678, 37831])).
% 12.49/12.79 tff(37833,plain,
% 12.49/12.79 (~r(s(s(s(elem!1))), z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[17465, 37832, 37812, 37763])).
% 12.49/12.79 tff(37834,plain,
% 12.49/12.79 (b(s(s(s(elem!1))), z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[377, 37833])).
% 12.49/12.79 tff(37835,plain,
% 12.49/12.79 ($false),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[23581, 391, 37830, 37834, 37743, 37828])).
% 12.49/12.79 tff(37836,plain,((elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | b(s(z), elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.79 tff(37837,plain,
% 12.49/12.79 (b(s(z), elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37836, 36604, 1, 36605])).
% 12.49/12.79 tff(37838,plain,
% 12.49/12.79 (b(elem!1, s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[20262, 36604, 10])).
% 12.49/12.79 tff(37839,plain,
% 12.49/12.79 (~r(s(s(s(elem!1))), s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37739, 36605, 10, 36604])).
% 12.49/12.79 tff(37840,plain,
% 12.49/12.79 (b(s(s(s(elem!1))), s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[223, 37839])).
% 12.49/12.79 tff(37841,plain,
% 12.49/12.79 (~b(s(s(s(elem!1))), elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[20387, 37840, 37838, 37837])).
% 12.49/12.79 tff(37842,plain,
% 12.49/12.79 (r(s(s(s(elem!1))), elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[230, 37841, 9])).
% 12.49/12.79 tff(37843,plain,
% 12.49/12.79 (b(s(z), z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[36668, 36604, 10, 37838])).
% 12.49/12.79 tff(37844,plain,
% 12.49/12.79 (r(s(s(s(s(z)))), z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[29425, 36604])).
% 12.49/12.79 tff(37845,plain,
% 12.49/12.79 (~(z = elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[97, 36604])).
% 12.49/12.79 tff(37846,plain,
% 12.49/12.79 (~(s(z) = s(elem!1))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[117, 37845])).
% 12.49/12.79 tff(37847,plain,
% 12.49/12.79 (b(s(z), s(s(s(s(z)))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37469, 36604, 10])).
% 12.49/12.79 tff(37848,plain,
% 12.49/12.79 (r(z, elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[33626, 36604])).
% 12.49/12.79 tff(37849,plain,
% 12.49/12.79 (~b(z, elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[4857, 37837, 37838, 37843])).
% 12.49/12.79 tff(37850,plain,
% 12.49/12.79 (~r(elem!1, z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37669, 37849, 10, 37848, 37847, 37838, 37843, 37846, 37844])).
% 12.49/12.79 tff(37851,plain,
% 12.49/12.79 (b(elem!1, z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[526, 37850, 36604])).
% 12.49/12.79 tff(37852,plain,
% 12.49/12.79 (~b(z, s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[21922, 37851, 37843, 37838])).
% 12.49/12.79 tff(37853,plain,
% 12.49/12.79 (r(z, s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[678, 37852])).
% 12.49/12.79 tff(37854,plain,
% 12.49/12.79 (b(elem!1, s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[10519, 37841, 1, 59, 37848])).
% 12.49/12.79 tff(37855,plain,
% 12.49/12.79 (~b(s(z), s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[4026, 37854, 37840, 37837])).
% 12.49/12.79 tff(37856,plain,
% 12.49/12.79 (r(s(z), s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[247, 37855])).
% 12.49/12.79 tff(37857,plain,
% 12.49/12.79 ($false),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[18997, 37856, 37853, 59, 37842])).
% 12.49/12.79 tff(37858,plain,(b(z, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.49/12.79 tff(37859,plain,
% 12.49/12.79 (b(z, s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37858, 1])).
% 12.49/12.79 tff(37860,plain,
% 12.49/12.79 (~(s(s(s(s(z)))) = elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[6252, 2881, 644])).
% 12.49/12.79 tff(37861,plain,
% 12.49/12.79 (~b(s(s(s(elem!1))), s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[10690, 31666, 22924, 36608])).
% 12.49/12.79 tff(37862,plain,
% 12.49/12.79 (~b(s(s(s(s(z)))), s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[5575, 391, 90, 31666, 36608])).
% 12.49/12.79 tff(37863,plain,
% 12.49/12.79 (r(s(s(s(s(z)))), s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[749, 37862])).
% 12.49/12.79 tff(37864,plain,
% 12.49/12.79 (r(s(s(s(elem!1))), s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[223, 37861])).
% 12.49/12.79 tff(37865,plain,
% 12.49/12.79 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[10698, 194, 37864, 2913, 37863])).
% 12.49/12.79 tff(37866,plain,
% 12.49/12.79 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[10947, 194, 37864, 2913, 37863])).
% 12.49/12.79 tff(37867,plain,
% 12.49/12.79 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[23863, 37866, 90, 22924, 37865])).
% 12.49/12.79 tff(37868,plain,
% 12.49/12.79 (s(z) = elem!1),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[2849, 37867])).
% 12.49/12.79 tff(37869,plain,
% 12.49/12.79 (~b(elem!1, s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[20271, 37868])).
% 12.49/12.79 tff(37870,plain,
% 12.49/12.79 (b(z, elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37057, 37869, 2])).
% 12.49/12.79 tff(37871,plain,
% 12.49/12.79 (~(elem!1 = s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[28049, 37869, 90, 2913, 36608, 37870, 2])).
% 12.49/12.79 tff(37872,plain,
% 12.49/12.79 (elem!1 = s(z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[1495, 37868])).
% 12.49/12.79 tff(37873,plain,
% 12.49/12.79 (~b(s(s(s(s(z)))), elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[9614, 37868, 37862])).
% 12.49/12.79 tff(37874,plain,
% 12.49/12.79 (~b(s(s(s(elem!1))), elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[1563, 37873, 37872])).
% 12.49/12.79 tff(37875,plain,
% 12.49/12.79 (~b(elem!1, s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[8314, 37872, 2881])).
% 12.49/12.79 tff(37876,plain,
% 12.49/12.79 (~r(z, s(s(s(elem!1))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[10519, 37871, 36606, 37875, 37874])).
% 12.49/12.79 tff(37877,plain,
% 12.49/12.79 ($false),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[24987, 37876, 37871, 90, 2881, 37861])).
% 12.49/12.79 tff(37878,plain,(b(s(z), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.49/12.79 tff(37879,plain,
% 12.49/12.79 (~b(s(s(s(s(z)))), z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37878, 2881, 2])).
% 12.49/12.79 tff(37880,plain,
% 12.49/12.79 (b(elem!1, s(z))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37503, 37879, 2881, 2])).
% 12.49/12.79 tff(37881,plain,
% 12.49/12.79 (~b(elem!1, z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[21922, 36608, 31666, 37880])).
% 12.49/12.79 tff(37882,plain,
% 12.49/12.79 (r(elem!1, z)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[526, 37881, 2])).
% 12.49/12.79 tff(37883,plain,
% 12.49/12.79 (~r(s(s(s(s(z)))), elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[37083, 194, 36606, 37882, 29426])).
% 12.49/12.79 tff(37884,plain,
% 12.49/12.79 (b(s(s(s(s(z)))), elem!1)),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[762, 37883, 37860])).
% 12.49/12.79 tff(37885,plain,
% 12.49/12.79 (~(elem!1 = s(s(s(s(z)))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[769, 37860])).
% 12.49/12.79 tff(37886,plain,
% 12.49/12.79 (~r(elem!1, s(s(s(s(z)))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[17579, 194, 36606, 37882, 29426])).
% 12.49/12.79 tff(37887,plain,
% 12.49/12.79 (b(elem!1, s(s(s(s(z)))))),
% 12.49/12.79 inference(unit_resolution,[status(thm)],[781, 37886, 37885])).
% 12.49/12.79 tff(37888,plain,
% 12.49/12.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 12.49/12.80 inference(rewrite,[status(thm)],[])).
% 12.49/12.80 tff(37889,plain,
% 12.49/12.80 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 12.49/12.80 inference(rewrite,[status(thm)],[])).
% 12.49/12.80 tff(37890,plain,
% 12.49/12.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 12.49/12.80 inference(monotonicity,[status(thm)],[37889])).
% 12.49/12.80 tff(37891,plain,
% 12.49/12.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 12.49/12.80 inference(transitivity,[status(thm)],[37890, 37888])).
% 12.49/12.80 tff(37892,plain,
% 12.49/12.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 12.49/12.80 inference(quant_inst,[status(thm)],[])).
% 12.49/12.80 tff(37893,plain,
% 12.49/12.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))),
% 12.49/12.80 inference(modus_ponens,[status(thm)],[37892, 37891])).
% 12.49/12.80 tff(37894,plain,
% 12.49/12.80 (~b(s(s(z)), elem!1)),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[37893, 391, 31645, 37887, 37884])).
% 12.49/12.80 tff(37895,plain,
% 12.49/12.80 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[10940, 26076])).
% 12.49/12.80 tff(37896,plain,
% 12.49/12.80 (~b(s(z), s(s(s(elem!1))))),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[36898, 36608, 36606, 37470, 29426, 26076])).
% 12.49/12.80 tff(37897,plain,
% 12.49/12.80 (r(s(z), s(s(s(elem!1))))),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[247, 37896])).
% 12.49/12.80 tff(37898,plain,
% 12.49/12.80 (~b(s(s(s(s(z)))), s(z))),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[17129, 391, 644, 37887, 37884])).
% 12.49/12.80 tff(37899,plain,
% 12.49/12.80 (r(s(s(s(s(z)))), s(z))),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[749, 37898])).
% 12.49/12.80 tff(37900,plain,
% 12.49/12.80 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[33040, 37899, 37897, 37483])).
% 12.49/12.80 tff(37901,plain,
% 12.49/12.80 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[15351, 37900, 37895])).
% 12.49/12.80 tff(37902,plain,
% 12.49/12.80 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[26327, 194, 37897, 37483, 37899])).
% 12.49/12.80 tff(37903,plain,
% 12.49/12.80 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[2853, 42, 26076, 37902])).
% 12.49/12.80 tff(37904,plain,
% 12.49/12.80 (~(s(s(s(elem!1))) = elem!1)),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[14872, 37896, 644])).
% 12.49/12.80 tff(37905,plain,
% 12.49/12.80 (~b(s(s(s(elem!1))), elem!1)),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[10959, 37903, 37887, 37901])).
% 12.49/12.80 tff(37906,plain,
% 12.49/12.80 (r(s(s(s(elem!1))), elem!1)),
% 12.49/12.80 inference(unit_resolution,[status(thm)],[230, 37905, 37904])).
% 12.49/12.80 tff(37907,plain,
% 12.59/12.80 (~r(s(s(s(elem!1))), z)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[23607, 37906, 36606, 37882])).
% 12.59/12.80 tff(37908,plain,
% 12.59/12.80 (b(s(s(s(elem!1))), z)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[377, 37907])).
% 12.59/12.80 tff(37909,plain,
% 12.59/12.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.59/12.80 inference(rewrite,[status(thm)],[])).
% 12.59/12.80 tff(37910,plain,
% 12.59/12.80 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.59/12.80 inference(rewrite,[status(thm)],[])).
% 12.59/12.80 tff(37911,plain,
% 12.59/12.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 12.59/12.80 inference(monotonicity,[status(thm)],[37910])).
% 12.59/12.80 tff(37912,plain,
% 12.59/12.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.59/12.80 inference(transitivity,[status(thm)],[37911, 37909])).
% 12.59/12.80 tff(37913,plain,
% 12.59/12.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 12.59/12.80 inference(quant_inst,[status(thm)],[])).
% 12.59/12.80 tff(37914,plain,
% 12.59/12.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 12.59/12.80 inference(modus_ponens,[status(thm)],[37913, 37912])).
% 12.59/12.80 tff(37915,plain,
% 12.59/12.80 (~b(s(s(z)), s(s(s(elem!1))))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[37914, 391, 37908, 31645, 37903, 37901])).
% 12.59/12.80 tff(37916,plain,
% 12.59/12.80 (r(s(s(z)), s(s(s(elem!1))))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[11041, 37915])).
% 12.59/12.80 tff(37917,plain,
% 12.59/12.80 (~b(z, elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[23112, 31666, 644, 37880])).
% 12.59/12.80 tff(37918,plain,
% 12.59/12.80 (~(elem!1 = s(s(s(elem!1))))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[22900, 37917, 37470])).
% 12.59/12.80 tff(37919,plain,
% 12.59/12.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.59/12.80 inference(rewrite,[status(thm)],[])).
% 12.59/12.80 tff(37920,plain,
% 12.59/12.80 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.59/12.80 inference(rewrite,[status(thm)],[])).
% 12.59/12.80 tff(37921,plain,
% 12.59/12.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 12.59/12.80 inference(monotonicity,[status(thm)],[37920])).
% 12.59/12.80 tff(37922,plain,
% 12.59/12.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 12.59/12.80 inference(transitivity,[status(thm)],[37921, 37919])).
% 12.59/12.80 tff(37923,plain,
% 12.59/12.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 12.59/12.80 inference(quant_inst,[status(thm)],[])).
% 12.59/12.80 tff(37924,plain,
% 12.59/12.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 12.59/12.80 inference(modus_ponens,[status(thm)],[37923, 37922])).
% 12.59/12.80 tff(37925,plain,
% 12.59/12.80 (~b(elem!1, s(s(s(elem!1))))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[37924, 391, 37908, 37887, 37903, 37901])).
% 12.59/12.80 tff(37926,plain,
% 12.59/12.80 (r(elem!1, s(s(s(elem!1))))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[424, 37925, 37918])).
% 12.59/12.80 tff(37927,plain,
% 12.59/12.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)))),
% 12.59/12.80 inference(quant_inst,[status(thm)],[])).
% 12.59/12.80 tff(37928,plain,
% 12.59/12.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1))),
% 12.59/12.80 inference(modus_ponens,[status(thm)],[37927, 5154])).
% 12.59/12.80 tff(37929,plain,
% 12.59/12.80 (~r(s(s(z)), elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[37928, 194, 37906, 37926, 37916])).
% 12.59/12.80 tff(37930,plain,
% 12.59/12.80 (s(s(z)) = elem!1),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[4730, 37929, 37894])).
% 12.59/12.80 tff(37931,plain,
% 12.59/12.80 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[4584, 37930, 118])).
% 12.59/12.80 tff(37932,plain,
% 12.59/12.80 (~(s(elem!1) = elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[158, 37904])).
% 12.59/12.80 tff(37933,plain,
% 12.59/12.80 (~(s(s(elem!1)) = s(elem!1))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[2279, 37931])).
% 12.59/12.80 tff(37934,plain,
% 12.59/12.80 (~(s(s(elem!1)) = elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[451, 37931])).
% 12.59/12.80 tff(37935,plain,
% 12.59/12.80 (b(s(s(elem!1)), elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[28592, 37931, 36606, 37470, 37882, 37906, 37934])).
% 12.59/12.80 tff(37936,plain,
% 12.59/12.80 (~b(s(elem!1), elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[25235, 37935, 118, 36606, 37470, 20633, 37882, 37926, 37933, 37908])).
% 12.59/12.80 tff(37937,plain,
% 12.59/12.80 (r(s(elem!1), elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[2168, 37936, 37932])).
% 12.59/12.80 tff(37938,plain,
% 12.59/12.80 (~b(s(elem!1), z)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[28617, 37937, 37882, 37906, 37470, 37931])).
% 12.59/12.80 tff(37939,plain,
% 12.59/12.80 (~r(s(elem!1), z)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[541, 37937, 36606, 37882])).
% 12.59/12.80 tff(37940,plain,
% 12.59/12.80 ($false),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[549, 37939, 37938])).
% 12.59/12.80 tff(37941,plain,(b(s(z), s(s(s(s(z))))) | (~b(s(z), elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.59/12.80 tff(37942,plain,
% 12.59/12.80 (b(s(z), s(s(s(s(z)))))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[37941, 644, 2])).
% 12.59/12.80 tff(37943,plain,
% 12.59/12.80 (b(z, elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[37429, 91, 2])).
% 12.59/12.80 tff(37944,plain,
% 12.59/12.80 (~b(s(s(s(s(z)))), z)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[28962, 31, 36606, 1, 150, 1234, 2])).
% 12.59/12.80 tff(37945,plain,
% 12.59/12.80 ($false),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[37759, 37944, 31, 10682, 2, 1234, 1])).
% 12.59/12.80 tff(37946,plain,(b(elem!1, s(z)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.59/12.80 tff(37947,plain,
% 12.59/12.80 (b(elem!1, s(z))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[37946, 1, 2, 37942, 10682, 20633])).
% 12.59/12.80 tff(37948,plain,
% 12.59/12.80 (~b(z, s(z))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[23112, 37943, 644, 37947])).
% 12.59/12.80 tff(37949,plain,
% 12.59/12.80 (r(z, s(z))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[678, 37948])).
% 12.59/12.80 tff(37950,plain,
% 12.59/12.80 (~r(elem!1, s(z))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[845, 37949, 36606, 181])).
% 12.59/12.80 tff(37951,plain,
% 12.59/12.80 (~r(elem!1, z)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[26814, 37950, 29426, 37943, 37949, 37942, 20620])).
% 12.59/12.80 tff(37952,plain,
% 12.59/12.80 (~b(elem!1, s(s(s(elem!1))))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[17700, 37951, 2, 29426, 10682, 20633, 37943])).
% 12.59/12.80 tff(37953,plain,
% 12.59/12.80 (r(elem!1, s(s(s(elem!1))))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[424, 37952, 1])).
% 12.59/12.80 tff(37954,plain,
% 12.59/12.80 (~b(s(s(s(s(z)))), elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[26707, 36754, 37942, 37947, 644])).
% 12.59/12.80 tff(37955,plain,
% 12.59/12.80 (b(elem!1, z)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[526, 37951, 2])).
% 12.59/12.80 tff(37956,plain,
% 12.59/12.80 (~(s(s(s(s(z)))) = elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[6966, 37955, 3446])).
% 12.59/12.80 tff(37957,plain,
% 12.59/12.80 (r(s(s(s(s(z)))), elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[762, 37956, 37954])).
% 12.59/12.80 tff(37958,plain,
% 12.59/12.80 ($false),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[37791, 37957, 37953, 36606, 29426])).
% 12.59/12.80 tff(37959,plain,(b(s(z), z) | (elem!1 = s(s(s(elem!1)))) | b(s(s(s(s(z)))), z) | (elem!1 = z) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.80 tff(37960,plain,
% 12.59/12.80 (b(s(z), z)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[37959, 3446, 1, 2, 10682, 644])).
% 12.59/12.80 tff(37961,plain,
% 12.59/12.80 (~r(s(s(s(s(z)))), elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[37791, 6124, 36606, 29426])).
% 12.59/12.80 tff(37962,plain,
% 12.59/12.80 (~b(elem!1, z)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[17542, 37961, 36606, 644, 37942, 37960, 3446])).
% 12.59/12.80 tff(37963,plain,
% 12.59/12.80 (r(elem!1, z)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[526, 37962, 2])).
% 12.59/12.80 tff(37964,plain,
% 12.59/12.80 (~b(z, elem!1)),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[4857, 37960, 644, 37947])).
% 12.59/12.80 tff(37965,plain,
% 12.59/12.80 (~r(elem!1, s(s(s(s(z)))))),
% 12.59/12.80 inference(unit_resolution,[status(thm)],[17579, 194, 36606, 37963, 29426])).
% 12.59/12.81 tff(37966,plain,
% 12.59/12.81 (s(s(s(s(z)))) = elem!1),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[20438, 37965, 37942, 37947, 37961])).
% 12.59/12.81 tff(37967,plain,
% 12.59/12.81 (elem!1 = s(s(s(s(z))))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[16908, 37966])).
% 12.59/12.81 tff(37968,plain,
% 12.59/12.81 (b(s(s(s(s(z)))), s(z))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[13738, 37967, 37947])).
% 12.59/12.81 tff(37969,plain,
% 12.59/12.81 (~b(s(elem!1), z)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[37329, 37968, 2, 37942, 4028, 37964, 10682, 37962, 644])).
% 12.59/12.81 tff(37970,plain,
% 12.59/12.81 (r(s(elem!1), z)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[549, 37969])).
% 12.59/12.81 tff(37971,plain,
% 12.59/12.81 (~r(s(elem!1), elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[541, 37970, 36606, 37963])).
% 12.59/12.81 tff(37972,plain,
% 12.59/12.81 (~r(elem!1, s(elem!1))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[9766, 37970, 36606, 37963])).
% 12.59/12.81 tff(37973,plain,
% 12.59/12.81 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[717, 37966])).
% 12.59/12.81 tff(37974,plain,
% 12.59/12.81 (~(s(s(elem!1)) = s(elem!1))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[2279, 37973])).
% 12.59/12.81 tff(37975,plain,
% 12.59/12.81 (~b(z, s(s(s(s(z)))))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[18671, 37965, 37942, 37960, 37961, 37964])).
% 12.59/12.81 tff(37976,plain,
% 12.59/12.81 (r(z, s(s(s(s(z)))))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[800, 37975])).
% 12.59/12.81 tff(37977,plain,
% 12.59/12.81 (s(s(s(s(s(z))))) = s(elem!1)),
% 12.59/12.81 inference(monotonicity,[status(thm)],[37966])).
% 12.59/12.81 tff(37978,plain,
% 12.59/12.81 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 12.59/12.81 inference(monotonicity,[status(thm)],[37977])).
% 12.59/12.81 tff(37979,plain,
% 12.59/12.81 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 12.59/12.81 inference(monotonicity,[status(thm)],[37978])).
% 12.59/12.81 tff(37980,plain,
% 12.59/12.81 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 12.59/12.81 inference(monotonicity,[status(thm)],[37979])).
% 12.59/12.81 tff(37981,plain,
% 12.59/12.81 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 12.59/12.81 inference(symmetry,[status(thm)],[37980])).
% 12.59/12.81 tff(37982,plain,
% 12.59/12.81 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 12.59/12.81 inference(modus_ponens,[status(thm)],[6124, 37981])).
% 12.59/12.81 tff(37983,plain,
% 12.59/12.81 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[37299, 37982, 37967, 37976, 29426])).
% 12.59/12.81 tff(37984,plain,
% 12.59/12.81 (~r(s(s(s(elem!1))), z)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[37303, 37983, 37967])).
% 12.59/12.81 tff(37985,plain,
% 12.59/12.81 (b(s(s(s(elem!1))), s(elem!1))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[37249, 37984, 10682, 37964, 20633, 4028, 37974, 37971, 37962])).
% 12.59/12.81 tff(37986,plain,
% 12.59/12.81 (~b(s(s(s(elem!1))), elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[2340, 37985, 37972, 427, 37971])).
% 12.59/12.81 tff(37987,plain,
% 12.59/12.81 (~(s(s(elem!1)) = elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[451, 37973])).
% 12.59/12.81 tff(37988,plain,
% 12.59/12.81 (b(s(elem!1), elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[2168, 37971, 426])).
% 12.59/12.81 tff(37989,plain,
% 12.59/12.81 (b(s(s(s(elem!1))), z)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[377, 37984])).
% 12.59/12.81 tff(37990,plain,
% 12.59/12.81 (~b(s(s(elem!1)), elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[25235, 37989, 118, 36606, 10682, 20633, 37963, 6124, 37974, 37988])).
% 12.59/12.81 tff(37991,plain,
% 12.59/12.81 (~r(s(s(s(elem!1))), elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[28592, 37990, 36606, 10682, 37963, 37973, 37987])).
% 12.59/12.81 tff(37992,plain,
% 12.59/12.81 ($false),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[230, 37991, 37986, 9])).
% 12.59/12.81 tff(37993,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (elem!1 = z) | (~b(s(z), elem!1)) | b(s(s(s(s(z)))), z) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.81 tff(37994,plain,
% 12.59/12.81 (b(elem!1, s(s(s(elem!1))))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[37993, 3446, 2, 644, 10682, 1])).
% 12.59/12.81 tff(37995,plain,
% 12.59/12.81 (s(s(s(s(z)))) = elem!1),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[20438, 37068, 37942, 721, 37084])).
% 12.59/12.81 tff(37996,plain,
% 12.59/12.81 (~b(z, elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[4857, 590, 644, 721])).
% 12.59/12.81 tff(37997,plain,
% 12.59/12.81 (~b(s(elem!1), z)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[37261, 1526, 484, 688, 1234, 37996, 10682, 26763, 26764, 530, 411, 721, 644])).
% 12.59/12.81 tff(37998,plain,
% 12.59/12.81 (r(s(elem!1), z)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[549, 37997])).
% 12.59/12.81 tff(37999,plain,
% 12.59/12.81 (~b(s(s(s(elem!1))), elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[21754, 1526, 411, 721, 590, 530, 448])).
% 12.59/12.81 tff(38000,plain,
% 12.59/12.81 (r(s(s(s(elem!1))), elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[230, 37999, 127])).
% 12.59/12.81 tff(38001,plain,
% 12.59/12.81 (b(s(s(elem!1)), elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[28592, 38000, 411, 10682, 530, 14410, 14411])).
% 12.59/12.81 tff(38002,plain,
% 12.59/12.81 (~r(s(s(s(elem!1))), z)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[23607, 38000, 411, 530])).
% 12.59/12.81 tff(38003,plain,
% 12.59/12.81 (b(s(s(s(elem!1))), z)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[377, 38002])).
% 12.59/12.81 tff(38004,plain,
% 12.59/12.81 ($false),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[28613, 38003, 38001, 411, 10682, 448, 14410, 14413, 15838, 37998, 14459, 4597, 530])).
% 12.59/12.81 tff(38005,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)) | (s(s(s(elem!1))) = elem!1) | b(elem!1, z) | (~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.81 tff(38006,plain,
% 12.59/12.81 (~b(s(s(s(elem!1))), s(z))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[38005, 3618, 10682, 448, 36606, 127, 484, 37995, 37942, 721, 644, 590])).
% 12.59/12.81 tff(38007,plain,
% 12.59/12.81 (r(s(s(s(elem!1))), s(z))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[223, 38006])).
% 12.59/12.81 tff(38008,plain,
% 12.59/12.81 (~b(s(z), s(s(s(elem!1))))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[36898, 590, 36606, 10682, 29426, 26076])).
% 12.59/12.81 tff(38009,plain,
% 12.59/12.81 (r(s(z), s(s(s(elem!1))))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[247, 38008])).
% 12.59/12.81 tff(38010,plain,
% 12.59/12.81 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[717, 37995])).
% 12.59/12.81 tff(38011,plain,
% 12.59/12.81 (~(s(s(elem!1)) = elem!1)),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[451, 38010])).
% 12.59/12.81 tff(38012,plain,
% 12.59/12.81 (~(elem!1 = s(s(elem!1)))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[1292, 38011])).
% 12.59/12.81 tff(38013,plain,
% 12.59/12.81 (~b(s(s(elem!1)), s(z))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[22561, 973, 644, 721])).
% 12.59/12.81 tff(38014,plain,
% 12.59/12.81 (r(s(s(elem!1)), s(z))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[362, 38013])).
% 12.59/12.81 tff(38015,plain,
% 12.59/12.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 12.59/12.81 inference(rewrite,[status(thm)],[])).
% 12.59/12.81 tff(38016,plain,
% 12.59/12.81 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 12.59/12.81 inference(rewrite,[status(thm)],[])).
% 12.59/12.81 tff(38017,plain,
% 12.59/12.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 12.59/12.81 inference(monotonicity,[status(thm)],[38016])).
% 12.59/12.81 tff(38018,plain,
% 12.59/12.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 12.59/12.81 inference(transitivity,[status(thm)],[38017, 38015])).
% 12.59/12.81 tff(38019,plain,
% 12.59/12.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 12.59/12.81 inference(quant_inst,[status(thm)],[])).
% 12.59/12.81 tff(38020,plain,
% 12.59/12.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 12.59/12.81 inference(modus_ponens,[status(thm)],[38019, 38018])).
% 12.59/12.81 tff(38021,plain,
% 12.59/12.81 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[38020, 194, 38014, 232, 183])).
% 12.59/12.81 tff(38022,plain,
% 12.59/12.81 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[1370, 38021, 297])).
% 12.59/12.81 tff(38023,plain,
% 12.59/12.81 (~b(z, s(s(elem!1)))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[24044, 38022, 10682, 315, 590, 183, 232])).
% 12.59/12.81 tff(38024,plain,
% 12.59/12.81 (r(z, s(s(elem!1)))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[324, 38023])).
% 12.59/12.81 tff(38025,plain,
% 12.59/12.81 (~r(elem!1, s(s(elem!1)))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[6189, 38024, 530, 38014])).
% 12.59/12.81 tff(38026,plain,
% 12.59/12.81 (b(elem!1, s(s(elem!1)))),
% 12.59/12.81 inference(unit_resolution,[status(thm)],[1307, 38025, 1457])).
% 12.59/12.81 tff(38027,plain,
% 12.59/12.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 12.59/12.81 inference(rewrite,[status(thm)],[])).
% 12.59/12.81 tff(38028,plain,
% 12.59/12.81 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 12.59/12.81 inference(rewrite,[status(thm)],[])).
% 12.59/12.81 tff(38029,plain,
% 12.59/12.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 12.59/12.81 inference(monotonicity,[status(thm)],[38028])).
% 12.59/12.81 tff(38030,plain,
% 12.59/12.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 12.59/12.81 inference(transitivity,[status(thm)],[38029, 38027])).
% 12.59/12.81 tff(38031,plain,
% 12.59/12.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 12.59/12.81 inference(quant_inst,[status(thm)],[])).
% 12.59/12.81 tff(38032,plain,
% 12.59/12.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 12.59/12.82 inference(modus_ponens,[status(thm)],[38031, 38030])).
% 12.59/12.82 tff(38033,plain,
% 12.59/12.82 ($false),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38032, 391, 973, 448, 38022, 38026])).
% 12.59/12.82 tff(38034,plain,((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~r(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.82 tff(38035,plain,
% 12.59/12.82 (~b(s(s(elem!1)), elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38034, 38012, 448, 3618, 10682, 590, 38007, 38009, 15838, 644, 721])).
% 12.59/12.82 tff(38036,plain,
% 12.59/12.82 (r(s(s(elem!1)), elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[872, 38035, 38011])).
% 12.59/12.82 tff(38037,plain,
% 12.59/12.82 (~r(z, s(s(elem!1)))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[867, 38036, 36606, 3618])).
% 12.59/12.82 tff(38038,plain,
% 12.59/12.82 (b(z, s(s(elem!1)))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[324, 38037])).
% 12.59/12.82 tff(38039,plain,
% 12.59/12.82 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[24044, 38038, 10682, 21729, 590, 38007, 38009])).
% 12.59/12.82 tff(38040,plain,
% 12.59/12.82 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[1370, 38039, 15838])).
% 12.59/12.82 tff(38041,plain,
% 12.59/12.82 (~r(s(s(elem!1)), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[8360, 38036, 36606, 3618])).
% 12.59/12.82 tff(38042,plain,
% 12.59/12.82 (b(s(s(elem!1)), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[2629, 38041])).
% 12.59/12.82 tff(38043,plain,
% 12.59/12.82 (~r(s(s(s(elem!1))), elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[28592, 38035, 36606, 10682, 3618, 38010, 38011])).
% 12.59/12.82 tff(38044,plain,
% 12.59/12.82 (b(s(s(s(elem!1))), elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[230, 38043, 127])).
% 12.59/12.82 tff(38045,plain,
% 12.59/12.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 12.59/12.82 inference(rewrite,[status(thm)],[])).
% 12.59/12.82 tff(38046,plain,
% 12.59/12.82 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 12.59/12.82 inference(rewrite,[status(thm)],[])).
% 12.59/12.82 tff(38047,plain,
% 12.59/12.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))))),
% 12.59/12.82 inference(monotonicity,[status(thm)],[38046])).
% 12.59/12.82 tff(38048,plain,
% 12.59/12.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 12.59/12.82 inference(transitivity,[status(thm)],[38047, 38045])).
% 12.59/12.82 tff(38049,plain,
% 12.59/12.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 12.59/12.82 inference(quant_inst,[status(thm)],[])).
% 12.59/12.82 tff(38050,plain,
% 12.59/12.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))),
% 12.59/12.82 inference(modus_ponens,[status(thm)],[38049, 38048])).
% 12.59/12.82 tff(38051,plain,
% 12.59/12.82 (~b(s(s(elem!1)), s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38050, 391, 38044, 10682, 38042, 590])).
% 12.59/12.82 tff(38052,plain,
% 12.59/12.82 (r(s(s(elem!1)), s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[362, 38051])).
% 12.59/12.82 tff(38053,plain,
% 12.59/12.82 ($false),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38020, 194, 38052, 38040, 38009, 38007])).
% 12.59/12.82 tff(38054,plain,(b(elem!1, z) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 12.59/12.82 tff(38055,plain,
% 12.59/12.82 (b(elem!1, z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38054, 37960, 10682, 9, 37994, 644, 37947, 2])).
% 12.59/12.82 tff(38056,plain,
% 12.59/12.82 (~(s(s(s(s(z)))) = elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[6966, 38055, 3446])).
% 12.59/12.82 tff(38057,plain,
% 12.59/12.82 (~b(s(s(s(s(z)))), s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[37769, 38056, 37942, 36606, 37947, 37960])).
% 12.59/12.82 tff(38058,plain,
% 12.59/12.82 (r(s(s(s(s(z)))), s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[749, 38057])).
% 12.59/12.82 tff(38059,plain,
% 12.59/12.82 (~b(z, s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[21922, 38055, 37960, 37947])).
% 12.59/12.82 tff(38060,plain,
% 12.59/12.82 (r(z, s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[678, 38059])).
% 12.59/12.82 tff(38061,plain,
% 12.59/12.82 (~b(s(z), s(s(s(elem!1))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[36898, 37960, 36606, 10682, 29426, 26076])).
% 12.59/12.82 tff(38062,plain,
% 12.59/12.82 (r(s(z), s(s(s(elem!1))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[247, 38061])).
% 12.59/12.82 tff(38063,plain,
% 12.59/12.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 12.59/12.82 inference(rewrite,[status(thm)],[])).
% 12.59/12.82 tff(38064,plain,
% 12.59/12.82 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 12.59/12.82 inference(rewrite,[status(thm)],[])).
% 12.59/12.82 tff(38065,plain,
% 12.59/12.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 12.59/12.82 inference(monotonicity,[status(thm)],[38064])).
% 12.59/12.82 tff(38066,plain,
% 12.59/12.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 12.59/12.82 inference(transitivity,[status(thm)],[38065, 38063])).
% 12.59/12.82 tff(38067,plain,
% 12.59/12.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 12.59/12.82 inference(quant_inst,[status(thm)],[])).
% 12.59/12.82 tff(38068,plain,
% 12.59/12.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 12.59/12.82 inference(modus_ponens,[status(thm)],[38067, 38066])).
% 12.59/12.82 tff(38069,plain,
% 12.59/12.82 ($false),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38068, 194, 38062, 38060, 29426, 38058])).
% 12.59/12.82 tff(38070,plain,(b(s(s(s(s(z)))), z) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (elem!1 = z) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.82 tff(38071,plain,
% 12.59/12.82 (b(s(s(s(s(z)))), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38070, 1, 644, 2, 10682])).
% 12.59/12.82 tff(38072,plain,
% 12.59/12.82 (b(elem!1, z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[29121, 38071, 2, 36606, 1, 37942])).
% 12.59/12.82 tff(38073,plain,
% 12.59/12.82 (b(s(s(s(elem!1))), elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[29228, 38072, 36606, 1, 37947, 37942, 10682, 38071, 118, 20633])).
% 12.59/12.82 tff(38074,plain,
% 12.59/12.82 (~b(z, elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[10743, 38073, 10682, 38072])).
% 12.59/12.82 tff(38075,plain,
% 12.59/12.82 (b(s(z), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[37429, 38074, 2])).
% 12.59/12.82 tff(38076,plain,
% 12.59/12.82 (~r(z, s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[29285, 38073, 10682, 38071, 37947, 20633, 36606, 38074, 37942, 38072])).
% 12.59/12.82 tff(38077,plain,
% 12.59/12.82 (b(z, s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[678, 38076])).
% 12.59/12.82 tff(38078,plain,
% 12.59/12.82 ($false),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[28088, 38077, 38075, 38071, 37942])).
% 12.59/12.82 tff(38079,plain,((elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.82 tff(38080,plain,
% 12.59/12.82 (~b(s(z), elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38079, 2, 1, 37859])).
% 12.59/12.82 tff(38081,plain,
% 12.59/12.82 (b(s(z), s(s(s(s(z)))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[37878, 90, 2])).
% 12.59/12.82 tff(38082,plain,
% 12.59/12.82 (b(elem!1, z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[29121, 1, 2, 36606, 90, 38081])).
% 12.59/12.82 tff(38083,plain,
% 12.59/12.82 (~(s(z) = elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[28819, 9, 2, 36606, 90, 38081])).
% 12.59/12.82 tff(38084,plain,
% 12.59/12.82 (b(elem!1, s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[28962, 38083, 36606, 90, 1, 38081, 2])).
% 12.59/12.82 tff(38085,plain,
% 12.59/12.82 (b(s(s(s(elem!1))), elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[29228, 38084, 36606, 90, 1, 38081, 22924, 38082, 118, 38083])).
% 12.59/12.82 tff(38086,plain,
% 12.59/12.82 (~b(elem!1, s(s(s(elem!1))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[28903, 38085, 22924, 38082])).
% 12.59/12.82 tff(38087,plain,
% 12.59/12.82 (~(s(s(s(s(z)))) = elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[8916, 38081, 2829])).
% 12.59/12.82 tff(38088,plain,
% 12.59/12.82 (~(elem!1 = s(s(s(s(z)))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[769, 38087])).
% 12.59/12.82 tff(38089,plain,
% 12.59/12.82 (r(s(z), elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[632, 38083, 2829])).
% 12.59/12.82 tff(38090,plain,
% 12.59/12.82 (~r(s(z), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[8931, 38084, 29426, 36606, 38089, 38088, 38081])).
% 12.59/12.82 tff(38091,plain,
% 12.59/12.82 (b(s(z), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[180, 38090])).
% 12.59/12.82 tff(38092,plain,
% 12.59/12.82 (~r(elem!1, s(s(s(elem!1))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[29249, 38085, 36606, 22924, 38091, 38084, 26982, 38082, 38081, 90])).
% 12.59/12.82 tff(38093,plain,
% 12.59/12.82 ($false),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[424, 38092, 38086, 1])).
% 12.59/12.82 tff(38094,plain,((elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.59/12.82 tff(38095,plain,
% 12.59/12.82 (~b(s(s(s(s(z)))), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38094, 38080, 2, 1])).
% 12.59/12.82 tff(38096,plain,
% 12.59/12.82 ($false),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[37836, 38095, 38080, 1, 2])).
% 12.59/12.82 tff(38097,plain,((elem!1 = z) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.82 tff(38098,plain,
% 12.59/12.82 (elem!1 = z),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38097, 1])).
% 12.59/12.82 tff(38099,plain,
% 12.59/12.82 (s(elem!1) = s(z)),
% 12.59/12.82 inference(monotonicity,[status(thm)],[38098])).
% 12.59/12.82 tff(38100,plain,
% 12.59/12.82 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 12.59/12.82 inference(monotonicity,[status(thm)],[38099])).
% 12.59/12.82 tff(38101,plain,
% 12.59/12.82 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 12.59/12.82 inference(symmetry,[status(thm)],[38100])).
% 12.59/12.82 tff(38102,plain,
% 12.59/12.82 (s(s(elem!1)) = s(s(z))),
% 12.59/12.82 inference(monotonicity,[status(thm)],[38099])).
% 12.59/12.82 tff(38103,plain,
% 12.59/12.82 (s(s(s(elem!1))) = s(s(s(z)))),
% 12.59/12.82 inference(monotonicity,[status(thm)],[38102])).
% 12.59/12.82 tff(38104,plain,
% 12.59/12.82 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 12.59/12.82 inference(monotonicity,[status(thm)],[38103])).
% 12.59/12.82 tff(38105,plain,
% 12.59/12.82 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 12.59/12.82 inference(monotonicity,[status(thm)],[38104])).
% 12.59/12.82 tff(38106,plain,
% 12.59/12.82 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 12.59/12.82 inference(symmetry,[status(thm)],[38105])).
% 12.59/12.82 tff(38107,plain,
% 12.59/12.82 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 12.59/12.82 inference(transitivity,[status(thm)],[38106, 38101])).
% 12.59/12.82 tff(38108,plain,
% 12.59/12.82 (b(z, s(s(s(elem!1))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[36603, 11])).
% 12.59/12.82 tff(38109,plain,
% 12.59/12.82 (~r(z, s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[10620, 2913, 36058])).
% 12.59/12.82 tff(38110,plain,
% 12.59/12.82 (b(z, s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[678, 38109])).
% 12.59/12.82 tff(38111,plain,
% 12.59/12.82 (~r(s(z), elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[5396, 33641, 36512, 2913])).
% 12.59/12.82 tff(38112,plain,
% 12.59/12.82 (~b(s(s(s(s(z)))), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[36013, 38111, 11, 38108, 66, 2881])).
% 12.59/12.82 tff(38113,plain,
% 12.59/12.82 (b(s(z), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[3205, 38111, 11])).
% 12.59/12.82 tff(38114,plain,
% 12.59/12.82 (~b(s(s(s(elem!1))), s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[10690, 38113, 38108, 38110])).
% 12.59/12.82 tff(38115,plain,
% 12.59/12.82 ($false),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[31585, 38114, 38112, 79, 66, 31])).
% 12.59/12.82 tff(38116,plain,(b(elem!1, s(z)) | (~(elem!1 = z)) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.82 tff(38117,plain,
% 12.59/12.82 (b(elem!1, s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[38116, 2881, 11])).
% 12.59/12.82 tff(38118,plain,
% 12.59/12.82 (~r(s(s(s(elem!1))), s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[32588, 38117, 79, 36058, 66, 2913])).
% 12.59/12.82 tff(38119,plain,
% 12.59/12.82 (b(s(s(s(elem!1))), s(z))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[223, 38118])).
% 12.59/12.82 tff(38120,plain,
% 12.59/12.82 (~b(s(z), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[10690, 38119, 38108, 38110])).
% 12.59/12.82 tff(38121,plain,
% 12.59/12.82 (r(s(z), elem!1)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[3205, 38120, 11])).
% 12.59/12.82 tff(38122,plain,
% 12.59/12.82 (~r(elem!1, s(s(z)))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[11485, 38121, 36512, 2913])).
% 12.59/12.82 tff(38123,plain,
% 12.59/12.82 (b(elem!1, s(s(z)))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[3394, 38122, 33689])).
% 12.59/12.82 tff(38124,plain,
% 12.59/12.82 (~r(elem!1, s(s(s(s(z)))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[14627, 38121, 36512, 2913])).
% 12.59/12.82 tff(38125,plain,
% 12.59/12.82 (b(elem!1, s(s(s(s(z)))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[781, 38124, 33909])).
% 12.59/12.82 tff(38126,plain,
% 12.59/12.82 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[31595, 2913, 36058])).
% 12.59/12.82 tff(38127,plain,
% 12.59/12.82 (b(s(s(z)), s(s(s(s(z)))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[3652, 38126])).
% 12.59/12.82 tff(38128,plain,
% 12.59/12.82 (r(s(z), z)),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[180, 38120])).
% 12.59/12.82 tff(38129,plain,
% 12.59/12.82 (~r(z, s(s(s(s(z)))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[31889, 38128, 36058, 2913])).
% 12.59/12.82 tff(38130,plain,
% 12.59/12.82 (b(z, s(s(s(s(z)))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[800, 38129])).
% 12.59/12.82 tff(38131,plain,
% 12.59/12.82 (b(elem!1, s(s(s(s(elem!1)))))),
% 12.59/12.82 inference(modus_ponens,[status(thm)],[38130, 35316])).
% 12.59/12.82 tff(38132,plain,
% 12.59/12.82 (b(z, s(s(elem!1)))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[3379, 38123, 11])).
% 12.59/12.82 tff(38133,plain,
% 12.59/12.82 (~b(s(z), s(s(s(elem!1))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[15561, 38119, 38108, 38110])).
% 12.59/12.82 tff(38134,plain,
% 12.59/12.82 (r(s(z), s(s(s(elem!1))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[247, 38133])).
% 12.59/12.82 tff(38135,plain,
% 12.59/12.82 (r(s(z), s(s(s(z))))),
% 12.59/12.82 inference(unit_resolution,[status(thm)],[23224, 38134, 11])).
% 12.59/12.83 tff(38136,plain,
% 12.59/12.83 (~r(s(s(s(z))), s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[31962, 4317, 11, 36058, 1216])).
% 12.59/12.83 tff(38137,plain,
% 12.59/12.83 (~r(s(s(s(elem!1))), s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[29740, 38136, 11])).
% 12.59/12.83 tff(38138,plain,
% 12.59/12.83 (b(s(s(s(elem!1))), s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[223, 38137])).
% 12.59/12.83 tff(38139,plain,
% 12.59/12.83 (b(s(s(s(z))), s(z))),
% 12.59/12.83 inference(modus_ponens,[status(thm)],[38138, 17635])).
% 12.59/12.83 tff(38140,plain,
% 12.59/12.83 (~r(z, s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[10620, 1216, 36058])).
% 12.59/12.83 tff(38141,plain,
% 12.59/12.83 (b(z, s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[678, 38140])).
% 12.59/12.83 tff(38142,plain,
% 12.59/12.83 (~b(s(z), z)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[10690, 38138, 38108, 38141])).
% 12.59/12.83 tff(38143,plain,
% 12.59/12.83 (r(s(z), elem!1)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[3205, 38142, 11])).
% 12.59/12.83 tff(38144,plain,
% 12.59/12.83 (~r(elem!1, s(s(z)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[11485, 38143, 36512, 1216])).
% 12.59/12.83 tff(38145,plain,
% 12.59/12.83 (b(elem!1, s(s(z)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[3394, 38144, 33689])).
% 12.59/12.83 tff(38146,plain,
% 12.59/12.83 (b(z, s(s(z)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[3375, 38145, 11])).
% 12.59/12.83 tff(38147,plain,
% 12.59/12.83 (~b(s(z), s(s(s(elem!1))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[15561, 38138, 38108, 38141])).
% 12.59/12.83 tff(38148,plain,
% 12.59/12.83 (r(s(z), s(s(s(elem!1))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[247, 38147])).
% 12.59/12.83 tff(38149,plain,
% 12.59/12.83 (r(s(z), s(s(s(z))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[23224, 38148, 11])).
% 12.59/12.83 tff(38150,plain,
% 12.59/12.83 (r(s(z), z)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[180, 38142])).
% 12.59/12.83 tff(38151,plain,
% 12.59/12.83 (~r(z, s(s(s(s(z)))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[31889, 38150, 36058, 1216])).
% 12.59/12.83 tff(38152,plain,
% 12.59/12.83 (b(z, s(s(s(s(z)))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[800, 38151])).
% 12.59/12.83 tff(38153,plain,
% 12.59/12.83 (b(elem!1, s(s(s(s(elem!1)))))),
% 12.59/12.83 inference(modus_ponens,[status(thm)],[38152, 35316])).
% 12.59/12.83 tff(38154,plain,
% 12.59/12.83 (b(z, s(s(elem!1)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[3379, 38145, 11])).
% 12.59/12.83 tff(38155,plain,
% 12.59/12.83 (~r(elem!1, s(s(s(s(z)))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[14627, 38143, 36512, 1216])).
% 12.59/12.83 tff(38156,plain,
% 12.59/12.83 (b(elem!1, s(s(s(s(z)))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[781, 38155, 33909])).
% 12.59/12.83 tff(38157,plain,
% 12.59/12.83 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[31595, 1216, 36058])).
% 12.59/12.83 tff(38158,plain,
% 12.59/12.83 (b(s(s(z)), s(s(s(s(z)))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[3652, 38157])).
% 12.59/12.83 tff(38159,plain,
% 12.59/12.83 (~r(s(s(s(s(z)))), s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[27854, 38148, 1216, 4317])).
% 12.59/12.83 tff(38160,plain,
% 12.59/12.83 (b(s(s(s(s(z)))), s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[749, 38159])).
% 12.59/12.83 tff(38161,plain,
% 12.59/12.83 (~r(s(s(z)), z)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[13565, 38160, 1216, 38158, 38156, 38145])).
% 12.59/12.83 tff(38162,plain,
% 12.59/12.83 (b(s(s(z)), z)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[1211, 38161])).
% 12.59/12.83 tff(38163,plain,
% 12.59/12.83 (b(s(s(elem!1)), elem!1)),
% 12.59/12.83 inference(modus_ponens,[status(thm)],[38162, 30006])).
% 12.59/12.83 tff(38164,plain,
% 12.59/12.83 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[25778, 38163, 38108, 38154, 38153])).
% 12.59/12.83 tff(38165,plain,
% 12.59/12.83 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[1370, 38164, 23216])).
% 12.59/12.83 tff(38166,plain,
% 12.59/12.83 (r(s(s(s(z))), s(s(z)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[4385, 38165, 11])).
% 12.59/12.83 tff(38167,plain,
% 12.59/12.83 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[32040, 38166, 1216, 38149])).
% 12.59/12.83 tff(38168,plain,
% 12.59/12.83 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[32518, 38167, 11])).
% 12.59/12.83 tff(38169,plain,
% 12.59/12.83 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[1095, 38168, 17615])).
% 12.59/12.83 tff(38170,plain,
% 12.59/12.83 (b(s(s(s(s(z)))), s(s(s(z))))),
% 12.59/12.83 inference(modus_ponens,[status(thm)],[38169, 23220])).
% 12.59/12.83 tff(38171,plain,
% 12.59/12.83 ($false),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[29674, 391, 38158, 38152, 38170, 38146, 38139])).
% 12.59/12.83 tff(38172,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.83 tff(38173,plain,
% 12.59/12.83 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[38172, 2913, 11])).
% 12.59/12.83 tff(38174,plain,
% 12.59/12.83 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[15351, 38173, 36511])).
% 12.59/12.83 tff(38175,plain,
% 12.59/12.83 (b(s(s(s(z))), s(s(s(s(z)))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[1673, 38174, 11])).
% 12.59/12.83 tff(38176,plain,
% 12.59/12.83 (b(z, s(s(s(z))))),
% 12.59/12.83 inference(modus_ponens,[status(thm)],[38108, 23189])).
% 12.59/12.83 tff(38177,plain,
% 12.59/12.83 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[32030, 38130, 38176, 38175])).
% 12.59/12.83 tff(38178,plain,
% 12.59/12.83 (b(s(s(s(s(z)))), s(s(s(z))))),
% 12.59/12.83 inference(modus_ponens,[status(thm)],[1114, 23220])).
% 12.59/12.83 tff(38179,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 12.59/12.83 tff(38180,plain,
% 12.59/12.83 ($false),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[38179, 38178])).
% 12.59/12.83 tff(38181,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(z)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.83 tff(38182,plain,
% 12.59/12.83 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[38181, 38177, 11])).
% 12.59/12.83 tff(38183,plain,
% 12.59/12.83 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[1095, 38182, 17615])).
% 12.59/12.83 tff(38184,plain,
% 12.59/12.83 (r(s(s(s(s(z)))), s(s(s(z))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[32518, 38183, 11])).
% 12.59/12.83 tff(38185,plain,
% 12.59/12.83 (~r(s(s(s(z))), s(s(z)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[32040, 38184, 2913, 38135])).
% 12.59/12.83 tff(38186,plain,
% 12.59/12.83 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[4385, 38185, 11])).
% 12.59/12.83 tff(38187,plain,
% 12.59/12.83 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[1370, 38186, 23216])).
% 12.59/12.83 tff(38188,plain,
% 12.59/12.83 (~b(s(s(elem!1)), elem!1)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[25778, 38187, 38108, 38132, 38131])).
% 12.59/12.83 tff(38189,plain,
% 12.59/12.83 (r(s(s(elem!1)), elem!1)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[872, 38188, 30072])).
% 12.59/12.83 tff(38190,plain,
% 12.59/12.83 (r(s(s(z)), z)),
% 12.59/12.83 inference(modus_ponens,[status(thm)],[38189, 33757])).
% 12.59/12.83 tff(38191,plain,
% 12.59/12.83 (~r(s(s(s(s(z)))), s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[12425, 38190, 2913, 38127, 38121, 38125, 38117, 38123])).
% 12.59/12.83 tff(38192,plain,
% 12.59/12.83 (~b(s(s(s(s(z)))), s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[13565, 38190, 2913, 38127, 38125, 38123])).
% 12.59/12.83 tff(38193,plain,
% 12.59/12.83 ($false),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[749, 38192, 38191])).
% 12.59/12.83 tff(38194,plain,(b(s(z), s(s(s(s(z))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.83 tff(38195,plain,
% 12.59/12.83 (b(s(z), s(s(s(s(z)))))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[38194, 11])).
% 12.59/12.83 tff(38196,plain,
% 12.59/12.83 (~r(s(s(s(s(z)))), s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[15864, 181, 36512, 33641])).
% 12.59/12.83 tff(38197,plain,
% 12.59/12.83 (b(s(s(s(s(z)))), s(z))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[749, 38196])).
% 12.59/12.83 tff(38198,plain,
% 12.59/12.83 (~r(s(s(z)), z)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[26737, 38197, 36058, 46, 181, 38195])).
% 12.59/12.83 tff(38199,plain,
% 12.59/12.83 (b(s(s(z)), z)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[1211, 38198])).
% 12.59/12.83 tff(38200,plain,
% 12.59/12.83 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 12.59/12.83 inference(monotonicity,[status(thm)],[63])).
% 12.59/12.83 tff(38201,plain,
% 12.59/12.83 (~(s(s(s(elem!1))) = elem!1)),
% 12.59/12.83 inference(modus_ponens,[status(thm)],[50, 38200])).
% 12.59/12.83 tff(38202,plain,
% 12.59/12.83 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[11865, 38197, 36512, 33641, 34471])).
% 12.59/12.83 tff(38203,plain,
% 12.59/12.83 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[8073, 38202, 33785])).
% 12.59/12.83 tff(38204,plain,
% 12.59/12.83 (b(s(s(s(s(s(s(z)))))), z)),
% 12.59/12.83 inference(modus_ponens,[status(thm)],[38203, 33854])).
% 12.59/12.83 tff(38205,plain,
% 12.59/12.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.59/12.83 inference(rewrite,[status(thm)],[])).
% 12.59/12.83 tff(38206,plain,
% 12.59/12.83 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.59/12.83 inference(rewrite,[status(thm)],[])).
% 12.59/12.83 tff(38207,plain,
% 12.59/12.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 12.59/12.83 inference(monotonicity,[status(thm)],[38206])).
% 12.59/12.83 tff(38208,plain,
% 12.59/12.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.59/12.83 inference(transitivity,[status(thm)],[38207, 38205])).
% 12.59/12.83 tff(38209,plain,
% 12.59/12.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 12.59/12.83 inference(quant_inst,[status(thm)],[])).
% 12.59/12.83 tff(38210,plain,
% 12.59/12.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 12.59/12.83 inference(modus_ponens,[status(thm)],[38209, 38208])).
% 12.59/12.83 tff(38211,plain,
% 12.59/12.83 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[38210, 391, 1235, 38176, 17636, 34218])).
% 12.59/12.83 tff(38212,plain,
% 12.59/12.83 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.59/12.83 inference(unit_resolution,[status(thm)],[6700, 42, 5009, 38211])).
% 12.59/12.83 tff(38213,plain,
% 12.59/12.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.59/12.83 inference(rewrite,[status(thm)],[])).
% 12.59/12.83 tff(38214,plain,
% 12.59/12.83 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.59/12.83 inference(rewrite,[status(thm)],[])).
% 12.59/12.83 tff(38215,plain,
% 12.59/12.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 12.59/12.84 inference(monotonicity,[status(thm)],[38214])).
% 12.59/12.84 tff(38216,plain,
% 12.59/12.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.59/12.84 inference(transitivity,[status(thm)],[38215, 38213])).
% 12.59/12.84 tff(38217,plain,
% 12.59/12.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 12.59/12.84 inference(quant_inst,[status(thm)],[])).
% 12.59/12.84 tff(38218,plain,
% 12.59/12.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 12.59/12.84 inference(modus_ponens,[status(thm)],[38217, 38216])).
% 12.59/12.84 tff(38219,plain,
% 12.59/12.84 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[38218, 391, 1235, 38176, 17636, 34218])).
% 12.59/12.84 tff(38220,plain,
% 12.59/12.84 ((s(s(z)) = s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[33813, 42, 38219])).
% 12.59/12.84 tff(38221,plain,
% 12.59/12.84 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[38220, 33800])).
% 12.59/12.84 tff(38222,plain,
% 12.59/12.84 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[17645, 391, 38195, 1759, 17636])).
% 12.59/12.84 tff(38223,plain,
% 12.59/12.84 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[38181, 38222, 11])).
% 12.59/12.84 tff(38224,plain,
% 12.59/12.84 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[1095, 38223, 17615])).
% 12.59/12.84 tff(38225,plain,
% 12.59/12.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.59/12.84 inference(rewrite,[status(thm)],[])).
% 12.59/12.84 tff(38226,plain,
% 12.59/12.84 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.59/12.84 inference(rewrite,[status(thm)],[])).
% 12.59/12.84 tff(38227,plain,
% 12.59/12.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.59/12.84 inference(monotonicity,[status(thm)],[38226])).
% 12.59/12.84 tff(38228,plain,
% 12.59/12.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.59/12.84 inference(transitivity,[status(thm)],[38227, 38225])).
% 12.59/12.84 tff(38229,plain,
% 12.59/12.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 12.59/12.84 inference(quant_inst,[status(thm)],[])).
% 12.59/12.84 tff(38230,plain,
% 12.59/12.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 12.59/12.84 inference(modus_ponens,[status(thm)],[38229, 38228])).
% 12.59/12.84 tff(38231,plain,
% 12.59/12.84 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[38230, 391, 38195, 1759, 17636])).
% 12.59/12.84 tff(38232,plain,
% 12.59/12.84 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.59/12.84 inference(modus_ponens,[status(thm)],[38231, 18390])).
% 12.59/12.84 tff(38233,plain,
% 12.59/12.84 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[1164, 38232, 17616])).
% 12.59/12.84 tff(38234,plain,
% 12.59/12.84 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(elem!1)))))),
% 12.59/12.84 inference(transitivity,[status(thm)],[60, 18458])).
% 12.59/12.84 tff(38235,plain,
% 12.59/12.84 (b(z, s(s(s(s(z)))))),
% 12.59/12.84 inference(modus_ponens,[status(thm)],[2064, 33907])).
% 12.59/12.84 tff(38236,plain,
% 12.59/12.84 (b(elem!1, s(s(s(s(elem!1)))))),
% 12.59/12.84 inference(modus_ponens,[status(thm)],[2064, 34153])).
% 12.59/12.84 tff(38237,plain,
% 12.59/12.84 (~b(s(s(elem!1)), s(z))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[3263, 1374, 1234, 1759, 1526])).
% 12.59/12.84 tff(38238,plain,
% 12.59/12.84 (r(s(s(elem!1)), s(z))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[362, 38237])).
% 12.59/12.84 tff(38239,plain,
% 12.59/12.84 (~b(z, s(s(elem!1)))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[25778, 1374, 10682, 973, 974])).
% 12.59/12.84 tff(38240,plain,
% 12.59/12.84 (r(z, s(s(elem!1)))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[324, 38239])).
% 12.59/12.84 tff(38241,plain,
% 12.59/12.84 ($false),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[22122, 38240, 38238, 722, 1484])).
% 12.59/12.84 tff(38242,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.84 tff(38243,plain,
% 12.59/12.84 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[38242, 38236, 1484, 38108, 35318, 722, 38195, 1759, 1526])).
% 12.59/12.84 tff(38244,plain,
% 12.59/12.84 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[1370, 38243, 23216])).
% 12.59/12.84 tff(38245,plain,
% 12.59/12.84 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[14274, 38244, 36586, 38233])).
% 12.59/12.84 tff(38246,plain,
% 12.59/12.84 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[1048, 38245, 2419])).
% 12.59/12.84 tff(38247,plain,
% 12.59/12.84 (b(s(s(z)), s(s(s(s(z)))))),
% 12.59/12.84 inference(modus_ponens,[status(thm)],[38246, 35381])).
% 12.59/12.84 tff(38248,plain,
% 12.59/12.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.59/12.84 inference(rewrite,[status(thm)],[])).
% 12.59/12.84 tff(38249,plain,
% 12.59/12.84 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.59/12.84 inference(rewrite,[status(thm)],[])).
% 12.59/12.84 tff(38250,plain,
% 12.59/12.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 12.59/12.84 inference(monotonicity,[status(thm)],[38249])).
% 12.59/12.84 tff(38251,plain,
% 12.59/12.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 12.59/12.84 inference(transitivity,[status(thm)],[38250, 38248])).
% 12.59/12.84 tff(38252,plain,
% 12.59/12.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 12.59/12.84 inference(quant_inst,[status(thm)],[])).
% 12.59/12.84 tff(38253,plain,
% 12.59/12.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 12.59/12.84 inference(modus_ponens,[status(thm)],[38252, 38251])).
% 12.59/12.84 tff(38254,plain,
% 12.59/12.84 ($false),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[38253, 391, 38247, 1235, 38195, 1759, 38235])).
% 12.59/12.84 tff(38255,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~(elem!1 = z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.84 tff(38256,plain,
% 12.59/12.84 (~b(elem!1, s(s(s(s(z)))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[38255, 1526, 1759, 11, 1484, 722, 1235])).
% 12.59/12.84 tff(38257,plain,
% 12.59/12.84 (r(elem!1, s(s(s(s(z)))))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[781, 38256, 33909])).
% 12.59/12.84 tff(38258,plain,
% 12.59/12.84 (r(z, s(s(s(s(elem!1)))))),
% 12.59/12.84 inference(modus_ponens,[status(thm)],[38257, 38234])).
% 12.59/12.84 tff(38259,plain,
% 12.59/12.84 (~r(s(s(s(elem!1))), z)),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[35429, 38258, 38233, 38224])).
% 12.59/12.84 tff(38260,plain,
% 12.59/12.84 (b(s(s(s(elem!1))), z)),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[377, 38259])).
% 12.59/12.84 tff(38261,plain,
% 12.59/12.84 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[13177, 38260, 38108, 35382])).
% 12.59/12.84 tff(38262,plain,
% 12.59/12.84 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[1370, 38261, 23216])).
% 12.59/12.84 tff(38263,plain,
% 12.59/12.84 (r(s(s(s(z))), s(s(z)))),
% 12.59/12.84 inference(unit_resolution,[status(thm)],[4385, 38262, 11])).
% 12.59/12.84 tff(38264,plain,
% 12.59/12.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 12.59/12.84 inference(rewrite,[status(thm)],[])).
% 12.59/12.84 tff(38265,plain,
% 12.59/12.84 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 12.59/12.85 inference(rewrite,[status(thm)],[])).
% 12.59/12.85 tff(38266,plain,
% 12.59/12.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 12.59/12.85 inference(monotonicity,[status(thm)],[38265])).
% 12.59/12.85 tff(38267,plain,
% 12.59/12.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 12.59/12.85 inference(transitivity,[status(thm)],[38266, 38264])).
% 12.59/12.85 tff(38268,plain,
% 12.59/12.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.59/12.85 inference(quant_inst,[status(thm)],[])).
% 12.59/12.85 tff(38269,plain,
% 12.59/12.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 12.59/12.85 inference(modus_ponens,[status(thm)],[38268, 38267])).
% 12.59/12.85 tff(38270,plain,
% 12.59/12.85 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[38269, 194, 38263, 38221, 38212])).
% 12.59/12.85 tff(38271,plain,
% 12.59/12.85 (b(s(s(s(z))), z)),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[1680, 38260, 11])).
% 12.59/12.85 tff(38272,plain,
% 12.59/12.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.59/12.85 inference(rewrite,[status(thm)],[])).
% 12.59/12.85 tff(38273,plain,
% 12.59/12.85 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.59/12.85 inference(rewrite,[status(thm)],[])).
% 12.59/12.85 tff(38274,plain,
% 12.59/12.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 12.59/12.85 inference(monotonicity,[status(thm)],[38273])).
% 12.59/12.85 tff(38275,plain,
% 12.59/12.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 12.59/12.85 inference(transitivity,[status(thm)],[38274, 38272])).
% 12.59/12.85 tff(38276,plain,
% 12.59/12.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 12.59/12.85 inference(quant_inst,[status(thm)],[])).
% 12.59/12.85 tff(38277,plain,
% 12.59/12.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 12.59/12.85 inference(modus_ponens,[status(thm)],[38276, 38275])).
% 12.59/12.85 tff(38278,plain,
% 12.59/12.85 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[38277, 391, 38176, 17636, 38271, 34218])).
% 12.59/12.85 tff(38279,plain,
% 12.59/12.85 ($false),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[29527, 42, 8094, 38278, 38270])).
% 12.59/12.85 tff(38280,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.85 tff(38281,plain,
% 12.59/12.85 (~b(s(s(s(elem!1))), s(z))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[38280, 38204, 11, 38197, 34471, 46, 38199])).
% 12.59/12.85 tff(38282,plain,
% 12.59/12.85 (b(s(s(s(s(z)))), z)),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[31585, 38281, 79, 66, 31])).
% 12.59/12.85 tff(38283,plain,
% 12.59/12.85 (r(s(s(s(elem!1))), s(z))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[223, 38281])).
% 12.59/12.85 tff(38284,plain,
% 12.59/12.85 (~r(s(s(s(elem!1))), z)),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[17465, 38283, 46, 34471])).
% 12.59/12.85 tff(38285,plain,
% 12.59/12.85 ($false),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[35414, 38284, 38282, 38108, 11, 38201, 38199])).
% 12.59/12.85 tff(38286,plain,(b(s(z), z) | (~(elem!1 = z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.85 tff(38287,plain,
% 12.59/12.85 (b(s(z), z)),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[38286, 31, 11])).
% 12.59/12.85 tff(38288,plain,
% 12.59/12.85 (b(s(z), elem!1)),
% 12.59/12.85 inference(modus_ponens,[status(thm)],[38287, 34442])).
% 12.59/12.85 tff(38289,plain,
% 12.59/12.85 (b(s(s(s(s(z)))), z)),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[31585, 11173, 79, 66, 31])).
% 12.59/12.85 tff(38290,plain,
% 12.59/12.85 (~b(s(s(s(elem!1))), z)),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[35701, 38289, 11, 38108, 38195, 38288])).
% 12.59/12.85 tff(38291,plain,
% 12.59/12.85 (r(s(s(s(elem!1))), z)),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[377, 38290])).
% 12.59/12.85 tff(38292,plain,
% 12.59/12.85 (~r(s(z), s(s(s(elem!1))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[29577, 38291, 79, 38108, 33641, 66, 11174])).
% 12.59/12.85 tff(38293,plain,
% 12.59/12.85 (~b(z, s(s(s(s(z)))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[22664, 38289, 38287, 38195])).
% 12.59/12.85 tff(38294,plain,
% 12.59/12.85 (r(z, s(s(s(s(z)))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[800, 38293])).
% 12.59/12.85 tff(38295,plain,
% 12.59/12.85 (~b(s(s(s(elem!1))), z)),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[11303, 379, 590, 10682])).
% 12.59/12.85 tff(38296,plain,
% 12.59/12.85 (r(s(s(s(elem!1))), z)),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[377, 38295])).
% 12.59/12.85 tff(38297,plain,
% 12.59/12.85 (r(s(s(s(z))), z)),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[4409, 38296, 11])).
% 12.59/12.85 tff(38298,plain,
% 12.59/12.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[4450, 194, 2053, 719, 38297])).
% 12.59/12.85 tff(38299,plain,
% 12.59/12.85 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[32518, 38298, 11])).
% 12.59/12.85 tff(38300,plain,
% 12.59/12.85 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[1095, 38299, 305])).
% 12.59/12.85 tff(38301,plain,
% 12.59/12.85 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[27316, 38300, 11])).
% 12.59/12.85 tff(38302,plain,
% 12.59/12.85 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[17481, 38301, 10682, 590, 379])).
% 12.59/12.85 tff(38303,plain,
% 12.59/12.85 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.59/12.85 inference(unit_resolution,[status(thm)],[15351, 38302, 15348])).
% 12.59/12.86 tff(38304,plain,
% 12.59/12.86 (r(s(s(s(z))), s(s(s(s(z)))))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38303, 17613])).
% 12.59/12.86 tff(38305,plain,
% 12.59/12.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 12.59/12.86 inference(rewrite,[status(thm)],[])).
% 12.59/12.86 tff(38306,plain,
% 12.59/12.86 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 12.59/12.86 inference(rewrite,[status(thm)],[])).
% 12.59/12.86 tff(38307,plain,
% 12.59/12.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 12.59/12.86 inference(monotonicity,[status(thm)],[38306])).
% 12.59/12.86 tff(38308,plain,
% 12.59/12.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 12.59/12.86 inference(transitivity,[status(thm)],[38307, 38305])).
% 12.59/12.86 tff(38309,plain,
% 12.59/12.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 12.59/12.86 inference(quant_inst,[status(thm)],[])).
% 12.59/12.86 tff(38310,plain,
% 12.59/12.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38309, 38308])).
% 12.59/12.86 tff(38311,plain,
% 12.59/12.86 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38310, 194, 2053, 719, 38297])).
% 12.59/12.86 tff(38312,plain,
% 12.59/12.86 ($false),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38311, 38304])).
% 12.59/12.86 tff(38313,plain,((~r(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.86 tff(38314,plain,
% 12.59/12.86 (~b(s(z), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38313, 38294, 11, 36511, 36058, 38108, 17615, 38287])).
% 12.59/12.86 tff(38315,plain,
% 12.59/12.86 ($false),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[247, 38314, 38292])).
% 12.59/12.86 tff(38316,plain,(b(s(s(s(elem!1))), s(z)) | (~(elem!1 = z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.86 tff(38317,plain,
% 12.59/12.86 (b(s(s(s(elem!1))), s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38316, 31, 11])).
% 12.59/12.86 tff(38318,plain,
% 12.59/12.86 (b(s(s(s(z))), s(z))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38317, 17635])).
% 12.59/12.86 tff(38319,plain,
% 12.59/12.86 (~b(s(z), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[28322, 38317, 38108, 38287, 38288])).
% 12.59/12.86 tff(38320,plain,
% 12.59/12.86 (r(s(z), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[247, 38319])).
% 12.59/12.86 tff(38321,plain,
% 12.59/12.86 (r(s(z), s(s(s(z))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[23224, 38320, 11])).
% 12.59/12.86 tff(38322,plain,
% 12.59/12.86 (~r(s(s(s(s(z)))), s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[18419, 38321, 36058, 46])).
% 12.59/12.86 tff(38323,plain,
% 12.59/12.86 (b(s(s(s(s(z)))), s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[749, 38322])).
% 12.59/12.86 tff(38324,plain,
% 12.59/12.86 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38230, 391, 38195, 38323, 38318])).
% 12.59/12.86 tff(38325,plain,
% 12.59/12.86 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38324, 18390])).
% 12.59/12.86 tff(38326,plain,
% 12.59/12.86 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[17645, 391, 38195, 38323, 38318])).
% 12.59/12.86 tff(38327,plain,
% 12.59/12.86 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38181, 38326, 11])).
% 12.59/12.86 tff(38328,plain,
% 12.59/12.86 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[1095, 38327, 17615])).
% 12.59/12.86 tff(38329,plain,
% 12.59/12.86 (~b(z, s(s(s(s(z)))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[17292, 38323, 38195, 38287])).
% 12.59/12.86 tff(38330,plain,
% 12.59/12.86 (r(z, s(s(s(s(z)))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[800, 38329])).
% 12.59/12.86 tff(38331,plain,
% 12.59/12.86 (r(z, s(s(s(s(elem!1)))))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38330, 18458])).
% 12.59/12.86 tff(38332,plain,
% 12.59/12.86 (b(s(elem!1), z)),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38287, 18406])).
% 12.59/12.86 tff(38333,plain,
% 12.59/12.86 (b(s(s(s(elem!1))), s(elem!1))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38317, 17624])).
% 12.59/12.86 tff(38334,plain,
% 12.59/12.86 (~b(s(s(s(elem!1))), z)),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[12799, 38333, 38108, 38332])).
% 12.59/12.86 tff(38335,plain,
% 12.59/12.86 (r(s(s(s(elem!1))), z)),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[377, 38334])).
% 12.59/12.86 tff(38336,plain,
% 12.59/12.86 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[35429, 38335, 38331, 38328])).
% 12.59/12.86 tff(38337,plain,
% 12.59/12.86 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[1164, 38336, 17616])).
% 12.59/12.86 tff(38338,plain,
% 12.59/12.86 ($false),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38337, 38325])).
% 12.59/12.86 tff(38339,plain,(b(elem!1, s(z)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.86 tff(38340,plain,
% 12.59/12.86 (b(elem!1, s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38339, 38098])).
% 12.59/12.86 tff(38341,plain,
% 12.59/12.86 (~(s(z) = elem!1)),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[20271, 38340])).
% 12.59/12.86 tff(38342,plain,
% 12.59/12.86 (b(s(z), s(s(s(s(z)))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38194, 38098])).
% 12.59/12.86 tff(38343,plain,
% 12.59/12.86 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 12.59/12.86 inference(monotonicity,[status(thm)],[38098])).
% 12.59/12.86 tff(38344,plain,
% 12.59/12.86 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 12.59/12.86 inference(symmetry,[status(thm)],[38343])).
% 12.59/12.86 tff(38345,plain,
% 12.59/12.86 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 12.59/12.86 inference(monotonicity,[status(thm)],[38104])).
% 12.59/12.86 tff(38346,plain,
% 12.59/12.86 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 12.59/12.86 inference(symmetry,[status(thm)],[38345])).
% 12.59/12.86 tff(38347,plain,
% 12.59/12.86 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 12.59/12.86 inference(transitivity,[status(thm)],[38346, 38344])).
% 12.59/12.86 tff(38348,plain,
% 12.59/12.86 (r(z, elem!1) <=> r(z, z)),
% 12.59/12.86 inference(monotonicity,[status(thm)],[38098])).
% 12.59/12.86 tff(38349,plain,
% 12.59/12.86 (r(z, z) <=> r(z, elem!1)),
% 12.59/12.86 inference(symmetry,[status(thm)],[38348])).
% 12.59/12.86 tff(38350,plain,
% 12.59/12.86 ((~r(z, z)) <=> (~r(z, elem!1))),
% 12.59/12.86 inference(monotonicity,[status(thm)],[38349])).
% 12.59/12.86 tff(38351,plain,
% 12.59/12.86 (~r(z, elem!1)),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[78, 38350])).
% 12.59/12.86 tff(38352,plain,
% 12.59/12.86 (r(s(s(s(s(z)))), z)),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[36057, 38351, 1])).
% 12.59/12.86 tff(38353,plain,
% 12.59/12.86 (r(s(s(s(s(elem!1)))), elem!1)),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38352, 38347])).
% 12.59/12.86 tff(38354,plain,
% 12.59/12.86 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 12.59/12.86 inference(monotonicity,[status(thm)],[38098])).
% 12.59/12.86 tff(38355,plain,
% 12.59/12.86 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 12.59/12.86 inference(symmetry,[status(thm)],[38354])).
% 12.59/12.86 tff(38356,plain,
% 12.59/12.86 (r(s(s(s(s(z)))), elem!1)),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38352, 38355])).
% 12.59/12.86 tff(38357,plain,
% 12.59/12.86 (z = elem!1),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[5453, 38098])).
% 12.59/12.86 tff(38358,plain,
% 12.59/12.86 (b(elem!1, s(z)) <=> b(z, s(z))),
% 12.59/12.86 inference(monotonicity,[status(thm)],[38098])).
% 12.59/12.86 tff(38359,plain,
% 12.59/12.86 (b(z, s(z))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38340, 38358])).
% 12.59/12.86 tff(38360,plain,
% 12.59/12.86 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 12.59/12.86 inference(symmetry,[status(thm)],[33695])).
% 12.59/12.86 tff(38361,plain,
% 12.59/12.86 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 12.59/12.86 inference(monotonicity,[status(thm)],[490])).
% 12.59/12.86 tff(38362,plain,
% 12.59/12.86 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.59/12.86 inference(symmetry,[status(thm)],[38361])).
% 12.59/12.86 tff(38363,plain,
% 12.59/12.86 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.59/12.86 inference(transitivity,[status(thm)],[3504, 38362])).
% 12.59/12.86 tff(38364,plain,
% 12.59/12.86 (b(elem!1, s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38339, 11])).
% 12.59/12.86 tff(38365,plain,
% 12.59/12.86 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 12.59/12.86 inference(symmetry,[status(thm)],[504])).
% 12.59/12.86 tff(38366,plain,
% 12.59/12.86 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 12.59/12.86 inference(symmetry,[status(thm)],[36118])).
% 12.59/12.86 tff(38367,plain,
% 12.59/12.86 (~r(s(s(s(s(z)))), s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[15864, 36091, 181, 36115])).
% 12.59/12.86 tff(38368,plain,
% 12.59/12.86 (b(s(s(s(s(z)))), s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[749, 38367])).
% 12.59/12.86 tff(38369,plain,
% 12.59/12.86 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38368, 38366])).
% 12.59/12.86 tff(38370,plain,
% 12.59/12.86 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 12.59/12.86 inference(monotonicity,[status(thm)],[488, 2401])).
% 12.59/12.86 tff(38371,plain,
% 12.59/12.86 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 12.59/12.86 inference(symmetry,[status(thm)],[38370])).
% 12.59/12.86 tff(38372,plain,
% 12.59/12.86 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[1234, 38371])).
% 12.59/12.86 tff(38373,plain,
% 12.59/12.86 (~r(s(s(z)), z)),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[34529, 34471, 721, 1234, 33689, 33909, 36115, 35025, 2053, 181])).
% 12.59/12.86 tff(38374,plain,
% 12.59/12.86 (b(s(s(z)), z)),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[1211, 38373])).
% 12.59/12.86 tff(38375,plain,
% 12.59/12.86 (b(s(s(elem!1)), elem!1)),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38374, 30006])).
% 12.59/12.86 tff(38376,plain,
% 12.59/12.86 (~b(s(s(elem!1)), s(elem!1))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[34586, 38375, 36090, 38372, 38369])).
% 12.59/12.86 tff(38377,plain,
% 12.59/12.86 (~b(s(s(elem!1)), s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[1033, 38376, 11])).
% 12.59/12.86 tff(38378,plain,
% 12.59/12.86 (r(s(s(elem!1)), s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[362, 38377])).
% 12.59/12.86 tff(38379,plain,
% 12.59/12.86 (~b(z, s(s(s(s(z)))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[10478, 38368, 1234, 35025])).
% 12.59/12.86 tff(38380,plain,
% 12.59/12.86 (r(z, s(s(s(s(z)))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[800, 38379])).
% 12.59/12.86 tff(38381,plain,
% 12.59/12.86 (r(elem!1, s(s(s(s(elem!1)))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[23210, 38380, 11])).
% 12.59/12.86 tff(38382,plain,
% 12.59/12.86 (r(s(elem!1), elem!1)),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[181, 17627])).
% 12.59/12.86 tff(38383,plain,
% 12.59/12.86 (~r(s(s(s(elem!1))), elem!1)),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[19658, 38382, 38381, 23202])).
% 12.59/12.86 tff(38384,plain,
% 12.59/12.86 (b(s(s(s(elem!1))), elem!1)),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[230, 38383, 127])).
% 12.59/12.86 tff(38385,plain,
% 12.59/12.86 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[6001, 38384, 448, 38375])).
% 12.59/12.86 tff(38386,plain,
% 12.59/12.86 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[1356, 38385, 21729])).
% 12.59/12.86 tff(38387,plain,
% 12.59/12.86 (~r(s(z), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[2201, 38386, 183, 38378])).
% 12.59/12.86 tff(38388,plain,
% 12.59/12.86 (b(s(z), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[247, 38387])).
% 12.59/12.86 tff(38389,plain,
% 12.59/12.86 (b(s(elem!1), s(s(s(elem!1))))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38388, 38365])).
% 12.59/12.86 tff(38390,plain,
% 12.59/12.86 (b(z, s(elem!1))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[35025, 34436])).
% 12.59/12.86 tff(38391,plain,
% 12.59/12.86 (~b(s(elem!1), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[25659, 38384, 36090, 10682, 38390])).
% 12.59/12.86 tff(38392,plain,
% 12.59/12.86 ($false),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38391, 38389])).
% 12.59/12.86 tff(38393,plain,(b(s(z), z) | (~(elem!1 = z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.86 tff(38394,plain,
% 12.59/12.86 (b(s(z), z)),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[38393, 11, 183, 10682, 448, 127, 1234, 721, 2053])).
% 12.59/12.86 tff(38395,plain,
% 12.59/12.86 (b(s(z), elem!1)),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[590, 34442])).
% 12.59/12.86 tff(38396,plain,
% 12.59/12.86 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[32476, 364, 721, 17618, 38395, 29981, 448, 36116, 23202])).
% 12.59/12.86 tff(38397,plain,
% 12.59/12.86 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[1370, 38396, 297])).
% 12.59/12.86 tff(38398,plain,
% 12.59/12.86 (~b(z, s(s(elem!1)))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[24044, 38397, 10682, 590, 183, 232, 315])).
% 12.59/12.86 tff(38399,plain,
% 12.59/12.86 (r(z, s(s(elem!1)))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[324, 38398])).
% 12.59/12.86 tff(38400,plain,
% 12.59/12.86 (r(z, s(s(z)))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[30084, 38399, 11])).
% 12.59/12.86 tff(38401,plain,
% 12.59/12.86 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[30450, 194, 2053, 33803, 38400])).
% 12.59/12.86 tff(38402,plain,
% 12.59/12.86 (r(s(s(elem!1)), z)),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[364, 30365])).
% 12.59/12.86 tff(38403,plain,
% 12.59/12.86 (~b(s(s(s(elem!1))), s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[10690, 10682, 664, 590])).
% 12.59/12.86 tff(38404,plain,
% 12.59/12.86 (r(s(s(s(elem!1))), s(z))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[223, 38403])).
% 12.59/12.86 tff(38405,plain,
% 12.59/12.86 (r(s(s(s(s(z)))), z)),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[991, 34708])).
% 12.59/12.86 tff(38406,plain,
% 12.59/12.86 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[3563, 32465])).
% 12.59/12.86 tff(38407,plain,
% 12.59/12.86 (r(s(s(s(elem!1))), s(elem!1))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[38404, 32331])).
% 12.59/12.86 tff(38408,plain,
% 12.59/12.86 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[1749, 32390])).
% 12.59/12.86 tff(38409,plain,
% 12.59/12.86 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[14540, 194, 991, 1538, 38408])).
% 12.59/12.86 tff(38410,plain,
% 12.59/12.86 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.59/12.86 inference(unit_resolution,[status(thm)],[1356, 38409, 27414])).
% 12.59/12.86 tff(38411,plain,
% 12.59/12.86 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 12.59/12.86 inference(modus_ponens,[status(thm)],[1749, 32389])).
% 12.59/12.86 tff(38412,plain,
% 12.59/12.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 12.59/12.86 inference(rewrite,[status(thm)],[])).
% 12.59/12.86 tff(38413,plain,
% 12.59/12.86 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 12.59/12.86 inference(rewrite,[status(thm)],[])).
% 12.59/12.86 tff(38414,plain,
% 12.59/12.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 12.59/12.86 inference(monotonicity,[status(thm)],[38413])).
% 12.59/12.86 tff(38415,plain,
% 12.59/12.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 12.59/12.87 inference(transitivity,[status(thm)],[38414, 38412])).
% 12.59/12.87 tff(38416,plain,
% 12.59/12.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 12.59/12.87 inference(quant_inst,[status(thm)],[])).
% 12.59/12.87 tff(38417,plain,
% 12.59/12.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 12.59/12.87 inference(modus_ponens,[status(thm)],[38416, 38415])).
% 12.59/12.87 tff(38418,plain,
% 12.59/12.87 ($false),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[38417, 194, 326, 2053, 2616, 6257])).
% 12.59/12.87 tff(38419,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.87 tff(38420,plain,
% 12.59/12.87 (~r(z, s(s(elem!1)))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[38419, 38411, 38405, 2616])).
% 12.59/12.87 tff(38421,plain,
% 12.59/12.87 (b(z, s(s(elem!1)))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[324, 38420])).
% 12.59/12.87 tff(38422,plain,
% 12.59/12.87 ($false),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[12932, 38421, 38410, 10682, 1374])).
% 12.59/12.87 tff(38423,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.87 tff(38424,plain,
% 12.59/12.87 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[38423, 1538, 1374, 2616, 991, 10682, 94])).
% 12.59/12.87 tff(38425,plain,
% 12.59/12.87 (b(s(s(z)), s(s(s(s(z)))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[3652, 38424])).
% 12.59/12.87 tff(38426,plain,
% 12.59/12.87 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.59/12.87 inference(modus_ponens,[status(thm)],[38425, 34705])).
% 12.59/12.87 tff(38427,plain,
% 12.59/12.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 12.59/12.87 inference(rewrite,[status(thm)],[])).
% 12.59/12.87 tff(38428,plain,
% 12.59/12.87 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 12.59/12.87 inference(rewrite,[status(thm)],[])).
% 12.59/12.87 tff(38429,plain,
% 12.59/12.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 12.59/12.87 inference(monotonicity,[status(thm)],[38428])).
% 12.59/12.87 tff(38430,plain,
% 12.59/12.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 12.59/12.87 inference(transitivity,[status(thm)],[38429, 38427])).
% 12.59/12.87 tff(38431,plain,
% 12.59/12.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 12.59/12.87 inference(quant_inst,[status(thm)],[])).
% 12.59/12.87 tff(38432,plain,
% 12.59/12.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 12.59/12.87 inference(modus_ponens,[status(thm)],[38431, 38430])).
% 12.59/12.87 tff(38433,plain,
% 12.59/12.87 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[38432, 391, 1374, 38406, 38426])).
% 12.59/12.87 tff(38434,plain,
% 12.59/12.87 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[1095, 38433, 32385])).
% 12.59/12.87 tff(38435,plain,
% 12.59/12.87 (r(s(s(s(z))), z)),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[4409, 34732, 1027])).
% 12.59/12.87 tff(38436,plain,
% 12.59/12.87 (b(elem!1, s(s(s(elem!1))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[23154, 10682, 1027])).
% 12.59/12.87 tff(38437,plain,
% 12.59/12.87 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 12.59/12.87 inference(monotonicity,[status(thm)],[932])).
% 12.59/12.87 tff(38438,plain,
% 12.59/12.87 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 12.59/12.87 inference(monotonicity,[status(thm)],[931])).
% 12.59/12.87 tff(38439,plain,
% 12.59/12.87 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 12.59/12.87 inference(transitivity,[status(thm)],[38438, 38437])).
% 12.59/12.87 tff(38440,plain,
% 12.59/12.87 (~b(s(z), s(s(z)))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[6275, 38425, 1234, 3563])).
% 12.59/12.87 tff(38441,plain,
% 12.59/12.87 (r(s(z), s(s(z)))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[1788, 38440])).
% 12.59/12.87 tff(38442,plain,
% 12.59/12.87 (r(s(elem!1), s(s(elem!1)))),
% 12.59/12.87 inference(modus_ponens,[status(thm)],[38441, 38439])).
% 12.59/12.87 tff(38443,plain,
% 12.59/12.87 (~b(s(s(z)), s(z))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[9374, 38425, 1234, 3563])).
% 12.59/12.87 tff(38444,plain,
% 12.59/12.87 (r(s(s(z)), s(z))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[3778, 38443])).
% 12.59/12.87 tff(38445,plain,
% 12.59/12.87 (r(s(s(elem!1)), s(elem!1))),
% 12.59/12.87 inference(modus_ponens,[status(thm)],[38444, 34637])).
% 12.59/12.87 tff(38446,plain,
% 12.59/12.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[24582, 194, 613, 38445, 38442])).
% 12.59/12.87 tff(38447,plain,
% 12.59/12.87 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[1356, 38446, 27414])).
% 12.59/12.87 tff(38448,plain,
% 12.59/12.87 (~b(s(z), s(s(s(elem!1))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[22188, 38447, 38436, 1374, 34517])).
% 12.59/12.87 tff(38449,plain,
% 12.59/12.87 (r(s(z), s(s(s(elem!1))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[247, 38448])).
% 12.59/12.87 tff(38450,plain,
% 12.59/12.87 (r(s(z), s(s(s(z))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[23224, 38449, 1027])).
% 12.59/12.87 tff(38451,plain,
% 12.59/12.87 (~r(s(s(s(s(z)))), s(z))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[27308, 38450, 38434, 38435, 1027])).
% 12.59/12.87 tff(38452,plain,
% 12.59/12.87 (b(s(s(s(s(z)))), s(z))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[749, 38451])).
% 12.59/12.87 tff(38453,plain,
% 12.59/12.87 (~b(z, s(s(s(s(z)))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[10478, 38452, 1234, 664])).
% 12.59/12.87 tff(38454,plain,
% 12.59/12.87 (r(z, s(s(s(s(z)))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[800, 38453])).
% 12.59/12.87 tff(38455,plain,
% 12.59/12.87 (r(elem!1, s(s(s(s(elem!1)))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[23210, 38454, 1027])).
% 12.59/12.87 tff(38456,plain,
% 12.59/12.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 12.59/12.87 inference(rewrite,[status(thm)],[])).
% 12.59/12.87 tff(38457,plain,
% 12.59/12.87 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 12.59/12.87 inference(rewrite,[status(thm)],[])).
% 12.59/12.87 tff(38458,plain,
% 12.59/12.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 12.59/12.87 inference(monotonicity,[status(thm)],[38457])).
% 12.59/12.87 tff(38459,plain,
% 12.59/12.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 12.59/12.87 inference(transitivity,[status(thm)],[38458, 38456])).
% 12.59/12.87 tff(38460,plain,
% 12.59/12.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 12.59/12.87 inference(quant_inst,[status(thm)],[])).
% 12.59/12.87 tff(38461,plain,
% 12.59/12.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 12.59/12.87 inference(modus_ponens,[status(thm)],[38460, 38459])).
% 12.59/12.87 tff(38462,plain,
% 12.59/12.87 ($false),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[38461, 194, 233, 38455, 1538, 38434])).
% 12.59/12.87 tff(38463,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.87 tff(38464,plain,
% 12.59/12.87 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[38463, 3563, 1234, 664, 1374, 38407, 94, 233, 2616, 991, 10682])).
% 12.59/12.87 tff(38465,plain,
% 12.59/12.87 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[1164, 38464, 32386])).
% 12.59/12.87 tff(38466,plain,
% 12.59/12.87 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[1741, 38465, 1374, 38406])).
% 12.59/12.87 tff(38467,plain,
% 12.59/12.87 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[1048, 38466, 1024])).
% 12.59/12.87 tff(38468,plain,
% 12.59/12.87 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 12.59/12.87 inference(modus_ponens,[status(thm)],[38467, 32387])).
% 12.59/12.87 tff(38469,plain,
% 12.59/12.87 (~r(z, s(s(elem!1)))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[38419, 38468, 38405, 2616])).
% 12.59/12.87 tff(38470,plain,
% 12.59/12.87 (b(z, s(s(elem!1)))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[324, 38469])).
% 12.59/12.87 tff(38471,plain,
% 12.59/12.87 (~r(s(z), s(s(s(elem!1))))),
% 12.59/12.87 inference(unit_resolution,[status(thm)],[24044, 38470, 590, 10682, 38404, 1374, 27414])).
% 12.59/12.88 tff(38472,plain,
% 12.59/12.88 (b(s(z), s(s(s(elem!1))))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[247, 38471])).
% 12.59/12.88 tff(38473,plain,
% 12.59/12.88 (b(s(elem!1), s(s(s(elem!1))))),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[38472, 1025])).
% 12.59/12.88 tff(38474,plain,
% 12.59/12.88 (~b(s(elem!1), s(s(s(elem!1))))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[19513, 38465, 2122, 38436, 38406])).
% 12.59/12.88 tff(38475,plain,
% 12.59/12.88 ($false),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[38474, 38473])).
% 12.59/12.88 tff(38476,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~(z = elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.88 tff(38477,plain,
% 12.59/12.88 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[38476, 38402, 590, 17618, 10682, 38397, 36119, 1234, 35025, 233, 29981])).
% 12.59/12.88 tff(38478,plain,
% 12.59/12.88 ($false),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[1714, 38477, 38401])).
% 12.59/12.88 tff(38479,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.88 tff(38480,plain,
% 12.59/12.88 (~r(s(s(elem!1)), elem!1)),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[38479, 233, 10682, 1234, 590, 2053, 11, 183, 232, 297, 721, 448])).
% 12.59/12.88 tff(38481,plain,
% 12.59/12.88 (b(s(s(elem!1)), elem!1)),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[872, 38480, 30072])).
% 12.59/12.88 tff(38482,plain,
% 12.59/12.88 (~b(s(s(elem!1)), s(z))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[22561, 38481, 721, 38395])).
% 12.59/12.88 tff(38483,plain,
% 12.59/12.88 (r(s(s(elem!1)), s(z))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[362, 38482])).
% 12.59/12.88 tff(38484,plain,
% 12.59/12.88 (r(s(s(z)), s(z))),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[38483, 18397])).
% 12.59/12.88 tff(38485,plain,
% 12.59/12.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))))),
% 12.59/12.88 inference(rewrite,[status(thm)],[])).
% 12.59/12.88 tff(38486,plain,
% 12.59/12.88 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(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(z), s(s(s(z))))))),
% 12.59/12.88 inference(rewrite,[status(thm)],[])).
% 12.59/12.88 tff(38487,plain,
% 12.59/12.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 12.59/12.88 inference(monotonicity,[status(thm)],[38486])).
% 12.59/12.88 tff(38488,plain,
% 12.59/12.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))))),
% 12.59/12.88 inference(transitivity,[status(thm)],[38487, 38485])).
% 12.59/12.88 tff(38489,plain,
% 12.59/12.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 12.59/12.88 inference(quant_inst,[status(thm)],[])).
% 12.59/12.88 tff(38490,plain,
% 12.59/12.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z)))))),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[38489, 38488])).
% 12.59/12.88 tff(38491,plain,
% 12.59/12.88 (~r(s(s(s(z))), s(s(z)))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[38490, 194, 38484, 23225, 32118])).
% 12.59/12.88 tff(38492,plain,
% 12.59/12.88 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[4385, 38491, 11])).
% 12.59/12.88 tff(38493,plain,
% 12.59/12.88 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[1370, 38492, 297])).
% 12.59/12.88 tff(38494,plain,
% 12.59/12.88 (b(s(s(s(z))), s(s(z)))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[2986, 38493, 11])).
% 12.59/12.88 tff(38495,plain,
% 12.59/12.88 (~r(s(s(s(s(z)))), s(z))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[34886, 38481, 17618, 36090, 23202, 36119])).
% 12.59/12.88 tff(38496,plain,
% 12.59/12.88 (b(s(s(s(s(z)))), s(z))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[749, 38495])).
% 12.59/12.88 tff(38497,plain,
% 12.59/12.88 (~b(z, s(s(s(s(z)))))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[10478, 38496, 1234, 35025])).
% 12.59/12.88 tff(38498,plain,
% 12.59/12.88 (r(z, s(s(s(s(z)))))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[800, 38497])).
% 12.59/12.88 tff(38499,plain,
% 12.59/12.88 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[4450, 194, 2053, 38498, 36117])).
% 12.59/12.88 tff(38500,plain,
% 12.59/12.88 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[32518, 38499, 11])).
% 12.59/12.88 tff(38501,plain,
% 12.59/12.88 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[1095, 38500, 310])).
% 12.59/12.88 tff(38502,plain,
% 12.59/12.88 (b(s(s(s(s(z)))), s(s(s(z))))),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[38501, 23220])).
% 12.59/12.88 tff(38503,plain,
% 12.59/12.88 (~b(z, s(s(elem!1)))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[24044, 38493, 10682, 590, 183, 232, 315])).
% 12.59/12.88 tff(38504,plain,
% 12.59/12.88 (r(z, s(s(elem!1)))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[324, 38503])).
% 12.59/12.88 tff(38505,plain,
% 12.59/12.88 (r(z, s(s(z)))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[30084, 38504, 11])).
% 12.59/12.88 tff(38506,plain,
% 12.59/12.88 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[18433, 38505, 2053, 38484])).
% 12.59/12.88 tff(38507,plain,
% 12.59/12.88 (b(s(s(s(s(z)))), s(s(z)))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[1714, 38506])).
% 12.59/12.88 tff(38508,plain,
% 12.59/12.88 (r(z, s(s(s(s(elem!1)))))),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[38498, 18458])).
% 12.59/12.88 tff(38509,plain,
% 12.59/12.88 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[2800, 38504, 29981, 38508])).
% 12.59/12.88 tff(38510,plain,
% 12.59/12.88 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[1048, 38509, 2419])).
% 12.59/12.88 tff(38511,plain,
% 12.59/12.88 (b(s(s(z)), s(s(s(s(z)))))),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[38510, 35381])).
% 12.59/12.88 tff(38512,plain,
% 12.59/12.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.59/12.88 inference(rewrite,[status(thm)],[])).
% 12.59/12.88 tff(38513,plain,
% 12.59/12.88 (((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.59/12.88 inference(rewrite,[status(thm)],[])).
% 12.59/12.88 tff(38514,plain,
% 12.59/12.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 12.59/12.88 inference(monotonicity,[status(thm)],[38513])).
% 12.59/12.88 tff(38515,plain,
% 12.59/12.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 12.59/12.88 inference(transitivity,[status(thm)],[38514, 38512])).
% 12.59/12.88 tff(38516,plain,
% 12.59/12.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(s(s(z))))))),
% 12.59/12.88 inference(quant_inst,[status(thm)],[])).
% 12.59/12.88 tff(38517,plain,
% 12.59/12.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[38516, 38515])).
% 12.59/12.88 tff(38518,plain,
% 12.59/12.88 ($false),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[38517, 391, 38511, 38496, 38507, 38502, 38494])).
% 12.59/12.88 tff(38519,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.88 tff(38520,plain,
% 12.59/12.88 (~r(s(s(s(elem!1))), elem!1)),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[38519, 232, 2053, 10682, 38394, 183, 11, 15838, 1234, 721, 448])).
% 12.59/12.88 tff(38521,plain,
% 12.59/12.88 (b(s(s(s(elem!1))), elem!1)),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[230, 38520, 127])).
% 12.59/12.88 tff(38522,plain,
% 12.59/12.88 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(s(elem!1)))),
% 12.59/12.88 inference(transitivity,[status(thm)],[30037, 1098])).
% 12.59/12.88 tff(38523,plain,
% 12.59/12.88 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 12.59/12.88 inference(monotonicity,[status(thm)],[38522])).
% 12.59/12.88 tff(38524,plain,
% 12.59/12.88 (~(s(elem!1) = s(s(elem!1)))),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[357, 38523])).
% 12.59/12.88 tff(38525,plain,
% 12.59/12.88 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 12.59/12.88 inference(monotonicity,[status(thm)],[488])).
% 12.59/12.88 tff(38526,plain,
% 12.59/12.88 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 12.59/12.88 inference(symmetry,[status(thm)],[38525])).
% 12.59/12.88 tff(38527,plain,
% 12.59/12.88 (r(s(elem!1), s(s(s(elem!1))))),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[232, 38526])).
% 12.59/12.88 tff(38528,plain,
% 12.59/12.88 (b(s(elem!1), elem!1)),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[38394, 35791])).
% 12.59/12.88 tff(38529,plain,
% 12.59/12.88 (~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[32362, 17618])).
% 12.59/12.88 tff(38530,plain,
% 12.59/12.88 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 12.59/12.88 inference(monotonicity,[status(thm)],[488])).
% 12.59/12.88 tff(38531,plain,
% 12.59/12.88 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 12.59/12.88 inference(symmetry,[status(thm)],[38530])).
% 12.59/12.88 tff(38532,plain,
% 12.59/12.88 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 12.59/12.88 inference(monotonicity,[status(thm)],[38531])).
% 12.59/12.88 tff(38533,plain,
% 12.59/12.88 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 12.59/12.88 inference(modus_ponens,[status(thm)],[5065, 38532])).
% 12.59/12.88 tff(38534,plain,
% 12.59/12.88 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 12.59/12.88 inference(unit_resolution,[status(thm)],[28695, 38521, 448, 38533, 38529, 38528, 38527, 23202])).
% 12.59/12.88 tff(38535,plain,
% 12.59/12.88 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[8073, 38534, 33785])).
% 12.59/12.89 tff(38536,plain,
% 12.59/12.89 (r(z, s(s(z)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[30084, 326, 11])).
% 12.59/12.89 tff(38537,plain,
% 12.59/12.89 (r(elem!1, s(s(elem!1)))),
% 12.59/12.89 inference(modus_ponens,[status(thm)],[38536, 29971])).
% 12.59/12.89 tff(38538,plain,
% 12.59/12.89 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[32487, 38537, 2741, 364])).
% 12.59/12.89 tff(38539,plain,
% 12.59/12.89 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[32502, 38538, 17618])).
% 12.59/12.89 tff(38540,plain,
% 12.59/12.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 12.59/12.89 inference(rewrite,[status(thm)],[])).
% 12.59/12.89 tff(38541,plain,
% 12.59/12.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 12.59/12.89 inference(quant_inst,[status(thm)],[])).
% 12.59/12.89 tff(38542,plain,
% 12.59/12.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 12.59/12.89 inference(modus_ponens,[status(thm)],[38541, 38540])).
% 12.59/12.89 tff(38543,plain,
% 12.59/12.89 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[38542, 194, 2053, 38536, 33802])).
% 12.59/12.89 tff(38544,plain,
% 12.59/12.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[11685, 42, 38543, 33868])).
% 12.59/12.89 tff(38545,plain,
% 12.59/12.89 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[9284, 326, 2053, 38402])).
% 12.59/12.89 tff(38546,plain,
% 12.59/12.89 (~r(s(s(s(s(z)))), s(s(z)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[32448, 38545, 11])).
% 12.59/12.89 tff(38547,plain,
% 12.59/12.89 (b(s(s(s(s(z)))), s(s(z)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1714, 38546])).
% 12.59/12.89 tff(38548,plain,
% 12.59/12.89 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[16255, 194, 2053, 33803, 38536])).
% 12.59/12.89 tff(38549,plain,
% 12.59/12.89 (b(s(s(z)), s(s(s(s(z)))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[3652, 38548])).
% 12.59/12.89 tff(38550,plain,
% 12.59/12.89 ($false),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[11113, 391, 38549, 38547, 38544, 38539])).
% 12.59/12.89 tff(38551,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.89 tff(38552,plain,
% 12.59/12.89 (~r(z, s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[38551, 364, 2741, 2053, 11])).
% 12.59/12.89 tff(38553,plain,
% 12.59/12.89 (b(z, s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[324, 38552])).
% 12.59/12.89 tff(38554,plain,
% 12.59/12.89 (b(elem!1, s(s(elem!1)))),
% 12.59/12.89 inference(modus_ponens,[status(thm)],[38553, 30009])).
% 12.59/12.89 tff(38555,plain,
% 12.59/12.89 (~b(s(s(elem!1)), s(z))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1302, 38554, 721, 38395])).
% 12.59/12.89 tff(38556,plain,
% 12.59/12.89 (r(s(s(elem!1)), s(z))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[362, 38555])).
% 12.59/12.89 tff(38557,plain,
% 12.59/12.89 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 12.59/12.89 inference(monotonicity,[status(thm)],[488])).
% 12.59/12.89 tff(38558,plain,
% 12.59/12.89 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 12.59/12.89 inference(symmetry,[status(thm)],[38557])).
% 12.59/12.89 tff(38559,plain,
% 12.59/12.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[24044, 38553, 10682, 590, 183, 232, 315])).
% 12.59/12.89 tff(38560,plain,
% 12.59/12.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1370, 38559, 297])).
% 12.59/12.89 tff(38561,plain,
% 12.59/12.89 (~r(s(z), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[4840, 38560, 232, 38402])).
% 12.59/12.89 tff(38562,plain,
% 12.59/12.89 (~r(s(z), s(s(z)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[23186, 38561, 11])).
% 12.59/12.89 tff(38563,plain,
% 12.59/12.89 (b(s(z), s(s(z)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1788, 38562])).
% 12.59/12.89 tff(38564,plain,
% 12.59/12.89 (b(s(z), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[30324, 38563, 11])).
% 12.59/12.89 tff(38565,plain,
% 12.59/12.89 (b(s(elem!1), s(s(elem!1)))),
% 12.59/12.89 inference(modus_ponens,[status(thm)],[38564, 38558])).
% 12.59/12.89 tff(38566,plain,
% 12.59/12.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 12.59/12.89 inference(rewrite,[status(thm)],[])).
% 12.59/12.89 tff(38567,plain,
% 12.59/12.89 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 12.59/12.89 inference(rewrite,[status(thm)],[])).
% 12.59/12.89 tff(38568,plain,
% 12.59/12.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))))),
% 12.59/12.89 inference(monotonicity,[status(thm)],[38567])).
% 12.59/12.89 tff(38569,plain,
% 12.59/12.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 12.59/12.89 inference(transitivity,[status(thm)],[38568, 38566])).
% 12.59/12.89 tff(38570,plain,
% 12.59/12.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 12.59/12.89 inference(quant_inst,[status(thm)],[])).
% 12.59/12.89 tff(38571,plain,
% 12.59/12.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 12.59/12.89 inference(modus_ponens,[status(thm)],[38570, 38569])).
% 12.59/12.89 tff(38572,plain,
% 12.59/12.89 ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[38571, 391])).
% 12.59/12.89 tff(38573,plain,
% 12.59/12.89 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[38572, 38565, 900, 38554, 36119])).
% 12.59/12.89 tff(38574,plain,
% 12.59/12.89 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1356, 38573, 315])).
% 12.59/12.89 tff(38575,plain,
% 12.59/12.89 ($false),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[2201, 38574, 38556, 183, 232])).
% 12.59/12.89 tff(38576,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.89 tff(38577,plain,
% 12.59/12.89 (~r(s(s(elem!1)), elem!1)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[38576, 232, 183, 38521, 721, 11, 15838, 10682, 38394, 38535, 2053])).
% 12.59/12.89 tff(38578,plain,
% 12.59/12.89 (b(s(s(elem!1)), elem!1)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[872, 38577, 30072])).
% 12.59/12.89 tff(38579,plain,
% 12.59/12.89 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[8697, 38578, 448, 38528, 38527, 38524, 30039, 38521])).
% 12.59/12.89 tff(38580,plain,
% 12.59/12.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[34598, 38578, 721, 1234, 38521])).
% 12.59/12.89 tff(38581,plain,
% 12.59/12.89 ($false),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1370, 38580, 38579, 15838])).
% 12.59/12.89 tff(38582,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~(elem!1 = z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.59/12.89 tff(38583,plain,
% 12.59/12.89 (~r(s(z), s(s(s(elem!1))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[38582, 183, 11, 23191, 38195, 38364, 10682, 2053, 127])).
% 12.59/12.89 tff(38584,plain,
% 12.59/12.89 (b(s(z), s(s(s(elem!1))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[247, 38583])).
% 12.59/12.89 tff(38585,plain,
% 12.59/12.89 (b(s(z), z)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[38393, 183, 11, 10682, 23191, 127, 38195, 38364, 2053])).
% 12.59/12.89 tff(38586,plain,
% 12.59/12.89 (~b(s(s(s(elem!1))), z)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[11303, 38584, 10682, 38585])).
% 12.59/12.89 tff(38587,plain,
% 12.59/12.89 (r(s(s(s(elem!1))), z)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[377, 38586])).
% 12.59/12.89 tff(38588,plain,
% 12.59/12.89 (~(s(z) = elem!1)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[20271, 38364])).
% 12.59/12.89 tff(38589,plain,
% 12.59/12.89 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[2849, 38588])).
% 12.59/12.89 tff(38590,plain,
% 12.59/12.89 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[10940, 38589])).
% 12.59/12.89 tff(38591,plain,
% 12.59/12.89 (~r(z, s(s(s(s(z)))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[38313, 38584, 11, 38590, 2053, 10682, 32512, 38585])).
% 12.59/12.89 tff(38592,plain,
% 12.59/12.89 (b(z, s(s(s(s(z)))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[800, 38591])).
% 12.59/12.89 tff(38593,plain,
% 12.59/12.89 (~b(s(s(s(s(z)))), s(z))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[17292, 38592, 38195, 38585])).
% 12.59/12.89 tff(38594,plain,
% 12.59/12.89 (r(s(s(s(s(z)))), s(z))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[749, 38593])).
% 12.59/12.89 tff(38595,plain,
% 12.59/12.89 (b(s(z), elem!1)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[36590, 38594, 17618, 36115, 29981, 38195, 38364, 38588])).
% 12.59/12.89 tff(38596,plain,
% 12.59/12.89 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[17288, 1235, 1234, 590, 1686])).
% 12.59/12.89 tff(38597,plain,
% 12.59/12.89 (r(s(s(s(s(z)))), s(s(z)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1714, 38596])).
% 12.59/12.89 tff(38598,plain,
% 12.59/12.89 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[32448, 38597, 11])).
% 12.59/12.89 tff(38599,plain,
% 12.59/12.89 (~b(s(s(s(s(z)))), s(z))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[17292, 1686, 1234, 590])).
% 12.59/12.89 tff(38600,plain,
% 12.59/12.89 (r(s(s(s(s(z)))), s(z))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[749, 38599])).
% 12.59/12.89 tff(38601,plain,
% 12.59/12.89 (r(s(s(s(elem!1))), z)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[377, 36895])).
% 12.59/12.89 tff(38602,plain,
% 12.59/12.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[30751, 35318, 10682, 379, 590])).
% 12.59/12.89 tff(38603,plain,
% 12.59/12.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1370, 38602, 297])).
% 12.59/12.89 tff(38604,plain,
% 12.59/12.89 (~b(s(s(elem!1)), s(z))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[22561, 35318, 721, 644])).
% 12.59/12.89 tff(38605,plain,
% 12.59/12.89 (r(s(s(elem!1)), s(z))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[362, 38604])).
% 12.59/12.89 tff(38606,plain,
% 12.59/12.89 (~r(z, s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[7327, 340, 327, 174])).
% 12.59/12.89 tff(38607,plain,
% 12.59/12.89 (b(z, s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[324, 38606])).
% 12.59/12.89 tff(38608,plain,
% 12.59/12.89 (b(z, s(s(z)))),
% 12.59/12.89 inference(modus_ponens,[status(thm)],[38607, 3367])).
% 12.59/12.89 tff(38609,plain,
% 12.59/12.89 (~r(s(z), s(s(z)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[6245, 340, 723, 6240])).
% 12.59/12.89 tff(38610,plain,
% 12.59/12.89 (b(s(z), s(s(z)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1788, 38609])).
% 12.59/12.89 tff(38611,plain,
% 12.59/12.89 ($false),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[17089, 391, 1235, 38610, 590, 38608])).
% 12.59/12.89 tff(38612,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~(elem!1 = z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.89 tff(38613,plain,
% 12.59/12.89 ($false),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[38612, 38605, 38603, 590, 11, 1235, 38601, 38600, 38598])).
% 12.59/12.89 tff(38614,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 12.59/12.89 tff(38615,plain,
% 12.59/12.89 (~b(s(s(z)), z)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[38614, 38595, 11, 15838, 38364, 38585, 10682, 38584, 38195, 38592])).
% 12.59/12.89 tff(38616,plain,
% 12.59/12.89 (r(s(s(z)), z)),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1211, 38615])).
% 12.59/12.89 tff(38617,plain,
% 12.59/12.89 (r(s(s(elem!1)), elem!1)),
% 12.59/12.89 inference(modus_ponens,[status(thm)],[38616, 30367])).
% 12.59/12.89 tff(38618,plain,
% 12.59/12.89 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[32476, 38617, 17618, 29981, 38595, 38364, 23191, 38587, 23202])).
% 12.59/12.89 tff(38619,plain,
% 12.59/12.89 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[1370, 38618, 15838])).
% 12.59/12.89 tff(38620,plain,
% 12.59/12.89 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 12.59/12.89 inference(unit_resolution,[status(thm)],[22188, 38619, 23191, 38364, 38584])).
% 12.59/12.90 tff(38621,plain,
% 12.59/12.90 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.59/12.90 inference(unit_resolution,[status(thm)],[1356, 38620, 21729])).
% 12.59/12.90 tff(38622,plain,
% 12.59/12.90 (b(s(elem!1), s(s(s(elem!1))))),
% 12.59/12.90 inference(modus_ponens,[status(thm)],[38584, 38365])).
% 12.59/12.90 tff(38623,plain,
% 12.59/12.90 (b(s(elem!1), elem!1)),
% 12.59/12.90 inference(modus_ponens,[status(thm)],[38585, 35791])).
% 12.59/12.90 tff(38624,plain,
% 12.59/12.90 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.59/12.90 inference(unit_resolution,[status(thm)],[19444, 38619, 23191, 38623, 38622])).
% 12.59/12.90 tff(38625,plain,
% 12.59/12.90 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 12.59/12.90 inference(unit_resolution,[status(thm)],[1048, 38624, 2419])).
% 12.59/12.90 tff(38626,plain,
% 12.59/12.90 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.59/12.90 inference(unit_resolution,[status(thm)],[14542, 38625, 29981, 38621])).
% 12.59/12.90 tff(38627,plain,
% 12.59/12.90 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 12.59/12.90 inference(unit_resolution,[status(thm)],[1164, 38626, 34126])).
% 12.59/12.90 tff(38628,plain,
% 12.59/12.90 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.59/12.90 inference(modus_ponens,[status(thm)],[38627, 38363])).
% 12.59/12.90 tff(38629,plain,
% 12.59/12.90 (r(s(s(s(elem!1))), elem!1)),
% 12.59/12.90 inference(unit_resolution,[status(thm)],[9853, 38587, 17618])).
% 12.59/12.90 tff(38630,plain,
% 12.59/12.90 (r(s(s(elem!1)), z)),
% 12.59/12.90 inference(modus_ponens,[status(thm)],[38616, 23180])).
% 12.59/12.90 tff(38631,plain,
% 12.59/12.90 (b(z, s(z))),
% 12.59/12.90 inference(modus_ponens,[status(thm)],[38364, 29])).
% 12.59/12.90 tff(38632,plain,
% 12.59/12.90 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.59/12.90 inference(unit_resolution,[status(thm)],[38476, 38619, 17618, 10682, 38195, 38631, 38585, 38630, 38629, 38623, 29981])).
% 12.59/12.90 tff(38633,plain,
% 12.59/12.90 (r(s(s(s(s(z)))), s(s(z)))),
% 12.59/12.90 inference(unit_resolution,[status(thm)],[1714, 38632])).
% 12.59/12.90 tff(38634,plain,
% 12.59/12.90 (~r(s(z), s(s(z)))),
% 12.59/12.90 inference(unit_resolution,[status(thm)],[33077, 38633, 38594, 38616])).
% 12.59/12.90 tff(38635,plain,
% 12.59/12.90 (b(s(z), s(s(z)))),
% 12.59/12.90 inference(unit_resolution,[status(thm)],[1788, 38634])).
% 12.59/12.90 tff(38636,plain,
% 12.59/12.90 (b(s(s(s(elem!1))), s(s(z)))),
% 12.59/12.90 inference(modus_ponens,[status(thm)],[38619, 33708])).
% 12.59/12.90 tff(38637,plain,
% 12.59/12.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 12.69/12.90 inference(rewrite,[status(thm)],[])).
% 12.69/12.90 tff(38638,plain,
% 12.69/12.90 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 12.69/12.90 inference(rewrite,[status(thm)],[])).
% 12.69/12.90 tff(38639,plain,
% 12.69/12.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 12.69/12.90 inference(monotonicity,[status(thm)],[38638])).
% 12.69/12.90 tff(38640,plain,
% 12.69/12.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 12.69/12.90 inference(transitivity,[status(thm)],[38639, 38637])).
% 12.69/12.90 tff(38641,plain,
% 12.69/12.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 12.69/12.90 inference(quant_inst,[status(thm)],[])).
% 12.69/12.90 tff(38642,plain,
% 12.69/12.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 12.69/12.90 inference(modus_ponens,[status(thm)],[38641, 38640])).
% 12.69/12.90 tff(38643,plain,
% 12.69/12.90 ($false),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[38642, 391, 379, 2439, 1669, 8553, 17493])).
% 12.69/12.90 tff(38644,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.69/12.90 tff(38645,plain,
% 12.69/12.90 (~b(s(s(z)), s(s(s(elem!1))))),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[38644, 38636, 38584, 38635, 38628])).
% 12.69/12.90 tff(38646,plain,
% 12.69/12.90 (r(s(s(z)), s(s(s(elem!1))))),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[11041, 38645])).
% 12.69/12.90 tff(38647,plain,
% 12.69/12.90 (r(s(s(z)), s(s(s(z))))),
% 12.69/12.90 inference(modus_ponens,[status(thm)],[38646, 38360])).
% 12.69/12.90 tff(38648,plain,
% 12.69/12.90 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[31008, 38627, 10682, 38631, 38584])).
% 12.69/12.90 tff(38649,plain,
% 12.69/12.90 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[1095, 38648, 32512])).
% 12.69/12.90 tff(38650,plain,
% 12.69/12.90 (r(s(s(s(s(z)))), s(s(s(z))))),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[32518, 38649, 11])).
% 12.69/12.90 tff(38651,plain,
% 12.69/12.90 (r(s(s(s(z))), z)),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[4409, 38587, 11])).
% 12.69/12.90 tff(38652,plain,
% 12.69/12.90 (r(s(s(z)), s(s(s(s(z)))))),
% 12.69/12.90 inference(modus_ponens,[status(thm)],[38625, 2402])).
% 12.69/12.90 tff(38653,plain,
% 12.69/12.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 12.69/12.90 inference(rewrite,[status(thm)],[])).
% 12.69/12.90 tff(38654,plain,
% 12.69/12.90 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 12.69/12.90 inference(rewrite,[status(thm)],[])).
% 12.69/12.90 tff(38655,plain,
% 12.69/12.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 12.69/12.90 inference(monotonicity,[status(thm)],[38654])).
% 12.69/12.90 tff(38656,plain,
% 12.69/12.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 12.69/12.90 inference(transitivity,[status(thm)],[38655, 38653])).
% 12.69/12.90 tff(38657,plain,
% 12.69/12.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 12.69/12.90 inference(quant_inst,[status(thm)],[])).
% 12.69/12.90 tff(38658,plain,
% 12.69/12.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 12.69/12.90 inference(modus_ponens,[status(thm)],[38657, 38656])).
% 12.69/12.90 tff(38659,plain,
% 12.69/12.90 ($false),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[38658, 194, 1749, 4428, 33697, 15704])).
% 12.69/12.90 tff(38660,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 12.69/12.90 tff(38661,plain,
% 12.69/12.90 (~r(s(s(z)), s(s(s(z))))),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[38660, 38652, 38651, 38650])).
% 12.69/12.90 tff(38662,plain,
% 12.69/12.90 ($false),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[38661, 38647])).
% 12.69/12.90 tff(38663,plain,((~r(s(s(s(elem!1))), s(z))) | (~(elem!1 = z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.69/12.90 tff(38664,plain,
% 12.69/12.90 (~r(s(s(s(elem!1))), s(z))),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[38663, 38098, 37859, 38352, 9])).
% 12.69/12.90 tff(38665,plain,
% 12.69/12.90 (b(s(s(s(elem!1))), s(z))),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[223, 38664])).
% 12.69/12.90 tff(38666,plain,
% 12.69/12.90 (~b(s(z), z)),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[10690, 38665, 37859, 38359])).
% 12.69/12.90 tff(38667,plain,
% 12.69/12.90 (~b(s(z), elem!1)),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[3200, 38666, 38098])).
% 12.69/12.90 tff(38668,plain,
% 12.69/12.90 (~r(s(s(s(s(z)))), s(z))),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[36590, 38667, 38357, 38356, 38353, 38342, 38340, 38341])).
% 12.69/12.90 tff(38669,plain,
% 12.69/12.90 (b(s(s(s(s(z)))), s(z))),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[749, 38668])).
% 12.69/12.90 tff(38670,plain,
% 12.69/12.90 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 12.69/12.90 inference(modus_ponens,[status(thm)],[38669, 38107])).
% 12.69/12.90 tff(38671,plain,
% 12.69/12.90 (r(s(z), elem!1)),
% 12.69/12.90 inference(unit_resolution,[status(thm)],[3205, 38666, 38098])).
% 12.69/12.90 tff(38672,plain,
% 12.69/12.90 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 12.69/12.90 inference(monotonicity,[status(thm)],[38098])).
% 12.69/12.90 tff(38673,plain,
% 12.69/12.90 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 12.69/12.90 inference(symmetry,[status(thm)],[38672])).
% 12.69/12.90 tff(38674,plain,
% 12.69/12.90 (b(z, s(elem!1)) <=> b(z, s(z))),
% 12.69/12.90 inference(monotonicity,[status(thm)],[38099])).
% 12.69/12.90 tff(38675,plain,
% 12.69/12.90 (b(z, s(z)) <=> b(z, s(elem!1))),
% 12.69/12.90 inference(symmetry,[status(thm)],[38674])).
% 12.69/12.90 tff(38676,plain,
% 12.69/12.90 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 12.69/12.90 inference(transitivity,[status(thm)],[38675, 38673])).
% 12.69/12.90 tff(38677,plain,
% 12.69/12.90 (b(elem!1, s(elem!1))),
% 12.69/12.90 inference(modus_ponens,[status(thm)],[38359, 38676])).
% 12.69/12.90 tff(38678,plain,
% 12.69/12.90 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 12.69/12.90 inference(monotonicity,[status(thm)],[38099, 38104])).
% 12.69/12.90 tff(38679,plain,
% 12.69/12.90 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 12.69/12.90 inference(symmetry,[status(thm)],[38678])).
% 12.69/12.91 tff(38680,plain,
% 12.69/12.91 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 12.69/12.91 inference(modus_ponens,[status(thm)],[38342, 38679])).
% 12.69/12.91 tff(38681,plain,
% 12.69/12.91 (~b(z, s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[10478, 38669, 38342, 38359])).
% 12.69/12.91 tff(38682,plain,
% 12.69/12.91 (r(z, s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[800, 38681])).
% 12.69/12.91 tff(38683,plain,
% 12.69/12.91 (r(elem!1, s(s(s(s(elem!1)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[23210, 38682, 38098])).
% 12.69/12.91 tff(38684,plain,
% 12.69/12.91 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[34627, 38683, 38357, 38680, 38677, 38665, 38671, 38359, 37859])).
% 12.69/12.91 tff(38685,plain,
% 12.69/12.91 ($false),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[38684, 38670])).
% 12.69/12.91 tff(38686,plain,(elem!1 = s(s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 12.69/12.91 tff(38687,plain,
% 12.69/12.91 ((s(z) = elem!1) <=> (s(z) = s(s(s(elem!1))))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38686])).
% 12.69/12.91 tff(38688,plain,
% 12.69/12.91 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 12.69/12.91 inference(symmetry,[status(thm)],[38687])).
% 12.69/12.91 tff(38689,plain,
% 12.69/12.91 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38688])).
% 12.69/12.91 tff(38690,plain,
% 12.69/12.91 (~(s(z) = elem!1)),
% 12.69/12.91 inference(modus_ponens,[status(thm)],[217, 38689])).
% 12.69/12.91 tff(38691,plain,
% 12.69/12.91 (s(s(s(elem!1))) = elem!1),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[129, 38686])).
% 12.69/12.91 tff(38692,plain,
% 12.69/12.91 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38686])).
% 12.69/12.91 tff(38693,plain,
% 12.69/12.91 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.69/12.91 inference(transitivity,[status(thm)],[38692, 3928])).
% 12.69/12.91 tff(38694,plain,
% 12.69/12.91 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38693])).
% 12.69/12.91 tff(38695,plain,
% 12.69/12.91 (~(s(s(s(s(z)))) = elem!1)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[1436, 38691])).
% 12.69/12.91 tff(38696,plain,
% 12.69/12.91 (~(elem!1 = s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[769, 38695])).
% 12.69/12.91 tff(38697,plain,
% 12.69/12.91 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.69/12.91 inference(modus_ponens,[status(thm)],[38696, 38694])).
% 12.69/12.91 tff(38698,plain,
% 12.69/12.91 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38686])).
% 12.69/12.91 tff(38699,plain,
% 12.69/12.91 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 12.69/12.91 inference(transitivity,[status(thm)],[38698, 3042])).
% 12.69/12.91 tff(38700,plain,
% 12.69/12.91 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 12.69/12.91 inference(symmetry,[status(thm)],[38699])).
% 12.69/12.91 tff(38701,plain,
% 12.69/12.91 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 12.69/12.91 inference(transitivity,[status(thm)],[38700, 93])).
% 12.69/12.91 tff(38702,plain,
% 12.69/12.91 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = z))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38701])).
% 12.69/12.91 tff(38703,plain,
% 12.69/12.91 (~(elem!1 = z)),
% 12.69/12.91 inference(modus_ponens,[status(thm)],[50, 38702])).
% 12.69/12.91 tff(38704,plain,
% 12.69/12.91 (r(s(s(s(s(z)))), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[29425, 38703])).
% 12.69/12.91 tff(38705,plain,
% 12.69/12.91 (s(s(s(elem!1))) = elem!1),
% 12.69/12.91 inference(symmetry,[status(thm)],[38686])).
% 12.69/12.91 tff(38706,plain,
% 12.69/12.91 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38705])).
% 12.69/12.91 tff(38707,plain,
% 12.69/12.91 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 12.69/12.91 inference(transitivity,[status(thm)],[38706, 698])).
% 12.69/12.91 tff(38708,plain,
% 12.69/12.91 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38707])).
% 12.69/12.91 tff(38709,plain,
% 12.69/12.91 (~(elem!1 = s(s(z)))),
% 12.69/12.91 inference(modus_ponens,[status(thm)],[1397, 38708])).
% 12.69/12.91 tff(38710,plain,
% 12.69/12.91 (r(z, elem!1)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[33626, 38703])).
% 12.69/12.91 tff(38711,plain,
% 12.69/12.91 (r(z, s(s(s(elem!1))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[10792, 38710, 38691])).
% 12.69/12.91 tff(38712,plain,
% 12.69/12.91 (~b(s(s(s(s(z)))), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[22897, 10, 38703])).
% 12.69/12.91 tff(38713,plain,
% 12.69/12.91 (b(elem!1, s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[20262, 10, 38703])).
% 12.69/12.91 tff(38714,plain,
% 12.69/12.91 (b(s(z), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[36668, 10, 38703, 38713])).
% 12.69/12.91 tff(38715,plain,
% 12.69/12.91 (b(s(z), s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[37469, 10, 38703])).
% 12.69/12.91 tff(38716,plain,
% 12.69/12.91 (b(s(z), elem!1)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[37742, 38712, 10, 38703])).
% 12.69/12.91 tff(38717,plain,
% 12.69/12.91 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38700])).
% 12.69/12.91 tff(38718,plain,
% 12.69/12.91 (~(z = elem!1)),
% 12.69/12.91 inference(modus_ponens,[status(thm)],[50, 38717])).
% 12.69/12.91 tff(38719,plain,
% 12.69/12.91 (~(s(z) = s(elem!1))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[117, 38718])).
% 12.69/12.91 tff(38720,plain,
% 12.69/12.91 (~r(elem!1, z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[37440, 10, 38691, 38704, 38710, 38719, 38713])).
% 12.69/12.91 tff(38721,plain,
% 12.69/12.91 (b(elem!1, z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[526, 38720, 38703])).
% 12.69/12.91 tff(38722,plain,
% 12.69/12.91 (r(s(s(s(s(z)))), elem!1)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[17542, 38721, 38710, 38716, 38715, 38714, 38712])).
% 12.69/12.91 tff(38723,plain,
% 12.69/12.91 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[2116, 38722, 38691])).
% 12.69/12.91 tff(38724,plain,
% 12.69/12.91 (~r(s(s(s(elem!1))), s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[30022, 38723, 38711, 38704])).
% 12.69/12.91 tff(38725,plain,
% 12.69/12.91 (~r(elem!1, s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[10022, 38724, 38686])).
% 12.69/12.91 tff(38726,plain,
% 12.69/12.91 (b(elem!1, s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[3394, 38725, 38709])).
% 12.69/12.91 tff(38727,plain,
% 12.69/12.91 (b(s(s(s(elem!1))), s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[16425, 38726, 38686])).
% 12.69/12.91 tff(38728,plain,
% 12.69/12.91 (~b(s(s(s(s(z)))), s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[36644, 38713, 38686, 38704, 38715, 38716, 38711, 38710])).
% 12.69/12.91 tff(38729,plain,
% 12.69/12.91 (r(s(s(s(s(z)))), s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[749, 38728])).
% 12.69/12.91 tff(38730,plain,
% 12.69/12.91 (~r(s(s(s(elem!1))), s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[37739, 38712, 10, 38703])).
% 12.69/12.91 tff(38731,plain,
% 12.69/12.91 (b(s(s(s(elem!1))), s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[223, 38730])).
% 12.69/12.91 tff(38732,plain,
% 12.69/12.91 (b(s(z), s(s(s(elem!1))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[14872, 38716, 38691])).
% 12.69/12.91 tff(38733,plain,
% 12.69/12.91 (~r(s(s(s(elem!1))), s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[30022, 2100, 2053, 184])).
% 12.69/12.91 tff(38734,plain,
% 12.69/12.91 (~r(elem!1, s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[10022, 38733, 125])).
% 12.69/12.91 tff(38735,plain,
% 12.69/12.91 (b(elem!1, s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[3394, 38734, 3820])).
% 12.69/12.91 tff(38736,plain,
% 12.69/12.91 (b(s(s(s(elem!1))), s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[16425, 38735, 125])).
% 12.69/12.91 tff(38737,plain,
% 12.69/12.91 (~r(s(s(s(elem!1))), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[15335, 2100, 2053, 184])).
% 12.69/12.91 tff(38738,plain,
% 12.69/12.91 (b(s(s(s(elem!1))), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[377, 38737])).
% 12.69/12.91 tff(38739,plain,
% 12.69/12.91 (~b(s(s(z)), s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[21394, 38738, 379, 1526, 38736])).
% 12.69/12.91 tff(38740,plain,
% 12.69/12.91 (r(s(s(z)), s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[3778, 38739])).
% 12.69/12.91 tff(38741,plain,
% 12.69/12.91 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[26388])).
% 12.69/12.91 tff(38742,plain,
% 12.69/12.91 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[16851, 2100, 2053, 184])).
% 12.69/12.91 tff(38743,plain,
% 12.69/12.91 (~r(elem!1, s(s(s(s(z)))))),
% 12.69/12.91 inference(modus_ponens,[status(thm)],[38742, 38741])).
% 12.69/12.91 tff(38744,plain,
% 12.69/12.91 (b(elem!1, s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[781, 38743, 3810])).
% 12.69/12.91 tff(38745,plain,
% 12.69/12.91 (~r(s(s(z)), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[14773, 38744, 38735, 2053, 184])).
% 12.69/12.91 tff(38746,plain,
% 12.69/12.91 (b(s(s(z)), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[1211, 38745])).
% 12.69/12.91 tff(38747,plain,
% 12.69/12.91 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[17288, 38746, 1234, 1686, 590])).
% 12.69/12.91 tff(38748,plain,
% 12.69/12.91 (r(s(s(s(s(z)))), s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[1714, 38747])).
% 12.69/12.91 tff(38749,plain,
% 12.69/12.91 (~b(s(z), s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[17501, 38746, 379, 1686, 38736])).
% 12.69/12.91 tff(38750,plain,
% 12.69/12.91 (r(s(z), s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[1788, 38749])).
% 12.69/12.91 tff(38751,plain,
% 12.69/12.91 ($false),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[10673, 38750, 38748, 723, 38740])).
% 12.69/12.91 tff(38752,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 12.69/12.91 tff(38753,plain,
% 12.69/12.91 (~b(z, s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[38752, 38723, 38686, 38704, 38715, 38711, 38714, 38732, 38731, 38729])).
% 12.69/12.91 tff(38754,plain,
% 12.69/12.91 (r(z, s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[800, 38753])).
% 12.69/12.91 tff(38755,plain,
% 12.69/12.91 (b(s(s(s(elem!1))), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[9553, 38721, 38686])).
% 12.69/12.91 tff(38756,plain,
% 12.69/12.91 (~r(s(s(z)), s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[19720, 38727, 38711, 38704, 38755, 38754])).
% 12.69/12.91 tff(38757,plain,
% 12.69/12.91 (b(s(s(z)), s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[3652, 38756])).
% 12.69/12.91 tff(38758,plain,
% 12.69/12.91 (~b(z, s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[21922, 38721, 38714, 38713])).
% 12.69/12.91 tff(38759,plain,
% 12.69/12.91 (r(z, s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[678, 38758])).
% 12.69/12.91 tff(38760,plain,
% 12.69/12.91 (~b(s(s(z)), s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[21394, 38727, 38755, 38732, 38731])).
% 12.69/12.91 tff(38761,plain,
% 12.69/12.91 (r(s(s(z)), s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[3778, 38760])).
% 12.69/12.91 tff(38762,plain,
% 12.69/12.91 (~r(z, s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[29795, 38761, 38704, 38759, 38757])).
% 12.69/12.91 tff(38763,plain,
% 12.69/12.91 (b(z, s(s(z)))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[18613, 38762])).
% 12.69/12.91 tff(38764,plain,
% 12.69/12.91 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[16851, 38723, 38711, 38704])).
% 12.69/12.91 tff(38765,plain,
% 12.69/12.91 (~r(elem!1, s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[14788, 38764, 38686])).
% 12.69/12.91 tff(38766,plain,
% 12.69/12.91 (b(elem!1, s(s(s(s(z)))))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[781, 38765, 38696])).
% 12.69/12.91 tff(38767,plain,
% 12.69/12.91 (~r(s(s(z)), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[14773, 38726, 38711, 38704, 38766])).
% 12.69/12.91 tff(38768,plain,
% 12.69/12.91 (b(s(s(z)), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[1211, 38767])).
% 12.69/12.91 tff(38769,plain,
% 12.69/12.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 12.69/12.91 inference(rewrite,[status(thm)],[])).
% 12.69/12.91 tff(38770,plain,
% 12.69/12.91 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 12.69/12.91 inference(rewrite,[status(thm)],[])).
% 12.69/12.91 tff(38771,plain,
% 12.69/12.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38770])).
% 12.69/12.91 tff(38772,plain,
% 12.69/12.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 12.69/12.91 inference(transitivity,[status(thm)],[38771, 38769])).
% 12.69/12.91 tff(38773,plain,
% 12.69/12.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 12.69/12.91 inference(quant_inst,[status(thm)],[])).
% 12.69/12.91 tff(38774,plain,
% 12.69/12.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 12.69/12.91 inference(modus_ponens,[status(thm)],[38773, 38772])).
% 12.69/12.91 tff(38775,plain,
% 12.69/12.91 ($false),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[38774, 391, 38755, 38757, 38768, 38763, 38727])).
% 12.69/12.91 tff(38776,plain,(b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 12.69/12.91 tff(38777,plain,
% 12.69/12.91 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 12.69/12.91 inference(transitivity,[status(thm)],[38688, 1270])).
% 12.69/12.91 tff(38778,plain,
% 12.69/12.91 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38777])).
% 12.69/12.91 tff(38779,plain,
% 12.69/12.91 (~(elem!1 = s(z))),
% 12.69/12.91 inference(modus_ponens,[status(thm)],[217, 38778])).
% 12.69/12.91 tff(38780,plain,
% 12.69/12.91 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38686])).
% 12.69/12.91 tff(38781,plain,
% 12.69/12.91 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), elem!1)),
% 12.69/12.91 inference(symmetry,[status(thm)],[38780])).
% 12.69/12.91 tff(38782,plain,
% 12.69/12.91 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 12.69/12.91 inference(monotonicity,[status(thm)],[38781])).
% 12.69/12.91 tff(38783,plain,
% 12.69/12.91 (~b(s(s(s(elem!1))), elem!1)),
% 12.69/12.91 inference(modus_ponens,[status(thm)],[463, 38782])).
% 12.69/12.91 tff(38784,plain,
% 12.69/12.91 (b(z, elem!1)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[22900, 38776, 38686])).
% 12.69/12.91 tff(38785,plain,
% 12.69/12.91 (~r(s(s(s(elem!1))), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[3969, 182, 38711, 38704, 38697])).
% 12.69/12.91 tff(38786,plain,
% 12.69/12.91 (~r(elem!1, z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[533, 38785, 38691])).
% 12.69/12.91 tff(38787,plain,
% 12.69/12.91 (b(s(elem!1), elem!1)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[14657, 38786, 38783, 38776, 38690, 38784, 38703])).
% 12.69/12.91 tff(38788,plain,
% 12.69/12.91 (~(s(s(s(elem!1))) = s(elem!1))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[14662, 38787, 38783])).
% 12.69/12.91 tff(38789,plain,
% 12.69/12.91 (b(elem!1, z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[526, 38786, 38703])).
% 12.69/12.91 tff(38790,plain,
% 12.69/12.91 (~(s(s(elem!1)) = s(elem!1))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[2279, 38788])).
% 12.69/12.91 tff(38791,plain,
% 12.69/12.91 (~b(s(s(elem!1)), elem!1)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[5286, 38790, 38784, 38789, 38787])).
% 12.69/12.91 tff(38792,plain,
% 12.69/12.91 (~r(elem!1, s(z))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[15317, 38791, 38710, 38789, 38788, 38691, 38711])).
% 12.69/12.91 tff(38793,plain,
% 12.69/12.91 (b(s(s(s(elem!1))), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[377, 38785])).
% 12.69/12.91 tff(38794,plain,
% 12.69/12.91 (~b(s(elem!1), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[24651, 38789, 38776, 38787, 38793])).
% 12.69/12.91 tff(38795,plain,
% 12.69/12.91 (r(s(elem!1), z)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[549, 38794])).
% 12.69/12.91 tff(38796,plain,
% 12.69/12.91 (~(s(elem!1) = elem!1)),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[13117, 38795, 38786])).
% 12.69/12.91 tff(38797,plain,
% 12.69/12.91 (~(elem!1 = s(elem!1))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[166, 38796])).
% 12.69/12.91 tff(38798,plain,
% 12.69/12.91 (~b(z, s(elem!1))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[6555, 38787, 38784, 38789])).
% 12.69/12.91 tff(38799,plain,
% 12.69/12.91 (r(z, s(elem!1))),
% 12.69/12.91 inference(unit_resolution,[status(thm)],[566, 38798])).
% 12.69/12.91 tff(38800,plain,
% 12.69/12.91 (~r(elem!1, s(elem!1))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[19851, 38795, 38710, 38799])).
% 12.69/12.92 tff(38801,plain,
% 12.69/12.92 (b(elem!1, s(elem!1))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[443, 38800, 38797])).
% 12.69/12.92 tff(38802,plain,
% 12.69/12.92 (~b(elem!1, s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[1930, 38801, 38710, 182, 38719, 38795])).
% 12.69/12.92 tff(38803,plain,
% 12.69/12.92 ($false),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[837, 38802, 38792, 38779])).
% 12.69/12.92 tff(38804,plain,(~r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 12.69/12.92 tff(38805,plain,
% 12.69/12.92 (b(s(z), z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[180, 38804])).
% 12.69/12.92 tff(38806,plain,
% 12.69/12.92 (~b(s(z), s(s(s(elem!1))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[36898, 38805, 38710, 38776, 38704, 38697])).
% 12.69/12.92 tff(38807,plain,
% 12.69/12.92 (~b(s(z), elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[14872, 38806, 38691])).
% 12.69/12.92 tff(38808,plain,
% 12.69/12.92 (r(s(z), elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[632, 38807, 38690])).
% 12.69/12.92 tff(38809,plain,
% 12.69/12.92 (r(s(z), s(s(s(elem!1))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[247, 38806])).
% 12.69/12.92 tff(38810,plain,
% 12.69/12.92 (~b(s(s(s(s(z)))), z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[37878, 2881, 38703])).
% 12.69/12.92 tff(38811,plain,
% 12.69/12.92 (~b(s(z), elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[37941, 2881, 38703])).
% 12.69/12.92 tff(38812,plain,
% 12.69/12.92 ($false),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[37555, 38811, 2881, 38703, 38810])).
% 12.69/12.92 tff(38813,plain,(b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 12.69/12.92 tff(38814,plain,
% 12.69/12.92 (~b(elem!1, z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[19366, 31, 38710, 38813, 38690, 38711, 38783, 38805])).
% 12.69/12.92 tff(38815,plain,
% 12.69/12.92 (r(elem!1, z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[526, 38814, 38703])).
% 12.69/12.92 tff(38816,plain,
% 12.69/12.92 (r(s(s(s(elem!1))), z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[533, 38815, 38691])).
% 12.69/12.92 tff(38817,plain,
% 12.69/12.92 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[5792, 38816, 38711, 38809])).
% 12.69/12.92 tff(38818,plain,
% 12.69/12.92 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.69/12.92 inference(transitivity,[status(thm)],[38693, 3929])).
% 12.69/12.92 tff(38819,plain,
% 12.69/12.92 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 12.69/12.92 inference(monotonicity,[status(thm)],[38818])).
% 12.69/12.92 tff(38820,plain,
% 12.69/12.92 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.69/12.92 inference(modus_ponens,[status(thm)],[38696, 38819])).
% 12.69/12.92 tff(38821,plain,
% 12.69/12.92 (~b(s(s(s(elem!1))), s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[8400, 31, 38691])).
% 12.69/12.92 tff(38822,plain,
% 12.69/12.92 (r(s(s(s(elem!1))), s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[223, 38821])).
% 12.69/12.92 tff(38823,plain,
% 12.69/12.92 (~r(z, s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[19761, 31, 38710, 38807, 38690])).
% 12.69/12.92 tff(38824,plain,
% 12.69/12.92 (b(z, s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[678, 38823])).
% 12.69/12.92 tff(38825,plain,
% 12.69/12.92 (r(elem!1, s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[837, 31, 38779])).
% 12.69/12.92 tff(38826,plain,
% 12.69/12.92 (~r(s(s(s(s(z)))), elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[10408, 38825, 38704, 38710])).
% 12.69/12.92 tff(38827,plain,
% 12.69/12.92 (~b(z, s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[33099, 38815, 38813, 38784, 38686, 38704, 38826, 38824, 38822])).
% 12.69/12.92 tff(38828,plain,
% 12.69/12.92 (r(z, s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[800, 38827])).
% 12.69/12.92 tff(38829,plain,
% 12.69/12.92 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[10090, 38828, 38711, 38704])).
% 12.69/12.92 tff(38830,plain,
% 12.69/12.92 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[15351, 38829, 38820])).
% 12.69/12.92 tff(38831,plain,
% 12.69/12.92 (b(s(s(s(s(z)))), elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[762, 38826, 38695])).
% 12.69/12.92 tff(38832,plain,
% 12.69/12.92 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[20820, 38831, 38686])).
% 12.69/12.92 tff(38833,plain,
% 12.69/12.92 (~(s(s(elem!1)) = s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[1962, 38719])).
% 12.69/12.92 tff(38834,plain,
% 12.69/12.92 (elem!1 = s(s(s(elem!1)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[38094, 90, 2, 2829])).
% 12.69/12.92 tff(38835,plain,
% 12.69/12.92 (s(s(s(elem!1))) = elem!1),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[129, 38834])).
% 12.69/12.92 tff(38836,plain,
% 12.69/12.92 (~b(elem!1, s(s(s(elem!1))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[15370, 38835])).
% 12.69/12.92 tff(38837,plain,
% 12.69/12.92 (~(s(z) = elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[8542, 38836, 38081])).
% 12.69/12.92 tff(38838,plain,
% 12.69/12.92 (b(z, elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[22900, 38834, 22924])).
% 12.69/12.92 tff(38839,plain,
% 12.69/12.92 (b(elem!1, z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[29380, 31, 36606, 90, 38081, 38838, 2])).
% 12.69/12.92 tff(38840,plain,
% 12.69/12.92 (~b(s(z), z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[19923, 31, 36606, 90, 38839, 38837, 38087, 2829])).
% 12.69/12.92 tff(38841,plain,
% 12.69/12.92 (~r(z, s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[19761, 31, 36606, 2829, 38837])).
% 12.69/12.92 tff(38842,plain,
% 12.69/12.92 (~r(s(z), z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[22964, 38841, 90, 38838, 2, 38081, 31])).
% 12.69/12.92 tff(38843,plain,
% 12.69/12.92 ($false),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[180, 38842, 38840])).
% 12.69/12.92 tff(38844,plain,(b(elem!1, s(z)) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 12.69/12.92 tff(38845,plain,
% 12.69/12.92 (~b(s(s(s(s(z)))), z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[38844, 31, 38703, 38807])).
% 12.69/12.92 tff(38846,plain,
% 12.69/12.92 (elem!1 = s(s(s(elem!1)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[37836, 3446, 2829, 2])).
% 12.69/12.92 tff(38847,plain,
% 12.69/12.92 (s(s(s(elem!1))) = elem!1),
% 12.69/12.92 inference(symmetry,[status(thm)],[38846])).
% 12.69/12.92 tff(38848,plain,
% 12.69/12.92 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 12.69/12.92 inference(monotonicity,[status(thm)],[38847])).
% 12.69/12.92 tff(38849,plain,
% 12.69/12.92 ((s(s(z)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(z)))),
% 12.69/12.92 inference(transitivity,[status(thm)],[38848, 698])).
% 12.69/12.92 tff(38850,plain,
% 12.69/12.92 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(z))))),
% 12.69/12.92 inference(monotonicity,[status(thm)],[38849])).
% 12.69/12.92 tff(38851,plain,
% 12.69/12.92 (~(elem!1 = s(s(z)))),
% 12.69/12.92 inference(modus_ponens,[status(thm)],[1397, 38850])).
% 12.69/12.92 tff(38852,plain,
% 12.69/12.92 (s(s(s(elem!1))) = elem!1),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[129, 38846])).
% 12.69/12.92 tff(38853,plain,
% 12.69/12.92 (~b(elem!1, s(s(s(elem!1))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[15370, 38852])).
% 12.69/12.92 tff(38854,plain,
% 12.69/12.92 (~(s(z) = elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[8542, 38853, 37556])).
% 12.69/12.92 tff(38855,plain,
% 12.69/12.92 (~r(z, s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[19761, 31, 36606, 2829, 38854])).
% 12.69/12.92 tff(38856,plain,
% 12.69/12.92 (b(z, s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[678, 38855])).
% 12.69/12.92 tff(38857,plain,
% 12.69/12.92 (b(z, elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[22900, 38846, 37743])).
% 12.69/12.92 tff(38858,plain,
% 12.69/12.92 (b(s(z), z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[36796, 31, 2, 3446, 37556])).
% 12.69/12.92 tff(38859,plain,
% 12.69/12.92 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[2849, 38854])).
% 12.69/12.92 tff(38860,plain,
% 12.69/12.92 (r(z, s(s(s(elem!1))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[10792, 38852, 36606])).
% 12.69/12.92 tff(38861,plain,
% 12.69/12.92 (~b(s(s(s(elem!1))), s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[8400, 31, 38852])).
% 12.69/12.92 tff(38862,plain,
% 12.69/12.92 (r(s(s(s(elem!1))), s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[223, 38861])).
% 12.69/12.92 tff(38863,plain,
% 12.69/12.92 (~(elem!1 = s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[172, 38854])).
% 12.69/12.92 tff(38864,plain,
% 12.69/12.92 (r(elem!1, s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[837, 31, 38863])).
% 12.69/12.92 tff(38865,plain,
% 12.69/12.92 (~r(s(s(s(s(z)))), elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[10408, 38864, 29426, 36606])).
% 12.69/12.92 tff(38866,plain,
% 12.69/12.92 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 12.69/12.92 inference(monotonicity,[status(thm)],[38846])).
% 12.69/12.92 tff(38867,plain,
% 12.69/12.92 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), elem!1)),
% 12.69/12.92 inference(symmetry,[status(thm)],[38866])).
% 12.69/12.92 tff(38868,plain,
% 12.69/12.92 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 12.69/12.92 inference(monotonicity,[status(thm)],[38867])).
% 12.69/12.92 tff(38869,plain,
% 12.69/12.92 (~b(s(s(s(elem!1))), elem!1)),
% 12.69/12.92 inference(modus_ponens,[status(thm)],[463, 38868])).
% 12.69/12.92 tff(38870,plain,
% 12.69/12.92 (~b(elem!1, z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[19366, 38858, 36606, 37556, 38854, 38860, 38869, 31])).
% 12.69/12.92 tff(38871,plain,
% 12.69/12.92 (r(elem!1, z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[526, 38870, 2])).
% 12.69/12.92 tff(38872,plain,
% 12.69/12.92 (~b(z, s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[33099, 38871, 37556, 38857, 38846, 29426, 38865, 38856, 38862])).
% 12.69/12.92 tff(38873,plain,
% 12.69/12.92 (r(z, s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[800, 38872])).
% 12.69/12.92 tff(38874,plain,
% 12.69/12.92 (~r(s(s(z)), z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[36295, 38873, 29426, 38860, 38859, 38856, 38858])).
% 12.69/12.92 tff(38875,plain,
% 12.69/12.92 (b(s(s(z)), z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[1211, 38874])).
% 12.69/12.92 tff(38876,plain,
% 12.69/12.92 (~b(s(z), s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[33073, 38875, 37556, 38857, 38856, 29426])).
% 12.69/12.92 tff(38877,plain,
% 12.69/12.92 (r(s(z), s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[1788, 38876])).
% 12.69/12.92 tff(38878,plain,
% 12.69/12.92 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 12.69/12.92 inference(monotonicity,[status(thm)],[38846])).
% 12.69/12.92 tff(38879,plain,
% 12.69/12.92 (r(s(z), elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[632, 38854, 2829])).
% 12.69/12.92 tff(38880,plain,
% 12.69/12.92 (r(s(z), s(s(s(elem!1))))),
% 12.69/12.92 inference(modus_ponens,[status(thm)],[38879, 38878])).
% 12.69/12.92 tff(38881,plain,
% 12.69/12.92 (b(s(s(s(s(z)))), elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[762, 38865, 37557])).
% 12.69/12.92 tff(38882,plain,
% 12.69/12.92 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[2201, 38862, 38880, 340])).
% 12.69/12.92 tff(38883,plain,
% 12.69/12.92 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[10940, 38859])).
% 12.69/12.92 tff(38884,plain,
% 12.69/12.92 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[10090, 38873, 29426, 38860])).
% 12.69/12.92 tff(38885,plain,
% 12.69/12.92 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[15351, 38884, 38883])).
% 12.69/12.92 tff(38886,plain,
% 12.69/12.92 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[20820, 38881, 38846])).
% 12.69/12.92 tff(38887,plain,
% 12.69/12.92 (s(s(elem!1)) = s(s(s(elem!1)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[18766, 38875, 2680, 37556, 38846, 38860, 38858, 38864, 38879, 38856, 38886, 38885, 29426, 38882])).
% 12.69/12.92 tff(38888,plain,
% 12.69/12.92 (s(s(s(elem!1))) = s(s(elem!1))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[314, 38887])).
% 12.69/12.92 tff(38889,plain,
% 12.69/12.92 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[9242, 38888, 38881])).
% 12.69/12.92 tff(38890,plain,
% 12.69/12.92 (~b(s(s(z)), s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[1243, 38889, 37556, 38856, 38875])).
% 12.69/12.92 tff(38891,plain,
% 12.69/12.92 (r(s(s(z)), s(z))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[3778, 38890])).
% 12.69/12.92 tff(38892,plain,
% 12.69/12.92 (~r(s(s(s(elem!1))), s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[11551, 38891, 38880, 38877])).
% 12.69/12.92 tff(38893,plain,
% 12.69/12.92 (~r(elem!1, s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[10022, 38892, 38846])).
% 12.69/12.92 tff(38894,plain,
% 12.69/12.92 (b(elem!1, s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[3394, 38893, 38851])).
% 12.69/12.92 tff(38895,plain,
% 12.69/12.92 (b(s(s(s(elem!1))), s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[16425, 38894, 38846])).
% 12.69/12.92 tff(38896,plain,
% 12.69/12.92 (r(s(s(s(elem!1))), z)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[533, 38871, 38852])).
% 12.69/12.92 tff(38897,plain,
% 12.69/12.92 (~b(s(s(z)), s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[18687, 38885, 37556, 38880, 38886, 38896])).
% 12.69/12.92 tff(38898,plain,
% 12.69/12.92 (r(s(s(z)), s(s(s(s(z)))))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[3652, 38897])).
% 12.69/12.92 tff(38899,plain,
% 12.69/12.92 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = elem!1)),
% 12.69/12.92 inference(transitivity,[status(thm)],[38849, 8492])).
% 12.69/12.92 tff(38900,plain,
% 12.69/12.92 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = elem!1))),
% 12.69/12.92 inference(monotonicity,[status(thm)],[38899])).
% 12.69/12.92 tff(38901,plain,
% 12.69/12.92 (~(s(s(z)) = elem!1)),
% 12.69/12.92 inference(modus_ponens,[status(thm)],[1397, 38900])).
% 12.69/12.92 tff(38902,plain,
% 12.69/12.92 (~r(s(s(z)), elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[6674, 38891, 38879, 38864])).
% 12.69/12.92 tff(38903,plain,
% 12.69/12.92 (b(s(s(z)), elem!1)),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[4730, 38902, 38901])).
% 12.69/12.92 tff(38904,plain,
% 12.69/12.92 (~b(s(s(s(s(z)))), s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[11012, 38894, 38881, 38903])).
% 12.69/12.92 tff(38905,plain,
% 12.69/12.92 (r(s(s(s(s(z)))), s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[1714, 38904])).
% 12.69/12.92 tff(38906,plain,
% 12.69/12.92 (~r(z, s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[30535, 38905, 29426, 38898])).
% 12.69/12.92 tff(38907,plain,
% 12.69/12.92 (b(z, s(s(z)))),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[18613, 38906])).
% 12.69/12.92 tff(38908,plain,
% 12.69/12.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 12.69/12.92 inference(rewrite,[status(thm)],[])).
% 12.69/12.92 tff(38909,plain,
% 12.69/12.92 (((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 12.69/12.92 inference(rewrite,[status(thm)],[])).
% 12.69/12.92 tff(38910,plain,
% 12.69/12.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 12.69/12.92 inference(monotonicity,[status(thm)],[38909])).
% 12.69/12.92 tff(38911,plain,
% 12.69/12.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 12.69/12.92 inference(transitivity,[status(thm)],[38910, 38908])).
% 12.69/12.92 tff(38912,plain,
% 12.69/12.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 12.69/12.92 inference(quant_inst,[status(thm)],[])).
% 12.69/12.92 tff(38913,plain,
% 12.69/12.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 12.69/12.92 inference(modus_ponens,[status(thm)],[38912, 38911])).
% 12.69/12.92 tff(38914,plain,
% 12.69/12.92 ($false),
% 12.69/12.92 inference(unit_resolution,[status(thm)],[38913, 391, 37743, 38875, 38856, 38907, 38895])).
% 12.69/12.95 tff(38915,plain,(b(elem!1, s(z)) | (~r(s(s(elem!1)), s(z))) | (elem!1 = z) | b(s(z), elem!1) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 12.69/12.95 tff(38916,plain,
% 12.69/12.95 (~r(s(s(elem!1)), s(z))),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[38915, 38845, 38703, 31, 38807])).
% 12.69/12.95 tff(38917,plain,
% 12.69/12.95 (b(s(s(elem!1)), s(z))),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[362, 38916])).
% 12.69/12.95 tff(38918,plain,
% 12.69/12.95 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[8345, 38917, 31])).
% 12.69/12.95 tff(38919,plain,
% 12.69/12.95 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[314, 38918])).
% 12.69/12.95 tff(38920,plain,
% 12.69/12.95 (~r(s(s(z)), z)),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[36295, 38828, 38711, 38704, 38697, 38824, 38805])).
% 12.69/12.95 tff(38921,plain,
% 12.69/12.95 (b(s(s(z)), z)),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[1211, 38920])).
% 12.69/12.95 tff(38922,plain,
% 12.69/12.95 ($false),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[18766, 38921, 38919, 38686, 38813, 38833, 38711, 38805, 38825, 38808, 38824, 38832, 38830, 38704, 38817])).
% 12.69/12.95 tff(38923,plain,(b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 12.69/12.95 tff(38924,plain,
% 12.69/12.95 (~b(z, s(z))),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[5970, 38923, 38784, 38805])).
% 12.69/12.95 tff(38925,plain,
% 12.69/12.95 (r(z, s(z))),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[678, 38924])).
% 12.69/12.95 tff(38926,plain,
% 12.69/12.95 (~b(elem!1, z)),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[13285, 38923, 38784, 38805])).
% 12.69/12.95 tff(38927,plain,
% 12.69/12.95 (r(elem!1, z)),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[526, 38926, 38703])).
% 12.69/12.95 tff(38928,plain,
% 12.69/12.95 ($false),
% 12.69/12.95 inference(unit_resolution,[status(thm)],[16803, 38927, 38925, 38710, 38808])).
% 12.69/12.95 % SZS output end Proof
% 12.69/12.96 % E exiting
%------------------------------------------------------------------------------